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File 629.13 Un3as/No. 714 • • AIR CORPS TECHNICAL REPQRT No. 4429
AIR CORPS INFORMATION CIRCULAR . .•. : .
PUBLISHED BY THE CHIEF OF THE AIR CORPS, WASHING TON, D. C.
Vol. VIII October 15, 1939 No. 714
TESTS OF A WIND ·TUNNEL FLUTTER MODE ·
•< PHASE I ,, /
THE CRITICAL FLUTTER SPEED AS A FUNCTION OF
CONTROL SURFACE DYNAMIC BALANCE AND
NATURAL FREQUENCIES OF VIBRATION
NO
(AIRCRAFT BRANCH REPORT)
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON : 1940
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TABLE OF CONTENTS
Page Page
SuIIllllary ____ _____________________________ _ 1 Part IV- Comparison of Test Results With
Acknowledgment _____ __ ______ __ _____ _____ _ _ 1 Materiel Division Flutter Criteria:
Date and Place of Tests __________ ___ _______ _ 1 Discussion_ _ 7
Object __ --------------- ------- ------ -- - - 1 Part V-Application of Test Results to the
Introduction_ _ _ ________________________ _ 1 Prediction of Critical Flutter Speeds of Full-
Description of MocleL ______________________ _ 2 Scale Airplanes:
Procedure ____ ___ _ - - - -- - --- -- -------------- 3 Discussion _____ _ _ _ _ 8
Part I- Effect of Au- Speed on Oscillations of Conclusions___________ _ _ _ _ 10
the Model: > Recommendations __________________________ 11
Results_r ____________ __ __________ _____ _ 3 References ___ __________ __ ___ ___ ___ _________ ll
Discussion ___ ___ ___________ ___________ _ 4 Data Sheets _______________ ______ ___________ 11- 14
Part II-Tests With a Free Rudder: Figures 1 to 23 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15- 29
Results _ ___ ____________ ___ __ __ ____ .. __ _ 4 Tables I and IL ___ ____ . __ ____ _____________ 30
Discussion __________ ___ ____ ____ ______ _ _ 5
Part III- Tests With a Restrained Rudder:
General Remarks __ ___ ____________ __ ___ _ 5
Results _ _________ ___ ___ ____ __ ___ __ ___ _ 6
Discussion ______ ___ __ ___ ___ ____ __ _____ _ 6
(II)
-- -
..r
The Critical Flutter Speed as a Function of Control Surface Dynamic Balance and Natural
Frequencies of Vibration
(Prepared by Benjamin Smilg, Materiel Division, Air Corps, Wright Field, Dayton, Ohio, December 28, 1938)
SUMMARY
This report describes tests made on a flutter model
in the Materiel Di vision wind tunnel. The particular
flutter modes studied were those in which oscillations
of the rudder interacted with torsional oscillations of
the fuselage or bending oscillations of the fin. The
model was designed so that comprehensive experimental
data could be obtained regarding some of the fundamental
factors involved in the flutter of airplane
control surfaces. Means were proviG!ed for changing
the static and dynamic balance of the rudder, the
natural frequency of the rudder, and the natural frequency
of the fuselage in torsion or the fin in bending.
Records of the motion of the rudder and the fuselage
or fin were taken by means of Sperry-M. I. T. vibration
pick-ups located inside the model. In general,
flutter of the model at a given air speed was studied
following an initial displacement of the fuselage in
torsion.
It was found that this model offered an excellent
of oscillation, or (2) the movable control surface is
dynamically underbalanced (but with a dynamic balance
coefficient not appreciably greater than 0.05) and
its natural frequency of vibration greater than that of
its supporting structure.
(g) The critical flutter speed is a minimum when the
control surface is dynamically underbalanced, the
natural frequency of its supporting structure low, and
when the natural frequency of the control surface is
slightly lower than the natural frequency of its supporting
structure.
(h) Experimental data obtained from wind tunnel
flutter models can be used to estimate the critical
flutter speeds of actual airplanes.
ACKNOWLEDGMENT
This project was initiated by Capt. P. H. Kemmer,
and the author desires to acknowledge his valuable
contributions and interest in this research study. The
author is also indebted to W. E. Stitz for bis helpful
means for studying flutter phenomena. Some of the cooperation.
more important conclusions drawn from the results of
these preliminary tests are as follows:
(a) The natural frequencies of vibration of aircraft
structural components oscillating in those modes in
which flutter might occur are almost independent of
the air speed.
(b) As the air speed is initially increased, the oscillations
following an initial disturbance damp out more
DATE AND PLACE OF TESTS
The tests described in this report were made in the
5-foot wind tunnel at Wright Field, Dayton, Ohio,
during, July 1938.
OBJECT
quickly, but as the air speed begins to approach the To report the results of a preliminary series of tests
critical flutter speed, this trend is reversed and the carried out on a flutter model in the Materiel Division
oscillations damp out more and more slowly until 5-foot wind tunnel in order to obtain comprehensive
when the critical air speed is reached, flutter takes experimental data regarding some of the fundamental
place. factors involved in the flutter of airplane control
(c) The critical flutter speed depends on the dynamic surfaces.
balance of the control surface involved, its natural
frequency, and the natural frequency of its supporting
structure (i. e., "fixed surface") .
(d) The critical flutter speed is raised as the dynamic
unbalance of the control surfac·e is decreased.
(e) For a given ratio between the natural frequencies
of the ruclder and the fuselage in torsion less than one,
the critical flutter speed is raised as the natural frequency
of the control surface supporting structure is
increased.
(f) Flutter involving oscillations of a control surface
will not occur if either (1) the control surface is completely
dynamically balanced with respect to the mode
(1)
INTRODUCTION
The solution of the flutter problem in airplanes has
been greatly hampered by the lack of suitable experimental
data that could be applied in a practical way
to airplane design and testing. Although a great
amount of theoretical work on flutter has been carried
out both here and abroad, no entirely satisfactory method
has yet been developed for calculating the air speeds
at which flutter of the wings or tail may occur. The
complete theoretical methods are difficult to apply and
are highly complicated even in the simplest cases encountered
in practice.
V
2
The criteria used by the Materiel Division up to
the present time are based upon practical experience
with flutter as observed on a rather limited number of
airplanes that are now obsolete. However, the speed
of airplanes, as well as their size, has been increasing
rapidly during the past few years and, in many cases,
the rigidity of the structural components does not
appear to have increased proportionately. As a result,
it has become evident that in order to avoid the
possibility of flutter occurring in new airplanes, it
would be necessary to determine the validity and
scope of present-day flutter criteria as well as to develop
new criteria, if required, by obtaining more definite
and comprehensive experimental data regarding flutter
phenomena.
DESCRIPTION OF FLUTTER MODEL
The flutter model was designed to provide a means
for obtaining comprehensive experimental data regarding
some of the fundamental factors involved in the
flutter of airplane control surfaces. The flutter modes
studied in this investigation involved rudder oscillations
interacting with torsional oscillations of the
fuselage or bending oscillations of the tin. These
particular modes were chosen on account of their
simplicity since many secondary variables were avoided,
such as angle of attack, downwash, symmetrical versus
unsymmetrical modes, et cetera. Moreover, a wind
tunnel model for these modes of flutter could be built
to a larger scale than for most of the other flutter
modes.
The model was designed by the vibration and flutter
research group and built by the engineering shops of
the Materiel Division in accordance vvith Air Corps
drawing X38K660. A schematic diagram of the
model is shown on Air Corps drawing S39D185 which
is contained in Figure 23 of this report.
The tail unit consists of a rudder, fin, and rear
fuselage section made of laminated mahogany. The
rudder is designed so that most of the leading edge and
certain sections behind the hinge line can be removed
and replaced with units of the same dimensions but
fabricated of aluminum, brass, or lead. In this manner
the static and dynamic balance of the rudder can be
varied by small increments over a considerable range.
Two sections of the rudder near its trailing edge were
cut out and replaced by balsa wood in order to obtain
a range of mass balance that would be representative
of modern airplanes.
The rudder is hinged by a pin passing through two
self-aligning ball bearings staked in housings which
are attached to the fin and fuselage. The front end
of the tail unit fits into a steel socket and is held in
place by eight wood screws. The socket, in turn, is
keyed to a shaft which is supported by two large selfaligning
bearings. The center-line of this shaft is the
effective torsional axis of the fuselage. Each of the
bearings is contained in a housing welded to a streamline
strut which serves to support the model in the wind
tunnel. The struts are braced fore and aft as well as
laterally by guy wires to the floor of the tunnel.
An arm clamped to the shaft and extending below
the model is used to restrain the motion of the fuselage
in torsion. Springs extending from the wall of the
wind tunnel are attached to a fitting which can be
moved vertically along this arm. Thus, the torsional
stiffness of the fuselage can be varied by changing
either the springs themselves or their location along
the arm. This, of course, allows the natural frequency
of the fuselage in torsion to be changed simply and easily.
The rudder control cables pass from the rudder
horns through cut-outs in the fuselage to an arm which
is supported on the shaft but pivoted at its center.
This arm, which follows the motion of the rudder, is
restrained by springs connected to a fixed arm which
is also supported on the shaft. This provides a means
for controlling the natural frequency of the rudder.
A stationary streamlined housing formed of sheet
dural completely encloses the front part of the model
and fairs into the tail unit. Suitable means are provided
for mounting two Sperry-M. I. T. vibration
pick-ups inside this housing, one following the fuselage
motion and the other following the rudder motion.
The Sperry-M. I. T. vibration-recording apparatus
located outside the wind tunnel is used to obtain
simultaneous records of the motion of the fuselage and
rudder. A cable attached to the fuselage restraining
arm serves the double purpose of providing the test
observer with a means for subjecting the model to an
initial disturbance as well as for preventing excessive
oscillations of the model during flutter.
Figures 20, 21, and 22 show the rudder control system
and the vibration pick-ups insicle the model. Front
and side views of the model as installed in the Materiel
Division 5-foot wind tunnel are contained in figures 17
and 18, respectively. The Sperry-M. I. T. vibrationrecording
apparatus is shown stacked upon the platform
outside the wind-tunnel door in figure 19.
Important dimensions and other data concerning the
model are as follows:
Over-all height of rudder _________ 14.60 in.
Area of rudder _______ _______ _____ 75.0 sq. in.
Area of fin ___________ ___ ___ ______ 40.2 sq. in.
Aerodynamic balance of rudder_ ____ 16.0 percent.
Over-all length of model_ __ ________ 49.5 in.
Airfoil section of fin and rudder_ ____ N. A. C. A. 0006
Weights of rudder:
Minimum ____ ___ _______ _____ 1.100 lb.
Maximum _______ ________ ____ 2.190 lb.
Products of inertia of rudder (with
respect to hinge axis of rudder and
torsional axis of fuselage):
Minimum.------------------- -1.766 lb.-in.2
Maximum _________ __ ________ 5.431 lb.-in.2
Moments of inertia of rudder about
its hinge line:
Minimum ___________ ________ 1.620 lb.-in.2
Maximum _________ ____ ______ 3.967 lb.-in.2
Polar moment of inertia of rudder
oscillating arm assembly (includ-ing
vibration pick-up) _____ _______ 1.703 lb.-in.2
Data regarding the dynamic balance of the rudder
for particular combinations of the balance weights are
given on data sheet No. 21, page 14, of this report.
3
PROCEDURE wind-speed was slowly increased and the test repeated.
Conversely, if the oscillations built up, the wind speed
The procedure used for determining the critical was lowered. Eventually an air speed was found at
flutter speed in the wind tunnel was as follows: After which the oscillations of the model remained constant in
the desired rudder balance condition and natural fre- amplitude, neither increasing nor decreasing. This
quencies of the rudder and fuselage were set up, the speed, defined as the critical flutter speed, was then
air-speed in the tunnel was set at a low value. The noted in the data book.
cable attached to the fuselage restraining arm was then Simultaneous records of the oscillations of the fusesharply
jerked and released, thus producing an initial lage in torsion and the rudder were taken by means of
displacement of the fuselage in torsion. The resulting the Sperry-M. I. T. vibration-recording equipment at
transient oscillation was carefully observed to determine various wind speeds, rudder balances, and natural
whether it would increase or decrease in magnitude. If frequency combinations regarding which more detailed
the amplitude of the oscillations decreased, then the information was desired.
Part I- Effect of Air Speed on Oscillations of the Model
RESULTS spond to frequencies of 490 c. p. m. for both the fuselage
All the test results described in Part I are based on and the rudder.
one series of vibration records during which all factors
were held constant except for the air speed in the wind
tunnel. The natural frequency of the fuselage in torsion
was 490 c. p. m., but the rudder was free, its control
springs being disconnected. The dyna,mic balance
coefficient of the rudder was 0.0504, and the ratio of
the product of inertia of the rudder to its moment of
inertia was 1.212. These conditions represent numerical
values which are of approximately the same order
of magnitude as those found on present-day airplanes.
Records of the oscillations of the rudder and the
fuselage in torsion were obtained by ineans of the
Sperry-M. I. T. vibration-recording apparatus. These
records were carefully traced from the film and are
shown on graph paper in figures 1 and 2. Record Nos.
5261, 5265, and 5267, shown in figure 1, were taken
below the critical flutter speed, whereas record Nos.
5270, 5271, and 5273, shown in figure 2, were taken at
or above this speed. It should be noted that an upward
displacement of the fuselage vibration record indicates
that torsion of the fuselage has occurred in such a direction
as to cause the fin to move toward the right-hand
side of the wind tunnel looking upstream, whereas an
upward displacement of the rudder vibration record
indicates that the rudder has rotated about its hinge
line in a direction so that its trailing edge moves
toward the left-hand side of the tunnel. Consequently,
if the two oscillations are in phase on the vibration
record, then the fin and the trailing edge of the rudder
are being displaced in opposite directions, that is, the
rudder is lagging the fuselage torsional oscillation by
180°.
Record No. 5261 was taken at zero wind speed (still
air) following an initial displacement of the fuselage in
torsion. The record shows how the amplitudes of the
fuselage and rudder oscillations slowly decrease with
time. Moreover, it can be seen that the trailing edge
of the rudder reaches its maximum displacement. about
one thirty-second of a cycle before the fin reaches its
maximum displacement in the opposite direction. This
signifies that the rudder lags the torsional motion of the
fuselage by approximately 169°. The wavelengths of
the oscillations, as measured from this record, corre-
Record No. 5265 was made in a similar manner at an
air speed of 30 m. p. h. in the wind tunnel. This record
indicates that although the fuselage oscillations damp
out more quickly than before, the rudder oscillations
damp out somewhat more slowly. Moreover, the ratio
of the amplitude of the rudder motion to that of the
fuselage has increased considerably. The phase lag of
the rudder is approximately 164°. The frequency of
the oscillations is again equal to 490 c. p. m.
Record No. 5267, taken at 60 m. p. h., shows a further
development of the trend observed in record No. 5265.
The frequency of the oscillations, as determined from
the record, is equal to 485 c. p. m.
Record No. 5270, made at a speed of 75 m. p. h.,
demonstrates oscillations of the fuselage and rudder in
the "steady state," that is, the amplitudes of the oscillations
remain practically constant in magnitude. By
definition, this is equal to the critical flutter speed. It
will be noticed that the rudder is lagging the torsional
motion of the fuselage by exactly 180°. The frequency
of the oscillations is 465 c. p. m.
Record No. 5271 was taken at a speed of 80 m. p. h.,
that is, 5 m. p. h. above the critical flutter speed. In
this case, the model was not subjected to any external
disturbances, but was allowed to build up its own
oscillations as a result of its inherent instability at this
speed. The record clearly shows how the oscillations
gradually increase in amplitude. The phase lag of the
rudder is again 180°, and the frequency of the oscillations
is 465 c. p. m.
Record No. 5273 was made at 90 m. p. h. which is
15 m. p. h. above the critical flutter speed. At this
speed, the amplitudes of the oscillations increase quite
rapidly. An unusual feature of this record lies in the
manner in which the phase relationship between the
fuselage and rudder motion gradually changes. During
the initial portion of the record, the rudder lags the
fuselage ·motion by 180° but as the oscillations continue,
this phase lag is decreased more or less uniformly until
at the end of the record the motion of the rudder is
actually in phase with the motion of the fuselage in
torsion. The frequency of the oscillations is again
equal to 465 c. p . m.
4
DISCUSSION ance coefficient of 0.0504. At speeds below the critical
flutter speed, each record was obtained following an
One question which is frequently brought up in initial displacement of the fuselage in torsion. At
flutter discussions concerns the variation of natural speeds above the critical flutter speed, the oscillations
frequencies with air speed. The main reason for this were allowed to build up without subjecting the model
question lies in the fact that most flutter and other to any initial artificial disturbance.
vibration criteria are based upon the results of vibra- Measurements made from these records show that
tion tests which are carried out on the ground without the frequency of the oscillations remains practically
taking into account the effects of air speed upon the constant at 490 c. p. m. for air speeds below 75 m. p. h.,
natural frequencies. Inasmuch as oscillations of con- the critical flutter speed. At the critical flutter speed,
trol surfaces and other airplane parts will tend to the frequency of the oscillations becomes 465 c. p. m.,
produce aerodynamic forces and couples of appreciable a decrease of about 5 percent from the frequency
magnitude, it has been argued that their natural fre- measured at zero air speed. For air speeds above the
quencies should vary with the air speed. ·without critical flutter speed, the frequency remains unchanged
going into detail, it is obvious that if these aerodynamic at 465 c. p. m . for air speeds up to at least 90 m. p. h.
effects cause changes in the effective mass or stiffness of The flutter occurring at these higher air speeds is of an
the structure, then the natural frequency must vary exceedingly violent nature.
with the air speed. Another school of thought believes Thus it appears, for at least this mode of flutter, that
that the effect of these aerodynamic forces and couples the natural frequency of vibration is almost independent
upon the elastic and mass characteristics of the structure of the air speed. In this particular case, the frequency
is negligible for all practical purposes and that their at the critical flutter speed was about 5 percent less than
primary effect is to contribute to the damping character- that measured in still air, but the magnitude and direcistics
of the oscillations. If this is correct, then the tion of this change may have been influenced by the
natural frequency should not be greatly affected by fact that the rudder control cables were disconnected
changes in the air speed unless this air damping during the tests so that the rudder was free to oscillate
becomes of great magnitude. Further theoretical with no spring restraint of any kind.
discussion of this question is out of place in this If time is available during the next series of wind
preliminary report. tunnel tests on this model, this question will be in-
The vibration records shown in figures 1 and 2 con- vestigated in more detail. In particular, it is proposed
tain some experimental data regarding this problem. to measure the natural frequency of the rudder at
These records were made under identical conditions of various air speeds with the fuselage rigidly restrained
the model with regard to natural frequencies and mass and then measure the natural frequency of the fuselage
distribution; namely, a natural frequency of the fuselage I at similar air speeds with the rudder locked in its
490 c. p. m., a free rudder, and a rudder dynamic bal- neutral position.
Part 11- T ests With a Free Rudder
RESULTS
The entire series of tests described in part II was
carried out with a free rudder, that is, with the rudder
control cables disconnected. This simulates a condition
that exists in rudder servo-control systems, or that
may arise in conventional control systems as a result
of slack control cables, or the breakage of a cable or
fitting in the control system.
The results of these tests are shown graphically in
figures 3 to 12, inclusive, of this report. It has already
been pointed out that the model represented the flutter
modes involving rudder oscillations interacting with
torsional oscillations of the fuselage or bending oscillations
of the fin. However, for the sake of simplicity,
the test results will be interpreted solely in terms of
the fuselage torsional mode, thus ignoring the fin
bending mode. It is, of course, obvious that any
conclusions reached with regard to the one mode of
flutter will be equally applicable to the other.
Figures 3, 4, and 5 each show the results of 12 tests
in which the natural frequency of the fuselage in torsion
was kept constant at 720 c. p. m. and the dynamic
balance of the rudder was varied. In figure 3, the
critical flutter speed is plotted against the dynamic
balance coefficient of the rudder; in fi~ure 4, t)le criti-cal
flutter speed is plotted against the product of inertia
of the rudder; and in figure 5, the critical flutter speed
is plotted against the ratio of the product of inertia
of the rudder to its moment of inertia. Each of these
three graphs clearly illustrates the effectiveness of
dynamic balance in raising the critical flutter speed.
In particular, as the rudder approaches complete
dynamic balance, the critical flutter speed is seen to
rise very rapidly .
Figures 6 to 12, inclusive, of this report show the
results of tests in which the natural frequency of the
fuselage in torsion was varied as well as· the dynamic
balance of the rudder. In figure 6, the critical flutter
speed is plotted against the natural frequency of the
fuselage in torsion with a family of curves to represent
different degrees of dynamic balance. The points
shown in this figure are actual test results as determined
in the wind tunnel. In figures 7 to 12, inclusive, the
test data shown in figure 6 have been replotted in a
form which is somewhat more convenient to use for
reference purposes. Thus in figure 7, the critical
flutter speed is plotted against the dynamic balance
coefficient of the rudder for various values of the natural
frequency of the fuselage in torsion; in figure 8, the
critical flutter speed is plotted against the ratio of the
product of inertia of the rudder to its moment of
inertia for various values of the natural frequency of
the fuselage in torsion; in figure 9, the critical flutter
speed is plotted against the natural frequency of the
fuselage in torsion for various values of the dynamic
balance coefficient of the rudder; in figure 10, the
critical flutter speed is plotted against the natural
frequency of the fuselage in torsion for various values
of the ratio of the product of inertia of the rudder to
its moment of inertia; in figure 11, the maximum allowable
value of the dynamic balance coefficient of the
rudder is plotted against the natural frequency of the
fuselage in torsion for various critical flutter speeds,
and in figure 12, the maximum allowable value of the
ratio of the product of inertia of the rndder to its
moment of inertia is plotted against the natural frequency
of the fuselage torsion for various critical flutter
speeds.
DISCUSSION
Study of the test results as shown graphically in
figures 3 to 12, inclusive, indicates that the following
conclusions can be drawn for this mode of flutter:
(a) The critical flutter speed depends on both the
dynamic balance of the rudder and the natural freqLiency
of the fuselage in torsion.
(b) For a given natural frequ ency of the fuselage iu
torsion, the criti cal flutter speed is raised as the dynamic
unbalance of the rudder is decreased. For values of t he
rudder dynamic balance coefficient above 0.035 or values
of the ratio of the product of inertia of the rudder to
its moment of inertia exceeding 1.6, the critical flutter
speed changes rather slowly with changes in t he dynamic
balance of the rudder. However, for values of the rudder
dynamic balance leRs than those mentioned above,
the critical flutter speed rises quite sharply as the rudder
approaches a condition of perfect dynamic balance.
This indicates that it is relatively ineffective to
5
attempt to prevent flutter by making only small changes
in the dynamic balance of the rudder if the rudder is
initially poorly balanced. Since flutter involving torsion
of the fuselage never occurred when the rudder
was completely dynamically balanced with respect to
this flutter mode even though the air speed in the wind
tunnel was raised to 200 m. p . h., it appe_ars that
dynamic overbalance is unnecessary for the prevention
of flutter even at extremely high air speeds.
(c) For a given mass balance of the rudder, the critical
flutter speed is raised as the natural frequency of the
fuselage in torsion is increased. The variation of the
critical flutter speed with the fuselage torsional frequency
is almost linear for frequencies above 500
c. p. m., the slope of the curve being dependent on the
degree to which the rudder is dynamically balanced.
(d) From the curves shown in figures 11 and 12, it is
possible to estimate the relative effectiveness of changes
of the rudder dynamic balance as compared with changes
of the natural frequency of the fu selage in torsion in
attaining a desired value of the critical flutter speed.
However, in actual cases, the means chosen to prevent
flutter will undoubtedly be determined by practical
considerations regarding the difficulties involved in
making these changes.
(e) Comparing the curves shown in figures 3, 4, 5,
7, 8, 11, and 12, it appears that as a criterion of rudder
balance, the ratio of the product of inertia of the rudd;
ir to its moment of inertia about the hinge line interprets
the test results somewhat better than the rudder
dynamic balance coefficient aud far better than the
n1dder product of iner tia. In addition, this criterion
has the advantage of being supported on more sound
theoretical and practical grounds. If subsequent tests
confirm the superior significance of this ratio, then the
Materiel Division criteria for the dynamic balance of
control surfaces should be revised accordingly.
Part II I- Tests With a Restrained Rudder
GENERAL REMARKS
The rudder of this flutter model was originally supported
on three ball bearings of the self-aligning type.
When the model was first assembled it was found that
a certain amount of binding was present in the rudder
control system. Although this was of relatively small
magnitude, nevertheless it was quite noticeable,
particularly when the rudder control cables were subjected
to any appreciable initial tension. On the other
- band, the friction in the fuselage torsional system was so
small that it could be considered negligible. Removal
of the center rudder bearing helped to decrease the
friction in the rudde.r control system although the
resulting condition was still not as frictionless as had
been desired. Nevertheless, it was decided to carry
out the wind-tunnel tests without making any further
changes to the model, in view of the fact that one of
the purposes of this initial series of tests was essentially
to determine whether wind-tunnel models of this type
offered a practical means for studying flutter. It was
also felt that the friction present in the rudder control
system of the model was not excessive when one considered
the amount of friction present in the rudder
control system of the average airplane.
It is believed that most of the friction now remaining
in the rudder control system occurs at those points
where the rudder control cables are at.tached to the
rudder oscillating arm and to the rudder horns. Suitable
bushings have been fabricated for reducing the
amount of friction at these points and will be incorporated
in the model before the next series of wind-tunnel
tests is begun.
The friction present in the rudder control system
made it practically impossible to measure the natural
frequency of the rudder by any direct means. It had
been hoped to make use of the fact that if a body, which
is elastically restrained, is displaced from its equilibrium
position and released, then the frequency of the resulting
oscillation of the body is equal to its natural frequency.
· Thus measurements made from the record of
such an oscillation would enable the natural frequency
of the body to be determined quite accurately. ·_ This
1
method was found to be very satisfactory for measuring
the natural frequency of the fuselage in torsion. However,
it could not be applied in determining the natural
frequency of the rudder because the friction present in
the rudder control system prevented the rudder from
executing a sufficient number of oscillations to allow
accurate measurements to be made from the vibration
record. Consequently it was found necessary to determine
the natural frequency of the rudder by calculation
based on data concerning moments of inertia and
spring stiffnesses. It is hoped that the use of the additional
bushings in the rudder control system will reduce
the friction sufficiently so that in the next series of
tests the natural frequency of the rudder as well as
that of the fuselage in torsion can be measured directly.
Another difficulty experienced with the model was
caused by the lack of flexural rigidity in the fuselage
restraining arm. Thus when attempts were made to
set up natural frequencies of the fuselage in torsion or
the fin in bending above 830 c. p. m., it was found that
bending of the fuselage restraining arm took place.
Consequently no test data are available for the higher
frequencies. The thickness of this arm has been appreciably
increased since these tests were completed,
and it is believed that in the next series of tests, the
fusdage restraining arm will be rigid enough to allow
flutter studies to be carried out at higher values of the
natural frequencies.
6
The critical flutter speed as defined in this report is
the minimum air speed in the wind tunnel at which
oscillations initially produced by an external disturbance
of the model would remain constant in amplitude,
neither building up nor d ying down.
Flutter investigators have frequently pointed out
that flutter occurs only within a given range of air
speeds, that is, under given conditions, there is not
only a certain minimum speed below which there will
be no flutter but, in addition, there is also a maximum
speed above which flutter in the same mode will not
occur. This flutter speed range was noticed during
the wind tunnel tests, but was not studied in any
detail because it is believed that this particular phase
of flutter research is of only academic interest.
During the t ests, it was observed that when the
rudder began to approach a condition of dynamic
balance (i. e., for values of the dynamic balance coefficient
less than 0.01), the critical flutter speeds
became difficult to measure accurately. This is undoubtedly
due to one or several of the following factors:
(a) The inertia forces become so small that they
cannot overcome the friction present in the control
system.
(b) The critical flutter speed tends to change very
rapidly with slight changes in the rudder mass distribution,
so that test points within this range will
appear to be somewhat erratic.
(c) The width of the flutter speed range becomes so
small that the test observer may pass through without
noticing it.
(d) The appea.rance of sideways bending oscillations
of the rear part of the fuselage rather than oscillations
of the fu~elage in torsion tends to eomplicate the interpretation
of the test results.
In measuring the flutter speeds, it was generally
found that the critical flutter speed depended to some
extent on the severity of the initial disturbance. A
small tug at the cable for starting and stopping the
flutter might result in oscillations that would decrease,
whereas a sharp jerk on the cable at the same wind
speed might result in ORcillations that would increase.
This condition, observed on the flutter model,
has been experienced in actual airplanes in flight inasmuch
as cases of flutter are well known to occur far
more frequently in gusty weather than in calm air. It
is believed that this is due to the static friction inherent
in airplane control systems and that a certain minimwn
shock is required to overcome this static friction. Disturbances
greater than this minimum shock did not produce
any further changes in the flutter characteristics .
For the purpose of obtaining experimental flutter data of
practical value, it is believed that the method of subjecting
the model to a large initial disturbance should be
employed. In using this method, it was observed that
flutter was quite sensitive to changes in the air speed.
A change of only 1 mile per hour at the critical flutter
speed would generally determine whether the initial
oscillations would die down or build up.
RESULTS
The results of tlie flutter tests carried out with the
rudder restrained, that is, with the rudder control
cables connected, are shown graphically in figures 13 to
16, inclusive, of this report. In each case, the critical
flutter speed is plotted against the ratio of the natural
frequency of the rudder to the natural frequency of the
fuselage in torsion.
Figure 13 shows the results of tests in which the mass
balance of the rudder was held const.ant and the
natural frequencies of the rudder and the fuselage in
torsion were varied. Figures 14, 15, and 16 show the
results of tests in which the fuselage torsional frequency
was held constant at 300, 720, and 830 c. p. m., respectively,
while the mass balance of the rudder and its
natural frequency were varied. Points labeled "bending"
in these figures, indicate that the flutter of the
model which occurred at these air speeds involved oscillations
of the fuselage in sideways bending about a
vertical axis passing through the rear shaft-bearing.
No torsional oscillations of the fuselage couid be observed
under these conditions. Consequently, for
such points, the rudder dynamic balance coefficients
shown have no significance for comparative purposes,
inasmuch as the products of inertia of the rudder were
calculated with respect to oscillations occurring about
the torsional axis of the fuselage and not its flexural axi;:.
DISCUSSION
The results of the flutter tests with the rudder restrained
are perhaps of more interest than the results
for a free rudder, because conventional rudder control
systems actually exert elastic restraints on the rudder,
particularly in the case of small rudder displacements.
Vibration tests have shown that the natural frequency
of an airplane rudder can be determined in the usual
manner by exciting resonant oscillations of the rudder
about its hinge line, but that, in general, the resonant
frequency band is quite wide because of the friction
present in the control system. Furthermore, such tests
have shown that the natural frequency of the rudder
does not depend on whether the pilot's feet are off the
rudder pedals or resting on them, as is usual in flight.
A study of the test results, shown graphically in
figures 13 to 16, shows that the following conclusions
can be dra,Yn for this mode of flutter:
(a) The critical flutter speed depends on the dynamic
balance of the rudder, the natural frequency of
the fuselage in torsion, and the natural frequency of the
rudder.
(b) Whenever the natural frequency of the rudder
exceeds the natural frequency of the fuselage in torsion,
flutter in this mode does not occur provided that the
dynamic balance coefficient of the rudder does not
appreciably exceed 0.05. Instead, if the air speed is
increased until a type of flutter does take place, it was
found in every case that this mode of flutter involved
oscillations of the fuselage in sideways bending about a
vertical axis passing through the rear shaft-bearing.
The frequency of these oscillations was about 1,500
c. p . m. (natural frequency in sideways bending) .
(c) In those cases where the natural frequency of the
rudder is less than the natural frequency of the fuselage in
torsion, then-
1. For a given dynamic balance of the rudder and a
fixed ratio between the natural frequencies pf the rudder
and fuselage in torsion, the critical flutter speed increases
as the natural frequency of the fuselage is
increased.
2. For any given values of the natural frequencies,
the critical flutter speed increases as the dynamic unbalance
of the rudder is decreased. This variation is
similar to that found in the flutter tests with a free
rudder.
3. For given values of the dynamic balance of the
rudder and natural frequency of the fuselage in torsion,
the critical flutter speed decreases as the ratio of the
natural frequency of the rudder to the natural frequency
of the fuselage in torsion is increased toward
unity. In other words, as long as the natural frequency
of the rudder remains below that of the fuselage in
torsion, then increasing the rudder frequency will lower
7
the critical flutter speed. The minimum value of the
critical flutter speed for this mode of flutter occurs when
the natural frequency of the rudder is slightly less than
the natural frequency of the fuselage in torsion.
The test data can also be interpreted· to show the
effect of slack or broken rudder control cables upon the
critical speed of this flutter mode. Under such conditions,
the ratio of the natural frequency of the rudder
to that of the fuselage in torsion will be zero. Study of
the test data shown in figures 13 to 16 indicates that if
the natural frequency of the rudder was originally less
than that of the fuselage in torsion, then the critical
flutter speed would generally be raised as the result of
slack or broken control cables. But if the natural frequency
of the rudder had been above that of the fuselage
in torsion, then slack or broken control cables
might lower the critical flutter speed. However, it
should be remembered that in actual airplanes, a
large amount of friction may be present in the control
system so that the effect of slack or broken control
cables would also be to eliminate this friction, thus
tending to reduce the speed at which flutter would occur.
An accident to the flutter model occurred during one
test, which probably simulated quite closely flutter
accidents that have occurred to actual airplanes. The
natural frequency of the rudder was approximately
three times that of the fuselage in torsion and the air
speed in the tunnel was about llO m. p. h., which was
just below the critical flutter speed for this condition.
During one of the transient oscillations, the cotter-pin
which safetied the rudder-horn pin fell out. The rudderhorn
pin, which was of the flat-head t ype, had been
inserted into the rudder-horn with its head on the
bottom so that the cotter-pin could be conveniently put
in place from the top. Consequently, the rudder-horn
pin likewise dropped out, thus disconnecting one of the
rudder cables. Immediately, the model began to flutter
very violently and could not be stopped although the
restraining cable was held as tightly as possible by the
test observer. The tunnel air speed was reduced to
zero as quickly as possible and the flutter ceased.
Upon examination of the model, it was found that the
fuselage restraining arm had been given a permanent
deflection of about 3 inches at its end and the bearing
in the oscillating arm had been pulled out of its housing.
Part IV- Comparison of Test Results With Materiel Division Flutter Criteria
DISCUSSION equal to the mass of the control surface multiplied by
The important criteria used by the Materiel Division its aerodynamic area. Although these criteria were
at the present time to estimate the likelihood of flutter not based on the results of quantitative flutter experiare
two in number: First, a minimum percentage in ments, but rather on statistical studies of several airthe
separation of the natural frequencies of those planes that are now obsolete, it is nevertheless obvious
structural components whose oscillations would that they were not very far on the unsafe side because
produce such couplings of the aerodynamic and in the years following their adoption, the number of
inertia forces that might result in flutter; and accidents attributed to flutter was reduced very sharply.
second, the magnitude of a nondimensional coefficient However, the speeds of airplanes, as well as their size,
called the dynamic balance coefficient and defined as have been increasing rapidly during the past few years
a fraction whose numerator is equal to the mass product and in many cases the rigidity of the structural comof
inertia of the control surface with respect to the ponents does not appear to have increased proporcritical
axes of oscillation, and whose denominator is tionately. Consequently, it is evident that to avoid
181999--40-2
the possibility of flutter occurring in new airplanes, it is
necessary to check the validity and scope of present-day
flutter criteria and, if possible, to develop a more
satisfactory means for flutter prediction.
E. S. M. R. Serial No. Str-51-146, entitled "A Proposed
Program of Flutter Research," contains a discussion
of the practical and theoretical deficiencies of
the flutter criteria now used by the Division. The
most important of these defects are as follows:
(a) No estimate of the critical flutter speed can be
made from the flutter criteria.
(b) The weight of the control surface is used instead
of its moment of inertia.
(c) The coefficient does not take into account the
stiffness of the structure.
. (d) Instead of evaluating the natural frequency relationships
by a ratio method so that the significance
of their .relative values can be considered, the Division
criterion is based only on the percent of separation.
Thus it is ambiguous in not specifying which one of
the two components bas the higher natural frequency.
If the Materiel Division criteria are compared with
the conclusions drawn from the flutter model test
results contained in Part, III, it is quite evident that
these criteria are inadequate, because:
(a) Although the criteria would imply that it made
no difference as to whether the natural frequency of the
rudder was higher or lower than that of the fuselage in
torsion, the test data clearly indicate that flutter in this
mode is possible only if the natural frequency of the
rudder is less than the natural frequency of the fuselage
in torsion, and will not occur if the natural frequency
of the rudder is above that of the fuselage in torsion,
provided that the rudder dynamic balance coefficient
does not appreciably exceed 0.05.
(b) In the region where this mode of flutter does
occur, then the actual value of the natural frequency
of the fuselage in torsion plays an important part in
determining the critical flutter speed, even though the
Division criteria indicate that it is the percent of separation
of the natural frequencies rather than their actual
values that is the important parameter.
(c) From a study of the data as plotted graphically,
it would appear that neither the dynamic balance coefficient
of the rudder nor even the product of inertia
itself interprets the test data as well as the ratio of the
8
product of inertia of the rudder to the moment of inertia
about its hinge line. This dimensionless ratio also has
the advantage of being more satisfactory from a theoretical
point of view than the dynamic balance coefficient
now used. Moreover, not only are its numerical
values more significant, but they are actually simpler
and easier to remember than those for the dynamic
balance coefficient.
If subsequent tests confirm the superior significance
of this ratio, then the Materiel Division criteria for the
dynamic balance of control surfaces should be revised
accordingly. Such a ratio could be named the "inertia
coefficient" of the control surface and be represented by
the symbol C;.
An excellent comparison of the Materiel Division
flutter criteria with the flutter model test data can be
made in applying them to a certain airplane, No. 11
in Tables I and II, for the flutter mode involving oscillations
of the aileron interacting with bending oscillations
of the wing. Vibration tests showed that the
natural frequency of the ailerons was 1,250 c. p . m.,
that of the wing in bending was 720 c. p. m., and the
natural frequency of the wing in torsion was above
2,000 c. p. m. The dynamic balance coefficient of each
aileron was 0.139 with respect to a wing-bending axis
14 inches from the center line of the airplane. The
maximum permissible indicated air speed for this airplane
is 320 miles per hour.
The present Materiel Division criteria would require
that the aileron dynamic balance be considerably
improved to prevent fluttn. As a matter of fact, the
latest requirements would limit the dynamic balance
coefficient of the aileron below a value of 0.014, which
is about one-tenth of the actual balance coefficient used.
On the other hand, the flutter model test data
indicate that since the natural frequency of the aileron
is higher than that of the wing in bending, flutter in
this mode is not likely to occur.
Records of the Materiel Division show that although
this airplane has been in service for over 3 years, not
one single case of flutter ha!' ever been reported.
This practical application of the results obtained
from the wind tunnel tests of the flutter n·odel to an
actual airplane clearly proves the superiority of the
flutter model test data over the flutter criteria now
used by the Division.
Part V-Application of Test Results to the Prediction of Critical Flutter Speeds of FullScale
Airplanes
DISCUSSION
A9 shmvn in E. S. M. R. serial No. Str-51-146, entitled
"A Proposed Program of Flutter Research," it is
theoretically possible to predict the flutter characteristics
of a full-scale airplane by <lat.a obtained from wind
tunnel tests of a fluttxr model if the model is built to
satisfy certain conditions of geometric and dynamic
similarity. These conditions of similarity, as developed
by dimensional analysis, can be listed as follows:
(a) Geometric dimensions.
(b) Mass distribution of control surface.
(c) Density ratio of structure to air.
(cl) Material damping and friction in the oscillating
systems.
(e) Natural frequency relationships·.
In particular, it was pointed out that if the above
conditions were satisfied and if the natural frequencies
of the model were made equ11l to that of the airplane,
then the critical flutter speed 1vas merely proportional
to the scale of the model.
The same conclusion can be reached from a study of
Kilssner's "reduced frequency" constant, as given in
N. A. C. A. Technical Memorandum No. 782. This
constant coefficient, as developed for wing flutter, is
,g
based on a fraction ,.-hose numerator is equal to the
oscillation frequency times the wing chord and whose
denominator is equal to the velocity of the airplane.
Thus, if the flutter oscillation frequency of the model
s equal to that of the airplane, then the critical flutter
speed of the airplane is equal to the critical flutter speed
of the model multiplied by the ratio of the wing chord
of the airplane to that of the model.
As a partial check of the validity of this relationship,
calculations were made to estimate the critical flutter
speed for 15 Air Corps airplanes based on the flutter
test data contained in Part III and figures 13 to 16,
nclusive, of this report. It is immediately obvious
that most of the similarity conditions will not be satis-fied,
but this will be ignored in these rough calculations.
In Table I , the calculations are made by the following
method: Knowing the natural frequencies of the rudder,
the fuselage in torsion, and the fin in bending, as
well as the dynamic bala nce coefficient of the rudder,
then the critical flutter speed of the model is estimated
from the test data, extrapolated if necessary. This
value is then multiplied by the ratio of the height of
the airplane rudder to that of the model rudder. The
result will be the predict ed critical flutter speed of the
airplane with respect to this mode of flutter. In Table
II, the calculations are made by the same method,
except that instead of using the ratio of the rudder
.heights as the scale factor, the square root of the ratio
of the airplane rudder area to that of the model is
used to multiply the critical flutter speed of the model
·n order to obtain the predicted critical flutter speed
of the actual airplane. It should be noted that in these
calculations, the dynamic balance coefficient, rather
than the ratio of the product to moment of inertia,
was taken as the criterion for the rudder mass distribution
due to lack of information regarding the rudder
moment of inertia of the full-scale airplanes.
The results of these calculations are given in the
following table, where-
V m = maximum indicated air speed permitted by Air
Corps stress and other criteria.
V1 = estimated critical speed for flutter involving
oscillations of the rudder interacting with
torsional oscillations of the fuselage or
bending oscillations of the fin.
Columns headed I and II represent the r esults of
the calculations of Tables I and II respectively.
Airplane
(Air Corps)
!_ __ ___ ____ ____ __ _
2 ________ ____ ____ 3 ______ ___ __ _____ 4 ______ ___ ____ __ _ 51 _______ __ ___ ___ _
6_ - --- - ---- - -- - - - -
7 ___ __ ___ _ - -- - - -- -
8 ______ ________ __ _
9 ______ ________ __ 1I0L_ _--__- -_-__-_-_- -_-__-_-_- -_-_
12 . - --- -- ---------
l13L_ -_-_-__-_-_--_-_-__--_-__-_- -_
15 __ ____ ____ ___ __ Vm
(M. P.H.)
275
260
260
195
221
220
210
261
382
397
320
221
218
240
195
(I)
V1(M . P. H .)
Very high _______ _ _
324 ____ __ __ _____ __ 293 _______ _______ _ 258 ________ _______ _
220476 __,_ _-_-_-_- -_-__- -__- -__-_- -_
252 __ ___ __ ____ ___ _ ? _____ ___ ____ ____ _
384 _____ _______ ___ _
Very high __ ____ __ _
~1rh high ________ g -- - -- - - --- -- -- Very high ______ __ _
Very high ___ ___ __ _
387 ______ ____ __ ___ _
(ll)
V1 (M. P.H.)
Very high .
325.
330.
321.
232.
239.
232.
?
388.
Very high.
Very high .
High.
Very high .
Very high .
481.
1 Flutter of t ail caused fusel age failure before the rudder was dynamically
balanced dunng a pull-out from a di ve at 240 miles per hour.
Study of the table indicates that most of the predicted
speeds for this mode of flutter are considerably
higher than the values of the maximum speeds permitted
by Air Corps stress and other criteria. However,
the predicted flutter speed is approximately of
the same order of magnitude as the maximum permissible
speed in three cases; namely, airplanes Nos. 5,
6, and 9.
In the case of airplane No. 5, this result is extremely
gratifying because flight records show that under thest:
conditions, tail flutter wa8 experienced during a pullout
from a dive at 240 miles per hour. The rudderfuselage
vibration was so violent as to cause failures of
the diagonal members of the sides of the fuselage truss.
Upon dynamically balancing the rudder, all -flutter
symptoms disappeared.
For airplanes Nos. 6 and 9, no cases of tail flutter
have been reported. The fact that the calculations
show that the predicted flutter speeds and maximum
permissible speeds are so close to each other is probably
due to the violation of the model similarity requirements,
particularly with respect to lack of horizontal
tail surfaces and differences in the damping of
the rudder control system. It is well known that the
friction in airplane control systems may raise the critical
flutter speed appreciably. In addition, the estimated
flutter speed for airplane No. 9 was based on a
considerable extrapolation of the test results since the
maximum fuselage t or sional frequency tested was only
830 c. p . m., "'hereas the natural frequency of the
fuselage in torsion of this airplane was 1,060 c. p . m.
Such extrapolation, of course, may introduce large errors.
No estimates were made for airplane No. 8 due to
the lack of test data regarding rudders that are dynamically
overbalanced to a considerable degree.
In studying the results of the calculations based on
the ratio of the rudder heights as compared with those
based on the square root of the rudder areas, it appears
that the latter is a better criterion for evaluating the
scale of the model when the so-called model and the
airplane are not geometrically similar. This is evident
for airplanes Nos. 4, 5, and 6.
It is of particular interest to apply the flutter model
test data to a certain airplane with twin rudders before
the rudders were dy n!tmically balanced. One of these
airplanes crashed in 1938, :is a result of rudder flu t ter.
The following data concerning this airplane are ext
racted from E. S. M. R . serial No. C- 51- 285:
MODE OF VIBRATION
C. P .M.
Natural frequency of rudders vibrating together_
Natural frequency of stabilizer in rocking about
attachment to fuselage _____ - .. - - - - - - - - - - - - - -
Natural frequency of rudders vibrating oppositely_
Natural frequency of stabilizer in bending ___ __ _
Natural frequency of fin in bending __ - - - - - - - - - -
382}
355
630}
550
980
The dynamic balance coefficient of each rudder was
about 0.08. -
lnterpreting this information in terms of the flutter
model test results, it is immediately seen that barring
slack or broken rudder-control cables, flutter would
not occur in either of the modes involving rocking or
bending of the stabilizer because the coupled frequencies
7
10
of the rudders in these modes are higher than the corresponding
natural frequency of the stabilizer in rocking
or bending. However, flutter of the rudder could
occur in the mode involving bending of the fin. This
conclusion is checked by the fact that examination of
the wreckage after the accident revealed that the fin
had broken off from its attachment to the stabilizer as
the result of several violent oscillations, whereas no
such failures were evident at those points where the
stabilizer was attached to the fuselage.
It might be of further interest to attempt to predict
the critical flutter speed of this airplane for the flutter
mode involving the rudders interacting with the fins in
bending. It is immediately obvious that the data
obtained from the flutter model are not directly applicable
to this airplane because the flutter model possessed
only one rudder, whereas the actual airplane has twin
rudders.
For want of anything better, the following hypothesis
will be offered to provide a means for applying the flutter
model test data: The twin rudders can be replaced by
a single rudder whose dynamic balance coefficient is
twice that of each of the original rudders, whose natural
frequencies are assumed to remain unchanged, and
whose scale factor is based on the dimensions of only
one of the original rudders. No rigorous justification
for this hypothesis can as yet be made inasmuch as no
test data are available, but as in the case of other
hypotheses, it appears that if these assumptions are
made, then the predictions check the available informat
ion for at least this case.
The critical flutter speed for such a model, as estimated
by extrapolating the test data given in Part III,
is 38 miles per hour for the mode involving the rudders
vibrating oppositely interacting with the fins in bending.
Since each rudder is 95X inches high and has an
area of 17.3 square feet, then the scale factor based on
the rudder heights is 6.51 and that based on the square
root of the rudder areas is 5.77. Therefore, the critical
flutter speed for this mode is equal to-
248 m. p . h., using scale factor based on the rudder
heights.
219 m. p. h ., using scale factor based on square root
of rudder areas.
Inasmuch as the speed of the a irplane at the time of
the accident probably exceeded 200 miles per hour,
this very rough prediction indicates why rudder flutter
could have occurred in this mode.
Summing up the results of these calculations, it should
be noted that in almost every case, the predicted
flutter speed is of a reasonable order of magnitude even
though the calculations are based on insufficient test
data and the similarity conditions are so grossly
violated.
CONCLUSIONS
Flutter models offer an excellent means for obtaining
experimental data which should prove of great value
in providing a more thorough understanding of the
mechanism of flutter as well as for determining the
validity of present-day flutter criteria.
Additional test data of a more comprehensive nature
are necessary before a;ny final conclusions can be
reached.
The preliminary results described in this report indicate
that the natural frequency of the oscillations is
almost independent of air speed.
Vibration records taken after an initial displacement
of the model show that as the air speed is ipcreased,
the ratio of the amplitude of the rudder motion to that
of the fuselage in torsion also increases.
As the air speed is initially increased, the fuselage
oscillations following an initial disturbance damp out
more quickly, but as the air speed begins to approach
the critical flutter speed, this trend is reversed and the
fuselage oscillations damp out more and more slowly
until when the critical speed is reached, flutter takes
place.
In the case of a free rudder, the critical flutter speed
depends on both the dynamic balance of the rudder
and the natural frequency of the fuselage in torsion.
The critical flutter speed is raised as the dynamic unbalance
of the rudder is decreased.and as the natural
frequency of the fuselage in t orsion is increased.
Dynamic overbalance of the rudder with respect to
the dangerous flutter mode is unnecessary even at
extremely high air speeds.
The ratio of the product of inertia of the rudder to
its moment of inertia about the hinge line appears to
be the best criterion of rudder balance for interpreting
the test data.
In the case of a restrained rudder, if the natural
frequency of the rudder is greater than that of the
fuselage in torsion, flutter in this mode will not occur
provided the dynamic balance coefficient of the rudder
does not appreciably exceed 0.05.
For a given ratio between the natural frequencies of
the rudder and the fuselage in torsion less than one,
then the critical flutter speed in this mode increases as
the natural frequency of the fuselage in torsion is
increased and as the dynamic unbalance of the rudder
is decreased. However, the critical flutter speed
decreases as the natural frequency of the rudder is
increased toward a value equal to the natural frequency
of the fuselage in torsion .
The minimum value of the critical flutter speed in
this mode occurs when the natural frequency of the
rudder is slightly less than the natural frequency of
the fuselage in torsion.
The effect of slack or broken control cables may be
either to raise or lower the critical flutter speed, depending
on whether the natural frequency of the rudder
was initially above or below that of the fuselage in
torsion.
Additional test data are needed to cover the range
of natural frequencies and dynamic unbalance of
control surfaces as found in modern airplanes as well
as to fill in the gaps in the test data contained in this
report .
The Materiel Division flutter criteria being used at
the present time are inadequate because:
11
(a) No distinction is made as to whether the natural
frequency of the control surface is above or below that
of the other interacting structural component.
(b) The actual values of the natural frequencies are
not considered, but merely their percent of separation.
(c) The ratio of the product of inertia of a control
surface to the moment of inertia about its hinge line is a
better criterion of its dynamic balance than the dynamic
balance coefficient now used.
Flutter test data obtained from models in the wind
tunnel can be used to predict the critical flutter speed of
full-scale airplanes provided that the model satisfies
certain similarity conditions.
RECOMMENDATIONS
It is recommended that further tests be carried out
on this model after the friction in the rudder control
system has been reduced and the fuselage restraining
arm has been reinforced.
Additional test data of a more comprehensive nature
should be obtained in order to extend the range throughout
which the critical flutter speed can be predicted for
full-scale airplanes.
It is further recommended that, based on experience
with the model described in this report, study be made
of the feasibility of building flutter models to simulate
wing or tail units of actual airplanes, particularly of
those types being procured by the Air Corps.
REFERENCES
1. "Airplane Vibration and
Roche-Air Corps Information
Corps, 1933.
Flutter," by J. A.
Circular No. 687, Air
. 2. "The Development of a Mechanically Operated
Frequency Meter and Tensiometer," by W. E. Stitz,
Information Circular No. 701, Air Corps, 1935.
3. "Vibration Characteristics of Twenty Air Corps
Airplanes," by W. E. Stitz, Information Circular No.
702, Air Corps, 1935.
4. "General Theory of Aerodynamic Instability and
Mechanism of Flutter," by T. Theodorsen, Technical
Report No. 496, N . A. C. A., 1934.
5. "Status of Wing Flutter," by
Technical Memorandum No. 782,
1936.
H. G. Kiissner,
N. A. C. A.,
6. "The Question of Spontaneous Wing Oscillations,"
Technical Memorandum No. 806. By B. von Schlippe,
N. A. C. A., 1936.
7. "Wind Tunnel Investigations on Flexural-Torsional
Wing Flutter," by H. Voight, Technical Memorandum
No. 877, N. A. C. A., 1938.
8. "Proposed Program of Flutter Research," by B.
Smilg, Engineering Section Memorandum Report
Serial No. Str-51-146, Air Corps, 1937.
9. "The Determination of the Product of Inertia of
Aircraft Control Surfaces," by B. Smilg, Information
Circular No. 711, Air Corps, 1938.
DATA SHEE'r No. 1.- Date of tests, July 18, 1938
Natural frequency C. P . M.
Fuselage in torsion Rudder
300 ____ ____ __ _ -------
303 ____ ____ ___ -- - ----
306 ____ ______________ _
309 ___ _____ __ ________ _
309 ___ _________ ------
309 __________________ _
308 __ _ --- - ------- -----
REMARKS.-
Lead rudder
weights
0 LMNOP _______ ____ .
0 LMNQ ___ ___ ________ _
0 LMN _ ______________ _
0 LM _____ ___ __________ _
0
0
0
JK ____ ____ _______ ____ JKAB __ ____ _________ _
(!) Rudder control cables disconnected.
Critical
flutter
speed
M. P.H.
38
39
41
46
47
57
1 160
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(3) Key to designations of rudder weights given In drawing
S39D1S5. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood
to be of wood.
DATA SHEET No_ 2_-Date of tests, July 18, 1938
Natural frequency C. P. M.
Fuselage in torsion Rudder
300 __ __ _____ ______ _ --
303 ___ __ __ _______ ____ 306 ____ __ __ ___ ___ ____ _
~~:::::::::::::::::::1
REMARKS.-
Lead rudder
weights
0 LMNOP __ _________ _ _
0 LMNO ___________ ___ _
G LMN ____ ___________ _
0 LM .. ______ _____ -____ _
0 ---- -- ---------- -
Critical
flutter
speed
M. P.H.
49
51
56
81
1180
(1) Rudder control cables connected.
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion ..
(3) Key to designations of rudder weights given in drawing
839Dl8fi. (Figure 23 .)
( 4) Rudder weigh ts not listed as being of lead are understood
to be of wood.
DATA SHEET No. 3.- Date of tests, July 18, 1938
Natural frequency C. P. M .
Lead rudder
weights
Fuselage in torsion I Rudder
300 __ __ _ -- -- -- ---- -- --
303. __ -- - -- --- - -- - -- - -
306 ___ - - -- -- -- ---- -- --
309 ___ _ ---- --- -- - ----
203 LMNOP ____ ________ _
206 LMNQ ____ _______ ___ .
212 LMN _____ _______ __ __
224 LM _________________ _
REMARKS'.
Critical
flutter
speed
M.P. H.
43
46
51
1 140
(1) Rudder frequencies are _approximate. _
(2) 1 Indicates fuselage motion dunng flutter was predommantly
sideways bending rather than torsion.
(3) Key to designations of rudder weight given In drawing
839D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
be of wood.
DATA SHEET No. 4.-Date of tests, July 19, 1938
Natural frequency C. P . M.
Lead rudder
weights
Fuselage in torsion I Rudder
100 __ ___ -- -- --- -- - -- - -
306 ___ _ - - - - - -- - - -
309 ____ _______ _______ _
309 ___ __ ----- ----- -- --
664619 LLMMNNO _P__ ____ _- -_-_-__--_-__-_-_- -_
705 LM _________ ___ ______ _
6SO JK ____ ______ ______ __ _
REMARKS'.
Critical
flutter
speed
M. P . H.
1 167
1 160
1 162
1 172
(1) Rudder frequencies are approximate.
(2) 1 Indicates fuselage motion during flutter was predominantly_
side><ays bending rather than torsion. . . . .
(3) Key to designations of rudder weights given m drawmg:
839D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
beof wood.
12
DATA SHEET No. 5.-Date of tests, July 19, 1938
Natural frequency C. P. M.
F uselage in torsion
300 ___ -- _ --------- --- -
306_ --------- ------- - -
309 ___ · - - --- ----- -- -- -
309 •• _ ------ ------ -· --
REMARKS:
Rudder
880
917
968
934
Lead rudder
weights
LMNOP ____________ _
LMN __ _______ ______ _
LM ___________ __ ___ __ _
JK _ -- - ---- - --- -- -- - --
Cri tical
flutter
speed ,
M. P.H.
1 127
1 119
1 118
'128
(1) Rudder frequencies are approximate.
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as heingof lead are understood to
be of wood.
DATA SHEET No. 6.-Date of test.s, July 19, 1938
Natural frequency C. P. M.
Fuselage in torsion
300 __ __ __________ __ __ 306 __ _______ · ____ ___ _
309 __ --------- ---- ----
309 ___ -- -- ----------·-
309_ -- --·- - ------- ----
REMARKS:
Rudder
Lead rudder
weigtits
1215 LMNOP ___________ _
1267 LMN ______ _________ _
1335 LM ___ _____ ____ __ ____ _
11421809 JK ________ ___ _______ _
Critical
flutter
speed,
M. P.H.
1 127
1 122
1119
1 117
1 ll2
( l ) Rudder frequencies are approximate.
(2) 1 Indicates fuselage motion during flu tter was predominantly
sideways bending rather than torsion.
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as being of lead "re understood to
he of wood.
DATA SHEET No. 7.-Date of tests, July 7, 1938
Natural frequency C. P. M.
Fuselage in torsion Rudder
449905 ______ _-_-_-_--_-__-_- _--__--_-__-_- -_
550040 ____ _-_-_-_-_--_-_-__-_-_- -__- _-_- -_-_
505 __ _________ ____ ___ _
503 _______ ___________ _
REMARKS:
Lead rudder
weights
LMNOP ___ ____ _____ _
LM NO ___ __ ___ __ ___ _ _
LMN __ _____ ________ .
LM _______ ______ ____ _ _
0
0
0
0
0
0 -JK __ ___ . ---- --- -------
(1) Rudder control cables disconnected .
Critical
flutter
speed
M.P.H.
60
62
63. 5
68. 5
70
80.5
(2) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
to~~
0~';~%ct. weights not listed as being of lead are understood
DATA SHEET No. 8.- Date of tests, July 21, 1938
Natural frequency C. P. M.
Fuselage in torsion Rudder
602 ______ ___ _____ ____ _
608 _________________ _ 614 ___ ________ _______ _
662200 ______ _-_- -__-_--__-_-_--_-_-__-_-_- -_
620 __________________ _
619 ___ __ ____ _________ _
~ REMARKS:
Lead rudder
weights
LMNOP ______ ___ ___ _
LMNO _______ ___ ____ _
LMN _______ ___ ______ _
LM __ , ________ ___ ___ _
0
0
0
0
0
g -nt-rn:::: :::::::::::
Critical
flutter
speed
M. P . H.
65
67
71
77
77
91
1 161
(1) Rud~er control cahles disconnected.
. (2) 1 Indicates fuselage motion during flutter was predominantly
sideways bendmg rather tban torsion.
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.) .
(4) Rudder weights not listed as being of lead are understood to
be of wood .
DATA SHEET No. 9.-Date of tests, July 21, 1938
Natural frequency C. P . M.
Fuselage in torsion
602 __________________ _
660148 ______ -__-_--_-__-_--_-_ -_-_-__-_-_- -_
620 _____________ _____ 620 __ __ -- -------------
620 ___ ----------------
REMARKS:
Rudder
0
0
0
0
0
0
Lead rudder
"eights
LMNOP ______ ______ _
LMNO ______________ _
LMN __ _____________ _
LM _______ ______ ____ _
JK __________ _____ ___ _
Critical
flutter
speed
M.P.H.
76
83
90
117
1 175
1 182
(1) Rudder control cables connected.
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood
to be of wood. ·
DATA SHEET No. 10.- Date of tests, July 21, 1938
Natural frequency C. P . M.
Fuselage in torsion
602 __________________ _
614 ____________ __ ____ _
620. _ - - -- ---- -- -------
662200 ______ _--_-_-_-__-_-_-_-_-_-_-_-_-_- -_
619 ______ ___ ---- ----- --
REMARKS:
Rudder
203
212
224
235
214
210
Lead rudder
weights
LMNQP _______ __ ___ _
LMN _______________ _
LM __________________ _
JK ___ __ __ ___ ________ _
JKAB __ ------- "<' ---- -
Critical
flutter
speed
M.P.H.
99
120
1 138
1 143
1 148
1140
(1) Rudder frequencies are approximate.
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(3) .Key to designations of rudder weights given In drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood
to be of wood.
DATA SHEET No. 11.- Date of tests, July 22, 1938
Natural frequency C. P . M. Critical
Lead rudder flu tter
Fuselage in torsion Rudder weights speed
M. P.H.
602 __ ______ __ _________ 641 LMNOP____ ___ ______ 1163
602_____ _____ ___ __ ____ 880 LM rop___ __________ 1135
REMARKS:
(1) Rudder frequencies are approximate.
(2) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
be of wood.
D ATA SHEET No. 12.-Date of tests, J uly 14, 1938
Natural frequency
C. P. M.
Lead rudder weights
Fuselage in
torsion Rudder
720 __ ___ _____ _
727 _____ _____ _
734. ______ __ _ _
740 ___ ____ ___ _
741. _________ _
740 __ ________ _
739_ ---------- 702 _______ ----
679158_ _ _-_--_-_-__- _--__- -_
730 ____ ______ _
;63757 __ -__-_- -_-__--__-_- -_
735_ ---- ------
REMARKS:
0
0
0
0
LMNOP - - -------------- --- ----
LMNO---------· --------------LMN--
----- -- -- ------------ ----
LM--- --- ------ -- ----- ---- ------
0 - - - ----------- --------------------
0
0
0
0
0
0
0
0
0
JK _____ _____ ____ __ ____________ _
JJKKAABB C__D__E- -F-G-- -__-_-_--__-_--__-_--_-_-__-_--_-_
JKABCDEFGHL ___ ______ ___ _
JJKKAHBLH __L__ ____-_ -__-_-_--_-__-_--__--_-__--_-_-_-__- _
ABCDEFGHIJKLMNOP ____ _
Np _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_--_-_-__-_- -_
Critical
flutter
speed
M.P. H .
69
73
76
83
84
97
115
1190
1195
1175
1 165
108
70
73
(1) Rudder control cables disconnected .
(2) 1 Indicates some fuselage side bending obser ved at these
speeds in addit ion to fuselage torsional oscillations .
(3) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
be of wood.
(5) Friction in rudder bearings was reduced to a minimum by
the use of very light oil before each test run.
13
DATA SHEET No. 13.-Date of tests, July 13, 1938
Natural frequency C. P. M. Critical
flutter
Fuselage in torsion speed
720 ___ ___ _____ ___ ____ _
7l9 ________ ___ __ __ ___ _
726_ -- - --- -- - -- -- - - -- -
733_ --- -- ----- --- -- - --
739 __ ------- - - ---- --- -
740_ -------- -- ---- -- --
REMARKS:
Rudder
Lead rudder
weights
0 LMNOP _______ _____ 0 JKLMNOP __ __ ___ __ _
0 JKLMNQ _____ ______ _
0 JKLMN ____ ______ ___ _
0 JKLM ___ ____ ___ __ ___ _
0 JK ____ _________ ______ _
M.P.H.
76
77
73
90
110
127
(1) Rudder control cables connected .
(2) Key to designations of rudder weights given in drawing
S39D 185. (Figure 23.)
(3) Rudder weights not listed as being of lead are understood to
be of wood.
DATA SHEET No. 14.-Date of tests, July 15, 1938
Natural frequency C. P. M.
Fuselage in torsion
719 __ _____ _____ ___ ___ _
720 _______ ___ ___ ____ _ 727 _________ ________ _ _
734_ ___ __ ____________ _
740 ___________ _______ _
741_ __________ _______ _
735 . _ ---- - -- -- -- - ---- -
773405 ______ _-_-_-_-_-_--_-_-_-_-_-__-_-_- -_
739_ ------ -- -- - - - -- - --
REMARKS:
Rudder
190
203
206
212
224
235
231
223
214
210
Lead rudder
weights
JKLMNOP __ __ ____ _ _
LMNOP _____ ___ ____ _
LMNO _____ _________ _
LMN ____ ___ ___ _____ _
LM .. __ ______ __ ___ ____ p ___ ___ _______ _______ _
N _____ ________ __ __ ___ _
JK ____ ______ __ _____ __ _
JKAB ____ ___ ___ _____ Critical
flutter
speed
M.P.H.
64
62
63
68
86
101
74
70
112
1185
(1) 1 Indicates fuselage motion during flutter was predominantly
sideways bending rather than torsion.
(2) Key to designations of rudder weights given in drawing
S39D 185. (Figure 23.)
(3) Rudder weights not listed as being of lead are understood to
beof wood.
DATA SHEET No. 15.-Date of tests, July 12, 1938
Natural frequency C. P. M.
Fuselage in torsion
720 ____ _____ ___ __ ____ _
773274 ______ _- _--_-_-__-_-_-_--_-_-__-_-_- -_
740 ______ ____ ________ _
741_ ____ ____ _____ ____ _
7.34 __________________ _
734 __ _________ ____ ___ _
735 ______________ ____ _
773345 ______ -__--_-_-_-_-__-_-_-_-_-_-_- ____
774201 _. ____ _-_- -_-__--_-_-__- -__--_-_-__- -_
REMARKS:
Rudder
641
650
669
705
744
684
694
732
700
647
680
670
Lead rudder
weights
LMNQP ____ ________ _
LMNQ ______ ______ __ _
LMN ___ ____________ _
LM __ _______ _______ _ _
LMO ________ ____ ____ _
LMP ______ __________ _
p _____ _______ ________ _
N _____ _______ ________ _
JKN ____ ___ _____ _____ _
JK ______ _______ ____ __ NOP _____________ ___ _
(1) Rudder frequencies are approximate.
Critical
flutter
speed
M.P.H.
57.
56.
58.
78.
Above 160.
57.
60.
.Above 100.
63.
64.
Aborn 150.
62.
(2) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
(3) Rudder weights not listed as being of lead are understood to
be of wood. .
DATA SHEET No. 16.-Date of tests, July 9, 1938
Natural frequency C. P . M.
Fuselage in torsion
727 __ ___________ ___ __ _
727 ___ ____ _____ ____ __ _
774304 _________- -_-_-__-_-_--_-_-__-_--_-_-_
741_ __ ___ _______ ___ __ _
740 _____ ________ ___ __ _
773198 ______ _-_- -_-__--_-_-__-_-_-_-_-_- -_-_
695 _____ _____________ _
REMARKS: 1
Rudder
1215
1231
1267
1335
1410
1289
1260
1245
1209
Lead rudder
weights
LLMMNNOO P__ -_-__- -_-__-_-_- -__-_-_- -_
LMN _ ___ __ ____ _____ _
LM. ___ __ ___ _________ _
JK _____ _____________ _
JKAB ___ ____________ _
JKABHL __ _____ ____ _
ABCDEFOHIJK __ _
Critical 1
flutter
speed
M.P. H.
144
137
135
123
118
123
119
127
141
(1) Torsional oscillations of fuselage during flutter almost negligible.
Motion of fuselage corresponded more closely to sideways
bending about a vertical axis passing through rear bearing of shaft.
(2) Rudder frequencies are approximate.
(3) Key to designations of rudder weights given in drawing
S39Dl85. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
beof wood.
DATA SHEET o. 17.-Date of tests, July 22, 1938
Natural frequency C. P. M.
Fuselage in torsion
830 _____ ____ ____ __ __ _ _
846 ___ - - - - -- - ---- - ----
854- __ - -- -- - -- -- -- - - --
854 ___ - - - - -- -- --- -- - - -
854_ - - - - - - - - -- --------
885237 __ _-_-_-_- -__- -_-_-__-_-_- -_-__-_-_- -_
REMARKS:
Rudder
Lead rudder weights
0 LMNOP ___ _________ _
0 LMN ______ ____ _____ _
0 LM ____ ____ ___ ______ _
0
0
0
0
JK ___ ____ ________ ___ _
JKAB. _ --- --- ------ -JKABHL
_ - - - - ----- - -
(1) Rudder control cables disconnected.
Critical
flutter
speed
M.P.H.
84.
91.
96.
97.
114.
130.
Above 200.
(2) Key to designations of rudder weigb,ts given in drawing
S39D185. (Figure 23.)
(3) Rudder weights not listed as being of lead are understood to
be of wood.
DATA SHEET No. 18.-Date of tests, July 22, 1938
Natural frequency C. P. M.
Fuselage in torsion Rudder
883406 __ -_-_-__-_-_--__--_-__-_-_-_- _-_-_- -_
854 ___ ______ _________ _
854_ ______ _____ ______ _
REMARKS:
0
0
0
Lead rudder
Weights
LMNOP __ ______ ____ LMN __ ___ ________ __ LM _____ ____________ _
0 - - - --------- - - - ---------
(1) Rudder control cables connected.
Critical
flutter
speed
M.P.H.
98
103
130
140
(2) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.) ~
(3) Rudder weights not listed as being of lead are understood to
be of wood.
r 14
DATA SHEET No. 19.-Date of tests, July 22, 1938
Natural frequency C. P . M .
Fuselage in torsion I Rudder
830 _____ _____________ _
846 ______ ____ ________ _
885544 ___ - -__-_- -__-_--_-__-_-_-_--_-_-__- -_
203
212
224
235
Lead rudder
Weights
LMNOP ___________ _
LMN ________________ _
LM ___ _______________ _
NOTE.-Fixed arm rubbing against bearing housing.
R EMARKS:
(1) Rudder frequencies are approximate.
Critical
flutter
speed
M . P.H.
80
92
105
108
(2) Key to designations of rudder weights given in drawing
S39D 185. (Figure 23.)
(3) Rudder weigh ts not lis ted as being of lead are understood
to be of wood.
DATA SHEET No. 20.-Date of tests, July 22, 1938
Natural frequency C. P. M.
Fuselage in torsion
830 ___ __ ___ ___ -- ---- --
846 ____ _____ ____ _____ _
854 __ ____ __ __ ________ _
854 ______ ____________ _
830 ___ ___ __________ _ _
REMARKS:
Rudder
-ii~
705
744
1,215
Lead rudder
Weights
LMNOP ____ ______ _ _
LMN _____ _____ ______ _
LM _ ____ ___ ___ ___ ___ _
-LMNOP ___ _____ ____ _
(1) Rudder frequencies are approximate.
Critical
flutter
speed
M .P.H.
73
73
77
I 108
1125
(2) Key to designations of rudder weights given in drawing
S39D185. (Figure 23.)
to i~ ~~!':J'. weights not listed as being of lead are understood
(4) ' Indicates irregular oscillations.
DATA SHEET No. 21
Lead rudder weights w K Cos
------
lb. lb. in.'
J _____ ___ __________ _____ __ ___ 1.100 2. 089 o. 0253 1.166 1. 880 . 0215
JK __ ___ ___________________ __ 1. 229 1. 823 . 0198 JKL _____ ______________ __ ___ 1. 269 1. 983 . 0208
JKLM ____ ______________ ____ 1. 307 2. 213 . 0226
JKLMN _____ ______ _________ 1. 421 3. 497 . 0328
JKLMN O ______ ________ ____ 1. 506 4. 490 . 0397 JKLMNOP ________________ 1. 565 5. 165 .0440
LMNOP __________ ____ ·_ _____ 1. 436 5. 431 . 0504 NOP _________ ____ ___________ 1. 358 5. 041 . 0495
p - --- - ---- ---- ----------- --- 1. 159 2. 7&1 . 0318
OP ____ ____________ ________ __ 1. 244 3. 757 . 0403
AB _______ ________ __ ________ 1. 301 1. 569 . 0161
ABCDEFG ____ __ ________ __ 1. 617 -.411 - . 00~4
ABCDEFGHL ____ ___ __ __ _ 1. 726 -1. 500 - . 0116
ABCDEFGHIJKLMNOP 2. 190 1. 576 . 0096
LMNO ___________________ __ 1. 377 4. 756 . 0461
LMN _______ __________ __ ___ 1. 292 3. 763 . 0389
LM ______ _______ _____ _______ 1. 178 2. 479 . 0281 ABJK ___ ____ ___ _______ _____ 1. 430 1. 303 . 0122
ABCEDFGJK _____ ________ 1. 746 - . 677 - . 0052
ABCDEFGHIJK __ _______ 1. 855 -1. 766 -.0127
ABHIJK ___ ___ _________ ____ 1. 539 + . 214 +. 0019 LMO ___ __ _________ ___ ____ __ 1. 263 3.472 . 0366 LMP ___ _________ _______ ____ l. 237 3.154 . 0340
JKN ___ _____ _____ __________ _ l. 343 3.107 . 0308 N ___ _____ ____ __ _______ __ ____ 1. 214 3. 373 . 0370 JKHL __ __ __ __ ___ ___ ___ ___ __ 1. 338 . 734 . 0073
NOTE.-
I
---
lb. in.'
1. 620
1. 953
2. 273
2. 467
2. 646
3. Q69
3. 304
3. 420
2. 7.67
2. 394
1. 736
1. 971
1. 795
2.072
2. 167
3. 967
2. 651
2. 416
1. 993
2. 448
2. 725
2.820
2. 543
2. 228
2. 109
2. 696
2. 043
2. 368
K
T
---
1. 290
.96 2
.804
. 804
. 835
1.140
1. 360
1. 51 0
1. 9 60
2. 105
1. 592
1. 901
.874
- . 198
- . 692
. 397
1. 795
1. 560
1. 242
. 532
- . 248
- . 626
. 084
1. 558
1. 496
1. 152
1. 650
. 310
(!) " K" represents rudder product of inertia with respect to its
binge line and to1sional axis of the fuselage.
. (2) " I" r epresents rudder moment o,f inertia about its hinge
hne. Values do not include inertia of rudder oscillating arm.
(3) Key to des1gna t1ons of rudder weights given in drawing
S39Dl85. (Figure 23.)
(4) Rudder weights not listed as being of lead are understood to
be of wood. ·
(5) " W" represen ts total weight of rudder, including spindle.
(6). "Cos" represents the rudder dynamic balance coeffi cient
and 1s equ al to K where "A" is the aerodynamic area of the
rudder.
(W) (A)
(7) "K» determined for all-wood rudder by experimental method
involving the determination of the mass moments of inertia about
three axes ly ing in the plane of the rudder.
15
V+8f!ATION RECORDS AT AIR SPEEDS 8ELO'tf CR+T!CAL [LUTTER SPEED
!NATURAL FREQU§NCY OF FySELACE IN TORSION "90 C.P.IA
'RvDDER NATU FREQUENCY O C.PM.,CONTROL C,,.BLES ,t,TTACHED
NOTE · l}PWARD 01$PL,t,CE"'E"T Of USEL"'GE R£CORD INOICATES FIN DEFLECTING TOWARD R.H. SIDE Of "40QEL
1/f':#!'RD Q+SPL-'CD,£NT Of RV0QER RECQRD INO!CATES TRAILING EDGE DEFLECT ING TQWJ'\RO L .H. SIDE OF MOOEL
liORIZONTAL SCAL.f READINC FROIA ~En TO RICHT RE,.RESENT$ TIME ",)(IS
FUSELAGE
f!ECORD NO. n§I AUi SPEED O M.P.H Fll.M SPEED +2t lN. PER $EC .
O!SCILL,t,TIONS SLOWLY QECRE,t,SING
M,EA5URED . FREQUl:NC Y •0 0 C.PM.
l!£CORD NO. 52e5 AIR SPEED 30 1.1.P H
OSCILLATION .DECREASING
FILM Sf'tED 12 j° IN. PER. ~EC.
MEf"SURED FREQUENCY .. 90 C.P.M.
RECORD NO ~201 AIR SP,EC> §OM.PH [ILM SPEED 1z-! IN.PER s~c
OSCILLATI NS SLOWLY DE~REASINO
ME,\SURED FREQUENCY '4)!5 C.P.M. SCALE -HALF SIZE
V+!!R,<nlON RECORDS AT Alfl - SPEED$ AT AtjD Al!l(NE CRITICAL FLUTJER SPEED
NATURAL FREQUENCY Of FUSELAGE IN TORSION 490 C. P.M.
f'UDOER NATURAL FREQUENCY O C.P.M., CONTROL CABLES ATTACHED
!:!Qll- UPWARD DISPLACEMENT OF FUSELAGE R(CORD INDICATES FIN DEFbECTING ·TOWARD RH.
UPWAfD DISPL-'CEMENT OF RUDDER RECORD INDIC,t, TES TRAILi NC EDGE DEFLECT INC TOWARD
RECORD NO. 5270 AIR -SPEED 75 M.P.H. FILM SPEED 12 t IN. PER . ~EC.
OSCILLATIONS OF APPROXIMATELY CONST/<NT AMPLITUDE
MEASURE\ FREQUENCY 465 C.P.M.
RECORD NO 5273 AIPI • SPEED 90 M.P.H.
OSCI LLATION S RAP IDLY INCRE.AS!f,r,10 IN AMPUTUQE
fy!E-ASUREQ FREQUENCY 465 C P.M SCALE - .HALF
18199~0- - 3
~ . FLU~MODEL
TESTED 7 -7- 36 .
FUSELAGE .
fY~LAC§
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FUJTUR MODEL
TESTED 7-7-36
PAO[ e4
190
180
170
160
150
140
130
120
110
100
90
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70
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VS.
DYNAMIC BALANCE COEFFICIENT OF RUDDER
NATURAL FREQ. OF FUSE.LA GE IN TORSION -
~
RUDDER CONTROL GABLES PIS CONNEQTEP
•
30~-~~~~~ ..... ---~~~-~~~~--~~---i - .01 0 .01 .02 .03 .04 .05
190
180
170
160
150
140
130
120
110
100
90
80
70
60
50
40
DYNAMIC BALANCE COEFFICIENT OF RUDDER - Coe
FIG.3
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PRODUCT OF INERTIA OF RUDDER
NATURAL FREQ. OF FUSELAGE IN
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FREE RUDDER , CONTR OL CABLES
0 DISCONNECTED.
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PRODUCT OF INERTIA OF RUDDER LB. l~ .2
16
CRIT ICAL FLUTTER SPEED VS.
RATIO OF PRODUCT TO MOMENT OF INERTIA
NATURAL FREQ. OF FUSELAGE IN TORSION - 720 C.P.M.
FREE RUDDER,CONTROL CABLES DISCONNECTED.
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RATIO OF RUDDER PRODUCT OF INERTIA TO MOMENT OF INERTIA
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NATURAL FREQUENCY OF FUSELAGE IN TORSION
FREE RUDDER, CONTROL CABLES DISCONNECTED.
SYMBOLS
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...foBREPRESENTS DYN. BAL. COEFF. OF RUDDER.
K REPRESENTS PROO. OF INERTIA OF RUDDER.
I REPRESENTS MOM. OF INERTIA OF RUDDER.
o~-~~~~~ ..... ---~~~-~~~~--~~
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
NATURAL FREQUENCY OF FUSELAGE IN TORSION -C.P.M.
FIG. 6
CRITICAL FLUTTER SPEED
vs.
DYNAMIC BALANCE COFFICIENT OF RUDDER
FREE RUDDER, CONTROL CABLES DISCONNEC.TED.
15
140
130
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DYNAMIC BALANCE COEFFICIENT OF RUDDER- COB
150
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RATIO OF PRODUC1" TO MOMEN1" OF INERTIA
FREE RUDDER, CONTROL CABLES DISCONNECTED.
FUSELAGE IN TORSION.
NATURAL FREQUENCIES OF/
1000 C.P. M.
900 C.P. M.
800. C.P.M.
700 C.P.M.
600 C.P.M.
500 C.P.M.
400 C.P. M.
300 C.P.M.
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Rf'1"10 OF RUDDER PRODUCT OF INERTIA TO MOMENT OF INERTIA.
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CRITICAL FLUTTER SPEED
vs.
NATURAL FREQUENCY OF FUSELAGE IN TORSION
FREE RUDDER·, CONTROL GABLES DISCONNECTED
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REPRESENTS DYN. BAL. COEFF. OF RUDDER
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
NATURAL FREQUENCY OF FUSELAGE IN TORSION - GP M
FIG. 9
CRITICAL FLUTTER SPEED
VS.
NATURAL FREQUENCY OF FUSELAGE IN TORSION
FREE RUDDER. CONTROL CABLES DISCONNECTEO
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NATURAL FREQUENCY OF FUSELAGE IN TORSION - C.P. M.
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MAXIMUM ALLOWABLE VALUES OF Cos-vs.
NATURAL FREQUENCY OF FUSELAGE IN TORSION
FREE RUDDER CONTROL CABLES DISCONNECTED
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MAXIMUM ALLOWABLE VALUES OF !$.
~- I-NATURAL
FREQUENCY OF FUSELAGE IN TORSION
. FREE RUDDER, CONTROL CABLES DISCONNECTED 1-
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. NATURAL FREQUENCY OF FUSELAGE IN TORSION -C.P M.
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/ -- 23
FIGURE 17.-Front view of flutter model installation in 5-foot wind tunnel.
24
--
FIGURE 18.-% front view of flutter model installation in 5-foot wind tunnel.
F1G U1<E 19.-Sperry-M. I. T. vibration recording apparatus used in connection with flutter model in Hoot wind tunnel.
l
26
FIGURE 20.- Tail of flutter model.
---
27
FIGURE 21.-View of flutter model with upper cap of fuselage removed.
-.
28
FIGURE 22.-View showing ~perry-M. I. T. vibration pick-ups installed in flutter model.
.,
BAlANCE WEt<.!IT"S
00
/?vDDE
FRotvr SHAFT'
FIGURE 23
RvD1J£R HtNG~ Axis
UPPER? RvoDER. BEARtN•
8£Af?ING
~~ Fo~ SrlfllTfNG
AND SroPPtNG FLurrE&
Sr~ur
DIAGRAM-FLUTTER MODEL
REF. NoTE : Ass'y X38Kb60
A . C . DRAWING S390185
30
T ABLE I
Calculation of critical flutter speed of Air Corps airplanes f <Jr the flutter mode involving oscillations of the rudder
interacting with torsional oscillations of the fuselage or bending oscillations of the fin
(Scale based on ratio of rudder heights)
Airplane Nat. freq. Nat. freq. Crit. speed of Rudder Con of of fuselage Nat. freq. of fin in height of Airplane rudder ht. Critical flut-
(Air rudder of rudder in torsion bending (c. p. m.) flutter model airplane Model rudder ht.
ter speed
Corps) (c. p. m.) (C. p. ID.) (m.p.h.) (in .) (m. p. h.)
----
J_ ____ ___ 2 ___ __ ___ 0. 024 1,000 700 1, 400 Very high 66 4. 51 Very high . 033 400 600 1, 650 57 83 5. 68 324
3 ______ __ . 095 270 400 960 40 107 7.33 293 4- ____ ___ . 093 450 600 1,180 48 78. 5 5. 37 258
5 ____ __ __ .116 500 525 1, 300 40 90 6. 16 246
6 ____ ____ . 102 600 750 1,800 50 60. 5 4. 14 207
7 _______ _ . 109 500 650 1,460 49 75 5. 13 252
g ____ ____ - . 056 350 570 Above 2,000 96 6. 57
9 ____ ____ .029 600 1,060 1,650 92 61 4. 18 384
10 ________ -000 550 780 1, 750 Very high 74 5. 06 Very high
11_ ___ ____ . 024 850 720 1,350 Very h i~h 66 4. 51 Very high
12 ________ . 147 720 1,350 1,750 Hig1 68 4. 65 High
13 _____ ___ . 025 800 500 1,300 Very high 76 5. 20 Very high 14 __ __ ____ . 044 675 525 1,380 Very high 80 5. 48 Very high
15 ________ . 044 200 430 800 51 111 7. 60 387
TABLE II
Calculation of critical flutter speed of Air Corps airplanes for the flutter mode involving oscillations of the rudder
interacting with torsional oscillations of the fuselage or bending oscillations of the fin
Airplane Nat. freq. Nat. freq .
(Air CDs of of fuselage Corps) rudder o(Cf . rpu.d IdDe.r) in torsion (c. p. m.)
-------
l_ ______ _ o. 024 1,000 700 2 ___ __ ___ .033 400 600
3 __ ____ __ .095 270 400
4 __ __ ____ .093 450 600
5 ____ ___ _ . 116 500 525
6 ____ ____ .102 600 750 7 _______ _ . 109 500 650
8 ___ _____ - . 056 350 570
9 ___ _____ .029 600 1,060
10 _______ _ . 000 550 780
ll_ ___ ___ _ . 024 850 720
12 ______ __ .147 720 1,350
13 ________ . 025 800 500
14 _____ ___ . 044 675 525
15 ________ .044 200 430
[Scale based on square root of ratio of rudder areas]
Nat. freq. of fin in Crit. speed
bending (c. p. m.) flu tter mod
(m. p. h.)
of
el
Rudder
area of
airplane
(sq. rt.)
/ Airplane rudder area
' Model rudder area
Critical flutter
speed
(m.p. h.)
-1----1--------- -1-----
l, 400
1,650
960
1,180
1, 300
1,800
1,460
Above 2,000
1,650
1, 750
1, 350
1, 750
1,300
1,380
800
0
Very hig
4
4
4
b
57
0
8
0
4
( .
Very hig
VEry hig
Rig
Very hig
Very hig
50
9
?)
92
h
h
h
h
h
51
10. 7 4. 54 Very high
16. 9 5. 70 325
35. 4 8. 25 330
23. 2 6. 68 321
17. 5 5. 80 232
. 11. 8 4. 77 239
11. 9 4. 78 232
23.4 6. 71 (? )
9. 2 4. 21 388
14. 7 5. 31 Very high
10. 7 4. 54 Very high
9.8 4. 34 High
13. 8 5. 15 Very high
l4. 6 5. 30 Very high
46. 3 9. 43 481
,.-
. -.)