COMPARISON OF THEORETICAL AND EXPERIMENTAL MODEL

v vr

AD

05 I- USAAVLABS TECHNICAL REPORT 66-77

COMPARISON OF THEORETICAL AND EXPERIMENTAL MODEL ROTOR

BLADE VIBRATORY SHEAR FORCES

Bj

Lawrence I. Bail

u. October 1967

S. ARMY AVIATION MATERIEL LABORATORIES FORT EUSTIS, VIRGINIA

CONTRACT DA 44-177,AMC-136(T)

UNITED AIRCRAFT CORPORATION

SIKORSKY AIRCRAFT DIVISION

STRATFORD, CONNECTICUT

<] - ill-, .: Il-ll

I III ultf.l

*">

Disclaimers

The findings in this report are not to be construed as an official Depart- ment of the Army position unless so designated by other authorized documents.

When Government drawings, specifications, or other data are used for any purpose other than in connection with a definitely related Government procurement operation, the United States Government thereby incurs no responsibility nor any obligation whatsoever; and the fact that the Govern- ment may have formulated, furnished, or in any w?»y supplied the said drawings, specifications, or othei data is not to be regarded by impli- cation or otherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights or permission, to manu- facture, use, or sell any patented invention that may in any way be related thereto.

Disposition Instructions

Destroy this report when no longer needed. Do not return it to originator

r.AXMWHSEO

i Dist. '! MAIL ml/*****]

•

m •

DEPARTMENT OF THE ARMY U S. ARMY AVIATION MATERIEL LABORATORIES

FORT EUSTIS. VIRGINIA 23604

This report has been reviewed by the U. S. Army

Aviation Materiel Laboratories and is considered

to be technically sound. It is published for the

dissemination and application of the information

contained herein.

—"

Task 1D121401A14203

Contract DA 44-177-AMC-136(T)

USAAVLABS Technical Report 66-77

October 1967

COMPARISON OF THEORETICAL AND EXPERIMENTAL MODEL ROTOR

BLADE VIBRATORY SHEAR FORCES

SER -50419

by

Lawrence J. Bain

Prepared by

United Aircraft Corporation Sikorsky Aircraft Division

Stratford, Connecticut

for

U. S. ARMY AVIATION MATERIEL LABORATORIES FORT EUSTIS, VIRGINIA

This document has been approved for public release and sale; its distribution is unlimited.

SUMMARY

An investigation was undertaken to obtain quantitative measurements of the vibratory forcing functions from the blades of rotary wing aircraft in the flight speed range encompassing both pure and compound helicopter operation. These measurements were made using dynamically scaled model rotor blades mounted on a specially instrumented rotor head. Testing was accomplished in the United Aircraft Corporation's 18 foot subsonic wind tunnel within a range of equivalent forward speeds from 75 to 300 knots and within a range of full scale rotor lifts from zero to 40,000 pounds. In addition to rotor performance, the final data include ten harmonics of the orthogonal blade root shear forces, rotor blade bending moments, and rotor control loads.

It was concluded from the experimental work that:

1) High harmonics of vibratory shear forces can be measured at the blade root over a wide range of speeds and lifts.

2) Only the first harmonic of flatwise and edgewise shear force is significantly effected by the flapping trim condition of the rotor.

3) Elimination of lag damping may increase or decrease the edgewise shear force, depending on its proximity of the operating condition to a blade natural frequency.

4) Increasing forward speed causes an increase in both flatwise and edgewise shear forces, the latter becoming predominant at the highest forward speeds.

5) Increasing rotor lift at constant forward speed causes a gradual increase in the magnitude of the flatwise shear force harmonics.

6) The radial shear force first harmonic longitudinal component takes on values which can be significant, but the fundamental nature of this force is not well defined.

The experimental results were correlated at seven test points with a fully coupled aeroelastic analysis. The evaluation of this work led to the following conclusions:

1) The inclusion of wake-induced velocity effects in the theoretical method shifts the calculated flatwise shear forces in a direction which improves the correb. zn but has no significant effect on the calculated edgewise shear rorces.

2) The overall degree of correlation is strongly influenced by the accuracy to which the blade natural frequencies are known, the continuity of the calculated induced velocity distribution, and the predictability of the edgewise rotor blade behavior.

PRECEDING PAGE BLANK

iii

FOREWORD

This program was sponsored by the U. S. Army Aviation Materiel Laboratories (formerly ü. S. Army Transportation Research Command ) Fort Eustis, Virginia, and was monitored by Mr. Joseph McGarvey.

The experimental and theoretical research program was carried out from May 1964 through November 1965. Assisting in this program was Mr. P. J. Arcidiacono of the United Aircraft Corporation Research Laboratories, who directed the development of the rotor head and the impedance analysis.

PRECEDING PAGE BLANK •

CONTENTS

Page SUMMARY iii

FOREWORD v

LIST OF ILLUSTRATIONS viii

LIST OF SYMBOLS xv

INTRODUCTION 1

DESIGN DATA AND DESCRIPTION OF EQUIPMENT 2

EXPERIMENTAL PROCEDURE 7

EXPERIMENTAL RESULTS 9

EVALUATION OF EXPERIMENTAL RESULTS n

CORRELATION OF THEORY AND EXPERIMENT 18

CONCLUSIONS 21

RECOMMENDATIONS 23

BIBLIOGRAPHY 24

DISTRIBUTION 123

APPENDIXES

I. Experimental Flatwise and Edgev/ise Shear Force Figures 125

II. Experimental Radial Shear Force Figures 236 III. Experimental Vibratory Moment Amplitude Figures.... 26I IV. Experimental Vibratory Control Load

Amplitude Figures 284

vii

ILLUSTRATIONS

Figure Page

1 Vibratory Shear Force Rotor Head .... 44

2 Vibratory Shear Force Rotor Head Details . . 46

3 Dynamically Scaled Blade-Exploded View . . 48

4 Dynamic Blade Physical Properties .... 49

5 Model Rotor Blade Calculated Natural Frequencies 50

6 United Aircraft's Subsonic Wind Tunnel ... 51

7 Sikorsky Helicopter Rotor Test Rig .... 52

8 Wind Tunnel Test Conditions 54

9 Effect of Trim Condition on Shear Forces, P = 0.2 55

10 Effect of Lag Damping on Shear Forces, fi = 0.2, a = -4 Deg. 59

s

11 Effect of Lag Damping on Shear Forces, H- =0.5, a = -4 Deg 61

s

12 Effect of Lag Damping on Edgewise Blade Bending Moment 63

13 Effect of Advance Ratio on Nondimensional Shear Force, C /* =0.035, ag =-4 Deg. ... 66

14 Effect of Advance Ratio on Rotor Blade Vibratory Moments 70

15 Experimental Flatwise Vibratory Shear Force, ag = -4 Deg 71

16 Experimental Edgewise Vibratory Shear Force, a = "4 ^g 73

s

vin

— —

Figure Page

17 Experimental Radial Vibratory Shear Force, a = -4 Deg. ..." 75

s

18 Experimental Blade Moments, fJ. =0.2, C /<r =0.071, a = -4 Deg 77

s

19 Experimental Blade Moments, p =0.3, CL/cr =0.019, a = -4 Deg. . . 80 s

20 Experimental Blade Moments, y. =0.3, C / <r =0.041,

a = -4 Deg. 83 s

21 Experimental Blade Moments, /* =0.3, C /a- =0.062, ag = -4 Deg 36

22 Experimental Blade Moments, p. =0.4, C /a- =0.046, ac = -4 Deg 89 s

23 Experimental Blade Moments, H- =0.5, C./o- =0.048, as = -4 Deg. 92

24 Experimental Blade Moments, M =0.7, C /o- =0.032, as = -4 Deg . . 95

25 Effect of Rotor Lift on Flatwise Vibratory Shear Force, M = 0.3, ag = -4 Deg 99

26 Effect of Rotor Lift on Edgewise Vibratory Shear Force, /i. = 0.3, ag = -4 Deg 10i

27 Effect of Rotor Lift on Radial Vibratory Shear Force, ^ = 0.3, ag = -4 Deg 103

28 Effect of Rotor Lift on Nondimensional Shear Forces, /x = 0.3, ag = -4 Deg 105

ix

Figure

29

Page

30

31

32

33

34

35

36

37

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes, /i=0.2, C./o- =0.071, a =-4 Deg. .

L> S

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes, P = 0.3, Cf /<r = 0.019, a = -4 Deg. .

L» s

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes..

At = 0.3, C./o- =0.041, a = -4 Leg. L s

Comparison of Theoretical and Experimental Vibratory Snear Force Harmonic Amplitudes,

M = 0.3, CT /<r =0.062, a =-4 Deg. Li S

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes,

M= 0.4, CT/<r =0.046, a =-4 Deg. L s

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes, /t = 0.5, CL/cr =0.048, ag = -4 Deg. .

Comparison of Theoretical and Experimental Vibratory Shear Force Harmonic Amplitudes,

M = 0.7, C./o- =0.032, a =-4 Deg. L, s

Comparison of Theoretical and Experimental Flatwise Rotor Blade Bending Moments, a = -4 Deg.

s

Comparison of Theoretical and Experimental Flatwise Rotor Blade Bending Moments, a = -

D

109

110

111

112

113

114

115

116

4 Deg. 118

38 Comparison of Theoretical and Experimental Edgewise Rotor Blade Bending Moments, M = 0.5, C. /o- =0.048, a = -4 Deg. ,

L s 119

Figure Page

39 Azimuthai Variation of Vibratory Shear force, a - "4 Deg. J20

APPENDIX I

40

41

42

43

44

45

46

47

48

49

Experimental Shear Forre, H- = 0. 2, a =0 Deg.

Experimental Shear Force, /•*• = 0. 2, a = -4 Dez. s

Experimental Shear Force, H- = 0. 2, a = -8 Deg.

Experimental Shear Force, A = 0. 2, a =0 Deg.,

Out-of-Trim, -4 Degree Longitudinal Flapping

Experimental Shear Force, /*• = 0.2, a = -4 Deg., s

Zero Lag Damping .......

Experimental Shear Force, H- = 0.3, a = 0 Df• s

Experimental Shear Force, H- = 0. 3, a = -4 Deg.

Experimental Shear Force, H- = 0.3, a = -8 Deg. s

Experimental Shear Force, H- = 0.4, a =4 Deg. s

Experimental Shear Force, H- = 0.4, a =0 Deg. s

50 Experimental Shear Force, H-= 0.4, a = -4 Deg. s

51 Experimental Shear Force, H- - 0.4, a = -8 Deg.

52 Experimental Shear Force, M = 0.5, a =0 Deg.

53 Experimental Shear Force, H- = 0.5, a = -4 Deg.

125

131

137

143

147

152

158

163

168

173

178

183

187

193

XI

Figure Page

54 Experimental Shear Force, \L = 0.5, a s

= -8 Deg. . 199

55 Experimental Shear Force, \L = 0.5, a s = -4 Deg.

205

56 Experimental Shear Force, H> =0.7, a s

= 4 Deg. . 211

ö*7 Experimental Shear Force, ft =0.7, as = 0 Deg. . 217

58 Experimental Shear Force, p = 0.7, a s = -4 Deg. . 222

59 Experimental Shear Force, /A = 1.0, a = 0 Deg. . 228

60

61

62

63

64

65

66

67

68

69

APPENDIX II

Experimental Radial Shear Force, fi = 0.2 .

Experimental Radial Shear Force, H- = 0.3 .

Experimental Radial Shear Force, M = 0.4 .

Experimental Radial Shear Force, H- = 0.5 .

Experimental Radial Shear Force, P = 0.7 .

236

237

238

239

240

Experimental Radial Shear Force, ft = 0.2, a =0 Deg. 241 s

Experimental Radial Shear Force, H- = 0.2, a = -4 Deg. 242

Experimental Radial Shear Force, P = 0. 2, a = -8 Deg. 243 s

Experimental Radial Shear Force, H- = 0.2, a =0 Deg. s

Out-of-Trim, -4 Degree Longitudinal Flapping . . 244

Experimental Radial Shear Force, /* = 0.2, a = -4 Deg. s Zero Lag Damping 245

xii

Fi igure Page

70 Experimental Radial Shear Force, H- = 0.3, a « 0 Deg. 246 s

71 Experimental Radial Shear Force, p - 0.3, a = -4 Deg. 247 s

72 Experimental Radial Shear Force, M = 0.3, a = -8 Deg. 248 s

73 Experime ital Radial Shear Force, P = 0.4, a =4 Deg. 249 s

74 Experimental Radial Shear Force, M = 0.4, a = 0 Deg. 250 s



77 Experimental Radial Shear Force, H- = 0.5, <* = 0 Deg. 253 s

78 Experimental Radial Shear Force, H- = 0.5, aa = -4 Deg. 254 s


80 Experimental Radial Shear Force, M- = 0.5, ö = -4 Deg. s Zero Lag Damping . - 256

81 Experimental Radial Shear Force, M = 0.7, a = 4 Deg. 257 s

82 Experimental Radial Shear Force, H- = 0.7, a =0 Deg. 258 s


84 Experimental Radial Shear Force, /* = 1.0, a =0 Deg. 260 s

xiii

•*•"•>•

Figure APPENDIX III Page

85 Experimental Vibratory Moment Amplitude, H- = 0.2 261



88 Experimental Vibratory Moment Amplitude, /* = 0.5 273


90 Experimental Vibratory Moment Amplitude, M = 1.0 281

APPENDIX IV

91 Experimental Vibratory Control Load Amplitude, ^ = 0.2 284

92 Experimental Vibratory Control Load Amplitude, /*=0.3 285

93 Experimental Vibratory Control Lead Amplitude, A* = 0.4 286

94 Experimental Vibratory Control Load Amplitude, M =0.5 287

95 Experimental Vibratory Control Load Amplitude, M = 0.7 288

96 Experimental Vibratory Control Load Amplitude, M =1.0 289

xiv

SYMBOLS

Dimensional

Is

B Is

c

D

L

Q

r

R

V

V.

a

0

P

Unit

lateral cyclic pitch degrees

longitudinal cyclic pitch degrees

blade chord feet

rotor drag pounds

rotor lift pounds

rotoi torque foot-pounds

radial distance to local blade station feet

rotor radius feet

forward speed feet per second

forward speed knots

shaft angle of attack degrees

rotor angle of attack, a Is degrees

collective pitch degrees

mass density of air slugs per cubic foot

azimuth angle, measured from downwind position in direction of rotation degrees

fl rotor angular velocity radians per second

xv

SYMBOLS

(continued)

Nondimensional

b

Ver

Ver

M (x, * )

er

number of blades

2 2 rotor drag coefficient-solidity ratio, D/7T R yo (ftR) cr

= D/R3/>Xl2bc 2 2

rotor lift coefficient-solidity ratio, L/7T R /> (XlR) a

= L/R°/>& be 2 2

rotor torque coefficient-solidity ratio, Q/TT R p (ÜR) Ro*

Mach number at radius station x and azimuth position \p .

radius station, r/R

advance ratio, V/&R

rotor solidity, bc/7rR

Note: All Fourier series coefficients for shear forces and

rotor blade flapping and lagging motions are based

on the assumption of a positive series; i.e.,

f (t) = AO + Al cos Si t + A 2 cos 2fU + + AN cos N ti t +

+ Bl sin D. t + B 2 sin 2 Ü t + + BN sin N St t + - - -

where AN = Nth harmonic cosine coefficient

BN = Nth harmonic sine coefficient

N = harmonic order

xvi

INTRODUCTION

As continual improvements have been made in the performance characteristics of rotary wing aircraft, attention to the problems of vibratory loading aid associated structural fatigue has increased. The achievement of low uselage vibration levels and subsequent improvement in aircraft component life and crew efficiency requires, however, a detailed knowledge of the origin of the forces which excite the fuselage. Prior to the start of this investigation, the cause-effect relationship between vibratory loading and fuselage response was not well defined. Previous studies, such as Reference i, have presented rotor blade vibratory airloads and stresses, and successful attempts have been made to measure vibratory loads by instrumenting the rotor shaft, as in Reference 2. None of these studies, however, have reached the source of fuselage forced response; that is, the vibratory forces fed into the fuselage from the rotor blades at the blade root.

It was not considered feasible to design and fabricate a rotor head which could be instrumented to measure these vibratory forces until two conflicting objectives were resolved. First, maximum sensitivity had to be achieved so that higher harmonics of the loads could be accurately measured; second, the stress in the structural components of such a rotor head had to be minimized to reduce the probability of failure. The development of the semiconductor strain gage effectively closed the gap between these two objectives, thus making possible a detailed investigation of rotor blade vibratory root shear forces.

The purpose of the present investigation was to obtain quantitative measurements of the vibratory forcing functions from blades of rotary wing aircraft within the flight speed range encompassing both pure and compound helicopter operations. In addition, the degree of correlation between experimental results and theoretical calculations, including the effects of wake-induced \ ^locities, was to be determined. The experimental data were to be obtained from wind tunnel tests of dynamically scaled model rotor blades mounted on a specially designed rotor head instrumented to measure flatwise, edgewise, and radial vibratory root shear forces.

The objective of this report is to present the experimentally obtained data and to place these data into a meaningful context by discussing, with specific examples, the effects of forward speed, rotor loading, lag damping, and flapping trim condition. The experimental results are correlated with a theory developed at Sikorsky Aircraft, described in Reference 3.

' - ... - .•>• -

DESIGN DATA AND DESCRIPTION OF EQUIPMENT

ROTOR HEAD

The model rotor head was designed to utilize semiconductor strain gages having a gage factor of approximately 100. The structural components of the head, namely, the upper and lower plates, are 7075-T6 aluminum alloy. A fail-safe mechanism with a safety factor of 20 was provided to prevent major damage in the event of failure in the instrumented section. Figure 1 (a) shows the basic rotor head with the in- stalled semiconductor strain gages, and Figure 1 (b) shows the assembly of the head. The pitch control horns are adaptable to pitch-flap coupling ratios of zero and unity, but the present investigation was conducted entirely in the 83=0 configuration. Figure 2 is a schematic diagram showing the force and moment conventions and the location of the strain gages.

CALIBRATION

The model rotor head instrumentation was statically calibrated to determine primary slopes, interaction constants, and temperature compensation factors. In the course of this work it was found that to obtain a satisfactory calibration matrix, it was necessary to include measurements of the tangential moment on the instrumented section caused by the lag damper reaction and the edgewise shear force. The resolution of the shear force measurements based on the static calibra- tions and the noise level of the data acquisition system was determined to be:

Flatwise ± 0.17 pound

Edgewise ± 0.12 pound

Radial ± 0.05 pound

The repeatability of the shear forces determined during the wind tunnel testing and the magnitude of the calibration matrix elements resulted in a final shear force accuracy of ± 0. 2 pound in all three directions. The flatwise and edgewise shear force strain gage circuits were each composed of two active and two dummy gages wired to measure the total shear force and to cancel bending in the instrumented section caused by the shear force. The radial shear force circuit was composed of four active gages in the Poisson arrangement. This circuit also measured the total shear force and cancelled bending. The tangential moment circuit was composed

of two active and two dummy gages to measure the bending moment on the upper instrumented section. All of the dummy gages were mounted on the unstressed center section of the upper plate.

ROTOR BLADES

The model rotor blades were untwisted, 9-foot diameter, 2.69-inch chord with an NACA 0012 airfoil section, and were dynamically scaled in flatwise, edgewise, and torsional stiffness properties from the Sikorsky S-56 (CH-37) main rotor blades.* With the specially instrumented, four- bladed rotor head, the rotor solidity is 0.0634. Figure 3 shows the components of a model blade and a fully assembled blade. The model spar was built up of laminations of fiber glass and paper. Trailing edge pockets were composed of balsa wood ribs covered with magnesium and were bonded to the spar. Figure 4 shows the blade spanwise mass and stiffness distributions, and Figure 5 shows the flatwise, edgewise, and torsional natural frequencies of the blade as functions of rotor speed.

The development of the fiber glass model blades evolved from dynamically scaled model rotor blades made of aluminum, used in studies such as Reference 4. These metal blades were designed to operate at full scale tip speeds, but the investigation of rotor behavior at high forward speeds necessitated the development of blades which would retain their dynamic similarity while operating at reduced tip speeds. The reduced speeds resulted from the desire to simulate forward speeds higher than the wind tunnel limit of 175 knots. Reference 5 describes the development of this type of blade using reduced-stiffness spars of fiber glass-paper laminate construction. The various scaling ratios, listed in Table III, are taken from reference 5. The stiffness of the composite spars is scaled in the flatwise, edgewise, and torsional directions from full scale values. The resulting stiffnesses are reduced from those of the aluminum model blades by a factor of 5.5, so that the reduced experimental velocities are 1/./5.5 times the full scale velocities. For example, at an actual tunnel speed ot x00 knots, the fiber glass rotor blades are dynamically similar to the full scale blades operating at 100 >/5.5 or 235 knots, and this speed is referred to as the equivalent forward speed.

* The full scale S-56 main rotor blades are twisted -8 degrees

WIND TUNNEL

Testir.g was conducted in the United Aircraft Corporation's large subsonic wind tunnel. This is an atmospheric-density, closed-return tunnel powered by a 9000-horsepower motor and having a maximum speed of approximately 175 knots. The test section is octagonal in cross section, 18 feet across the opposite flats. Remotely controlled air exchangers are employed to maintain constant stagnation temperature during operation. Figure 6 is an artist's drawing depicting the general arrangement of the tunnel.

HELICOPTER ROTOR TEST RIG

The helicopter rotor test rig (HRTR) is equipped with a six-component strain gaged balance and is powered by a variable frequency electric motor rated at 375 horsepower at 6000 rpm. Figure 7 (a) shows an overall view of the HRTR mounted in the wind tunnel, and Figure 7 (b) shows the details of the hub and swash plate area. The coincident flapping and lagging hinges are located at the 5.6 percent radius station. Lagging motion is restrained by rotary viscous dampers having a nominal damping factor of 1.9 foot-pound-second for a lag motion amplitude of 1 degree. This value represents 55 percent critical damping. The model dampers have an adjustable damping feature which permits the selection of any desired damping factor within a moderate range determined by the work- ing fluid in the damper. The dampers were set to the above value by calibrating them in a special calibration fixture which operates the damper at a specified frequency and amplitude and records the resulting torque output. The damper was adjusted in small increments until the proper combination of frequency, amplitude and torque was reached. There was a small phase difference between the application of the force to the damper and the minimum force output indicating the presence of spring force in the damper. This was taken into account in the calibration so the value stated above represents the pure damping output. Rotary transformers are used to sense flapping and lagging motion. A conventional swash plate is driven by three precision electric actuators. Collective and cyclic pitch are remotely set from a servo system in the wind tunnel control room, and the yaw table of the wind tunnel provides variation in shaft angle of attack.

The HRTR drive motor is supported by frictionless hydrostatic oil bearings. The motor case is restrained from rotation by a strain gage torque beam to measure rotor torque. Axial displacement of the motor- shaft system is limited by a strain gage thrust beam. The rotor head is supported by a four-component strain gage balance which was not used in

4

this rest program, as this balance is sized for larger forces than were anticipated for this test. Electric signals are transmitted from the rotating system to the stationary system through a 100-channel slip ring assembly.

Dynamic data from the rotor test rig are recorded on a 20-channel EPSCO data acquisition system. Each channel is scanned 36 times per revolution for six revolutions. The information is received from the HRTR in analog form, digitized, and recorded on magnetic tape. These data are transmitted to an IBM 7094 data processing unit and reduced. The primary data reduction program reduces the performance data to dimensional and coefficient form in the wind and shaft axes systems. Tare forces and moments on the rotor hub, obtained with the blades removed, are subtracted from the measured data, so that the reduced performance data correspond to that from the rotor blades alone. Blade motions and bending moment data are reduced to average and peak-to-peak values. The secondary data reduction program performs a harmonic analysis on all 20 channels of information. The measured shear force and tangential moment data are further reduced to correct for calibration interactions and blades-off tares, and finally these data are corrected for the effects of hub flexibility, as discussed in the section on experimental procedures.

THEORETICAL METHOD

The theoretical method of Reference 3 was used to correlate the experimental data obtained in this program. This method is a fully coupled flatwise, edgewise, tor sional aeroelastic analysis based on an extension of Myklestad1 s method for rotating beams. A variable inflow analysis, developed by the Cornell Aeronautical Laboratory, Inc. (CAL) and described in Reference 6, was combined with the blade aeroelastic analysis. The analytical procedure included an initial determination of flatwise and tor sional rotor blade motion with a uniform inflow iteration to obtain required values of rotor lift and propulsive force. This information was used in the CAL analysis to obtain a distribution of induced velocity at ten radial blade stations and twenty-four azimuth locations. With this distribution, using the first flatwise shear force harmonic as a boundary condition, a second iteration was made on the rotor life and propulsive force, which gave final values of blade motions and loadings.

SIGN CONVENTIONS

The sign convention used is that a positive sign indicates:

Measurement Direction

Flatwise Shear Force Upward Edgewise Shear Force In direction of rotor rotation Radial Shear Force Radially outward from rotor (^ Flatwise Bending Moment Upper surface in compression Edgewise Bending Moment Trailing edge in compression # Torsion Moment Leading edge upward 0 Leading edge upward as Rotor Shaft tilted downstream Als Pitch reduction at \|/« 0 degrees Bls Pitch reduction at \\t = 90 degrees

EXPERIMENTAL PROCEDURE

HELICOPTER ROTOR TEST RIG IMPEDANCE

Since it .is desirable to have vibratory shear force results which are independent of the particular rotor test rig employed, the measured shear forces must be corrected for the effects of the displacements of the hub, which induce extraneous forces in the instrumented section of the rotor head. These displacements are caused by the shear forces themselves; therefore, the correction factors must be determined from the test data in conjunction with predetermined properties of the rotor test rig.

The analytical background of this procedure is based on the fact that the deflections of the rotor hub can be predicted with a knowledge of the applied forces. Such deflections are determined by dividing the measured shear forces by an experimentally determined rotor hub impedance. The product of this quotient and the rotor blade impedance, determined analytically, yields the force induced on the blade by the hub motion. This force is then subtracted from the measured results to produce "the final shear force, reflecting only the effects of the rotor blade loading and no effects of the supporting structure motion. The correction can be written in the form of a matrix equation, as follows:

[corrected shear force\ = [measured shear force} -

x r . x fmeasured 1 \shear force/

["theoretical 1 [blade impedance]

[experimental ] HRTR impedance]

To determine the rotor test rig impedance, a special rotor head was fabricated which matched the weight of the one to be used in the wind tunnel testing. This head was mounted on the HRTR in the wind tunnel, and to it was attached an electromagnetic shaker with appropriate instrumentation to measure forces and displacements. By taking measurements over a range of excitation .frequencies in the axial and in-plane directions, the variation of HRTR impedance and principal axes was determined within the range of frequencies to which the rig would be subjected during actual testing. For a rotor with "n" blades, the nth

harmonic of the flatwise root shear forces combine to produce an n/rev vertical excitation of the fuselage. The (n + 1) and (n - 1) harmonics of the flatwise root shears combine to form n/rev hub moments resulting in vibratory pitching and rolling moments of the airframe. The ( n + 1) and

(n - 1) harmonics of the edgewise root shear forces combine to form n/rev longitudinal and lateral in-plane forces at the rotor head. Since the

test rotor was a four-bladed configuration, only the third, fourth, fifth, seventh, eighth, and ninth shear force harmonics affected hub motions. Because in an "n" bladed rotor system only integer multiples of the nil frequency will be seen in the fixed system, the hub motion corrections were confined to the four-per-revolution and eight-per-revolution frequencies. The final test conditions were selected, whenever possible, so that the rotor speeds would correspond to frequencies away from those of low HRTR impedance, in order to minimize the correction factors on the measured data. The corrections of the shear forces based on this analysis were approximately 0.1 pound throughout the test, and the maximum correction was approximately 0.7 pound. It was determined prior to testing that the motion of the HRTR would not alter the rotor blade impedance characteristics by a significant amount, so that these characteristics were reduced to functions of rotor speed only. An example of the HRTR impedance matrix for a rotor speed of 636 rpm is given below.

4 per rev 8 per rev

upstream direction real imaginary

advancing blade direction real imaginary

. [ - 1570 lb/in. - 765 lb/in. - 7050 lb/in. - 2420 lb/in.l

. [ - 3750 lb/in. - 4920 lb/in. - 4920 lb/in. - 4750 lb/in.J

The impedances in the rotor shaft direction were large enough to be considered infinite in comparison to the impedances shown in the above matrix.

WIND TUNNEL TESTING

The wind tunnel testing procedure was to set a desired rotor tip speed, shaft angle of attack, and tunnel speed and then to record data at each of a series of increasing collective pitch settings. The minimum value of collective pitch was that required for zero thrust; and at each collective pitch, longitudinal and lateral cyclic pitch were adjusted to eliminate first harmonic flapping in respect to the rotor shaft. This cyclic pitch condition was defined as trimmed. For some test conditions, the cyclic pitch values were set to yield longitudinal first harmonic flapping of -4 degrees (forward), while holding the lateral flapping at zero to determine the influence of out-of-trim flapping on the vibratory shear forces. The maximum collective pitch was determined by the limiting vibratory stress amplitude on the rotor head or blades. The tested rotor operating conditions are shown in Figure 8 and Table I. In the remainder of the report these conditions are referred to by the nominal advance ratio values, 0.2, 0.3, 0.4, 0.5, 0.7, and 1.0.

EXPERIMENTAL RESULTS

Table I is a listing of each test point in this program. Shaf: and rotor angle of attack, non-dimensionalized thrust and torque, nominal collective pitch, and flapping and lagging motion are listed for each advance ratic. The flapping and lagging motion harmonic amplitudes are printed to three decimal places since the reproduction of the table was done directly from the test data through the data processing unit, but these amplitudes are only accurate to one decimal place or 0.1 degree.

The complete test results are presented in the appendices, and the most significant of these are presented again and discussed in the following section.

The first through tenth harmonic orthogonal components of flatwise and edgewise vibratory shear force obtained in the wind tunnel tests are presented in Appendix I. The flatwise force coefficients are shown as functions of rotor lift coefficient-solidity ratio, and the edgewise force coefficients as functions of rotor torque coefficient-solidity ratio. These data are grouped by advance ratio, each group covering a range of shaft angle of attack.

The first through fourth harmonic orthogonal components of radial shear force are presented in Appendix II. The first harmonic cosine coefficient is shown as a function of rotor angle of attack for constant collective pitch at eack advance ratio. The variation of this coefficient with changes in trim and lag damping is indicated by flagged and double flagged symN)ls, respectively. None of the other harmonic coefficients of radial shear force reached magnitudes approaching those of the first cosine harmonic, instead, they were approximately one pound or 0.3 percent of the steady radial load. The radial shear force harmonics above the fourth did not exceed the one pound level at any test point and are not presented. The remaining radial shear force coefficients are given as functions of rotor lift coefficient-solidity ratio.

Flatwise rotor blade bending moments were measured at four radial stations on the blade at 21, 33, 47, and 64 percent radius. Throughout the range of test conditions, the flatwise moment at the inboard station, 21 percent radius, was consistently the largest measured moment. This fact is substantiated in the following section of the report. The radial locations of the largest measured edgewise and torsional moments are also verified in that section. Part (a) of the figures in Appendix III gives the one-half peak-to-peak values of the flatwise moment at 0.21R as it varies with rotor angle of attack for constant collective pitch and

,

advance ratio. A flatwise moment of 21 inch-pounds at this radial station on the blade corresponds to a stress of 10,000 psi on an equivalent rotor blade made of aluminum; i.e., it has the same unit strain. Edge- wise bending moments were measured at 21, 33, and 47 percent radial stations on the blade. The location of the maximum measured value varied between the inboard and outboard stations within the range of test conditions. Part (b) of the figures in Appendix III presents the one- half peak-to-peak edgewise moment at the 21 percent station as a function of rotor angle of attack for constant collective pitch and advance ratio. An edgewise moment of 56 inch-pounds at this station on the blade corresponds to 10,000 psi edgewise stress on an equivalent aluminum blade. Part (c) of the same set of figures is a plot of the moments measured in the edgewise direction at the 47 percent radial station, with 29 inch-pounds giving the equivalent of 10,000 psi stress. The rotor blade torsional moment was measured at the 17.5, 38, and 90 percent radial stations. The inboard moment was largest at all test points, and its one-half peak- to-peak value is presented in part (d) of the figures of Appendix III in a manner identical to that of the other blade moments. A 35 inch-pound torsional moment at the 17.5 percent radial station corresponds to 10,000 psi on the equivalent aluminum blade. The change in each of the three blade bending moments resulting from out-of-trim operation is indicated by the flagged symbols on the plots for the advance ratio of 0.2. The change resulting from elimination of lag damping is indicated by double- flagged symbols on the plots for advance ratios 0.2 and 0.5.

Rotor control loads were measured on the push rod for the instrumented blade. The one-half peak-to-peak values of this load are presented in Appendix IV in a form identical to that of the blade bending moments.

10

EVALUATION OF EXPERIMENTAL RESULTS

OUT-OF-TRIM OPERATION

The effect of out-of-trim operation of the flatwise and edgewise vibratory shear forces can be seen by comparing parts (a) and (b) of Figure 9, which are taken directly from Appendix I. The only force harmonic which is significantly altered by adjusting the first harmonic flapping with respect to the shaft to -4 degrees in the longitudinal direction is the first harmonic, which produces a pitching moment in the fixed system of coordinates. In particular, the amplitude of the first harmonic shear in both the flatwise and edgewise directions takes on a value on the order of double that of trimmed operation. This behavior is what would be expected since a one per revolution forcing function is being introduced in the system. Figure 9 also shows that the phase of the first harmonic shear force becomes less sensitive to changes in rotor lift when the rotor is taken out-of-trim. The effect on the cosine component of the first radial shear force harmonic is not well defined, but the points in Figure 60 of Appendix II indicate that this component is generally increased by operation out-of-trim. The data in Figure 85 of Appendix III reveal that the principal effect of out-of-trim operation on blade bending moments is ai increase in the one-half peak-to-peak flatwise moment approximately equivalent to that resulting from a 2-degree increase in collective pitch or roughly a 7500-pound increase in full-scale rotor lift. However, the edgewise and torsional moments are not significantly altered. It should be noted that because of the flapping and lagging motion of the blades, the blade bending, and the variation of the blade pitch over the rotor disk; the axis system in which the blade bending moments are measured is being continually displaced in both translational and rotational directions with respect to the axis system in which the root shear forces are measured. As a result, there is a large interaction between events occuring in any one direction of the blade axis system and the three directions of the shear force axis system. This effect is seen above where operation out-of-trim caused a change in the edgewise shear force with no significant change in the edgewise blade bending moment.

EFFECT OF LAG DAMPING

The effect of lag damping on the vibratory shear forces and blade moments must be evaluated in light of the proximity of the rotor operating condition to an edgewise blade natural frequency. For this reason two rotor speeds are considered. At the advance ratio of 0.2, the first edgewise bending frequency is very nearly three per revolution, whereas

li

at the higher advance ratio , 0.5, at which the rotor tip speed is reduced, the first edgewise bending frequency is farther removed from a resonance point, as shown in Figure 5. Comparing parts (a) and (b) of Figure 10, which is taken directly from Appendix I, it is seen that removal of the lag damping at the condition near the edgewise natural frequency results in an increase in the edgewise shear force harmonics shown, particularly the third; which displays an increase in maximum amplitude of about 25 percent. Removal of lag damping at the other condition results in a decrease in the edgewise shears, as seen by comparing parts (a) and (b) of Figure 11. The third harmonic amplitude decreases 20 percent at CQ/O" =0.005 for this case. The remaining shear force harmonics for these four test conditions, given in Appendix I, show that the edgewise force harmonics above the fourth behave essentially the same as those shown in Figures 10 and 11 and that the flatwise shear force increases with the removal of lag damping at both rotor speeds. The latter effect results from the increase in flatwise blade bending moments discussed below. The effect of lag damping on the radial shear force is not clearly indicated by the data taken from JJL =0.2, but Figure 63 of Appendix II for /x =0.5 shows a definite pattern in which the first cosine harmonic is initially reduced but later reverses as the collective pitch is increased and eventually increases at the higher collective pitches.

The data in Appendix III show that removal of lag damping results in a slight increase in flatwise and torsional blade bending moments at both rotor speeds. This moment increase is largest at the high collective pitch settings and is essentially zero at the low settings. This effect is a result of the fact that, xperimentally, more longitudinal cyclic pitch was required co maintain the rotor in a trimmed condition when the lag damping was removed than with full lag damping. It is not clear why this additional cyclic pitch is necessary, but the effect is consistent throughout the test. The edgewise bending moments at the inboard radial station are increased at both rotor speeds by an amount equivalent to a one degree increase in collective pitch or an increase in full scale lift of approximately 4000 pounds. At the outboard station the increment in edgewise moment due to the removal of lag damping is much larger at the higher rotor speed than it is at the lower speed. The increase at the lower speed at this station is of the same order of magnitude as the increases on the inboard station. This is seen in Figure 12, which is a plot of data extracted from Appendix IV. This effect of rotor speed on the edgewise r°sponse to changes in lag damping, is related to the effects of the rotor operating condition's being near an edgewise natural frequency, already discussed in connection with the edgewise shear force. It would be expected that the removal or reduction of lag damping at rotor speeds

12

4

remote from an edgewise natural frequency would cause a reduction rather than an increase in the edgewise bending moments because the restraining load on the blade root is reduced. For the rotor speed in question, however, Figure 5 shows that the test point is not sufficiently removed from the critical speed to preclude the presence of resonant excitation effects. The trend of reduction in edgewise bending moment and shear force with changes in roior speed away from the critical value is clear, nevertheless, and for an advance ratio of 0.7, Figure 12 shows edgewise moments which are considerably lower than those measured with full lag damping.

EFFECT OF FORWARD SPEED

Figure 13 shows the effect of forward speed on the flatwise and edgewise shear forces. The amplitudes of the second through tenth harmonic coefficients, derived from the data presented in Appendix I, are presented as functions of advance ratio for a constant rotor lift coefficient - solidity ratio of 0.035 and a shaft angle of attack of -4 degrees with the rotor trimmed to zero flapping with respect to the shaft. The shear force amplitudes are noncümensionalized by the lift per blade to provide an indication of the magnitude of the vibratory loads relative to the steady loading on the rotor. The flatwise vibratory loading shows a general increase with forward speed in all harmonics. In some harmonics, particularly the third and fourth, the increase is very rapid as the advance ratio exceeds 0.5. The same pattern is evident in the edgewise vibratory loading, with the third and fourth harmonics again reaching very large values at fj, =0.7. This flatwise and edgewise shear force response stems directly from the change in the behavior of the rotor blade in the edgewise direction as the forward speed is increased. This change is discussed below. The effect of forward speed on the first cosine harmonic of the radial shear force can be assessed from Figures 60 through 64 in Appendix II. In general, increasing forward speed causes this shear component to change from a nose down pitching moment component to a nose up component. The magnitude of this shear force was not anticipated and the cause of the measured behavior could not be determined without an extensive analytical effort; beyond the scope of the present study.

Figure 14 presents the one-half peak-to-peak blade bending moments as functions of advance ratio. The test points, listed in Table II, included those for as= -4 degrees for ß = 0.2, 0.4, 0.5, and 0.7, and for fi =0.3 with CL/r = 0.062. The lift coefficient-solidity ratios are not

constant for these five points but decrease with forward speed, as would be the case in compound helicopter operation, from

13

•»

CL/O- =0.071 at /x=0.2tocL/cr =0.032 at /x=0.7. The results shown represent a more realistic situation as compared,for instance, to the case with a constant CL/o* equal to 0.032. The blade moments in all three directions increase with advance ratio. The edgewise and torsional moments are strongly influenced by the forward speed above the 0.5 advance ratio. It is notable that the maximum flatwise bending moment occurs at the inboard radial station throughout the forward speed range as does the maximum torsional moment, while the edgewise moment shifts from the inboard end of the blade to the outboard end as the forward speed is increased. The time histories of these moments can be seen in Figures 18, 21, 22, 23, and 24; and it is evident that the shift of the maximum edgewise bending moment station is a result of the change in the participation of edgewise bending modes. At the low advance ratios the first elastic mode predominates, but as the speed is increased additional modes become significant so the station of maximum bending moment ?«? changed accordingly. It should also be noted that with the flatwise stiffness distribution given in Figure 4, the maximum bending stress tends to occur at the 64 percent radial station, which is in accord with flight measurements.

The time histories of the flatwise, edgewise, and radial shear forces at the same five test points are shown in Figures 15, 16, and 17; from them the change in harmonic content with forward speed can be observed. As the advance ratio is increased from 0.2 to 0.4, the first harmonic predominates in all three directions with some high harmonics of small amplitude appearing in no definite pattern. Above 0.4, all of the forces are predominately fourth harmonic. This effect would cause a change in the fuselage forcing functions from a steady moment at the low speeds to a four per revolution excitation at the high speeds. The cause of this variation of shear force harmonic content can be determined from the points in question shown in Figures 18 through 24, which present the azimuthal plots of blade bending moments at all seven points listed in Table II. The striking feature in these plots is the character of the edgewise bending moment at the high advance ratios. Essentially, it is composed of the fourth harmonic with an amplitude on the outboard station reaching 20 inch-pounds. Since the flatwise bending moment does not exhibit the same character, it can be concluded that at the 0.7 advance ratio the shear forces are primarily influenced by the edgewise blade bending through the mechanism of the displacement of the blade axis system from the shear force axes system.

Looking now at the change in harmonic content of the blade bending moments with forward speed in Figures 18, 21, 22, 23, and 24, the edgewise moment is seen to be essentially third harmonic at the lower

14

advance ratios as would be expected because of the nearness of the rotor speed to the edgewise natural frequency point. At the higher advance ratios, however, the rotor speed is reduced and moves away from the critical speed, but does not closely approach the four per revolution natural frequency. Therefore, the edgewise behavior at these high advance ratios cannot be categorically attributed to resonant excitation. The list of lag motion harmonics in Table I for the ft = 0.7 data point shows a fourth harmonic amplitude larger than any others but the first, and a comparison in Table I with the lower speed points reveals that the first harmonic lag motion dominates all other harmonics in amplitude. Although the magnitudes being compared are on the borderline of the measuring system accuracy, an aerodynamic source of the high speed edgewise behavior is implied; but this has not been positively determined. It was observed during testing that removal of the lag damping at the high forward speeds resulted in a reduction of the fourth harmonic magnitude and in an increase in the third harmonic magnitude of the edgewise blade response. It should also be noted that the test data at fjL = 1.0 show the same effect: a large fourth harmonic with lag damping and a shift toward the third harmonic with reduced lag damping, even though the rotor speed is 15 percent lower at this condition than it is in the fJL - 0.7 condition. Investigation of this phenomenon is impeded by the shortage of experimental dynamic data at high forward speeds and by the complexity of the actual lag damper behavior. While the moment output is nominally pure damping linearly related to the velocity, as discussed in the section entitled "Helicopter Rotor Test Rig"; there is some spring content which varies in a complex manner with frequency and amplitude. The exact determination of these characteristics is beyond the scope of the present study. In this program, the structural limitations of the special rotor head precluded extensive data taking at the high advance ratios because of the very large vibratory forces involved. Designing for such large forces would have reduced measuring accuracy at lower values of advance ratio, fi .

The torsional moment in Figures 18 through 21 is essentially first harmonic in character at the low forward speeds, reflecting the cyclic pitch input. At the higher speeds, appearing first at an advance ratio of 0.4, the torsional moment has an increasing content of high harmonics, particularly at the inboard stations. At the two highest advance ratios, 0.5 and 0.7, presented in Figures 23 and 24, the eighth harmonic response can be traced to the proximity of a natural frequency at 580 rpm. The harmonic content of the flatwise bending moments is difficult to visualize because of the effects of high seventh, eighth, ninth, and tenth airload harmonics at all forward speeds. It is apparent, however, from Figures 18 through 24, that the third and fourth harmonics

15

show a large increase with increasing forward speed relative to the increases that take place in the high harmonics. None of this is attributable to resonant excitation of flatwise modes, but coupling with edgewise blade response undoubtedly contributes to this part of the flatwise response, particularly since both the collective and cyclic pitch settings are high under these conditions; i.e., 0 = 12 degrees, Bi s=l3.7 degrees at fi s 0.7 .

EFFECT OF ROTOR LIFT

Figures 25, 26, and 27 present the time histories of the flatwise, edgewise, and radial shear forces at a constant advance ratio of 0.3 for a range of rotor lift under trimmed conditions. A phase change in the first harmonic is readily apparent in all three components. In addition, the initail reduction and subsequent increase in this harmonic can be seen by comparing the middle load conditions with the high and low conditions. This comparison also reveals that the magnitude of the higher harmonics changes very little over the range of lift. It should be noted that the lowest equivalent forward speed in this program was approximately 75 knots, and due to the variation of wake-induced velocity effects with forward speed the results discussed herein cannot generally be extra- polated to lower speeds.

The correlation between rotor thrust level and vibratory loading is shown in Figure 28. The amplitudes of the flatwise and edgewise shear force harmonics, obtained from Figure 50 of Appendix I, are presented as functions of rotor lift coefficient - solidity ratio at an advance ratio of 0.3 and a shaft angle of attack of -4 degrees. The amplitudes are nondimensionalized by the lift per blade, and data for CL/ O" below 0.04 are not plotted in order to avoid the distortion that takes place as the lift goes to zero. The low flatwise harmonics show an increase as the rotor lift increases. Except for the seventh and tenth, the harmonics above the fourth remain low throughout the range of lift. The rotor speed at this advance ratio, /x = 0.3, yields an operating condition close to the seven per revolution natural frequency of the third flatwise blade bending mode and the ten per revolution natural frequency of the fourth flatwise mode, explaining the departure of the seventh and tenth harmonics from the pattern of the others. Looking at the harmonics of flapping motion for fj. = 0.3 and a s= -4 degrees,it is seen that the ampbtudes of second, third, and fourth harmonic flapping increase with rotor lift. It is this effect which produces the increase in the flatwise shear force second, third, and fourth harmonics seen in Figure 28. The correlation between the rotor thrust level and the nondimensional edgewise shear force harmonic amplitudes is similar to that of the flatwise case for the

16

low harmonics although it is not as marked. The edgewise amplitudes above the fourth harmonic remain low throughout the lift range and do not exhibit even the small increase at the highest lift that was seen in the flatwise harmonic amplitudes.

The vibratory shear forces data presented in Figures 9, 10, 11, 13, 15, 17, and 25 through 28 are taken from only a very small number of the test conditions included in Appendix I. Sufficient information is given in Table I and Appendix I to enable the reader to replot the data of any of the 116 test conditions in any of the forms used herein and to evaluate specific operating conditions in more detail.

17

I CORRELATION OF THEORY AND EXPERIMENT

The experimental data for the seven test points listed in Table II were correlated with the theoretical method of Reference 3.

Figures 29 through 35 present the meroured and calculated shear force harmonic amplitudes. In Figures 29, 32, 33, and 35, the results of uniform inflow computations are also shown. In comparing the measured flatwise shear force harmonic amplitudes with the calculated variable inflow values, the second and fifth harmonics show the most consistent difference among the seven subject points. In all cases, except at fj, * 0.7, it was found that the fourth and/or fifth harmonic of induced velocity on the inboard segment of the blade, as computed in the variable inflow analysis, was higher than any other harmonics above the second. The effect of this on blade response can also be seen in the calculated flatwise blade bending moments at fj, ~ 0.3, 0.4, 0.5, shown in Figure 36. In the case of a large second harmonic difference, it was found that the calculated rotor wake produced a flatwise loading on the outboard portion of the blade which was essentially composed of a two per revolution load. This resulted in a blade flapping motion in which the primary component was second harmonic. For example, examination of the flapping coefficients given in Table I for the /JL = 0.5 point reveals a second harmonic magnitude of 0.8 degrees as opposed to the calculated value of 1,3 degrees.

Looking in particular at the fj. * 0.2 case, the flatwise bending moment presented in Figure 37 shows a sharp peak at the 165-degree azimuth in the calculated values that are present, but is greatly attenuated in the measured values. The cause of this peak was traced to the representation of the rotor wake, in which a tip vortex from one blade is passing under the inboard end of the following blade. Since the circulation is assumed to be concentrated at the vortex core, a rapid increase in induced velocity is felt by the blade, and the high peak in bending moment results. In the physical case with a finite vortex core, the increase in induced velocity is more gradual and the blade response is less drastic, as seen from the measured results in Figure 37. It was analytically determined that a peak such as that given by the calculations would cause an increase in the magnitudes of all harmonics, and it is seen that a downward shift of the calculated shear force harmonics in Figure 29 would yield a much better correlation in every harmonic. As the forward speed and rotor lift are increased and the wake is washed away from the rotor, this peaking effect is diminished as the subject vortex passes under the aft part of the rotor.

18

* ...

•

The remaining significant differences in the measured and calculated flatwise shear forces are in the seventh harmonic at fj. = 0. 2 and the fourth harmonic at fi = 0.7, as shown in Figures 29 and 35, respectively. The latter difference stems from the fact that the large fourth harmonic edgewise blade bending discussed earlier in conjunction with the measured shear force data is not predicted in the computations, even though the flatwise blade bending moment correlation is not unreasonable, as seen in Figure 37. The magnitude of the computed seventh harmonic at the low speed is a result of a resonant excitation of the third flatwise bending mode of the blade caused by a seventh harmonic-induced velocity component over the inboard blade segments having a value nearly equal to the steady induced velocity.

The flatwise shear force harmonics calculated with the assumption of uniform inflow show a steady decrease in magnitude as the harmonic order is increased. The measured results, however, do not follow this pattern, and it is evident that without the higher harmonic excitation provided by a variation in induced velocities, there is no possibility of accurately predicting the harmonic content of the vibratory shear forces. At the high advance ratio, /j. = 0.7, the difference between the uniform and variable inflow results is very small, but the analysis of wake- induced velocities used in this program was not developed for use at high speed. Therefore, the similarity of the two results does not necessarily imply that the effects of wake-induced velocities can be neglected at high speeds. Figure 39a, which shows the measured and calculated flatwise shear forces as functions of azimuth position, verifies that an accurate knowledge of harmonics is the key to vibratory sheai rorce analysis.

Comparison of the measured values of edgewise shear force harmonic coefficients with the calculated variable inflow values, Figures 29 and 32 through 35, reveals a steady decrease in the degree of correlation as forward speed is increased. This is primarily evident in the low harmonics, where the measured values display a magnitude increase not matched by the theoretical values. The agreement of the higher harmonics is better, but only to the extent that both calculated and measured values remain small. It was shown earlier that all the harmonics of edgewise shear force tend to increase with forward speed, but no such trend is evident in the calculations. This absence, then, is the major deficiency in the edgewise shear force analysis. Since the nature of the blade edgewise behavior at the high advance ratios is not well understood because of the undefined effects of such things as the lag dampers and the blade counterweights, and even though calculated results compare favorably at an advance ratio as high as 0.5, as seen in Figure 38, very little can be said about the correlation of edgewise shear forces.

19

The results presented do, however, highlight the need for additional theoretical and experimental analyses of rotor behavior at high forward speeds.

The uniform inflow results and the comparative time histories of the edgewise shear forces, Figure 39b, add nothing to the understanding of the problem at hand. There is no significant difference between the uniform and variable inflow results, and both results differ from the measured values to a large extent. The induced velocity analysis does not account for variations of in-plane velocities, but whether or not the inclusion of these would effect the degree of correlation of the edgewise shear forces could not be determined within the scope of this investigation.

With respect to the overall correlation effort, it is felt that although there is considerable room for improvement, the results are encouraging in view of the fact that it has been impossible to even attempt such a correlation in the past for lack of detailed experimental data. The deficiencies in the flatwise shear force calculations clearly point to the areas in which improvements should be made. Namely, the especially restrictive comparison by harmonics demands that the wake-induced velocities be free of sudden large variations and that the rotor blade natural frequencies be well defined through the high modes. In addition, the strong influence of the aeroelastic behavior of the rotor blade in the edgewise direction necessitates a fundamental understanding of this behavior before a better degree of correlation can be achieved at high speeds.

20

i

CONCLUSIONS

The results of the experimental investigation of the vibratory shear forces generated by an individual helicopter rotor blade of a four bladed rotor system led to the following principal conclusions:

1) The harmonic content of vibratory shear forces can be accurately determined over a wide range of forward speeds and rotor lifts through the use of high sensitivity semiconductor strain gages.

2) The trim condition of the rotor exerts a strong influence on the amplitude and phase of the first harmonic flatwise and edgewise shear forces, but has no appreciable effect on other harmonics. The change in amplitude of the first harmonic forces is proportional to the amount of out -ot -trim flapping. The trim condition exhibited no well defined effect on radial shear forces.

3) Removal of linear viscous lag damping results in a slight increase in the flatwise shear force and either an increaseor a decrease in the edgewise shear force, depending on the nearness of the rotor speed to a rotor blade edgewise natural frequency.

4) Increasing forward speed over a range of from 75 to 300 knots results in a gradual increase in the flatwise shear force. The edgewise shear force remains essentially constant from 75 to 175 knots and then increases rapidly irom 175 to 300 knots, becoming the predominate force at the highest speeds. At forward speeds above 200 knots, the edgewise bending of the blade dominates the shear forces in all three directions to result in a significant change in the harmonic content of the shear forces over the total speed range.

5) Increasing the rotor lift at constant forward speed produces a gradual increase in the flatwise vibratory shear force. A similar effect takes place in the edgewise shear force, but it is confined to the low harmonics.

6) The longitudinal first harmonic component of the radial shear force can take on values having a magnitude equal to those of the other shear forces under high rotor lift conditions at low forward speeds and under low rotor lift conditions at high forward speeds. The fundamental nature and significance of the radial shear force could not be determined within the scope of this investigation.

The comparison of experimental results and theoretical results obtained with a fully coupled aeroelastic analysis led to the following

21

principal conclusions:

1) The inclusion of tne effects of wake-induced velocities alters the theoretcial results in a direction which improves the correlation of the flatwise shear forces.

2) The natural frequencies of the rotor blade must be well defined through the high harmonic range, because the use of wake-induced velocities in the theoretical analysis necessarily introduces high harmonic forcing functions which excite a response in the blade that can be directly reflected in the vibratory shear force harmonics.

3) The theoretical distribution of induced velocities must be free of singular points having velocities greater by an order of magnitude than the surrounding points, because the singular points tend to introduce errors in all the harmonics of a force under consideration.

4) The deterioration of the degree of correlation of edgewise shear forces with increasing forward speed indicates the need for an improved theoretical and experimental definition of edgewise rotor blade aeroelastic behavior.

5) The inclusion of wake-induced velocities has no significant effect on the degree of correlation of edgewise shear forces.

•

22

RECOMMENDATIONS

A more complete understanding of the origin of fuselage excitation requires additional research in the following areas:

1) The existing model rotor should be tested through the low speed range in a wind tunnel having a larger cross section than that of the tunnel used in this investigation. Such a test will provide not only an indication of the magnitude of the effects of the tunnel-rotor diameter ratio (2:1 in this program) on the vibratory shear forces, but will also provide supplementary data at forward speeds below those evaluated herein.

2) A new rotor head having strengthened instrumented sections and fitted with the existing fiber glass blades should be tested to provide more data at forward speeds in the vicinity of 300 knots. Theoretical analyses should be made in conjunction with this experimental work so that specific questions can be answered, such as those arising in connection with the dominance of the edgewise rotor blade bending over the vibratory shear forces.

23

BIBLIOGRAPHY

1.

2.

3.

4.

5.

Scheiman, J., A Tabulation of Helicopter Rotor Blade Differential Pressures, Stresses, and Motions as Measured in Flight, NASA TM X-952, March 1964.

Gabel, R., In -Flight Measurement of Steady and Oscillatory Rotor Shaft Loads" CAL/TRKCOM Symposium, Buffalo, New York, June 1963.

Carlson, R., and Hilzinger, K., Analysis and Correlation of Helicopter RotorBlade Response in a Variable Inflow Environment, USAAVLABS Technical Report 65-51, September 1965. (Sikorsky Engineering Report 50405).

Rabbott, J. P., Jr., Comparison of Theoretical and Experimental Model Helicopter Rotor Performance in Forward Flight, TCREC Technical Report 61-103, July 1961. (Sikorsky Engineering Report 50129).

Fradenburgh, E. A., andKiely, E. F., Development of Dynamic Model Rotor Blades for High Speed Helicopter Research , Symposium on Aeroelastic and Dynamic Modeling Technology, Wright-Patter son Air Force Base, Ohio, September 1963.

Piziali, R. A., and DuWaldt, F. A., A Method for Computing Rotary Wing Airload Distributions in Forward Flight , TCREC Technical Report 62-44, July 1962. (Cornell Aeronautical Laboratories Report BB-1495-S-1).

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o o • O o>"«lW#in«fc«»«

o O

i/i ap"nQ»a»9'-"

_j -. r* <" "M - -* o •-« C O OJ «•........ — oooocooooo W> I I I I

o "s o o w — BSBIioajvlisiu

« ik m o m nt o O O O O C O x •••••<••... a ooooouoooou -I II III « o

ÔTf-i/i*--"-«1-»" fH(«n,ir,c<CC>OtO rnOOOOOOOOO

OOOOOOOOOO

* "O m < CO -j -

o f St CO CO CO CO CO 33 CO

m • r* « « r- _t r* m O Q rv o O OC Neoeoe oc

o-**m + iti'Ot~-m

o o

o 0> —

oo

o*-

• o oo

^0»i"'--"«O«#

---»O-fOO-OO

oooooooooo III I I

o o

»ir*i-#«'">*mir>inf>«if> _i«m««m«im««»«o u.««*000»*^,«-0000

oooouoouoco i i i

o

B«rgm«.oOOCO wo-<-«cooooc oooooooooo III I

c Z CBOBaDUSOCCSi

o < *)>^crii"Mn'«-4oou ^«oooooooooo •ôooooooooo

I I o

-• ^ in r. r- -a -* -» r- -o — o » -o <-» — o~oo

oooooo oooe i i i

o I o» -"

— CO s co • « m

IOO-.00 — INOOO

0-"M"«"4r»ff-

40

TABLE II SHEAR FORCE HARMONIC COEFFICIENTS, LB.

ADVANCE RATIO " 0.191

AlJtlA S = -4 Al-PIIA C = -6.9 I HEIA = 6 CL/SIC = 0.O7I CD/SIC = -0.0041 OQ/SIC - 0.0024

FLATWISE EDGEWISE RADIAL

N COSINE SINE COSINE SINE COSINE SINE |

1 0.5 0.9 1.8 1.1 -7.9 0.9 2 -0.6 o.c 0.3 0.0 0.4 1. 1 3 1.6 ().( -0.5 -0.5 0.6 1.2 4 -0.2 o ^ O.i -0.2 -0.5 0.4 5 0.3 0.! 0.0 -O.I 0.3 0.0 6 Ü. 1 o.: -O.i 0.2 -0.2 0.2 7 0.2 0.1 -0.5 0.0 0.0 -o.i ! 8 0.0 -0.1 -0.2 0.0 0.0 0.0 9 -0.1 0.0 -0.2 0. i -0.1 -o.o

10 0.2 0. 1 -0.1 0.2 -0.2 0.2

ADVANCE RATIO -- 0.283

ALPHA S = -4 ALPHA C - -4.8 THETA = 2

CL/SIC = 0.019 CD/SIC - 0.0007 CQ/SIC • 0.0004

1 -0.4 -3.3 2.3 1.1 -2.3 1.6 2 0.3 -0.3 -0.2 0.3 0.1 -0.7 3 0.4 -0.1 -0.4 -0.3 -0.0 0.4 4 0.2 0.0 0.2 0.2 -0.2 0.0 5 0.0 -0.0 -0. 1 -0.0 -0.0 0 1 6 0.0 0.1 -0.0 -0.1 0.0 0.0 7 -0.3 -0.0 -0.0 -0.0 -0.0 0.0 ! 8 0.0 0.0 -0.0 -0.0 0.0 o.o ! 9 -0.1 0.1 -0.0 -0.0 (1.1 0.0 |

10 -0.3 -O.I 0.2 0. I -0.1 -0.1

AIPHA S = -4 ALPHA C = -6.5 THETA = 4

CL/SIC ^ 0.041 CD/SIC = -0.0OO8 CQ/SIC = 0.00)1

1 -1.0 -2.3 0.5 -0.1 -1.2 0.1 2 -0.3 -0.3 -0.3 0.5 -0.0 -0.7 3 0.7 -0.2 0.0 0.2 -0.2 0.2 4 0.2 0.4 -0.2 0.1 -n. 2 -0.1 5 0.1 -0.0 0. 1 0. 1 0. 1 0.1 6 -0.0 0.1 0.0 -0. 1 -0.0 0.0 7 -0.3 -0. 1 -O.I -0.0 -0.1 -0.0 8 0.0 -0.1 0.0 0.1 -0.1 -0.1 9 0.1 -0.2 0.1 0.3 -0.2 -0 2

.0 -0.3 -0.2 0. 1 -0.0 -0.0 -0.1

ALPHAS = -4 ALPHA C = -7.9 THETA = 6

1 CL/SIC = 0.062 CD/SIC " -0.0029 CQ/S1G = 0.0022

1 -2.4 -1.0 -2.2 -0.3 -0.5 -0.2 2 -0.7 0.6 0.0 0.9 -0.2 -0.9 3 1.4 0.^ 0.5 0.8 -0.5 -0. 1 4 0.0 0.4 -0.2 -0.1 0. 1 -0.2 5 0.3 -0.2 0.3 0.3 0.2 -0.1 6 0.0 0.1 0.0 CO -0.0 -0.1 7 -0.6 -0.2 0.2 -O.C -0.0 -0.1 8 -0.1 0.4 0 1 0.2 -0.2 -0.2

1 9 0.2 0 1 -0.3 -0.0 U. ! 0.1 10 0.4 -0.3 0.1 0.0 -0.0 -0.0

•

41

TABLE II CONCLUDED

ADVANCE RATIO = 0.389

ALPHAS = -4

CL/SIC = 0.046

FLATWISE

N COSINE SINE

ALPHA C = -9.5

CD/SIC = -0.0018

EDGEWISE

COSINE SINE

THETA = 6 CQ/SIG = 0.0022

RADIAL

COSINE SINE

I -2.1 -1.5 -0.5 -0.2 •0.6 -0.2 j 2 -1.2 -1.8 -0.6 -1.2 0.0 1.0

3 10 -1.4 -0.9 0.5 0.8 0.5 4 0.7 0.3 -0.2 -0.4 -0.3 0.3

IS 0.2 0.0 0.0 -0.3 0.4 0.2 6 -0.2 0.2 -0.2 0.1 -0.1 -0.1 7 0.2 0,3 0.1 0.1 -0.3 -0.1 | 8 -0.4 0.1 -0.1 -0.2 0.2 -0.1 9 -0.2 0.3 -0.2 -0.2 0.0 0.3

10 0.0 0.1 -0.1 -0.1 0.0 -0.0


ALPHA b = -4 ALPHA C = -11.9 THETA = 8

CL/SIC = 0.048 CD/SIG = -0.0024 CQ/SIG = 0.0034

I -0.5 -0.2 0.0 0.4 0.2 -0.3 2 -1.3 -2.4 -0.9 -1.5 0.5 1.4 3 0.0 -2.6 -1.3 1.2 0.6 0.3 4 0.6 -1.0 -0.7 1.0 -0.3 0.5 5 0.4 -0.2 -0.1 0.0 0.4 -0.1

' 6 -0.2 0.2 0.0 0.3 -0.1 -0.0 7 0.3 -1.1 -0.3 -0.2 0.1 1.0 8 0.1 0.4 0.3 0.3 -0.4 -0.2 9 -0.2 0.3 0.0 0.3 0.1 -0.7

10 -0.3 -0.1 0.0 0.0 0.2 -0.2


ALPHAS = -4 ALPHA C = -17.7 THETA = 12

CL/SIG = 0.032 CD/SIG = 0.C033 CQ/SIG = 0.0042

1 2.0 0.0 2.0 0.0 -1.0 -0.7 2 -2.9 -2.4 -2.9 2.4 2.3 1.1

i 3 -2.0 -2.7 -2.0 2.7 2.2 -1.0 i -4.3 -4.3 -4.3 -' 3 4.6 2.9

| 5 0.3 0.0 o.o 0.3 0.3 -1.3 6 1.0 -0.' 1.0 -0.1 -0.7 0.1 7 0.0 0.4 0.0 0.4 0.1 0.3 j 8 0.4 -0.9 0.4 -0.8 -0.6 0.4 9 0.3 0.2 0.3 0.3 -0.1 -0.1 0 0.8 0.3 0.8 0.3 -0.4 -0.0

42

—~ — • ,

'

TABLE III - SCALING RATIOS

Model linear dimension = 1/S x full scale linear dimension

Subscript m Subscript fs -

- model full scale

Parameter Full Scale Blade

Radius & other linear dimensions R /R. | nr fs

1/S

Areas- A /kr nr fs i/s2

Mass per unit length m /.n 1/S2

Total mass MK /M. bm/ bfs i/s3

Stiffness EL— /EIVV , etc. ^m ^s i/s5

Angular velocity Ü / £> , m ts >/§

Linear velocities (AR ) / ( il R )fs i/Vs

Mach number M^/M, nv fs lA/S

Froude number 1 (ü2R/g)m/(ü2R/g)fs

3 1/S2 | Reynolds number RN /RNf

Output forces Fm/Ffs i/s3 !

Output moments Mom. m/Mom. fs i/s4

Output elastic strains € _/ € fs 1

Natural frequencies wm/ U)f8 v/S

A3 p

' '

• I

£

LAG DAMPER MOMENT SIMULATION STRUT FOR CALIBRATION ONLY

(a) BASIC INSTALLATION

Figure 1. Vibratory Shear Force Rotor Head.

44

• "^ -

-ALTTRNATC POSfflCH Of ROD ENÜ«..4S,>

1A&

B SPIDER LOWER

t

(b) ASSEMBLY DRAWING

Figure 1. Concluded.

45

•

o cc o z

UJ

< III 2? z V» Z

o hi V- %n o *

< UJ

Ul CC

UJ o cc o

cc UJ

Z Ul o

v- Z Ul

o

z o I- Ü < UJ cr

or UJ a.

< o

o <

o z <

<n UJ Ü cr

£ cr < UJ X if)

u. o z o

u. UJ a

CN

cc ui a. a.

cc Ul

46

-<w

•

UPPER INSTRUMENTED SECTION - TOP VIEW

-TANGENTIAL MOMENT GAGE

L-j FLATWISE SHEAR GAGE

(TOP A BOTTOM SURFACE) A LAG HINGE

TANGENTIAL MOMENT GAGE

LOWER INSTRUMENTED SECTION - TOP VIEW

0.28

"^

<J EDGEWISE SHEAR GAGES

^

/.

LAG HINGE

RADIAL SHEAR GAGES (TOP 6 BOTTOM SURFACE)

"\

(b) SEMICONDUCTOR STRAIN GAGE LOCATIONS


47

MM

>

3 & W i

Ä

CQ

| s

8

El«

43

-«•*-

•

•

in CM I

8

"T-

s

2 o •- < ac O kl

Ul >• o

A

iii: o o» o *o

CM g" O III tE

o £ -i

3-ft:

-CD i-

O </> z> a

10 < O cc

_I <

o z o CO z UJ z

(M O o

C\J o

•u.-qi

90I*WI3 *SS3NddllS 3SIM1V1J

Oo

ui/qi 'SSVW 30VT8

^l-Nr^"

«I r r-Nr 8 CM CO

o O

-JO

Ik

jui-qi »01 * AAI3 'SS3NdiliS 3SIM39Q3

- a, •s. la

CO

6 «2 3 O *

• ° -1 d

0.4

DIM

EN

SIO

NA

.CM Z o 1 O

* CM o o O

SUI -Ql *k0l • CO S3NJJ US 1VN0I« HOI

49

••'••• • - . , _„ .

in

i tin

tdo 'ADN3n03aj

50

1

I 3

C/3

CD

h a u o u

T3

I D

bO •iH

51

' •—

w«

v I

'I

' I • -

52

§

JS en Z H

w O

O

Cd M >

% to

o

«0

bO

(4 M CA Q)

H Ö s peS u <u M

8- U

• r-i r—*

Ü |

0) i bO

3 H

S o w M

Ö o

1 ü C 0 U

53

d

o

6

d

CO

§ •»-1 w

O U M CO CD

h l-H 0)

3 h 'S

CO

CÜ

tin

td* 4Q33dS dIJL 13QOW

o 8 O

O o 00

o o to

o o

o o (Si

«dj 'CJ33dS dll 1N31VAI003

54

***..

CO </> 1- H z z III uj ••» _i

O ü Ik u. U. u. U id oo O O

UJ z

UJ — *£ - o tf> o O Q

O 2

£/ ••;

:3? j b

VG- -JL •1

\- / 0) o

\ o al o

H

8 * °. * CM

-{• >• ? -I A K "

.5 * 9 ^ o P -J UJ

ft 5 H -^

1 * £ . X CNJ K • 1- o z «

• I4I —» =: wo 0 a w .± iX .:£ u.

O 0

fr- ft! u.

CSS o CM 1 1 I

q I J30o0d UV3HS 3SIM1V1J '1N3OIJJ303 OINOWMVH

CO

H

§

1

ft

w

i

55

O SINE COEFFICIENTS Q COSINE COEFFICIENTS

Ist HARMONIC

z - o U. u. UJ o u

o z o a

UJ o

2

< UJ z to

UJ (A

i UJ o o UJ

-.002 0 002 004

T0R0ÜE COEFFICIENT- SOLIDITY RATIO, CQ/<r

a.»-4deg ft «0.2

.010

Figure 9(a) Continued.

56

»


LÜ

U E

8 O

Ü

i

o

£

< Id

(0

I9f HARMONIC - 14

12

10

8

**

Fl ^ /

^^ 1. *- > b-

9

a I

LI

-.02 0 .02 04 .06 .08

FT COEFFICIENT - SOLIDITY RATIO, CL/*

a s =Odeg. /i=0.2

-4 d«g. FIRST HARMONIC LONGITUDINAL FLAPPING

(b) OUT-OF-TRIM

Figure 9. Continued.

57


x w

u u

gs Ik

O Ul

s o x w o 2 2 5 * s

UJ

Ist HARMONIC 10 I

a„ . _ ii._i y*

6 W^ £ 4 <*<>-.,,_ /r T 2 Su£ 2 4^

a±„t -2^ 1 1 1 1 1 1 1 1 1 1 U .002 0 .002 .004

TORQUE COEFFICIENT - SOLIDITY RATIO, CQ/«r

as =Odeg. ^ s°-2

Figure 9(b) Concluded.

58

^

O SINE COEFFICIENTS

Q COSINE COEFFICIENTS

nd HARMONIC

Z Id Id o

28 b. Ik U. w er 0 2 W UJ

z o </> z O UJ 2 (A

o o Id

-2

I u »2 *f B — __j j_ — — — — — — 3 p = - = = ^p = s = = e_5

3rd HARMONIC

1 4 —•• a . m •• — Plfl MM ^B Ml —• —

1T

4th HARMONIC 2

0 H JJu •— 4j -^ GW 0

2

4 -.002 0 .002 .004 .006 .008 .010

TORQUE COEFFICIENT - SOLIDITY RATIO, Cg/r

as =-4 deg. n =o.2

(a) FULL LAG DAMPING

Figure 10. Effect of Lag Damping on Shear Forces.

59

BB0W •*' -*•*""

O SINE COEFFICIENTS

D COSINE COEFFICIENTS

2 nd HARMONIC

Z m in o

Ik Ik u.

o? » 2 z O iii

is O u

3rd HARMONIC

illlHititttitilP 4

4** HARMONIC ^ 1 T 1 1 1 1 xnz n i|i S ...L. n

m9 _ ._. . * -.

-J 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 1J -.002 0 .002 .004 .00«

TORQUE COEFFICIENT - SOLIDITY RATH), CQ/*

a8 *-4deg. /x«02

( b) ZERO LAG DAMPING


60

O SINE COEFFICIENTS

O COSINE COEFFICIENTS

2 nd HARMONIC

UJ O

s

X (A

UJ CO

i UJ o Q UJ

Z UJ

Ü

u. u. UJ o o

o z o a e < z

* ^

-H —

3rd HARMONIC 2(-r :::££:: —-f J — «=5,-_ä;

4LL

2 4 |th HARMONIC

1

0 T ««J •4L -2 T^

•1 1

-4 _j

-.002 0 .002 .004 .006 .008 .010

TORQUE COEFFICIENT - SOLIDITY RATIO, Cg/*

as *-4dtg. /x «0.5

(a) FULL LAG DAMPING

Figure 11. Effect of Lag Damping on Shear Forces,

61

O SINE COEFFICIENTS


UJ O

I < UJ

UJ

Q UJ

UJ

5 u. u. ui O u

on < X

2 n* HARMONIC

L i^

^

3rd HARMONIC i

Q

__

9r

4t* HARMONIC C I

U •fee: W — =< -- • 9 - C

-A. 1 -.002 .002 .004 .006

TORQUE COEFFICIENT-SOLIDITY RATIO, CQ/C

as* -4 deg. fi «0.5

(b)ZERO LAG OAMPING

Figure 11. Concluded,

62

o 2

Ö Q. Z 2

IS

ÜJ

u. < Ü

SI o o </> _ o

CD

-I >- o v> CD

j in

< UJ u. e> o uj < -j -I CD

z o

'aoîOoao A- U \-B _ ± J j pj A- iH 4 41 s 24 4T A _ ]£ * N W

'" Et S t^-E \ ^ 1

- 4 * l T: I

CD

CVJ

ID w co ^r o T

qi-ui 'aorundwv XN3W0W AdOlVäSlA

c\j

- T Ê*- SX «tt-- :t , ^J .. \ JeS ^t- 4 at t . LjnJ Ä.S.-C - -.»L. jpil

-^5 uifc V- ffi 4 4- i^3 -t ^n -

IL± ±. C\J

oc

CVJ

t/> 00 O 7

Ü <

u. o

UJ _l o z <

0L o K o or

ü < l-

a. O

UJ _J o z <

or o »- o or

CM

d ii

4.

W

CN

0)

fc

Qi-u! 'aanindwv 1N3W0W AdOlVdQIA

63

21 % R

•Zr z ^ s I " * c h

5 „ b ^QG I -u*- I /

> O ? *- •• c r 7

5 ^ tî ° J- r H — 4 - "l ?T^ "^

< -1 4

rik Uc^ K Q. r T: •* *

> <

oL i • 1 1 -20 -16 -i? -8 -4

ROTOR ANGLE OF ATTACK, a , deg.

47 % R

5 H / s£ 7 a / / Sc V -,? $• r- 2-8 2 3^ v J "* £ -T-i-f r/ >a _t 7. 7 ^t V §= x_ 2 »-/ „£ 5^4 ^ _5t _2 ^' « tt» 4^ V -j**^ri^G] -._ «s * ir o^.ß>'4* o—*0 4 - «* LJ

r> -—J. L

-16 -12 -8 -4

ROTOR ANGLE OF ATTACK, a , deg.

(b) ft »0.5


64

21 %R

H ,2

z .0 UJ

I s fl^^Ü^Q ~1 . 8~-,,A~ -g1fi*?^^ v- W T L T

0 f3 It 1- t tr Q. CD 2 J^ 5 < ~r

0- -1- -12 -8 -4

ROTOR ANGLE OF ATTACK, a , deq.

(c) ,x = 0.7

Figure 12, Concluded.

65

ÜBSPi355* '•

ui

0.8 2 nd HARMONIC

0.4

3 rC HARMONIC ! -

0.8

0 4

1 t

0 .1 ,.J i

4 th HARMONIC

1.2

0.8

0.4

—' —\ |

r—

- ]

{ i

J f J

) f i ' /

r i

0.2 0.4 Q6 0.8

ADVANCE RATIO, p

1.0

C\_/v »0.035 , o$«-4«jtq.

(o) FLATWISE SHEAR

Figure 13. Effect of Advance Ratio on Nondimensional Shear Forces.

66

5 th HARMONIC

1 1 T l 1

»J-

UJ o

-J ft.

UJ o <

CE UJ Q.

et < UJ

I w

UJ en * <

04 6 th HARMONIC

1 1 i /

A -H

r 1

th 0.4

HARMONIC ; i Hir i [

— —

04 8 th HARMONIC

ElEfeEEEE

0.4 9 fh HARMONIC

0.4 10 n HARMONIC

i 1

. <" '

-L. T u , 0.2 0.4 06 0.8 1.0

ADVANCE RATIO, fx.

CL/JT=0 035 , Q8s-4deq

Figure 13(a). Continued.

67

2 nd HARMONIC

j /

_. j'__ ": . ,*-

=.--* A oLLLJJ: :±±

U 3 rd HARMONIC ö 0.8

CO

£ 0.4 o.

fr- it -. o ;^:::::::::::z:

0.8

0.4

16

41 h HARMONIC V

i /

V /

/ A '

^ 0.2 0.4 0.6 Q8

ADVANCE RATIO, p.

1.0

C^/a • 0.035 , a8*-4deg.

(b) EDGEWISE SHEAR


68

5th HARMONIC 04

04 6 1* HARMONIC

04 7 h HARMONIC

*• 8th HARMONIC 04

4 9th HARMONIC

1 i

0 -L

04 10 th HARMONIC

02 04 OS ADVANCE RATIO, fi

OB

Z\_/<r «0 035 , a,= -4deq

Figure 13(b). Concluded,

69

FLATWISE

02IR

0-33R 0.64R

EDGEWISE

0-2IR 033R 0.47R

TORSIONAL

OI75R

0.3BR

090R

ADVANCE RATIO, fj,

Figure 14. Effect of Advance Ratio on Rotor Blade Vibratory Moments.

70

[

fi> 0.2 CL /<r »0.071

-2-

M-- - - i

• "

O 6 i r

••©--- - -4 j

TT

i • aJ-a.

- *

1 ' V

• -+ i -f •

DATA POIKTS ARE NOT SHOWN IN REMAINDER OF A2IMUTHAL PLOTS.

fi. "0.3 CL/O"-0.062

/x-0.4 CL/<r • 0.046

40 80 120 160 200 240

AZIMUTH, \fr, d«g

as * -4deg

265—"520—^H

Figure 15. Experimental Flatwise Vibratory Shear Force.

71

JA« 0.5 CL/ff-0.048

»

ft»0.7 CL/ff» 0.032

40 80 '" 120 160 200 240

AZIMUTH, ^, dtg

260 320 360

'


72

/*.• 0.2 CL IV • 0.071

ui o K o u.

IE CL o < m

JA« 0.3 CL /""' 0.062

ft "0.4 Ci_/C"" 0.046

120 160 200

AZIMUTH, ^, dtg

as s -4deg

32Ö ' 3. 0

Figure 16. Experimental Edgewise Vibratory Shear Force.

73

/*• 0.5 CL/<r-0.048

/i-0.7 CL/o- -0.032

120 160 200 240

AZIMUTH, ^. dtg

Qs = -4d«q

360


74

ji«0.2 cL fa ' D.07I

\

,J \ ' >

\ ü

\ \ V / \

I \

10 \

Si - /

fi'0.1 CL/<r «0.062

fX'OA CL 19 «0.046

40 80 120 160 200

AZIMUTH, (//, d.g

Oss -4deg

240 280 320 360

Figure 17. Experimental Radial Vibratory Shear Force.

75

I

i

ff 0.3 CL /<r « 0.048

[ 1

2 S A i i

2 y \ >. J *\ ' \ o / \J

\ rr/>^ \ r

-4 u W O

2

UJ I

/I-0.7 CL/<r "0.032

40 80 '20 160 200

AZIMUTH, v|/, deg.

as = -4 deg

240 280 320 360


76

2I%R

?S r-i* \* 3 £2

1 u 2r~rr

33 %R i i i i i i i i i - TT 75__

Ü-r ,- - • >-** •s _ ~£> - S$:s*2 fc?

- nil'. j^ -fc^_ . __^^4L_S=i -^ T i j 4SZ% l?--t 1 — 1 j O- \. * ± ~ _:: £ -2-~:

47 % R 4| 1 ; i I I 1 I > i i i

Ml l~X B ]_

£ ± < - A

u. u , _ 1 -^ .__ : : ± * _::: 5~iz £. ,e=? '^ :2CE? :: _^-7

n_s^_ ::2^: Z_ SSZlt s?.__ ^

.»U LU—I 1 1

64% R

i _ : ± 2 r _ 2 - : L 2 _ . it _. ,, i

- -, -,^ ^ = r- ^ 4 ,^ ZS - -,Z5 Z S " 4 ha"

„Z^SZLJ^L .âz __ -^«£__ s.

: _ .^t :. ±~ :: : 2__ _ ___ __ ± l±.±fc

40 80 120 160 200 240 «.40

AZIMUTH, f, deg

320 360

/i ».0.2 CL/O"»007l a,« -4d*g

(0) FLATWISE MOMENTS

Figure 18, Experimental Blade Moments.

77

21 %

33% R

0 7

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[b) EDGEWISE MOMENTS


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AZIMUTH, ^, deg

fi'O.l CL/O" • 0.015» asx -4d«g

(a) FLATWISE MOMENTS

Figure 19. Experimental Blade Moments.

80

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fj.*0S CL/a * 0041 a,«-4deg

360

(0) FLATWISE MOMENTS


83

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40 80 120 160 200 240 280 320 360

AZIMUTH, + , deg.

(b) EDGEWISE MOMENTS


84

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120 160 200

AZIMUTH, t. deg

M»03 CL/<r «0.062 at«-4d«g

(o) FLATWISE MOMENTS

360


86

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AZIMUTH, t. deg.

(c) T0RSI0NAL MOMENTS


88

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40 80 120 160 200 240 280 320 360

AZIMUTH, i|r, deq.

^=0.4 CL/o- = 0.046 as=-4deg.



89

2i % n # • i • .....

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AZIMUTH, if, deq

360



90

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90% R

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40 80 120 160 200 240 280 320 360

AZIMUTH, t. deg

(c) TORSION AL MOMENTS


91

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40 80 120 160 200 240 280 320 360

AZIMUTH, f, deg

(C) T0RSI0NAL MOMENTS


94

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95

•

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33XR

(b) EOGEWISE MOMENTS


96

47%R

c

z ui z o 2

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Figure 24(b). Continued.

97

175% R

1

]~t-:-r:::t-f:r:|:rv,|.! j •l-Ll-l-i

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90% R

120 SCO 200 t*0 2S0

AZIMUTH, •, d«g

(c! T0RSONAL MOMENTS


98

•

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f 0

u -2

*• -4

* -6

CL /<r • 0 019

:zs

Cu la • 0 041

CL /a- 0 062

80 120 160 200

AZIMUTH, tj>, dog

240 280 320 360

/i «03 a,« -4d«9

Figure 25. Effect of Rotor Lift on Flatwise Vibratory Shear Force,

99

• •'

CL IV 0 077

360

fji* 0 3 a,» -4d»fl.


100

CL irr --0 002

CL Ar • 0.019

CL /«T =0.041

t\_ Kr ' 0.062

40 80 120 160 200

AZIMUTH, <p, dig

240 280 320 360

/i'0.3 a,* -4d«g.

Figure 26. Effect of Rotor Lift on Edgewise Vibratory Shear Force,

101

n

CL/cr. 0 077

CL .'er '0.087

40 60 120 160 200

AZIMUTH, <^, o.g

240 280 320 360

/A «0.3 a,> -4dtfl.


102

Ci /<r • -0.002

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o § 0 u.

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1 1 - -1 •

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Figure 27. Effect of Rotor Lift on Radial Vibratory Shear Force

103

CL/<r -0 077

10

8

CL I* " 0.087

A

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..._4_

-2

-"-%•«<%

r

"60 40 80 120 160 200

AZIMUTH, <//, deg

240 280 320 360

/A «0.3 at»-4d§g.


104

03

02

2 nd HARMONIC

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0 1 4th HARMONIC

1

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5 th HARMONIC

:::^_._::___x: ~

0 02 04 06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/tf

/A • 0.3, a% * - A deg

(o) FLATWISE

Figure 28. Effect of Rotor Lift on Nondimensional Shear Forces,

105

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8th HARMONIC

•

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L- ^

10th HARMONIC 0.1

0 .02 .04 .06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/<r

—

/ '

/x = 0.3, as = -4deq.


106

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4th HARMONIC

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LIFT COEFFICIENT - SOLIDITY RATIO, CL/a

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Figure 28(b). Concluded.

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115

MEASURED

\CALCULATED (V*"IAW-E wrLOW JWM.wuL»itu \un,roM» INFLOW

»»•OS C.WOOH

t»«O.S CL/»« 0.041

M'O.S CL'c-.0 0«Z

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Figure 36. Compare0.1 of Theoretical and Experimental Flatwise Rotor Blade Bending Moments.

116

MEASURED U.,^,,.«, /VARIABLE INFLOW ^CALCULATED |UNIF0RM |NFL0W

ft'0.4 CL/T« 0.046 6rr i i i i i i i i—n—I i I i I I I I i I I I i I I I 1 1 1 I I I 1

+ _ 1 4f_^ rr _

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8 1 1 II 1 1 1 1 1 1 1 1 1 1 II 1 1 1 1 II 1 1 1 1 1 1 1 1 M 1 1 1 1

e

tt

/i"0.5 CL/<r-0.048

120 160 200 240 260 320 360 AZIMUTH, \\f, deg


117

s*

MEASURED i , ,„n /VARIABLE INFLOW

JCALCULATEO (UNIF0RM INFL0W

II'0.7 cL/(j-. 0.03 2

12 O 5

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^

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40 80" I2C 160 ü><$ *240~ 28( " 320 " 960

AZIMUTH, f, dig

O, • -4d»fl

Figure 37. Comparison of Theoretical and Experimental Flatwise Rotor Blade Bending Moments.

118

MEASURED

CALCULATED, UNIFORM INFLOW

6 -T-

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AZIMUTH, +, deg.

240 260 320 360

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Figure 38. Comparison of Theoretical and Experimental Edgewise Rotor Blade Bending Moments.

119

•

WCASUftCD \CALCUL.Tc0 rv»RI»8LE INFLOW JCALCUL4TE0 \UN|F0R- WLOm

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a,. -4Ö.0

Figure 39. Azimuthal Variation of Vibratory Shear Force,

120

£ MEASURED

^CALCULATED rVAR,ABLE ,NR-0W /CALCULATtD \UN|F0RM INFLOW

ffO.z cL/»»o.on

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AZIMUTH, i^. da9

240 2tO 320 SM

«, • -4*»


121

DISTRIBUTION

llS Army Materiel Command 3

US Army Aviation Materiel Command 5

United States Army, Pacific 1

Chief of R&D, DA 1

Director of Defense Research and Engineering 1

US Army R&D Group (Europe) 2

US Army Aviation Materiel Laboratories 28

Army Aeronautical Research Laboratory, Ames Research Center 1

US Army Research Office-Durham 1

Plastics Technical Evaluation Center 1

US Army Engineer Waterways Experiment Station 1

US Army Test and Evaluation Command 1

US Army Electronics Command 2

US Army Combat Developments Command Experimentation Command 1

US Army Aviation School 1

US Army Aviation Test Activity 2

Air Force Flight Test Center, Edwards AFB l

Air Proving r round Center, Eglin AFB 1

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Naval Air Systems Command, DN 7 PRECEDING PAGE BLANK

123

I

*

Office of Naval Research

Commandant of the Marine Corps

Marine Corps Liaison Officer, US Army Transportation School

Lewis Research Center, NASA

Manned Spacecraft Center, NASA

NASA Scientific and Technical Information Facility

NAFEC Library (FAA)

US Army Board for Aviation Accident Research

Bureau of Safety, Civil Aeronautics Board

US Naval Aviation Safety Center

Federal Aviation Agency, Washington, DC

US Army Medical R&D Command

US Government Printing Office

Defense Documentation Center

1

1

1

1

1

2

2

1

2

1

2

1

1

20

124

APPENDIX I

EXPERIMENTAL FLATWISE AND EDGEWISE SHEAR FORCE FIGURES


A

HA

RM

ON

IC

CO

EF

FIC

IEN

T,

FL

AT

WIS

E

SH

EA

R

FOR

CE

, lb

10

8

6

i it HARMONIC j

J

2

0

-2

-4

-6

-8 -.0

LI

/

J j f

4 /

ffl '

C ^^0

2

F* r C

C

OE

>

:F FI CM

.0

EN

2

T •» SC

.0

)L

4

ID IT Y

.0

F

6

IA Tl 0,

.0 8

C L <•

.10

/i=0.2 as:0

(a) FLATWISE

Figure 40. Experimental Shear Force.

125

•

K . Z id Id O

Sf

w Id X

h II.

O SINE COEFFICIENTS


2nd HARMONIC o

4

i ^j^

x 1 1 J .Q-'-*'-*'

£ 1 1 1

3 rd HARMONIC 4

2 -Gr''

|

•2

4tfc HARMONIC 4. . • | • i

2 ^ „-«*>-

0 J"

-j 1 1 1 1 : ::F::-:r-"!__ -.02 0 .02 .04 .06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/*

/i« 0.2 ass 0 deg.


126

KMUMMMI

O SINE COEFFICIENTS O COSINE COEFFICIENTS

Ui o oc o u.

on < UI X

ui

i

U.

UI

5 n HARMONIC 1.5 1

1.0 ^' .-'

.0 n""

p 0

-.5

1.0

.5

0

-.si

•i.o

6 rh HARMONIC

r^ ]

1

u. u. UJ o u

X

th HARMONIC 1.0

.5

0

-.5"

—i 1

G 1 ,

- "TT -M-

— i—]— —

1 i 1 I i •I.O1

-.02 0 .02 .04 .06 .0« .10

LIFT COEFFICIENT-SOLIDITY RATIO, CL/*

/i «0.2 a3--0deg.


127

**•*•» _ .

UJ o K O U.

ith

O SINE COEFFICIENTS

Ü COSINE COEFFICIENTS

1.0 HARMONIC

.5

0

-.9"

•1.0

•

Jl. U I

r""

< UJ X «ft

UJ (ft i -I u.

UJ

th HARMONIC

5r- III III "III IIII

gIII3E = = »lHQlIIî?-IIII-

o

U, U. UJ o Ü

-.02 0 .02 .04 .06 .08 .10


ft* 02 as*0<teg.


128


UJ o

§ u.

< UJ X v>

Ul <n i UJ o o Ul

z Ul

5 u. u. Ul o Ü

o i o s < X

1 rt HARMONIC

fr> f

la s' P s-c

(* r

2 nd HARMONIC

L r 'T * 1 3 rd HARMONIC wm 4»* HARMONIC

MB -2 -.002 0 .002 .004

T0R0UE COEFFICIENT -

SOLI 01TY RATIO, Cg/r

/x« 0.2 as= Odeg.

(b) EDGEWISE


129

——

z ÜJ

UI o o o u, u. u. UI cr o < o UI

z </>

o ^M

z UI o V)

o: < z

UI o o UI

5 th HARMONIC

.5

0

f -.5

1.0

.5

0

-.0

1.0

.5

0

-.5

th HARMONIC

e^

0 SINE COEFFICIENTS


th 8• HARMONIC —

X

6 th HARMONIC

= T* •n 1

gift 1

9th HARMONIC

t 5-« J

-^

10th HARMONIC

a •* = •B *M M

1 . -.002 0 .002 .004 -.002 0 002 .004

(1*0.2 a8 * 0 d«g.

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*


130

[

O SINE COEFFICIENTS D COSINE COEFFICIENTS

lrt HARMONIC

u u ac o to.

< W X

bl I»

i to.

Z to! 3

toi O o

<

M 2B-HARMONIC

. . _|_ , ... • 4- - AT

0 *- "~ ±a" z—z? : : ":"¥"!: t *

411 1 1 1 1 1 1 L 3

3rd HARMONIC 4 :: :::: x::-::_x

0----»---« * -^=>==^q- \

4- + ^ 4I 1 1 l 1 1 1 1 1 J u—1—11111

4th HARMONIC

-.02 0 .02 .04 06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/r

/A« 0.2 as= -4deg

(0) FLATWISE


131

O SINE COEFFICIENTS


hi o K O h.

5th HARMONIC I.U

•.5"' "~

1-0' * 1 1 1 'I 1 ' 1 1 1 1 1 1 1 1 II 1 1 1 II 1

hi

hi «A

5 -I

hi

th HARMONIC 1.0

.5

0

".5

1.6

Ik h. hi O u

o z §

-I

7th HARMONIC 0

5 El

.:::::-•" *s •5 î o L-" ± 3

-.02 0 .02 .04 .06 .08 .10


ft* 0.2 a**-4d«g.


132

Ul o ft o Ik

a: < ui X

Ul

i

Ul

u. u. US o u

z

X

1.0

.5

0

-.5-

1.0

0 SINE COEFFICIENTS CJ COSINE COEFFICIENTS

6th HARMONIC

T e--

H 1— ö

th HARMONIC .b — —

0 w •« n £ D B- ~~

-.5 V 1.0

\

1.5 ü

1.0 10th HARMONIC

-.9

J 1 0 Q- ? 1 1 R .— **

I

-|.0L

-.02 0 .02 .04 .06 .08 .10

LIFT COEFFICIENT-SOLIDITY RATIO, CL/o»

ft «0.2 aa*-4d«g.

Figure 41(a). Continued,

133

•

UJ o

!

a: < UJ X w

111 (A

111 O o UJ

Z UJ

o u. It. UI o Ü

o z o 2 tr <

6 tt H AP (MONK •

0 G

SINE COSINE

COEFFICIENTS COEFFICIENTS

2 4 -T

2 ^ *fc P i

3* > 4u 0

! IH •«• —•

Hi' - •2 , T —

2 2nd HARMONir

1 II ill i

0 J

2 I i L i

2 3 rd HARMONIC j_ 1

0 Th •»• J + = FV 2 1 ,

r~

2 4th HARMONIC

1

0 LU —,41 L n r & HP ? 1 ! ! I

-,002 0 .002 .004 .006 .006 .010

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/<r

ft «0.2 as=-4deg.

(b) EDGEWISE


134


1.0

.5

0

-.3

-1.0

5 rti HARMONIC

ti = k 3ä== XI A _J 1__ l>

UJ o 1 __!_.

< UJ X

UJ

UJ o a UJ

UJ

o u. u. UJ o

6 th HARMONIC 1.0

.5- C

".3

1.0

7th HARMONIC 1.0

S .5 o z < X

1 —

^ > J

u -.5

-1.0 -.002 0 .002 .004 .006 .006 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*

/x*0.2 a8*-4deg.


135

-.


1.0 81 1i HARMONIC

r"i

.5 \ - ft

id c -.5

1.0

s

in

UJ in

o o UJ

bl U

u. Ul o u o i o 3

z

9 th HARMONIC 1.0

Id

"• n

1.0

.0 10* HARMONIC

.5

•* — 0

\5

A

-.002 0 .002 .004 .006 .006 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, Cg/r

fx* 0.2 as« -4deg.


136

Ist HARMONIC


u u K O b.

_L _J L _i i j j n P!

£r- i i / ~P £i^ü L ± ?E*_ *"llâ ,

^ LlLMUuUH^KI ! -4- PN^~ —i—

± _ ± "JO s^L < bl

bl to

2•* HARMONIC

» 2

-4

l_~---4«,«s = = = a= =

UJ

u. bl O o

3 r* HARMONIC

PTT I 1 1—1 1 1 ' I 1 1 1 1 1 1 1

-«-Q-flQ ± -IN-sEE •tt --C T

2L_LLL ± ± 1 1 ± b

< X

4*fc HARMONIC

-.02 0 .02 -04 .06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/«r

/A >0.2 as«-8dtg.

(a) FLATWISE


137

th HARMONIC


UJ o r o

< UJ X (ft

m «ft

-J u.

Z UJ

ll U. UJ o o

.v/

.5 §

0 e

.J

A

1.0 6 rh HARMONIC

P .5

0 -G B

.5

1.9

th HARMONIC 1.0

• .5

-.5

^ ! --MS ->^

' ^**3'"^ 0^** • H"*"""' — >—"-^ ^*J

-1.0 -.02 0 .02 .04 .06 .06 .10 LIFT COEFFICIENT-SOLIDITY RATIO, CL/*

fjL-O.Z as = -8deg.


138

O SINE COEFFICIENTS G COSINE COEFFICIENTS

1.0 6th HARMONIC

o O

.5

0

-.5

•1.0

I

"o 3S~

< ill Z

UJ

* 5 -I u.

Z UJ

u I b. UJ o o

s

9 th HARMONIC (.0

.5

u A v • u ~.Ä

1.0 i

1.0

.5

0

10th HARMONIC

X -.5

-1.0

1 J

1 Q. -.a

1 ± o. _

L

i

-.02 0 .02 .04 .06 .00 .10


ft« 0.2 as«-8deg.


139

-

.

UJ ü c o u.

«r < UJ X (A

INHARMONIC


£ 2 * lit (9 O w

2 nd HARMONIC

0

-2 -^5"3Ê=S""=S=355*

UJ X 2

u. o HI O o -2

3rd HARMONIC

1 . _ _ n44 :=S-

2 *" 1 HARMONIC

r T | 1 ! al k i Qmmmm f ttT

9 1 1 t± _i •

-.002 0 .002 .004 .006 .008 .010

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/<r

/isO.2 as=-8deg.

(b) EDGEWISE


140

.».

1.0

.5

0

-.5

5 th HARMONIC

O SINE COEFFICIENTS


iii o -I.0 m 2

JG 5" •"» &. Ik «-— —•"*"" r s_fc~.,t_^-.___,£--

1

X (A

UJ to i in o o Ul

- Ü u. u. UJ o '->

u z o z <

%* HARMONIC 1.0

.5| C

d ir % J t -

",9 1 1

KO

th HARMONIC 1.0

.5

0

-1.0 -.002 0 .002 004 .006 .006 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, Cg/r

/i =0.2 a8*-8deg.

i! -*


141

.

1.0 8 th HARMONIC

G SINE COEFFICIENTS

G COSINE COEFFICIENTS

.5

0-

UJ o

-.5

1.0

- e —— =t

, „ _| u . c ... - — ä^_

Ul z 10

Ul «n * Ul o o Ul

Ul Ü ü u. Ul o u

o z o

9 th HARMONIC 1.0

.9 | ) E

warn P I fK, *

".3

1.0

1.0 .0,h HARMONIC

.5

0 (

•.a

i n -.002 0 .002 .004 .006 .008 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, Cg/r

/*'0.2 as = -8deg.


142


UJ o K O

a: < UJ X V)

UJ v>

UJ

o u. u. UJ o

o z c <

Ist HARMONIC

14

12

10

8

6

4

2

0

: 1

Jp E i 2Ü M>J L/

î, - vT

"MM 1

, i 1 i 1 1

—?i—H =t = ^--* — 1 t 1 ::S !:± 1 •

i 1—i—1 ,_

2nd HARMONIC

-2

I 1 !

ck ,. L ^H ̂ TT0 FH%-\ _i i H T M M P

2 3rd HARMONIC

L 1 «s J 3 fi fl- N—* 4- —

V i 1 ? —i_I—1—1 i 1

4 ID HARMONIC z I 1 1 1 i

fn 1 hl L mm

| I •> __ 1 1

-.02 0 .02 .04 .06 .08


/x«0.2 as= 0d«g.

(a) FLATWISE

Figure 43. Experimental Shear Force, Out of Trim, -4 Degree Longitudinal Flapping.

143


• th HARMONIC 9

E fe=i*- »L- 4= 4- 5 4" 4 ==!^

6th HARMONIC

tei U K O u.

1 1 TT~ ^

...

• •sÊssisa =Ur- ., 1..] I 1 1. | 1

ut X

UJ

7 tu HARMONIC 5 | i 1 I 3 1

0 1 1 -1 J

TV—H--^ -41

5 Mill ,,

u. 8th HARMONIC

X !S -.9 o ill u. o -5

o 0

u 5 -.s

:

9 tli HARMONIC 1 : 1 1 [ I

J 10th HARMONIC .5

0-

••%

\M\M )Z 0 02 .04 .06 .08

LIFT COEFFICIENT- SOLIDITY RATIO. CL/»

ft «0.2 a$s Odeg.

Figure 43(a). Continued

144


u tc O u.

a: < bJ X

i UJ o a u

I^HAPXONIC

10 i |

8 ~-T X • t ^T

«t j£" 6 g H 4 <^«Sr.„

r7 TT - 2 5u z . n _ _L_ _ L — —

-j 1 ' 1 ' ' 1 1 1 1 ' 1 1

m 2 nd HARMONIC

1 1 1 «h-löi-..-

i ~TW* 2L_LL t±±. 11

III

* 2 lb ik ui 0 o a

-2 o z o

<

3rd HARMONIC

g - E5

4th HARMONIC

bfi±: -2 -.002 0 .002 .004

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/«r

/A = 0.2 a5= Odeg.

(b) EDGEWISE


145

i O SINE COEFFICIENTS


5th HARMONIC 5! 1 U1 1 JhB'+il MF8PU 5^ 1

ü

S« HARMONIC 3 II II

S Mill 1 I

7,h HARMONIC x VI

= -a

o

Ui

UJ o o

z o s K

z

1

.8r- th HARMONIC

1 r p X a t 1 \*i

V-U I —j 1

9th HARMONIC

10 th HARMONIC 1 ; in r i

1 11 . . "5 •002 0 .002 .004


/i «0.2 a8s Odeg


146

-

Id ü K O U.

K < Id X en

Id V>

i -i u.

»- z Id

O

Id O Ü

O SINE COEFFICIENTS O COSfNE COEFFICIENTS

!•* HARMONIC

2nd HARMONIC —'—' T~T~I

3 rd HARMONIC

] 1 ! ! 1! — -r

i n - f i •M

•ft! 1 i ! ! 1 . i 1 I L. i .

< x

4th HARMONIC

ttt+rttt 0 02 .04 06 08 10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/v

fj.*02 as= -4deg

(a) FLATWISE

Figure 44. Experimental Shear Force, Zero Lag Damping.

147

UJ u

o

5th HARMONIC

O SINE COEFFICIENTS


x

V)

i -i u.

u I*. u. UJ O Ü

XX. <

6 \\ HARMONIC 1.0 ! 1 ' ! _ r j

i d H-n .5 : —fO|^" ^—

0 —1—li—^P 1 ! 1

1 L_' 1 .5 T Mill

10 1 1 1 1 1 i i 1 1

7th HARMONIC I.Sr i i i

0 .02 .04 .06 .06 .10

LIFT COEFFICIENT-SOLIDITY RATIO, CL/<r

ft = 0.2 as= -4deg.


148

ü c o

< UJ X «0

UJ

* 5

Z UJ

ü

1.0

.5

0

-.5

1.0

8 th HARMONIC

O SINE COEFFICIENTS


• i — -»- —

U U i

9 th HARMONIC

••UL 4: !

.5

°H—t— fc-B==sB"nS- .*=ä^~ • -3 —e —j—

*.8j i i.J LLLLL • i ... i i i 1 I 1 i

UJ O u

ü z o z

I0,h HARMONIC 1.0

.5

0

-.5

-1.0

1 1 ! ^^P üKTi i ! Z V*^\\P\

1

it!'

i 1 1 i • Ur 1 1 i IE? nrn rWf Hi '

i ! 1 1 1 . ' M 1

> i i [ 111 i i 1 i i Mil i i -.02 0 .02 .04 .06 .08 .10


ft = 0.2 as= -4deg


149

-

O SINE COEFFICIENTS


- 4

Ui o at o

< Ui X

INHARMONIC 1

| . 1

i | 5fc«i .x*

:5dfeB:: i 1 1 1 . . _ j__ r ± 1 1

= 0

o o Ui

I- z UI

o u. Ui o o

o z o 3 ae < x

-2

2ndHARMC »NIC

|

1 I \Az *h h* SB Sl_ T _ 1

3 rd HARMONIC

4th HARMONIC 2i -T | | |-7

^î** 'S ^^\

i -2 -.002 0 .002 .004 .006

T0R0UE COEFFICIENT SOLIDITY RATIO, CQ/«T

ft =0.2 as= -4deg.

(b) EDGEWISE


150


5,h HARMONIC 1.0 ' i i

-nTr «j ^nV

p PT «

-,5L 1 Mill II

6th HARMONIC

< Ui X «/>

tu

* UJ

Q

T 'T T —r T~ [ J ] J" 0

-.9— ill III

7** HARMONIC

-5 SSiSE

9th HARMONIC •9rr TTiirn

1 0lh HARMONIC

-n- 0 •KM V -lfcfti ft 1 I 1

002 0 .002 004 .006 TOROUE COEFFICIENT

SOLIDITY RATIO, Cg/r

ji*02 as* -4deg


151

O SINE COEFFICIENTS


u K O Ik

Id X V»

w

»

-I I*

UJ

o S! »A. UJ o o

I* HARMONIC

i i 1 , n. 4Ä- 1 ' ~QJ— K

-—•—i—• —«i I , / -*r \l±/ JJ°^ *ii

!! .

2"* HARMONIC

I I nH y t nJ-fl-'ir ^Ü"SC-_ -it X - -X J N

\ -- \t 6L Iti s>

3 * HARMON IC 1 1 1

I--V , ^^ ^

1—^^t^^-r— ^ — S T^ 4LI—LLU ± _ ±_sr

< 4,fc HARMONIC X

0

-2 -04 -.02

•: ss BSS

.02 .04 .06 .08

LIFT COEFFICIENT - SOLIDITY RATIO, CL/(

ft« 0.3 a8*0deg.

(0) FLATWISE

Figure 45. Experimental Shear Force,

152

Ul ü

o u.

1.5

1.0

.5

0

-.5

O SINE COEFFICIENTS

Q COSINE COEFFICIENTS 5' HARMONIC

f i

;

3 <* 11 r i •— t

r~ u -s- mm m— 7

111

< Ul

hJ

5

Z Ul o sz Ul O Ü

1.0 6 rh HARMONIC

| i- .5 1 j k- -*

0 fc ** -dr H

.9

I.O

-.5

= -1.0

-1.5

z -2.

-1.5

7 th »• IA RWONIC

n C

i f)

M <y >

y \ v 1

. .-i -J04 -02 0 .02 .04 .06 .08

LIFT COEFFICIENT -SOLIDITY RATIO, CL/*

/x*0.3 as*0deg.


133

1.0 8 th HARMONIC

O SINE COEFFICIENTS 0 COSINE COEFFICIENTS

in o

IM

i 5

.5

0

-.s-

•1.0

"

^ **•»*.

- %r ^r

UJ

u

9n 1 HARMO NIC 1.0 "

1 ) .5

w II ^ s V \. ".5"

I 1* L"

\ I.Or }l

Ul o Ü

o s

or

10th HARMONIC .u

•5 I

, a 1 ,. JLH* • X2C—-dt-3E3E3 ^fco-i*r -4- n*V '.5 9 t X X 5

e\

r _± ^ -.04 -02 0 .02 .04 .06 .08

LIFT COEFFICIENT -SOLIDITY RATIO, CL/o>

/i« 0.3 a8« Odeg.


154

• . •-

INHARMONIC


LÜ O fie o

a: < bJ X

bJ

UJ (9 Q bJ

UJ

o u. U. UJ o Ü

o z o 2 <

• . - •:: 4 4 e i^-

G*o_ ^r*J' c r5* «s, ^. •**" "* iu3? •<**

it ^^^"^^ ' ^ """Q

4 i 1 .. .

2 2" < HARMONIC

0 «L SJ D

2

4

2 ,rd HARMONIC

0 0 «1 r —• In ^ -a: Tm0mm\ \\- — — rO

2 _ i j *r ^F •

4*h HARMONIC

:_:_"T -2 -.002 0 .002 .004 .006 .006 .010

TOROUE COEFFICIENT- SOLIDITY RATIO, CQ/v

/i = 0.3 a$= Odeg.

(b) EDGEWISE


155

1.0

.3

5 th HARMONIC

O SINE COEFFICIENTS


-.5-

o -I.01

in E — = ! : = •o

< Ui X </>

i o o 111

UJ o

U. W O U

6th HARMONIC 1.0

.5 3

0 — r n*.

".9

1.0

7th HARMONIC I.V

^° .5 Z?! o . Sat"» "z*—

".3

IQLLLLI -002 0 .002 .004 .006 .008 .010 TORQUE COEFFICIENT- SOLIDITY RATIO. Cg/r

/x«0.3 as«0deg.


156

1.0

.5

0

8 th HARMONIC


U

£ a. <

vt

UJ en

UJ o o kl

UJ

Ü

u. u. UJ o Ü

o Z < X

9 th HARMONIC

10th HARMONIC

.5

n i

m s* T

n

0| | | | [ | | | I | | i | | | | | | | | | | | | |

0 SE-srl" ÜI*. 0 B3^====S===5C,___ 9 1 m

0 -L-

i

Q.

\m •s*- -^£^ss^ i 1 ^s_

1 -.5

-1.0 -002 0 .002 .004 006 .006 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, Cg/e

/A* 0.3 as=0deg


157

I

O SINE COEFFICIENTS

I- HARMONIC D C0S'NE ÊFFICIENTS

0

-2 A - -4

o • K P -8

I • I 1 1 i 1 ny M^> w i i

i i

*. ? 1 I ; \ 1 \

Uf ' ! i ! 1 i li ! 1 1 i ,

2"* HARMONIC

i

2 1—i 1 I l l 0

L "— - ffl -44- *

3

-2 4f •N ±

PN i

V !>l 1

-6 1 1 1 1 1 1

3* HARMONIC

o o

§ 5

4(—j-

2-- JLD 1

0-- ._4b== *===£: ?=ES I 2-4-

41—L 1

4-- ---%—

2 4 Ih HARMONIC

1 4^ + 4- H 0 T h4=* =F -

s* i 1 1 ! i 1 -.02 0 .02 .04 06 .08 .10

LIFT COEFFICIENT - SOLIDITY RATIO, CL/»

;x = 0.3 as = -4deg.

(a) FLATWISE


158

th HARMONIC TT


o

o

< UJ I

tu V)

i.Of-r 6th HARMONIC

ui

u. UJ o Ü

o z o X or < X

7 th HARMONIC

-.02 0 .02 .04 .06 .08 .10


fi- 0 3 as = -4deg.


159

i

1.0 8 th HARMONIC


LU O ec o u.

< UJ

UJ

-J u.

UJ

Ü

u. u. Ul o o

o K < X

.5

0

-.5-

1.0

1 "! - — • i ! ! i ! ! i 1

i 1 i -1— t;?-"a— "til i

— P _ rr Q

! •

i . i —i — 1 I - *—

9 th HARMONIC 1.0

! l i i I 1 ] | j • r 111

.5 1 -H- 1

i I j =F= 4r i 0 U •f-H

.. L i HD" "Tl f ".5 ! ' LL 1.0

' ! I i 1 1 ! t 1 i i 1 1 1

.5 10th HARMONIC

! ' 1 ill 1 1 *— —1

0 1 .

-.5 C -=c~ 2>«L-

-+c 1.0

1.5

•

i i * - . 1 1 1 t—•-—| - I'ii

1

_L. ill! — 1 1 1 ToIT -.02 0 .02 .04 .06 .08 .10

LIFT COEFFICIENT-SOLIDITY RATIO, CL/«r

/i= 0.3 as= -4deg.


160


1 2

0

-2

-4

UJ o <r o

a: < UJ X <n

UJ w 0 i UJ -9 O o uj .4

1 •* HARMONIC i .cj J i

> .

"T" U<-IJ m ^^

* i

2 nd HARMONIC

si

j

£ 2 u tl u. UJ o u o z o 2 a: < x

1 9

,rd HARMONIC |

0 |

9 1 1 1

2

0

-2 -.002

4 th HARMONIC j 1 !

J t Mi n tf Tr r~h •• -<'! j| ; ! 1

.002 004 .006 ooe T0R0ÜE COEFFICIENT- SOLIOITY RATIO, Cg/a

ft* 0.3 as*-4deg.

(b) EDGEWISE


161

•

O SINE COEFFICIENTS

O COSINE COEFFICIENT»

I 6th HARMONIC

81 -O-

5 9

2 o M

7 th HARMONIC

„, -.5 w » -i.o

u 9 th HARMONIC • 5f

o

5 ••

10 th HARMONIC

r~T ! r i - T4- 44— •^r -_ZL±

I'Tfl*. -44H i r r 1 t ^

1 1 .---F ^t"*1 *• -

i 1 i

-.002 0 .002 .004 .00« OOt

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/«

^t* 03 a8« -4d«g


162


l,f HARMONIC

u u CE O

< Ui X l/>

UI in

* »- < -I

UJ

Ö u. u. UJ o o

2 m HARM ONIC 1 i 1 1

nil L B i ,0 "•4= *3*3 cf- •^ft

5£-i J I i i i i r*

3 rd HARMONIC i V

> »** 4 ,.

:fc 5 ( • — 1 N 1 u 1 i 1

a: < 2

4 t* HARMONIC 1 1 HT

0 D 1 f J J L ' i 1 1 P

> -.02 0 .02 04 .06 OS FT COEFFICIENT - SOLIDITY RATIO, CL /*

/i* 0.3 as= -8deg.

(a) FLATWISE


163


th HARMONIC

UJ o K O

w

A>

2 = 4= ch ,» 0- -U H • i •• f T T ± a —

sn ü ,

o^-

< Id Z

UJ V»

i

th HARMONIC I.Oj—|—p : x x it J .5 — 4^ -P -*+ 1 -3^3= = = 3~SI_ I ^d

i -P ® ".3 j t

i.o^-^- 1

UJ o o

ü

z o z

th HARMONIC 1.0

.J

0

-.5

1

1—1

__l _ 1 -1.0 -.02 0 .02 .04 .06 .08


^.= 0.3 a8s-8deg.


164

G SINE COEFFICIENTS


th 1.0

.5

0

8 '" HARMONIC

UJ o o

a: < UJ X

Id

-I

I- z UJ

Ü

u. u. UJ o Ü

o

-.5-

1.0

1 1 04 .AL.

!

9 th HARMONIC 1.0 1

.5 ! n 0 - 4 t- u

.9

i.a i

1.0

.s

0

-.5

-1.0

10 ** HARMONIC

=

3=|^ö

-.02 C .02 .04 .06 .08 LIFT COEFFICIENT-SOLIDITY RATIO, CL/,

(u=0.3 as=-8deg.


165

I

U a. o u.

< UJ X

ui

i bl O O UJ

z UJ

o E u. UJ o u

o z o s K

INHARMONIC

0 SINE COEFFICIENTS


2 is« • -^-C

2-~L.-Q^---L- .

4

2 nd HARMONIC

-e-TjMy — ir: ::3c:-S' —J

:::f:5:?::!3 -i»- -»-

|l || W

3'« HARMON IC I

d- •a-

C k- <

4th HARMONIC

-.002 0 .002 .004 .006 .006 .010

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/a

fi*0.3 a$* -8deg.

(b) EDGEWISE

Figure 47. Continued,

166

5 th HARMONIC .5n—r


a =3 5 •| T

*

r I !

-.5L

UJ o

2 < UJ X V)

i o

z UJ

- 6 ,h HARMONIC

9{— 1 14-- :5I -*i^; .X

°l t UT i 1 -i w— - _L n ^ r 1

5

0

7th HARMONIC 1 1

j ^ ] j L 1 T~

i j

5 8 th HARMONIC

i k Lj-fe —* LR L J 1 IJ>

5 1 _ 1 i i m 11 1 UJ o o

o 2 a: < x

9 th HARMONIC

10 th HARMONIC .5 1 4- J 1 F-£ =:=£ —h = 33 tt1 ̂ -4*i=:=_db =+4« —•+

1 I 1 . I -.5 -002 0 .002 .004 .006 .000 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*

fi- 03 ass -8deg


167

UJ U m o u.

bi

Ul

i -j


1 •t HARMONIC i 1 ! 1 1 h i M M 1 1 | C i P U \ 1 . -

•-

I | _. i—J 1 1 1

4 2"* HARMONIC | j

Z

l r^ ~~H K r i— , » ^

H —

2 <* i

UJ

b. UJ O ü

K <

2 3 r4 HARMONIC

0 i r~ i

? i _

4«h HARMONIC 2[—[ =+=

=as3:: 1 x : zLLL 1 Ti 1

-.02 .02 .04 .06 .08


/x = 0.4 a%- 4deg.

(0) FLATWISE


168

UJ u CL o

ft: < UJ X

UJ (ft

Z UJ

u

UJ o

1.0

.5

0

-.5

1.0

O SINE COEFFICIENTS


th HARMONIC

1

r 1

I 1 ^

—• - w L i

6 th HARMONIC

o 2

< Z

7f* HARMONIC ! 1 j

% r i 4 1

i 1

1.0

.f

0

-.5

-1.0 -.02 0 .02 .04 .06 .08

LIFT COEFFICIENT -SOLIDITY RATIO, CL/*

IJL'OA a8* 4deg.


169


th 1.0

.5

O

8 HARMONIC

o -.5

1.0

:Eä?;

m

lii «2 *

9 th HARMONIC

UJ

U

U. UJ o o

u

I <

1.0

.5

n > y "3 r- — -a i—i •«« 1 r i i

.9

1.0'

10th HARMONIC 1.0

.?

0

x -.5

-1.0 -.02 0 .02 .04 .06 .08


1

^. = 0.4 o5= 4deg.


170

ARROWS INDICATE DIRECTION OF

INCREASING COLLECTIVE PITCH

G SINE COEFFICIENTS


o

INHARMONIC

O O -2

Id K 4 O < O UJ

X CO

2 2 Z UJ o w

x g -2 UJ

-4

-S^M- •> X 1 ll s^t -iT^t

Vp*

2 nd HARMONIC

v'^-G

^^ 51 '&% ' ] r~ \r *

-.002 .002

2

0

-2

-4

3rd HARMONIC

S

2

0

-2

-.002

4 th HARMONIC

ffi a is ; i i

.002 TORQUE COEFFICIENT - SOLIDITY RATIO, CQ/«r

/i = 0.4 as= 4deg

(b) EDGEWISE


171

5 th HARMONIC 5

0- h« m 5 n n 11


th 8 *" HARMONIC 5 !

0 JLiA

vJp\

5

z UJ o

o o u u. u. UJ o: o < Ü UJ

X (f)

u —w* z UJ o (/> 2 < X

UJ

o Ui

9 th HARMONIC

6 tl * HARMONIC i.o- 3 " I s .5

0- f !ftö. ,

t JM rjfl • —f— I 5 -.5L 1 . 1

7 th HARMONIC

0

-5

-1.0 -.002

* *

10 th HARMONIC

-.5 .002 -002 .002

TORQUE COEFFICIENT - SOLIDITY RATIO, CQ/*

/i = 0.4 as= 4deg.


172


UJ o a: o

< Ul X V»

UJ

i <

2 l" HARMONIC

j_ i

0 , f ? .1 P If — > ^J-

4 ! 1 i i i 1 !

2nd HARMONIC 2i I I I i I I I I | I I | i I I I I

3 rd HARMONIC UJ

o u. u. UJ o Ü

= 2

2p |—

r 1 r~~ i ka

^ T •c

2' ' ' ' * 1 i J J

4th HARMONIC

(r < z

1 _L --I ft-p- —— — --b- *= -: l j r '

LI

-2 -.02 0 .02 04 .06 .08 FT COEFFICIENT - SOLIDITY RATIO, CL /<r

^ = 0.4 as= Odeg.

(a) FLATWISE


173

o <r o

O SINE COEcFICIENTS

Q COSINE COEFFICIENTS th HARMONIC

.5

of -.5-

1.0

• v V •0 i /

kt

] tf \

1

t»

UJ

-J

6 rh HARMONIC 1.0

.5 L 0 *

*.s

i.a i

UJ o u

o

7 th HARMONIC

-1.0 -.02 0 .02 .04 .06 .08


/x*0.4 as = 0


174

O SINE COEFFICIENTS


th 6 HARMONIC 1.0

.5

0

-.5

1.0

o a: o

a: < tu i

UJ CO

* < _J I».

x -i.O ui

• XT F

• I itT ;

tt -Ü— 1- --0 ±'^^Ä ^"1 !u -

EP T: I i L_ ' . .. -

9 th HARMONIC 1.0 J -X TT 4T ii d .5 L lii 11 U) -+ TrlT-hf-Un 1 !

•fl oC yr r^« ".5f f *T I

.« ILL

u. UJ o o

c>

z o z or <

10th HARMONIC

-I.51

-.02 0 .02 .04 .06 .08


fi = 0.4 ass Odeg


175


1* HARMONIC 4 ~

tal Q [ r 2 -» ' I ' (Z. z—'—'—'—•*-J—'—'—l -1—l -1

2 <K 2 nd HARMONIC UJ Q

«n -z ^r

5 .4± it : o o

Ä 3rd HARMONIC

H _ X- 5 n IBL^T+fi u i — 9. . _, a u. ... .1 •• — • ¥ -4' > 0 * u

S> 4*h HARMONIC

O 2 X

5 ° IPX'T" 2 .2 ±± ±± .002 0 .002 .004


ft «0.4 as=0deg.

(b) EDGEWISE


176

O SINE COEFFICIENTS


z "

u. o 

ü Z Ui O (A

* 5

UJ

6 th HARMONIC

0'

.5 Sm 7 th HARMONIC

5

0

5

.5

0

8 th HARMONIC

-.5

^-jr-

1 Wr$ 1 t Ml

9 th HARMONIC Spy

-^#- ,-;>—

•HI S3' aM- [

10 th HARMONIC 9 1 0 r •f HBB -V m w 5 1

P02 0 .002 .004 TORQUE COEFFICIENT

-.002 0 .002 .004 S0LI0ITY RATIO, CQ/*

/x =0.4 as --Odeg.


177

UJ

< Ul X to

Ul

-A u-

Ul

5

O Ü

or <

0 SINE COEFFICIENTS

0 COSINE COEFFICIENTS

I •* HARMONIC

1 I !

r. ^T-

1"

.. 1 1— ..i._

2* HARMONIC 2U 1 1 1 1 1 1 1 1 1 1 1 1 1 i i 1 1 1 1 0 —-i - 2 *--=* ^b^L

Sr- 4' ' M 1 1 1 1 1 M M II 1 T 1 1 1 1

2

-4

2

0

4" HARMONIC

3" HARMC N C JL

t .. .

-.02 0 .02 04 .06 .06

LIFT COEFFICIENT - SOLIDITY RATIO, CL /«

fi »0.4 as =-4deg.

(a) TLATWISE


178

lü ü oc o

or < UJ X

UJ

<

z

ü

1.0

.5

0

-.5

1.0

1.0

.5

0

-.5

1.0


•h HARMONIC

6 th HARMONIC

v-c 1 J

i Cl

UJ o o

o z oc < r

1.0

• ?,

0

-.5

th HARMONIC

>

-I.01

-.02 0 .02 .04 .06 .08

LIFT COEFFICIENT-SOLIDITY 3ATI0, CL/9

p =0.4 as * -4 deg.


179

UJ o o u.

0 SINE COEFFICIENTS 0 COSINE COEFFICIENTS

1.0

.5

0

-.5

-1.0

1 ,,h HARMON! C

•< fl

--I 'c

< UJ x

UJ CO

i

I- z UJ

u ü u. Ui o o

1.0 t 1

rh HARMONIC i

.5

0

'.3 VI

i n i 1

10th HARMONIC 1.0

1

0 1 ' X 1 11 1

".3

1 A

-.02 0 .02 .04 .06 .08 LIFT COEFFICIENT -SOLIDITY RATIO, CL/9

/x »0.4 a • -4deg.


180


UJ o AC o U.



UI M

UJ o o Ui

UJ

u u. u. UJ o o

u z o s a: <

I* HARMONIC ' r

. r

5t Ui * 's, **fl 1 ^J .Tc^ ITT i 1 3—t^ I 1

2 nd HARMONIC

)

3rd HARMONIC

& L j !

r£ i 1 r ^Ml

._ 4U I 3 1—.—i—

4»h HARMONIC

e"3>-" 1 1 ZTIEJ j -2 -.002 0 .002 .004 .00«

TOROUE COEFFICIENT - SOLIDITY RATIO, CQ/«r

/A «0.4 a% »-4 deg.

(b) EDGEWISE


181

O SINE COEFFICIENTS


5* HARMONIC

'3 III 0 ^4_L .rJ> P**Z: :

-8- S„ ''I I ^Sr. • 0-± £___

:th HARMONIC

Ul M

» IÜ

U

O o

U X o * SI

illlltfH8

7,h HARMONIC .5rr

-.5 m

th HARMONIC

i«ä

8 t*i HARMONIC

1.0 1

5 10 th HARMOHIC

0

.002 0 .002 004 OOt TORQUE COEFFICIENT -

SOLIDITY RATIO, Cg/*

^.•0.4 at »-4 deg.


182


in o K O la.

I,f HARMONIC

a-B^fls-

< Id X «ft

(ft i 5

2 2 nd HARMONIC

2

4

Z UJ

6

u o u

? ' rd HARMONIC

T 1; r-a=a:F .±=if: H*^-*~: 1"

2 '[

4L

z o 3 K <

4:il HARMONIC 2 1 1—1—1

0 ih- •— ^^ "B 1— 3- H—- fl R

T -2 .02 0 .02 .04 .06


/x«04 a$ • -8 deg

(0) FLATWISE


183

«


5 h HARMONIC

1 f

5

tu o r o k.

M

«9

M

-I

X UJ

u

«tfc HARMONIC .5 !

1 T ,5

9 Hi HARMONIC

0 i 3 1 1

8 HARMONIC

o u

u

I

,«. HARMONIC 5

o -

9

10th HARMONIC

-.5 -J02

:""•;:

0 .02 .04 .06 LIFT COEFFICIENT-

SOLIDITY RATIO, CL/*

fi «0.4 a5 • -8 deg.


184

.


u o 0 s Ik -2

* «* -4 u X <A

? UJ CO ^v

IE 0 Ul

o -2

("HARMONIC 4 * I

2 *>», :_

0 "S5I^ •2 *~s* E : A

2 nd HARMONIC

. 3 T » a

• PI 0

K Z UJ

u u. u, o Ü

3rd HARMONIC

u |=St|t;|-i8

= 2 4»* HARMONIC

i: 1^ • 5;l -2 .002 0 .002 .004 .006

TORQUE COEFFICIENT - SOLIDITY RATIO, CQ/a

\L «0.4 a5 > -8 dtg.

(b) EDGEWISE


185

*tW9mn

O SINE COEFFICIENTS


z IAJ

UJ O or

O o u u. b. bJ o: O < Ü u

x t/>

O ^» z UJ o CO 2

< X

UJ

o UJ

5 th HARMONIC ft ' ! 1 0

Q

i

5 ' 1 i *©

6th HARMONIC

-' 0

-.5 .002 0 .002 .004 .006


IN THIS TEST CONDITION THE MAGNITUDE OF THE EDGEWISE HARMONICS ABOVE THE SIXTH DID NOT EXCEED THE REPEATABILITY OF THE SYSTEM AND ARE NOT PRESENTED.

fi -0.4 as ' -8 deg.


186

••"[ iMWij


l'( HARMONIC

tu

2n-HARMCNIC

'Ü1K- 1 0 ;:stt.

„ , 1 "SS-J- * 2531 5IIZZE-5E31 2 - . "2:SES«_ -4 ?l -« -^

-6 T 45 - 6 ± ± 3r :: -a 5r-

io' 1 ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 iJJ

3 '* HARMONIC

0

-2

-4

-6

-8

1 W*f ft» ;=±i—r 1 1 i ' rr T Tks i

V ~t~i~ *.

L t i. Cklk i — r 1 ' |

2 4 •0 HARMONIC

1 J 1 1 1 1 1 0 Ja d i r H Hh |

kTl njwUîr ? 1 1 n TTl ! ! 1-

0 .02 04 .06 .OS .10 LIFT COEFFICIENT - SOLIDITY RATIO, CL f

ft* 0.5 a$*Odeg.

(o) FLATWISE


187

IMMMM

.


th

0 w « -.5 o u- -1.0

HARMONIC _ —_,_

A-.-—X "~* 7

• "a;?"" J H r —

< UJ X .5

0 til £ -.5

< -J u.

-1.0

-1.5

€ to HARMONIC

C 1 |i £ \

— 3-

*l

7 th HARMONIC

o u. u. UJ o u

1.0

.5

0

o -5

O -1.0 5 i: -1.5 x

•2.0 0 .02 .04 .06 .08 .10


1 1 , C

i / { y \S\

1 I L ff 1—J —1 1 ' U+j

1 0 N,! ! j !

L. i_X i !

_i— u—1— i ' i

/i= 0.5 as=0deg.


188

O SINE COEFFICIENTS


;

UJ

5 u. b. UJ o u

Ü

z o z <

3.0

2.5

2.0

1.5

1.0

.5

tu u or o b.

< bl Z

bl (0 * ••»

-I b.

1.0

£ .5 0

-.5

8 th HARMONIC

i £ 7 r - -7 r : i

/

/

;*.;:£ jj • . r

2zmzz?ztt- _ !J2ü

9 th HARMONIC MM 1/ )K i

, - 4 T* h j i A i .y

— _ B , •if ,—i i

10th HARMONIC •* I ft

0

-.5

-1.0 0 .02 .04 .06 .00 .10


/A = 0.5 as=Odeg.


189


INHARMONIC

4 -±rÛ

.... y. ._ . .. *r*^ „

s I **" + f 0 „5B*.„ it " "zz*-~msz*z^z:± w -2 w^ — U- • -2(31 " l£ _t_ _r -ti£_t§ 5-4 1 1 Ml

< 2 nd HARMONIC w 2r

«A

i '2

o -4 c. Ml

-6

i-x::::: : br :: :

^~ * 5"»Ij 1 -it î i r* 1 1 i

w Srd HARMONIC 3 2

2 * O

4»" HARMONIC

r -r t —r- •

-4 -.002 0 .002 .004 .000 .000

TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/I

fta 0.5 a5=0deg

(b) EDGEWISE


190

O SINE COEFFICIENTS


.5 5 rh HARMONIC

0 fc a o

o

-.5

1.0

z •

UJ Ü a:

Ü o u U. U. UJ DC o < o UJ

X </)

Ü

X UJ o </> 2 a: UJ

6th HARMONIC 5r

[ZZ 0- It <v L tv sa 9 c "

oU

o o UJ

7 th HARMONIC

"f" mffltfftffl 0

-.5

-1.0 -.002 0 .002 .004 .006 .006


/x = 0.5 as=0deg.


191

P

ui

* UI o a ui

UJ

o u. u. UI o o o i o

5

O SINE COEFFICIENTS


8 * HARMONIC £.3• 1

6.0 y ^"

j 1 ^' 1.5 -< ^

r -*^ —^ i fi

K _, I Ô- I • uC^^"*" r ^^S»

o T»2?_ " ~rtlt -.5' ' 1 ' rl ' ' ' ' ' 1 1 ' ' ' ' ' ' ' i

,S| 9 tt HARMONIC

*1 i C J

f «•"•

(ft .9 i

in — 1

If Ith HARMONIC .5

0 L li

1 i V)

-002 0 .002 .004 .006 .006 TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*

^. = 0.5 as = 0deg.


192

© SINE COEFFICIENTS 0 COSINE COEFFICIENTS

!•* HARMONIC

I 1 Mil ac;= r-%-*si-ir+i ^P1 1 .

- - f f-?f

i L*r (ill Q-: iri \ ! ! ! 1

2

0

-2

.o -4

o

O 2"* HARMONIC •»• 2

UJ -4

1 s =* -8

. -10-

D- -A^ :__3L.^ O-iNszJ-^-^ziRr

H H i :: : v n _ S ]

LJ 4 V

I ... _i

2 3 r« HARMONIC

-2 •e (

r> d \

-6 p S >4

-8 —i _ 1 i

4»» HARMONIC

-2

Ö- Hi -.02 C .02 .04 06 .08

LIFT COEFFICIENT - SOLIDITY RATIO, CL/r

ft «0.5 at'-4dtg.

(o) FLATWISE


193

.


o

Z < Id Z

111

i 5

z UJ

o iZ M. IU O u

z z

.5

0

-.51

-1.0

-1.5

-2.0

6 rh HARMONIC

4 0 * C n «< s J'l "V s

Sft 1\

?,h HARMONIC 1.5 "" — 10 a^: :: ^^t

_ SJL _,1,^ £ o--B---=a^__

* - -5L 9 .. ^

-1.0 ds;

IB - *. - - ^s

*4i 6 Xi .04 .<6 Ti LIFT COEFFICIENT- SOLIDITY RATIO, CL/V

^ = 0.5 as«-4deg.


194

O SINE COEFFICIENTS


u O u.

< Ul X in

Id

i -i ik

&-" z Ul

E -•* it. w -1.0 o o

o z

§ < X

8 th HARMONIC 2 3

tW A

IS *£ 1.5 3" *-

io + - V 10 .. ? 5 *?

Q-i-ir-jr^' f-C^ 0 o - *r ' ^ *K

-5 5J- 3 \

-I * — — — —— —__ — _-.____

.5

0

3 ,h HARMONIC __ ... T I c i I

— S--;r-aB-=g55;;4EdL- 1 "p* v

I Si

±.. lE-^

10th HARMONIC .?— !

1_- 1 | 1 llll

1)

0-- iZ± -.5-- B

"IT" --r-==5=JC^

1 A 1 -I. -.02 0 .02 .04 .06 .08


/is 0.5 as»-4deg.


195


ui u

< UI X (A

111 (A

i iu o Q IU

at ui u u. 8 O

o

i s

e

2

0

-2

-4

2

0

-2

-4

2

0

-2

-4

I9* HARMONIC ^2r

J* &>-. —a^"*'

5s-T Ê

-^t*-— a L 1 i s ^ ""t t— »0-4— -< > j 'i ! ! i 1

2 nd HARMONIC

t r L_

3

3rd HARMONIC

î!ii!=t 4*h HARMONIC

°BBffl

0 002 .004 .006 .008 010 TOR' JE COEFFICIENT - SOLIDITY RATIO, CQ/,

ft = 0 5 a8s-4d«g.

(bi EDGEWISE


196

O SINE COEFFICIENTS


5th HARMONIC

.5

.0

- •? H a •*

r n S5 5 g i

* *. s 1 1 1

z LJ

UJ o a:

O o u. ÜL U. !&I a: o < Ü U!

X CO

o Z UJ o t/> 2 at < X

UJ

o UJ

6 th HARMONIC ; ! r ] i •f -«—-3r"—T" ^'"""••^

^^= —-*^. ^K j^âiî- T ^ v-ti

7 th HARMONIC

0

.5

.0

.5

0

-.5

-1.0 0 .002 .004 .006 .006 .010

TORQUE COEFFICIENT- SOLIDITY RATIO,

•>

_r i

T /*

/x = 0.5 as=-4aeg.


197

'

.

Id ü

O

< U X

ÜJ

id © o UJ

Id o u. k. UJ O O

o z <

25

2 0

2.5

1.0

.5

0

-.5

0

-.5

1.0

O SINE COEFFICIENTS


8 th HARMONIC 1 T" • "

•JtL.

H •* + -«£

^* V

""'P ^

— ^J^B-Slfc»*.^

Erf-i'^ _ ^3L Iff* ^ ̂i

9 th HARMONIC f k

i • •i -H 3 4 - fc

- 1

10 th HARMONIC 5 1 .4 L-

0 r^ b 92 u _j >_ 1

—1_

0 .002 .004 .006 .006 .010


/x-0.5 as = -4deg.


198

r


a I* HARI'ONIC III III

2 1 " 1 1

« n Tp-ir , f I i - T JP ^ t/ . .2 > *sur : w Jif T > C -4 E- I \ P - —i • — • ' 3, , * J II 1 1 i | •c < X 2nd HARMONIC •> Z |

* .2_.2_i3c=tg=3=±=a. n1 -4 â-

c I Z 111 G 3r< HARMONIC £ " .,-, *JJ.I i

° -2 ^-~^ ^H i -4L : zi^0" § s < 4»" HARMONIC

0—±;^3g=a=ac:*^: -.02 0 .02 04 .06 .08

LIFT COEFFICIENT - SOLIDITY RATIO, CL t*

/1 = 0.5 (?8«-8deg.

(0) FLATWISE


199


HARMONIC

z UJ Id U

II. »«•

6 th HARMONIC

O ?. -.5 UJ

o <*> -1.0

OB * 7 «£ 1.0 x <

s! .5

1 I-* -li

y D -> 4 P "** ^N k. r —

î i

th HARMONIC

0

-5

Q Ml •* H X a H E C

--• r-a -1 J-

r 3

i b. -1.0 -.02 0 .02 .04 .06 .08

LIFT COEFFICIENT- SOLIDITY RATIO, CL/*

/A = 0.5- as=-8deg.


200

^m

O SINE COEFFICIENTS


z UJ

o \Z u. UJ o o

- -1.0

UJ o or o u.

8,n HARMONIC 10 _ S a X *><

- -,r = ~&' n.. «L-JrJ,"*"rE">>> . N

E- - a

ce

z

< UJ z </>

UJ (A

* < _J U.

.5

0

-.5

,0th HARMONIC

1 !

T i r !

! .. 1 ! -1.0 -.02 0 .02 .04 .06 .08


/x=0.5 as = -8deg.


201


I* HARMONIC

o

!

Ul

i Ö O Ui

6

bJ O u

z o

2 2 n( HARMONIC

[

0 ; -I

2 I - 1 |

4 . i -I— J_

2, *" HARMONIC

1 1 1 r >

j «UXi- 1 1 1 1

0 4th HARMOI 11 B

p m p n -2 |

-4 1 1 1 -.002 0 002 .004 006 .00« .010

TORQUE COEFFICIENT - SOLIDITY RATIO, Cg/«r

^•0.5 as»-8deg.

(b) EDGEWISE


202

O O

IAJ CC O < O u

X {/>

o 2 OJ o w>

Is UJ

O SINE COEFFICIENTS


.5 5

n HARMONIC

! ' I I ! I'll I ! > . i :

0 —a= 1

'_J*" i

".5

i r\ L i rt

6th HARMONIC 5 I

•L

>> 5 1

0 1

5 7 ii HARMONIC

I

0 B3 ]

=»u_ r 5 1

n I I i i -1.0 -.002 0 .002 .004 .006 .006 .010 TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*

/i = 0.5 as = -8deg.


203

•

•

O SINE COEFFICIENTS


UJ o K O

< UJ X v>

UJ

* UJ O O UJ

U£

O

u. u. UJ o Ü

u z o 2 < z

B1 fh HARMONIC 1.5 I i

10 «"> .

p> .5

•—• hfi — m 0 - r f •••

-.5 i T

.5

0

•8

-1,0

-1.5

-2.0

9 th HARMONIC

kit G !

' ICâ i p t^^«^ î_v "^^^ i i J& i I

i ^^fct""l ^ \ urSs_

^.

i i r]

! ! ! 1 i

I01 h HARMONIC 5 j } X

• =—tt 1 J 1 . l -.5

-.002 0 .002 .004 .006 .008 010 TORQUE COEFFICIENT- SOLIDITY RATIO, CQ/*

/x=0.5 as=-8deg.


204


l,f HARMONIC

u o

2 *i 4ARMONIC 2 i ! !

E* I "k •V,

d i I •*fll-i_ 1 V" p • 4L I I i I I I I J

< -I

U

3* HARMONIC I I ^,3

^ ~~IE^' ' -- --P "* -I

i ^ r r T c^ ^

5*- - 5*

_SL its, . T T\H

4f* HARMONIC

0 .02 .04 .06 LIFT COEFFICIENT -

SOLIDITY RATIO, G^/9

ft »0.5 as=-4deg

la) FLATWISE

Figure 55. Experimental Shear Force, Zero Lag Damping.

205

-.•MMW4

.


UJ u K O

5th HARMONIC 1.5 1 1 1 | | | | | 1 1 1 1 1 | 1 | 10 »T ,0- S .5 r ft^'ll

0:•==^:?:!!^:: -.51 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 !

*'

< bl X «n

5

6 th HARMONIC u I 5 i) p

u- 1, m < P

y- r —• -i i

5

I-

UJ

o u. u. UJ o o

I - a: <

71 h HARMONIC 1.5

10 U

.9 ß

0 s -.5 s, s ]

-1 0 s \ C N \

-1.5 11 24 2 « .C »2 .c 4 .0

LIFT COEFFICIENT- SOLIDITY RATIO, CL/*

/xs0.5 a3*-4deg.


206

•

O SINE COEFFICIENTS


8 th HARMONIC

tzzzzzzzzzzz-1—

•—i-

5 ' L l

z UJ UJ Ü

9 th HARMONIC

O w 0th HARMONIC

-.02 0 .02 .04 .06 LIFT COEFFICIENT-

SOLIDITY RATIO, CL/<r

/x=0.5 as = -4deg.


207

»•_....


2 I* HARMONIC

ri

0 O-C - o n .îr

2 *B- L> .

2 nd HARMONIC UJ u

IM <r O o u. u. u. UJ or o < Ü UJ

X <0

Ü ••w

z UJ o </>

< X

UJ

o UJ

]

w] VJ

2 3 rd HARMONIC

0 O

2

4th HARMONIC

B^5s=3: 0

-2 -.002 0 002 .004 .006


^.= 0.5 ass-4deg.

(b) EDGEWISE


208

O SINE COEFFICIENTS

• COSINE COEFFICIENTS

UJ

ü

u. u. UJ o o

ü

z o 2 < X

5 th HARMONIC

4 I

.0=S=Jb^±_ - °— o*N

:__ . _ T" Ü

£ 6th HARMONIC .P

ft - j UA-^r i UJ w B5^ X

.3

UJ

5 7 th HARMONIC UJ .3 (!) m Q ta

-s^-îCs^Sf 1

r

-.002 0 .002 .004 .006 TORQUE COEFFICIENT -

SOLIDITY RATIO, CQ/*

fi'0.5 as=-4deg.


209

• • •

.

O SINE COEFFICIENTS


1.0

.5

0

8 th HARMONIC

*, Id Id o O oc

o b. Ii. Ii. UJ o tc Ü <

Id o X

CO z o Id 2 </> cc < * X Id

O Q Id

-.5 1?=?*:==

9 th HARMONIC 5 1

•• i *• & •* =} t 5

«0th HARMONIC 5 1 0 i & •• -1 bi ••«• —• ^ -

i -d i

-.5 -.002 0 .002 .004 .006


/i =0.5 as = -4deg


210


Ist HARMONIC

UJ o

2 •• HARMONIC a: < Ui X

i 2

5 -4

-6

- 0

1 c-^r

5s T

3,d HARMONIC

UJ o o

ill "f He

j 1 1 1 [ _L_

a:

4 * HARMONIC ^

G

2

A 1 1 .02 .04 06 .06 wIFT COEFFICIENT -

SOLIOITY RATIO, CL/<r

fts 0.7 as=4deg

(a) FLATWISE


211

r

G SINE COEFFICIENTS O COSINE COEFFICIENTS

z UJ UJ o

5§ u.

W UJ X

o <*>

Is 2 •- X <

-I u.

5 th HARMONIC

6 th HARMONIC

-.5

-1.0

> = =» lÜpO-

th HARMONIC

-5

1

C i_ 3 J - "lie 5 ! n --4-f-

i 1

SL

0 .02 .04 .06 .08 LIFT COEFFICIENT-


/i = 0.7 as=4deg.

Figure 56(a). Continued,

212

O SINE COEFFICIENTS


UJ o et o

< UJ X

Ui

i < -i

1.0

.3

0

-.5

1.0

.5

0

-.5

1.0

8 th HARMONIC

1

s

j o 1 1 i

c th HARMONIC I

r\ 1

T T -- 1 1 1 1 i !

10 th HARMONIC

u, u. UJ o o

o .


SOLIDITY RATIO, CL/«r

/xs 0.7 as=4deg.


213


S

< tu x

Vt

» hi O a

UJ o h, h. hi O O

Irt HARMONIC

1 1

3 rd HARMONIC

4th HARMONIC

2 2 n* HARMONIC

1 L-J '

2

4 1

i i—l 1 1 i 1

III -U jHi*""^

-J ; W TTT ' i ! 1

002 0 .002 004 TORQUE COEFFICIENT-

SOLIDITY RATIO, CQ/»

fi» 0.7 a8»4deq

(b) EDGEWISE


214

O SINE COEFFICIENTS


UJ UJ ü

cc o o u u. U, tu K o < o UJ

X CO

o M

z UJ o CO

a: < X

Ul

UJ

1.0

0

5 th HARMONIC

-.5

JT

••• mm

y <j

ff?Tl J? =4 ^r 3

6th HARMONIC

i

•••

* « mm J i J

7th HARMONIC

j* ti

r- | •**

^ 1 ft

-.5 .002 0 .002 .004


fi- 0.7 as = 4deg.


215

O SINE COEFFICIENTS


UJ o oc o u.

a: < UJ X </>

UJ to

UJ o o UJ

UJ

u. UJ o Ü

u

o Z tr <

5 8 * HARMONIC

.Mr re v

A M, s »11

WJ -f ^

s F4- T

9 th HARMONIC .5

.9

1.0

1.0

.5

0

-1.0

-1.5 -.002

10'h HARMONIC

-e^X X 1_ _fl 1 L. L_

" "'a**"-

1 * "i) 4 N^ S, it x ^r

_. i_L_ . _ —L_ 0 .002 .004


ft* 0.7 a8=4deg.


216


•• HARMONIC

tat

m 0

8- -I * -4

2n-HARMONIC

-I =i-Q ""**r J

^••^S-r- TM

z tal

G C u. tal O u

3 r4 HARMONIC ^•HJ -VI F

2

4 |

i o i -2

4«* HARMONIC

X -4 Q_m,. _

0 .02 .04 .06 LIFT COEFFICIENT -

SOLIDITY RATIO, CL/r

fx* 0.7 as*Odeg

(a) FLATWISE


217

Z UJ lil Ü

Is X

< h- I <

0 SINE COEFFICIENTS D COSINE COEFFICIENTS

1.0

.5

0

-.5

1.0

.5

0

-.5

1.0

th HARMONIC •'

c

1

6th HARMONIC

G

th HARMONIC

Q



/i = 0.7 as=Odeg.


218

O SINE COEFFICIENTS


th

Z UJ U! O

55 Ik *• u.

X

o w

< K, X <

.5

0

-.5

1.0

8 HARMONIC

3- *h- H Lent

lZit~*KZ Ik^ 5x, 1 ^ L

t~

9 th HARMONIC

1.0

.5

0

-5

0th HARMONIC

-1.0

r Fl JL r

E

G (•



/x=0.7 as=0deg.


219

O SINE COEFFICIENTS a COSINE COEFFICIENTS

I*1 HARMONIC

z w

MJ °

Ik in e o 

* s UJ

3rd HARMONIC

==EE!:E ih«= -

4 til HARMONIC

2 nd HARMONIC

-2

1 i ^1» s.

•^ HI El R

.002 004 004 TORQUE COEFFICIENT -

SOLIDITY RATIO, CQ/<r

ta' 0.7 as = Odeg.

(b) EDGEWISE


220

O SINE COEFFICIENTS


th HARMONIC

iii w

- AC O O •I * u.

O < O UJ

X </>

o z ui O w

UJ o o UJ

r -.5

UJ

fmttf IrT I .

! ID

6 th HARMONIC 5

0

7th HARMONIC

-.5

8 th HARMONIC

9 th HARMONIC

.5

0

-.5

.5

0

-.5

-|.0L

0

n c

ö* •G

10 th HARMONIC

dP„ 8ft Tte E > ̂

002 .004 0 .002

TORQUE COEFFICIENT SOLIDITY RATIO, CQ/<T

fi =0.7 as=0deg.

004


221


1** HARMONIC

i c* <joic 1 !

jc J

y/* 1 1 c. 1 t 1 1

X Z«i HARMONIC

-+-J- n 1 R- 3, 0 > 31

>

J-L - 1 1 1

- Ö u. b. UJ O u

I? z §

2 3'- 1ARMONIC

J _ TTW L^**

2 f ̂ I.

A

I** HARMONIC

.02 0 .02 .04 LIFT COEFFICIENT-


/A »0.7 a8«-4deg.

(a) FLATWISE


222

*

.

O SINE COEFFICIENTS a COSINE COEFFICIENTS

HARMONIC

-° -.5

z ui IAJ O

u. *- u.

X o <*>

o W IÜ < h- X <

1.0 6 th HARMONIC

.5

0

-.5 Ü G i —

.0 7 th HARMONIC

\*. 3

ID T

1 I

-.5 -.02 0 .02 .04

LIFT COEFFICIENT- SOLIDITY RATIO, CL/cr

A

fjL'Ol as=-4deg.


223

O SINE COEFFICIENTS


8th HARMONIC

ui o 5g b. I'- ll.

X

iui

X < -J U.

9 th HARMONIC 1 J fl-e =i •*

V3L . in : 0

-.5

1.0

.5

0

-.5 -.02 0 .02 .04

LIFT COEFFICIENT- SOLIDITY RATIO» CL/*

10th HARMONIC

i S J

1 —i

1

/x*0.7 ass-4deg.


224


INHARMONIC

2 nd HARMONIC

3 rd HARMONIC ! ~]

_ __)

! !

,^_L- i i i i rt-Moi- 1 1

4»* HARMONIC

002 C 002 .004 00« TORQUE COEFFICIENT -

SOLIOITY RATIO, CQ I<r

/A» 0.7 as=-4deg

(b) EDGEWISE


225

• -.5

UJ

u. u. UJ o o

o z o s K < X

UJ o c o u.

< UJ X

UJ en

i UJ o c UJ

-.5

G SINE COEFFICIENTS


5 th HARMONIC

—a...

L B5fc&: A!"*- *9-o-'

6th HARMONIC

L—" ^

Q *Sj>.. *? _ ..

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0

.5 -.002 0 .002 .004 .006


fi'01 as2-4deg.


226

t

O SINE COEFFICIENTS


8 th HARMONIC

•

UJ

Id Ü

^^ cc o o u. U. U. UJ a o < o UJ

X (/>

o z tu o (/> 2 Q: < T

at UJ

o UJ

0 th HARMONIC

.5

-.5

1.0 9

th HARMONIC

1 | 1 Ml' i

.5 1 1 L- , fTl 1 i

: 1 1 IM. i .

0 u[ j I 1 : ! i ! !

-.5 Mi! 1 lii,,

i 1

T~ T i

P i

.A 1 t •

*Jr± > J i _rtirs_ i

^f I TO ! ! / ! IV. 1 i i

002 0 .002 .004 .006 TORQUE COEFFICIENT-

SOLIDITY RATIO, CQ/<r

4

/I* 0.7 as=-4deg


227

I

I- . Z Id Id O

2§ u. •*• u.

85 w id X

o o ti- ls» 5? X <

u.

-2

-4


ltf HARMONIC 10

8

6

4

2

0

-2

-4

-6

Ä 2nd HARMONIC 0

1 —

! '

V \ 1 r 1 V \s > k. >

^ s 1" ,

1 1

«2

C^ 1 ^ rf—-" '""-N L ^^^^"•^^0 N

—ik:*^"*3 ^Ji" ^) ^_^_^_

^^ _.__... ... "11 1

0 2 4 6

COLLECTIVE PITCH, Ö, deg.

10

/x= 1.0 as= Odeg.

(o) FLATWISE


228


z UJ bj o

u. ^ u.

X

o u

is u.

3 rd HARMONIC 6

4 •»'

2 ""7k_

0

2 I 4

—

8 4 th HARMONIC

6

4 H r < 1

2 \ F

0 C }

2 r i ! i

4 C 1 J

1 ~ 4

iO 3S > ! L_

0 2 4 6 8 COLLECTIVE PITCH, 0, dtg

10

/x= 1.0 as« Odeg.


229

ÜJ ü

Ul o LÜ

z <

0

2

-2 -2

O SINE COEFFICIENTS


5th HARMONIC

1 () l

* feg Q I II )

—•

i • x 11 •— — tA

u

6 th HARMONIC

1 r ••• •= K -S

••• >— wm i H *^ V + =^\-

7th HARM ONIC 1 | 1

fr "^11

-HJ

0 2 4 6 8

COLLECTIVE PITCH, 0, deg.

10

/x= 1.0 as= Odeg.


230

hi O

h X

ü (ft

i» x <

.4

-2

0 SINE COEFFICIENTS


4 1 B1 fh HARMONIC

2 o -JLJ

l

2 n

4

9 th HARMONIC

-2

10th HARMONIC

0 2 COLLECTIVE

—

•J u

i : 1 i

- -4t=*«4- 4 dij. i] (p2:: -4-LLJ ""!_ _- — sj r" 11 1 i

4 6 8 PITCH, 0, deg.

/x= 1.0 as = 0deg.


231

'*


I•* HARMONIC

z Ul

Ul o a:

O O u. u. u. ui <L o < Ü Ul

X </>

o z Ul o (A 2 < Ul

10 r~i !—~

H J>

6 ^ i

4

2 ^ 8 ^ ̂

0 J M*

J r ̂

-2 T

-A

o Ul

4 2 nd H AR MONIC

2 ( I

{

k :> 1

V

2 J 1 >

4 t k K-

*•< "1 1

.« -202468


10

fi- 1.0 as= Odeg.

(b) EDGEWISE


232

3rd HARMONIC

O SINE COEFFICIENTS


UJ u O

< UJ X

UJ

UJ o o UJ

Z UJ

o u. u. UJ o o

o

10M 1 ! I I 1 ] 1 ! 1 1 1 11 1 I ! 1 ;*r

i i , .^ — - jr

o ["" "'•""• ' ••• t y

1 l>~ T~ ' - -ft" 2 it

" """l^ -4 -4_ I I

• 4 th HARMONIC ! I

6 .-< |> j

4 ' i A

2 ( 1

0 i i

-2

-4 i 3

-6 vC 1

-8 i | I

I0 i I ! I I I I -2024 6

COLLECTIVE PITCH, S, deg. 10

fi = 1.0 ass Odeg.


233

bi

UJ Ü

ü o u u.

u. Ul tr o 

o z UJ o en 5 <

* UJ o o UJ

O SINE COEFFICIENTS


2 * **

th Hü .RMONIC

0

p II

4

6 th HARMONIC

1 A- »•• —— 1 P

f P

7 th HARMONIC

0 2

COLLECTIVE

6 8

PITCH, 0, dtg.

/i.= 1.0 as= Odeg.


234

O SINE C0EFF5CIENTS


A 8th HARMONIC

2 ' -* -^ -(L^

~ iL. gtsic- ~B *^ 0-|

lbr=-i|""*"^- - •- -^— -

2: _ :p^ iac it .4 J—l—U Mill

* UJ UJ o

UJ o a: o <

ui t_> x

z °UJ

< * X UJ

o UJ

9 th HARMONIC 4 )

2

u U

2

10 th HARMONIC

JL_ 1 '

0-

^***

— IF -H r

oU 1 L. —L -2 0 2 4 6 8


10

/i= 1.0 as= Odeg,


235

APPENDIX TL

EXPERIMENTAL RADIAL SHEAR FORCE FIGURES

z UJ

t* UJ • O ui u y o E §s is

o a: •-

K

FLAGGED SYMBOLS INDICATE OUT-OF-TRIM OPERATION DOUBLE FLAGGED SYMBOLS INDICATE ZERO LAG DAMPING 8m ill1 i i i i rr

0 Jl_ dtg -

A V 14

J^ :^~'| ±:J H O 12 "

- 3 z IU

Jß-i ̂ ^D * * *_ 4 8 1

0 j E-«- —IF— «B o

^ - L- r— i in 2 - * r * ^ -at ̂ > '^" ^ on. ^^ "* " "J " s? ^ -2 .

. 4 L ^r-H \ Kl^ !*" ± lb -4

^Nl jL >»-. Z -6

K- V ~R\- ^v 3 L

-v* vs £^ V ^^ •12— f s i

•- *

is'—'—' .. , _L .

-20 -16 -12 -8-4 0 4

ROTOR ANGLE-OF-ATTACK, a , <kQ

u«0.2

Figure 60. Experimental Radial Shear Force.

236

UJ o

«to t £ O UJ o o

e o p — u. 5 « 2 < tr m < X x </> UJ -1 z < </) Q o , 5Sir 0 2 u— "r s£ si oo

* N. ^v <g-2

"""^ "Î ^ it -4 VX N* -

% _. _% _ ?.^ ^ v

=>r '*s ~8 i~î^ TX ' i s

B *2±Z J5S_ •^ >

\7

16 - -20 -16 -12 -8 -4 8

ROTOR ANGLE-OF-ATTACK,a,d§g.

M«0.3


237

,

'*« a ^ *> sit

Ct Ei- lt 7 ± _JL_^^_±_ _ 1 * 2-Z Z it

^

7 7^ J -£

•4 Z t $T > r I -,& $ z

-/• ^

? J O AJ <f y

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APPENDIX m

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EXPERIMENTAL VIBRATORY MOMENT AMPLITUDE FIGURES

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APPENDIX 15

EXPERIMENTAL VIBRATORN CONTROL LOAD

AMPLITUDE FIGURES

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289

UNCLASSIFIED Secunt^CI«Mtfic«lion

DOCUMENT CONTROL DATA -R&D (S*curity clai title ation of till», body of abtttact and indening annotation mum! be »nfrrd whan tha ovarall rmporl It cla**lll*d)

I ORIGINATING » C I i vi T r /Corporal, author)

Sikorsky Aircraft Division of United Aircraft Corp. Stratford, Connecticut

2a. REPORT SECURITY CLASSIFICATION

Unclassified *6. CROUP

J REPORT TiTLC

"Comparison of Theoretical and Experimental Model Rotor Blade Vibratory Shear Forces"

4 DESCRIPTIVE NOTES (Typ* of report and Incluaiv» data*)

8 AUTHORISI (Flrtt Mm, mlddla initial, laat nama)

Lawrence J. Bain

• REPORT DATE

October 1967 !*. 107AL NO. OF PACES

305 76. NO- OF REPS

6 So. CONTRACT OR CRANT NO M. ORIGINATOR'S REPORT NUMBER!*!

DA 44-177-AMC-136(T) b. PROJECT NO.

Task ID 121401A 14203

USAAVLABS Technical Report 66-77

ah. OTHER REPORT NOISI (Any oific/ numbar* thai may b* aaalaytad thl* rtport)

SER-50419 10. DISTRIBUTION STATEMENT

This document has been approved for public release and sale; its distribution is unlimited.

II. SUPPLEMENTARY NOTES 12. SPONSORING MILI TARY ACTIVITY

U. S. Army Aviation Material Laboratori Fort Eustis, Virginia

is

i

1*. ABSTRAC T

An investigation was undertaken to obtain quantitative measurements of the vibratory forcing functions from the blades of rotary wing aircraft in the flight speed range encompassing both pure and compound helicopter operation. These measurements were made using dynamically scaled model rotor blades mounted on a specially instrumented rotor head. Testing was accomplished over a range of equivalent forward speeds from 75 to 300 knots and wer a range of full-scale rotor lifts from zero to 40,000 lb. In addition to rotor performance, the final data include ten harmonics of the orthogonal blade root shear forces, rotor blade bending moments, and rotor control loads.

A portion of the experimental results were correlated with a fully coupled aeroelastic analysis which included the effects of wake induced velocities. It was found that the inclusion of these effects improved the correlation of the flatwise shear forces over that obtained assuming uniform inflow.

DD,'r..1473 <P*GE " I NOV

S/N 0101.807-6801

UNCLASSIFIED Security Cl»*sific«lion

UNCLASSIFIED Security Claiailication

KEY ttOROl OLE WT ROLE «! «OLE WT

Helicopter Rotor Blade Vibratory Shear Force Tests Correlations

DD ,?„?..1473 I"«) (PAGE 2)

UNCLASSIFIED Mcurity Classification

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COMPARISON OF THEORETICAL AND EXPERIMENTAL MODEL