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SMITHSONIAN
MISCELLANEOUS COLLECTIONS

VOL. b2

‘“*EVERY MAN IS A VALUABLE MEMBER OF SOCIETY WHO, BY HIS OBSERVATIONS, RESEARCHES,
AND EXPERIMENTS, PROCURES KNOWLEDGE FOR MEN’’—SMITHSON

(PUBLICATION 2716)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
1923

The Lord Waltimore Press

BALTIMORE, MD., U. S. A.

ADVERTISEMENT

The present series, entitled ‘“ Smithsonian Miscellaneous Collec-
tions,” is intended to embrace all the octavo publications of the
Institution, except the Annual Report. Its scope is not limited,
and the volumes thus far issued relate to nearly every branch of
science. Among these various subjects zoology, bibliography, geology,
mineralogy, and anthropology have predominated.

The Institution also publishes a quarto series entitled “ Smith-
sonian Contributions to Knowledge.” It consists of memoirs based
on extended original investigations, which have resulted in important
additions to knowledge.

GHARE RSD? WANECOMM:
Secretary of the Smithsonian Institution.

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CONTENTS

. Advisory Committee on the Langley Aerodynamical Laboratory.

july 17371913. 5 pp. (Publino:2227.)

. RicHarpson, H. C. Hydromechanic experiments with flying boat

hulls. April 20, 1914. 9 pp.,6 pls. (Publ. no. 2253.)

.Zaum, A. F. Report on European aeronautical laboratories.

Wily 27,1914. 23 pp, 11 pls: (Publ; no.2273.)

. Hunsaker, J. C., BuckincHaM, E., Rosset, H. E., Douctas,

D. W., Branp, C. L., and Witson, E. S. Reports on wind
tunnel experiments in aerodynamics. January 15, 1916. 92
pp., 5 pls. (Publ. no. 2368.)

. HUNSAKER, JEROME C. Dynamical stability of aeroplanes. June

30, 1916. 78 pp., 3 pls. (Publ. no. 2414.)

(v)

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SMITHSONIAN MISCELLANEOUS COLLECTIONS

VOLUME 62, NUMBER 1

Hodgkins JFund

ADVISORY COMMITTEE ON THE LANGLEY
AERODYNAMICAL LABORATORY

SAE INCAS

(PuBLicaTion 2227)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
JULY 17, 1913

The Lord Baltimore Press

BALTIMORE, MD., U. S. A.

FHodgkins Fund

ADVISORY COMMITTEE ON THE LANGLEY
AERODYNAMICAL LABORATORY

ORRICEAE S LATUS

Authorization.—On May 1, 1913, the Regents of the Smithsonian
Institution, approving a general scheme submitted by Secretary
Walcott, authorized the Secretary, with the approval of the Execu-
tive Committee, to reopen the Langley Aerodynamical Laboratory ;
to appoint an Advisory Committee; to add, as means are provided,
other laboratories and agencies; to group them into a bureau organi-
zation; and to secure the cooperation with them of the Government
and other agencies.

Functions—The Committee is to advise as to the organization and
work of the Langley Aerodynamical Laboratory and of the bureau
organization when adopted, and the coordination of their activities
with the kindred labors of other establishments, Governmental and
private ; it is to plan for such theoretical and experimental investiga-
tions, tests and reports, as may serve to increase the safety and
effectiveness of aerial locomotion for the purposes of commerce,
national defense, and the welfare of man. But neither the Com-
mittee nor the Smithsonian Institution will promote patented devices,
furnish capital to inventors, or manufacture commercially, or give
regular courses of instruction for aeronautical pilots or engineers.

The organization, under regulations to be established and fees to
be fixed by the Secretary, approved by the Smithsonian Executive
Committee, may exercise its functions for the military and civil de-
partments of the Government of the United States, and also for any
individual, firm, association, or corporation within the United States;
provided, however, that such department, individual, firm, association,
or corporation shall defray the cost of all material used and of all
services of persons employed in the exercise of such functions.

With the approval of the Secretary of the Institution, the Com-
mittee is to collect aeronautical information, such part of the same as
may be valuable to the Government, or the public, to be issued in
bulletins and other publications.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 62, No. 1

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Membership and Privileges—The Advisory Committee is to be
composed of the Director of the Langley Aerodynamical Laboratory,
when appointed, and one member to be designated by the Secretary of
War, one by the Secretary of the Navy, one by the Secretary of
Agriculture, and one by the Secretary of Commerce, together with
such other persons, to be designated by the Secretary of the Smith-
sonian Institution, as may be acquainted with the needs of aeronautics,
the total membership of such Committee not to exceed fourteen.

The members of the Advisory Committee, as such, are to serve
without compensation, but will have refunded the necessary expenses
incurred by them in going to Washington to attend the meetings of
the Committee and returning therefrom, and while attending the
meetings.

Approval of the President—On May 9, 1913, the President of the
United States, by request of the Secretary of the Smithsonian Institu-
tion, approved the designation of representatives of the above-named
Departments to serve on the Advisory Committee.

ORGANIZATION

Officers —The Advisory Committee, as constituted at its organiza-
tion meeting, convened by Secretary Walcott at the Smithsonian
Institution, May 23, 1913, comprises a Chairman, a Recorder, and
twelve additional members, all of whom are to serve for one year.
The officers are to be elected annually on or about May 6, and the
members for the ensuing year are to be appointed prior to the date
of such election.

The Chairman has general supervision of the work of the Advisory
Committee, presides at its meetings, receives the reports of the Sub-
committees, and makes an annual report to the Secretary of the Smith-
sonian Institution. Said report must include an account of the work
done for any Department of the Government, individual, firm, asso-
ciation, or corporation, and the amounts paid by them to defray the
cost of material and services, as hereinbefore mentioned.

The Recorder keeps the minutes of the meetings of the Committee,
and assists the Chairman in conducting correspondence and preparing
reports pertaining to the business of the Committee.

Subcommuttees.—The Chairman, with the approval of the Advisory
Committee, may appoint standing and special Subcommittees to per-
form such functions as may be assigned to them.

The standing Subcommittees may have assigned to them investiga-
tions and tests of a permanent character, which they may prosecute

NOT I ADVISORY COMMITTEE, LANGLEY LABORATORY 3

from year to year, and on which they are to make quarterly reports
to the Chairman followed by an annual report. Each Subcommittee
comprises a Chairman who must be a member of the Advisory Com-
mittee, and others, chosen by him from that Committee or elsewhere.

AGENCIES, RESOURCES, “ANDI EACIEITIES

Snuthsonian Institution—The Advisory Committee has been pro-
vided by’ the Smithsonian Institution with suitable office head-
quarters, an administrative and accounting system, library and publi-
cation facilities, lecture and assembly rooms, and museum space for
aeronautic models. The Langley Aerodynamical Laboratory has an
income provided for it not to exceed ten thousand dollars the first year
(of which five thousand dollars has been allotted), and five thousand
annually for five years.

U.S. Bureau of Standards—For the exact determination of aero-
physical constants, the calibration of instruments, the testing of
aeronautic engines, propellers and materials of construction, the
Committee has the cooperation of the U. S. Bureau of Standards, from
which the Secretary of Commerce has designated one representative.

This Bureau has a complete equipment for studying the mechanics
of materials and structural forms used in air-craft; for standard-
izing the physical instruments—thermometers, barographs, pressure
gauges, etc——used in air navigation; and for testing the power,
efficiency, etc., of aeronautical motors in a current of air representing
the natural conditions of flight.

In these general branches the technical staff of the Bureau is
prepared to undertake such theoretical and experimental investiga-
tions as may come before the Advisory Committee on behalf of
either the Government or private individuals or organizations.

U. S. Weather Bureau.—For studies of and reports on every phase
of aeronautic meteorology, besides the usual forecasting, the Com-
mittee has the cooperation of the U. S. Weather Bureau, from which
the Secretary of Agriculture has designated one representative.

This Bureau has an extensive library of works on or allied to
aeronautics, an instrument division for every type of apparatus for
studying the state of the atmosphere, a whirling table of thirty foot
radius for standardizing anemometers, a complete kite equipment with
power reel, and a sounding balloon equipment with electrolytic hy-
drogen plant, all of which are available for scientific investigations.
For special forecasts, anticipating field tests or cross country voyages,
the general service of the Bureau may be called upon.

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

War and Navy Departments—These Departments, while especially
interested in aeronautics for national defense, can be of service in
advancing the general science. Each has an aeronautical library ;
each has an official representative in foreign countries who reports
periodically on every important phase of the art, whether civil or
military; each has an assignment of officers who design, test, and
operate air craft, and who determine largely the scope and character
of their development; each has its aeronautic station equipped with
machines in actual service throughout the year. Besides various
aviation establishments, the War Department has a balloon plant at
Fort Myer, Va., and at Omaha, Neb.; the Navy has its marine Model
Basin, useful for special experiments in aeronautics, its extensive
shops at the Washington Navy Yard, available for the alteration or
repair of air craft, or the manufacture of improved military types,
and at Fort Myer, three lofty open-work steel towers suitable for
studies in meteorology or aerodynamics in the natural wind. Further-
more, the Navy Department has detailed an officer for special research
in aeronautics at one of the principal Engineering Schools.

Because of their fundamental interest in aeronautics, each of these
Departments has two representatives on the Advisory Committee,
and each will be able to place at the service of the Committee one or
more skilled aviators and aeroplanes for systematic experimentation.

PRESENT NEEDS

In presenting the needs of the organization, it is well to remark
that the Smithsonian Institution possesses the unique character of
being a private organization having Governmental functions and
prerogatives. It can receive appropriations directly from Congress;
it can be the recipient or the custodian of private funds for the increase
and diffusion of knowledge; it can deposit such private funds with
the United States Treasury, or place them otherwise, as may be
required by the donor. Likewise, it can be the recipient or custodian
of material objects representing any province of nature, or any
branch of human knowledge or art. This unique character allows the
public to anticipate or supplement the cooperation of Congress in
promoting the aerodromical (aeronautical) work of the Institution.

Endowment Funds.—Persons approving the pur pose of the organi-
zation and desiring its continuity and permanence can not do better
than to provide for it a steady income, either for general or for
specific use. Individual endowment funds bearing the name of the
giver or other person, and presented to the Smithsonian Institution,

NO. I ADVISORY COMMITTEE, LANGLEY LABORATORY 5

or placed in its custody at the disposal of the Committee, may be
recommended ; also collective funds bearing the name of a society,
organization, or section of the country, whether in the interest of
scientific progress or of national defense.

Temporary Funds.—For the prompt achievement of definite results,
funds may well be offered for immediate application, both of principal
and interest; as, for example, for the erection of laboratories or other
buildings ; for the purchase of experimental air craft, or apparatus,
instruments, etc.

Most needed is an expansion of the Langley Aerodynamical Labor-
atory providing a large and a small wind tunnel, ampler shops, and
instrument and model rooms. Adjacent to this, or forming a part of it,
may well be the headquarters of the Committee, with the collections
of aeronautic publications and exhibits, and with designing rooms
where plans for air craft may be matured by fabricators in consultation
with the technical staff. This new building, if placed on the Smith-
sonian grounds, should be of good architecture and cost not less than
$160,000.

Of immediate importance is an air-craft field laboratory, adjacent
to ample flying space of land and water, and adapted to assembling,
adjusting and repairing several full scale land and water aeroplanes ;
and subjecting them to indoor tests and measurements, as of stress,
strain, factor of safety, center of gravity, moment of inertia, working
condition, etc. One such plant suitably located would serve all Gov-
ernmental and civilian requirements for the present. A suitable site is
the public land in Potomac Park in the vicinity of the Smithsonian
Institution. Here might be held air-craft competitions under the
auspices of the Government.

Prizes and Awards—As a stimulus to the highest aeronautic
achievement, or as an honorable recognition thereof, suitable prizes or
awards might advantageously be offered. Provision should be made
for liberal cash prizes for competitive tests of motors, propellers, etc.,
in a purely scientific way not trenching upon the province of aero
clubs.

Fellowships —For the prosecution of special aeronautic investiga-
tions in cooperation with the advisory Committee, educational insti-
tutions and scientific or engineering organizations should be provided
with research fellowships whose incumbents may have the counsel of
the Committee and the advantage of its equipments.

Until adequate appropriations have been made by the Government,
the activities of the organization and Committee will have to be
sustained largely by private resources.

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SMITHSONIAN, MISCELLANEOUS COLLECTIONS

VOLUME 62, NUMBER 2

bodgkins Fund

ADVISORY COMMITTEE ON THE LANGLEY
AERODYNAMICAL LABORATORY

HYDROMECHANIC EXPERIMENTS: WITH
FLYING BOAT HULLS

(With Six PLATEs)

BY
H. C. RICHARDSON, Navat Constructor, U. S. Navy

Chairman of Sub-Committee on Hydromechanic Experiments in Relation to Aeronautics

: ee yi
St
yl MF LY
ERO ey

(PusLicaTion 2253)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
APRIL 20, 1914

TBe Lord Baltimore Press

BALTIMORE, MD., U. S. A.

Fiodgkins Fund

ADVISORY COMMITTEE ON THE LANGLEY
AERODYNAMICAL LABORATORY

HYDROMECHANIC EXPERIMENTS WITH FLYING BOAT
BULLS

By H. C. RICHARDSON, Navat Constructor, U. S. Navy
CHAIRMAN OF SUB-COMMITTEE ON HYDROMECHANICS IN RELATION TO AERONAUTICS

(WitH Six PLATES)

During the latter half of 1913 the following work of interest was
carried on at the Model Basin at the Washington Navy Yard.

This work comprised an investigation of the forms of hulls, of
flying boats in order to determine (1) their resistance at “ displace-
ments corresponding to speeds,” on the water, and (2) their resist-
ances “ submerged,’ as a means of approximating their total head
resistances in air and of determining an approximate “ coefficient of
fineness of form.”

As a result a form of hull has been derived which appears to
have decided advantages over those already in use in the Navy, so
far as resistance on the surface and in the air is concerned. Such
a hull slightly modified to overcome structural difficulties 1s now
being tried on a new navy machine.

Plates 1, 2, and 3 contain plots of the results of the experiments,
while plates 4, 5 and 6, illustrate the models used.

PEATE 1

This plate contains plots of model runs for the following models,
1591-3, 1592-I, 1592-5, 1593-1, 1602-1, and 1617-1.

At the foot of the sheet are plots of net resistance, and of
derived e. h. p. for the full size computed on the assumption that
the total resistance of the full size model at the corresponding speed
is proportional to the displacement. As the models were all 1/9 full
size the corresponding speeds for the full size are V9=3 times those
for the models, and the resistances 9* = 729 times those of the models.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 62, No. 2

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

This assumption is interesting as a means of comparison but the
e. h. p.’s so determined are inaccurate and exceed the true values,
because the frictional resistance which is an important component
varies with the speed to some power less than the square, approxi-
mately the 1.85 power. It is probable that the maximum error is less
than 40% and the minimum as high as 20% in excess of the actual
e. h. p., but the discrepancies are not considered to invalidate their
value for comparative purposes. At the top of the plate the change of
level curves are plotted.

The resistance curves were determined by towing the models at
‘displacements corresponding to speeds,” with the models at a set
“trim” but free to rise and fall under the influence of “ suction” or
“ planing,” and the change of level curves show how much the plan-
ing effect changes the draft at each condition.

All models were towed under conditions representing a full load
of 2,200 lbs. and the assumption that the get-away occurs at 45 m. p. h.
All were of the ventilated step type. An inspection of the resistance
and trim curves will show the following general features:

a. At low speeds, suction is present.

b. This is succeeded by a condition in which the models run hard.

c. Which is succeeded by a condition at which the model begins to
plane.

d. And just before the planing is established the slope of the curve
lessens rapidly.

e. And when planing is established the resistance falls off sharply
with one exception.

f. Just preceding the “ get-away” there is a tendency for the
resistance to remain at an appreciable value, which

e. Falls to nothing sharply at the last.

Model 1591-3 was designed to obviate the defects of the flat scow
bow type, and introduces the V bottom for the purpose of parting
rather than pushing the water aside. The ventilated step was located
so as to be slightly to the rear of the center of gravity. This model
1591-3 was derived from 1591-1, which was a true V type. I59I-I
ran very well except for a remarkable-sheet of spray at a speed cor-
responding to 12 m. p. h. This sheet of spray is shown in plate 4,
fig. 2. Due to this spray it was considered necessary to modify the
model and this was done by making the V sections “ full,” the prin-
cipal effect of the change was to augment the sheet of spray, so the
opposite tack was next taken, that of making the V sections hollow
in wake of the position from which the-sheet of spray originated,

NO. 2 HYDROMECHANIC EXPERIMENTS—RICHARDSON 3
and 1591-3 was thus derived. The result was that the spray was held
down, the planing effect increased and the resistance reduced, an all
round improvement.

Model 1592-1 was made from the lines of the Navy Flying Boat
C-I.

Model 1593-1 was made from the lines of the Navy Flying Boat
D-1.

Model number 1602-1 was derived from 1591-3, but the beam was
increased from 30” to 34”, otherwise the bottom was the same, at
the same time an attempt was made to improve the form by changing
the form of the front hood, and by sloping the upper deck abaft the
position of the planes. The results of these changes are apparent in
the submerged runs.

Model 1592-5 was derived from 1592-1 by adding a shallow V
bottom just forward of the step of 1592-1.

Model 1617-1 was designed on the general lines of the E-1, combi-
nation type (Owl, type). The object of this experiment was prin-
cipally to determine whether the shorter form was disadvantageous
from an air resistance point of view.

An inspection of the performance of 1591-3, shows that from
a resistance point of view it excels all but 1592-5, and an inspection
of the change of level curves will show this to be intimately asso-
ciated with the valuable “ planing ” qualities of 1591-3.

1592-1 behaves very similarly but the resistance is higher, while
1592-5 behaves very similarly but the resistance is lower than either
of the two preceding and the change of level curves clearly demon-
strate that the improvement is due principally to the improved “ plan-
ing” effect, and it is also due to the better flow induced by parting
rather than pushing the water aside, due to the V-shape at the step.

1602-1 behaves much the same, but the broader beam appears to
increase the resistance slightly except where the planing effect
reaches its maximum:

1593-1 behaves well at low speeds, but the resistance grows to a
maximum at a much higher speed than any of the other models and
falls off steadily but much less sharply than any of the others. The
hump for the resistance curves occurs at about 27 m. p. h. for this
model ; at about 21 m. p. h. for 1591-3, 1592-1 and 1602-1, and at
19.5 m. p. h. for 1592-5. The sustained hard running of this model
is Clearly due to its failure to “ plane” as is evidenced by the change
of level curve.

1617-2 has high resistance at speeds corresponding to 24 m. p. h.,
but in general behaves similarly to the other central step models.

4 ; SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Comparison of the model results with the actual performance of
full sized machines, show a fair analogy exists, confirming satis-
factorily the behavior of the models. Certain experiments indi-
cate that up to about 15 or 20 m. p. h. the aeroplane controls have
very little influence on the change of trim of the full size machines,
and thus practically require the full size machines to follow the trim
imposed by the flow of the water about the hulls, and the models
were set to closely approximate the “ natural trim.’ Once planing
is attained, or the same thing once “ suction” is broken, the controls
become effective and may be used to modify the trim. In the case of
D-1, however, this condition is not reached till about 39 m. p. h.
These experiments have also shown that the “planing” effect is
very sensible to improvement if the angle of the bottom is increased,
and as this can be brought about once planing is attained this shows
a further advantage for those models which plane early.

The conclusions drawn from these and previous experiments
are as follows:

a. The step should be close to the position of the center of gravity,
to eliminate a nosing tendency, to facilitate change of trim while
planing, to avoid change of balance when getting away or landing.

b. Hollow V sections keep the spray down, cut the water more
easily and cleanly, plane better, and greatly reduce shock on land-
ing or when ploughing through broken water, and practically elimin-
ate the necessity of shock absorbers.

c. A shallow step is sufficient, but ventilation is een to facili-
tate the breaking of suction effects.

d. The bottom forward of the step should be inclined to the axis
of the machine, but

e. The inclination must not be so great as to cause planing before
the controls are effective, and this is particularly necessary when
running before the wind. If the planing of the hull is too pro-
nounced, the machine rises to the surface with but very little control
available to maintain balance, and when running before the wind
this is more apt to occur due to the higher water speed necessary
before the machine can take the air.

f. The bottom abaft the step should rise strongly as this favors a
steepening of the planing bow before suction is eliminated, and gets
the tail well clear when planing begins.

PLATES 2 AND:3
Plate 2 shows the logarithmic plots of the resistance of the pre-
ceding models towed submerged at speeds up to 15 knots; and also
for model 1350-15, a quarter sized model of the original Curtiss

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VOL. 62 NO. 2 PL. 2

6 FA

EXPERIMENTAL MODEL BASIN
CuRVES oF GRoss RESISTANCE FOR MODELS oF
Frying Boats AnD AEROPLANE PonTOONS

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NO: 2 HYDROMECHANIC EXPERIMENTS—RICHARDSON 5

pontoon. It will be seen that a straight line on the logarithmic plots
very closely represents the locus of the observed points and thus
indicate that the resistances of the models closely approximate the
law of the square of the speed. As is well known, any equation of
the form Y=a x" will plot as a straight line on a logarithmic plot,
and the slope of the curve transferred to the origin passes through
the margin at the upper end at a point corresponding to the exponent
n. The exponents are given in line 12 of Table 1, which shows the
value of the exponent n in the equation of the lines plotted on Plate
3 from the equation Rx V" the points being taken direct from the
straight line plots.
TABLET

Table 1 shows the computation of the head resistance in water for
each of these models, in detail, the final results appearing in lines 10,
20 and 21, giving results by three different methods of computation.

TABLE Tf

Line 22 gives the head resistance computed by analysis of the total
resistance of the model into frictional resistance and residual resist-
ance, and then augmenting these values to the “ full size” values in
accordance with Froude’s method.

Line 23 gives the head resistance in the same manner as line 22,
except the residual resistance is determined on the basis of relative
areas and relative speeds, being proportioned to the latter in accord-
ance with the exponent determined for the variation of residual
resistance of the model, instead of using the law of the square.

Line 24 is an approximation, assuming the resistance to be directly
proportional to the cube of the linear ratio at “ corresponding
speeds.”

Line 25 is computed on the basis of the Lord Rayleigh method,
which has been found reasonably satisfactory for the comparison of
dirigible models in England. In England ebonite models 1 inch in
diameter were used in water, and in air gold beater’s skin models
3 feet in diameter.

The National Physical Laboratory formula, which is based on the
Lord Rayleigh methiod, is

H = xpv#L16V186

in which « is a constant of form to be derived by experiment, p is the
density of the medium in which the experiment is carried on, v is the
kinetic viscosity, L is the length in feet, and V is the velocity in feet
per second.

This method has been introduced at the suggestion of Naval Con-

VOL. 62

SMITHSONIAN MISCELLANEOUS COLLECTIONS

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8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

structor J. C. Hunsaker, in commenting on the proofs of this paper as
originally written. He further suggested the comparison with line
24, which is of peculiar interest as shown by the percentage relation
of these values. Investigation of the relation of the two methods as
per line 27, shows that if we confine the use of the “approximate ”’
method to the “ corresponding speed,” as per the Law of Comparison,
the values as determined by Lord Rayleigh’s method should be 90.25%
of the values attained by the approximate method, for models one-
ninth the full size, and 107% for models one-quarter the full size, so
that the approximate method which is much simpler can be used with
a fair degree of accuracy if we put it in the form—
Hi, =00170K2-
This assumes ©! = 00123 and =e

9

Line 26 gives the head resistance of a plane of the maximum
section according to Eiffel’s coefficient for flat plates normal to the
wind. —

Line 28 gives a fineness coefficient based on the comparison of
lines 25 and 20.

Line 30 gives the value of xpv'4 for each of the boat models. These
“form factors” are of interest when compared with the values of
the same coefficients for models of dirigibles in which the form is
unrestricted by requirements such as enter into the flying boat prob-
lem. Thus, to make the comparison more ready, Table III is com-
piled:

TABLE ITT.

Model Type Kpv.}4 (Air)
IN-ORY Dna bs ack ss oh sas) Dinigibless eapoeeaoeereceoee .OOO00T 52
Betas eis islet dee ayoc cerevars badieal oe poh Ole ence Seem ee ee . 0000164
Gamma. 06 Nicole tsa oe | aes ee WOn ce eee eee emer . 0000165
Bet s30.5 cb dic ds gusts sits. lane oe AO canny ae Cro cWACIET Se Caer Ie . 0000142
Webawdy: i.e coop Sock eek| aren oc Osares eho ee a Ore eee 0000124
Bo Bs 32). os. ci 0 ene ek on ch lee sis od Ose ca ae ee eee eee . 0000140
Bate oo basves, oes os enll (RONTOOH Aer a. Slee Seer .0000258
G1 Bilyinge boats... eee eee . 0000364
Datcecs ods sheds class dc the al Gees Oe COV AS aoe cease ene rere .0000298
INa2. 5 obec nssag tore oe alll Sets MLO! Soc sar nee re oem .0000183
N-3 Owls. So 55.0 ae eee .0000261

It thus appears that the N-2 form, while superior in the air to the
other flying boat forms, may still be improved, and if the efficiency of
the Lebaudy form could be approached its head resistance might be
reduced to 684% of the present value.

[lowever, when we come to consider that the total head resistance
of the N-2 model is only about 11# in air at 60 m. p. h., and consider

7

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 2, PL. 4

FIG 1.—BOW END OF MODELS

FIG. 2.—SHEET OF SPRAY MADE BY MODEL AT SPEED OF 5.5 M. P. H.

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 2, PL.5

SIDE VIEW OF MODELS

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 2, PL. 6

VIEW OF MODELS FROM ABOVE

NO. 2 HYDROMECHANIC EXPERIMENTS—RICHARDSON 9

the difficulty of construction involved, particularly if the surface run-
ning qualities are to be retained, we see that the present forms are
reasonably satisfactory. While the possible saving of 3.54 head
resistance is worth considering, it must only be considered if its
attainment does not involve increased weight, cost or difficulty of
construction to such a degree as to outweigh the small gain possible.
Such savings increase in importance in proportion to the square of
the speed desired. It thus appears that increased efficiency must be
aimed at in those members of the structure which offend to a greater
degree than the hull, namely, the multiplicity of the truss members ;
and the exposed power plant, especially the water cooled power
plant.

The peculiar form of Model 1617-1 is due to an attempt to utilize
the advantage of the flying boat arrangement of bottom and step,
together with a good shape stream line hood in place of the ordinary
pontoon with the hydro-aeroplane type of machine.

It is interesting to note that the coefficient of fineness of this
model is less than that for Model 1602-2 which indicates that per unit
of area of maximum section the resistance of this form is slightly
less than that of the 1602 model. An inspection of line 29 will show
that the probable reason for this is due to the very low value of the
frictional component of the resistance of this model. However, when
the comparison is based on xpv'*, the form factor used by Lord Ray-
leigh, this form is much coarser than the 1602 model.

An independent experiment is worthy of note at this time. An
experiment was made to determine the existence and amount of
“nosing” torque on model 1350, at various angles of incidence.
Unfortunately the apparatus carried away before the experiments
were completed, but it was found that there is a “ nosing”’ torque
of about go ft. Ibs. when the deck of the pontoon is parallel with the
line of flight. To this torque should be added that due to the head
resistance which is approximately 5.42 lbs.x5 ft.=26.10 ft. lbs. or
a total torque due to the pontoon tending to make the machine head
down of about 116 ft. Ibs. This with the c. p. of the diving rudder
15 ft. abaft the c. g. would require the diving rudder to carry a
negative load of about 7.75 lbs. if the machine were “ balanced’ for
all other effects, at 60 m. p. h.

Additional experiments on submerged models are contemplated
with a view to determining the stream line flow about the models as
a means of arriving at improvement of form, and other experiments
to determine the effects of the cockpit openings, sponsons, etc., and
a more complete series for determining torque at different angles.

L
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SMITHSONIAN MISCELLANEOUS COLLECTIONS

hodgkins Fund

REPORT ON EUROPEAN AERONAUTICAL
LABORATORIES

(With E Leven PLATES)

BY
A. F. ZAHM, Ph. D.

(PuBLICATION 2273)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
JULY 27, 1914

The Lord Baltimore Prees

BALTIMORE, MD., U. S. A.

Hodgkins Fund

REPORT ON EUROPEAN AERONAUTICAL
EABORATORIES
By. A. F.. ZAHM, Pa.D:

(WitH ELEVEN PLATES)

GENERALITIES

Places visited —During August and September, 1913, in company
with Jerome C. Hunsaker, Assistant Naval Constructor, U. S. N.,
I visited the principal aeronautical laboratories near London, Paris,
and Gottingen, to study, in the interest of the Smithsonian Institu-
tion, “ the latest developments in instruments, methods, and resources
used and contemplated for the prosecution of scientific aeronautical
investigations.” Incidentally we visited many of the best aero-
dromes (flying fields) and air craft factories in the neighborhood of
those cities, and took copious notes of our observations. We also
visited many aeronautical libraries, book-stores, and aero clubs, in
order to prepare a comprehensive list of the best and latest publi-
cations on aerial navigation and its immediately kindred subjects.
In each of the countries, England, France and Germany, we spent
about two weeks. We were made welcome at all the places visited,
and thus established personal relations which should be valuable in
future negotiations with the aeronautical constructors and investi-
gators in those countries. But these incidental visits and studies,
though they may prove serviceable, do not seem germane to the
present report. Neither does it seem advisable to take more than
passing notice of the aeronautical laboratories themselves in those
manifold details which have been already published in large and
comprehensive reports now accessible in the Smithsonian Library.

Organization, resources, and scope of laboratories —The labora
tories examined by us are in particular (1) the aeronautic research
and test establishments of the British government near London; (2)
the Institut Aerotechnique de St. Cyr, and the Laboratoire Aero-
dynamique Eiffel, both near Paris; (3) the Gottingen Modelver-

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 62, No. 3

bo

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62
suchsanstalt at Gottingen; and (4) the newly organized laboratory
adjoining the flying field at Johannisthal near Berlin, known as the
“ Deutsche Versuchsanstalt fur Luftfahrt zu Adlershof.”

These establishments. resemble each other in some important
features, but differ in others. All are devoted to both academic and
engineering investigations. All are directed by highly trained
scientific and technical men. The directors are not merely execu-
tives ; they are the technical heads—scientists or engineers specifically
qualified by superior training in aeronautical engineering and its
immediately cognate branches—who initiate the researches, and
assist their technical staffs in devising apparatus, interpreting results,
and making systematic reports.

The establishments differ in their organization, resources, and
equipments, and, to a considerable extent, in the scope and character
of their investigations. Of the five institutions mentioned, the one
in England and the one at Gottingen are now supported largely by
governmental appropriations ; and the other three are maintained by
_ private capital, allotted as required, or accruing from fees or endow-
ment funds. Again, the laboratories near London, at St. Cyr, and at
Adlershof are practically unlimited in the scope of their researches,
while Eiffel’s and the Gdttingen laboratory have confined their
activities substantially to wind-tunnel experiments.

The aeronautical researches of the British government are in
charge of the British Advisory Committee for Aeronautics, a self-
governing civilian organization which was appointed by the Prime
Minister of England to work out theoretical and experimental prob-
lems in aeronautics for the army and navy, and comprises twelve
to fourteen expert men, under the presidency of Lord Rayleigh. This
committee initiates and directs investigations and tests at the Royal
Air Craft Factory, at the National Physical Laboratory, at the
Meteorological Office, at Vickers Sons and Maxim’s, etc. It expends,
in performing its regular functions, a sum exceeding the income of
any private aeronautical laboratory, and received directly from the
government treasury. ‘

The committee is primarily occupied with work for the government,
but also performs researches and tests for private individuals, for
suitable fees, but without guaranteeing secrecy as to the results.
The work of the committee is manifold and comprehensive. Whirl-
ing-table measurements, wind-tunnel measurements, testing of en-
gines, propellers, woods, metals, fabrics, varnishes, hydromechanic
studies, meteorological observations, mathematical investigations in

NO. 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAH M 3
Huid dynamics, the theory of gyroscopes, aeroplane and dirigible
design—whatever studies will promote the art of air craft construc-
tion and navigation may be prosecuted by this committee. A detailed
program and the results of actual investigations have been pub-
lished in the annual report of this committee.

M. Eiffel has paid from his personal fortune all the expenses of
his plant and elaborate researches, though it is understood that he
may sometimes charge nominal fees for investigations made for
private individuals who wish exclusive rights to the data and results
obtained. The general director of the laboratory is FKiffel himself—
who initiates the researches and publishes the results. He has in
immediate charge two able engineers, MM. Rith and Lapresle, aided
by three trained observers who are skilled draughtsmen. Two
mechanics and one janitor complete the personnel. The work of the
laboratory is all indoors, and is confined to researches in aerody-
namics alone, or more specifically to wind-tunnel measurements and
reports thereon.

The institute at St. Cyr was founded by Deutsch de La Meurth,
who gave $100,000 for the original plant and has provided $3000 per
year, during his life, for maintenance. It was presented by him to
the University of Paris, and is now under the general direction of the
professor of physics, M. Maurain, aided by a technical staff and a
large advisory council of eminent engineers, scientists and officers of
the university, officers of the French government and members of
various clubs and aeronautical organizations. The staff comprises
the director in charge and his assistant, together with such students,
two or three at a time, as may come as temporary volunteers from
the University of Paris.

The institute conducts large-scale experiments in the open field as
well as indoor researches, makes investigations for general publica-
tion or for private interests, on payment of suitable fees, and per-
mits private persons to conduct researches in the laboratory. The
scope of the work is practically unlimited, as is the case in the English
aeronautical laboratories. A special feature of the institute is its
three-quarter mile long track with electric cars for tests on large
screws, large models and full-size aeroplanes.

The Gottingen aerodynamical laboratory was begun as a private
enterprise, but is now to be enlarged and maintained in part by finan-
cial aid of the Kaiser Foundation. The original building, with its
wind-tunnel, was erected in 1908 after the plans of its director, Prof.
Prandtl, of the University of Gottingen, at a cost of 20,000 marks,

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

supplied by the Motorluftschiff-Studiengesellschaft. Its available
income is said to be $7,000 a year. The enterprise was inaugurated
on a small scale because of the uncertainty, at that date, as to the
practical value of such an establishment. The work of this labora-
tory, as in EFiffel’s, has been practically limited to wind-tunnel experi-
ments, though Prof. Prandtl has written some valuable theoretical
investigations, and is reported to be undertaking large-scale experi-
ments in the open air by use of a car on a level track, as at St. Cyr.

The Deutsche Versuchsanstalt fiir Luftfahrt zu Adlershof has
been recently founded by the Verein Deutscher Ingeniure. The
laboratory adjoins the great Flugplatz, with its two square kilometer
flying field surrounded by numerous air craft factories, scores of
hangars, an aero club house and a grand stand. Major Von Tschudi,
a retired German officer, is general manager of the organization,
which operates the flying field in the interest of all aero manufac-
turers and experimentalists, whether civilian or governmental. Dr.
Eng. F. Bendeman is director of the laboratory and has ten assist-
ants, comprising, among others, Dr. Fuhrman, who was formerly
assistant in the Gottingen iaboratory. I have not ascertained the
financial resources of the laboratory; but a prelude to its present
operations was a competition, involving some three score German
aeronautical motors, for the Kaiser Prize and additional contributions
from the country at large, aggregating in all 125,000 marks. It is
understood that the laboratory is liberally supported, is unlimited in
the scope of its work, and will conduct both indoor researches and
field experiments similar to those at St. Cyr.

After this general view, a technical account of the foregoing
aeronautical establishments may be useful.

BUILDINGS, EQUIPMENT AND OPERATION
ENGLISH AERONAUTICAL LABORATORIES

Aeronautical laboratories used by the British government—Of
the various aerotechnical plants supervised or used by the British
Advisory Committee for Aeronautics, we visited the one at the
National Physical Laboratory, at Teddington, and the one at the
Royal Air Craft Factory, at Farnborough ; but not the meteorological
stations, nor the plants of private concerns working for the com-
mittee, such as Vickers Sons and Maxim.

The National Physical Laboratory, which corresponds to the
U.S. Bureau of Standards, is under the directorship of Dr. R. T.
Glazebrook, F.R.S., Chairman of the Advisory Committee for

NO. 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAH M 5
’

Aeronautics; its engineering department is directed by Dr. T. E.
Stanton ; and the subdivision of this assigned to aeronautic investiga-
tion is in general charge of Mr. L. Bairstow.

The part of the National Physical Laboratory devoted exclusively
to aeronautics comprises the whirling-table house, the large wind-
tunnel house and the small wind-tunnel house with its liberal space
for minor apparatus. The parts available for aeronautics, but not
exclusively devoted thereto, are the general grounds, the large marine
model tank, the ample shops for wood and metal working, the store
rooms, the offices and library, the heating and lighting system, etc.

The whirling-table house, a separate building, 1s a corrugated iron
shed some 8o feet square, having an earth floor, and at its center a
motor driven vertical shaft which supports a trussed horizontal arm
and causes it to whirl at any desired speed, its outer extremity describ-
ing a circle about 60 feet in diameter, and carrying in steady flight
any model that has to be tested. The most important use of this
whirling tabel hitherto made seems to have been to prove what was
demonstrated and published in America by myself about one decade
previously, viz., that a suitably designed pressure-tube anemometer is
competent to measure the velocity of a uniform air current accurately
to one per cent, or less,’ and needs no calibration when its readings
are interpreted in accordance with Bernouili’s theorem. The whirling
arm has also been used to test model screw propellers, but is not
necessary for this work, and is much less convenient for the purpose
than the wind-tunnel, as used by Eiffel, for example. It is therefore
questionable whether the Smithsonian Institution will require a
whirling table for its aerodynamic studies.

The large wind-tunnel house, a wing of the engineering labora-
tory, isa concrete structure 100 feet long, 40 wide and 30 high, having
a wooden horizontal wind-tunnel placed equidistant from the side
walls, and midway between floor and ceiling, and supported between
concrete columns reaching from floor to ceiling.

The large tunnel is some 80 feet long and 7 feet square in cross-
section from its mouth to its middle ; it expands considerably through
the rest of its length. Its larger extremity abuts against the end
wall of the room, while its mouth stops well short of the oppo-
site wall. At mid-tunnel, just aft the enlargement, is placed a low-
pitch wooden screw actuated by a 30-horse electric motor, and
designed to give a current of 60 feet a second in the fore part of the

The calibration made at the British laboratory is reported to be reliable
to one-tenth of one per cent.

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

tunnel. The screw sucks the air of the closed room through the
mouth of the tunnel, which is somewhat flaring, thence through a
metal honeycomb, into the experimental part of the tunnel where the
models are placed for study. Thence the air flows into the expanded
half of the tunnel, passing first through the screw, then laterally
outward through innumerable holes in the tunnel wall, thence in uni-
form circulation through the unobstructed room till it curves again
easily into the mouth at the opposite end. The air stream so produced
is, where it emerges from the honeycomb, uniform in velocity at all
parts of a section, at least to a fraction of one per cent, if due care
be taken. The expanded and perforated part of the tunnel is said
to be the final outcome of long months of trial and study by the tech-
nical staff, and has enabled them to produce the steadiest aerodynamic
current in the world; thus removing one of the greatest difficulties
in the accurate determination of the flow and pressure of air about
wind models. The current velocity 1s reported to be uniform to
one-half per cent both in time and in space.

The complete structure of the tunnel need not be delineated here,
as it may be had better from the general plans and detailed working
drawings which the director of the laboratory has kindly offered to
furnish the Smithsonian Institution. It may be explained, however,
that the “ honeycomb,” just within the flaring mouth of the tunnel,
consists of crossed metal sheets forming, post-office-box-like, a
tubular partition of many cells through which the air entering the
tunnel is straightened and deprived of eddies. It may also be ob;
served that a glass door is placed on the side of the tunnel, through
which one may take observations, or enter to adjust the models to
be tested.

The cost of the seven-foot wind-tunnel is given as about $2,000,
and of its wind balance about $2,000. This, with an expenditure of
$12,500 for the building, makes a total of $16,500 for the plant.

The velocity of the air flow in the unchecked current, near the
model held inside the tunnel, is computed from the observed pressure
difference between the inside and outside of the tunnel wall. The
accuracy of this method was experimentally proved by me in 1902 at
the request of the Navy Department, and, together with a mathe-
matical proof, was set forth in the Physical Review the following
year. It was there shown that the speed of air rushing steadily
through a horizontal cylindrical tube from the quiet atmosphere of
the room into a chamber at low pressure is, for ordinary trans-
portation speeds, given truly to a fraction of one per cent by the

NO. 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAHM vi

formula V= yl 28 (ho—P), po—p being the pressure difference
p

between the room and chamber, V the speed * of inrush, and p the
nearly constant density. The method has since been adopted at
Eiffel’s laboratory and at the National Physical Laboratory.” This
for the speed of flow ; the direction may be shown by fine silk threads
moored in the current, or by floating particles, fine streams of smoke,
etc. In passing it may be mentioned that the direction of flow in the
unchecked current is parallel to the tunnel walls truly to a fraction
of one degree.

The pressure difference in question is found by connecting the
interior of the tunnel wall by means of external nipple and hose, to
one branch of a U tube manometer whose other branch opens into
the quiet air of the room; then observing the difference of ievel of the
liquid in the two arms. Manometers are made in many forms, accord-
ing to the accuracy desired. The English one, known as the “ Chat-
tock tilting gauge,’ made public in 1903, measures barometric
pressure differences truly to one five hundred thousandth of an
atmosphere. My gauge, made in 1902 on a different principle, was
graduated to millionths of an atmosphere and for the most accurate
measurements of static pressure differences was always read to
tenths of a graduation. At Eiffel’s Laboratory, and at various
other places, a less accurate, but somewhat simpler, manometer
gauge is used. It consists merely of an inclined alcohol tube suitably
mounted beside a graduated. scale. The latter instrument, a long
known type of gauge, I would recommend for its convenience; but
where great precision is required the English gauge or mine would
perhaps serve better.

* More strictly speaking, V is the increase of velocity of the air as it flows
from the room into the tunnel; but as the air starts from near rest, the
increase of velocity is practically the whole velocity of inflow. A consider-
able error may ensue if V be taken as the true speed of inflow for the case of
a tunnel of goodly section as compared with that of the room. Thus for the
new English tunnel the cross-section is 7 x 7 feet in a room whose section is
30 x 40 feet. Hence the average speed of flow through the room is 4 per cent
of the speed through the tunnel. Hence something like 4 per cent must be
added to the speed computed from the true static pressure difference in
question.

* At the National Physical Laboratory, the velocity along the axis of the
tunnel as computed from the pressure difference inside and outside the tunnel
wall is corrected by use of a small calibration constant obtained by placing a
Pitot tube in the center of this tunnel before the place where the models are
tested.

8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Such gauges are equally useful for measuring the difference
between some standard pressure and the actual pressure at various
points on the surface of a model, or elsewhere. Thus one arm of
the U tube may be connected with the internal surface of the tunnel
while the other arm is connected successively to various points on
the surface of a model. The difference between the standard wall
pressure and that at each point of the model surface may then be
plotted giving a diagram of surface pressure distribution all over
the model.

The wind balance.—Besides the pressure distribution and resultant
pressure on models, it is desirable to determine also the total wind
force, which is composed of both the pressure and the friction of
the air. To this end the English experimentalists use a bell-crank
balance which is a modification of the type devised and used in my
laboratory, and now employed also by Eiffel for the accurate meas-
urement of small wind forces. The English balance consists of two
horizontal weighing arms, one parallel to the tunnel, the other
perpendicular, attached to a round vertical tube, or arm, supported
at its center on a conical pivot just beneath the tunnel floor. The
vertical arm of the bell-crank balance has its upper half extending
through the tunnel floor up to the center of the current and is duly
shielded by a stream-line encasing sheath, while its lower half extends
downward from the pivot and dips into a pail of oil intended to
damp the oscillations. The upper half supports at its extremity
the wind model and near the pivot has a graduated joint, so that it
can be rotated about its own axis, and thus orient the model as
desired. Sliding weights on the two weighing arms are made to
measure the components of wind force parallel to the flow and per-
pendicular thereto. If the wind force tends to rotate the balance
about the vertical axis, this tendency, or wind moment on the model,
is determined by observing what horizontal restraining force must
be applied to one of the horizontal arms to prevent such turning.
Thus the balance may be used to measure lift, drift and center of
pressure. There are numerous ingenious and important details,
such as those for studying stability coefficients, which can best be
obtained from the British Aeronautical Committee’s technical report
for 1913, or from the working drawings which the laboratory has
furnished the Smithsonian Institution. Though this aerodynamic
balance is accurate and moderately convenient, | am of the opinion
that several new types can be devised which shall be equally precise
and probably more expeditious, requiring less adjustment at each

NOS 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAHM 9

change of model. Such new types I have had in contemplation since
first devising the bell-crank aerodynamic balance, in 1902.

The small wind-tunnel house, a wing of the engineering building,
is of structural iron and covers rather more space than the room
just described. Its chief apparatus is a four-foot wind channel for
testing small models. Other apparatus in this room are an engine
testing plant, now dismantled ; a horizontal water channel, described
in the Advisory Committee's report for 1912-13; and a small vertical
tube down which tobacco smoke, formed at its top, can be sucked
by an up-draft in a parallel pipe beside it having a burning gas jet
in the bottom to maintain a heated column, the purpose of the
descending air mingled with the smoke being to delineate the flow
about models immersed therein and visible through the glass sides
of the tube.

The small wind-tunnel is the working prototype of the seven-foot
tunnel already described. Made of one inch lumber, it measures
some 40 feet in length and is supported more than 6 feet above tne
floor by heavy angle iron trestle work which also forms the fram-
ing for the wooden tunnel wall. The first half of the tunnel measures
4 feet square; the second half, joined to it by an expanding metal
cone, measures 6 feet square, is thickly perforated with inch square
holes in its sides, and has its farther end abutting against the brick
wall of the room. In the expanding cone at mid-tunnel is a low-pitch
four-blade wooden screw driven by a steel shaft proceeding from a
ten horse-power electric motor on a wall bracket at the large closed
end of the tunnel, and capable of maintaining an air current of 40
feet per second in the four-foot tunnel. The character of the air
flow and the instruments used are practically the same for the small
as for the large tunnel. Some $20,000 was expended in developing
and constructing this small tunnel and its appurtenances.

The small water channel, some 4 inches square in cross-section,
has been used to exhibit the stream-line flow about models of ships’
hulls, aeroplane posts, inclined wing forms, etc. By photographing
the stream, duly dotted with tiny particles of foreign matter, clear
pictures of the stream-lines and eddies have been obtained. These
serve to show what forms are likely to encounter least resistance
in moving through a fluid. But it can hardly be supposed that the
phenomena of flow about a model slightly submerged in a shallow
stream of water are identical with those for deep submergence in
the atmosphere, unless for very slow speeds.

IO SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Wind towers.—On the ground to the west of the National Physical
Laboratory buildings, two wind towers, each 60 feet high and pro-
vided with rotating platforms 20 feet long, are used to determine
the flow and pressure of free air about large-scale models. The first
results of such determinations were published by Dr. Stanton in the
proceedings of the Institution of Civil Engineers for 1907, and iater
studies may be found in the reports of the Advisory Committee.
The Smithsonian Institution can doubtless obtain a like service from
the three tall radio towers in its neighborhood.

The Royal Air Craft Factory, under the direction of Mr. Mervin
©’Gorman, member of the Advisory Committee, is adjacent to the
headquarters and flying grounds of the Military Wing,’ at South
Farnborough. Its work is coordinated with the aeronautical re-
searches of the National Physical Laboratory, and is professedly
- concerned with the scientific improvement of air craft construction,
though in reality directed at times to the manufacture, on a large
scale, of aeroplanes, propellers and parts of dirigibles. The factory
construction and research are in charge of a civilian staff which
cooperates with the Advisory Committee for Aeronautics in perform-
ing aerotechnical work for the naval and military branches of the
aerial service. The close coordination of the Air Craft Factory with
the Flying Corps and with the Advisory Committee is an obvious
advantage to the progress of aerotechnics, which might be still
further enhanced if all the experimental plants were in one locality
as proposed for the United States.

Apparently no very sharp line separates the aerotechnical work
of the Royal Air Craft Factory from that of the National Physical
Laboratory. Both have a whirling table; both have an engine
testing plant; both have studied the materials of construction; both
design instruments. But this overlapping is not excessive. Broadly
speaking, the laboratory investigates models; the factory full-scale
air craft, their parts and appurtenances.

The factory investigates, develops, manufactures, and tests air
craft. It is a mammoth plant, covering many acres and comprising
half a dozen large buildings. It is said to expend half a million

*It may be noted that the entire military aerial service of England is known
as “The Royal Flying Corps,” and is under general supervision of the Air
Committee, itself a subcommittee of the Committee on Imperial Defense. The
Flying Corps comprises at present four branches: The Central Flying School;
the Naval Wing; the Military Wing; the Reserve. The Advisory Committee
for Aeronautics is an independent body, appointed by the Prime Minister,
and receiving its appropriations directly from the Lord of the Treasury.

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 3, Pl. it

WATER CHANNEL AT NATIONAL PHYSICAL LABORATORY, ENGLAND

to

NOUS EUROPEAN AERONAUTICAL LABORATORIES—ZAHM If

dollars per year and to employ 700 men, 400 of them working on
aeroplanes. It has facilities for producing daily one complete
aeroplane, excepting the engine, which at present is bought elsewhere.
Its air craft are systematically tested on the great flying field nearby,
bearing instruments which reveal their complete working in practi-
cal maneuver. One instrument alone, called the “ ripograph,” records
simultaneously the angles of pitch, roll and yaw, the speed through
air, the altitude, the three control movements and the time. The
stress in the wires, the propeller thrust and the pressure distribution
on the wings and other surfaces may likewise be recorded.” The
establishment does in fact the work planned in the United States
for both the field laboratory and the experimental air craft factory.
But the Royal Air Craft Factory lacks some of the facilities planned
for our plant, such as an expanse of water for testing naval aero-
planes, and the immediate accessibility of allied laboratories, work-
shops and other resources.

The result of the full-scale experiments has been to disclose the
defects of the leading types of aeroplanes, and to indicate means of
betterment. Substantial improvement has been made in the efficiency,
stability, factor of safety and range of speed of the aeroplanes
specially studied at the factory. The final outcome has been to pro-
duce a stable, efficient and safe biplane having a range of speed of
40 to 80 miles an hour. It is expected shortly that a standard control
will be adopted after the best types have been given a comparative
test. The type at present most in favor is the Deperdussin control,
which rotates a wheel for warping, shoves it for elevating, and
uses a foot lever for steering. Such practical full-scale work cannot
be too strongly recommended for the Smithsonian Institution, es-
pecially if the army and navy will, as already intimated, furnish for
such tests their typical air craft and their experienced pilots.

Reports——The scope and character of the activities of both the
factory and the laboratory can best be gathered from the annual
reports of the Advisory Committee. These set forth all the work
initiated by the committee, including, besides reports of experiments,
all the theoretical researches, and all the summaries made by its
members, in any form, whether of elaborate memoirs, translations
or abstracts. The catholic character of these reports is praiseworthy,
but their literary form and editing could well be improved. In this
latter respect Eiffel’s reports form more elegant models.

* All these measuring and recording devices can be purchased from the Cam-
bridge Scientific Instrument Co.

12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Other English aeronautical laboratories worth mentioning are
those of the Northampton Polytechnic Institute, London, and of the
~ East London College. For want of time I did not investigate these ;
but as their resources are very moderate and their reports have been
irregular and meager, it is doubtful whether they contain any equip-
ment materially worth adding to what has been hitherto described.

FRENCH AERONAUTICAL LABORATORIES

The Laboratoire Aerodynamique Eiffel consists of a single build-
ing with offices, a wind tunnel and various appurtenances, there being
no workshops in the establishment. The wind-tunnel room measures,
in round numbers, 4c by 100 feet, by 30 feet high; the three office
rooms and garden cover about half as much additional space. Two
wind-tunnels, a large and a small one, placed side by side, occupy
the center of the room. They are placed well above the floor, ‘to
admit of a more nearly symmetrical flow of air. Considerable fur-
niture—shelves, drawers, etc.—is placed about the walls; but the
body of the room is kept somewhat free of obstructions to secure
a less disturbed circulation.

Each tunnel comprises three main parts: the short bell-mouth
intake, the model chamber, the long bell-mouth exit. The air from
the room traverses the intake through honey-combs placed at either
end of the bell-like form; then passes at its maximum speed in
uniform rectilinear current across the model chamber ; then flows in
gently expanding stream and with diminishing speed onward to the
larger end of the exit, where it encounters the fan which drives it
with replenished energy into the open room. The model chamber is
thus seen to be an enlargement of the tunnel proper, spacious enough
to accommodate observers, and so sealed from the surrounding room
as to have the same barometric pressure as the inflowing current at
its narrowest section.

This type of tunnel, adopted by Eiffel after mature experience,
has been patented by him as having features of considerable value.
He prizes particularly the vacuum chamber for the observers, and
for the freer flow of air about the models, uninfluenced by constrain-
ing walls. He also prizes the expanding exit, or “ diffusor,” for
slowing the air as it approaches the fan and exhausts into the room,
thus realizing great economy of power in maintaining the circula-
tion. It is doubtful, however, whether any of the main features of
Eiffel’s tunnel are patentable in America. The bell-mouth entrance
and exit have been known here many years. The vacuum chamber

i)

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was employed by Mr. Mattullath and myself in our wind-tunnel
constructed in IQOr ; was disclosed to many others then; and shortly
thereafter was described in public prints.

The true function of the “ diffusor,” or expanding exit, seems to
be to prevent turbulence, and thus to promote economy of flow, rather
than to increase the pressure of the stream before it reaches the
fan, as taught by Eiffel. In other words, the economy of circulation
can be achieved by placing the screw at a narrower part of the exit
cone, if the pitch of the blades be properly adapted to the stream at
that sections But Eiffel’s present arrangement presents structural
advantages.

The circulation in the large tunnel is maintained by a Rateau screw
suction ventilator with helicoidal blades. The screw is driven by
a fifty-horse electric motor, which is found sufficient to maintain a
constant flow at any desired speed up to 32 meters per second, or say
up to 70 miles an hour. This is a notable result, since the air stream
at its swiftest section measures two meters in diameter. Though
the motor takes its current from the public mains, it requires little
adjustment of the rheostat to maintain steady speed for the time of
an observation, though it may vary in longer periods.

The air velocity in E1ffel’s tunnel seems to be satisfactory while
used for engineering studies rather than for exact researches in
physics. The velocity at all points of a cross-section is uniform
in magnitude to within two per cent, and varies but little in direction.
A fine silk thread, however, moored in the current, plays a trifle to
and fro in both the horizontal and the vertical direction. The current
velocity also fluctuates in time, say I to 2 per cent.

The velocity is determined, as in the English and other laboratories,
from the pressure difference between the vacuum chamber and the
large room enclosing the tunnel. This pressure difference is meas-
ured with a Shultze manometer, or inclined tube containing alcohol
and provided with a graduated scale. In ordinary practice the end
of the alcohol column plays several per cent above and below a mean
reading, but can easily be located on the scale to within 4 per cent
by a capable observer. This means that the velocity can be deter-
mined truly to within two per cent.

For convenience, in the determination of the wind effect on the
various kinds of models, Eiffel places his measuring instruments on
a platform, or bridge, spanning the vacuum room, and supported on
either side by wheels resting on iron rails secured to the walls, so
as to be moved aside when desired. Sometimes also the models are

14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

supported on a frame which can be wheeled along the floor. Thus
apparatus can be adjusted outside the tunnel, quickly run into place,
and again removed without dismantling. This is a unique advantage
of Eiffel’s arrangement. The main apparatus so employed are the
aerodynamic balances, the propeller tester, and the instruments
respectively for finding the distribution of pressure and the magni-
tude and line of action of the total wind force.

Of the two balances the simple bell-crank one for the precise
measurement of smaller forces has been sufficiently explained as to
principle in describing the English laboratory. The large aerody-
namic balance, invented by Eiffel himself for determining the lift
and drift of the whole wind force, and its line of action, is elaborate
in theory, structure, and practical operation, and is well explained in
Eiffel’s book, “ The Resistance of the Air and Aviation.” It is not
sensitive enough for measuring the smaller forces on inclined planes
and on small models.

The propeller tester is elegantly simple in design and operation.
A vertical electric motor, mounted on the bridge above the tunnel,
and having its shaft extended down through a wind shield to the
center of the air stream, there engages, through bevel gearing, with
the horizontal shaft of the model propeller. The shafting of the
armature and the propeller are encased in a sheathing which also
contains the bearings, and transmits the propeller thrust and torque
to the base of the motor. The motor, in turn, is so mounted on
pivots and hydraulic gauges as to measure the thrust and torque
without material displacement. At the same time the motor speed
is indicated by a tachometer attached to the upper end of the arma-
ture shaft. The wattmeter method, however, has lately replaced
the direct method of measuring propeller torque.

The apparatus for measuring the distribution of air pressure over
the surface of models has long been used by others, and in principle
is like that employed in the English laboratory, and hitherto described
in this report. The instrument for finding directly the line of the
resultant air force, or ‘center of pressure,’ on a model surface is
also an old contrivance, and need not be explained here. It is fully
described in Ejiffel’s book.’

*It may be noted, however, that Eiffel’s and the English method of allowing
a model to rotate about a vertical axis by supporting it on a step bearing is not
very delicate, even when a jewel step is used. A more accurate way is to
suspend the body from a wire, or float it on a liquid. The writer, in 1901,
discarded the jewel pivot and supported his models on a fine steel wire, an oil
damper being provided to deaden oscillations. With a float no damper is
needed.

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The Institut Aerotechnique de ! Universite de Paris is described
in sufficient detail as to its material plant and operation in its pros-
pectus, and in the following article published in the Engineering
Magazine for October, 1911:

The area of the site occupied is about eighteen acres. The buildings com-
prise a central hall, surrounded on three sides by workshops, stores, labor-
atories, and a power house. In the central hall will be installed experimental
apparatus devoted to the study of aerial phenomena, which will include a large
fan, six feet six inches in diameter, and an aerodynamic balance, whereby the
pressure of a jet of air on surfaces of various shapes will be determined. There
will also be an air chamber supplied by another fan wherein it will be possible
to measure the strength, the center of pressure, the components, and the
resultant of the reaction of a current of air at any speed up to 65 feet per
second. A tunnel similar to that used by Colonel Renard will also be erected
for studying the stability of models. An arrangement for measuring the
friction of air on surfaces of various natures when the air is moving at all
velocities, an electric dynamometer for measuring the torque of propellers
fixed in position, apparatus for studying helicopter screws, and a test bench
for trials on the output, endurance, and fuel consumption of aeronautical
motors will also be installed. A closed chamber is to be erected, wherein the
resistance of helical screws at speeds far in excess of those normally arranged
for, and almost at the rupturing speed, will be investigated.

In the chemical laboratory the study of light gases, suitable for balloon
work, will be carried on, and questions relating to their manufacture, puri-
fication, properties, etc., will be investigated. - The chemical features of
various envelope materials, the changes which occur in them under the in-
fluence of heat, light, and humidity, the properties and features of the various
varnishes applied to render the material airtight and to preserve it, and similar
subjects will also be studied. In the physical laboratory the instruments used
in aeronautical work, the accuracy of their indications, their reliability and
the modifications which are called for in their design to meet aeronautical
conditions, will be investigated, while the densities and coefficients of expan-
sion of light gases, and the best means of storing and transporting them will
also receive attention.

A photographer’s department has been provided next to the physical labora-
tory. In the workshops it will be possible to manufacture and repair all the
experimental appliances required by the institution. A part of one wing is
reserved for the installation of machines designed specially to test the
materials employed in the construction of aircraft. In the power house,
situated at the west end of the building, are two vertical compound steam
engines coupled directly to dynamos supplying power and light to the entire
institute.

One of the most interesting features of the institute is the provision made
for certain large-scale experiments with planes and propellers. To this end
a long, narrow strip of ground is laid out with a normal gauge railway about
seven-eighths of a mile in length. The rails are laid on oak sleepers, and are
bonded in pairs by the aluminothermic process. The line is level over its
entire length, with the exception of an incline at each end. At the starting
point the line for a length of about 235 feet is given a slope of I to I00 to

3

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

facilitate the starting of the vehicles. At the terminus a slope of half this
amount, but extending over about 490 feet, is provided to facilitate the arrest
and return of the carriage. On each side of the line and extending along its
full length is laid an electrical conductor, whereby current is fed to the motor
of the carriage. The return circuit is made by way of the rails. For the last
300 feet or so of the track an additional pair of rails is laid down alongside the
running rails. On these additional rails, slippers carried by the vehicle bear
so that over this distance, or at least a portion of it, the carriage skates instead
of rolling. This facilitates stopping, and in addition furnishes a safety device
in case of emergency.

It is intended ultimately to have four electric carriages to work on the line
described above. One has already been constructed, and has been used for a
number of experiments. The employment of four carriages has been adopted
in view of the fact that each series of experiments requires a different equip-
ment of the carriage and different registering apparatus. If only one were
used the time lost in dismantling and remounting it with each series of experi-
ments would be very considerable. It is essential also that each vehicle should
be specially designed to meet the conditions of the particular class of experi-
ment for which it is intended. According to present intentions the first
carriage will be used to measure the horizontal and vertical components and
the resultant of the air pressure on surfaces of sustentation, whether plane
or curved, simple or compound. The determination of the direction of the
resultant, the center of pressure, its displacement when the angle of incidence
is changed and the “angle of attack” will also be undertaken with this
carriage. The second and third vehicles are intended for experiments on
propellers or tractors, one being used for the large screws employed for
dirigible balloons and the other for the smaller aeroplane screws. The
tractive effort, the power absorbed and the mechanical efficiency of each type
of propeller will be determined at all speeds. A-further important subject
of study with these two carriages will be the effect of the translational motion
on the output and efficiency of the propellers. A comparison will be instituted
between the efficiency, etc., of a propeller when rotating on a fixed axis and
when moving with the same speed of rotation, but with various different speeds
of translation. The fourth carriage will be specially equipped for measuring
the resistance or “drift” of the various parts of a flying machine.

The weight of the first carriage is about three and three-fourths tons, ex-
cluding the motor, and a little less than five tons with the motor. The body
of the carriage is built up of steel plates stiffened with angle irons and
measures twenty feet in length and six feet six inches between the longitudinal
members of the frame. Current is supplied to the motor by means of two
pairs of sliding contacts carried in the side of the truck. The movement of
the carriage is controlled from a lookout-post commanding the whole line.

All the carriages will be furnished with appropriate measuring instruments.
A chronograph will register the number of revolutions of the wheels in a
given time, from which the speed will be deduced. In addition there will be
a direct speed recorder registering the value of ds/dt at each instant of the
travel. A recording watt meter will register the power furnished to the motor
either on a time or a distance basis. One or more recording dynamometers
will also be carried whereby the particular data being determined will be
measured. The efficiency of the whole plant at all speeds, the frictional

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resistance of the driving and recording gear, the resistance to rolling of the
carriage and the air resistance of its elements, will all be determined once for
all, so that the power actually absorbed by the surfaces or screws under test
may be readily determinable.

Full-scale measurements—We saw a full-scale Bleriot monoplane
mounted on one of the electric carriages in such manner that its lift,
drift and moment, or center of pressure, could be determined at one
time, as it speeds across the field. The speed through the air is
measured by means of a pressure-tube anemometer whose pressure
collector is a Venturi tube, and has to be calibrated, since its readings
are larger than those of a standard instrument such as used by Eiffel,
Prandtl and others. The relative importance of such large scale
experiments as compared with model tests, or full scale flights with
instruments mounted on the aeroplane, has yet to be determined. If
of new type, the full-scale machine may be tested more safely on a
car. The measurements of lift here are said to be in error about
5 per cent; the drift measurements are much less accurate.

A roundhouse, which measures 120 feet 1n diameter, shelters a
whirling table, the extremity of whose whirling arm describes a
circle 300 feet in circumference, and carries the models subject to
aerodynamic study. This can be used in any weather, while the
electric road can be used only at special times, and most effectively
only during fair and calm weather. The whirling table, however,
does not seem to be so popular in the leading aerotechnical labora-
tories as the wind-tunnel and large field track. It is not an indis-
pensable part of an aeronautical laboratory, except where studies in
circular motion are to be made.

Ancillary buildings have been erected on the grounds near the main
laboratory, one for the director immediately in charge, another for
the caretaker, who is also a workman assisting in the experiments.

The reports of the investigations are published in the Bulletin
de l'Institut Aerotechnique de | Universite de Paris. The annual
issues for 1912 and 1912 are in the Smithsonian library.

Other French aeronautical laboratories, operating on a smaller
scale, are worth mentioning, though unvisited by me for want of time.

The military establishment at Chalais-Meudon, in charge of the
Engineer Corps, and under direction of Commandant Dorand,
resembles the English Royal Air Craft Factory, in developing ex-
perimental air craft and making full scale tests; but it does not

manufacture air craft on such a large scale, and does not compete
with commercial firms in building for the government, but rather
stimulates and helps them to do their best work.

18 SMITHSONIAN MISCELLANEOUS. COLLECTIONS VOL. 62

The Conservatoire National des Arts and Metiers, corresponding
to our Bureau of Standards, does some aeronautical work in cali-
brating instruments, testing materials and motors, and furnishes
a“ mouline Renard ’—a standardized revolving bar with paddles at
either end—for attachment to a motor to determine its power at
various speeds of rotation.

By the use of automobiles on a smooth road Chauviere has tested
screw propellers mounted above the vehicle and advancing at natural
working speed, and the Duc de Guiche has measured the lift, drift
and pressure distribution on aerofoils of considerable size. The
accuracy of the automobile method has, however, still to be proved
satisfactory. The Chauviere propeller experiments are now made
at St. Cyr Institut; but the researches of the Duc de Guiche still
continue, and are reviewed from time to time in aeronautical litera-
ture. The earlier reports comprise two volumes published by
Hachette, Paris.

GERMAN AERONAUTICAL LABORATORIES

The Gottingen aerodynamical laboratory, apart from the con-
structional and executive departments, is a one-story brick building,
in size about 30 by 40 feet, comprising a wind-tunnel and two rooms,
one for desk work, the other for instrumental observations. It stands
alone, in a remote little meadow on the outskirts of the city, about
fifteen minutes walk from Prof. Prandtl’s university headquarters.
It is very cheaply constructed, lighted by electricity, and heated by
a little stove in one office.

The wind-tunnel consists of a continuous closed channel, two
meters square in cross-section, running round the four walls of
the main room. Through this tunnel the air is forced in a steady
closed circulation by a screw ventilator two meters in diameter,
belt driven from a thirty-horse electric motor placed in a little off
room. As the blast from the blower. is too fast along the tunnel
walls, it is accelerated at the center of the stream by use of sheet
metal fixtures placed in it near the screw, which also help to elimi-
nate whirls. The air stream next passes through a honeycomb
(fig. 1), made of 400 equal sheet metal cells, each about 4 inches
square and 20 long, the sheet metal being in two thicknesses, or two
ply, so that either cell can be constricted at will by spreading the
cell wall inwardly. Actually, many of the cell walls were so con-
stricted. In fact, the honeycomb looked badly distorted as 1f much
time had been spent in adjusting the cells so that each should deliver

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the same amount of air. The adjustment once made assures, we were
told, an air stream uniform in velocity at all points of a cross-section
and at all speeds. One would think that a considerable change of
speed would require a new adjustment of the cells to maintain uni-
formity. Emerging from the first honeycomb, the air passes through
vertical sheet metal guide blades, each a double sheet and of turbin
blade form, which turn the stream 90°, without eddies; thence
through similar blades giving 90° more turn; thence through a
much finer honeycomb to remove minor eddies. This last comb,
placed just before the test part of the tunnel where the models are
inserted, is made of sheet metal strips Io centimeters wide reaching
from floor to ceiling of the tunnel, and held in position by their

Fic. 1.—Prandtl’s Honeycomb in Wind-tunnel

mutual pressure, comprising among them go,000 cells. The stream oi
air issuing from the last honeycomb is said to be uniform, and has
a speed ranging up to 10 meters per second.

The measuring instruments employed are numerous; but as
several of them resemble the ones already described, they need not
be noticed. One favorite method used by Prandtl to measure the
resistance of a model, say of balloon form, is to suspend it in the
current by fine wires, and hold it against stream by horizontal moor-
ing wires whose tension is measured in the adjoining room by means
of a bell crank and sliding weight. Very accurate measurements
can be made without the mooring wires, if the weight and dis-
placement of the model along stream be observed, as in my expert-
ments of 1902. This method, as extended by Mr. Mattullath, has been

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

adopted at Gottingen to measure the resistance of hulls, etc., held
obliquely to the current. Prandtl’s differential pressure gauge, con-
sisting of inverted cups suspended from opposite arms of a balance,

WL

Fic. 3.—Prandtl’s Manometric Balance

and dipping into a liquid, is like the one devised and used by me
early in 1902, and found capable of measuring differential pressures
truly to one millionth of an atmosphere, or less. This gauge was

NO: 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAHM 2.

described in the Physical Review for December, 1903, half a decade
before Prandtl’s experiments.

The pressure distribution over model screw propellers having
perforated hollow blades was measured by transmission through.
a hollow shaft to a pressure gauge. The screws were made of copper
electrically deposited on wax models, and were then emptied of the
wax by heating. To show the direction of air flow past the blades,

Fic. 4.—Prandtl’s Pressure-tube Anemometer

sulphureted hydrogen was allowed to exude from perforations in
their surfaces, and thus to stain them. The staining streaks extend
fore and aft and very slightly outward radially along the screw
blades.

The results of the experiments in the Gottingen laboratory have
been published in various German periodicals, and in part translated
and republished in Engineering, London, for 1911 and 1912, all
of which are on file in the Smithsonian library. Particularly interest-
ing are Prandtl’s determination of pressure distribution on models of

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

balloon hulls designed in accordance with hydrodynamic theory ;
also his measurements of the resultant wind force on oblique hulls
and wing forms by the method devised and used by H. Mattullath
in 1902; also the resistance of wires and ropes, ete. Prandtl found
in fair shapes a large difference between total resistance and the
pressural resistance, and ascribed the difference to skin-friction ; but
this he did not attempt to measure directly.

The Deutsche Versuchsanstalt fiir Luftfahrt su Adlershof com-
prises one main building used for offices and full-scale aeroplane
testing; one used for construction; and five small houses each con-

Fic. 5.—Prandtl’s Suspension for Measuring Side Force

taining an engine testing apparatus. In addition to this plant, it is
intended to fly full-scale machines with measuring instruments, and
to mount large apparatus on an aerodynamic car pushed by a loco-
motive on a railway.

The laboratory of the main building is a large square room with
a tower in its center 100 feet high, on top of which wind observa-
tions may be made, and inside of which suspension cords run down
to support an aeroplane just above the floor, to determine its moment
of inertia. In a corner of the room an aeroplane inverted and
weighted with sand, as in Langley’s method, was under test for
stress and strain of its wing framing. In another corner was an
apparatus for measuring the force applied to the controls of an

NO! 3 EUROPEAN AERONAUTICAL LABORATORIES—ZAHM 23

aeroplane by a pilot in practical flight. This instrument may help
to determine the most suitable mechanism for a standard control.

The shop and the engine testing houses contain nothing that need
be reported. The engine torque and thrust were measured by
ordinary mechanical methods, and no special apparatus was used
to furnish a stream of cooling air, as in the British laboratory.

Other German aeronautical laboratories worth passing mention
are: the testing department of the Zeppelin Airship Co.; the aero-
dynamical laboratory used by Prof. Reissner of the technical high
school at Achen; the laboratory in charge of Major v. Parseval in
the high school at Berlin; the experimental plant of Prof. Dr. Fr.
Ahlborn, at Hamburg. The Zeppelin laboratory is not, under any
consideration, open to visitors from abroad; and as to the others
just mentioned, I had time only for a brief visit to Ahlborn’s place.
Ahlborn’s experiments have been confined mainly to determinations
of flow about models in a tank of water. The results are well por-
trayed in numerous excellent photographs and publications, the
best of which are in the Smithsonian Institution. His apparatus and
photographs and those at the National Physical Laboratory in
England are, for hydromechanical studies, the most instructive that
have yet come to my notice, except perhaps the more restricted ones
of Hele-Shaw. For stream-line delineation in air, however, the
classical apparatus and methods of Marey have not yet been sur-
passed, though more precise instruments of this nature are much
to be desired.

CONCLUSION

In closing I would gratefully acknowledge the courteous assistance
extended to Lieut. Hunsaker and myself, by the American Embassies
at London, Paris and Berlin, by the aero clubs in those cities, and by
the directors of the laboratories and factories we visited. We are
especially indebted to Mr. G. F. Campbell Wood, foreign representa-
tive of the Aero Club of America, at Paris, and to Major G. J. F.
Von Tschudi, of the German Army, Director of the Flug und Sport-
platz at Johannisthal, for many kind services which enlarged our
opportunities and facilitated our work in France and Germany.

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SMITHSONIAN MISCELLANEOUS COLLECTIONS

VOLUME 62, NUMBER 4

bodgkins FFund

REPORTS ON
WIND TUNNEL EXPERIMENTS IN
AERODYNAMICS

(With Five PvatEs)

BY

J. C. HUNSAKER, E. BUCKINGHAM, H, E. ROSSELL, D. W. DOUGLAS,
C. L. BRAND, AND E. B. WILSON

(PUBLICATION 2368 )

: CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
JANUARY 15, 1916

The Lors Baltimore Vress

BALTIMORE, MD., U.S. A.

a:

III.
IV:

VI.
Wil

VIII.
IX.

CONTENTS

PAGE
. The wind tunnel of the Massachusetts Institute of Technology. By
Aes Gee liiri Salers tere recor minins sey ares ot ie oar siett I
Notes on the dimensional theory of wind tunnel experiments. By
HES ES C1 CI Ta TIN eter reese oo rs ie oktecsiciaie cole tebe Gatererelseteiels leben siege wloss I5
The Pitot tube and the inclined manometer. By J. C. Hunsaker... 27

Adjustment of velocity gradient across a section of the wind

tunnel By Hl. . Rossellsand) Dy We Douglass. 24se.. sere - 37

. Characteristic curves for wing section, R. A. F.6. By H.E. Rossell,
Cae rand wan cea arD) O11 e las cm esioreqe. oe eiereyelet mere ctersloverelereisie <i 390
Stability of steering of a dirigible. By J. C. Hunsaker............ AI

Pitching and yawing moments on model of Curtiss aeroplane chassis
and fuselage, complete with tail and rudder, but without wings,
struts, or propeller. By J. C. Hunsaker and D. W. Douglas.... 47

Swept back wings. By H. E. Rossell and C. L. Brand.. aerate 55
Experiments on a dihedral angle wing. By J. C. Hansaees and
pm YO orl Sere uate elas siacoyctote mir eetarths teretet aie rear cise ele arm orrere cs ore 74

. Critical speeds for flat disks in a normal wind. By J. C. Hunsaker ;

Withepreratony mn OteaD yu aw De VV US OMe eeercicparsctstcie sed ceverets crete area iors i,

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hodgkins Fund

REPORTS ON WIND TUNNEL EXPERIMENTS
IN AERODYNAMICS

I. THE WIND TUNNEL OF THE MASSACHUSETTS
INS TE OF ECHNOLOGY

By J. C. HUNSAKER, Assistant Navat Constructor, U. S. Navy

INSTRUCTOR IN AERONAUTICS, MASSACHUSETTS INSTITUTE OF TECH NOLOGY

An aeroplane or airship in flight has six degrees of freedom, three
of translation and three of rotation, and any study of its behavior
must be based on the determination of three forces—vertical, trans-
verse, and longitudinal—as well as couples about the three axes in

space. Full scale experiments to investigate the aerodynamical
characteristics of a proposed design naturally become mechanically
difficult to arrange. The experimental work is much simplified if
tests be made on small models as in naval architecture, and a further
simplification is made by holding the model stationary in an artificial
current of air instead of towing the model at high speed through still
air to simulate actual flying conditions.

The use of a wind tunnel depends on the assumption that it is
immaterial whether the model be moved through still air or held
stationary in a current of air of the same velocity. The principle of
relative velocity is fundamental, and the experimental discrepancies
between the results of tests conducted by the two methods may be
ascribed on the one hand to the effect of the moving carriage on the
flow of air about the model and to the effect of gusty air, and on the
other hand to unsteadiness of flow in some wind tunnels.

The wind tunnel method requires primarily a current of air which
is steady in velocity both in time and across a section of the tunnel.
The production of a steady flow of air at high velocity is a delicate
problem, and can only be obtained by a long process of experimenta-
tion. A study was made of the principal aerodynamical laboratories of
Europe from which these conclusions were reached: (1) That the

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 62, No. 4

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

wind tunnel method permits a leisurely study of the forces and
couples produced by the wind on a model; (2) that the staff of the
National Physical Laboratory, Teddington, England, have developed
a wind tunnel of remarkable steadiness of flow and an aerodynamical
balance well adapted to measure with precision the forces and couples
on a model in any position; and (3) that the results of model tests
made at the above laboratory are applicable to full scale aircraft.

Consequently it was decided to reproduce in Boston the four-foot
wind tunnel of the National Physical Laboratory, together with the
aerodynamical balance and instruments for velocity measurement.
Dr. R. T. Glazebrook, F. R. S., director of the National Physical
Laboratory, most generously presented us with detail plans of the
complete installation, including the patterns from which the aero-
dynamical balance was made. Due to this encouragement and assist-
ance we have been able to set up an aerodynamical laboratory with
confidence in obtaining a steady flow of air of known velocity. The
time saved us by Dr. Glazebrook, which must have been spent in
original development, is difficult to estimate.

The staff of the National Physical Laboratory have developed
several forms of wind tunnel in the past few years. In 1912-13 Mr.
Bairstow and his assistants conducted an elaborate investigation into
the steadiness of wind channels as affected by the design both of the
channel and the building by which it is enclosed.’ The conclusions
reached may be summarized as follows:

(1) The suction side of a fan is fairly free from turbulence.

(2) A fan made by a low pitch four-bladed propeller gives a
steadier flow than the ordinary propeller fan used in ventilation, and
a much steadier flow than ians of the Sirocco or centrifugal type.”

(3) A wind tunnel should be completely housed to avoid effect of
outside wind gusts.

(4) Air from the propeller should be discharged into a large
perforated box or diffuser to damp out the turbulent wake and return
the air at low velocity to the room.

(5) The room through which air is returned from the diffuser to
the suction end of the tunnel should be at least 20 times the sectional
area of the tunnel.

(6) The room should be clear of large objects.

‘Technical Report of the Advisory Committee for Aeronautics, London,

1912-13. Report No. 67.
21t is of interest to note that Mr. Eiffel has used a helicoidal blower in his.

new wind tunnel.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 3

The wind tunnel of the Institute of Technology was built in
accordance with the English plans, with the exception of several
changes of an engineering nature introduced with a view to a more
economical use of power and an increase of the maximum wind speed
from 34 to 40 miles per hour.

Upon completion of the tunnel an investigation of the steadiness
of flow and the precision of measurements was made in which it
appeared that the equipment had lost none of its excellence in its
reproduction in the United States.

As will be shown below, the current is steady both in time and
across a cross-section within about I per cent in velocity. Measure-
ments of velocity by means of the calibrated Pitot tube presented by
the National Physical Laboratory are precise to one-half of 1 per cent.
Force and couple measurements on the balance are precise to one-
half of 1 per cent for ordinary magnitudes. Calculated coefficients
which involve several measurements of force, moment, velocity,
angle, area, and distance, as well as one or more assumptions, can be
considered as precise to within 2 per cent. It is believed that it is
not practicable to increase the precision of the observations to such
an extent that the possible cumulative error shall be materially less
than the above.

DESCRIPTION OF WIND TUNNEL

A shed 20 by 25 by 66 feet houses the wind tunnel proper, 16
square feet in section, and some 53 feet in length (pl. 1). Air
is drawn through an entrance nozzle and through the square tunnel
by a four-bladed propeller, driven by a to H. P. motor. Models
under test are mounted in the center of the square trunk on the
vertical arm of the balance to be described later.

The air entering the mouth passes through a honeycomb made up
of a nest of 3-inch metal conduit pipes 2 feet 6 inches in length.
This honeycomb has an important effect in.straightening the flow
and preventing swirl.

Passing through the square trunk and past the model, the air is
drawn past a star-shaped longitudinal baffle into an expanding cone.
In this the plans of the National Physical Laboratory were departed
from by expanding in a length of 11 feet to a cylinder of 7 feet diam-
eter. This cone expands to 6 feet in the English tunnel. M. Eiffel
affirms that the working of a fan is much improved by expanding the
suction pipe in such a manner as to reduce the velocity and so raise
the static pressure of the air. Since the fan must discharge into the

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

room, the pressure difference that the fan must maintain is thus
reduced. Also with a larger fan the velocity of discharge is reduced,
and the turbulence of the wake kept down.

The propeller works in a sheet metal cylinder 7 feet in diameter,
and discharges into the large perforated diffuser. The panels of the
latter are gratings and may be interchanged fore and aft. The grat-
ings are made of 14-inch stock with holes 14 by 13 inches. Each hole
is then a square nozzle one diameter long. The end of the diffuser
is formed by a blank wall. The race from the propeller is stopped by
this wall and the air forced out through the holes of the diffuser. Its
velocity is then turned through 90 degrees. The area of the diffuser
holes is several times the sectional area of the tunnel, and the holes
are so distributed that the outflow of air is fairly uniform and of low
velocity (pli2: fier):

A four-bladed biack walnut propeller (pl. 2, fig. 2) was designed on
the Drzwiecki system and has proved very satisfactory. In order to
keep down turbulence a very low pitch with broad blades had to be
used. To gain efficiency such blades must be made thin. It then
became of considerable difficulty to insure proper strength for 900
R. P. M. as well as freedom from oscillation.

The blade sections were considered as model aeroplane wings and
their effect integrated graphically over the blade. The blade was
given an angle of incidence of 3 degrees to the relative wind at every
point for 600 R. P. M. and 25 miles per hour. The pitch is thus
variable radially.

To prevent torsional oscillations, the blade sections were arranged
so that the centers of pressure all lie on a straight line, drawn radially
on the face of the blade. This artifice seems to have prevented the
howling at high speeds commonly found with thin blades. The pro-
peller has a clearance of 4 inch in the metal cylinder.

The propeller is driven by a “ silent’ chain from a 10 H. P. inter-
pole motor beneath it. The propeller and motor are mounted on a
bracket fixed to a concrete block and are independent of the align-
ment of the tunnel. Vibration of the motor and propeller cannot be
transmitted to the tunnel as there is no connection.

The English plans for power contemplate a steady, direct current
voltage. Such is not available here. A 15 H. P. induction motor is
connected to the mains of the Cambridge Electric Light Company.
This motor then turns at a speed proportional to the frequency of the
supply current for a given load. Fluctuations of voltage are without
sensible effect, and the frequency may be taken as practically constant.

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 4, PL. 1

Fig. 1. SUCTION END OF WIND TUNNEL

Fig. 2. ENTRANCE NOZZLE, SHOWING END OF HONEYCOMB

ue

7

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.

He
i
| :
He

=

a a a |

* Leta

SESS

ele
oe ee ae | :
Se ee ee ee

beta kK ane

~ SS SS SSaeeee Ce ee

ee ee a a

Fig. 1. INTERIOR OF DIFFUSOR, LOOKING FROM PROPELLER

Cael

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et
4
s
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Fig. 2. PROPELLER OF WIND TUNNEL, LOOKiNG UP STREAM

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NGS A WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 5

The induction motor is directly connected to a 12 H. P. direct cur-
rent generator, which is turned at constant speed and which gener-
ates, therefore, a constant direct current voltage for given load.

By change of the generator field rheostat and motor field rheostat
the propeller speed can be regulated to hold any wind velocity from
4 to 40 miles per hour. The control is very sensitive. Left to itself,
the speed of the wind in the tunnel will vary by 2 per cent in 2 or 3
minutes. This variation is so slow that by manipulation of the rheo-
stats the flow can be kept constant within $ per cent. The cause of
the surging of the air is not understood, but is probably due to hunt-
ing of the governor of the prime mover in the Cambridge power
house causing changes in frequency too small to be apparent. The
gustiness of outdoor winds seems to have no effect, although the
building is not air-tight.

AERODYNAMICAL BALANCE

The aerodynamical balance (pl. 3) was constructed by the Cam-
bridge Scientific Instrument Company, England, to the plans and pat-
terns of the National Physical Laboratory. The balance is described
in detail by Mr. L. Bairstow in the Technical Report of the Advisory
Committee for Aeronautics, London, 1912-13. For details of oper-
ation and the precision of measurements reference may be made to
the original article.

In general, the balance consists of three arms mutually at right
angles representing the axes of coordinates in space about and along
which couples and forces are to be measured. The model is mounted
on the upper end of the vertical arm which projects through an oil
seal in the bottom of the tunnel.

The entire balance rests on a steel point, bearing in a steel cone.
The point is supported on a cast-iron standard secured to a concrete
pillar, which in turn rests on a large concrete slab. The balance is
then quite free from vibration of the floor, building, or tunnel.

The balance is normally free to rock about its pivot in any direction.
When wind blows against the model, the components of the force
exerted are measured by determining what weights must be hung on
the two horizontal arms to hold the model in position. Likewise the
balance is free to rotate about a vertical axis through the pivot. The
moment producing this rotation is balanced by a calibrated wire with
graduated torsion head.

Force in the vertical axis is measured by means of a fourth arm.
The model for this measurement is mounted on a vertical rod which

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

slides freely on rollers inside the main vertical arm of the balance.
The lower end of this rod rests on one end of a horizontal arm having
a knife edge and sliding weight.

For special work on moments, the interior vertical rod is replaced
by another having a small bell crank device on its head which con-
verts a moment about the center of the model into a vertical force to
be measured as above (pl. 4).

In this way provision is made for the precise measurement of the
three forces and the three couples which the wind may impress on
any model held in any unsymmetrical position to the wind.

The balance is fitted with suitable oil dash pots to damp oscillations,
and devices for limiting the degrees of freedom to simplify tests in
which only one or two quantities are to be measured. The balance
can be adjusted to tilt for 1/10,000 pound force on the model. In
general, the precision of measurements is not so good as the sensi-
tivity, and in the end is limited by the steadiness of the wind and the
skill of the observer.

The weights and dimensions of the balance were verified by the
National Physical Laboratory, where also the torsion wires were
calibrated.

For ordinary forces, weighings may be considered correct to 0.5
per cent. Naturally for very small forces, such as the rolling moment
caused by a small angle of yaw, the measurements cannot be so
precise.

ALIGNMENT OF TUNNEL

The axis of the wind tunnel was desired to be horizontal from the
honeycomb to the baffle plates in front of the propeller. To accom-
plish this an engineer’s level was mounted on a platform, built on the
floor of the house, opposite the mouth of the tunnel, and sighted on
the intersection of diagonal threads placed at 6-foot intervals. By
this means the distance of the center line of the tunnel above or below
the horizontal line could be estimated to one-eighth of 1 inch.

The tunnel beling low in the center, it was raised by wedges
until the reference marks coincided with the horizontal. This was
attained to within one-eighth of I inch in 6 feet of tunnel length.
The tunnel may, therefore, be said to have its axis horizontal to within
one-tenth degree.

ALIGNMENT OF VERTICAL AXES OF BALANCE

A concrete foundation having been built for the balance, the latter
was set in its approximate position. Three wedges were then

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62, NO. 4, PL. 3

AERODYNAMICAL BALANCE

SMITHSONIAN MISCELLANEOUS COLLECTIONS

eR AE

MODEL WING MOUNTED IN WIND TUNNEL ON MOMENT DEVICE OF BALANCE

VOL. 62, NO.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 7

inserted under the base plate of the balance standard, and the whole
balance raised to its proper height. It was now necessary to rectify
the vertical axis of the balance.

To bring the axis of the balance more nearly vertical by more
sensitive means the following method was employed: The small
torsion wire, used in aerodynamical measurements with the balance,
was set in place. The lower pivot of the balance was engaged in its
bearing, leaving the balance free to rotate about its vertical axis, but
constrained from tipping laterally.

The torsion wire was adjusted by means of the micrometer head
until the cross-hair on the fixed telescope coincided with that on the
mirror attached to the balance proper.

A weight of 0.4 pound was placed on one balance arm. The
micrometer head was again turned until the cross-hairs were coinci-
dent. By setting up on the holding-down bolts. the balance axis was
adjusted until placing a weight on either of the arms required no
further rotation of the torsion head to maintain coincidence of the
cross-hairs. In such case the axis of the balance is vertical. The
final adjustment admits of a possible error of less than 1/400 inch-
pound on the torsion wire. The angularity of the balance axis
remaining uncorrected may be computed as follows:

eet

F = force hung on arm.
B=angle of balance axis to vertical.

Then, taking moments about the vertical axis
F sin B X 18”=0.4 X sin B X 18” =1/400
or B=0-025.

DETERMINATION OF WIND DIRECTION IN THE HORIZONTAL PLANE

As a first approximation, the wind was assumed parallel to the axis
of the tunnel. A vertical flat plate was mounted on the balance arm
and carefully set parallel to a line drawn on the floor of the tunnel in
the direction of its axis. The plate was inclined 8 degrees to right
and left of this position and the transverse force measured on the
balance. The observations were repeated for 6 degrees and for a
second plate to eliminate errors due to irregularities in the plates.
The transverse force on one side was greater than on the other, indi-
cating an error in the assumed wind direction. A new line was drawn
on the tunnel floor making an angle of 0.3 degrees with the original
line. The observations for transverse force were repeated. It was
then found that the average of transverse force readings taken for

8 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

equal angles to right and left of mid position differed 0.5 per cent from
the mean of all readings. The extreme error of one observation,
including the error of 0.5 per cent due to lack of sensitivity of the
balance and the personal error of the observer, may then be as great
as I per cent in case the two errors are cumulative.

It is not considered practicable to obtain a closer setting with the
methods of alignment employed.

SETTING ARMS OF BALANCE

Knowing the true direction of the wind, it is necessary to set the
horizontal arms of the balance parallel and perpendicular to this
direction. To do this the floating part of the balance was rotated by
an adjustment provided by the design until the force recorded on the
“drift ” arm (the resistance) was equal for equal angles of the plate
to right and left of the wind direction. The final setting indicates a
remaining error of .2 per cent.

After making the slight adjustment required here the error in the
transverse force measurement was not found to be increased.

MEASUREMENT OF AIR VELOCITY

The velocity of flow in the wind tunnel is measured by a pressure
tube anemometer commonly called a double Pitot tube.

Our laboratory standard is a double Pitot tube presented by the
director of the National Physical Laboratory, England. This tube
was compared with the National Physical Laboratory standard which
had been calibrated on a whirling arm by F. H. Bramwell.’ Its con-
stant had been determined to be unity to a precision of 0.1 per cent.
Our tube was compared with it by a method allowing a precision of
0.25 per cent. A discrepancy of about 0.25 per cent was found. Its
readings may then be taken as correct to this degree of precision. In
all cases a uniform rectilinear current is implied.

The Pitot tube, in common with all anemometers, has the disad-
vantage of obstructing the channel, and where models are to be tested
the channel should be kept entirely clear. The expedient of using a
side hole in the channel is due to M. Eiffel.

In a channel of uniform section, air is forced to flow practically
parallel to the axis of the channel. Hence stream lines are all parallel
and across any section, taken normal to the channel axis, there should
be no component of velocity at any point. This statement is of course
true only for a steady, uniform flow free from turbulence. The

“Technical Report of the Advisory Committee for Aeronautics, London,
1012-13.

2

La Resistance de l’Air et Aviation, Paris, 1912.

=
\O

\

INOS 2: WIND TUNNEL EXPERIMENTS IN AERODYNAMICS

static pressure should be constant across a section, for if pressure
differences existed there would be a transverse flow of air created.
Tests in our wind tunnel showed constant pressure across a section
to a good approximation. Incidentally the constancy of this static
pressure across a section is a measure of the uniformity of flow.’

A small hole in the side of the tunnel can then be used to measure
the static pressure, but the dynamic pressure measured by the impact
end of the Pitot tube is

2
p+ Be = p,, by Bernoulli’s equation,
where
p=pressure at any point in a stream line.
v=velocity at any point in a stream line.
p=—density at any point in a stream line.
po=pressure where v is zero.

In our wind tunnel a fan sucks air through the tunnel which is
therefore all under suction. The air is discharged by the fan through
a strainer into the building at one end, whence it returns at low
velocity to the other end to pass again into the tunnel. At a point in
the room the pressure transmitted by an impact tube would be

pe+&

20 Po
=e

But the room is 30 times as large as the section of the tunnel, and
when a wind of 30 miles is blowing in the tunnel there is only a gentle
Op I

draft in the room of about 1 mile per hour. Thus the ratio potas ae
Js C

c

gy 2
r

and the pressure in the room can be taken as
ee ee
pr iad Po = p ais 2¢
neglecting v;’.

* The static holes of the National Physical Laboratory Pitot tube were con-
nected to an alcohol gage, and the velocity being kept constant, the tube was
moved along the vertical center line of the tunnel. The following readings
were taken:

Head in 3 mm. alcohol Distance from wall
440.2 Bu
438.0 6”
439.5 12"
439.8 18”
439.5 24”
441.2 30m
441.0 360”
441.0 42”

uN”

441.2 45

10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

If then we connect a hole in the side of the tunnel with one end of
a liquid manometer, and leave the other end open to the room, the
gage reading is proportional to the difference in pressure or to

v2
Debt a

The reading of the manometer thus is a measure of the velocity.

Due to loss of head from friction in the mouth of the tunnel and
in the honeycomb, the relation

pu"

pr=pt 2g

is not strictly true. An unknown loss in friction would be repre-
sented by adding a term to indicate the friction head pressure. Then

2

pea pe,

The use of the side plate method ignores the effect of py. A com-
parative test showed an error of 3 per cent when velocity was calcu-
lated from side plate readings. It is, therefore, necessary to calibrate
the side plate and its manometer against the standard Pitot tube and
its manometer.

The side plate used (fig. 1) consists of a thin brass disk about 3
inches in diameter set flush in the wall of the tunnel. The disk is flat
and highly polished. Near its center, five holes 0.02 inch in diameter
are drilled. These holes are connected with a brass tube soldered to
the back of the plate and projecting through the side of the channel.
Rubber tubing is used to transmit the static pressure from the small
holes to one end of a manometer. As explained above, the other end
of the manometer is open to the air in the room.

The pressures transmitted by the side plate have been found to
respond very quickly to changes in velocity, and the method is even
more sensitive than the Pitot tube. Naturally its precision is no
better than that of the Pitot used for its calibration.

The pressure difference transmitted by the side plate is read on an
inclined alcohol manometer on the Krell principle. Both the side
plate and this alcohol manometer require calibration against a
standard. For convenience, the side plate and its manometer were
calibrated together against the standard Pitot tube and a Chattock
manometer.

The standard National Physical Laboratory Pitot tube was
mounted in the center of the tunnel in the place where models are
tested. This tube was connected to the Chattock gage. The side
plate in the wall opposite the tube was then connected to the alcohol

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS TE

gage. The wind speed was then adjusted to 2, 4, 6, 8, etc., up to 40
miles per hour and both gages read. Some 100 readings were taken.
From the Chattock gage readings the true speed was taken from its
calculated curve (for standard air). The readings of the alcohol gage
were then plotted on true speeds. The curve so made was then a
calibration of the side plate and alcohol gage in combination. The
Pitot tube and Chattock gage may now be removed, and in future

wall of Tunnel

a S HOLES—.02 DA.

Mano meter

Fic. 1.—Side pressure plate.

model testing the alcohol gage readings may be used to measure the
velocity at the center of the tunnel.

It is shown below that the velocity over the section varies about
I per cent over a 2 foot 6 inch square at the center of the tunnel.

CHATTOCK MICROMANOMETER

The Chattock gage mentioned above has been adopted as our
laboratory standard, but is used only for the calibration of other
gages which may be preferred on account of ease of reading. The
following notes on this gage are introduced here in the hope that
someone may have use for a delicate pressure gage. Working draw-

I2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOE;.62

ings will gladly be supplied to anyone contemplating the construction
of such a gage.

The Chattock micromanometer was devised by Professor A. P.
Chattock and Mr. J. D. Fry for the precise measurement of very
small pressures. The gage is described by Dr. T. E. Stanton in the
Proceedings of the Institution of Civil Engineers, December, 1903.
Dr. Stanton used this gage in his experiments on the air resistance of
small plates.

The principle of the gage is that of the inclined liquid U-tube, but
instead of giving the tube an initial pitch and observing the change of
level of the liquid, the Chattock gage is fitted with an elevating screw
and micrometer by which the gage is tilted to balance the pressure
difference in its two ends. By reading on the micrometer the amount
of tilt given, the head in inches of liquid is computed. By this means
there is no motion of the liquid in the glass, and errors due to capil-
larity and viscosity are eliminated. Furthermore, the condition of
the surface of the glass has no effect.

The gage (pl. 5 and fig. 2) consists of a glass U-tube mounted on a
tilting frame T. The pressures to be measured are connected to the
bulbs A and C, which are in communication with each other through
a horizontal tube bearing a third bulb B at any intermediate point.
The bulbs A, C and the lower part of B are filled with water. The
upper part of B is filled with castor oil. The water in B and C is in
free communication and hence the oil in B is at the pressure of C.
The water in A is led through a thin walled tube through the bottom of
B extending into the castor oil. An excess of pressure in 4 over the
pressure in C will cause water to flow from A into B. A water bubble
will then grow at D and expand into the oil. The gage can be tilted
so that this bubble remains of uniform diameter. The pressures in
A and C are then balanced. To provide this tilting the manometer
proper is mounted on a tilting frame 7, which pivots on the knife
edges at G and is elevated by the screw F. The whole is carried ona
bed frame Z fitted with three leveling screws J, a retaining spring
H, anda scale S, on which may be read the full turns of the screw F.

A microscope, /, fitted with cross-hairs is mounted on the frame 7”
and directed at the bubble B. A small mirror on the opposite side
illuminates the surface of the bubble.

The screw F is fitted with a large drum divided into 100 parts.
The screw has 20 threads to the inch. The gage is sensitive to one-
half of a division on the drum, and hence to a movement of the screw
of 1/4000 inch.

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NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS es

Before a measurement is taken, the bulbs 4 and C are opened to
the air of the room and the frame tilted by moving the micrometer
until the top of the bubble B is brought tangent to the horizontal cross-
wire of the microscope. This is the zero reading. The bulbs 4 and
C are then connected to the two parts of a Pitot tube and the frame
tilted until the bubble is again on the cross-wire. The amount of tilt
is then read on the micrometer.

Fic. 2—Chattock micromanometer.

Naturally too wide an excursion of the bubble will result in its
rupture. The loss of a bubble transfers a drop of water from A to B,
and hence a new zero reading must be found by balancing up again.
To avoid sudden change of pressure and breaking of the bubble, a stop
cock at E is fitted. This cock can be closed to make the instrument
portable, and in taking a reading an approximate balance is made
with E partly opened. The cock is then opened full.

The gage is filled with a solution of salt and water of s. g. 1.06.
The addition of a little salt keeps the castor oil from growing cloudy.

Two gages were constructed, one by a skilled glass blower and
the other by a student, with a viéw to determining the effect of
workmanship and dimensions. The frame and stand were made

2

I4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

identical in the two gages, but the glass work was purposely altered.
The tip of the tube at B was ground to a knife edge in one gage and
in the other ground off square. One tube was .20 inch in diameter
and the other .15 inch in diameter.

The two gages were connected to the same static pressure and gave
readings identical to 0.25 per cent. It was found that the gage in no
way is affected by minor variations in workmanship.

In the gage with the ground knife edge tip it was found that the
bubble did not break so readily as in the gage with the square tip. It
was suggested by Professor Gill that the tenacity could further be
increased by coating the outside of the tube below the bubble with
paraffin. This was tried and was found to be of great assistance. A
height of bubble from three to four times the diameter of the tube at
its base could be allowed without rupture. The reason for this is to
be found in the fact that castor oil sticks very tight to glass but will
not stick to paraffin. By the use of this wax the bubble could not
creep over the edge of the tube and so slide down it causing a break.
However, any large excursion of the bubble is to be avoided as tend-
ing to cause a slight change in the zero reading. In all tests the zero
should be taken at intervals. The effect of the paraffin on the tip
could not be detected in the readings of the gage.

The consistency of the gage readings with these various alterations
in the base of the bubble as well as in the size of the bulbs and con-
necting tubes gives great confidence in this type of gage. It was not
possible to calibrate this gage experimentally because there was no
other gage available to measure it against which was equally sensitive.
However, we have Professor Chattock, Dr. Stanton, and the National
Physical Laboratory as authority for the calibration of the gage by
calculation from the dimensions of its parts, and the density of the
liquid. It may be noted that the density of the oil used has no effect on
the principle of the gage and is not considered.

For the calculation of tilt, it is then necessary to measure the dis-
tance between the centers of the bulbs A and C and the distance from
the knife edge G to the screw F. An error of 0.1 inch in either of
these measurements is an error of I per cent in head or 0.5 per cent in
velocity. There is no difficulty in getting these distances to the
nearest hundredth of an inch. The screw thread was cut so precisely
that it was impossible to detect any error in the pitch of the thread.
The hole in Z was tapped with a standard Brown and Sharp tap.
The calculation of the change in level of the surfaces of the liquid in

NO. 4 WIND TUNNEL EXPERIMENTS IN: AERODYNAMICS 15

A and C is precise to 0.1 per cent. The density of the solution was
taken on a Westfall balance to the same degree of precision.

Since the gage is sensitive to less than 0.1 per cent for heads of
more than 0.3 inch, the measurement of velocity depends on the pre-
cision of the Pitot tube. The latter is good to probably 0.25 per cent
in velocity. However, the air current always has some fluctuation at
high speeds so that in the end the velocity measurement is limited in
precision by the closeness with which such fluctuations can be aver-
aged. Ina very steady current, such as our wind tunnel, it was found
that the error in estimating velocity was less than 0.5 per cent. The
average of a number of observations is of course better than this.

Change in density of the salt solution is 4 per cent for a change
of 60 degrees F. in temperature. A temperature correction is ordi-
narily unnecessary.

An alcohol gage is a sensitive and consistent instrument, but
requires calibration to eliminate errors due to viscosity and capil-
larity. The question of its suitability for precise work will be dis-
cussed later in another paper. It has the great advantage over the
Chattock gage in that it requires no delicate manipulation to-get a
balance, no cross-wire and microscope, and with it it is possible to
estimate the mean of fluctuations. The alcohol gage has been suc-
cessfully used to measure air speeds as low as two miles per hour.
It is shown with the Chattock gage in plate 5.

Mm. NOTESJON THE DIMENSIONAL THEORY ‘OF
WIND TUNNEL EXPERIMENTS

By EDGAR BUCKINGHAM

UNITED STATES BUREAU OF STANDARDS
INTRODUCTION

The forces which will act between a solid body and a fluid in con-
tact with it in consequence of a relative motion of the two, cannot,
except in a few of the simplest cases, be predicted by computation
from the size and shape of the body, the relative velocity, and the
physical properties of the fluid: the information can be obtained only
from experiment. Such experiments may be expensive or impracti-
cable, and it often appears desirable to get the required information,
in advance of the final decision on the design of a structure which is
to be subject to aerodynamic or hydrodynamic forces, by making
preliminary experiments on a small model of the proposed structure.

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

In order that the results of such observations shall be interpretable
as definite statements about the behavior of the full-sized original of
which the model is a copy, certain requirements must be satisfied, and
when they are satisfied the original and the geometrically similar
model are said to be dynamically similar. The conditions for
dynamical similarity are bound up with the general question of the
possible forms of equations which describe relations subsisting among
the physical quantities involved in physical phenomena.

NATURE OF THE PROBLEM TO BE DISCUSSED

Let us suppose that a solid body is moving, with the constant
velocity S, through a fluid which is itself sensibly at rest at points
far distant from the body; and let us consider the forces exerted on
the body by the surrounding fluid. Since these forces are evidently
due to the relative motion, they would remain unchanged if the body
were held at rest and the fluid made to flow past it with the velocity
(—S). The boundaries of the fluid are supposed to be so distant
from the solid body that no sensible disturbance reaches them, and
their nature can then have no influence on the forces with which we
are concerned and need not be further referred to. If the fluid is a
liquid with a free surface, the foregoing condition requires that the
moving body be so deeply immersed as not to cause any surface dis-
turbances.

Let R be any force exerted by the fluid on the body ; for example,
the component in any specified direction of the force on some par-
ticular part of the solid surface; or, to make it more definite, let R
be the total head resistance in the direction of motion. Then F& will
depend on and be completely determined by the relative speed, the
size, shape, and attitude of the body, and the mechanical properties
of the fluid; and there must be a definite relation connecting these
various physical quantities, which can be described by an equation.
We wish to consider the nature of this equation in so far as it is fixed
by the natures of the separate quantities involved in it.

THE PHYSICAL QUANTITIES WHICH INFLUENCE FLUID RESISTANCE

Let D be some linear dimension of the body, such as its greatest
length. The shape of the body and its attitude, 7. e., its orientation
with regard to the direction of motion can be specified by stating the
ratios of a number of lengths to the particular length D. If these
ratios are denoted by 7’, 7",7’”,...., etc., the size, shape, and attitude
of the body are completely specified by the values of D,7’,r”,...., ete.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS iy

The properties of the fluid which determine its mechanical behavior
are its density p, its viscosity », and its compressibility. Instead of
the viscosity, it is generally more convenient to use the kinematic

< : Th . . ‘ 2 . e
viscosity v= which will do equally well when p is given. And simi-
p

larly, the speed C of sound waves in the fluid is fixed by the density
and compressibility so that, conversely, C together with p fixes the
compressibility. The properties of the fluid which concern us may
therefore be specified by stating the values of the density p, the kine-
matic viscosity v, and the acoustic speed C in the fluid.

We have now enumerated the quantities on which the force R may
be supposed to depend, and if nothing has been overlooked there
must be a complete relation connecting /¢ with the other quantities.
We may state the fact that such a relation subsists by writing the
equation

fe Sea a ter as py) 10g (1)
and our first task is to obtain from general principles any information
we can about the form of this unknown function f, which will enable
us to restrict the amount of experimentation required to finish the
work of finding the form of the equation.

APPLICATION OF THE PRINCIPLE OF DIMENSIONAL HOMOGENEITY

By the well known “ principle of dimensional homogeneity,” all the
terms of a complete physical equation must have the same dimen-
sions, and this fact enables us to simplify equation (1). Let II repre-
sent a dimensionless product of the form

Maite sey Cs (2)
the numerical exponents a, f, y, etc., being such as to satisfy the
dimensional equation

eS pC |= (3)
when the known dimensions of R, s, D, p, v, and C are inserted. Then
it may readily be shown: Ist, that since three fundamental units are
needed as the basis of an absolute system for measuring the six kinds
of quantity, R, S, D, p, v, and C, the number of possible independent
expressions of the form (2) is 6—3 or 3; and 2d, that if these expres-
sions are denoted by II,, I., U,, any correct equation involving the
quantities which appear in equation (1) and no others, must neces-

* Physical Review (2), 4, p. 345, October, 1914.

18 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

sarily, in order to have all its terms of the same dimensions, be
reducible to the form

P(e 3 fee =O: (4)
In addition to the dimensionless ratios 7’, r”, etc., there now appear
in the equation only three instead of the original six variables, so that
the labor of determining by experiment the form of the unknown
function is much less than if we had to deal with all six variables.

Tue More Specific ForRM OF THE EQUATION OF FLUID RESISTANCE

The dimensions of the quantities on the familiar mass, length, time,
or [m, l, t] system are:

[R]=[mlt*], [e]=[ml*],
[S]=[le"], [yJ=[Pe*],
[DJ=[4], [C]=[ie*],;
and we see by inspection that the expressions
Wee shure eps age:
il,= pD?S” ’ Il, = a ’ Il, = C

are dimensionless products of the required form (2), and that they
are independent. Accordingly, we know that equation (1) must be
reducible to the form
(, es )
P22 iy eC mee Si
This equation is fundamental to the experimental study of the
hydrodynamic or aerodynamic forces acting on totally immersed
bodies.
Solving for IL, we now have
psa eo" a (6)
in which the form of the unknown function ¢ remains to be found,
if it needs to be found at all, by experiment or by other than dimen-
sional reasoning.

= (5)

SIMPLIFICATION WHEN COMPRESSIBILITY MAy BE DISREGARDED

A simplification is possible when the motion is not rapid enough to
cause any sensible compression in the fluid. In this event it is imma-

terial what the compressibility is, so that may be omitted from con-

c
sideration and equation (6) reduces to
Rea DS a yy
(ps = se scaire

ne
av,

NOW WIND TUNNEL EXPERIMENTS IN AERODYNAMICS IQ

The approximation attainable when compressibility is thus left out

of account depends on the value of a et = is a small fraction, as

it nearly always is with liquids, equation (7) is a satisfactory sub-
stitute for (6). The speed of sound in air under ordinary conditions
is of the order of 1100 feet per second, or 750 miles per hour. For
rifled projectiles ?
(7) would be entirely misleading if used in studying projectile resist-
ances. But at the speeds which occur in aeronautics, with the excep-

may be as high as 2.5 or even 3, so that equation

> is a sufficiently small fraction

that the air acts nearly like an incompressible fluid, 7. ¢., like a liquid
of the same density and viscosity ; and equation (7) may be used as a
sufficiently approximate substitute for the more general equation (6).

tion of propeller tip speeds, the ratio

Equation (7) supplies the basis for the experimental investigation
of the aerodynamic problems which occur in connection with aero-
nautics and aviation by means of reduced scale methods.

RESTRICTION TO GEOMETRICALLY SIMILAR BODIES

Let us now confine our attention to a series of bodies of various
sizes but all of the same shape, and presented to the wind in the same
attitude. The bodies are geometrically similar, and any one may be
regarded as a reduced or enlarged model of any other. The ratios

f.

r’, r’,.... are now constants, so that equation (7) assumes the

simpler form
ieee eS 9
Dea , (3)

V

in which the form of the unknown function y of the single argument
Ze remains to be determined by experimenting on bodies of the
Vv

given series. The nature of this function will depend on the shape
and attitude of the bodies but not on their size, if our disregard of
compressibility, leading from (6) to (7), was a justifiable approxi-
mation.

The obvious procedure, in investigating y by analyzing the results
of experiments, is to plot observed values of _ against values of
. p
is and draw a curve through the points thus obtained. If we are
V

using air of constant density and viscosity the experiments may con-

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

sist most simply in measuring, by the aerodynamic balance, the force
R exerted on a given body at various values of the wind speed S.

Variations of =e may equally well be produced by varying D while S

is constant, 7. e., by experimenting at a fixed speed but with a series
of models of different sizes ; or, D, S, p, and v may all be varied simul-
taneously. But while such experiments furnish a desirable check
on the results obtained when S alone is varied, they are not neces-

DS

sary, if compressiblity is negligible ; for it is immaterial whether ——
Vv

is changed by changing D, S, or v.
If the plotted points obtained in any of these ways do not all lie on
a single curve, within their experimental errors, equation (8) is not
accurate enough. And if the models have been exactly geometrically
similar, we must conclude that compressibility has played some part
in the phenomenon. This means that in the more general equation
R 1S aS)
psc) ee
obtained by applying (6) to geometrically similar bodies, the effects

of varying = are not of entirely negligible importance.

HEAD RESISTANCE PROPORTIONAL TO S?; Viscosity NEGLIGIBLE

At ordinary speeds and for bodies that are not too small, experi-
ment shows that in air of standard density, R is very nearly pro-
portional to S?. It follows that, to the degree of approximation to

which equation (8) is valid, w (72) is merely a constant and is
Vv

independent of the values of D, S, andy. If we write

; eS _K

Vv
equation (8) reduces to

R= Kp D752. (10)
As is seen by referring to equation (7), K depends on the values of
r', © ,...+, etc.; it isa shape factor for the given series of ssea-
metrically similar bodies in the given attitude.

It is to be noted that viscosity does not appear at all in equation
(10), so that when the resistance is found to be proportional to the
square of the speed, if compressibility is negligible the value of the
viscosity is of no importance. This is not equivalent to saying that
viscosity plays no part at all in the phenomena; for if viscosity did

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 21

not exist there would be no eddies of finite size, no dissipation, and
at a constant speed no resistance. It means, rather, that the drag on
the body by the fluid is due to the continual drain of energy needed
to set up anew the turbulent eddying motion about the body; and
that when these eddies have once been created it makes no difference
how fast they are dissipated by viscosity after the body has left them
behind.

THE CRITICAL SPEED
In the foregoing case of resistance proportional to S*, the plot of

ee TS: ar ;
as ordinate against as abscissa gives, of course, a hort-

a
pD?S? v
zontal straight line for bodies of a given series. But if the experi-

~

: DS ee
ments are carried down to smaller and smaller values of ,acritical
Vv

value may be reached where the relation ceases to hold and the
character of the fluid motion changes very rapidly, though apparently
not discontinuously, so that the function y ceases to be a constant for

ADI : : : 3 Sete
low values of . For a given body in a given medium this critical
Vv

value of ze corresponds to a critical speed So which may be com-
Bite : Si DS;

puted a priori from the values of D and », if the critical value ( )

C
has once been determined for bodies of the given shape by varying
any one of the variables D, S, and v, or all together. Eiffel’s observa-
tions on spheres * confirm the foregoing statements when we take into
consideration not merely a single speed for each diameter but the
whole critical range within which the rapid change in the form of y
occurs.

Mr. Hunsaker’s observations on sharp cornered disks of different
diameters, but the same thickness, are very interesting as showing the
possible importance of such sharp edges or corners. The disks were
not geometrically similar ; but the corners at the edges were not only
nearly similar but, inch for inch, very nearly identical. Accordingly,
that part of the total resistance which may be regarded as due to the
sharp corners at the edge reached its critical value always at about
the same speed, irrespective of the diameter of the disk which was
bounded by the edge. The rapid change in the total resistance near
this speed seems to indicate that the “
considerable fraction of the whole.

corner resistance’ formed a

1C. R. 155, p. 1597, December 30, 1912.

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The occurrence of a critical speed for a given body in a given atti-
tude is paralleled by the practically much more important phenome-
non of the occurrence of a critical attitude at a given speed. Just as
the nature of the fluid motion and the law of resistance of a given
body change rapidly at a certain critical range of speed, so there are
similar rapid changes in the motion and the forces at the critical angle
of attack for a given aerofoil at a given speed.

REMARKS ON THE RESISTANCE OF FLAT PLATES NORMAL TO
THE WIND

From equation (8) it would appear that when RF is proportional to
S* it must also be proportional to D?, and yet this does not seem to
be true for flat plates normal to the wind. On the contrary, while

nee is nearly independent of S, the results of various observers
indicate that it increases somewhat as the diameter of the plate
increases froma few inches to a few feet. Leaving aside the improb-
able supposition that this effect is only apparent and due to observa-
tional errors, the most obvious explanation is that compressibility
may not be entirely negligible. If that is the explanation, equation
(g) and not equation (8) is the one to be used, and it is quite con-
DSRS:
AG
ent of S without being entirely independent of D. Computations of
the amount of compression to be expected at the speeds in question’
seem to show that the discrepancies are too large to be accounted
for in this way. But it may be remarked that in some of the details
of the turbulence much higher speeds may occur than the speed of the
wind as a whole. Hence compression might occur locally, in some
parts of the field about the body, to such an extent as to modify the
flow and so affect the resistance, even though computations based on
the average speed of the wind might iridicate that the effects of com-
pression could not possibly be appreciable under the given experi-
mental conditions.

Mr. Hunsaker’s observations on circular disks suggest, however,
that there may be another interpretation of the effect in question
which does not oblige us to have recourse to the unlikely supposition
that compressibility is of importance. If,-as appears from these ex-
periments, there is a critical range of speed determined by the form of

ceivable that «( ) might have such a form as to be independ-

*See Bairstow and Booth: Rep. British Adv. Committee for Aeronautics,
IQIO-II, p. 21.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 23

the edge and not dependent on the size of plate, it seems possible that
some of the apparent discrepancies between = =constant and = =
variable may be due to the experimental results of various observers
having been influenced by such critical phenomena, which were not,
however, sufficiently marked to attract attention.

To decide whether an explanation of this sort is applicable would
require an experimental study of the forms of edge which have been
used ; for until the critical speeds for these edges—if they have any—
have been investigated, it is impossible to say whether the speeds at
which various experimenters have worked may have overlapped with
these critical ranges. Nothing more definite can be said, at present,
than that it is well to pay close attention to geometrical similarity ;
but it seems that a further experimental study of the resistance of
flat plates, undertaken with the foregoing possibilities in mind, might
lead to interesting results.

DYNAMICAL SIMILARITY

Let us suppose that we are confronted with a problem of design
which requires our knowing, in advance, the head resistance, at a pre-
scribed speed, of some body such as an air-ship which is too large
for direct experiment. The question is, how to get the desired infor-
mation from experiments on a small model which can be made at a
permissible cost.

Returning to equation (9) or

papbrsy (25, 5 (11)

we notice that whatever be the form of ¢, if its two arguments have
the same values during two different experiments on geometrically
similar bodies, the value of ¢ itself will be the same in both experi-
ments. This observation leads to the notion of corresponding speeds
and dynamical similarity.

Let us suppose that we require the resistance FR of a body of size D
at the speed S in a medium with the properties p, v, C; and that we
have a model of the size Dm, which can be run in a medium with the
properties pm, vm, Cm. Then if we run the model at a speed Sm, such
that

DS )

m~m — DS Sys _— S
eS es and Cae (12)
and observe the resistance Rm, we know by equation (11) that
ieee pz oe

Ro Le (13)

24. SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

For when equations (12) are satisfied, pas . “| =4(2, 2),
V Vv

so that ¢ cancels out when we divide equation (11) for the full-sized
original by the corresponding equation for the geometrically similar
model. Speeds which satisfy equations (12) are “ corresponding
speeds,’ and when two geometrically similar bodies are run at cor-
responding speeds they are “ dynamically similar.”

If the speeds are low enough that compressibility may be disre-

m m

garded, the value of = is unimportant and the condition for corre-

sponding speeds, which ensures dynamical similarity, is merely the
first of equations (12). If we use only a single medium so that
pm=p and vm=v, the condition for corresponding speeds reduces to
Sine ead
Se
and geometrically similar bodies will be dynamically similar if their
speeds are inversely as their linear dimensions. Any great reduction
in scale might therefore involve our running the model so fast as to
make the effects of compressibility no longer negligible. But if the
original is to be run in air while the model can be run in water, this
difficulty may be avoided. For under ordinary conditions the kine-
matic viscosity of water is from 1/10 to 1/20 that of air, and for a
model of given size the speed required for dynamical similarity with
the original is reduced in the same ratio as the kinematic viscosity.
In practice the foregoing method of experimentation is usually
unnecessary. For under ordinary working conditions the resistances
of aeroplanes and their separate structural elements are so nearly
proportional to the square of the speed, and the effects of compressi-
bility are so small, that for practical purposes ¢ in equation (11) or
in equation (9) may be treated as a constant and equation (10) used
for computation, within any ordinary ranges of D and S. Any speeds
may then be regarded as corresponding speeds, and geometrical
similarity suffices by itself for dynamical similarity. If the constant
K of equation (10) has been determined by experiments on any body
of the given shape at any convenient speed, the same value may be
used in equation (10) for computing the value of RF for a different
speed or a different size or both.

m

CoMPLETE DYNAMICAL SIMILARITY

The experience with flat plates, showing that even though R. is
proportional to S? it may not be to D?, warns us to be cautious in

NOt: WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 25

assuming that equation (10) may be relied on for great accuracy
when the size D changes over a very large range; and it seems
possible that it may sometimes be desirable to make experiments
guided by equation (11) which holds for any series of geometrically
similar bodies, whatever the speeds may be.

The conditions for dynamical similarity given by equations (12)
can evidently not be satisfied if we work with only a single medium ;
fortiv., =a C,—C, we have S~—s and ,,—DL,-so that no seale
reduction is possible while preserving dynamical similarity. This
difficulty may, in principle, be surmounted by running the model in
water if the original is to run in air. Suppose, for instance, that the
original is an air-ship which is to run 40 miles an hour in air, and let
the model be run in water at such a temperature that its kinematic
viscosity is 1/15 that of the air. We then have v=15vm and the first
of equations (12) gives us

LoD SS. (14)
The second condition requires that the speed of the model shall be
the same fraction of the speed of sound in water as 40 miles per
hour is of the speed of sound in air. Since sound travels about four
times as fast in water as in air, the model must move at the very high
rate of 160 miles per hour, or about 235 feet per second. With this
condition that S;,=4S, and the previous condition stated by equation
(14), we have

I
Di a dD.

A model to 1/60 scale run in water will then be dynamically similar
to the original in air, if it is run four times as fast. Having thus
satisfied equations (12) we may use equation (13); and if we set

piece le oe en eee ig
R eam Oe Xx (=) ey

™m

The resistance of the original in air will therefore be about one-
quarter of the resistance of the dynamically similar 1/60 scale model
in water. How soon it will seem worth while to attempt experiments
of this sort cannot be predicted, but the notion of dynamical similarity
shows how the problem may be attacked.

Rae Pitot LTuBe

Hitherto we have let FP be the total head resistance of a solid body,

but if D is the diameter of the impact opening of a Pitot tube, 2 may

26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

evidently be regarded as a quantity which is proportional to the
impact or velocity pressure p. Hence equation (6), as applied to the
Pitot tube at rest ina current of fluid, may be written

papStp(=2, 2s tr....), (15)
and it is interesting to compare this with the known behavior of Pitot
tubes and with the Pitot equation as ordinarily given.

In the first place, we know by experience that if the impact opening
is the mouth of a long tube pointed up stream, the precise form of
the tube and the shape and diameter of its mouth have no appreciable
influence on the impact pressure recorded. This means not only that
the shape variables 7’, 7”, .... , etc., are of no importance and may be
omitted from among the arguments of ¢, but also that D is likewise

of no importance, so that the argument oD in which it appears may
Vv

be omitted. Equation (15) thus reduces to the form

p=oSty (7). (16)

When the fluid is nearly incompressible, like water, the compres-
sion caused by the impact pressure p will be so slight that it cannot
affect the general behavior of the fluid. Hence compressibility may
be left out of account and y treated as a constant, so that we have

5 = const x 2 (17)

If p is measured as a head h of the liquid, we have p= gph, and equa-
tion (17) reduces to

S=const X V gh.
The value of the constant, which cannot be found by dimensional
reasoning, is, in practice, V2 for a properly constructed tube.

If the fluid is a gas, equation (17) is still applicable when the speed
is low. But when the speed is so high that the pressure p causes

appreciable compression cannot be neglected and we must return

’ C
to equation (16). A form of wy ( 2) for high gas speeds may readily

be found from thermodynamics, but so many approximations and
unproven assumptions have to be made in the course of the argument
that the results are not at all convincing.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 27

Ill. THE PITOT TUBE AND THE INCLINED MANOMETER
By jC. “HUNSAKER

For aeronautical purposes the absolute measurement of velocity is
of less importance than the measurement of impactual pressure. For
this reason, an anemometer from which the velocity may be deduced
from a pressure measurement is preferable to any of the vane ane-
mometers which measure velocity directly, and require a somewhat
laborious calculation of the density of the air before the effect of the
wind can be evaluated.

The most common as well as the most convenient form of pressure
anemometer is the double Pitot tube. Reference may be made to the
papers of Taylor* and Zahm,’ in which it is shown that the equation
to a stream line in any perfect gas may be simplified in the case of air
by considering the air incompressible for velocities below 100 feet per
second. The simplified expression connecting pressure and velocity
in moving air is then Bernoulli’s equation as used in hydraulics:

pu - Us

ae + p= ee + Pos
where v, and p, are velocity and pressure at any point, and v, and
p. are corresponding values for some other point in the same stream
line.

Let us choose the point where v, is zero, then

oe +Pi=pe
In air ae is the barometric pressure. Let us change the notation

so that - ee Bp p)=barometric pressure, a constant.
2g

p is now the pressure in the unchecked stream, the “ static ’’ pres-
sure, and /p, is the pressure in the impact tube where the current is
brought to rest. This is called “ dynamic’’ pressure.

The ee tube is a device for transmitting the pressure difference,

bo —p= P_, from which the velocity may readily be calculated. The
2s

)
2

. 5 . . ”
quantity ae is commonly called “ velocity ”’ pressure.
5

* Experiments with Ventilating Fans and Pipes, by D. W. Taylor, Naval
Constructor, U. S. Navy, Trans. Soc. Naval Architects and Marine Engineers,
1905.

* Measurement of Air Velocity and Pressure, A. F. Zahm, Ph. D., Physical
Review, December, 1903.

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

If one end of an open tube be pointed into a stream of air and the
other end be attached to a manometer, the total dynamic pressure will
be recorded. On the other hand, if a tube with closed end be pointed
into the wind and further fitted with a conical or parabolic tip, the
stream line is only slightly deflected and distorted. If then small
holes or slots be cut in this tube at a distance well back from the tip,
the wind should blow past these openings and the interior of the tube
should be subjected to the static pressure of the stream. This pres-
sure can be measured by connecting the tube to a manometer.

It is generally accepted from the results of tests that any open-
ended tube of any size, 1f pointed fairly into the wind, will correctly
transmit the dynamic pressure.

It is equally common knowledge that the correct transmission of
the static pressure is not so simple. Widely different values are
obtained with different forms of tube and static orifice, and many
tubes, such as the Dines and the Recknagel, must be calibrated against
some standard. It is obvious that the nose of the tube should be of
easy form, that the tube should not be large in diameter, and that it
should be carefully polished in order that the air stream may pass
undisturbed. The best form of entrance will introduce some disturb-
ance, so that such static openings as are used should be placed well
back from the nose on the cylindrical portion. The form and size of
the openings will be discussed later.

The Pitot tube may consist of two separate tubes or a double tube
made up of a pair of concentric tubes, the dynamic tube being enclosed
within the static tube. Since the dynamic tube transmits the pressure

pv”
Pa ae
the two tubes to the two ends of a U-tube filled with liquid. The
reading of the instrument is then proportional to the difference

=p,, and the static tube transmits f, it is sufficient to connect

pv"

between the pressures transmitted and hence to

Knowing the

g
density, the velocity may be computed. The density of air depends
on the pressure, temperature, and humidity. Avoidance of the
necessity for calculating the density for ordinary aerodynamical tests
would be of great assistance.

ELIMINATION OF DENSITY OF AIR

It is generally accepted that the forces produced by a fluid in
motion with reference to any solid object depend on the size, shape,
and attitude of that object, the velocity, the density of the fluid, and

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 29

its viscosity, and upon nothing else for ordinary transportation
speeds.

The most general expression * for this statement which satisfies the
theory of dimensions is

ST 2172 Ee
R=pL2V f( a
in which
L denotes the length of any linear dimensions of the solid,
V, the relative velocity of solid and fluid,
p, the density of the fluid,
p, the coefficient of viscosity of the fluid,
Vip
a

It will be noted that the compressibility of the fluid has been neg-
lected.

and f is a function of the single variable

The value of f (==) is very nearly constant for bodies of a
be

given shape in a given orientation when the motion of the fluid is
sufficiently turbulent. Experimentally it is found that R« V’’, nearly,

and hence not only is f ( a2) nearly constant, but the influence
pe

VLp

7

of viscosity is small. The changes in f ( with change of scale,

density, and viscosity are hence in the nature of a correction.

For objects moving through the air at very low speed, especially
objects of easy form, turbulence is not marked and viscosity is of
importance. Consequently for such tests the assumption of f con-
stant is not justified.

However, for aeroplane wings, parts, etc., moved through the air
at high speeds the resistance to motion is largely due to turbulence,
R varies nearly as pV? and f (=) is constant nearly. Therefore,
we may assume that for the ordinary work of an experimental wind
tunnel, forces to be measured will vary as the density of the air.
Likewise, the manometer reading obtained from a Pitot tube will
vary as the density of the air.

It has been decided to adopt a standard density for air to be used
throughout. Velocity computed from a manometer reading is then
referred to this standard air, and forces measured on the balance are

* Helmholtz, Wissenschaftliche Abhandlungen, Vol. I, p. 158; O. Reynolds,
Phil. Trans. Roy. Soc., 1883, p. 935; Lord Rayleigh, Phil. Mag., 1899, p. 321.
3

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

referred to the same standard. Standard air is taken to be dry air
under the following conditions:

Barometric pressure, 29.921 inches mercury.

Temperature, 62 degrees Fahrenheit.

Density, 0.07608 pound per cubic foot.

COMPARISON OF Pitot TUBES

Opportunity was taken to compare the National Physical Labora-
tory standard Pitot tube, calibrated by Bramwell,’ with several forms
of tube in use by engineers in the United States.

‘C /e w
Nene

Fic. 3.—N. P. L. tube.

The tube under investigation was mounted in the center of the
tunnel and connected by rubber tubing with a Chattock micromanom-
eter. Care was taken to eliminate leaks in the leads, and to point
the tube parallel to the axis of the tunnel. A steady wind was then
blown through the tunnel and its velocity read from the alcohol gage
connected with the side suction plate which had already been cali-
brated as described in a previous paper. The velocity from the side

* Technical Report of the Advisory Committee for Aeronautics, London,
1912-13.

AERODYNAMICS

EXPERIMENTS IN

WIND TUNNEL

4

NO.

‘Vy oqny—s ‘OI

f}— = = - 72) —— - —___ - —_____ -______5

DIS HVF~-bIZ FOO VII]

oolW

FANL SHALNO Ni WHIT ,TO” HOF
YOIVEG SP ANON LY SFTIOH T

32 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

plate was then compared with the velocity indicated by the Pitot
tube under test. Comparisons were made at a number of speeds for
each tube.

pa else
oo). a Se
Hi SeeRe

38

36

34

w
rR

w
S

at
oe

ere
Lee ce
=

34 35 3637

Fic. 6.—Comparison of three forms of Pitot tube. Each point represents
one observation, and serves to bring out the sensitivity of the Pitot tube and
manometer measurements employed.

It was demonstrated that the velocity is correctly measured by any
tube having an easy entrance and a long cylindrical portion parallel
to the wind in which a number of small holes are drilled to transmit

a

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 33

the static pressure. The arrangement of the holes appeared to have
no effect. Long slots in the tube introduced large errors if the tube
were not pointed fair into the wind. The size of the tube appeared
to be immaterial.

The results of comparison of three tubes with different arrange-
ments of holes from 4 to 24 in number are shown on figure 6. The
tubes are shown on figures 3, 4,and 5. The agreement is very close—
within 4 per cent at velocities above Io miles per hour.

| 2 (ae)

eee
ED I PLANE OF HOLES
EDN PLANE OF HOLES
ED PRERPEINDICIULAR| TO

PLANE OF | HOL

Fic. 7.—Effect of inclining Pitot tubes to wind.

Tests were made to determine the effect of inclining the tubes to
the wind. The tubes with holes show an error of but 1 per cent for
an inclination of 4 degrees. The results are shown on figure 7.

The following conclusions may be drawn from these tests:

(1) Static openings should be small holes about 0.03 inch in diam-
eter to minimize effects of bad alignment or turbulence.

(2) An error of 2 degrees in aligning the tube causes no impor-
tant change in velocity reading.

(3) If a tube is correct at two speeds it remains correct at all
others within the range of our experiments.

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

(4) Holes should be symmetrically distributed on the cylindrical
portion of the tube.
(5) Any new type of tube should be calibrated against a standard.

Tue INCLINED MANOMETER

Granted that a Pitot tube is at hand which will correctly transmit
the static pressure, measurements of velocity are no better than the
manometer used. The ordinary U-tube filled with water, gasoline,
alcohol, or other light liquid shows a head of less than 1 inch for ordi- .
nary velocities. To obtain the velocity head within 1 per cent, it
would be necessary to read the displacement of the meniscus to within
0.01 inch. This is hardly practicable, and various devices are used
to magnify the reading. It is at once apparent that if the U-tube be
canted at an angle of I in 20, a 1-inch head of liquid corresponds
to 20 inches on the scale. With an inclined tube, the diameter of
the tube must be kept small in order to obtain a good meniscus for
reading. On the other hand, in any gage in which the imperfections
in the glass produce changes in capillarity, the liquid sticks at some
places. A large tube tends to reduce this source of error. The
American Blower Company recommend an inclined U-tube filled
with gasoline for use with the Pitot tube. This type involves the
simultaneous reading of the meniscus level in each leg of the tube, a
somewhat difficult feat in an unsteady current.

The German “ Krell’ manometer is filled with alcohol colored to
give a visible meniscus. One leg of the U-tube is an inclined glass
tube, and the other is a reservoir bottle whose section is some 400
times the section of the tuve. Hence, as liquid rises in the glass tube
the depression in the reservoir is unimportant. Only one meniscus
level then need be read.

An inclined tube manometer on the Krell principle was con-
structed, and an investigation made of its errors by comparing it with
a Chattock manometer known to be nearly correct. This alcohol
manometer is shown in figure 8. It is seen to include a reservoir R
mounted on a hinged plate with leveling screw. By means of the
latter, the liquid in the tube is brought to the zero of the scale at the
beginning of a test, thus making a zero correction unnecessary. The
glass tube T is likewise mounted on a brass plate pivoted at the knife
edge K, and adjusted in pitch by the screw S. To the brass plate are
attached permanently two small machinists’ spirit levels L, and L,,
set at 3 degrees and 6 degrees to the axis of the tube. The corre-
sponding pitch is roughly I in 10 and I in 20. For a low velocity

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 35

measurement (below 30 miles per hour) the screw S is turned until
the level L, shows horizontal. The tube is then inclined 3 degrees.
The instrument is thus quite independent of the leveling of the table
or bench on which it may be used. Connection between the reservoir
and glass tube is made by a short piece of rubber tube. Displace-
ment of the liquid in T is read on a scale of 600 half millimeters
attached to the frame. This manometer was made by a skilful instru-
ment maker, and great care was taken to set the spirit levels at the
correct angles. The best grade of German glass tubing was used, and
each tube was carefully cleaned with strong sulphuric acid and potas-
sium bichromate.

If there are no appreciable errors in the leveling, the correct head
of liquid (alcohol, 95 per cent, stained red with fuchsine dye) is

Te TUnwen a

Base Soord

pea gees ee eA ae!

Fic. 8—Alcohol manometer.

given from the geometrical construction. Thus: Head of liquid =
displacement in JT Xsine of inclination. A small correction can be
made for the depression of the liquid in FR as the level in T rises.
This also can be computed from the dimensions.

The density of the alcohol was taken on a chemist’s “ Westfall
Balance ” to a precision of 0.1 percent. The effect of surface tension
is to cause the level in T to be slightly higher than the level in Rk
when the two ends of the manometer are under the same pressure.
This is not an error in the instrument, since the zero setting takes
account of it.

Tests were made by connecting both the reservoir end of the
alcohol gage and one leg of the Chattock gage to the same static
pressure made by a water column. In this way errors due to fluctu-
ations of pressure were eliminated. The Chattock gage readings
were taken as a standard for reference. The same Chattock gage

36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

was used in all tests. The alcohol gage was fitted with a straight
glass tube 0.15 inch in diameter. The tube was clean and dry. The
velocity calculated from the alcohol gage was found to be 12 per cent
low. The tube was then wet by blowing the liquid to the top of the
scale and then allowing it to settle back to zero. Readings taken
subsequently were only 4 per cent low. The experiment was repeated
using a glass tube 0.17 inch in diameter, clean and wet. The velocity
recorded was 4 per cent low. A different tube, but of same diameter,
was then put in the alcohol gage. Its average readings were found
to be 10 per cent low. Examination of the glass tube showed two
minute cracks in the glass hardly to be seen with the naked eye. A
glass tube 0.2 inch in diameter was then tested and read 2 per cent
low. <A tube 0.22 inch in diameter read 1.5 per cent low. A tube
0.25 inch in diameter could not be used on the 3-degree pitch, as the
alcohol would not form a meniscus.

In all, some 1,000 check observations were made, and the following
conclusions drawn:

(1) The inclined type of liquid gage as commonly employed in
ventilation work is not an instrument of precision.

(2) For consistent results, the glass tubing used must be free from
all slight flaws on the inner surface which might cause changes in
capillarity throughout the bore.

(3) The tube must be uniform in diameter.

(4) The tube must be as large as it is possible to use and still get
« good meniscus.

(5) For alcohol at 3 degrees inclination an internal diameter of
0.22 inch is suitable.

(6) The maximum precision with such a gage used to measure
air speeds from 4 to 40 miles per hour is about 1.5 per cent on
velocity.

(7) The alcohol gage properly constructed is consistent and very
sensitive.

(8) The alcohol gage may be used as an instrument of precision
when calibrated against a standard.

In its final form with 0.22-inch tube, this alcohol gage was found
to measure speeds within 1.5 per cent. Such precision is ample for
engineering work, and this type of gage is recommended for a cheap
portable instrument. For a laboratory standard, however, an error
of 1.5 per cent cannot be accepted. Since the gage responded to
changes of velocity of less than }$ per cent, its sensitivity is such that
it may be calibrated against a better manometer, and when calibrated,
may be as precise as the standard.

NOs A WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 37

he AD USPMENYT OF VELOCITY (GRADIENT JACROSS
ASSECTION OF THE WIND TUNNEL

By H. E. ROSSELL, Asst. Nava Constructor, U. S. Navy, AND
D. W. DOUGLAS, S. B.

In any wind tunnel experiments, it is important that the velocity
of the air striking different parts of the model shall be the same.
Consequently, after developing precise methods for measuring
velocity, the cross-section of the tunnel was explored to detect vari-
ations in velocity from point to point.

The procedure was as follows: The side plate described above
(Report I, page 10) was connected to the Chattock gage. One
observer by regulating the motor field rheostat kept the velocity as
nearly constant as possible, indicated by keeping his gage reading con-
stant. A speed of about 28 miles per hour was selected as standard.
The Pitot tube (National Physical Laboratory tube) was mounted on
a standard and moved parallel to itself along vertical lines 6 inches
apart. Great care was taken to point the tube in the axis of the wind.
The Pitot tube was connected to the alcohol gage. A velocity reading
was taken every 6 inches by a second observer. The same two
observers made the entire test.

The first preliminary tests showed the velocity over the section for
a constant static pressure, as shown on the Chattock gage to be far
from uniform. The velocity near the sides was higher than near the
center. Sucha result could be caused by the honeycomb at the suction
mouth of the tunnel. The air entered the mouth in converging lines
of flow as was shown by the direction taken by fine silk threads. The
honeycomb was at the very end of the tunnel, and probably straight-
ened out this flow too soon to allow a sufficient volume of air to reach
the center:

To assist the air to flow more to the center, the honeycomb was
shoved 1 foot into the tunnel. The effect was satisfactory, but not
enough.

The honeycomb was then shoved 1 foot farther into the tunnel.
The exploration of velocity over the section showed that a fair result
had been obtained, and it was concluded that no advantage would
be gained from further movement of the honeycomb.

Since models not greater than 18 inches in span are to be used, the
useful part of the tunnel is included within a square 2 feet on a side.
The parts of curves, drawn through the experimental points, which
passed through the 2-foot square, show an average velocity of 27.8

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

miles per hour. The per cent difference between the velocity at each
point and the average velocity of 27.8 miles per hour was then calcu-
lated. The results are shown marked on the section of the tunnel in
figure 9. It is seen that the variation in velocity over the useful part
of the tunnel is from + 1.1 to — 1.2 percent. It is believed that this

TOP CF TUNNEL
oO 6 fo” 8 <4 SO", B6ul 42 sae

WEST WALL
EAST WALL

BoTTom

Fic, 9.—Variation of velocity across section of wind tunnel. Points represent
per cent above or below mean velocity in dotted square which is 27.8 miles
per hour.

variation is not too great for our purposes, and that the uniformity
of flow compares well with that to be found in other wind tunnels.
With regard to the effect of the variation in velocity across the
section, it may be stated that such a small variation in velocity is
only of importance in tests on the moment tending to turn a model
aeroplane away from or into the wind. An excess of velocity on one
wing would give a tendency of the model to show a “lee helm.”
However, if the model be reversed and the experiment repeated, the

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 39

average of the measurements taken in both tests will have eliminated
any error due to lack of symmetry in the flow.

Rotation or twist of the air in the tunnel has not been detected, and
if present must be small. The honeycomb at entrance and baffles at
exit are designed to prevent the air spinning with the propeller.

VGH AWwAC Rh Sot CURVES ]FOR WING SECTION,
RAsA 6

By H. E. ROSSELL, Asst. Navat Constructor, U. S. Navy, C. L. BRAND,
Asst. NavaL Constructor, U. S. Navy, anp D. W. DOUGLAS, S. B.

In order to furnish a final check upon the calibration of instru-
ments, the alignment of tunnel and balance and general methods of
testing, it was considered desirable to repeat the determination of the
aerodynamical constants published by the British Advisory Com-
mittee for Aeronautics, Report 1912-13, for the wing profile, desig-
nated-as R.A. F. 6.

Two models 18 inches span by 3 inches chord were cut in brass,
and carefully filed and scraped to form. The surface was highly
polished to remove tool marks.

Each model was mounted vertically in the wind tunnel and its
“lift” and “ drift” forces measured on the balance for angles of the
chord to the wind from —4 degrees to +18 degrees.

The moment of the resultant force about the vertical axis of the
balance was measured on the torsion wire. It was then possible to
lift
queens
magnitude by WLift?+Drift?, and its line of action from:
observed moment
magnitude —

determine the direction of the resultant from the ratio

= perpendicular distance from axis.

The center of pressure is usually defined arbitrarily as the inter-
section of the resultant force with the plane of the chord. This point
was calculated for each incidence.

On figure 10 are plotted the values of lift and drift coefficients,
defined by :

Wleitt pe Wriit
Eye ee Aya
where 4 is the wing area in square feet, and V the velocity of the
wind in miles per hour. Lift and drift are in pounds force, hence Ky

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

-2° ° 2° Be 60 Se lor a 12e' see SS
Fic. 10.—Wind characteristics.

Aerofoil R. A. F. 6.
Velocity 29.85 miles per hour.
Density of air 0.07608 pound per cubic foot.
[:] Nat. Phys. Lab. observations. :
— A Mass. Inst. Tech. observations, model A.
--- © Mass. Inst. Tech. observations, model B.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS AI

is the force in pounds on 1 square foot due to a wind of 1 mile per
hour, of air of standard density (i. e., .07608 pound per cubic foot).

The “center of pressure’ is also shown on figure Io in terms of
distance from leading edge in fraction of chord.

On the same sheet are shown the experimental points published by
the National Physical Laboratory for this wing, using the same size
model and the same speed, 7. ¢., 29.85 miles per hour.

It is seen that there is only slight discrepancy between the lift
observations up to an incidence of 14 degrees, the useful range in
aviation. The English points lie from 1 to 3 per cent higher than the
corresponding points for model B, and coincide with those of
model A.

Similarly for the drift observations there is very good concord-
ance up to 14 degrees.

The curve of center of pressure coefficient is in practical coinci-
dence with the English observations.

It appears that undetected differences in workmanship and finish
between two models may cause a change in coefficients of not more
than 3 per cent. Actual observations are precise within one-half of
I per cent. Consequently, our results may be considered sufficiently
precise for purposes of aeroplane design.

Viz SLABLEITY OF STEERING OF A DIRIGIBLE
By J. C. HUNSAKER

When floating in the air with no way on, a dirigible takes an atti-
tude such that the center of gravity lies on the vertical passing
through the center of buoyancy of the envelope or gas bag. The
ship is then in stable equilibrium. When under way, the thrust of
the propellers is balanced by the resistance of the air. In order that
the attitude shall not be changed, the moment of the propeller thrust
and the moment of the air resistance taken about any point must
balance one another. It is convenient to take axes of coordinates,
vertical, transverse, and horizontal, located at the center of buoyancy.
If it be assumed that the ship is in equilibrium on her course, then the
component forces along and moments about the three axes through
the center of buoyancy are each zero.

This is equivalent to the statement that the motion of the ship is
one of pure translation in the direction of the fore and aft axis of
the envelope, which axis is horizontal.

42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Any angular deviation of this axis will call into play moments
about the axes chosen above as well as forces along those axes. The
forces will cause the trajectory of the center of buoyancy to be
deflected, and the moments will swing the ship’s axis. The motion
is stable if the forces and moments tend to restore the original attitude
and state of motion.

If we consider only the moments produced by angular deviation
of the ship’s axis, we may say that the ship is stable if the moments
tend to restore the original attitude, and unstable if they tend to
magnify any initial deviation.

With a model held fixed in a current of air by a spindle passing
through the center of buoyancy, the stability of any attitude is
measured by the moments about the spindle.

An elongated ellipsoid, as can be shown by hydrodynamic theory,’
has three positions of equilibrium in a wind, corresponding to the
directions of the three axes. Only one position, however, is stable,
and the body tends to place itself broadside to the wind. For torpedo-
shaped bodies, the stable position is intermediate between the broad-
side-on position and the desired bows-on position, and for any such
body there is a stable “ drift-angle”’ at which the body tends to hold
its major axis to the wind. This angle may be between 50 and go
degrees to the wind.

A feathered arrow with weighted head is stable for a translation
along the direction of its shaft. In general, it is not practicable to
fit sufficient fin surface at the stern of a dirigible envelope to give it
such weather-cock stability, but it is possible to reduce the “ drift-
angle” to 20 degrees.

A dirigible must be steered both in a vertical and in a horizontal
plane and its stability of route requires both horizontal and vertical
fins and rudders.

A wooden model of a dirigible hull was fitted with rudders and
fins in accordance with usual practice and tested in the wind tunnel
at 35 miles per hour. The fin and rudder area was then adjusted
until a satisfactory combination was obtained. |

The principal interest in the research lies in the fact that it is gen-
erally possible to base the designed fin and rudder area upon such
experimental wind tunnel tests instead of rule of thumb.

The model was mounted in the wind on a vertical spindle passing
through the center of buoyancy as calculated from the plans. The

*Lamb, Hydrodynamics, p. 121.

43

WIND TUNNEL EXPERIMENTS IN AERODYNAMICS

4

NO.

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at aaa

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me piepurys “H ‘d ‘W C¢ oF spunod Ut S9d10\F ‘youd JO so]

RTE PE FG

sos

Ta

SIRS

*

Bue 10J sdopaaua aqISIIIp |?

ai
oe

FMS omy
a

pow uo soot0fF queyNsoy— Il “OIA

44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

moment about the vertical axis through the spindle, M@, was mea-
sured on a torsion wire with the model inclined 0, 5, 10, 15, and 25
degrees to right and left of the tunnel axis. Similarly the longitu-
dinal and lateral components of resultant wind force in the horizontal
plane were observed, 7. e., Re and Ry.

The total resultant force is then

R= hey
The direction of this force is at the angle
R
é=tans =
an R.

measured from the axis of the tunnel. The resultant force R has
an arm A, the perpendicular distance from the center of buoyancy to
the line of action of R. Thus
M
A= R°

The force FR is then determined in magnitude, direction, and line of
application, and is laid out graphically on the model drawing for each
angle of inclination.

Experiments were made with the model swung on its vertical axis
through the center of buoyancy to obtain the yawing moments, and
with the model on its transverse axis to obtain the pitching moments.

The resultant forces for angles of pitch are shown graphically on
the side elevation of the model, figure 11. It appears that with the
horizontal fins fitted, the resultant forces pass forward of the center
of buoyancy. The model is, therefore, unstable when moving in the
direction of its longitudinal axis, and if left to itself will take a
“drift angle” of about 20 degrees up or down. In practice this
pitching moment is counterbalanced by the powerful righting couple
due to the weight of the car suspended beneath the envelope.

For example: If the center of gravity of the whole ship be a dis-
tance d below the center of buoyancy, the righting couple for a pitch
of 6 degrees is

M.,=Wasin 6
where lV is the total weight.
On the other hand, the upsetting moment on the envelope due to

wind forces is a function of the inclination, as shown, and the velocity
squared, or

M.=KV’f (6)
where K is a constant.

45

AERODYNAMICS

WIND TUNNEL EXPERIMENTS IN

NO. 4

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/
H
' !
4
1 i
I
'
'

TS Ta

i"
1S
&
la
/
/ ‘
i ’
1 yh
I 1 ! ' ‘
i 1 ' 1 /
1 I 1 1 ve
' ' Y ,
I i ! ?
I It 1 1 J
1 ! ! I 1 /
ROT lais | ' 1 ! J
/ bas I! 1 ! ‘i <
/ Voifel \ I i iM wi
/ he Fe 1 1 ! ¥ 7
iy 1 ’
hi asf 1 ' i 1 s
bi 1 | ' 1 I Re
/ ia i ! i / ,
/ Ife ' I i i ih
1 | ' I | / 4
/
/ 1 i ! ! 1 z
| ' 1 I

ele

46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

For longitudinal stability, the following inequality must be satis-
fied :
M;.>M-.
Wasin 6>KV°*f(6).

For given incidence, f(@) and sin @ are constant, and hence the
righting moment due to weights is constant. The upsetting moment
of the wind increases as the square of the velocity. At some critical
velocity the upsetting moment may preponderate and the ship become
unmanageable.

This is the critical velocity first pointed out by Colonel Renard,
which led to serious difficulties in the early dirigibles.

For a given design, it is possible from wind tunnel tests to deter-
mine this critical velocity, and by suitable additions to the horizontal
fin area or lowering of the car to insure that in operation the critical
velocity can never be reached.

The tests as described above were repeated for angles of yaw. In
the first series, a single vertical fin of 5.6 square inches area was
fitted as shown in figure 11. The resultant forces are drawn on
figure 12. The model is very unstable, and tends to swing to the right
or left of its course until the axis makes an angle of about 4o degrees
to the wind. The fin area is obviously insufficient. It will be noticed
that the resultant force for 5 degrees yaw passes outside the model.
This is no doubt due to the arbitrary mechanical definition of resultant
force. The resultant force as drawn merely represents that force
which, acting along the line shown, will have the same moment about
the center of buoyancy as the complicated distribution of pressure
about the model. This experimentally observed moment might as
well be represented by a couple.’

To improve the stability of steering, a larger vertical fin and a
vertical rudder were next fitted and the test repeated. The rudder
was fixed in the plane of the fin. The resultant forces are shown on
the lower part of figure 12. It appears that the drift angle has been
reduced from 40 to 20 degrees, but that the ship is still unstable. It
is not practicable to fit more fin surface, and the remaining instability
must be met with the rudder.

The rudder was then set at 164 degrees to the keel line and the test
repeated. The resultant forces shown on figure 12 are seen to lie

* This position of the resultant force at small angles was predicted by Sir
George Greenhill, and later verified experimentally by L. Bairstow, Tech.
Report of the Advisory Committee for Aeronautics, p. 35, London, 1910-11.

NO. 4. WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 47

abaft the center of buoyancy. The ship is therefore stable. At 10
degrees angle of yaw, the resultant force passes nearly through the
center of buoyancy, and if the ship should get in this position the pilot
would have to use slightly more than 164 degrees rudder angle to
bring her back.

The conclusion from these tests is that with the size rudder and
fin fitted, 7.79 and 3.47 square inches, the ship can be held on her
course by the use of not more than 164 degrees of rudder.

The importance of an adequate vertical rudder is apparent, since
the weights give no restoring moment for yawing as they do for
pitching.

It appears impossible in practice to give sufficient vertical fin area
to hold the ship on her course without use of the helm.

VII. PITCHING AND YAWING MOMENTS ON MODEL OF
CURTISS AEROPLANE CHASSIS; AND* FUSERAGE.
COMPER TE WITTE TAIL AND RUDDER, BUT WITH-
OUT WINGS Ss TRULS, OR “PROPELLER:

By J. Cc. HUNSAKER anp D. W. DOUGLAS

A wood model of the Curtiss tractor body, complete with all
appendages except wings, was constructed to a scale 1 inch to the
foot and 24.5 inches actual length. The model was held in its ordi-
nary position in the wind tunnel by a vertical spindle attached to the
balance. The angle of yaw was varied, and observations were made
to determine the components of force directed down stream and
across the stream, as well as the twisting moment about a vertical
axis passing through the supporting spindle. The axis of the model
was kept in a horizontal plane during this test.

The model was then removed from the spindle shown in figure 13,
side elevation. A new spindle was set into the side of the model as
shown in figure 13, plan. The model was again placed in the wind
tunnel but now lay on its side. Rotation about the new spindle axis
made it possible to set the model at various angles of pitch, the angle
of yaw being held constant. Measurements were made as above of
down stream and cross stream components of force, and moment
about the axis of the spindle.

24%

ee oe
RAMA ea tt

pimeerion on Wind

.

Fic, 13—Resultant forces due to pitching and yawing of Cur

lane body. Forces on model given in pounds for 30 M. P. H.

50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The forces and moment measured in the first test are called

R,, drift component,

Ry, cross wind component,

Mz, yawing moment ;
and in the second case,

R;, drift component,

R,, lift component,

My, pitching moment.

Forces are measured directly in pounds and moments in pounds-
inches on the model for a wind velocity of 30 miles per hour. Density
of air is 0.07608 pound per cubic foot.

For any angle of pitch we may substitute for the lift, drift, and
pitching moment a resultant force vector defined as that force which
is the mechanical equivalent of these. It is to be noted that we here
deal only with forces in the plane of symmetry of the aeroplane.

Similarly in the second test, where the angle of pitch was kept
constant at 1.5 degrees, the drift, cross wind force, and yawing
moment are represented by a vector in the horizontal plane passing
through the intersection of the body axis and vertical spindle.

These two resultant force vectors may be called for convenience
pitching resultant and yawing resultant. They are shown in posi-
tion, magnitude, and direction on the two views of figure 13.

The artifice of representing a force and a moment by a vector
makes it immaterial where the axes of support of the model were
originally taken. In aeroplane design, the axis of the propeller
usually is made to pass near the center of gravity, and it is hence
necessary to locate the center of gravity at such a point that angular
deviations from normal flight attitude will produce moments about
the center of gravity tending to restore the original attitude.

The usual location of the center of gravity well forward in the
body will insure that the pitching resultants pass to the rear of the
center of gravity and that the pitching is stable. See figure 13, side
elevation, where the pitching resultants are shown graphically.

For convenience, the resultant force on the model is given on figure
14 in terms of lift and drift components marked R:z and R,. The reso-
lution of the forces is shown on the upper figure. It appears from
figure 15 that the drift R, is practically constant from +2 degrees to
—2 degrees pitch, but the lift PR, is zero only for 14 degrees pitch.
It would be of some advantage to fly the machine at full speed with
the body “ tail heavy ” 14 degrees.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS

an
4

uw +
Yawine (Torrent (about C6) = Ne (),- Yo

Nore :- Ale FoRCES ON MoDEL ARE IN POUNPS , AT _FOM-PM-_

Fic: 14:

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

on
bo

It is also possible to resolve the force R into components X along
the axis of the machine and Z perpendicular thereto. Since a force
may be resolved at any point in its line, we choose the intersection of
the line of action with AB. This point is a center of pressure and is
a distance “1,” from the nose of the machine. See upper figure of
figure 14. A force is completely defined by X, Z, and J,, and these
quantities are given in the upper table. The component X has no
moment about the center of gravity if the center of gravity be on
line AB, and if the center of gravity be a distance y from the nose, the
pitching moment is (/,—y)Z. Upward forces are plus. In general,
for a center of gravity with coordinates +, y as shown on figure 14,
the pitching moment is:

X,—Z(l,—-y).
By use of figure 14 and this formula, a curve of pitching moments
can be readily obtained for any assumed position of the center of
gravity.

In a similar manner the model was held at a pitch angle of 14
degrees to the horizontal wind, and placed at angles of yaw from
15 degrees right to 15 degrees left. Observations right and left have
been averaged. The resultant forces are shown in direction, magni-
tude, and application in the lower figure of figure 13. The cross wind
and drift components A, and F, are tabulated on figure 14.

As above, the components along the axis of the body X, and at
right angles Y, are also tabulated. The intersection of the line of the
resultant force with the vertical plane of symmetry is taken as a
center of pressure and is a distance /, from the nose of the body.
The yawing moment about the center of gravity placed a distance y
from the nose is hence

Y(1l,—y).

It is apparent from the last test that the aeroplane is directionally
unstable, unless the center of gravity be well forward of the forward
passenger’s seat. The addition of a propeller and the fin effect of
biplane struts will augment this tendency to instability of steering,
and require a still farther forward position of the center of gravity.

Forces are given in pounds on the model for a wind speed of 30
miles. If the model is toa scale of 1 inch to the foot, the forces on the
full-size body will be 144 times. as great and at 60 miles four times
greater. Thus the resistance of this body at 60 miles would be about

0.137 X 144 X 4=79 pounds,
on the assumption that the resistance varies as the square of the

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 53

speed. The true resistance would be less than this on account of the
exponent of Y being somewhat less than two. On the other hand, in

me omen Gon om Gon = At i= 2 Oo = to-) ASG l Smell ec a:
PiITCHING ANGLES

Bies 15:

a tractor type aeroplane, the body resistance may be considerably
augmented by the slip stream from the propeller. The assumption
of the “ square law ” is usual in design.

MISCELLANEOUS COLLECTIONS VOL. 62

SMITHSONIAN

15°

SS eee ae ee
eee

To show the precision of the experimental work, curves of R,, Ry,
and R,, plotted on pitch and yaw are given on figures 15 and 16. The

ANGLE OF Yaw

Fic. 16.

individual observ

ations are there shown by the small circles which

appear to permit a fair curve to be passed through them.

cn

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 5

Vit. SWEPT BACK WINGS]

By H. E. ROSSELL anp C. L. BRAND, Asst. NavaL CONSTRUCTORS,
U. S. Navy

Part I.—Lirt, Drirt, AND CENTER OF PRESSURE

To determine the effect on the aerodynamical properties of a wing
of sweeping back the wing tips, as in the so-called German “ Pfeil”
aeroplanes, a series of tests was made on the model described as
R. A. F. 6. The right and left halves of the wing were swept back
10, 20, and 30 degrees to the normal position as shown in figure 17.

The first part of the investigation deals with the variation in lft and
resistance coefficients, and the movement of the center of pressure
for the different models as the angle of incidence changes. The wind
velocity of 29.85 miles per hour of standard air * remains in the plane
of symmetry of the wing.

The curves of the above characteristics for the four wings are
given in figures 18, 19, 20.

The ratios of lift to resistance coefficients are given in figure 21.

* Abstract from a research submitted for the degree of Master of Science
in the Department of Naval Architecture, at the Massachusetts Institute of
Technology.

* Standard air is of density 0.07608 pound per cubic foot.

Drift Ke=AV*

56 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The following key will serve to identify the wings:

Wing Swept Back
Tee a ortexors sels eae Cae eOndeStees
TAD eva rovarcase eels Serra ae 10 degrees
eRe ae arte sa hee ecOrdergirees
Tie ee hee cee eo eee OVC STEES

.0006

0005

0004

0003

,0002

°
°
2

° oe ae i eae

Soe E 16° a APG eee Ope el a Ouro oe
Angle of Incidence Fic. 18.

Coefficients are given as pounds force per square foot per mile per
hour velocity.

It appears that a sweep back of 10 degrees and 20 degrees is of no
disadvantage from considerations of lift and resistance. There is,
however, no gain. For a sweep back of 30 degrees, the lift coeffi-
cient is diminished and the ratio of lift to resistance is seriously
reduced. What advantages there may be as regards lateral sta-

TAG
ee
ey
ee |

58 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

bility for wings swept back 30 degrees are therefore paid for by a

: : : sg os
considerable loss in effectiveness. The ratio K- of 16.5 for the
#8

normal wing and for No. II is reduced to 12.9 for No. IV.
The center of pressure motion is shown by the curves of figure 20,
in which it appears that the motion is similar for all the wings tested.

y be
E
BS
HE
a
ae
ee
By
a
ae
naa

:
D

i

io

Fr O|F POINT A

BR LONGITUDINAL S
ING

FP
' ; OF z

ISTA
N >

C.

POOP

CE OF

on
anv
=i
CJ
mo
we
x

OVEMENT ?f CENTER i
VELOCITY WIND- 29 F R
p° 4° 6 g° 2 CS aa

Fic. 20.

The center of pressure motion gives rise to the same degree of longi-
tudinal instability. The center of pressure is referred to the forward
point of the middle longitudinal section of each wing, and it appears
that for a given angle of incidence the center of pressure is thrown to
the rear by about two-tenths of the chord for a sweep back of 10
degrees, and four-tenths of the chord for a sweep back of 20 degrees.
The center of gravity of an aeroplane will, therefore, have to be
placed farther to the rear if swept back wings are used.

60 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Part Ii.—ROLLING, PITCHING, AND YAWING MoMENTS

The object of this test is to determine the effect on stability of
sweeping the wing back to various angles, as described in Part I of
this report.

The wing uncut was first mounted horizontally on the balance, and
forces and moments as enumerated below were measured for angles

42

IN
SS
NS
Wind SS z
DIRECTION ~S
NN

F1e: 22;

of yaw of 0, 5, 10, 15, 20, 25, and 30 degrees in both directions for
each of the following angles of incidence: 0, 3, 6, and 9 degrees. The
velocity of wind was kept constant at 29.85 miles per hour. The same
measurements were made with wing models swept back to 10, 20, and
30 degrees. The method of manipulating the balance to make these
measurements is given in detail in Report 68, Technical Report of the
Advisory Committee on Aeronautics, 1912-13 (London).

NO: 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 61

It is convenient to calculate the forces and moments about moving
axes fixed relative to the wing. The axes are lettered OX, OY, and
OZ. In figures 22 and 23, point O we have located at the middle of
the leading edge of each wing. OX is the fore and aft, OY the trans-
verse, and OZ the normal axis of the wing. When the wing has zero
incidence and yaw, the position of the axes is shown in figure 22 by

Zz

y'
Fic. 23.

OX,, OY,, and OZ,. Now suppose the wing to be turned about
OZ, through a positive angle of yaw y. Then the axes will be in the
position, OX;, OY, and OZ,. Now if the wing is given an angle of
incidence of 6 about OY, the axes will swing into the positions OX,
OV OZ:

In making the calculations it is easier first to refer the forces and
moments to a set of axes parallel to OX, OY, and OZ, which we have

62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

designated as O’X’, O'Y’, and O’Z’. The origin of these axes is
coincident with the origin of axes about which rolling and pitching
moments were measured.

Forces along axes OX, OY, OZ are called AX, AY, AZ, A being
the area of model in square feet ; and moments about these axes are
called L, M, and N. Forces along and moments about axes O’X’,
O'Y’, and O’Z’ are represented in the same way, 1. e., AX’, AY’, etc.

The notation used for the measured forces and moments is as
follows:

(1) Force along O’Z,’=V,. Measured on vertical force lever.
(2) Moment about O'7,’=M,. Measured on torsion wire.
(3) Moment about O’Y’ =Vp. Measured on vertical force lever.
(4) Moment about O’X,’=V,. Measured on vertical force lever.
(5) Moment about an

axissparalielito Ov

and distant /below it =M,. Measured on drift beam.
(6) Moment about an

axis parallel to O’X,’

and distant /below it =M-. Measured on cross wind beam.

The forces and moments desired can then be calculated by the fol-

lowing equations :*

L'=V pcos 6—M, sin 6.

M = >:

N’=V pz sin 6+M, cos 6.

AK. cin OCs Cosca =~ cinta) a

Mire Vp—Mc cos 6—Mp sind
= ni

AZ =V; cos 6+ (Mp cos ¢—Me¢ sin ¢—Vp) ae
=e CAve
M =M’'—cX+aAZ.
N =N’—aAY.
Where a and ¢ are the X and Z coordinates of the origin O taken
froniaxes Oe 101) eand. O42
Figures 24 to 31 show the forces X, Y, Z, and moments L, M, N
plotted on angles of yaw as abscissz for constant angles of incidence
of 0, 3,6, and 9 degrees. At any incidence the chord of the wing at its

*Technical Report of the Advisory Committee for Aeronautics, London.
1912-13. Report No. 75.

NOTA: WIND TUNNEL EXPERIMENTS IN AERODYNAMICS OR

ELOCITY |OF

ANGLIE OF INC

ING| SWE BACK Il0°
ING) SWE BACK 20°

64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

center coincides with the OX axis. In figure 32, X, Z, and M are
plotted with angles of incidence as abscissze and with o degrees yaw.
The notation used is as follows:
Subscript 1—wing straight.
Subscript 2—wing swept back Io degrees.
Subscript 3—wing swept back 20 degrees.
Subscript 4—wing swept back 30 degrees.

Fig, 25.

For the application of the theory of the dynamical stability of aero-
planes, reference should be made to the excellent papers by Mr. L.
Bairstow.’

It is shown that for longitudinal stability the rate of change of the
quantities X, Z, and M with angle of incidence determines the
so-called resistance derivatives. It appears from the observations
made on swept back wings that there is no appreciable change in the
slope of curves of X, Z, and M plotted on angle of incidence for the

*Technical Report of the Advisory Committee for Aeronautics, London,
1912-13. Report No. 79.

x

NO 4: WIND TUNNEL EXPERIMEN'TS IN AERODYNAMICS 65

different wings. Figure 32 shows some difference in form for curves
M plotted on angle of incidence. It must be borne in mind, how-
ever, that the origin of these curves is at a greater distance from the
center of pressure the farther the wing is swept back. A better idea
of the variation in pitching moment with change in incidence can be
obtained by plotting the curves with the estimated center of gravity

Pelee

Fic. 26.

of the machine as the origin. Figure 20, Part I of this report, shows
the movements of the centers of pressure to be similar for all wings.
The conclusion is that sweeping back wings has no effect on the cor-
responding derivatives of XY, Z, and MV, and consequently no effect
on longitudinal stability. It is of course to be expected that swept
back wings may slightly increase the radius of gyration for pitching
and so affect the motion indirectly. Aerodynamically, however, no
advantage is to be expected.

o

66 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

For lateral stability the derivatives affected by the wings are the
rate of change of Y, L, and N with angle of yaw. From consider-
ations of symmetry, Y, L, and N are not affected by angles of roll.

MOMIENTS JON eee Bea ae A
Src eee pate

| a

EECA

—_—

Fic. 27.

NTS G POUNDS
4 \ :
S O Cp h 4

The curves of lateral force Y give evidence of difficulties in experi-
mentation. The force Y on the model was in the neighborhood
of 0.004 pound. It does not appear that there is any consistent

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 67

change in Y due to sweep back which can be brought out. In
any case the force Y is so small that small changes would be of no
interest.

eS

J
| A
= oe

LBS

HHI

cH

a ye ea eee ae

een ia See eee

eee - pes
at > >
estes)

zm

PT

Fic. 28.

The curves of yawing moment N with angle of yaw show an
extremely small moment, which was obviously impossible to measure
with sufficient precision to detect changes between the various wings.

68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Indeed, as in the case of lateral force Y, the effect of changes in V
produced by the wing is of no account.

On the other hand, L, the rolling moment produced as the wing is
yawed out of its course, is large and of the greatest importance, as it

ie

~
alee

i
i
te

ie See

m™

oO

mT
P, x

>
a

jaa ea
eis ae

o>
“2 [\\

a
ie aa Fa a

<

Ze

ena
OMENTS ON WIN
ANGLE OF INCIDENCE

Fic. 29.

ale a ee

oe |

interconnects directional and lateral stability. For a normal wing
flying at any reasonable incidence a deviation from the course causes
a small rolling moment tending to bank the machine in a manner
appropriate to making the turn. The couple may be called a “ natural

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 69

banking” moment. This “natural banking’’ moment is increased
nearly 100 per cent if the wing has a sweep back of but to degrees.
The moment for a sweep back of 20 degrees is still greater.

ee
SSP
er

! L

| aaa ee
tr
a
/ /
el
oar
A
ened
Alea
Aa
ile Naalies ene

HL

S

ORCES ON WING
oc ee WIND

MAL Pr

S ees BACK 20°
We SWEPT | BACK 30°

FORCES IX A oD LBs PER 5Q.F

oe
Fic. 30.
In view of the structural difficulties in making strongly swept back
wings, and the loss of effectiveness as carrying surface for a sweep

of more than 20 degrees, one would conclude that if any sweep back
be used, about 10 or 15 degrees is sufficient.

U
—

MOMENTS L AND N—-JIN. LBS

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

yal

WIND TUNNEL EXPERIMENTS IN AERODYNAMICS

4

NO:

eet is see
NSC eT
BeNOGESEe eee Se see
Eee eg tb te gd

Fic. 32.

CCA
Ae

72 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. .62

The banking moment is appreciable on the aeroplane, as may be
shown by the following calculation :

Incidence 6 degrees, yaw 15 degrees, sweep 10 degrees, moment
L, on model .18 pound-inch at 29.85 M. P. H., moment on biplane of
400 square foot area L, at 60 M. P. H.

0.18), —s ie ( 60 _
12 364 29.85

The greatest value of swept back wings is to be found on a side
slip. If by any accidental cause an aeroplane with swept back wings
is heeled over, it begins to side slip toward the low side. The appa-
rent wind is no longer from dead ahead, but is a little to one side as
compounded from the velocity of side slip and velocity of advance.
The effect is the same as if the machine had yawed from its course,
and with swept back wings the “ natural banking ’”’ moment becomes
a much greater righting moment than with straight wings. The
machine then has a degree of lateral stability.

For lateral stability, swept back wings can be made to give a
righting couple without introducing a lateral force or yawing couple.
The absence of a yawing couple and lateral force is of advantage if
the machine is to be kept on its course as it rolls.

Naturally, it is purely a matter of judgment whether too large a
righting couple is disadvantageous. Ina gusty wind, a machine with
swept back wings will tend to roll as side gusts strike it. This may
be uncomfortable for the pilot, but if his aileron control be power-
ful, he can always overcome the rolling moment due to the wings.
Approaching a landing, this is especially necessary. In the air, it
would be both unnecessary and fatiguing for him to fight the natural
rolling of his machine.

i = 1,560 pound-feet.

3)

A “natural banking” moment can be obtained by the use of a
vertical fin above the center of gravity, or by giving the wings an
upward dihedral angle. The equivalence of these methods has not
yet been determined.

These tests bring out simply the fact that with a sweep back of
10 degrees an appreciable righting moment may be expected without
change in any of the other aerodynamical properties of the straight
wing.

No reference is made here to the “ rotary derivatives ” or changes
in forces and moments produced by angular velocity. The damp-

NI
Hn

NO; 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS

ing effect of wings on such oscillations can hardly be appreciably
affected by sweep back, and accordingly this question has not been

investigated.

TRACTOR BIPLANE

LV.G.
AG.G,

ARROW Bi PLANE

AGO
ALBATROSS

ARROW BIPiAnNe

L.-.S
ROLAND
UNION

ARROW BIPLANE
D.F. w-

BiPLANE
AVIATIK

ARROW TAUBE
MONOPLAWE
HARLAN

BIPLANE
DUNNE

irees:

.—Recent aeroplanes.

os)
Ww

Figure 33 shows some types of aeroplanes used in Germany at the
present time, and also the English Dunne machine. Both the
German machines and the Dunne are reported to be laterally stable
in normal flight.

7A SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

IX. EXPERIMENTS ON A DIHEDRAL ANGLE WING
By J. C. HUNSAKER anp D. W. DOUGLAS

Following up experiments by Rossell and Brand showing the effect
on the lateral stability of sweeping back the wings of an aeroplane,
additional tests have now been made to determine whether the
righting moment given by the above procedure cannot be better
obtained by another method. To this end, a brass model 18 inches by
3 inches having curvature, known as R. A. F. 6," was made identical
in every way with the straight wing tested by Rossell and Brand,
except that each half of the wing was inclined upwards and outwards
24 degrees from the horizontal. This gave a dihedral angle upward
of 175 degrees. The use of this amount of angle has come into
general practice in aeroplane design.

The wing was mounted horizontally on the balance and forces
and moments were measured for angles of yaw of 0, 5, 10, 15, 20, 25,
and 30 degrees to right and left and at angles of incidence of 2, 4, 6,
and g degrees. The velocity of the wind was kept constant at
30 M. P. H. standard air. The method of manipulating the balance
to make the necessary measurements is described fully in Report 68,
Technical Report of the Advisory Committee for Aeronautics, 1912-
13 (London). The calculations, from the measured forces and
moments, to obtain the final results, were made as is outlined in the
preceding report on Swept Back Wings, by Rossell and Brand
(page 61).

The axes along and about which the calculated forces and moments
act are as follows:

OX—longitudinal axis coincident with chord at middle section.

O Y—transverse axis of wing, perpendicular to OX.

OZ—normal axis of wing, perpendicular to OX and OY.

The origin O is the intersection of the axis OX with the leading
edge of the wing.

The forces are:

X—acting along OX, positive when in direction of wind.

Y—acting along OY, positive when tending to increase side

slipping to left.

Z—acting along OZ, positive when acting upwards.

The moments are:

L—acting about OX, rolling moment, positive when wing tends to

take proper bank for turn to right.

*Technical Report of the Advisory Committee for Aeronautics, London,
1912-13.

NOVA WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 75

M—acting about OY, pitching moment, positive when wing tends
to stall.

N—acting about OZ, yawing moment, positive when wing tends
to turn to right away from wind.

REC
a,

ey
ee
=

EE
PPE
Paes

Pee Slee

es

Sele
eee

i

iy alae ave
F
Pie

=a
a ou
eee ea ee ae
08
JS eS Sass ae
: Bee One
Be ee | ia
Reese i eae
(el ia nn Ss Gass Bee SS SS Sal
eas ee eee
Beret ee ee
) EI LO a 3

es

Fic. 34.
(Subscripts designate angle of incidence.)

In figure 34 we can see the changes of the forces X, Y, and Z with
yaw and incidence. It will be noted that Y is plotted to a scale of
ordinates ten times greater than X and Z. This force, although
negative and hence acting to resist a side slip, is so small in magni-

76 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

tude that it is negligible. Z falls in magnitude with increase of yaw
angle as is to be expected, and as was the case with the swept back
wings.

Figure 35 shows the moments on the wing. WN, the yawing
moment, is very small and does not change appreciably with the
incidence of the wing.

M, the pitching moment, shows at the smaller angles of incidence
a tendency for the machine to stall in side slipping. At the larger

NO 4: WIND TUNNEL EXPERIMENTS IN AERODYNAMICS wy,

angle of incidence of 9 degrees, however, this stalling tendency dis-
appears. This is a good feature, as it shows that the wing should
not get into a bad stalling position when side slipping. The dihedral
angle seems in this respect superior to the swept back wing, which
has a stalling tendency at all incidences.

The curves for rolling moments, L, show for all incidences a roll-
ing moment which increases rapidly with angle of yaw and with the
incidence. This moment is a natural banking moment, and hence is
one which is favorable for lateral stability. Comparing the rolling
moments curve at 6 degrees incidence, for a normal wing, with the
dihedral curve, it is seen that the magnitude is from two to three times
greater in the case of the dihedral. Comparing this same dihedral
rolling moment curve with those for the swept back wings (fig.
29), it is seen that the dihedral gives a rolling moment of magnitude
about equal to that obtained with 20 degrees swept back wings,
except at a large angle of yaw.

As it is much more difficult structurally to build a 20-degree swept
back wing than a dihedral, and as the latter is as effective, it seems
that the dihedral is of more value for purposes of lateral stability.

It is of interest to note in this connection that Professor Langley’s
“aerodrome” of 1902, as well as his previous power-driven models,
were given dihedral angle wings inclined upwards by about 6 degrees.

CRiLiGAt SPEEDS FOR BEAT DISKS: INSTA
NORMAL WIND

By J.C. HUNSAKER

1. PREFATORY Note on NorMAtL FLow Past A CirRcULAR DISK
By E. B. WILSON, Proressor oF MATHEMATICS, MASSACHUSETTS INSTITUTE
oF TECHNOLOGY

Theoretical hydrodynamics cannot yet give a very satisfactory
quantitative account of Mr. Hunsaker’s experiments to which this
note is attached. The classical theory treats two cases which are
qualitatively somewhat like nature: First, symmetric continuous
flow ; second, asymmetric discontinuous flow. In both cases the flow
is irrotational and the fluid incompressible. In the first case, owing
to the symmetry of the lines of force, there is theoretically no result-
ant pressure to urge the disk down stream. Such a condition may
possibly approximate to nature in cases of slow flow under high
pressures. In the second case, as the method of solution depends on

78 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

the theory of a complex variable, the problems treated are those of
two dimensional flows, and here the whole fluid is divided by a sur-
face of discontinuity (for velocity) into a moving and a stationary
portion with the stream lines in the moving portion diverging instead
of closing in behind the obstructing object. This state of affairs may
be found in nature to a certain approximation in the case of jets. It
is clear that the theory of the continuous solution is entirely inapplic-
able in the discussion of the pressure exerted on the disk by the fluid,
and that for that problem the discontinuous solution would be neces-
sary. And it is equally clear that for a discussion of the possibility
of a critical velocity the discontinuous solution is disadvantageous,
and the continuous solution must in the present state of our knowl-
edge be used for what information it may afford.

We shall henceforth assume that the fluid is incompressible, that
the motion is irrotational, symmetric fore and aft of the disk, and
identical in all planes through the axis of the disk; that the eddies
which are known to form are to be disregarded ; and that the viscosity
may be neglected. We know that the ordinary continuous symmetric
solution must break down at least as soon as cavitation appears, and
we may with reasonable safety assume that the velocity w=U of the
stream sufficient to induce incipient cavitation at the edges of the
disk will be an upper limit for the critical velocity found by Mr.
Hunsaker. (There is unfortunately no assurance that the upper
limit may not seriously exceed that critical velocity.) Now if the
disk has a perfectly sharp edge, cavitation will take place for any
velocity of the general stream, no matter how small that velocity
may be. To get any result of value we must therefore replace the
disk by a body of rounded contour, such as an ellipsoid of revolution.
The theoretical problem which we shall solve is therefore this: To
find the velocity U at which cavitation begins in the case of an
extremely flat ellipsoid of revolution whose axis coincides with the
general course of the stream; and for this we shall determine a very
simple approximate expression in terms of the axes of the ellipsoid.
For an ellipsoid 6 inches by 1/16 of an inch we shall find U=22
foot-seconds, or thereabouts, and this result will be discussed in the
light of the experiments.

As the motion is irrotational, by assumption, there is a velocity
potential ¢, and as the density is assumed constant, the velocity
potential satisfies Laplace’s equation,

O°*d 4 Oh a

Op
Ox?" Gy?" G22 ~°

NO. 4 ‘ WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 79

We have to find a solution of this equation which is the same at all
points of circles about the axis of rotation (owing to the assumed
rotational symmetry), which reduces to ux at all points at great
distances from the ellipsoid (the axis of + being taken along the axis
of revolution and u being the general velocity of the stream), and

which satisfies the condition that the normal derivative a vanishes

at each point of the ellipsoid (as the flow must be tangential to the
ellipsoid).
We first introduce cylindrical coordinates with the axis of revolu-
tion as axis. Then
V—="COS. 0, 2—7/ SIN 0;
and
a o? 10 EPO?
= a ant ar ar eae as a
As we are interested only in solutions which do not depend on 6,
Laplace’s equation reduces to
Ge a? 10
at at q 5 oa (t)
We next replace # and r, the rectangular coordinates in a plane
through the axis, by a system of coordinates ({, ») derived from the
system of ellipses and hyperbolas in the xr-plane confocal with the
ellipse in which that plane cuts the ellipsoid” If c be the distance
from focus to center, we write
Hache, r=cVI-wVC +I. (2)
The elimination of » and ¢ respectively gives
x 2 x? 4?
ep ae eC) ae
A small value of ¢ gives a narrow ellipse ; a large value, a large ellipse.
The set of ellipses may therefore be represented by values of ¢ from
oto co. A small value of » gives a sharp hyperbola nearly coincident
with +=o0, a value of » equal to 1 gives the line r=o, the axis of
revolution. By assigning different signs to » and to one of the
radicals in (2) we may represent all points (x, r) of the plane; but
the symmetry of the figure is such that we may work only in the

+ = and

This system of coordinates is that used by Lamb, Hydrodynamics, 2d ed.
(1895), p. 150, for treating the motion of an ellipsoid of revolution in a fluid
at rest at infinity. We could use Lamb’s analysis and make a correction to
bring the ellipsoid to rest in a moving fluid. It seems as easy to solve our
problem independently with all the simplifications it admits.

8o SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

quadrant in which x and r are positive, and hence deal only with
positive values of » and the radicals.
In terms of the coordinates (£, w) equation (1) becomes

0 2 Of oO Snr s¢|= (

sp Nae |g are (4)
as a straightforward change of variable will show.’ We follow the
usual method of integration and try for particular solutions of the
form

$=Z(f)M(n),

a product of a function of ¢ by a function of w. Then (4) becomes
rd , dZ rg eee VE
Z dt i poker Mt au jc pe) a
Here the variables are separated and the equation could not hold
identically unless the two parts were equal and opposite constants.
If we set

d >», dM * ae

ay | tw i, | tun t)M=o, (5)

Oye, a RS

a KG ea) a n(n+1)Z=0, (6)
we see that the first is Legendre’s equation and the second a slight
modification of it. For n=0, 1, 2,...., the polynomial solutions of
(5) are respectively constant multiples of 1, uw, 3u7—1, ....; and of

(G), BiG Bea, eae

A consideration of (2), or of the figure made up of the confocal
ellipses and hyperbolas, shows that for large values of €, 7. e., in the
distant portions of the plane, cC=p and 6=cos p are approximately
polar coordinates with the 7-axis as polar axis. Then in these regions
we have approximately

Op _ Ob _

= —sin 6 -

Pr) One (tangential velocity along p=const.).

*It is easier to transform (4) into (1), and still easier to express directly
in terms of € and uw the condition of continuity; for if dse and dsn are ele-

ments of arc along the ellipses and hyperbolas, the velocities are — =e
e
and — O¢ | and the flux is 3
7 a Sn fene
Of, O¢ = ( p \=
Sal? Se )+ Sul” Og )=°

which is readily expressed in terms of €, u.
*See, for example, Wilson’s Advanced Calculus, Chapter XX.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 81

By the hypothesis this velocity is —u sin 6, where u is the velocity of
the stream. Hence, when ¢ is large, we must have for all values of
pf approximately
O¢ _ Z dM
Clon co du ~
It follows that 17 cannot be of higher order than 1, and the only possi-
bilities for mare o and 1. The solution for ¢ must therefore be of the

form

o=Z,+HZ,, (8)
where Z, and Z, are solutions of (6) for m=o and 1 respectively.
Moreover, for the radial velocity in distant regions we have

= —u, independent of up. (7)

SC A Cee =
Malia Le Tee =u cos 6= up. (9)
We have next to express the condition that flow along the ellipsoid
dd

shall be tangential, 2. e., that the normal derivative ae shall vanish.
C

The normals to the elliptical section of the ellipsoid are the hyper-
bolas along which p» is constant. The normal dv is
|v? +O?
= 1g
au doo N aires
The particular ellipse which is the profile of the disk is determined
by some value ¢, of €. Then

an Vax +dr=c(u + (1—p?)

dd [f?+1 (Fe dZ zu
ease O.
dn TN WG? dé ye Tae he
As this equation holds for every p, we have
a) eh (=) =
acs == Oe =O! IO
( dé / ¢-% df} ¢-t el

The equations (7), (9), (10) should suffice to determine what
values of Z, and Z, are needed in (8) to represent the flow.

The general solution of (6) for =o may be obtained at once by
integration,

Zea C, tang. CRIs)

The general solution for »=1 may be obtained from the above-
mentioned particular solution ¢ by the substitution Z=Z’¢, which
gives

Zo NG (€tan?¢€+1)+K.€. (12)
From (10), (11), (12) we find:
Cs = a -1 | oe an =<
f2-41 =0, aS (tan me 241) +K,=0:

82 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Hence C,=0, and the ratio K,:K, is determined. From (7) and
(9) we have the approximate equations

K, (tan +1) + Kg == (tan ote A) +K,=—cu.

ce +i
Hence K, =~ +K,—=—cu and
Ke eee WO a ROUT ENC BAL (tan f+, $0) ‘
cots! f— _ $0 i. cot-2£, —— 29 — C,2+1
eee Eee

As the solution for Z, reduces to a constant by C,=0, the value of
¢ may be taken as merely »Z, in (8) ; or

ob Ee ae | -< tan? ¢€—1+¢ (tan ed |.

Cu |

aed
Gano

We are dealing only with very small ellipsoids and hence , is
small. Hence ¢ reduces approximately to

oa a [—ftan+ £—1+ 2€,€].

2

The velocity along the ellipse €=¢, may be obtained like the normal
velocity. The element of arc ds is

S/F pal Ape per Gos *+1) Cet pe
ds=V dx? =dr =e ee? aa Ie dy" du= ca] a dp,

_ 1 au | ae
oe Nee aL].

The value of this eae is greatest when p=0, 1. e., at the ends of

the ellipse, as was to be expected; and its value is then ae The
So

value of £, may be expressed in terms of the axes of the ellipse.
From (3),

=v Cli b=ce:

Indeed the value is €,= B = : approximately. Hence the velocity is
approximately
Maximum velocity = 7" @ .
i a b

By Bernoulli’s principle for a stream line or Kelvin’s theorem on
irrotational motion we have

Pp + : == CONS bt.
p 2

NOTA: WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 83

When cavitation begins, p=0, v=2a e The value of 2 + a
7 p 2
at large distances from the disk may be taken as Po , where f, is the
p

atmospheric pressure in pounds per square foot. Hence we find

Loe 1 4a?U? U= a Po (1)

p 2 mb? ’ a 2p

As numerical data we may take p,=(22X12)’, p=.08. Then
U=2100 i foot-seconds. (14)

In the case of an ellipsoid 6 inches by 1/16 inch, the velocity U is
about 22 foot-seconds. For smaller disks of the same minor axis the
velocity U should be larger in inverse ratio to the size of the major
axis.

The upper limit of 22 foot-seconds here found for the critical
velocity is not surprisingly above the actual range of 10 to 20 foot-
seconds found by Mr. Hunsaker. But a noteworthy result shown on
his diagrams is that the critical velocity does not vary proportionately
to the reciprocal of the diameter of the disk—it is practically con-
stant—and had we taken to test the theory his smallest disk, we should
have had an upper limit decidedly above the experimental value. This
lack of accord between his experiments and the present theory can
hardly be regarded as surprising. His disks were all equally sharp
upon the edge, and all considerably sharper than an ellipsoid of the
same length and breadth, particularly in the smaller disks. Once the
edge is sharp enough to start cavitation at a given velocity of the gen-
eral stream, the motion becomes such that we can no longer expect our
theory to hold, and it is entirely possible that the thickness of the disk
is unimportant above a certain value. The effect of a 6-inch disk
1/16 of an inch thick may not differ appreciably from that of one
1/32 of an inch thick. The effects of the changing density of
the air and of viscosity might also, and probably would, be of some
importance. On the whole we may consider the correlation of
experiment and theory as fairly satisfactory; at least it is good
enough to indicate strongly the existence of a critical velocity for
these disks at reasonably small velocities of the stream.

84 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

2. CRITICAL SPEEDS FOR FLAT DisKs IN A NorMAL WIND

The value of tests on the resistance of small models in a wind tun-
nel depends upon the precision with which such results may be
applied to larger models at different speeds. The resistance of thin
disks normal to the wind is not of great practical interest in aero-
nautics, but certain theoretical conclusions of general importance.
may be drawn from experiments with disks.

The resistance of the air depends upon the density, viscosity, and
compressibility of the fluid. Except in gunnery, the velocities in
common use do not approach the velocity of sound in air, and hence
compressibility is neglected. :

Two well-defined types of flow are recognized. The first is the
so-called stream line flow in which the fluid flows around the body
in steady lines, closing in behind it $0 that no turbulent wake
is formed. Such flow may be expected about a fish-shaped body at
low speeds. The second form is called the discontinuous or turbulent
flow, in which eddies are formed on the body and are carried down
stream as a turbulent wake. Such flow may be expected about bodies
of abrupt form moving at high speeds.

If no eddies are formed, the resistance to motion is a viscous drag
depending on the viscosity of the fluid, a linear dimension, and the
velocity.

With the formation of eddies, additional resistance is caused by
the energy lost in imparting kinetic energy to the fluid in the eddies.
It is observed that, in general, eddies are left behind and so represent
a loss of energy. The eddy making resistance should depend on the
kinetic energy imparted to the fluid and hence should vary as the
density, the square of the velocity, and the extent of the disturbance.
The latter should be proportional to the square of a linear dimension
of the body, or the cross-section of the wake.

In any real case both viscous and eddy resistance are present. For
bodies of easy shape, the turbulence is not great and we should expect
viscosity to play an important part, and the resistance to vary less
rapidly than V?.

However, for a thin disk with its face normal to the wind we
should expect eddy making to be violent and the resistance to vary
with the density of the air, area of face of disk, and square of velocity.
Under such conditions the viscous drag might be negligible.

At very low speeds, if it be possible for the fluid to turn the corner
and close in behind the disk, eddy making may be so much reduced

NOS 4, WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 85

that the viscous drag is important. An entirely different form of
flow may then exist, and the resistance should no longer vary as the
square of the velocity. The change from turbulence to steady flow
should be marked by a critical velocity. The resistance of disks, aero-

Pear Na |
= 3 P
mae ———

oT [esate ae crete
Osa 2 : [een p 5! pise

° q 2. © m “|
a. o ° : p 3 o- 4’ pdisc
2002 + T
lo _2)0 _3\0 4/0 5/0 e 7\0 So go ido 120 130 140 1§0 160 |7o pe igo
CALE| FO VD\, D2) DIAMETER | IN INCHES, V= VELOCITY IN MILE JHOUR
ASL. + Tr iain oe +
fe}
°
O00
°o 6 i
° oh4 i
Mn doe Og 6 - C 6 2 3'\Dise
000\25° 2, Ss @oP a 3 } 4 } IL
° @
° RESIBTANCE COEFFICIENT
000/29 JFOR ial oo aha SHOw
RIT(CAL | RATIO OF VD
K ees ES sl K| Bo, jal
©) R=| PounDs -FORCE
P-=| DEN$SITY-|LBS. FER CUFT.
mo SSS = =SQst
G Z V:| VELGCITY IN MILES /HouR
00025, a P EEE eed oa [eee
of
io
00020 He
Fic. 36.

plane wings, and all sharp-edged objects is usually represented by a
formula as follows:
R= KipAy 2;

where

R is resistance in pounds,

p is density in pounds per cubic foot,

A is area in square inches,

V is velocity in miles per hour,

K a coefficient assumed constant.

86 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

To verify this law of resistance, it was decided to test in the wind
tunnel a series of thin disks placed normal to the wind. Disks of
sheet brass 1/16 inch thick with square edges and diameter 2, 3, 4, 5,
and 6 inches were used. The resistance of each disk was measured
for a series of speeds. The measurements were repeated with the
face of each disk reversed and the results averaged.

If resistance be correctly represented by the formula above, the
constant K computed from the observed resistances should remain
constant. In figure 36 the values of K computed from each observa-
tion are plotted on the product VD as abscissz, when D is the diam-
eter in inches. It appears that K does not remain constant even for
a given disk. The points represent actual observations, and it is seen

20 30 40 50 60 Jo 80 9o joo jlo 120 +130 /4o 150 /60 S70 (80 190

Fic. 37.Resistance coefficient as a function of VD.

us
k=
where

R= force in pounds.

P = density in pounds per cubic foot.
A = area in square inches.

V = velocity in miles per hour.

D = diameter in inches.

that below a value of VD of 40, K becomes very erratic. A great
many check observations were taken in this region, but the flow seems
to be unstable and K cannot be determined with precision. The mean
curves are replotted on figure 37 on VD as abscisse, and again on
figure 38 on V as abscisse. The critical velocity apparently dis-
covered seems to be about 9 miles per hour for all the plates.
Theoretically, if the resistance due to viscosity be important the
coefficient K should be a function of the product VD. Thus, Lord
Rayleigh has suggested* that where both density and viscosity are

* Phil. Mag., p. 66, July, 1904.

eee
aan

_
Seen eee a
Y ms ~

ae
ee ale eee
IR STAN OQ Cl

ae c =
S A |FUNC OF VELOCIT
NOTATION Af RGR

Fic, 38.

ote
|e:
ele
CRIN
| NAY ds
Bi.
tt
Saeeae
ee
eo oe

88 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

important, the most general form of the resistance equation which
satisfies dimensional requirements is the following:

R=pAvs(“*),

when L isa linear dimension, such as diameter of disk ; v the kinematic
viscosity of the air, taken constant ; and f an unknown function of the

V

single variable (" =) 3
This expression may be written

R=pAV’¢(VD), when » is sensibly constant.

The coefficient K should then be a function of VD and the curves of
figure 37 should coincide. This is not the case, and it may be con-
cluded that the effect of viscous drag is not important, or that the
disks are not geometrically similar since the thickness remains con-
stant. The critical velocity appears by figure 38 to be about the same
for each disk.

For velocities above 27 miles per hour, the value of K remains
practically constant for all speeds and all disks. The usual formula
can, therefore, be applied if model tests are run at speeds greater than
27 miles per hour. Our wind tunnel testing will in future be con-
ducted at speeds between 27 and 4o miles per hour.

The values of K for larger disks appear to be larger than those for
the smaller disks. This discrepancy may be eliminated when it is con-
sidered that the 6-inch disk obstructs 1.25 per cent of the tunnel and
should cause us to underestimate the mean velocity past the disk by
about 1.25 per cent, and consequently K as computed will be 2.5
per cent too large. The actual discrepancy between values of K for
the 2-inch and 6-inch disks is about 3.5 per cent, leaving I per cent
to be laid to experimental errors.

It seems safe to conclude that for speeds above 27 miles the coeffi-
cient K remains constant and the same for all disks.

The same conclusion was reached by Stanton* and by Riabou-
chinski,’ but Eiffel * states that K is greater for larger surfaces. His
tests in the wind tunnel certainly show an increase of K with area, but

*T. E. Stanton, Proceedings of the Institution of Civil Engineers, Vol. 156,
Part II, London, 1904.

* Bulletin de l'Institut de Koutchino, Moscow, 1912.

* La Resistance de I’Air et l’Aviation, Paris, 1912.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS 89

this may largely be accounted for by the effect of the walls.” M.
Eiffel’s tests in the open air with large plates dropped from the Eiffel
Tower indicate still larger values of K, but here velocities were as
great as 90 miles per hour. In addition to the extreme difficulty of
obtaining precise measurements of resistance and speed with this
method, a further complication is injected into the problem from the
fact that the velocity of fall was accelerating.

It seems obvious that the resistance to accelerated motion should
be greater than that due to uniform motion, since the energy system
accompanying the disk is being built up.

In conclusion, then, within the limits of these tests, the resistance of
a flat disk normal to the wind for speeds above a certain minimum may
be correctly represented by

R= KpAy:

The existence of a critical velocity for disks has not been detected
in previous experiments. M. Eiffel’s tests were not run at sufficiently
low velocity, Riabouchinski’s tests were not very precise; but the
experimental work of Stanton or FOppl might have been expected to
bring out a critical velocity.

One explanation may lie in the fact that the critical velocity at
which eddy making begins to become a stable phenomenon depends
largely on the quality of the wind in the tunnel. It is reasonable to
suppose that a turbulent wind would cause the critical velocity to be,
reached sooner than it would be with a more steady wind.

Experiments at Gottingen on spheres showed a marked critical
velocity at a certain point. When the wind was made more turbulent
by a fish net up stream, the critical velocity came at about two-thirds
of the former value.’

The Gottingen tunnel in which Foppl’s tests were made is a closed
circuit in which the wind is guided around the corners by vanes,
strained through diaphragms and wire mesh and forced to flow in
horizontal lines where the model is placed. The result of such fore-
ing the air to take unnatural lines of flow must introduce a degree of

*Lord Rayleigh, “On the Resistance Experienced by Small Plates Exposed
to a Stream of Fluid,” Phil. Mag., July, 1915. A simple yet delicate experi-
ment showed that the resistance of two small plates was equal to that of a
single large plate of the same area for the same speed. This is in agreement
with the results presented above for disks, and indicates that if there be a
critical velocity, this velocity is the same for both large and small areas. Lord
Rayleigh used disks cut from cardboard, which had presumably a square edge
resembling that of the brass disks.

* Zeitschrift fiir Flugtechnik und Motorluftschiffahrt, May 16, 1914.

go SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

turbulence into the translational motion that is finally realized. The
turbulence of the wind may make the flow about the model turbulent
at all speeds used. Hence no critical velocity would be found.

Stanton’s tests were made with a Pitot tube placed 1 foot up stream
from the model. The tube was made up of two 4-inch tubes. The
disks were then placed in the wake of these tubes and we might expect
the critical velocity to be affected. That the effect of such an arrange-
ment is appreciable was determined from a simple test. In the course
of our test on the 5-inch disk above, a glass tube 3/16 inch in diameter
was run across the tunnel 1 foot up stream from the disk. The resist-
ance of the disk was found to be reduced by about 6 per cent. Increas-
ing Stanton’s value of K by 6 per cent brings it into agreement with
our mean value of K. The following table summarizes the values of
K for flat plates normal to the wind given by the several experi-
menters. The notation and units used are as as above.

Diameter Blacitel| ss
Authority | piste. "Mites. K Remarks
Fel eee ernie. 4 25m .000240 | 4.9 ft. wind tunnel.
SO OES ASR re Om yh 25 SOOO2ASh V4 sO kta as “
ee eee Le est Os W225 ,0002A7 | 4.9 ft... “ 5s
Eel erties are SS 40-90 | .000263. Open air.
2 iets ole £20 40-90 .000275 .
SoD RA Te a es eo 40-90 .000284 | s
Sle ee eee SO) aa40-00! #000200 «
Riabouchinski.. 0.5 3-15 | .000255 | 3.9 ft. wind tunnel.
oe a I 3-15), 0002525) suOnrtt: ae. ss
# r 2 2-15) ||| 000252 | 320 ft. = Ks
Hopp laesrancces 7. O.4) AS30416 OOO255 44) Gr yattacarge ¢
ATIC OTe is are ere) Gee | eS 5 .000265 |.4.0 ft. “ f
Se Le Syste. aes! Taal As3 ic) | .000265 | 4.0 ft. “ of
ERT +, Agen Aen ess OOO 265q\t4) Onitmen cs
ss eles | .000265 | 4.0 ft. “ se
cs Giess i) }0002688|/4RO tan ws ss
| | corrected for influence of walls.
Stantonee eee lees aeTis .000243 | 2.0 ft. wind tunnel.
ef ail Loe | 13 | FOO0250"| 220%ht.) os >
4 Wer le feske'S | 13 |; .000248 72, 01L., ts
2 lane | OOO24On|N2e Obits sues f
6 By ars .000268 | 2.0 ft. “ ce

It has been suggested that the critical velocity found by us is not
that of the disks but a critical velocity for the tunnel. It is well known
that there is a marked critical velocity for the flow of air or water
in pipes where the fluid becomes suddenly turbulent.

From the experiments of Stanton and Pannel* on the flow of air,
oil, and water through pipes, it was concluded that turbulence began

* Phil. Trans. Roy. Soc., 1914, p. 200.

NO. 4 WIND TUNNEL EXPERIMENTS IN AERODYNAMICS gl

,

for a value of the “ Reynolds Number ’ ae = 500m blere Dis
V

diameter of pipe, V is velocity, and v the coefficient of kinematic vis-
cosity. A very rough calculation for the square 4-foot wind tunnel,
using the above figure, indicates a critical velocity of 1/16 mile per
hour. For the 3-inch pipes of the honeycomb, the critical velocity is
about 1 mile per hour. Our experiments were conducted well above
these speeds.

Similarly there is a limiting velocity for the flow of air at atmos-
pheric pressure to be deduced from St. Venant’s equation for motion
of a compressible fluid.

For air at ordinary temperatures this limiting velocity is about
770 miles per hour.

A more practical condition which may occur at ordinary speeds may
account for the existence of an apparent critical velocity at which
the fluid refuses to turn a corner due to its inertia. Thus, for true
stream line motion about a disk, the air is required to turn sharply over
the edge and close in on the back of the disk. The stream line has a
finite radius of curvature and a finite velocity at any point, and there
is consequently a centrifugal force on each particle of the fluid.
Unless the pressure gradient is sufficient to balance this centrifugal
force, the curvature of the stream line cannot be maintained. A dead
water then forms at the rear of the disk which is dragged away by
the viscosity of the moving air in contact with it, thus setting up a
turbulent wake. A considerable increase in resistance might be
expected to take place when turbulence is set up.

Our experiments show an abrupt change near 13 feet per second
for thin disks, with unstable flow for velocities between 10 and 20 feet
per second. This range is of the same order of magnitude as the
critical velocity for a flat ellipsoid deduced by Mr. E. B. Wilson in the
prefatory note above.

NOTE ON AN EMPIRICAL EQUATION TO EXPRESS THE EXPERIMENTAL
RESULTS

Within the limits of these experiments the normal resistance of a
thin disk may be represented by the expression
R=.0018 D*V +.00103 D?V?,
in which
F is total force on disk in pounds,
D, diameter in feet, and
V, wind velocity in feet per second.

Q2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

This leads to the equation to a straight line drawn on figure 39,

R
D2V
It appears that for velocities above 20 feet per second the values of

re tA Sa A [LT
rasa ne a SAL
se de Sa ea Se) 8
oR ee
spiel oe ae aL ea
oe raed ca ee

= .0018+ .oo103/.

OSE

O52

°
[ZEIGE CON RCH 128. ae ae 4o 4H“ 4e S$ 36 60
Fic. 39.—Units. :
R= Pounds, force. 2 6 ft disk
D= Feet, diameter. x Sa ne
V = Feet per second, velocity. iK : “4
/\ 2 ‘ “
-.. as observed for all disks lie near the line. It should be noted
D2V

that the above expression is not dimensionally homogeneous, and it
is therefore not safe for extrapolation. However, it was pointed out
that the disks used were of uniform thickness and hence not geo-
metrically similar.

SMITHSONIAN MISCELLANEOUS COLLECTIONS
VOLUME 62, NUMBER 5

hodgkins jJFund

DYNAMICAL STABILITY OF AEROPLANES

(With THREE PLATES)

BY;
JEROME C. HUNSAKER, Ene. D.
ASSISTANT NAVAL CONSTRUCTOR, U. S. NAVY
Instructor in Aeronautical Engineering, Massachusetts Institute of Technology
ASSISTED BY
i HeeUiE Kh. S..B:,. Di W..DOUGLAS, S.B., H. K. CHOW, SS: M..
anp V. E. CLARK, Captain, U.S. Army

eoee Cleese

i
*,

(PuBLIcATION 2414)

CITY OF WASHINGTON
PUBLISHED BY THE SMITHSONIAN INSTITUTION
JUNE 30, 1916

The Lord Baltimore Press

BALTIMORE, MD., U.S. A.

CONTENTS

PART I. LONGITUDINAL MOTION PAGE

Sime nitro ductionrsand MConchusioms: s.2¢ eae cise nd acieia som coateseack nates I

Somalia Clo) CST OT) vam eeyer tes rte tetere se sncns -e Sicreisiste sva;e'e5; obit cere a¥averetoteraisiete ale eter oie 6

Gem VIO Cle late eee aeaceasermsterereteseu cane coe Sosa cheeo ais. ich Gusts vas ayeyareiaara Saisie sin Sheva soars 7

AMMA O2 (CO CL CICIIES sence yausuaie sale cut, sitereiane aim ale cose oot a yeyolensoveyave ) enealiesorsrercler 7

Seameoneiidinal Balances e: n2 2654 acednn neers oaihe oa Sl etincsalnaeeeasces 12

em ECLOL AR CIPESCHLALION 41 Siea.c® ds cide%-as%.wn wind Bile a Oana eae vie wears 16

See DOGLORINANCE | GUE VES Macc rare ajc, Scans 6 a rsi0e «6 Gras trieys eterowrero oe saie Rioters oases: 17

ROMme ACRES eral] CIN OEAET OM acc nc o suet -1shove e1eleleveyeipiedetesera asthe a ave)e Gis << corsteversierete ehevers 18

§9. Equilibrium Conditions and Dynamical Equations of Motion........ 20

§10. Conversion to Moving Axes, Longitudinal Data.................2.- 25
SniepelvesistanceyWerivatives, Ioneitidinall ss !re wisi. scsi o/\ o i\ele) ois. eis cles rere 30
SS IE) UTD PIT egress trs cP Sb, ays a SL oie Sid. SHA Hn a teseyaeierers lot sinh s olayeisisiecerneteless 31
SEO SCI At ONS lle b1CCH saretq sien orsrcreiei o's ace! Suave bse eects ovels arouse eels ereieie-sierete 33
Sideleoneitudinal Stability, Dynamical. : <2. .2.4. cee sot ecacs vemeoesoees 35
§15. Conclusions (Longitudinal Dynamical Stability)................... 43

PART II. LATERAL MOTION :

Site ALehaL Or ONSVIMMNGLTICAl LGSESs 52% sin s.sia sie eseeye dee we sewers deere s 45

Some Waterall Resistance Derivatives... ...-..cce-c se. cn seine ers tes usemees 2

So. Rolling Moment due to Yawing..0.cc..6i cede ce ctes cesses otuweecs 53

SA Yawine; Moment due to Rolling. «20. .ce.ce0r ss cca sccsa cscs seecs 55

SoD ATID I oMOr we Olle 1s crs scuctevsinc mietere iss erttarese piece Orie cioens or eon ean 57

SOMMU ADIN TOhs LAW Cases s Cicer na anieeh oh sind eens Gas netaad ann dese eee 50

Nzar Nec lected™ COCHICIENTS: sca. c axie es pies Daa se eles eden ein 38 800.9% Sind wap sere cws 2

§8. Independence of Longitudinal and Lateral Motion.................. 62

Som slateral Stability, Dynamical <. sisi se a area e00-ncmeeocrn treeenedleas aged 64

Riommenanacter or Lateral MOtiOits <2.s schrieee00s dda bee ais samba eawions 66
SMa SMITA: IG. 2 rk tice! wre.adscumirane ears Da tase erden wade. dure aeiacenleavbe 68
Seria heh ase at Ooh Le fic < dhdiat w aia en. avtsaovd Sacsevien sevgcheetdaeaaes 70
Neon epur lO Meh IOI, Ar F.5. Hate. cve.cysicrcre cis oe ersveréy ora crercretey 5 cre deeloretareaahelele 71
§14. Comparison with other Aeroplanes............. 0.0. cccee cess c cee 75

ili

Hodgkins Fund

PART I. LONGITUDINAL MOTION
§1. INTRODUCTION AND CONCLUSIONS

The present dynamical investigation of the stability of motion of
aeroplanes is based upon the well-known theory of small oscillations
of rigid dynamics as first applied by Bryan* to aeroplanes and ex-
tended by Bairstow.” The necessary coefficients for use in the equa-
tions of motion were determined by model tests in the wind tunnel of
the Massachusetts Institute of Technology.

The application of model experiments to predict the performance
of full-size aeroplanes is now so well established that no general
discussion of the theory of models is undertaken. A great part of
the actual experimental work was performed by Messrs. Huff and
Douglas. The oscillating apparatus was designed by Mr. Chow
under the direction of Professor E. B. Wilson of the Department of
Mathematics. Captain V. E. Clark, U. S. A., while a student in
aeronautical engineering, designed an aeroplane which was selected
as one type for investigation.

It is necessary to acknowledge the cordial interest taken in the
work by Professor C. H. Peabody, head of the Department of Naval
Architecture. From the beginning of aeronautical research in his
department, Professor Peabody has offered the warmest encourage-
ment by countless arrangements to facilitate progress and to pre-
vent interruptions.

Following the analysis of Clark’s aeroplane, the work was repeated
for a model of a military aeroplane known as Curtiss JN2.° The

*G. H. Bryan, “ Stability in Aviation.”

* Technical Report of the Advisory Committee for Aeronautics, London,
1912-13.

* Plans and description given in “ First Annual Report of the National Ad-
visory Committee for Aeronautics” (Report No. 1, “ Report on Behavior of
Aeroplanes in Gusts,” by J. C. Hunsaker and E. B. Wilson, Washington, D. C.,
1916), Senate Document No. 268, 64th Cong., Ist Sess.

SMITHSONIAN MISCELLANEOUS COLLECTIONS, VOL. 62, No. 5

2 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Curtiss Aeroplane Company gave their full cooperation with a desire
to learn what improvements in the design might be suggested by our
stability calculations. Dr. A. F. Zahm of the research department
of that company made careful tests to locate the center of gravity
and to determine the moments of inertia of the actual aeroplane.

The Curtiss machine is a practical aeroplane with powerful con-
trols, which does not pretend to possess any particular degree of
stability. The Clark aeroplane, on the other hand, was designed to
be inherently stable while departing as little as possible from the lines
of the ordinary military aeroplane as typified by the Curtiss J N2.

The comparison of these two aeroplanes is interesting and leads to
the conclusion that inherent dynamical stability, both longitudinal
and lateral, may be secured in an aeroplane of current type by careful
adjustment of its surfaces and without material effect on controlla-
bility or performance.

The discussion in detail is confined to the Clark model, for brevity
of presentation, and the results only of the parallel calculations for
the Curtiss model are introduced where a comparison is suggested.

In Part I the general equations of motion are deduced in a simplhi-
fied form which applies to horizontal flight in still air. The longi-
tudinal motion is then considered separately and the necessary
aerodynamical constants determined from wind tunnel tests. It is
found that the longitudinal motion, if disturbed by any accidental
cause, is a slow undulation involving a rising and sinking of the
aeroplane as well as a pitching motion. This undulation is stable for
high aeroplane speeds since it is rapidly damped out. At lower
speeds, the undulation is less heavily damped until at a certain critical
low speed the damping vanishes. For speeds below this critical
speed, the undulations tend to increase in amplitude with each swing
and the longitudinal motion is, therefore, unstable.

Similar calculations for the Curtiss aeroplane show a _ similar
critical speed below which the longitudinal motion is unstable. It is
believed that the existence of instability at low speeds has not been
indicated before, and it is hoped that the recommendations made to
reduce the critical speed may be of assistance to designers.

It appears a simple matter to secure any desired degree of longi-
tudinal stability by the use of properly inclined tail surface, and by
the use of light wing loading. It is pointed out that excessive statical
stability, as indicated by strong restoring moments, is undesirable
and may cause the motion to become violent in gusty air. This vio-

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 3

lence of motion may seriously impair the pilot’s control and the
aeroplane may “ take charge ”’ at a critical time.

However, the longitudinal motion for any particular speed of flight
may be made dynamically stable, while at the same time only slightly
stable in the static sense, by the use of a large tail surface which lies
very nearly in the relative wind. If the minimum of statical stability
be combined with the maximum of damping, the pitching will be very
slow and heavily damped. The longitudinal motion can then be
dynamically stable and yet be without violence of motion in gusty air.

The general prejudice among pilots against “ very stable ’’ aero-
planes is believed to be justified. It cannot be too strongly insisted
upon that true dynamical stability is better given by damping than by
stiffness.

Experience with rolling of vessels has led to the design of vessels
of small metacentric height (a measure of statical stability) fitted
with generous bilge-keels (damping surface) for passenger carrying.
An effort is made to get away from the violence of motion associated
with stiffness.

In Part II, the lateral or asymmetrical motion is investigated. The
necessary aerodynamical constants are determined by wind tunnel
tests wherever practicable and two coefficients which cannot readily
be found experimentally are calculated by a simple approximate
method. The character of the motion as indicated by the solution of
the determinant formed from the equations is then discussed.

It is found that the lateral motion is a combination of a roll, yaw,
and side slip or “ skidding.’ Using approximate methods, the com-
bined motion is resolved into three components, two of which are
important.

One type of motion is a spiral subsidence if stable or divergence
if unstable. The Clark aeroplane becomes spirally unstable at low
speed. The motion is a “ spiral dive ” due to an overbank and a side
slip inwards. The aeroplane makes a rapid turn with rapidly increas-
ing bank accompanied by side slipping inwards. The instability is
such that an initial deviation from course will double itself in about
7 seconds.

It is shown that the spiral motion may be made stable by adequate
fin surface above the center of gravity or upturned wings and by
reduction in “ weather helm” due to too much rudder or fin sur-
face aft.

4 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The Curtiss aeroplane shows the same sort of spiral instability at
high speeds. This aeroplane had no dihedral angle of wings and
had a large rudder and deep body.

The second type of motion has been called a “ Dutch roll” from
analogy to a figure in ice skating. The aeroplane takes up an oscilla-
tion in yaw and roll simultaneously. It swings to the right banking
for a right turn, then swings back to the left banking for a left turn.
The combined yaw and roll has a fairly rapid period. The Clark
model at all speeds shows that this motion is heavily damped and
hence stable. At high speed, the period is 6 seconds and an initial
amplitude is damped to half value in less than 2 seconds. At low
speed the period is 12 seconds, damped to half amplitude in 6 seconds.

It appears from an approximate calculation that the “ Dutch roll ”
may become unstable if an aeroplane has too much high fin surface
and if there be not sufficient ‘“‘ weather helm” or rear fin surface. It
is seen that these conditions are the reverse of those for spiral insta-
bility. The conflicting nature of the requirements for stability in
these two kinds of motion suggests that an aeroplane is unlikely ever
to be unstable in each sense. It also indicates the difficulty of obtain-
ing lateral stability by raised wing tips.

In confirmation of theory, we found the Curtiss spirally unstable
at high speed and stable in the “ Dutch roll,” while at low speed the
spiral motion was stable and the “ Dutch roll” unstable. The period
was 6 seconds and an initial amplitude doubled itself in 8 seconds.

It is believed that the majority of modern aeroplanes of ordinary
type are spirally unstable because of excess of fin surface aft. When
attempts have been made to remedy this fault by use of a large
dihedral angle upwards for the wings, matters have been made
worse. It is only to be expected that in overcorrecting spiral in-
stability a “ Dutch roll” of more or less violence may be introduced.
Especially in gusty air would one expect high fin surface to produce
violent rolling.

The Clark aeroplane has very slight rise of wings, about 1°6,
and a small rudder. It is shown that at ordinary speeds this aero-
plane is stable in every sense, both longitudinally and laterally.
Whether this stability is excessive can only be determined by actual
flight experience in turbulent air. However, it has appeared possible
to secure a degree of stability in every sense in an aeroplane of con-
ventional type.

The object of the research has been to show how various features
of design may affect the motion of the aeroplane and only incidentally

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 5

to produce a stable aeroplane. The discussion has been confined to
motion in still air. If an aeroplane be unstable in still air it is
obviously worse off in gusts. The converse is, unfortunately, not
true, for an aeroplane which is very stable in still air may be so stiff
that in turbulent air it will be violently tossed about.

It is conservative to conclude that aeroplanes should not be un-
stable and that they need not be, since slight changes in the nature
of adjustments suffice to correct such instability of motion.

In view of the military use of aeroplanes inside the zone of fire the
probability of controls becoming inoperative is ever present. An
inherently stable aeroplane, with controls abandoned or shot away,
could still be operated by a skilful pilot by manipulation of the motor
power alone.

Any sort of automatic (or gyroscopic) stabilizer which operates
on the controls is of no use when those controls fail, and it should
be judged as an accessory to assist a pilot rather than as a cure-all
for the inherent instability of an aeroplane’s motion.

The ordinary type of aeroplane readily lends itself to adjustments
which make for inherent stability of motion and there is no reason
to seek radical changes of type to insure stability. Freak aeroplanes
of great “ stability’? may be excessively stable in some ways and
frankly unstable in others. It is likely that the most satisfactory
aeroplane will be only slightly stable and that this aeroplane will in
any possible attitude be easily controlled by the pilot.

Controllability and statical stability are to some extent incompatible.
Dynamical stability requires some amount of statical stability and
considerable damping. It appears to be of advantage to provide the
minimum of statical stability and the maximum of damping. Then
the aeroplane’s motion will be of very long period but heavily damped.

It is believed that the methods of investigation here described may
be applied to any type of aeroplane, and, by the systematic variation
of one feature of design at a time, a full understanding may be had
of the effect on the motion of each change. The process is of
necessity laborious, but compared with the difficulty of full-scale
experiment in the open air, the model method is rapid and inex-
pensive. It is rarely possible in actual flying to obtain any idea of the
effect of slight changes in design. Weather conditions, motor
troubles, personal peculiarities of pilots, etc., tend to add to the com-
plexity of an otherwise very simple problem.

Furthermore, experimental flying is dangerous. For example, |
knew a pilot who, to determine whether a new aeroplane was spirally

6 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

unstable, took his machine up to a good altitude and allowed it
to get into a spiral dive. The machine made five turns of a rapidly
winding and contracting helix before he could bring it out on a
horizontal path. If the controls had been only a little less powerful
the machine would surely have crashed to the ground. That the
controls were adequate was purely a matter of good fortune. The
experiment was a success in that spiral instability was demonstrated.
Only a few minutes of time was required. However, no information
was obtained as to the degree of instability present nor as to what par-
ticular changes would remedy matters. To complete the experiment,
it would be necessary to repeat the dangerous feat for every change
which suggested itself. Naturally, a designer will be very economical
in his suggestions under such conditions.

§2. TYPE DESIGN

The type aeroplane selected for the first investigation is a two-place
biplane tractor designed by Captain V. E. Clark, U. S. A., while a
student in the graduate course in aeronautical engineering at the
Massachusetts Institute of Technology. This aeroplane is considered
to be representative of modern practice in aeroplane design. Its
principal dimensions are as follows:

Wing area, including ailerons. ......... 464 sq. ft.
Sate eae eater cut stat ae lanel oeteteuaaterel ce AI max., 40.2 mean.
AE DCCE Tal tO ta tok or henner cintetene 2 Sih eee iecesys 7,
(Grd Or a yals sere ioseeb ete a one maa 6.27) 7 1t:
Dihedralot wines, deorees: 202.5. sc se 176.75
Area otabilizer: fev taes aisesiore here orc taer ees 16.1 “tsqn it:
Area elevatOrs’, 2126 tat eiies © sae 16:00 eSqebe
Areay fudder «oe ee ee eee ete 9:35 Sd: at.
Lenoth; body iat mye nce et eee ces 24.5 © ett.
Depth-bodyemaxinititiig. te © cts. eee Beans kt.
Whaidth, bods; aamaxiimntndlas clei ee oar dee tte
W eichicbaret.- sc 9 ncuerant is cine teers 1,070 lbs.
Weight.apersonnel..7...5. eee ee 320 Ibs.
Weecht, ftieltamd Orla ee ontsiee erate 415 lbs.
Weight: full load... .eeG- ese ee 1,805 lbs.
52> thine roll,
Radii-of eyrationvaks.. see hte 4.65 ft., in pitch.
6.975 ft., in yaw.
Brake horse-poOwer acdc. cite epee 110

Fueland oil per bat. Ps Moun. .as ee 0:73," Ab:

NO..5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 7.

Wier ieiiaa Speeds. Merier. a8 cle. aie e le ebache 2 87 miles per hour.
NVinigadtan etna SPCCE seat) aa, atethle ss Se aay sens P< 35 miles per hour.
Ernie era CenO CLAIR) s yecra dhs cMarseieie ciere’ore goo ft. per min.
PSG Cire ine Reng t teas ue (este ace ob ete aa 1ing
Pndirance: full powere%.<. x5.4. Mis ceas Oh 5.6 hours.
Endurance, reduced power, 14 hours at.. 47 miles per hour.
$3. MODEL
I a
A model, SG scale, was made by Edward Tighe, model maker,

giving a span of 1.58 feet.. The size of the model was limited by the
size of the wind tunnel which is 16 square feet in section. The model
is shown in figure I (see pp. 8 and 9). Note that wires are omitted
and struts are made round instead of “ stream line” in section. It is
believed that the effects of these changes on total resistance largely
counterbalance each other. This model was carefully shellacked and
polished to minimize skin friction. The model is, of course, much
more smooth than the full-size aeroplane, as it should be, in order that
the surfaces may remain geometrically similar. Model work was to
the nearest hundredth of an inch. No propeller was fitted, but in the
design account was taken of the propeller race in augmenting
resistance.

For simplicity, the model was made with trailing ailerons or wing
flaps integral with the wings. This somewhat increases the effective
supporting area. The stabilizer and elevator were made in one,
corresponding to the elevator flaps in neutral position. These points
are made clear on figure I.

$4. WING COEFFICIENTS

In the course of the design, a wing section was devised by Clark
which showed a low resistance at high speed and small angle of
attack and at the same time was thick enough to permit the use of
robust wing spars. A model of this wing was made, of 18 inches
span by 3 inches chord, and tested in the wind tunnel. For various
angles of wing chord to wind, the lift L, drift D in pounds, and
pitching moment M in pounds-inches were observed for a wind of
30 miles per hour; air of density .o7608 pound per cubic foot.

The wind tunnel and balance are duplicates of the 4-foot installa-
tion at the National Physical Laboratory, England, and reference
may be made to the technical report of the Advisory Committee for
Aeronautics, year 1912-13, for a description of the apparatus and
method of operation.

VOL. 62

SMITHSONIAN MISCELLANEOUS COLLECTIONS

Pode Seole gk Fel/ Size

Fic. IA.

Fic. 1B.

HUNSAKER AND OTIIERS

STABILITY OF AEROPLANES

NO. 5

*S — ie} §S10}D9A 9d10F JULINSdY “OI “OY ly ‘aovey bi/pucdvatsoo sey
pum of pacys bia yo a/bliy Sayo2IpUl {JlIISGNE
oP, oH oF oft 20 of. ;

400Y 4ad bali OF Jo /PPOf/ 0 SIIAOY
£ = ps Oo fPWOyY

Saya
Z S 7 0 Say ILy

buimoaig £2 2/229

10 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The lift and drift coefficients Ky and Kx were computed from the
observed L and D, using such units that the coefficient is pounds force
per square foot area per mile hour velocity. Curves of coefficients
are given on figure 2, which also shows the ratio L/D, a measure of

de ie
/7or72} oe Vu79 ee | Cael
Ap
Te
ect. TO

.20028

&

8

Yn O07 SVode/ flere fAfare Wig

©
= YY

09d OY “Aix (77 bvnds Ler Sgvare foot Ler /U/8 flour Oj7s
~
Detta OF Lt kA Je LOVE

Oo

AHHH

v

Coek¥1c/a77s of Lif f- wy

&

S

»
eee

i mee oO Ld we 6 -3 70 12 SF lO 3
Angle of 479 Chord fo Wind 17 Qegrees

Fic. 2.—Wing coefiicients.

the effectiveness of the wing. A maximum L/D ratio of 18 was
found for an angle of attack of 3°. For a 41-foot wing at 70 miles
per hour, it is believed that the lift coefficient is not greatly different,
but that the drift coefficient at small angles is materially reduced.
The effect is to increase the ratio L/D. Results of tests at the
National Physical Laboratory (Tech. Rept. Adv. Comm. Aero., 1912-

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS II

13, p. 81) were applied to the 1 /D curve for our model to obtain an
approximate curve of L/D to apply to the full-size wing. As a
monoplane surface, we get a maximum value of L/D of about 20.
The particular design is a biplane of aspect ratio 7. Well-known
corrections for biplane interference loss and aspect ratio gain were
applied to get a corrected curve for use in the design.

Se

Fic. 3——Wing section dimensions and resultant force vectors.

The center of pressure for this wing is shown by figure 3, as well
as the contour of the section. Center of pressure is defined as the
intersection of the resultant force on the wing (represented as a
vector) with the plane of the chord. It is seen that the wing section
is unstable longitudinally at small angles. That is, if the wing heads
down so that the angle of attack becomes — 3°, the moment of the
resultant force tends to turn it down still farther.

Applied to the aeroplane, it is necessary to balance and correct this
tendency to dive by horizontal tail surfaces of proper size and
attitude.

12 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

§5. LONGITUDINAL BALANCE

The complete model, using wings of the section described above
and fitted with the tail shown in figure I, was mounted in the wind
tunnel on the balance with the wings vertical. A vertical spindle
from the balance was driven into the side of the body at the point
shown on figure 1. By swinging the model about the vertical axis
passing through the spindle, the angle of the wind to the wing chord
was varied from +20° to —8°. At each attitude the force across
the wind or lift L, force down wind or drift D, and the pitching
moment about the spindle were measured. The wind velocity was
30 miles per hour for all tests. The signs were taken so that an
actual lift, actual drift, and a stalling moment are positive. Density
of air is ‘at 15° ©, 770 mm, He, dry.

Test No. [ was made with the horizontal tail surface making an
angle of —2°75 with the wing chord. That is to say, the rear edge
of the tail was tilted up. Test No. II was a repetition but with the
tailat —7°. Test No. III had the tail surface at —5°.

The lift and drift in pounds on the model at 30 miles per hour are
given below, and on figure 4.

Case I Case J] Case III

(aS SS [aaa

1 TE D 6 D L D
— 4 — 049 +.1147 — 172 +.1363 — 115 +.128
— 2 + 18 +.1011 1 O35 a anos + .112 +.108
— I + .32 0988 + .143 1047 + .240 +.104
Oo + .454 .099 + .298 .IOI4 * 360 IOI
sand 509 1016 437 .IOII .490 .102
+ 2 .703 .106 ye .1028 625 105
4 .927 eT .807 L135 872 Sigs
6 fret 143 Ce re wtavbs ae
8 1732 S107 1.224 1381 TesOs D5
10 1.484 195 sages 5 Aes Sees wats
I2 1.604 .236 1537 2253 1.568 2s
14 1.653 ‘12 a ee cee. Ps
16 ore Be 1.640 3Or 1.64 .370
18 1.606 547 1.614 509 1.58 .498

The lift and drift at first sight appear to differ for the three cases,
but it will be observed that the maximum lift is 1.65, 1.64, and 1.64,
and the minimum drift is .099, .101, and .ror for the three cases

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 13

Ree Se a
ea]
ee PeVelae at
Suef fe
ef ef! lela

Nd bee TIN fs ae
LNA Hilt

er.
FECTS
NSS
CACAO
TAO a
CCC
NE
Heer Ne
Pooyge eS

ALTO M7 ES a Du po
t Ik

tf me a
Case SS
fade 34-5?

On ee oi Be Sc Yoo (2? V7 Orn SF?

Fa gd

Angle or Kveage Cord Jo Ko7g
Fre. 4—Curves L, D, and M for three tail settings.

14 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

respectively. The discrepancy is I per cent only and is about the
precision of the measurements. The comparison is best brought out
by eliminating reference to angle of attack as the effect of the change
in tail angle appears to be mainly to move the curves of L and D,
plotted on 7, to the right or left.

Figure 5 shows the ratio L/D for the model for cases I, II, and ITI,
plotted on L in pounds as abscisse. Bs or small values of L and angles
of incidence between —2° and +2°, corresponding in practice to
high-flight velocity, the curves are practically identical. For angles

3
Za
Nh
x
x 3:
\
\4
I
\ eg ea
XZ
XN PS OS or
5 D4 ae lad
9 2 el Adve Chore
x CaseZ eS
S Ca\seZZ
AA ote

40 SS 4a eas “EF iD, MG Cora
Lee LL; ee S¥ode/ @7- 2A oie Aer froor

Fic. 5.—Curves of L/D plotted on L for three tail settings.

of incidence near 8°, the L/D ratio for case III is 8.6, while it is 8.2
for case II, and 8.0 for case I.

It appears, therefore, that changing the angle of tail surface has
but slight effect on the lift and drift of the aeroplane. The actual
aeroplane should have the same maximum and minimum speeds in
any case since the maximum lift and minimum drift are about the
same regardless of angle of tail surfaces.

The statical stability against longitudinal pitching is, however,
very different for the three cases. Thus the pitching moments (ob-
served about the spindle and converted to pitching moments about
the assumed center of gravity) are as follows, in pounds-inches on
the model at 30 miles per hour. Positive angles and positive moments
are stalling angles and stalling moments respectively.

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 15

PitcHinG Moments, PouNpbs-INCHES

t Cased Case Case Ty
4 + .089 2509 + .26
—2 + .008 + .473 +.16
—I + .022 + .454 +.12

O + .016 + .292 +.12
+1 + .030 + .143 +.07
+2 + .037 + .037 —.O1
+4 + .039 — .159 —.12

6 +.016 ich se

8 + .023 — .476 — .28

10 Behe Heke af

I2 + .086 — 884 — .39

14 : on ae

16 —.013 — 1.328 —.53

18 — .336 —1.378 — 82

Case I, with tail at — 2°75, shows very small pitching moments and
may be said to be neutral for ordinary angles of incidence. Thus
if the aeroplane be flown at +2° incidence, in order to maintain
balance at this attitude the pilot must impress a diving moment of
—.037 pound-inch (on the model) to overcome the stalling moment
+ .037 given above. Then if the aeroplane be accidentally tilted up to
+12° by a wind gust or other cause, in the new attitude the net pitch-
ing moment is still positive, and hence tends to tilt the machine still
more. It is, therefore, unstable unless the pilot intervenes with the
horizontal rudder.

For case II, tail at —7°, there is a strong righting moment always
acting to prevent stalling or diving. The machine is very stable, in
fact excessively so. For instance, flying at 2° incidence, the moment
to be held by the pilot is very small. Suppose, however, he wishes
to fly at +12° corresponding in the full-scale aeroplane to about 36
miles per hour. To maintain a balance at +12° incidence, he must
exert a stalling moment by use of the horizontal rudder equal to about

a (26)° (3) =1,970 pounds-feet. The arm of the elevator is:

about 20 feet (distance aft of center of gravity), requiring a lift of
100 pounds,on the elevator flaps. The elevator is able to exert this
force if turned up about 10°. The elevator motion available for con-
trol in gusty air is thus largely used up in maintaining balance. The

16 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

drift on this elevator flap may be over 20 pounds, making a waste of
3.5 propeller horse-power, or about 6 brake horse-power.

It is preferable to balance a machine at high speed by placing the
center of gravity well forward. Then the pilot will have to carry
his elevator turned up when flying at low speed. But at low speed,
he is most in need of the full elevator motion for control of pitching.
We, therefore, conclude that case II, with fixed stabilizer at —7°,
is very much too stable or stiff longitudinally, and case I, with
stabilizer at 2°75, is not stable enough.

Case III, with stabilizer at —5°, appears to balance longitudinally
at +2° incidence, and at + 12° incidence to have (full size) a natural
diving moment which could be held by a negative lift on the elevator
of only about 44 pounds, corresponding to about 4° elevator angle.
Consequently, it was decided to adopt the arrangement of case ITI
for the subsequent stability investigation.

$6. VECTOR REPRESENTATION

A clearer conception of longitudinal balance is obtained by repre-
senting the resultant forces acting on the model as vectors. Thus, for
case II, we observed on the balance the lift L and drift D. The
resultant force acting was then of magnitude R= VL?+D?. This
resultant force lay in a direction making an angle @ given by
d=tan™ L/D. The lineof action of this resultant was at ayper-
pendicular distance from the spindle axis given by d=M;/R, where
M, is the observed pitching moment about the spindle. The re-
sultant force, RX, is thus defined in magnitude, direction, and line of
application, and may be represented graphically as a vector. In
figure I, the resultant force vectors for case III are drawn on the
side elevation of the model. The model is considered to be fixed and
the wind direction to change so that the angle of incidence varies
from —1° to +8°. The vectors are, therefore, dsawn relative to
the aeroplane.

The vector for 2° passes near the center of gravity. If it were
desired to balance the machine at some other attitude, 6° for example,
the center of gravity should be located at some point on the vector
foto

Note that on figure 1, for angles greater than 2°, the vectors pass
to the rear of the center of gravity indicating diving naoments and
vice versa. Thus the machine is in stable equilibrium at 2°, and if
deviated from this angle, righting moments are at once created which
tend to restore the normal attitude. |

=

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 17

Such stability is “inherent” in the design of the aeroplane and
depends wholly on the location of the center of gravity and setting of
the stabilizer. No automatic devices are required which may or
may not function inan emergency. The inherent stability here shown
is static only. Later we will investigate the effects of inertia and
damping involved in dynamical inherent stability. However, dy-
namical stability is impossible unless there be statical stability, and
before undertaking a study of the former property, we were obliged
to provide a reasonable righting moment to oppose diving and
stalling.

§7. PERFORMANCE CURVES

In the design of this aeroplane, the resistance, and hence the speed
for given power, was estimated from tests on wings, body, struts,
wires, etc., considered separately. The test results were corrected
and expanded to full speed full size, using reasonable corrective
factors. As is well known, the resistance of many parts does not
increase so rapidly as the square of the speed, on account of skin
friction. Making all allowances a speed of over 85 miles per hour
was predicted for 110 brake horse-power.

If we use the lift and drift observed on the model (= full size )

at 30 miles per hour and convert to full size by assuming the “law
of squares,” the performance is not quite so favorable and a maxi-
mum speed of but 75 miles per hour is indicated.

For a stability investigation we are little concerned with the exact
speed, and for simplicity, the 2 and D from the wind tunnel test on
the complete model of figure I are converted to full size by multiply-
ing by the squares of speed and scale.

A total weight of 1600 pounds is assumed, corresponding to tanks
half full. For any speed /’ the lift is a function of speed and atti-
tude and must equal the weight V.

By the “ law of squares ”

_Force on Model _ (35)
; Po

7 30 ([W
ia eur

where L is lift on model at 30 miles per hour.
For a series of values of L, corresponding to a series of attitudes
or angles of incidence, the required speed ’ was computed. The

hence:

18 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

head resistance of the aeroplane moving at these attitudes and with
these speeds was computed from:
r=p(2)"
30
where D is drift on model at 30 miles per hour, and 7 total thrust
required.

730

s | ie
i umes epee Bai
120 | Da
cl asl oul eles sr eee
. BERGER Me ae
palace aaa

Ang le-Legrees- 29 Chord 7o tind

spectre “forse Fawer eguired

F7LLIF II AF OE FT IE SD OS OTIS nT DO FOOT MIL, IS
4ir Speed isos per flour

Fic. 6—Characteristic performance curves.

The effective horse-power required, angle of wing chord to wind
and thrust required are plotted as “characteristic performance
curves ”’ on figure 6.

§8 AXES AND NOTATION

We shall adopt a notation similar to Bairstow’s for the study of
dynamical stability. The normal attitude of the aeroplane is its
position when in steady flight in a straight line. We select rectan-
gular axes with origin at the center of gravity and fixed in the aero-

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 1g

plane and moving with it in space. In the normal attitude, the axis
of * is tangent to the trajectory of the center of gravity with its
positive direction toward the rear. The axis of g is normal to + and

a

me

Fic. 7—Coordinate axes, x, y, ¢.

y in the vertical plane, and the axis of y horizontal and directed to the
left. The axes are shown in figure 7. As the aeroplane rolls, yaws,
and pitches these axes move with it, so that z is no longer in the
vertical plane of «, nor y horizontal.

/

20 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Let the aerodynamical forces along the axes +, y, ¢ be denoted by
X, Y, Z and expressed in pounds force per unit mass." The moments
about these axes are L, M, N in pounds-feet per unit mass. Angular
velocities about the axis are p, g, r in radians per second. Let angles
of pitch, roll, and yaw away from the normal attitude be 6, ¢, w in
radians. Signs are positive in the directions ry, yz, and zx.

The radii of gyration about the axes 4, y, 2 are Ky, Kz, Ke in feet.
The mass of the aeroplane is m in slugs. The products of inertia are
D, E, F. Two are zero for reasons of symmetry, and one is small in
ordinary aeroplanes.

In normal flight in still air, the apparent wind blows in the posi-
tive direction of the axis of x. Let this velocity be produced by
the forward velocity U of the aeroplane in normal flight. U is a
negative number of feet per second.

Let small changes in velocity components along the axes 4, y, 2
be u, v, w when any departure 1s made from the normal flying attitude.

In normal flight it is assumed that the power available maintains
the aeroplane at such a speed that the weight is sustained and also
that the normal attitude is that proper for the speed.

§9. EQUILIBRIUM CONDITIONS AND DYNAMICAL
EQUATIONS OF MOTION
Let the inclination * of the flight path to the horizontal be @,.. Since
normal flight takes place in a straight line, y,=¢,=0. There is no
oscillation and p,—¢, =7,=—0, and, — N,, =0:
If the propeller thrust 7, be exerted in a line above or below the
center of gravity h feet, then

Me=— Th;
To=—gsin4,—Xo,
Zi 38 COSiUn.

In this aeroplane h=o, and hence M,=o.

If any accidental cause slightly disturbs the normal attitude of the
aeroplane, the relative wind is no longer symmetrical and the aero-
dynamical forces and moments are X, Y, Z, L, M, N.

In general, the aerodynamical forces and moments caused by the
deviation from “ normal attitude ” depend upon the relative motion
of the aeroplane through the air, which motion is defined by U, u
v,w, p,g,r. Thus X=f(U, u,v, w, p, gq, r) where the form of the
function f is not known; and five similar expressions for Y, Z,
EVN:

ues mass is the slug of 32.2 pounds weight.
* Consider 4 positive for an upwardly inclined path as when climbing.

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 21

In the theory of small oscillations u, v, w, p, g, y are small by hy-
pothesis and we may expand X by Maclaurin’s theorem, neglecting
squares and products of these small quantities. Hence,

X=X,+uXytvXyr+wxwt pXptqXqtrxr,
"= Vy tuVutvVYetwYwt pYotqVveatrys,
and similar equations for 7, L, M, N.

Here Xu, Xv, etc., are the partial derivatives of X with respect to

_ u,v, etc., and are the rates of change of X with u, v, etc. That is,
Ox ax :

“~OU” ue

There are, therefore, 36 “resistance derivatives” ifivolved which

are constants for the aeroplane and depend upon the arrangement

of surfaces and their presentation to the relative wind.

Fortunately, for reasons of symmetry, 18 of these derivatives
vanish, for example: X», Xp, Xr. We then write:

X=X,tuXytwxwtqrxe
M=M,+uMitwMwt+qZ,
Z=Z,t+UZytwZywt+qM,,
V=V,tvYotpYotrYr,
L=Ly,+vuly+plyt+rLly,
N = N, + vNy + PN p + rNr.

The above expressions are only approximate if u, v, w, etc., are not
small. .

The equations of motion for a rigid body having all degrees of
freedom, are:

xX

iP +wq—vr=X+T,+g sin(4,+86),
dv 1

ay + U +) wp ¥—g sin ¢,

OW +op—(U+u)g=Z—g cos(4,+8),
dhy —rh,+qh,=mL,

al

so — phs+ rhy= mM +hT,,

dh. =

ie —gh, +ph,=mN,

where
h,=pKim—qF —rE,
h,=qK3zm—rD — pF,
h,=rK¢m—pE—qD.

22 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

But the products of inertia (relative to moving axes fixed in the
body) D=F=0, because the aeroplane is symmetrical about the rz
plane. Substituting the above expressions for h,, h,, hz, in the
equations of motion, and neglecting products of small quantities,
we have:

adi) x anne dp. Ear
a =X+T7,+¢ sin(6,+8), Kit rr rig
& +Ur=\V+g sinysin(@,+6) —g sin ¢ cos(@,+ 4),
9 dq _ oa
aver aes M+hT,,
dw i eo eT dr ~E dp _
dt =—g=Z gcos(§+8@), Koa; m dt =)

If we substitute for X, Y, etc., their values from the expansion in
terms of the first powers of u, v, w, etc., and observing that from the
conditions of equihbrium,

M,+T,h=T,+X,+¢ sin 0,.=Z,—g cos 6,=0,
we will have, making sin ¢6=4, sin y=y, sin 6=6, and cos 6=1.

=uXutwXw+qXq+g6 cos %,
ae =qU+uZyt+wZwt+qZqt+ g0 sin 8,
se =—rU+vYyt+pYptrYr ty igen cos 4,
Ky =uM,+wMw+qMy,,
K o = ee =vLy+pLpt+rLr,
Kt —_ ee Sen een

We here assume 7, a constant, or that there is no change of pro-
peller thrust with small change in forward speed. With a motor in
‘“ free route,’ if the machine speeds up, the propeller tends to race or
to speed up so that the slip shall be about constant, and hence the
thrust is not materially changed. Since the forward speed (U+w)
is approximately equal to U, the thrust 1s approximately constant
and equal to 7).

We have also assumed that 7, lies parallel to the axis of x. At
very slow speed this is not exactly the case and 7, has a small vertical
component assisting in sustaining the weight of the aeroplane. At
high speeds, 7, is, however, usually parallel to 1 and the assumption

ee a i ti i ai cl a rm he aia a

e

NO? 5) STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 23

that it always is so parallel is here made for simplicity. In any case
T, is eliminated by the conditions of equilibrium. ;

In the present investigation the normal flight path is assumed
horizontal, or 6,=0. The product of inertia & is small for ordinary
aeroplanes with the heavy weights fairly symmetrical above and
below the axis of x. In view of the probable insignificance of / and
the fact that E cannot easily be determined for an aeroplane by
simple experiments, it is here neglected. In the simplified form the

equations of motion then are:

a = UX y 35 WK w Sa qXq a £9, ( Ia)
OY = qU +uZut+wZo+qZw (1a)
OY = — gp —rU+0V t+ PY tr», (1b)
Kae =yL,+pLy+rL,, (1b)
9 dq as
Ko aes uM +wM w» ar qM a, (1a)
L72 dr T T Ti
K oFe =vNy+pNo4+rN-. (1b)

It is seen that equations (1a) involve only the longitudinal motion
or motion in the plane of symmetry -vz of the aeroplane, since Pp, 7, v,
and # do not appear. Likewise, equations (1b) involve only the
asymmetrical motion, lateral and directional, and do not contain
6, u, w, and g. The two sets may then be considered separately, the
former on integration giving the “
latter the “ asymmetrical motion.”

symmetrical motion’’ and the

: dé : :
Since = =gq, equations (1a) may be written in terms of three

dt

variables u, w, and @ and their first derivatives. The “ resistance
derivatives” Xx, Xv, Xq, etc., are constant coefficients. The three
variables are each functions of the time, and the three equations at
any instant of time must be satisfied by a concordant set of values of
u, w, and 6. The equations are, therefore, simultaneous and .are
linear differential equations with constant coefficients.

Writing the operator D to indicate differentiation with regard to

time or @
dt’
(D—X,)u—Xww—(Xw+zg)6=0,
—Z,u+ (D—-—Zw)w— (Zqt ee
—M,u—Myw+ (Kz’?D?—M,D)6=0. |

(2a)

24 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

_ The right-hand members of these equations are no longer zero if
any wind gusts are assumed." The complementary function may be
found by the well-known “ operational method ”’ by algebraic solution
for D. (See: Wilson’s “ Advanced Calculus,” p. 223.)

The physical condition that the three equations shall be simul-
taneous is expressed mathematically by equating to zero the determi-
nant A formed by the coefficients of the variables u, w, and 6. Thus:

Ga ie eee at
A=) =Z,, D=Ze, 2(Z40)D) ~ \=o
—My, -—My, (K3D?—M,D) |

Expanding the determinant we obtain:
A,D*+B,D*+C,D°?+D,D+E,=0,
where for abbreviation :
Ate,
(3 = (Mi XK G+ Zs),
Fe |Z, U+Zq | Xu, Xq Nan ae
+ |Mw, Mg | Mw, Mg igh eb
|Xu, Xw, Xq : |
—|Zu Zan) U+Ze| 8196" Cosas
|\Mu, Ma, Ma a :
Au Xw, COS G,
B= — 62a, Zs Oy
| Mu, Mw, 0 |
The solution of the biquadratic A for D is of the form:
ID=0,05 46.40% as
6=K,e%+ K,e®*+ K,e*' + K,e%,
where K,, K,, K,, Ka, K;,.-..K,, are constants determined by initial
conditions. Solutions for w and w are similar.

The condition for stability of motion is that 6, u, and w shall
diminish as time goes on. Hence, each of the roots of the biquadratic
must be negative if real, or, if imaginary, must have its real part
negative. This condition for stability may be applied without finding
the constants K, to K,., by solving only the biquadratic for a, b, c, d.
Indeed, Bryan has shown that by use of Routh’s discriminant the
biquadratic need not be solved. The condition that a biquadratic
equation have negative real roots or imaginary roots with real parts
negative; is that A. 6,, C,, D3, 2, and-5 CC.) —A DA bebe
each positive. f

+K%

|

d

dD,

* Loc. cit., p. 1, §1, footnote 3.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 25

In a similar manner the equations (1b) defining the asymmetric
motion may be expressed as linear differential equations with con-
stant coefficients.

Substitute D*¢ for oe and Dé for pp.” Then:

(D—Y,y)v+(U—YV,)r+(g—YpD)o=0,
—Ly—Lrr+(K?D?—L,D)¢=0,
—N,w+(Ki{D—-N,)r—N,D¢=0,

Ag=A,D*+-5,D*+C,D*+D)D.)D+E,=0,

where:
igh ols as
B,= —Y,K(K,—K(L,—N,K%,
Co= —LrNpt+NrlLpt KolpVotNrV Ki t+ NURS
—(Ly Y» Kt +Ny YK ) ;

D,=Vy(LrNp—NrLy) +Lo(UNp+¢K%) —UL Ny

EAI i Vpleg— ea Yel LY ple NN oY plee)s
Ho=—o(N,L,;—L,N,).

As before, the condition for stability is that the real roots and real
parts of imaginary roots of the biquadratic be negative.

§1o. CONVERSION TO MOVING AXES, LONGITUDINAL DATA

-Horizontal flight at 0° incidence i of wing chord requires a
speed of 112.5 feet per second, or about 77 miles per hour (see the
characteristic performance curves). The normal attitude then has
the axis of + parallel to the wing chord and horizontal. The axis ¢
is vertical. For slow speed with an angle of incidence 7 of 12°, a
speed of 54 feet per second, or about 37 miles per hour, must be main-
tained. In this case, the normal attitude has the axes « horizontal
and z vertical, but the axes are entirely different from those used for
tlfe high-speed condition if they are considered with reference to the
aeroplane. The axis of y is, however, the same in both cases.

* Since we consider only the small oscillations, @ and ¥ are of the nature of
infinitesimals, and hence compound vectorially as do p and r. Professor
E. B. Wilson suggests the important implification of the treatment given by

Bryan or Bairstow due to making ae => and =r. They used angular

coordinates giving expressions for af and oe in terms of p and r and the

angles which are initially cumbersome but ultimately reduce to the simple
form here given.

26 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The aeropiane may pitch about its normal attitude. At any instant
the angle of pitch is the angle @ between the normal attitude axis of
ax and the new position of x. The axes, of course, pitch with the
aeroplane. The axes are fixed by the equilibrium conditions and
differ for each speed since each speed requires a different attitude.

x

ae = 4/40

\ fa N
g °
C2 gael
‘ ek
v \ 608
») g ‘

Ve SO tT ¥Od

er ee
oe

eee yo 77?
= (eee S| ia -/60 Q
Fo =22 D®* e* FEO AED SEO "SIO ie 7G) TIO ia
A7¢g/e otto g Borge “yva/ Zo A776 Biagle. 7,
Hic, 8=——X. Z, and Wf for1—o-
®

It was convenient to measure in the wind tunnel the lift and drift
on the model referred to axes always vertical and horizontal. The
corresponding forces along the moving axes x and g are readily
obtained from:

Z’=T1)c0s 6--D sin ¢,

X’=D cos 6—L sin 6.
Here L and D are pounds on model, @ is angle of pitch, and Z’ and X’
are pounds force along the moving axes. X’ and Z’ are then con-

Se a Ee

— cel ta ee a el

LS)
NI

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS

verted to full-speed full scale as usual and divided by the mass m in
slugs to obtain XY and Z in pounds per unit mass on the full-size aero-
plane at the proper speed.

. ie i:
SS
IN
CPS 7
: Li ore
KE |
RN oy
a NS :
Z| SON
\ 7X 7” AN,
¢ , 4
f|
\2 - I NnION
y \ s
9 sa) *)
Le C5 ILO
Fd
70

Bat (Fen Goo FES FI” CO FF ea” 7F*
DIP CE of Wiig € oral, €
J -2° -7° Of 4f° #e 7° 7¢#° 7G". 76°
A260? F179/E ©
Fic. 9.—X, Z, and M for 1=3°.

The pitching moment full size is obtained from the observed model
pitching moment about the center of gravity by an obvious manipula-

tion. The moment is expressed in pounds-feet per unit mass and
lettered M.

28 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

For this aeroplane we have, for example,

Soale Xor X

fO te FAO FS OS TO ire
Angle af Mig Coord, €
“6 ee Oe eT ee On
Ai7ele 77rg/e, ©
Fic. 10.—X, Z, and M for i=6°.

For this aeroplane we have, for example:

m=50 slugs, 6,=0,

U=—112.5 foot-seconds (high speed, 76.9 miles per hour),
1=0O, normal attitude.
a 6° xX Ze M
—4 —4 + 10.66 + I1.00 + 50.2
—I —I + 9.62 + 21.18 + 23.2
O O + 8.98 + 32.06 + 23.0
+1 +1 + 8.28 + 43.74 + 13.5
2 2 + 7.38 + 56.00 — 1.93
4 4 + 4.80 + 78.26 — 23.2
8 8 — 2.58 117.00 — 54.0
I2 TZ — 10.68 140.6 — 75.3
16 16 — 8.72 149.00 — 102.3

18 18 — 1.25 147.00 —158.2

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 29

ee a
sce Cease eee
Re i
ee WO +h
PSEC CEPTS
Ns No
EAA ie

+k0
VO. 116
oe
. <8
‘
3 ae
5 = as ed
>)
44
wo. 2
-#
“6° -2°) O° 7B 4K 46° 418° WO” HE HE HE” WB”
Airgle or LOG CLOT A, <
an ge te AIO” 8 6° =e ee OF pe 7 eG
Five? *Fag/E) ©
Fic. 11.—X, Z, and M for i= 12°.
U=—54 foot-seconds (low speed, 36.9 miles per hour),
¢,=0, t=12°, normal attitude.
1° @° xX Z M
—4 —16 +1.87 — 3.0 +11.6
O —12 + 3.58 + 68 + 5.30
+4 — 8 +4.84 +17.4 — 5.32
8 — 4 + 5.02 + 26.6 —12.5
12 O + 4.38 + 32.3 —17.4
16 4 + 5.24 + 34.2 — 23.6
18 6 +6.78 ae — 36.5
When 6=0, note that Z, should equal 32.2 a check on the

table.
Curves of X, Z, M for the four speed conditions are. given on
figures 8,9, 10, and 11. These curves are not “ faired,’ but drawn
3

30 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

through the experimental points to show the consistency of the
measurements and calculations.

§11. RESISTANCE DERIVATIVES, LONGITUDINAL

The longitudinal oscillations of the aeroplane are given by three
equations of motion of §9, in which certain “ resistance derivatives ”’
are required.

The quantity X, is the rate of change of X with change of forward
speed u. Since X varies as the square of the speed, X,=CU? where
C is some constant. —

Ox. eae 9 22 ee Ze
Then aU =a — Tr =X ail 2 i ar ee that these

coefficients are readily calculated.

The derivatives Xx, Zw, Mw» represent the effect of a vertical com-
ponent of velocity w. The vertical component of velocity w acts with
the horizontal velocity U to cause the resultant wind to have an
inclination to the horizontal

Ad=tany a = 57.3 a
when Aé is a small angle measured in degrees.
Hence
(Aa AX = 5b ieou AX “
Ww w U Ad -
= 57.3 AZ
Li OT Ag
ye Sea
Me= 8”

a : AX AZ AM

lhe method practically substitutes the slopes AG! RONG of
the tangents to curves of X, Z, M, at 6=0, for the actual curves. We
have assumed A@ small. If a curve be nearly a straight line, we may
substitute the tangent for the curve without great error. Thus it
may not always be necessary to assume AO very small. In fact, a
range of from 5° to 8° is tolerable.

Since we assume M/,=0, the balance should be undisturbed by
change of forward speed. Therefore, M,=0 in all cases.

Note that a positive value of 17» corresponds to a curve of pitching
moments giving statical stability or a righting moment. If My is
positive it does not necessarily follow that the aeroplane will be
dynamically stable, but if MW» is negative, instability is of course
certain. X, should be negative to indicate increased resistance for
increase of forward speed —u. For stability, Z. should be large and
negative, indicating increase lift for larger angles of incidence and
vice versa. At stalling angles, Z, tends to approach zero.

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 31

§12. DAMPING

The derivative M/, is the rate of change of pitching moment due to
angular velocity, or rapidity of pitching g. For a pitch of velocity
= =q, there is a moment of qM, tending to resist such pitching.
This is the damping due to the horizontal stabilizer, elevator flaps,
body, and all parts forward and aft of the center of gravity. The
pitching takes place about the center of gravity. The damping is
increased by a large tail and a long body.

The damping of a surface should depend on the area of the sur-
face, the moment arm of that surface, the linear velocity with which
it swings through the air (which varies also as the moment arm), and
with the velocity of advance. Thus: gMq~ql'U, where / is a linear
dimension.

If we can measure M, for the model at any wind speed, we may
convert it to M, for the full-scale aeroplane at its proper speed by
multiplying by the fourth power of the scale and the ratio of aero-
plane speed to wind speed. Naturally this is an approximate method,
but it is the best available since full-scale tests for M, are not
practicable.

Similarly NV, and Ly) may be obtained from model tests. These
refer to the damping of a yaw and a roll respectively.

In order to measure My, N,, and L, a special oscillator was de-
signed, shown in the photograph in figure 12. By setting the appa-
ratus to oscillate in pitch, roll, or yaw the corresponding damping
coefficients can be computed from the observed decrement. The pho-
tograph (pl. 1) shows the apparatus with model as used for pitching
oscillations.

iets

J=moment of inertia of all oscillating parts in slug foot units,
m'=mass of all oscillating parts in slugs,
M,=moment of air forces on model at rest,
M,=moment of springs at rest,
Ké=additional moment of springs when deflected,
c=center of gravity of entire apparatus above pivot, feet,
é=angle of pitch from normal attitude in radians,
a

Po =damping moment due to friction,
Ly = = damping moment due to wind on apparatus,

bn Ge =damping moment due to wind on model,

cm’6=static moment due to gravity.

32 SMITHSONIAN MISCELLANEOUS COLLECTIONS .VOL. 62

The equation of motion then is:

2
of a a5 (py + hw + pm) = a (K—cm’')6+M,—M,=0.
But /,= MM, by the initial condition of equilibrium. Let

=o + Pw + Bm 5

d26 dé
Hie i ae

The solution of this equation is well known to be:

= oi Zi IN tl pc

6=Ce\z cos | ty (Kem ) Tyas tah,

where C and a are arbitrary constants. If time be counted when the
amplitude of swing is a maximum, then cos{}=1, and 0=6,, the
initial displacement. Also if the number of beats be counted by
observing the times for succeeding maxima, a plot of amplitude on
time will have for its equation the simple form:

then

I + (K—cm’)0=0.

. ut
6=6e al.

The coefficient » is the logarithmic decrement of the oscillation and
must be numerically positive to insure that the oscillation dies out
with time.

The apparatus was fitted with a small reflecting prism by which a
pencil of light was deflected toward a ground glass plate set in the
roof of the tunnel. Nine lines spaced 0.2 inch were ruled on this plate.
With the model at rest the beam of light was brought to a sharp focus
on the line marked zero. By means of a trigger the observer started
an oscillation of the model, and the spot of light was observed to
oscillate across the scale. The time ¢ was observed in which an
oscillation was damped from an amplitude of 9 to an amplitude of 1,
for example.

Then: log, - = = t=log, 9, and knowing / and f, » 1s calculated.

Preliminary tests showed that the same value of » was obtained
whether the timing stopped at 0=5, 4, 3, 2, or I.

Oscillation tests were made at five wind velocities varying from 5
to 35 miles per hour. The coefficient » appeared to vary approxi-
mately as the first power of the velocity.

Similar tests were made with the model for no wind to determine
fy, Which may be said to be due almost wholly to friction and very
slightly to the damping of apparatus and model moving through
the air.

ei a i a ile sri

sta tae eee

aarti aa i ta te

4OOH NO 31VOS OL G31037430 LHD 40 WONA3d ‘Vv
SN431 310VLO3adS 71 “ALIAVYS SO YSLNSO LNOGV SNOILVITIOSO ONIHOLId HOS NOILISOd NI THQOW—"el “Sid

b "Id “9 “ON ‘29 “110A SNOILO31100 SNOANVIISOSIW NVINOSHLIWS

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 35

Likewise py» Was obtained by oscillating the apparatus without
model in winds from 5 to 35 miles per hour.

The coefficient y,, has the dimensions p/'l’, where p is density of
air, Ja linear dimension, and )’ the velocity of the wind. To convert
fm to M, for the full-size machine at full speed, multiply by the fourth
power of 24, the scale, and by the ratio of full speed to model speed.

The model is mounted in such a manner that the axis of oscillation
through the two steel pivot points passes through the assumed center
of gravity location for the aeroplane. The actual center of gravity
of the model is not considered.

Transverse arms carry counter weights by which the natural period
may be adjusted. The springs insure that the motion shall be
oscillatory. Knife-edged shackles bearing in notches in the trans-
verse arms carry the pull of the springs. The springs are not cali-
brated as the calculation eliminates the spring coefficient.

Friction is kept small by careful design. All pivots are glass-hard
tool-steel points bearing inside polished conical depressions of tool
steel. A convenient period for observation is 4 second. In still air,
the apparatus will oscillate.over 300 times before the amplitude 1s
diminished to 4 the initial displacement. The latter 1s about 3°.

Numerical results for the pitching oscillation follow:

sig: SOSCIELATIONS IN PITCH

Inertia, model and apparatus = .03945

Inertia, apparatus = .03680
APPARATUS
Wind velocity, miles per hour....... 30 20 fo)
PO rere cot Pen Gusts tes, aca ae 94.0 607.2 105
Gotan Oe ta ca he abies .OO172 .00168 .OOT54
Beg (MESS Aoi 0)) | aa aera eee .00018 .OOOI 4 O

APPARATUS AND MopeL, INCIDENCE oF WING, 0°

Velocity, miles per hour 35 30 24 18 8
Peseconds: 222.2 eee 15.5 ie 5 ZO 26.5 50
yh eee en a ee .OII2 .00994 .00828 .00656 .00348
PEE Ph eee 8S kk ays bs .OOI5 .O00154 .00154 .00154 .00154
Rae ge hs Pha sie eS eaes 3 .0002. .0002. .O0001I6 .O00I2 .00005

MMLC) cee one isk aw .00950 .00820 .00658 .00490 .o0189g

34 SMITHSONIAN MISCELLANEOUS COLLECTIONS

VOL. 62
APPARATUS AND MopEL, INCIDENCE oF WING, 6°
NVelocitye . hte s:eee: 30 24
Bi yo) ait ounces ciona Shu, taps fans 8 20 24
[iy Sid AE re pare eae 0087 00725
high. eaata eee ae ose 00160 00156
Pian li eacret aie oie eee ks 0002 0002
inn Cts eget reer 00690 00550
JOO lee
Sele eae
‘Dr -77¢
‘ ceed
= as
JO
i =
‘
\
\ 0 >
\ X
S
So
\ 40 x
;
, ae aa
<:
Z va XN
«<0 tH 2002 3
ae :
1) : \
Gr <3

S Ys Vo cor 2 eos Sa
Air Sbeetl SI (es Ler doer

Fic. 13——Curves for w (net) and ww for oscillations in pitch.

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 35

APPARATUS AND MOobEL, INCIDENCE oF WING, 12°

NelOGILY 2% ccxt 5 35 30 24 18 8 O

Bee 2s iaeg 2h) Gates 2236. 2500 S20 3b. Se -5.as 112
MIR ia, hp a Te ale .0074 .00696 .00600 .0049 .00314 .O00156
NEAR fes5i. 5 ice hapa 0016 .00156 .0016 .0016 .00T56 .00156
[1 SON wee ea ae .0002. .0002. .0002. -.000I_~=—.00005_—-.00000
PereCTLOL \ oe 0 isca: Fas .0066 .0052 .0042 .0032 .00153 .00000

Values computed as above for p», net, for the three cases are plotted
in figure 13. The points appear to lie along straight lines in justifica-
tion of the assumption that the damping coefficient varies as the first
power of the velocity of flight, To convert to full-speed full-scale,
we use the formula,

M,_= ie (26)4 | vecetty aeroplane

4

Velocity ace |

forz=0 , M,=(—)102.0=1.71U,
1=6°, Mg=(—) 03.7=1.43U,
t=12 Ma=(— ) 00.5 =F .12U..

The marked decrease in damping at slow speed must impair
stability. For the Curtiss Tractor JN2, with a somewhat shorter
tail, we found M,=1.32U at 1=2°, and My=1.66U at 1=15°5.
Bairstow found for the Blériot, My=1.84U at i=6°. We should
expect greater damping to be shown there, since the horizontal tail
surface is very large.

§14. LONGITUDINAL STABILITY, DYNAMICAL

We have now determined the resistance derivatives needed for
the three equations of the longitudinal motion in the plane of sym-
metry with the exception of X, and Z,. From a consideration of
various terms in the criteria for stability it is concluded that both
Xq and Z, enter into products which are small and relatively unim-
portant. They are consequently neglected.

The biquadratic has been calculated, following the formule given
above, for several speeds and attitudes of flight. The results are
summarized in the following table. The curves of figures 8, 9, Io.
and 11 were used to obtain the resistance derivatives.

36 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL.. 62

V miles per hour 70.9 53. 44.6 36.9
U, feet per seca —Vii2.5 — 78. — 65.3 — 54.0
Normal incidence 0° 2° Ge 12

aise ose ease _ 158 — {52> YTO4 =e 62
Kegon teat bas oetaee 4 3506 + .249 + °»# .245 O

Lh egy Ieee — 57 = 823. — {O85 «1 SS ait@
A ae eee = §:62 = 3277- — .2.92 — 1.0
IVES Ais aie ape 20 o faes +e 202 + 3.99 + 2.25 + 1.41
Aaa, eae lnm — 192.0 —123.0' — 93.7 — 60.5
VAG Ra Sark, See, 2126 BEG BEM 226
Be ee heaut does 217.0 207.0 TsO3 Sena
GAS Seer riers 1492.0 804.0 444.0 150.0
DD) aear cen oa past 260.0 128.3 7240 2a
POo® iS 50 Le eigeere eins 59.2 106.0 71.4 54.0
Routh’s: diser. .- HIIZ 410°) TOs4 410° “322 X10°) — 22) op
WN sar Ade eu 50 50 50 50
Long period, sec. BAL, 17.6 15.8 10.56
Time to damp, 50% Sea LTO ToL se
Time to double. nas ae Cree 2A,
Character. 242 .. Stable Stable Stable Unstable

The coefficients of the biquadratic computed from the formule of
Sg give for high speed
21.62D* + 317.0D* + 1492.0D? + 266.0D + 59.2=
Each coefficient is positive and Routh’s discriminant
BCD, A.D? BEE
is also positive and equal to 117x 10°. The motion is, therefore,
stable. The aeroplane if set pitching will return in time to its normal
attitude.

Bairstow has shown that, considering the usual values of the
coefficients of the biquadratic, it may be factored approximately,
giving:

(D as z Dat A. *) (De+ Foo =| D+ Zt) =o.
The first factor reduces to:
D?+14.75D+69.0=0,
D=—7.38+ 3.831 where i= V —1.
This is the well-known condition for a simple damped oscillation of
period,
27

—- = 1.64 seconds:

P= 3.83

* By interpolation.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS oi/.

and damped to one-half amplitude in time,
pa 809
7:38
For most aeroplanes, this first factor corresponds to a short oscilla-
tion so heavily damped that it is of no importance. Indeed, it could
not be observed on the actual aeroplane in flight.
The second factor, similarly, reduces to:
D? +.17D + .04=0,
D=—.085+.1811,

=0.094 second.

= *" —347 seconds
isi *
0.6

j— ne, = 8.1 seconds.
O85

This is a longer oscillation but heavily damped. The period of 34.7
seconds for the motion is great, and at high speed this aeroplane if
left to itself after an accidental longitudinal disturbance should follow
an undulating path with rising and sinking of the center of gravity,
together with pitching and periodic changing of forward speed.
There is an oscillation in u, w, and @. In 34.7 seconds, the aeroplane
runs 3900 feet, which is the distance from crest to crest of the flight
path. In one period the amplitude of the undulation is almost com-
pletely damped. It is unlikely that this motion would be uncom-
fortable to the pilot even if the initial disturbance due to a gust or
other cause were severe.

At high speed, this aeroplane is very stable compared with other
machines which have been tested. The natural period of the Curtiss
JN2 is about 34 seconds, damped 50 per cent in 11 seconds, according
to calculations made by us. A Blériot monoplane model tested by
Bairstow had a period of pitching of 25 seconds, damped 50 per cent
in 15 seconds.

There is no other published data of this character. It appears that
great statical stability or large M, will give a stiff machine with a
rapid period. Such a machine, though very stable, may be so violent
in its motion as to lead the pilot to pronounce it unstable. The design
tested here appears to have as easy a period as the Curtiss and Bleriot,
both considered very satisfactory in flight, together with greater
damping.

High speed and a long tail tend to damp the pitching. What we
aim to secure—namely, steadiness in flight—may better be obtained
by large damping factors rather than by strong righting moments
(statical stability). It is well known that the French monoplane pilots

38 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

demanded at one time a neutral aeroplane with no stability whatever
against pitching, on the ground that “ stable’’ aeroplanes were too
violent in their motion in gusty air. Another disadvantage of ex-
cessive statical stability lies in the tendency of the machine to “ take
charge ” and take a preferred attitude relative to the wind at a time
when such a maneuver may embarrass the pilot, as when approaching
a landing. However, it appears possible that a machine with the
minimum of “ statical’’ stability may be given the maximum of damp-
ing and so have a very slow period of pitching. The motion will be
nearly dead beat.

This digression with regard to damping vs. “ statical”’ stability
applies with equal force to the rolling and yawing motions of the
aeroplane to be considered under “ lateral stability.”

For low speed, 36.9 miles, similar calculations give for the longi-
tudinal motion

21.6D*+85.1D*+ 149.8D? + 22.1D+54=0.
Routh’s discriminant
B,C,D,—A,D/7—B,?E,=—12xX10*.. Unstable.
Short oscillation : |
D? + (B,/A,)D+C,/A,=D?+3.9)D+6.94=0,
D=—TOs= 1.773,

21
= = co SeConus,
Pe
f= 0-99 — 46 dto d : Stabl
=T95 3 second to damp 50 per cent. Stable.

Long oscillation : |
DD? CD, / C,— BE, /C?) DEE, /Ci=D* — 056). 260:
D= + .028+.594i,

27
=. 10.50 seconds:
P -594 P

f= 5, = — 24.7 seconds;

or +24.7 seconds will double the initial amplitude. Unstable.

At this speed Routh’s discriminant is negative, indicating that the
motion is unstable. The instability is seen to appear when the real
parts of the roots corresponding to the long oscillation become posi-
tive. The motion is rapid: only 11 seconds’ period compared with
35 seconds at high speed, and any initial displacement will double
itself in two periods. The damping of the motion has vanished and
although the increase of amplitude is not so rapid that there is danger

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 39

x

oO LO Ga FO LOT IO 60 LG ES: IO
Air Sheed. S71/es Ler (four

Fic. 14.—Routh’s discriminant, variation with velocity.

40 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

of the pilot’s losing control, yet it is clear that he cannot fly at this
speed unless he is alert.

Taking Routh’s discriminant as a measure of dynamical stability
we have its value +117X10° at high speed and —0.12x 10° at low
speed. Compared with the high-speed value, the latter is insignificant
and we may conclude that the instability at low speeds is of relatively
slight danger. Indeed, we may say that the aeroplane is stable at high
speed and about neutral at low speed.

The progressive change in Routh’s discriminant with speed is more
clearly shown on figure 14. On the same plot, we give a similar curve
for a Curtiss type tractor. The “ critical velocity ” for the Clark type
is about 40 miles per hour and 47 miles per hour for the Curtiss type.

All aeroplanes of normal type are probably longitudinally stable at
high speeds but lose this stability for all speeds below a certain critical
speed where Routh’s discriminant becomes zero or changes sign.

The examination of the longitudinal stability of the Blériot men-
tioned above applied only to high speed. The importance of investi-
gating stability at low speeds has, it is believed, never before been
shown.

The reason the stability of the longitudinal motion vanishes at a
critical velocity must be found in the approximate factor representing

the long oscillation.
Berd od) ae
Oey Clee ae

Stability vanishes where D,/C,=E,B,/C?, or where D,C,=E,B,. In
other words, stability is reduced as £,B, is made large or D,C, small.
At high speed we have 266 1492>59.2 x 317, but at low speed
22.1 X149.8<54x85.1. It appears that B, is smaller at low speeds,
which is desired, but D, and C, are reduced to a greater degree, which
is not desired.

E

The cause of the reduction in the magnitude of D, from 266 to
22.1 can be shown in the effect of change in resistance derivatives in:
| Xu, X ws Xq
D,=- | Zu, Lae U+Zq| = £
| Mu, Mw, Mg |

My, sin @
iG, Os 0, | :

|
For ),=0;.%9= 4, = Onwemlave
Ds = XuLwM 4- eo OM: + Lig rap lr:
The first term is reduced at low speed because 7, 1s less than 4 and
M, 4 of their values at high speed. Since U and My are smaller, the

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 4!I

second term is but 4 of its high-speed value. The third term is

unimportant.
From
Zak U = a ‘ . ;
CG = | Mo, Mg +X wl ls K Fal xX Zon =X ia )

we see by inspection that the principal reduction in C, at low speed
-is due to smaller values U, Mw, Zw, and M, which greatly reduce the
terms Z»M/,and UM». These two terms are the principal numerical
ones in the expression for C,.

In general, E, = —gZ,Mw will increase in value due to increase in
Z, and My, but the effect on the motion jis not great. On the other
hand, B, = —M,—K%3,(Xut+Zw) will drop rapidly for large angles
of incidence due to drop in MW,q and in Zy. This is favorable to
stability.

It is seen that the quantities U, Z», and M, preponderate in the
numerical values of the coefficients D,C, and E,B,. For ordinary
speeds, or speeds above the speed of minimum power, we have,
approximately,

D,=—Xul(ZwMq—UMw) + 2ZuXwMg= —Xu(ZwM_g—UM a),
C,=(ZwMqg—UMw) + XuMqt Ki XZ w— XwZu)= (ZwM_g—UM w),
B,= —M,—K3(XutZw) = —Mq—KiZw,

E,=—-gZuM yw.

The condition for damped motion then becomes :

D.C, >E,B, or (ZuM,—UMw)?>— Se ® Mw(Mg+K2Zw),
a
r a — Zo - arlwc G 4 . % -
where oo oe and W/, are nearly constant. Damping of the long

u 0

oscillation is then favored by large values of Zw, Mg, and U. That
is, by light wing loading, large damping surfaces, and high velocity.
As speed is reduced these quantities become smaller and the oscilla-
tion is less strongly damped.

For very low speeds, including those below the speed for minimum
power, the value of Z,, nearly vanishes and /, becomes small. Here
the approximate expressions would be written,

D,=XiwM wt ZuXwMg,
C,=—-—UM»w,
B,=—M,—K3(X14+Zw),
FE,=—gZ.uM w,

I|

and

= (3 M,,U + MX) oa (Mit K3(Xu +Zw) ).

=.0

42 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

For very low speeds, the quantity X» is often found to change sign;
therefore, the two terms on the left may be of opposite sign and a
large value for My, diminishes D,C, and increases B,E,. Ina “ stall-
ing ” attitude the aeroplane should have My, small, M large, and, if
possible, the radius of gyration in pitch Kg small.

The attitude of a “stalled” aeroplane is not ordinarily considered
a “normal” attitude of flight, but, unfortunately, an aeroplane is
frequently “stalled” by an inexperienced pilot. The longitudinal
motion of an aeroplane if held in a “stall’’ would be, in general,
unstable, but under favorable circumstances with Zq, Zw, Kz small
and Mw» large it 1s possible to have a stable motion. For example,
in an extreme case with 7, zero, if the aeroplane head up higher due
to large Xwy it slows down, loses lift and sinks. In sinking, My», if
large, will head the machine down, speed will be gained on the dive
and the resultant gain in lift causes the aeroplane to rise again. The
oscillation will not increase in amplitude with time if the machine is
able to respond quickly to the righting moment My». The damping
M, and radius of gyration Kg must not be’too large. If M, and
Ke are too large, the machine is dynamically unstable by having
PAC are

The question of safe flight at a stalling attitude is complicated by
the fact that the lateral controls become ineffective, but by manipula-
tion of the power delivered by the motor, combined with skilful use
of the rudder, an expert can land an aeroplane at surprisingly low
speed.

The period is given by the imaginary part of the roots, or

Tore
p= ee tt as
1 4Ea GS —BiE, is

Ne C2
—— 2 . . .

Since — Ss is usually small, we may write approximately,
1

a M,—UM
= w w Ga as a
san jf eZee G

p=tyfau (u— 2%),

At low speed, U as well as Z» and M, are reduced and the period
becomes short. A stiff machine with large M would have a rapid
period. For given speed, if we make M, large in order to provide
heavy damping, care must be taken that My shall be small in order to

then

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 43

secure a slow motion in pitch. It will be remembered that My» is a
measure of statical stability or “ stiffness’’ and was mentioned as
somewhat analogous to metacentric height for a ship.

By adjustment of Z», M,, and M, it appears possible to combine
heavy damping with a fairly long period and so obtain great steadi-
ness in normal flight.

§1s. CONCLUSIONS (LONGITUDINAL DYNAMICAL STABILITY)

Stability calculations are of greater interest when they can be com-
pared for different aeroplanes. At present, information is scanty but
we may obtain by inference some general conclusions by comparing
the Clark type aeroplane just described with a Curtiss type aeroplane
previously tested by us.

The two aeroplanes are designed to have about the same perform-
ance. The principal difference at first sight is the greater wing area
of the Clark—about 3.45 pounds per square foot against about 4.7
pounds per square foot for the Curtiss. In consequence of the ighter
wing loading, the Clark type should have a steeper curve of Z giving
Zw large, which is favorable to stability.

The Clark aeroplane has a smaller horizontal tail area than the
Curtiss, but the fixed part is inclined at — 5° to the wing chord against
—3°5 in the Curtiss. The Clark tail is only a trifle longer than the
Curtiss and we may conclude that the pitching moment due to air
pressure on the tail surfaces is about the same in the two machines.
However, the Clark model uses a wing section on which the center of
pressure motion for small angular changes is very slight. The
Curtiss has a section described as R. A. F. 6* in which this motion is
considerable. For equal tail moments we may then expect My to be
larger for the Clark machine. This is favorable to stability.

Due to the smaller tail, the damping of the pitching for the Clark
model might be less than for the Curtiss. However, we find Mz at
high speed —150 for the Curtiss against —192 for the Clark model.
The increase must be due to the greater wing area of the latter since
a calculation of the damping due to the tail alone gives a result less
than one-half that observed for the whole machine.

The greater stability of the Clark model at high speeds is then due
principally to greater values of Z,» and My. At low speeds, the
resistance derivatives of these two aeroplanes are not greatly differ-
ent. Both become very slightly unstable in their longitudinal motion.

1See Technical Report Advisory Committee for Aeronautics, 1912-13.

44 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The following table facilitates comparison :

Stable High Speed Unstable Low Speed
. ——————— ed ———————————————EE—EEee
Curtiss Clark Curtiss Clark
1 Tee 0° 14° 125
NGe ~ 128 — .158 — $222 — .162
Xie + 162. + 7356 ~ a2 O
Lae Noe — 557 — “57. — .993 — 1.19
We satan Gate — 3.95 — 5.62 - 555 — 1.0
Vig stone + 1.74 + 3.2 + 1.99 + 1.41
1 ee ee —150.0 — 192.0 —108.0 —60.5
Te tas cae te 34.0 210 34.0 21.6
Ae etna ae 34.0 21.6 34.0 21.6
Bait. 2 es, epZOOMO 3170 134.0 85.1
CS eae 834.0 1492.0 213.0 150.0
DD) hie o hes the LAO 266.0 28.0 225 i
| SS aE ee 31.2 5O.2 63.6 54.0
Routh’s discer. 18108 117 x 10° —.37Xi10® . = .12x108°
De SOG rca 24.0 BA. La5 1056
LPSECS a chanics 11.0 =. 8 — 24.7 —24.7
UL, “it<=seC aes — E55 —112.5 — 64.8 —54.0

We may infer in general that:

t. Any ordinary aeroplane is likely to be unstable longitudinally
below a certain critical speed.

2. Stability is improved by large wing area, 1. e., light load per
square foot.

3. Stability is improved by large horizontal tail surfaces.

4. Stability is improved by high speed.

5. Stability is improved by great head resistance or a poor lift drift
ratio. 3

6. Stability is improved by a small longitudinal moment of inertia.

7. Stability is improved by wings with slight center of pressure
motion.’

There appears to be no reason to depart from the normal type of
aeroplane in a search for longitudinal stability. A steady motion in
flight is to be obtained by careful adjustment of surfaces in the ordi-
nary type aeroplane, and the invention of freak types to accomplish
reat stability at the expense of speed or climb is to be discouraged.

Furthermore, the ordinary type of aeroplane may be made dy-
namically stable longitudinally without material sacrifice of desirable

oO
S

‘For a biplane combination giving a stationary center of pressure without
I y
material loss in other desirable features, see “ Stable Biplane Arrangements,”
by J. C. Hunsaker, Engineering, London, Jan. 7 and 14, 1916.

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 45

flying qualities, such as ease of control. In this connection it is im-
portant not to give too great statical stability. Safety in flight may
well depend more upon ease of control than upon stability. The
almost universal prejudice among accomplished flyers against so-
called “ stable aeroplanes’ appears to have a rational foundation.

PART II. LATERAL MOTION
§r. LATERAL OR ASYMMETRICAL TESTS

When the aeroplane is yawed to right or left of its course through
an angle of yaw y, the wind blows through the wings obliquely and
gives rise toa lateral force Y at right angles to the longitudinal axis +
of the aeroplane, a rolling moment L tending to roll the aeroplane
about the x axis, and a yawing moment N tending to yaw the machine
about the ¢ axis.

To measure the force Y and moments L and N as the aeroplane
yaws, the model was mounted in the wind tunnel and held at various
‘angles of yaw to the direction of the wind. At each position measure-
ments were made from which the component forces X, Y, Z and
moments L, 7, N could be calculated.

The details of the method are given in the Technical Report of the
Advisory Committee for Aeronautics, 1912-13, p. 128, where a de-
scription is found of the special apparatus required.

Briefly stated, the balance is arranged to measure the moments of
the air forces about axes parallel to those axes used for calculation,
whose origin is at the center of gravity of the aeroplane. A yawing
moment is measured about a vertical axis passing through the main
pivot of the balance. The moments of the drift and cross-wind forces
are measured about horizontal axes parallel and at right angles to
the tunnel axis and passing through the same point. In order com-
pletely to determine all forces and moments, a special fitting is pro-
vided on which three more measurements may be made. This moment
device measures the pitching and rolling moments about horizontal
axes passing through the pivot of the attachment. In addition, the
total lift or vertical force is measured on the balance. We then have
five moment observations and one force observation, as follows:

V », measured on vertical force lever (a lift),

Mz, measured on torsion wire (a yawing moment),
V p, pitching moment about a high point 0,,

Vr, rolling moment about a high point 0,,

Mp, moment of drift force about a low point 0,,
Mc, moment of cross-wind force about 0,5.

46 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

We first reduce to the origin 0, about which VP and |] # are
measured, which is / inches vertically above o,.

Denote by primes forces and moments in pounds and pound-inches
on the model for 30 miles per hour wind velocity referred to axes
through the point 0,. Then:

L’=V rcos 6—M;z sin 8,
M=Vp.
N'=Versin 64+ Mz cos 6,

X’=—Vrsin 0+4Mncosy—Me sin y—V rf © ©,
Ve Vre—Mccoswy—Mopsiny

= —Anaieee
2’ =Vrcos §+4Mncos y—Mesiny—Ve}

l

If the center of gravity of the aeroplane (model) be arranged to
have the y coordinate zero, and its x and zg coordinates a and b (in
inches) referred to 0,, we have for the axes passing through the
center of gravity:

X,=X’,

Y,=Y’,

Tae

a ete yas
M,=M'—cX'+aZ’,
N,=N’-aY'’,

where X,, Vi; Z,, L,, M,, N, are the quantities expressed in* pounds
and inch-pounds on the model at 30 miles per hour. Converting to
full-speed full-scale and to units of pounds and pounds-feet per unit
mass, we obtain the required X, Y, Z, L, M, N.

The model was first set at an angle of wing chord to wind of
0° corresponding to high speed. Measurements were then made
as above for angles of yaw of =25°, +15, =10°, +5 , 0°, keepme
the incidence constant. In reducing the observations, values for left-
and right-hand angles of yaw were averaged to eliminate errors due
to lack of symmetry in the model. In the first test the angle of pitch
@ is zero, and the axis of x horizontal. The test was repeated with the
model at angles of incidence of 6° and 12°, corresponding to the
intermediate and slow speed conditions. Here, again, 6 in the
formule of reduction is zero, since each new axis of 4 is also
horizontal.

It is apparent that the labor involved’in the complete solution for
X,Y, Z, etc., is considerable and, unfortunately, the method requires

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 47

the use of formulz in which the difference between products of ob-
served quantities is involved. Naturally, the precision of the result
is poor when we are left with a small difference between large
quantities.

The measurements |’r, Mz, V p, Vr, Mp, M¢ are probably correct
within 2 per cent. JL involves no difference and may be taken as
equally precise.

Since N,=N’—aY’ we may make the distance a very small in
setting up the apparatus and so keep the precision of N about 2 per
cent,

From

y= ae sin v
we note that (Wecosw+Jopsinw) is from three to five times as
large as x. The precision of Y should then be between 2 and 6 per
cent.

From similar reasoning, we may expect Z and X to be precise
within 10 per cent, but in special cases, where we must take the
difference of quantities of nearly equal magnitude, the precision 1s
not so good.

The quantity 1/ is a small moment which should be nearly zero if
the aeroplane is balanced properly. Obviously, no estimate of the
precision of MW as a per cent can be given in such a case. Where J/
is large, as in the 12° condition, the measurement is precise to about
£O -per cent:

Fortunately, for a study of lateral stability, we are concerned with
Y, L, and N only, and these quantities are determined with fair
precision.

The values computed for XY, Z, and M for zero yaw may be com-
pared with X, 7, M, determined independently in the tests on lift
and drift discussed in Part I. The latter are probably precise within
2 per cent. Consequently the computed Y, Z, and MW obtained from
the asymmetrical tests have been adjusted to make them agree with
X, Z, M obtained from the symmetrical tests.

The change of X, Z, and W/ with y is not important, and X, Z,
and M are not used in the theory of asymmetrical or lateral stability.
Since by our equilibrium conditions, the pitching moment 1/7, must be
zero for normal flight, we must assume that the pilot makes /, zero
by shght adjustment of his elevator flaps. In the tables below, the
small value of 1/7, observed when the angle of yaw y is zero has been

48 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

subtracted from the observed M for each angle of yaw. This adjust-
ment is required to give longitudinal equilibrium to the aeroplane
when in its normal attitude.

The following tables summarize the data upon which the subse-
quent calculations are based:

High-speed attitude, 7=0°, ]=26 inches,

c=6.37 inches, a= — 2.41 inches.

OBSERVED
y Vig Ve Mz Mp Mc Vr
O O 1.74 O 4.25 O .463
5 -284 1.74 .0333 4.41 511 -453
10 .518 1 72 .0474 A527 1-01 .450
15 - 704 1365 .0676 4.73 1.566 -445
25) 5222 52 .O851 5.43. -2.050 . 409

CALCULATED
y ae Z M y i N
G 4.0500 2 13252 O O O O
5 9.99 31.5. + 1.92 = 2.06 25.9 = 4.42
TO. 30572 21.2%). 95029 (=. 4.31 “4or2” eas
rs. 9.66 30:8 —15.37 — 6:74 54.0 ~=22%m
25 8.69 28.3 — 3.84 —12.23 66.9 -—47.4

Intermediate-speed attitude, i=6°, 1=26 inches,
c=6.67 inches, a= — 2.06 inches.

OBSERVED
y Vr Vp Mz Mp Me Vr
O O 3.84 oO 6.26 oO 1.061
5 .416 3.80 .OO41 6.39 .309 =—-1.046
10 770 3372 . 0090 6.50 .033° 2.51 021
D5 ie lme B22 .0054 6.62, " e173 .993
2 1.455 2.69 —.0128 FU 22 .891

CALCULATED
y XG Zz M Ww ic N
On 8209 93222 oO O O oO
Be 4.035 932507 e240 — .516 19.55 — 2.04
10 4.07 3150 — 4.6 — 1.124 34.1 — 4.43
To 4 Ansgar =, 190) - 438) ey oso4
25), AAON 42722 Oso — 3.97. 36.9 —18.6

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 49

Low-speed attitude, 1=12°,.1=26 inches,

¢=6.01 inches, @=—1.71 inch;
OBSERVED
y Vr Vp Mz Mp Me Vr
O O 3:73 Oo 9.395 Oo 61.483
be =e4o 9-71 == -0105. - 9-53 -094 1.464
10 .718 3.67 —.0541 9.61 259 1.441
15 1.059 3.52 —.0847 9.68 .464 1.402
oo 0705 3.27. —.1455 9.86 O17 ln27O
; CALCULATED
y x Z M y ie N
Oo V4.4 22.2 ©) O O O
5 4-5 31.7 oO = FAS eh G 05m 52753
TO. Y 4.40°+ 29.2 oO O57 -17s0 0.505
Poe 44s. 20.6 = 3-5 = 151 24079 — 9.35
25 4eld 23.1 O — 2.45 37.8 —15.85

The variation, with angle of yaw, y, of the rolling moment L, yaw-
ing moment JN, and lateral force Y, are shown by the curves of figure
15. In its symmetrical position, the aeroplane has no tendency to roll,
yaw, or slide slip, and L,, N,, and Y, are zero, as stated in connection
with the discussion of equilibrium conditions.

As the aeroplane yaws from its course, the plane of symmetry
swings through an angle y, measured positive to the pilot’s right
hand. The momentum tends to carry the center of gravity forward
in its original direction of motion. As a result, the apparent wind
seems to strike the left cheek of the pilot. The curves of N show
that, if this aeroplane yaw to the right, a negative yawing moment is
produced which tends to turn the aeroplane to the left and hence to
put it back on its course. The aeroplane is hence “ directionally ”
stable, having a preponderance of fin surface behind the center of
gravity, and the pilot need not use his rudder to stop the yaw. Nu-
merically, we see that for a yaw of 10° at high speed, the value of
N is —13.5 units, or about 670 pounds-feet. For a perfectly neutral
aeroplane, to produce an equal yawing moment the pilot must exert
a force of about 34 pounds on a vertical rudder 20 feet to the rear of
the center of gravity.

When flying straight ahead, if the direction of the wind suddenly
shifts so as to bring the apparent wind 10° to the left of the fore and
aft axis of the aeroplane, the aeroplane tends to head over into the
wind. An excessive amount of “directional” stability, indicated by

50 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOR. 62

a steep curve of yawing moments N, may cause the aeroplane to be
unmanageable in gusty air. It may “take charge” and, due to
excessive “ weather helm,” be difficult to keep on any desired course.

+ 70% O
+60 ee
+50 ae
+#0 ae i
aN
+J0 aN
3
0
+20 =/0")
N
v
4 1/0 -/k
:
oO q
8
ug
-/0
.
$
“£0
)

veloes ly A7 7p pee
veloa/s 7; F677 A Lo

6. H,
ed ae ;
O° = A 2 JO °

LG iO ZS
Mngles o* saw

“50

Fic. 15.—Curves of lateral force, rolling moment, and yawing moment, as
angle of yaw changes.

It will be shown later that the so-called “ directional ” stability is not
only undesirable in gusty air, but is the determining factor in “ spiral
instability.” Indeed, “ directional stability ” is very nearly incom-
patible with inherent dynamical stability in roll, yaw, and side slip
considered together.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 51

If the aeroplane yaw to the right, it is practically starting off on a
turn to the right. As is well known, to make such a turn safely an
aeroplane should be “banked” to such an angle of roll that the
centrifugal force, acting to the left, is about balanced by the hori-
zontal component of the normal force Z acting to the right. In other
words, the bank proper to a right turn requires a positive angle of roll

given by a positive rolling moment 1. The curves of L in the figure
show that for this aeroplane the natural rolling or banking moments
are positive for a positive yaw, and hence tend to bank the aeroplane
suitably for the turn. This property is extremely valuable in prevent-
ing capsizing.

As in the case of the yawing moments, an excessive amount of
natural banking may be uncomfortable, especially in gusty air. Thus,
if the wind shifts to the left, the relative angle of yaw is positive, the
aeroplane tends to turn to the left due to its “ directional” stability
and to bank for a turn to the right due to the natural banking or
rolling moment 1. The result may be to throw the aeroplane about in
a somewhat violent manner, or it may capsize. This motion is dis-
cussed later under the heading “ Dutch roll.”

Large banking moments / can be given by vertical fin surface
above the center of gravity, by a dihedral angle upwards or a
“retreat ’ or sweep back of the wings. All these arrangements are
probably equivalent and, though tending to give a stable motion in
still air, tend toward violence in gusty air.

The model under test has, as is shown by the drawings, a dihedral
angle upwards of the wings made by raising each wing tip 1.6°. This
amount of dihedral has been found in practice to be not excessive on
ordinary aeroplanes.

The curves of lateral force Y are negative for a positive yaw. This
means that if the aeroplane yaws to the right in still air, it is pushed
to the right and started off on a right turn. We saw above that the
natural banking is suitable for the turn. In gusty air, if the apparent
wind shifts 10° to the left the lateral force pushes the aeroplane to
the right.

Numerical values are interesting. Suppose a pls yaw of 10° in
still air. The rolling moment at high speed is 2,000 pounds-feet.
This is equivalent to a down load of 55 pounds on the right aileron
and an up load of 55 pounds on the left aileron. The pilot with his
aileron control can, if he wish, produce a rolling moment over three
times this magnitude, so that he can prevent the aeroplane taking
charge and hold it level. Approaching a landing, it is most important

52 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

that the aileron control shall be very powerful compared with the
natural banking tendency. Excessively stable aeroplanes may be
really dangerous to land in gusty air. In any aeroplane design, the
relative magnitudes of the natural rolling moment and the aileron
control available should be carefully considered.

If the aeroplane side slip with a lateral velocity v, the resultant
velocity of the center of gravity of the aeroplane is obtained by com-
bining v as a vector with the forward speed U. The apparent wind
in still air is then inclined to the axis of the aeroplane as it would be
were the aeroplane yawed from her course by an angle

= Se
—y=tan ie
A side slip to the left is equivalent aerodynamically to a positive or
right-hand yaw. The sign of the lateral force Y is negative for a
plus yaw and hence resists the side slip, as is desired.

The asymmetrical motion is a combination of rolling, yawing, and
side slipping as is indicated by the qualitative discussion given above
and by the equations of motion in Part I, §9. In order that, under
the influence of N, L, and Y, acting in concert, the disturbed motion
shall be stable, the aeroplane must tend to return in time to its original
attitude. It is impossible to determine whether the aeroplane is thus
stable from a consideration of N, L, and Y separately. - The term
“ directional stability,” frequently used, means very little with regard
to the probable motion of the aeroplane.

The quantitative determination of the stability of the motion can be
made only after we have found the numerical values of the coeffi-
cients needed in the equations of motion in Part I, §9.

§2. RESISTANCE DERIVATIVES

The rates of change of N, L, and Y with velocity of side slip v are
the partial derivatives Nx, Ly, Yy. The side slip velocity wv is equiva-
lent to an angle of yaw yw given by:

v

U ”

If y is small and measured in degrees, the tangent is equal approxi-
mately to the circular measure of the angie, or

tat

ey ee
i B78
and

Teo U Ay’

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 53

The fraction is the slope of the curve of N plotted on angle of yaw

w as abscisse.

Similarly : ae 57:3, AL
U Ay
and ;
Virssi= San Ay

a U Ay

Taking the slopes of the curves of L, N, Y at y=o from figure 15,
we obtain the following “resistance derivatives” needed in the
lateral equations of motion.

High speed:
( Y»=—.204,
40°) L5= +306,
| N= — 449.

Intermediate speed:

7y= — .0878,
1=6°2 Ly =+ 3.44,
oes
Slow speed :
Geek
4=12°2 L,=+1.01,
| we= 53

Note that these derivatives do not change greatly with speed. In
the longitudinal motion the effect of change of speed (attitude) was
more marked.

§3. ROLLING MOMENT DUE TO YAWING, Lr

It is obvious that if an aeroplane yaws quickly, the outer wing tip
moves through the air more rapidly than the inner wing tip and,
hence, due to the spin, the lift on the outer wing is the greater. The
resultant rolling moment tends to bank the aeroplane suitably for the
turn. The magnitude of this rolling moment was in dispute in the
recent Curtiss-Wright patent litigation. The following calculation
leads to a simple formula to determine the roll due to angular velocity
in yaw.

In our notation, a rolling moment L is expressed in pounds-feet
per unit mass. In pounds-feet on the aeroplane, the moment is mL.
where m is the mass W/g in slugs.

54 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

The derivative L, is the rate of change of rolling moment with an
angular velocity in yaw of r radians per second, or

OL
ara =i.
Let U=the velocity of advance of the center of gravity of the aero-
plane in feet per second. U is a negative number.
S=span of the aeroplane (one plane) in feet.
b=chord of one plane in feet.
W/g=m=mass of aeroplane in slugs.
y=angular velocity of yaw in radians per second, positive for a
right-hand turn.

Consider an element of wing area on the left wing of width dy in
the y axis and depth b in x axis. The distance from the center of
gravity of the aeroplane to the center of this element is y feet, positive
for the left wing.

The velocity through the air of this element is U—vyr, since the
increase of air speed due to spin is‘yr.

If we assume that the lift of the wings is equal to the weight of the
aeroplane, we neglect the small vertical forces on body and tail only.

The lift in pounds per square foot per foot-second velocity is the
usual “lift coefficient’ for the wing, which can be computed from
the model tests for Z. Thus:

Where:
A= 2065, the total area of both wings.

Then the lift in pounds on the elementary strip of wing of area

bdy is
Kbdy(U—yr)?.
The rolling moment on the aeroplane of this elementary lift force is
Kbydy(U?—2Uyr+y’r"),

and the total rolling moment on one whole plane is,

Kb ie (U?—2Uyr+ yr?) ydy.

But |’ oytay=1, the moment of inertia of the area of one plane,

and

S

l U?ydy=0= E y*dy.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 55
Hence the rolling moment on one plane is —2U/K/r, and substitut-
ing for K its expression above,

5 Z,m
AU
For two identical wings of rectangular form, we have for our com-

plete aeroplane a total rolling moment in pounds-feet per unit mass:

Ir.

—— aus r, making Z,—¢,
= = gs? for horizontal flight
a. 6U Cc S .

It appears that L, can be made small by short span and high speed.
The sign of L, 1s such that the bank is proper for the turn.
Numerically, we have, making the mean span S=40.2 feet and
D=5.62 feet,
L,= —8660/U,

=+77.0, high speed, +=0°,

='+-132.5, intermediate spéed, 1=6°,

= + 160.0, slow speed, 1=12°.

Note that 1, (which is unfavorable to “spiral” stability) becomes
larger at low speed.

§4. YAWING MOMENT DUE TO ROLLING, No

When an aeroplane rolls with an angular velocity p radians per
second (positive when right wing goes down), an elementary area of
the right wing has its angle of incidence increased and a correspond-
ing element of the left wing has its angle of incidence diminished by
the same amount.

If p is small, the resultant air velocity at a point y feet from the
center line is

V U?+ p*y?=U, neglecting p?. .
On the right wing, the angle of incidence at any point is increased by
a small angle a, given by tana=py/U. Due to the greater angle of
incidence, the head resistance of the element is increased.

On a curve of the “ drift coefficient’ for the wing shape (see
fig. 3, Part 1) we may draw a tangent line at the point on the curve
corresponding to the angle of incidence for normal flight. For small
changes in incidence from normal incidence, we may substitute this
tangent line for the actual curve without material error. The value

50 ' SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62
of the drift coefficient in pounds per square foot per foot-second is
then

K

Ly

=k ge Os

where K,, is the coefficient when 7 is the normal angle, o is the slope
of the tangent line and « the small change in incidence defined above.
The slope o is conveniently measured in units of Kz change per degree

angle. If the subtangent or projection of the tangent line is 7 degrees,
ee
/

and
1 eee ;
The head resistance of an element of the right wing is
~bdyK,U?=— (K.,+ ee | bdyU?,
and the yawing moment on the aeroplane due to it is
+(K,,+K,, 4) bU*ydy.
But tana= fp OF a=57.3 ie , if a is small. Then the total yawing

moment on a single plane is
(. ( a *) bU?ydy.

The integral of the first term is zero, and the second term reduces to
oe VS
* I
where J is moment of inertia of one plane. For a biplane of two
rectangular wings, the total yawing moment in pounds-feet is

mN — sas UK ,,bS* P

6)
Elence:
a — 57:30 in bS2
Np 6jm :
To calculate N,, we have:
i U Kay j b Ss m Np

O bi2)5 Sed 00° 5.62 40.2 50 O
6 ee 3 Roouie 6.0 5.62 40.2 50) (33-5
I2 — 54.0 .0001047 6.9 5.62 40.2 50 +57.0

Since U is feet per second, K,;, must be in pounds per square foot
per foot-second velocity. Values for the drift coefficient were taken

~—

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 57
from a curve corrected to apply to full-speed full-scale, aspect ratio 7,
and biplane of gap 1.1 times chord.

Note that the positive sign of N, indicates that for a positive roll
(to the right) a yaw to the right is assisted. At high speed the aero-

plane flies at a small angle of incidence where the drift curve plotted
on incidence is about horizontal. JN’, is, therefore, zero at this attitude.

§s. DAMPING OF ROLL, Lp

The wide spreading wings very effectively damp the rolling, and
the resisting or damping moment in pounds-feet on the aeroplane is
mpL», for an angular velocity p radians per second in roll.

The method of oscillations previously used to determine the damp-
ing of the pitching M, is applied to determine Ly. Figure 17 (pl. 2)
shows the oscillating apparatus set up to impress an oscillation in
roll about the center of gravity of the model.

Using a similar notation, the equation of motion of the complete
apparatus with model is

1 &# + (Aytrwtn) 5? + (KC!) 6+M,—M.=0.
Where A, represents damping due to friction, A» due to wind on
apparatus, and A, due to wind on model. The moment of inertia of
the entire oscillating mass J is found by a simple experiment.

The solution for points of maximum amplitude is of the form

_At
p= Hoe 21,
or
At i.e
21 = log, : = log, Q,

since the ratio ®° is arranged to be as 9 to I on the scale for the pencil

of light.
The numerical work follows:

OSCILLATION IN ROLL

Po

I model and apparatus = .0399, rs =9
I apparatus =3.0373
Test oN BArE APPARATUS
Veewane welocity, miléSieo.. oc. <0 30 20 oO
PSE COUMGS Open hte ie oc sls go's dias 2 608 78 98 197
PI Re a 5 dea 5 Gb won wa HRT .0021 .OO168 .00083

Due LESS ASCO) a, ae ere .OO13 .00085 oO

58

Sealed faet/

© Ye! (elle 1° \<,

Fic.

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

TEST ON APPARATUS WITH MODEL

INCIDENCE OF WINGS 0°

35 30 24 18 6.8 O
Tents 6.0 823 I2 30 175
.024? .0292 .O2II .O146 .0058 .OOI
.OOI .OOI .OO1 .OOI .OOI .OOI

= ZO we eo ON eee
eee CV) (0.3 2 6 r Your

16.—Curves of damping coefficient for rolling.

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SNOILO31100 SNOANV11S0SIN NVINOSHLIWS

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 59

INCIDENCE OF WINGS 12°

[a ge a aaa 35 30 24 18 oO
pee aS aera 6.5 8 II 14.5 175
A dis Rue einge ane ence .027 .022 .O16 .O121 .OOI
NEC rage te ior asi'e “glia see v= .OOT .OOI .OOI 2001 .OOT
WRI i ee is or D2 .OOI .OOI .OOL .OO1 O
NMR eer to eo ohsge iste 08) 5 025 .020 O14 .O1O0 Oo

The values of A,» due to wind on apparatus are taken from the curve
of A» on figure 16 and applied in the calculation to find A,, net. Figure
16 shows the values of A,,. It is obvious that the values of A» for i=0°
at 35 miles per hour is grossly in error. This point is, therefore,
rejected.

The curves of A,, appear to increase more rapidly than the velocity :
in fact, a plot on logarithmic paper shows that over the range of wind
tunnel speeds A, varies approximately as ]/1:*°,

Since this damping helps to stop violent rolling, we shall be on the
safe side in our stability calculation if we assume that the damping
varies directly as the velocity.

To convert Am to full scale, we have

eee a
m V in
Where /’,, is the speed at which 4,, was measured. Taking the scale
factor 26, m=50 slugs, Vm=30 miles, Y’=76.9 miles for 1=0°, and
V =36.9 miles for i=12°, we have
Lp= —631=5.61U, for high speed,
Lp= —224=4.15U, for low speed,
and for the intermediate speed, by interpolation,
L=—=3219=4.80U0.

. Am .

§6. DAMPING OF YAW, Nr

The damping of an oscillation in yaw is probably due to the long
body and vertical surfaces at the tail, as well as to the wings. It is
not practicable to compute this, and we have employed the same
apparatus as before to determine the damping in yaw by the method
of oscillations. The model set for the oscillation in yaw is shown on
eure 18 (Cpl. 3).

The equation of motion is cal to that for roll and pitch, thus:

poe + (1 +r +9m) F H+ (K—em Vit Ma =o,
and

pene, or log, #9 =. 9

60
Vo ee
BE Se ooh
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Uap woneaet ste
Pig cee tae
hie ses crea Se
Lepromonata’ ater scat aatentslers
Ue eee Reena
Washes ean Petia
Wap hee one) caske.ie to ocetete
Uae ec de CAM martha
Vane Tota ens fais carlos
ban caren och es
Ver greens a ,aeehebene. ete
Vara tansus, = Wee voiteshs eke
Pig anavaue use stoner © 6.6
Vit ccs cate teieteastere-
awe
bo aes
Ve Saree ts
Yo
Vege eotae
Vargas el ete

SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

OSCILLATION IN YAW

I model and apparatus = .0396
I apparatus 043

Test ON BARE APPARATUS

Es 20 0
29 LOS I15 120
-« sOOT4 .OO131 .00126
<2 sO0OT3 . 00126 . 00126
xp HOOOL . 00005 oO

Test oN APPARATUS WITH MODEL

INCIDENCE OF WINGS 0°

35 30 24 12
52 57 64 LOSE
.00335 .00306 .00272 .00166 ?
. 00126 . 00126 . 00126 . 00126
. 00013 .OOOTI . 00009 .00004
. 00196 . 00169 .00137 .00036 ?

INCIDENCE OF WINGS I2°

35 30 18 8
33 36 47 73
.00528 .00484 .00371 . 00239
. 00126 . 00126 .00126 .00126
.OOOT3 .OOOII . 00000 . 00003
.00389 .00347 . 00239 .OOTIO
INCIDENCE OF WINGS 6° 7
Ser 1 825 30 20
= SAO 53 7a
-= 400370 . 00329 .00245
. 00126 . 00126 . 00126
Le OOOTS .OOOII . 00007
.. .00240 .OO192 .OOII2
267
Daan Te

N-=.35U =—390:4, fori=o0;,;
Nr=.398U=—260, for1=6°,;
N,=72U. =—=380, f0ori=i12

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NO. 5 STABILITY OF AEROPLANES--HUNSAKER AND OTHERS 61

The curves of v», of figure 19 show that the damping of the yaw
increases with speed approximately as the first power. The damping
of yaw N, is in magnitude only about 31, the damping of roll Lp.
Consequently, the precise determination of NV is attended with some
experimental difficulty.

It is to be noted that N, diminishes with the velocity, while at the
same time it increases with the angle of attack. The value of N, at

LDar7Zb/tag Co

yor b 6-47

°

°

5S uP 3
et) 2 6 07k

oo/6
>
.
x oo/
o: F
X x
_GO/# soak
‘
4
ue: SEE
\ core L \ 8
N eo -Vro X 8
4 v8
= ce wi ’
1 v
v
: 4
0006 $
ha ¥
3
PGIO¢F ee .0O/ 0002 s
~ :
: u
ooo2z eae g00f N
y
La oO. og0°

oO 7 sO YD MLO 25 “FO 22 FO
Ar S4ee/ SU (2s A ia SIovor

Fic. 19.—Curves of damping coefficient for yawing.

high speed .35U is practically equal to its value at low speed .72U.
It seems reasonable to expect that at large angles of incidence the
damping of yaw due to the wings would be much greater than at
small angles were the speed the same.

For the intermediate speed i=6° the coefficient NV, is least. This
is due to the fact that from 0° to 6°, U drops from —117.5 to —65.3
feet per second, while from 6° to 12° U drops very little more: only
from —65.3 to —54 feet per second.

5

62 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

§7. NEGLECTED COEFFICIENTS

The changes in laterai force Y due to angular velocity of roll and
yaw, represented by the coefficients Y, and Y,, are neglected as un-
important. The surface of the aeroplane is fairly symmetrical about
the center of gravity and it is unlikely that any appreciable lateral
force could be created by any small angular velocity p or r. In the
calculations to follow Y, and Y, are made zero.

The products of inertia are also neglected as not important and
difficult to estimate for an actual machine.

§8. INDEPENDENCE OF THE LONGITUDINAL*AND
LATERAL MOTION

It is seen on figure 20 that the values of X, Z, and M are some-
what changed as the aeroplane yaws, and to this extent it is not strictly
correct to consider the lateral motion separately. We may imagine
that if there be set up a combined oscillation about the flight path in
roll, yaw, and side slip, the aeroplane will be influenced to take up an
oscillation in pitch of the nature of a forced oscillation. However,
any oscillation in pitch has already been shown to die out rapidly
(since the longitudinal motion is stable and strongly damped). We
may then consider the pitching induced by yawing, etc., as of the same
nature as that caused by any accidental disturbance of longitudinal
equilibrium, such as might result from gusty winds, shifting of
weights, or the firing of a gun. If the longitudinal motion be stable,
that stability should be quite independent of the nature of any dis-
turbing agent which gives the initial amplitude to the oscillation, pro-
vided the phenomenon of resonance is not present. That is, if the
natural period of the lateral motion, if oscillatory, happen by some
remote chance to be equal to the natural period of the longitudinal
oscillation, it may be possible for a machine which is unstable laterally
to seriously compromise its longitudinal stability.

If the lateral motion be stable and, if oscillatory, damp out quickly,
it is difficult to see how any marked disturbance of the longitudinal
motion can be induced by the lateral motion.

In circling flight, there is a constant angular velocity of yaw and
probably some side slip. In this. case, the lateral and longitudinal
motions are interdependent, and the methods of calculation of this
paper will not apply. Indeed, we should have to combine the six
general equations of motion giving rise to a single equation of the
eighth order, which must then be solved for all the roots. In the

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 63

present state of our knowledge, the calculation of the stability of
circling flight appears impracticable.

mo

[iit Py Tk

Wy

rh |

=

NX
PS

WGeal/e “or 4/7
&
Q
x

I
ch
/

tA |

Sib
Pie eA

BN | Sea eral

\
9
270" FO \
ee poakeect ;
le/0 4/ TARP,
- z 6
a 7 ve/oa as7y FS. La 0)

x
CRA

oes

oe

LAL

> S

“Ae ag
ae
coe
ive
iN

=

or Mae Ve SS? woe
A779 (OS OF yaw

Fic. 20.—Curves of normal force, longitudinal force, and pitching moment as
angle of yaw changes.

For flight in a straight line, we may reasonably conclude that if the
lateral motion be stable it will not compromise the stability of the
longitudinal motion, and vice versa. Such a machine should, in still

64 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

air, follow its trajectory without the aid of the pilot. In gusty air, it
would roll and pitch and yaw as well as side slip and rise and sink,
but, if the altitude be great, there should be no danger. The machine
would not follow a fixed course, if controls were abandoned, but
would adjust its trajectory constantly to the changing conditions of
the air in an effort to maintain the same relative velocity through the
air and the same angle of incidence.

On the other hand, if the lateral motion be unstable and the angle
of yaw become as great as 10°, the curves of figure 16 show that the
head resistance X is not greatly changed for slow-speed attitudes and
increases but 10 per cent at high speed. This should tend to slow
down the aeroplane very little.

The change in Z, or lift, is insignificant.

However, the change in M is most interesting. For 1=12° no
change in M is produced by yaw, but for =6° a small diving moment
is induced. For an angle of yaw of 15° or more, this diving moment
is enormously increased. For i=6°, y=15°, mM =37X50=1,850
pounds-feet, corresponding to a force on the elevator of nearly 100
pounds.

If the pilot attempt to turn without banking he may side slip so
rapidly that he has the relative wind making an angle of 15° to the
longitudinal axis of the aeroplane. The aeroplane will then tend to
dive sharply. Similarly, an excessive bank may induce a side slip
inwards and the same tendency to nose dive. The cause of this
tendency to nose dive shown here is not understood, but it is signifi-
cant that many accidents have occurred to inexperienced pilots in
turning.

. $9. LATERAL STABILITY, DYNAMICAL

The combined asymmetrical motion in roll, yaw, and side slip will
be called “ lateral.’’ For simplicity we will consider horizontal flight
in a straight line in still air, and for this condition investigate the
character of the disturbed motion.

From the detail plans, the radii of gyration K4 and Kg have been
calculated. It is assumed that these values are not appreciably
changed by change of axes corresponding to the changed attitudes
proper for different speeds. K,4 and K¢ as given are referred to the
axes used at high speed. The products of inertia are neglected as
unimportant.

From Part I, $9, we obtain the following simplified formule for
the coefficients of the biquadratic equation which is characteristic of

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 65

the lateral motion. The quantities }’,, Y,, 6 are made equal to zero.
Then: .
A,D*+B,D°+C,D?+D,D+E,=0.
Where:
oi
B= — Y,KKY— Kol, — KiNy:,
C= (NrLp—LrNp) + Yelp K+ Ki(NLU+N-Y2),
D,=—Vv(NrLp—LrNp) +U(NplLv— Nol) + 2 KCL»,
E,=g(N.L+—LN,).

These coefficients may now be calculated from the known constants
of the aeroplane, and Routh’s discriminant, B,C,D,—A,D,?—B,°E,,
found. The condition that the motion shall be stable is that A,, B,,
C,, D,, E, shall each be positive as well as Routh’s discriminant.

The numerical work is laborious and the results only are given in
the table.

COEFFICIENTS AFFECTING LATERAL MOTION

High Intermediate Low
speed speed speed
Pmole OF incidence, 1... 5 44 - om 6° 12°
Welacity, ut-sec, Ul... sees. —I112.5 — 65.3 — 54.0
MASS SWISS: Pticowcd:: iin's aise 5 os 50.0 5Os0 50.0
ON a Bach Bric vashen ce 2 wing ce tse 6 5-2 Bae Bee
Pe tomate ese vse’ 3 6.975 6.975 6.975
aa t alee stecasas So etianse ft Bb di 2s — .204 — .0878 — — .106
Se 2 tele cook ta an tae eebeianci okie + 3.06 + 3:44 + 1.91
IN gists to 2 Sr se — .449 — 351 — u5a
MRE Ita, wom PG Gen tin 65 O O O
eee ite fie a laa ge 3s — 631.0 — 319.0 — 224.0
EME sila ie Pot ig, BCS bw, S55 Se O + 33.5 + 57.0
NEE iat iss 62 See S29 = ae O O oO
Pa a Geb ae ss + 77.0 +132.5 +160.0
ee et her testes gs Ge we 5.62 — 30.4 — 26.0 — 38.9
EMD Sees le Sid. ge 3 oon as 1310.0 1310.0 131020
MMe ARs Ne rare ao sc09e 3+ 2, 3 31830.0 16350.0 12090.0
(CAD aera eae ee 2274.0 5910.0 1630.0
POEM ee Ore heresies ek habe 43 41780.0 5490.0 3490.0
Pe fe og Sg ooh ay Bo Sys 2770.0 1386.0- — 335.0
Peete — Ae Babs eee 3 37400 X 10° 122 10: 227 M10"

Gharacter of motion........ Stable Stable Unstable

66 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

It is seen that, for the particular aeroplane under consideration,
Routh’s discriminant and the coefficients of the biquadratic are all
positive at high and intermediate speeds. The motion in these two
cases is, therefore, stable.

At low speed, however, we observe that E, becomes negative,
indicating that the lateral motion is unstable. That is to say, one at
least of the roots of the biquadratic increases with time. In this case
Routh’s discriminant continues to be positive, but is small compared
with its value at high speed.

It is unfortunate that this lateral instability is associated with the
longitudinal instability which was found in Part I to be present at low
speed.

§1io. CHARACTER OF LATERAL MOTION

Bairstow has shown that for the usual values of the coefficients of
the biquadratic equation for the lateral motion, the equation in ques-
tion may be factored approximately, giving:

fe Bie ALC, Co Ee BSD: aA
(D+ pe) (D+ “age ) (Bit (BP pt) P+ pe = AC,) =°
provided F, is small compared with B, or D,, and B,D,—C, is small
compared with C,?.

In our cases, the second condition is not satisfied but the error made
is found by trial solutions to be unimportant.

High Speed.
Thus for the high-speed condition :

First factor, D= — [a 0665.
D,
This is a subsidence which tends to reduce the amplitude of an initial
disturbance to half value in t= - oe. = =10.4 seconds. We may con-

sider this motion fairly stable.
For the second factor we have another subsidence given by

ae Spe eae, SS aay
= TAB. == 23.2,

‘ : 0.6 a .
which reduces to half value in t= = 2 =.03 second. Such motion
23.2
is so heavily damped that it would never be observed on the aeroplane.
The third factor oS upon substitution :

or

D=—.484+1.071.

a a iain te te al,

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 67

This is a ae of imaginary roots indicating an oscillation of natural

period p= To = 5.9 seconds, which is damped to half the initial
amplitude in t= a =1.4 second. The motion is so heavily damped

as to be of no consequence. The period is fairly rapid, and if the
damping were not great, the oscillation might become uncomfortable.

For the high-speed case, it appears that the lateral motion is quite
stable.

Intermediate Speed.
At the intermediate speed, where 1=6°, we have for the first factor:
D= = 252,
a subsidence which damps to half amplitude in
0.69

-254
This motion is very strongly damped, even more than at the high

speed.
Similarly, the second factor gives an enormously damped sub-
sidence.

i= = 2.72 seconds.

D=—12.1,
0.69
f= =.057 second.
on 57

The oscillation corresponding to the third factor is of fairly slow
period, but so strongly damped that it is of slight importance. Thus:

’ D?+.11D+.346=0,
D=- oe
p= - 586 =10.7 seconds’ period,
i= 06 = 1.25 second to damp 50 per cent.
Slow Speed.
For the slow-speed condition, i=12°, we observed that the coefh-

cient E, is negative indicating instability of motion. Mathematically,
that is to say, the real root corresponding to the first factor of Bair-
stow’s approximate method,

E
= 22800,
ere
is now no longer a subsidence, but a divergence which doubles itself
ne — 22 =7.2 seconds. This is not an alarming rate of increase,
09

since 7 seconds should be ample time for a pilot to observe a devia-

68 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

tion from normal attitude and to correct it by use of his controls.
However, the aeroplane could only be flown at this speed even in still
air provided the pilot were alert.
The second factor is a strongly damped subsidence D= —9.12,
which damps to half amplitude in .08 second.
The third factor is an oscillation,
D? + .231D+.292=0,
D= =~ 16 5287,

having a period of ,= 12 seconds, which is damped to half ampli-

528
tude in t= ue =6 seconds. This oscillation is stable, but the damp-
ing is only moderate, and it may well be felt on the aeroplane in flight.
In some types of aeroplane, it is likely that this motion may be
undamped and hence the amplitude of successive oscillations will be
increasing, giving rise to instability of a new character.

Sa... THE SPIRAL DIVE

The motion found corresponding to FE, negative, as at slow speed,
may be traced to the resistance derivatives involved in the expression
for... hus:

E,=g(NLr—LN_z),
and E, will be positive only when L,/N; is greater than L,/Nr. For
stability, or E, positive, L, and N, should be large and N, and L,
small.

The derivative L, depends on the rolling moment due to side slip
and can be made large and positive by an upward dihedral angle to
the wings or by vertical fin surface above the center of gravity of the
aeroplane. At low speed and high angle of incidence we see that L,
is diminished. Thus, at 6° and 44.6 miles, Ly, =3.44, while at 12° and
36.9 miles, L,=1.91. The drop in speed is only about 18 per cent.
Hence the drop in L,, cannot be due to the lower speed, but must be
due to the greater angle of incidence.

Let 7 be the angle between the wind direction and the center line of
the wings where yaw y is zero. Let ¢ be the angle through which
each wing tip is raised, and let the angle between the wind direction
for a yaw yw and the plane of the chord of the up wind wing be 7’.
Then it can easily be shown by geometry that approximately

4 =1,+ BY,

when i, y, and 8 are small* and expressed in circular measure.

1A. Fage, “The Aeroplane,” p. 82, Griffin, London, 1915.

ee EEE

a

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 69

In-our case B=1.6, then for4=12° and ~=10°, += 1223, while
for 1=6°, 7’ =6°3. This is an increase of incidence with 10° yaw of
but 2.5 per cent at low speed, and 5 per cent at intermediate speed.

Since a side slip is equivalent to a yaw, and since the rolling moment
due to side slip is largely caused by greater lift on the wing which is
toward the wind, it appears reasonable to conclude that this greater
lift is a consequence of the greater angle of incidence. But we see
above, by a rough calculation, that the relative increase in incidence
on a dihedral wing for given angle of yaw is much greater for the
6° attitude than for the 12° attitude. The falling off of L, observed
experimentally is, therefore, to be expected for an aeroplane with
raised wing tips.

A discussion might be opened here as to whether it would not be
preferable to use vertical fin surfaces above the center of gravity or
a swept back wing (“ retreat ’’) to obtain the desired righting moment
Ly on side slip, rather than the dihedral arrangement. Until further
experiments have been made, it is not profitable to speculate on this
question, but one would see no reason a priori to expect the coefh-
cient L,, given by vertical fins, to depend in any way upon the angle
of incidence of the normal flight attitude.

To preserve stability, we must make N; large also. This coeff-
cient is a measure of the damping of angular velocity in yaw, and
can be made great by vertical surface forward and aft of the center
of gravity. A rectangular body with flat sides, vertical fin surface at
the tail (rudder), and the increased drift on the forward moving
wing all combine to resist or damp the spin in yaw. The designer can,
at his pleasure, increase both L, and N; by proper fin disposition.
Note that N, is not different at different speeds.

On the other hand, it is necessary to make N, or the yaw due to
side slip small. A preponderance of fin surface aft will make NV,
large and is, therefore, dangerous. A machine that shows strong
“weather helm” or has great so-called directional stability is likely
to be unstable because the large N, may make E, negative. The
vertical fin surface should be fairly well balanced fore and aft, and
directional restoring moments should not be great. Note that Ny
does not vary much with different speeds.

The derivative L, is characteristic of the rolling moment due to
velocity of yaw or spin and was shown to be caused by the greater
air speed on the outer wing in turning. It is not generally possible
for a designer to make L, small, though a short span will help matters.

70 SMITHSONIAN MISCELLANEOUS COLLECTIONS VoL. 62

Note that L, is greatest at low speed and high angle of incidence. It
should be unaffected by dihedral angle of wings.

The instability corresponding to E, negative is, therefore, a ten-
dency on side slip to the right, for example, to head to the right
toward the relative wind on account of much fin surface aft. At the
same time, due to the spin in yaw, the machine tends to overbank on
account of the greater lift on the left wing. The increased bank,
increases the side slip, the yaw becomes more rapid and in turn the
overbanking tendency is magnified. The aeroplane starts off on a
spiral dive and will spin with greater and greater angular velocity.
The term “ spiral instability ’’ has been given to this motion.

Spiral instability appears to be the most probable form of insta-
bility present in an ordinary aeroplane. It appears to be readily
corrected by modification of fin surface and there appears to be no
excuse for leaving it uncorrected. It is true that an alert pilot should
have no trouble in keeping an aeroplane out of a spiral dive, but in
case of breaking of a control wire disaster would be certain if the
machine were spirally unstable.

$12. “ROLLING”

The second approximate factor

eee ee
when A.C, is small compared with B,*, is seen to reduce to:
fees
Di A, =)
or
uae B, = Ly Ne
D= Aa a ae ae

Now Y», Ly, and N; may be expected to be always negative in
ordinary machines, and the radii of gyration K, and Kz are essen-
tially positive. Hence this root D will always be negative and the
motion a damped subsidence. It will be observed that Y, expresses
resistance to side slip, L, damping of an angular velocity in roll due
to the wings, and N, damping of an angular spin in yaw. In magni-
tude L, is usually so great that Y, and N; may be neglected, giving
roughly

» VE ee 224k
D= gha— Hh=-83

at low speed, or a subsidence damped 50 per cent in t=.08 second.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS Ja

The more exact calculation made in §11 showed t=.076 second.
In a machine of very short span and great moment of inertia in roll,

-

we might expect --”,to become small, but never positive so long as

ie
forward speed is maintained.

When an aeroplane is at such an attitude that further increase in
angle of incidence produces no more lift (“stalled ’’), the damping of
a roll by the wings L, may vanish. Then the downward moving wing,
although its angle of incidence be increased, has no additional lift
over the other and, hence, there is no resistance to rolling. In this
critical attitude, pilots have reported that the lateral control by
ailerons has no effect and the aeroplane is unmanageable.

In any reasonable attitude short of stalling, there appears to be no
reason to fear instability in “ rolling ’’ corresponding to this second
factor of the equation.

93

S73, THE “DUTCH ROLL”

In the approximate solution of the biquadratic, the third factor,
2 C, ms = _ BD, _ Ed

as (F eee

for most machines will have A,C, small compared with B,?, and we

may write:
>, (Cr _E ee
D+ (pt pi) D+ Bi =e

Considering the usual magnitudes of the derivatives entering in
B,, C,, D., Ez, we may write very approximately :

B,=—Ko?L»,

C,=(NrLy—LrNp),

D,=+gKo'Ls,

E,=g(NvoLr—LeNr).

The motion is damped and stable, provided 2 — A is positive, and

the period

215

ae J De (Ge E,\?’
oN Bs Bs D')

or approximately = p= 27 \ eS :
Since ee is ordinarily of the order of 1 or 2 the period may be
2
of the order of 6 or 12 seconds. This period is rapid compared with

72 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

that of the longitudinal motion and unless strongly damped, the
motion may become so violent as to be uncomfortable. Note that
since Ny, Ly, Np, Lp, Nr, Lr are involved, the motion must consist of
a combination of side slipping, rolling, and yawing.
The motion is stable and the oscillation tends to damp out in time
and the aeroplane to return to her course if "3 — a is positive. To
0.69

8)
2 lead),

Substituting approximate expressions we have
Cy_ F,_ Ly 2 = 7)
B,D PG? AE ye

Since Ly is positive, in order for the damping to be real, —Ny/L»
must be greater than \V,/L, and positive.

Stability of this motion is, therefore, assisted by:

1. Large negative yawing moment due to side slip (“ weather
cock” stability) \,. This is incompatible with stability against a
“spiral dive.’

2. Large damping of the rolling due to rolling Lp.

3. Small positive rolling moment due to side slip Ly. This 1s also
incompatible with stability against the “ spiral dive.”

4. Small yawing moment due to rolling N>.

5. Large rolling moment due to yawing velocity L,; another re-
quirement incompatible with “ spiral” stability.

6. Small radius of gyration K, in yaw.

It does not appear practicable to make N, small on account of the
steepness of the drift curve at high angles of incidence. The drift of
the downward moving wing when the aeroplane rolls is increased
while the drift of the rising wing is decreased. The resultant yaw-
ing moment tends to swing the aeroplane away from her course. Note
that at slow speed, near stalling angles, NV, becomes large. This is not
desirable, but is unavoidable.

The rolling is heavily damped by the wings and L, will always be
large and negative. This assists stability.

To avoid “ spiral ”’ instability, we saw above that it was necessary
to make the weather cock or “ directional stability ’’ small. That is,
N, was to be small and the preponderance of vertical fin surface aft
slight. In the motion now under discussion, we wish to make NV,
large. The two conditions imposed are unfortunately conflicting.
We must compromise and make NV, numerically not too great, but
still essentially negative.

damp to half amplitude requires t= seconds.

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 73

In a similar manner, the rolling moment, due to side slip, or restor-
ing moment, such as is given by high fins or raised wing tips, should
be large to avoid “ spiral” instability. In the present case, however,
we wish to make L, small.

Likewise the natural banking due to spin in yaw we wish small
for “spiral” stability, but we now wish to have this coefficient large.

The conflicting nature of the requirements for stability is here
shown by the use of rather drastic simplifications in the more exact
formule. For the analysis of stability the exact formule are easily
applied, and the present approximate forms are deduced only in order
to trace the effect on the motion of such changes as the designer may
be tempted to make on a machine.

°

It is believed that an excessive dihedral angle upwards is not a
cure-all for stability problems. Indeed, in practice, aeroplanes with
a large dihedral angle for the wings have been found so violent in
their motion under certain circumstances that the average pilot has a
firm prejudice against the use of such a wing arrangement. That
this prejudice has some physical basis has been shown here. A
dihedral angle machine is not likely to run into a “ spiral dive,” but
it is very likely to be unstable on what we may term a “ Dutch roll,”
from analogy to a well-known figure of fancy skating.

We may imagine an aeroplane to yaw to the right accidentally.
Due to L, and L, the aeroplane banks in a manner proper for the
turn, but the roll is retarded by the large damping due to Ly. The
turn is assisted by the increased drift on the lower wing due to N,»,
and were it not for the much discussed “ weather helm” given by Nz,
the aeroplane would run off on a right turn. However, NV, tends to
turn the aeroplane back to her course. If NV, be sufficient, the machine
will swing back to her course and the bank will flatten out. But since
the moment of inertia in yaw is considerable, the machine will swing
past her course and start on a turn to the left. This swinging to right
and left of her course is accompanied by rolling outward and some
side slipping.

The analogy to a “ Dutch roll” on skates is obvious. If the skater
lean too far out he may fall, and if the aeroplane roll too far on the
side swings it may happen that the motion will become unstable. If
the air be gusty it is very likely that such an aeroplane may be caught
on the roll by a side gust and capsized.

The “ Dutch roll” in ordinary aeroplanes (which are “ spirally ”
unstable) is not likely to be present, since there is no dihedral and a
large rudder. The average pilot would much prefer to deal with a

74 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

machine which tended to swing down into a “ spiral dive”’ if left to
itself because there is no oscillation of rapid period involved.

The production of a laterally stable aeroplane is attendant with
many compromises, and it cannot be too strongly insisted upon that a
freak type designed to be “very stable” is likely to be rapid and
violent in its motion, and even if stable against a “ spiral dive ” to be
frankly unstable against the ‘ Dutch roll.”

One may inquire whether a machine made directionally neutral can
be made stable. In the notation here used N, would be approximately
zero. The condition that “ spiral”’ instability be not present is:

Lyp/No>Lr/Nr.
But for N, zero, we need only make L, slightly positive to insure
stability in this motion. LL, may be made positive by a very slight
preponderance of fin surface above the center of gravity, raised wing
tips, etc. .

However, in the approximate criterion for stability in the “ Dutch

roll,’ we have

—Nv/Lv>Np/Lp,
and for N,, zero, the motion is clearly unstable unless the magnitude
of the neglected terms is greater than N,/L», which is unlikely.

Replacing neglected terms in C,, we obtain as a more nearly exact
expression :

e _ 5] _ L, l= a ne] ay es Nona
Bi D; Tage ie ee Ya, KG ae

D
If we make N, very small as in the case under analysis, the last
term vanishes as well as the second, and we have as a condition for
Cane

—2 positive:
Bees

Ve a (xt):
0 p
Substituting numerical values for the derivatives, for the slow-speed
condition, we find
— Y,= +.106,

and

Le Np __ _160X 7 — — 8x6.

Kee, 48.6X224 .
The slow-speed motion would, therefore, be very unstable if NV» were
zero. Consideration of the magnitude of the derivatives leads us to
the conclusion that in any aeroplane, if NV, be made very small, the

a

OO EE EEE oO Eel Ue

NO. 5 STABILITY OF AEROPLANES—-HUNSAKER AND OTHERS 75

motion called “ Dutch roll” will probably be unstable at low speeds
where NV, becomes great.

For high speed, if both NV, and N, are zero, the lateral motion should
be stable regardless of the magnitude of the other derivatives.

With the yawing moment due to rolling as measured by N, increas-
ing from zero at high speed to +57 at low speed, it would seem that,
at the maximum speed, any reasonable aeroplane will be stable so far
as the “ Dutch roll”’ is concerned, but at low speed it may become un-
stable in this particular motion.

In general, for high speed, considering the two possible kinds of
lateral instability, it is believed that very slight modifications in fin
disposition will suffice to render any ordinary aeroplane laterally
stable. Likewise, at high speed, longitudinal stability is easily
secured. At low speed, the longitudinal motion tends to become un-
stable as well as one or the other kind of lateral motion.

§14. COMPARISON WITH OTHER AEROPLANES

Any stability discussion is much more suggestive if several aero-
planes can be analyzed in parallel. The only published information
on lateral stability is Bairstow’s investigation of the Blériot mono-
plane used above in connection with the longitudinal stability discus-
sion. This monoplane had only a very small rolling moment due to
side slip L,=.83 as against L,=3.06 for the Clark aeroplane for high
speed. The coefficient N,, yawing moment due to side slip, is not
greatly different in the two machines. The other coefficients are of
the same order of magnitude, except Lp, the damping of a roll, which
is small in the monoplane on account of the small wings of short span.

Without further knowledge, we should expect the Blériot to be
stable on the “ Dutch roll” on account of the small L,. Bairstow
finds a period of 6.5 seconds damped to half amplitude in 1.65 second.

On the other hand, the small L, would lead us to suspect the sta
bility of the spiral motion, especially as Ly is also small. In fact, the
coefficient E, was found to be slightly negative and the aeroplane,
in consequence, spirally slightly unstable. The motion is a slow
divergence which doubles itself in 68 seconds. This is an extremely
slow change and should give no trouble to a pilot. Indeed, the well-
known steadiness in flight of this famous aeroplane is in full agree-
ment with the theoretical conclusions. The Blériot makes no claim to
lateral stability, but is essentially a steady aeroplane easily controlled.
In the “ Dutch roll” the Blériot is very strongly damped and hence
very stable. The spiral motion is not damped, but is so slow that the
stability may be called neutral. The aim of the French school has

76 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

always been a machine whose lateral stability is neutral so that it will
not be thrown about by the wind.

The Curtiss type military tractor tested by us in a manner identical
with that described in this paper, was found at high speed to have
resistance derivatives of the same order of magnitude as the Clark
tractor, except that a large rudder and deep rectangular body make
N, twice as large for the Curtiss, and there being no high fin surface
L, for the Curtiss is small. As would be expected the spiral motion
is slightly unstable, tending to double itself in 28 seconds. The
“Dutch roll” is very stable, having a period of 5.25 seconds and
damping to half amplitude in 1.77 seconds. The machine in flight at
high speed should then have the characteristics of the Blériot and be
steady and easily controlled. This is, in fact, the general reputation
of this type of aeroplane. ;

At low speed, matters are not so favorable. We have no data for
the Blériot at slow speed, but the Clark model is seen to become
spirally unstable to such an extent that an accidental deviation doubles
itself in 7.2 seconds.

The “ Dutch roll” for the Clark model remains stable at low speed,
but is somewhat less strongly damped than at high speed. The period
is 12 seconds damped to half amplitude in 6 seconds. This motion
should be not uncomfortable.

The Curtiss, at low speed, due to falling off of N, and marked
increase in Ly, becomes spirally stable. The spiral motion is a sub-
sidence damped 50 per cent in 3.3 seconds. The wings had no
dihedral angle. A separate test’ made on a single wing without
body or tails showed a small rolling moment for an oblique wind
indicating a small and positive L,. At large angles of incidence this
effect was considerably magnified. The decrease in Ny (or in the
weather helm) at large angles of incidence cannot be laid to the
straight wings. Tests on a wing alone show a small negative NV,
which is not changed at large angles of incidence.

The increase in Ly and decrease in Ny for the Curtiss aeroplane,
favorable to stability of the spiral motion, are unfavorable to stability
in the “ Dutch roll.” Furthermore, Np increases from zero at high
speed to +38 at the low speed, and Ly decreases from — 314 to —78.
These changes are very unfavorable and, as we should expect, the
“Dutch roll” for the Curtiss is unstable. The natural period is
about 5.7 seconds and any initial amplitudeis doubled in 7.66 seconds.

1 Smithsonian Mise. Coll., Vol. 62, No. 4. ‘ Experiments on a Dihedral Angle
Wing,” J. C. Hunsaker and D. W. Douglas.

— Te

sa ria eal

a a i aa a i a ati ale

NO. 5 STABILITY OF AEROPLANES—HUNSAKER AND OTHERS 7G.

The motion is a swaying of the aeroplane of increasing amplitude and
intensity. However, we must always point out that an alert pilot
with powerful controls can check the natural motion of the aeroplane
before it has became violent and so maintain his equilibrium.

The increase in Np at low speed or rather large angle of incidence
is due to the steeper drift curve for a wing at large angles. As the
aeroplane rolls, the downward moving wing has its drift relatively
more increased as the normal flight attitude requires a larger angle of
incidence.

The drop in Ly is due to the less steep lift curve at high angles of
incidence. As the aeroplane rolls, the increase in angle of incidence
of the downward moving wing gives very little increase in lift on
that wing if the wing be already near its angle of maximum lift. We
might imagine an aeroplane flying at an angle of incidence giving the
maximum lift. Any increase in incidence can produce no additional
lift. In most aeroplane wings, an increase in incidence beyond the
optimum angle causes the wing to lift less at the same air speed.
Now if the aeroplane in such an attitude roll, the increased angle of
incidence of the downward moving wing gives no more lift on that
wing and hence the rolling is unresisted. The damping of the roll
will be zero, or even negative. In the Curtiss aeroplane, the low speed
chosen required an incidence of 15°5, very near the “ burble point,”
or angle of maximum lift for the wings. The small value —78 of L,
appears to-bé one of the principal causes of the instability. In the
Clark model, the wing loading is smaller and an equal speed about
44 miles per hour is obtained for an incidence of only 6°, giving
Lp=—319. The lowest speed of the Clark model is taken as about
37 miles per hour where an incidence of but 12° is needed. Ly at this
angle is —224.

It appears that lateral dynamical stability is incompatible with a
high wing loading which requires a large angle at landing speed.
The analysis of longitudinal stability led to a similar conclusion.

If we turn to practical aviation we observe that aeroplanes which
are noted for their steadiness at low speeds are the light Antoinette,
Farman, and the various German Taubes derived from the Etrich.
All these aeroplanes have large wing area and light loading, probably
between 3 and 4 pounds lift per square foot. The hght loading
enables these aeroplanes to gain a safe low speed without having the
angle of incidence near the angle of maximum lift.

In the Clark model the loading is about 3.55 pounds per square
foot, while it is 5.2 in the Curtiss type discussed. More recently the

78 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 62

Curtiss has been given greater wing area in order to reduce the
loading. It should be stated that the comparison is not quite fair,
since the total weight of the Clark aeroplane was taken as 1,600
pounds which includes only half the full 5.6 hours’ gasolene supply.
However, the advantage of light wing loading is more clearly brought
out by the marked difference in weight per square foot wing area.

The following table summarizes all the information available and
may be used to make further comparisons if desired:

Clark Tractor? Curtiss Tractor? Teen ee

Wiitivereneee lang oo oad levis ll soecg || Goooc 384.0 | 244.0
Mean span........ AOh2 an are eam Meco 36.0 gees
Mean chord...... C7. Ga a ili ecrcnanla a ueteioesc
Miean! calipers ciel: 6.37 | Ger Se asl pmiate ys arcu Meee

_ Area, fixed tail.... TOA OL Macias ell Capea D2ViOW sl Morse. s A wee
Area, elevators.... 16.0 as LOCO me acces
Area, rudder...... 9.35 | ae 7S. Wiliyceen er
Length, body......| 24.5 a 26 Ol macnn |) le seiae
Weight; Ibs. a... TOOO\= ||. wre oe 1800 1800
Rise of wing...... 163 me ae 0° 1°8
Lbs: perssq: tt...3. 3555 ge dl taco Bia2. Geka ae 7.38
Angle of incidence 0° | 650 12°0 T°o 15°5 6°0
VY smiles; hour. ..- 76.9 44.6 .| 36.9 78.9 43.6 | 65.0
U, ft.-seconds.....—112.5 |— 65.3 [|— 54.0 -+—11I5.5 |— 63.8|— 95.4
DN Ne ORs leet: sO) i nance 56.0 ei 56.0
KOA, RCCU eR tec ate Sea | IMeaekerores 6.06 | | 5.0
KEG LECT tones Pee OLO7 Semele (iene eee. Bran ie eee 6.0
Vayda, cota alee — .204— .0878— .106— .248\— .09— _ .108
PANO Steen Stee + 3.06 |+ 3.44 |+ 1.91 |+ S44 2-7 | 4- e7o
Nie eee accuse tae — .449— .351 — .53 — .894-— -45/— .44
Yo GueWotononaishokshetelcresenere oO | oO | oO oO | oO Oo
Dia ie Bic Re Meee —631.0 |—319.0 224.0 —314.0 |— 78.0 | —167.0
IND wicca tah ere aecA @ 4-933)55. 2-5 7-0 Oo I+ 37.7| + 24.0
Vinee miere oeretesctor O | oO | O O | oO oO
Usp sigs trac ton eecten toe + 77.0 +132.5 |+160.0 + .55.2 \+101.0/+ 54.0
Nisa. Sag nae eres — 39.4 — 26.0 — 38.9 — 27.0 — 30.4 |— 31.0
Aon Wed piece etek 1310.0 | 1310.0 1310.0 | 2590.0 | 2590.0! 900.0
Bowe tee coe 31800.0 16350.0 12090.0 23800.0 6860.0 6780.0
Gate ee 32700.0 | 5910.0 | 1630.0 |18000.0 } 209.0]! 5580.0
DD yep a atte Steers 41780.0 | 5490.0 | 3490.0 34600.0 5590.0, 6649.0
Eo enc Sane che 2770.0 | 1386.0 (—335.0 —855.0 | 1175.0 |— 68.0
Routh’s discres sc: 37X10"), 12X 10° |.4X10" |-oxX 107 \—7 X10"|2r.5 X10.

Spiral Motion | |
Damp 50% in, sec. 10.4 27m WN cetores puoi B.S p oectee
Doutblein;, sec... 2\) fees: learns e702 eee Oe tl sca | 68.0"
Rolling |
Damp 50% in, sec. 03 .06 | .076 08 | 26, .10
“Dutch Roll” |
Periods Secasa-ane: 5.9 10.7. | 12.0 | 5.24 | Se, 6.5
Damp 50% in, sec. 1.4 | I. 5.05) TO97 Wi eee 1.65
Doubles, Sets. c.ch. "ees soul: poet Ul rc eee a 7:00) > estes
* Unstable.

* Tested at Mass. Institute of Technology, Boston.
* Tested at Teddington, England.

ED AN
a)

"WANN NUN

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