Document
ROTOR AEROELASTIC STABILEY
COUPLED %TI" HELICOPTER BODY MOTION
Wen-Liu Mia0
Boeing Vertol Company
Philadelphia, Pennsylvania
H e h u t B . Huber
Messerschmitt-Boelkow-Blohm Gmbh
Ottobrun-Munich
Federal Republic of Germany
Abstract
A 5.5-foot-diameter, soft-in-plane, hingeless-
rotor system was tested on a gimbal which allowed the
L - ' r - - - ~ - - UGllbup'.rL - ~ - - d r I - k d x r z ' 5 ' - ""-J nitrh r - - . .. nnd roll motions. With this
model, coupled rotor/airframe aeroelastic stability
boundaries were explored and the modal damping ratios
were measured. The time histories were correlated
with analysis with excellent agreement.
The effects of forward speed and some rotor de-
sign parameters on the coupled rotor/airframe stabilitj
w e r e explored both by model and analysis. Some phys-
ical insights into the coupled stability phenomenon w e r e
suggested.
Introduction
The coupled rotor-airframe aeroelastic stability
Figure 1. Dynamic Model Helicopter With 5.5-Foot-
phenomenon of air resonance has received considerable
Diameter Single Rotor
attention in recent years. A scaled model of the BO-105
helicopter was built and tested to explore this pbenom-
enon and its sensitivity to design parameters.1 An ex-
(see Figire 2) to allow excitation of the model at the
tensive analytical study was performed and correlated
desired frequency. This enabled the measurement of
with BO-105 flight test data. 2
the modal damping ratios at each test point. The meas-
ured modal damping permitted the precise determina-
To further explore this coupled stability phenom-
tion of the stability boundaries and also showed the
enon, a large scale model having different resonance
%tent of stability when the model was stable.
Characteristics than the BO-105 was built and tested.
Parameters that were influential to the stabilityI9
were incorporated into the model and their effects w e r e
examined. An improved test technique enabled the de-
termination of modal damping ratio at every test point,
providing better data for correlation and better assess-
ment of stability.
Description of Model
The model, shown in Figure 1 , consisted of a
Froude-scaled model rotor mounted on a rigid fuselage,
which in turn was mounted on a two-axis gimbal having
The model had a
2 1 0 degrees travel in pitch and roll.
5.5-foot-diameter, soft-in-plane, hingeless rotor with
pertinent hub parameters such a s precone. sweep, and
control system stiffness being variables to enable in-
vestigation of their effects on coupled rotor-airframe
stability.
A proportional (closed-loop) control system
equipped with a cyclic stick provided lateral and longi-
tudinal control to fly the model in the pitch and roll de-
grees of freedom. In addition, a shaker system was
installed in the longitudinal and lateral cyclic system
Figure 2. Details of Model Rotor Hub and
Swashplate
- N A S A - A m e s Specialists Meeting
on Rotorcraft Dynamics, February 13-15, 1974.
/ The stability and control augmentation system was Figure 3 shows the test flow of events for each
based on position feedback. Position potentiometers on : /
data point taken. After the test conditions had been set
/
the helicopter gimbal axes provided position feedback up (rpm, tunnel speed, and collective pitch), the model signals which were amplified, filtered, and fed into the was trimmed and was held at the trim attitude with the / cyclic actuators for automatic stabilization of the model.
stability and control augmentation system (SCAS). The / The filter was designed to block any feedback at a fre- shaker and the tracking filter frequencies were set to
/
quency of _-_5 and thus eliminated any control inputs _-_ and _ respectively, with the absolute magni- that would tend to interact with the air-resonance mode.
tudes dependent on the rotor speed. Both the multiplex tape recorder and the CEC recorders were turned on to: Collective pitch was set by means of an open-loop record the steady-state response of the model. The control and a pitch-angle indicator. Other controls pro- swashplate was then oscillated in the lateral control vided for the operator included mounting-pylon pitch direction. After the termination of the excitation, re- attitude, stick trim, and quick-acting and slow-acting, cording was continued until steady-state conditions were self-centering snubbers to lock out the pitch and roll again reached, when practical. The decay of the filtered, degrees of freedom. The horizontal stabilizer was in-plane, bending-moment trace was reduced to obtain manually trimmable and rotor speed was controlled by the modal damping ratio.
the wind tunnel operator.
CV_Q6_T C ,"vk'r T'_ T m T 6_Nt Signals from the blade flap, torsion, and chord O STABLE strain gages, along with body pitch and roll motion,
d _RCI_AL
cyclic stick position, and 1/rev, were recorded on os- • UNSTABLE ciiiograph as weii as on multiplex tape recorder. One of the chord-bending traces was filtered to display the chord bending at the critical lag natural frequency to 200 -- 0 allow quick determination of modal damping on line.
0 0 0 Most of the testing was performed in the wind tunnel at O the University of Maryland.
_O O OO O _kO 0 O0 0 0 0 Test Technique 160 -- OR O O O O O O As discussed in References 1 and 2, the air- 00_ 000 0 0 000 E_ resonance mode stability is determined by the blade z O O \OOO O O OOO collective pitch as well as the rotor speed. Therefore,
\oo o oo d
for every airspeed, a comprehensive variation of rpm
and collective pitch was conducted. / o o'%o o o od
, OOO O O O_ O oO@
J T'"E U T'ON ]
ooo o o o o",,q,, o ood
> 80 --O O O O O, O__
I T_Z._o_L l O O OO O O O O@e lg
O O OOO O O OOO PRZOUENCY ] o
i 0 0 0 O0 0 0 000
o 40 - CEC IIJ_CORDER AND COND]rTION 0 0 000 0 0 MAGNETIC TAPE ,-'4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 No Y:co,u I -40 -O O O O O O O O O O O O O O O O O O O O O
I i I I
-8060 80 100 120 ROTOR SPEED NORMAL ROTOR SPEED - PERCENT Figure 4. Typical Map of Test Points in Hover Test Results PITCH [ P.PM Figure 4 shows a typical map of test points taken Figure 3. Flow Diagram of Test Technique at a constant tunnel speed, in this case in hover. Two stability boundaries were present: one at about 70 per- Figures 6, 7, and B show the time histories of cent of normal rotor speed and 120 percent of normal three hover air-resonance points which are at constant collective pitch and another at about 135 percent rpm collective pitch of 133 percent 0NO R (lg hover collec- and 100 percent collective. Examination of the coupled tive at NNOR) with rotor speeds of 100 percent, 72 frequency variation with rotor speed while holding con- percent, and 67 percent NNOR respectively. At NNOR stant thrust, Figure 5, reveals that the low-rpm bound- the chord bending decayed after the excitation termi- nated, at a rate of approximately I percent of critical ary corresponds to the resonance with the body-pitch- predominant mode and the high-rpm boundary with the damping, and the body participation was barely detect- body-roll-predominant mode. able. Approaching the stabilityboundary at 72 percent rpm, the chord bending took longer to decay compared to the 100 percent rpm case. Body participationwas 1.0 quite pronounced in both pitch and roll. While the fil- tered chord-bending gage in the rotating system was indicatingat the blade lag natural frequency, _ , the 0.8 / body pitch and roll motions responding in the same air- resonance mode were at the fixed-system frequency of a-_r • It is of interest that these a-m_ body motions 0.6 ° T F are _uperimposed on some very low-frequency, flying- quality-type motions.
At 67 percent rpm, Figure 8, the air-resonance O.
mode started to diverge after being excited; when the body was snubbed, the blade motion decayed and re- turned to the 1/rev forced response.
60 70 80 90 100 110 120 130 ROTOR SPEED PERCENT NORMAL ROTOR SPEED The response characteristics described here held true for all airspeeds tested up to a scaled test speed Figure 5. Coupled Resonance Characteristics limit of 225 knots.
HOVER, 100% NNO R, 133% 0NOR, RL_ NO. 8 BLADE CHORD L BLADE CHORD FILTERED
^ n AAA A AA AAAA AAAAA AA^ ^^ ^^-. ,, _ _; --- ._
I " ^ -- -
BODY PITCH BODY ROLL _TERAL EXCITATION i/_v I | I I I I I I I I 1 I I ! ! I I I I I I I I ! I I I 1 i I I I I I I I I I I I I I i ! I I I I I I I I I I 'l I |' I I Figure 6. Response Time Histories in Hover at NNO R I BLADE CHORD HOVER, 72% NNOR, 133% 0NOR, RUN NO. 13 ..... ..iJ AAlllm.,,.m.J AIAAIAIAIilAAJJAJJIiAAIAIJALt_IlaauI..,,,j,,,,.,,..,.. .............. .....
--,,- .....I !,,.. _
--"-v,,vi lVVlWVvvvvwvwnvv,v, tVlViillVlllVVlWV lpVVilVVVVVVVVlVVVVVVnV -
BODY PITCH
vL, V x_,-,_'_ x..f
' VV v
Y ROLL
AA A A
vvvvvv
LATERAL EXCITATION
v _../V v v v _./ v .... -----
1/REV
IIIIIIIlllllllllllllllllllllllllllllllllllllllllllllllllllllll IIIlllll I I I II I IIIlll I1111I IIIIIIlllllllil Ill I II IIIIII Figure 7. Response Time Histories in Hover at 72 Percent NNO R Analytical Model The airframe has five rigid-body freedoms: longitudinal, lateral, vertical, pitch, and roll; and two To treat the dynamically and aerodynamically flexible freedoms: pylon pitch and pylon roll. The coupled rotor-airframe air-resonance problem, the equations of motion are nonlinear and are solved by a analytical model shown in Figure 9 is used. In this numerical time-history solution technique. The blade model, the elastic cantilevered blade is represented by degrees of freedom are calculated for each individual blade.
a spring-restrained, hinged rigid blade. Three hinges are used to simulate the first flap, first lag, and first torsion modes, in that order from inboard to outboard.
To evaluate the aeroelastic stability, the aircraft In addition, a pitch degree of freedom is provided in- can be perturbed from the trimmed state. For air- board of the flap hinge to facilitate the simulation of any resonance investigations this is usually done by oscil- torsional stiffness distribution relative to the flap and latory stick excitations, which can be simulated in any lag hinges. The blade model includes built-in pitch axis frequency. The time history of each degree of freedom precone, blade sweep, kinematic pitch-flap and pitch- is then subjected, to an oscillation analysis program to lag coupling, and a variable chordwise center-of-gravity obtain the frequencies, amplitudes, phases, and distribution over the blade span.
damping coefficients. A more detailed discussion of this analytical procedure can be found in Reference 2.
The aerodynamic model is based on current blade- element theory and can handle all hover, forward flight, Using a linear lift-curve slope, this coupled and maneuver flight conditions. It uses two-dimensional analysis in hover can be reduced to a set of second- airfoil data with stall, reverse-flow, and compressibil- order differential equations with constant coefficients ity effects.
by applying the quasi-normal coordinate transformation HOVER, 67% NNOR, 133% 9NOR, RUN NO. 12 _. _o_..,.,., ,,,.,,,ili,, ,,. ,,.,,.,,,.,. ,,., ,,,,,_i_,i, ii,ii,iiilldlii_i_i,, ,liii_iiliUiiiiiidilil
""'"'""vvvvvllvvvvvvvvvvvvvll rvvvv"'vvvvvvvvvvvv 'vvvvvvv l,!VVVlYViVlll$ v"",vlvvvvymnn
:2"'._, ,,',..,',. Am..--, .,_..,',. A A A A A A _"
M//. /'x,"kA f', AA/\//A '
EXCITATION ] _'rEI_L - '_ I/REV _J V .... _ IIIIIIIIIIIIIII IIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIII IIIIIII IIIII IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII!11111111111111111111111111111111 Figure 8. Response Time Histories in Hover at 67 Percent NNO R for the rotating coordinates3. This enables the closed- Correlation form solution. The eigenvalues and eigenvectors thus Rotor Thrust obtained yield the information on frequencies, damping, and mode shapes.
Figure 10 shows the air-resonance mode modal damping ratio variations with thrust at NNOR in hover.
The agreement between test and analysis is quite good.
PITCH FLAP LAG TORSION ,'f-",_ The propitious trend with increasing collective pitch is
\ / )
due partly to the increase of aerodynamic damping, but is mainly a result of the favorable pitch-flap-lag coupling. A typical blade elastic coupling is shown in Figure 18 where the blade flap, lag, and pitch torsion responses to a cyclic-pitch input are indicated. The type of elastic coupling of this rotor system is discussed in more detail in a subsequent section.
Rotor Speed Shown in Figure 11 are the test correlations of the air-resonance mode damping variation with rotor speed at constant collective pitch (133 percent 0NOR) in hover. The analytical results are in good agreement _N_G I TUDINAL _TICAL LATERAL with test points over the whole rotor speed range. The stability boundary corresponding to the resonance with the body-pitch-predominant mode at low rpm is pre- dicted well by theory. The somewhat higher level of Figure 9. Coupled Rotor-Fuselage Analytical Model damping of the test points might indicate that the struc- tural damping of the real model blade is higher than the 0.5 percent damping assumed in the analysis.
6.0 H_QVER I V = HOVER COLLECTIVE PITCH = 133% 8NO R NNO R = 100 PERCENT ROTOR SPEED = 72% NNO R 5.0 IT E S T] O TEST POINT -- ANALYSIS
/ LATERAL EXCITATION
i 4.0
o_
z_ BLADE CHORDWISE MOMENT
3.0 ae O 2.0 BODY ROLL
A
O • n _m
!
2O0 50 i00 150 _-_ COLLECTIVE PITCH -_ PERCENT HOVER lg COLLECTIVE PITCH IANALY S I S I Figure 10. Effect of Thrust on Air-Resonance Stability LATERAL EXCITATION HOVER BLADE IN-PLANE MOTION COLLECTIVE PITCH = 133% 8NO R IN-PLANE DAMPING m 0.5% CRITICAL CONTROL STIFFNESS = 642 IN.-LB/RAD OH 1 Z_ HH BODY ROLL TEST POINTS --ANALYSIS -I l _-_ 50 60 70 80 90 100 110 ROTOR SPEED PERCENT NORMAL ROTOR SPEED TIME ONE-PER-REV MARK IIIII11111111111111111111111111111111111111111111111111111111111 Figure Ii. Effect of Rotor Speed on Air-Resonance Stability Figure 12. Correlation of Test and Analysis of Time Histories in Hover The good agreement of Figure ii is merely a Forward Flight reflection of the excellent correlation between test and The test trend of air-resonance mode damping analysis in the time-history waveform of blade and body with airspeed is also verified by analysis in Figure 13.
motions. One example is shown in Figure 12. For this case the oscillation analysis program yields a damping Test points shown in this diagram were obtained with constant collective pitch, so that they do not correspond coefficient of 0.39 percent at blade lag natural frequency to a lg-thrust/level-flight condition. The analysis was for the rotating blade.
performed under the same collective/shaft-angle set- 80 KNOTS FORWARD FLIGHT tings to get an exact simulat ion of the test conditions.
At 150 knots, the collective pitch is slightly reduced, COLLECTIVE PITCH = 133% 0NO R from 133 percent to 111 percent, which produces a ROTOR SPEED = 100% NNO R sharp decrease in rotor thrust. Therefore the air- SHAFT TILT ANGLE = -4 DEGREES
[TESTI
resonance mode is less stable than for a normal 1g- thrust condition.
COLLECTIVE PITCH = 133% 0NO R (111% 0NOR) LATERAL EXCITATION ROTOR SPEED = 100% NNO R IN-PLANE DAMPING = D.5 PERCENT CRITICAL CONTROL STIFFNESS = 642 IN.-LB/RAD !
A TEST POINTS --ANALYSIS BLADE CHORDWISE MOMENT
I
r I i i i i, [ 2 , I I 1.25g I _ 1.35g i H _ 1 • 50C I z _ = 0.8g H H _iii% 0NOR _ 1./ , z STABLE O_ /= 0.6g CYCLIC 0 : : BODY ROLL UNSTABLE 0 40 80 120 160 200 VELOCITY - KNOTS Figure 13.
Effect of Forward Speed on Air- A N A L Y S I S] Resonance Stability at Constant Collective Pitch LATERAL EXCITATION Theory shows some influence of cyclic control on air-resonance stability at high speed. As longitudinal cyclic also controls rotor thrust in forward flight, this BLADE IN-PLANE MOTION variation of air-resonance stability comes solely from the change in rotor thrust. With thrust held constant the stability is insensitive to steady 1/rev cyclic-pitch vari- ation. This is shown in a later section.
In Figure 14 one example of a typical time history at a scaled airspeed of 80 knots is compared between test and analysis. When one considers the complex fre- quency modulations during this excited air-resonance case, the correlation can be said to be excellent. This should indicate that theory allows a definitive and reli- able view of a helicopter's stability characteristics.
1/REV
BODY ROLL Additional test results of air-resonance stability in forward flight are illustrated in Figure 15. This trend, which was obtained for a ig/level-flight condition, follows the rotor power curve quite well. As shown in Figure 10, for a moderate range of thrust variation, say around Ig, the air-resonance mode becomes more stable with increasing thrust and less stable with de- creasing thrust. The forward-speed trend here simply ONE,PER-REV MARK _ TIME reflects this thrust (and aerodynamic coning angle) de-
pendency. This trend, which shows that the air- IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
resonance mode stability improves significantly at high forward speeds, is also apparent in the BO-105 flight Figure 14. Correlation of Test and Analysis of test data2.
Time Histories in Forward Flight I I I TEST AIRFOIL 0t SYMBOL TEST POINTS --CURVE FIT THROUGH TEST POINTS RTS 6-FT ROTOR V23010 -7° z_ RTS 6-FT ROTOR VR7 -9° [] RTS 6-FT ROTOR VR7/8 -9°
]
14-FT ROTOR V23010/13006 -10.5" UHM COMPOSITE V23010 -i0-5° (3 UIiM 6-FT ROTOR VR5 -14° o o MBB TIEDOWN 0012 0° AMRDL MODEL 23012 0°
+/
LgH 0.07 Z_ I o : 0.061 0.06 I I ii 0.05 -- T T TA _ _" TEST DATA
I I I_1
o I
AT 0 =0°
0 40 80 120 160 200 0.04 VELOCITY - KNOTS Effect of Forward Speed on Air- Figure 15.
,.Z 0.03 Resonance Stability in lg Level ,-4 Flight 0.02 U
==
Physics of Air Resonance 0.01 General The mechanism and the stability characteristics of air resonance have been well described in numerous papers. 1, 2,4, 5, 6 It suffices to say here that the soft- -0.0 in-plane hingeless-rotor system derives its inherent stability mainly from the powerful flap damping. While rotors with untwisted blades may have substantial reduc- -0.02 tion in the flap damping near zero thrust, the damping -4 -2 0 2 4 6 0 available remains essentially unchanged for blades with COLLECTIVE PITCH, e.75 - DEGREES nominal twist. Figure 16 shows the test data for various blades of different twist. Above a thrust coefficient of 0. 005, the twisted blade and the untwisted blade both Figure 16. Effect of Blade Twist on Thrust Coefficient have the same thrust-per-collective slope. While the untwisted blade has a drastic reduction in slope with re- duction in thrust in both theory and test, that of the twisted blade remains the same.
I
Let us examine the coupling terms that are inher- .owm
/ \
nOTOn spECv = Iooi NNO R
ent in the hingeless rotor system with an equivalent / \
t hinge sequence of pitch-flap-lag from inboard to out- ,0 / board. One term that stands out is the perturbation 'o
/
pitch moment produced by the induced drag (steady _
force) acting through a moment arm of vertical-flapping _ _ /
/
displacement (perturbation deflection). This flap-pitch _ coupling term due to the induced drag has the _ense of i_ ,o flap up/pitch noseup. Figure 17 compares the air- /_. z,_oc_ _,_ _za_P-pz_ ¢OUPLIS6 resonance mode damping of the same rotor system with this particular coupling term suppressed. With the // induced-drag term suppressed, the air-resonance mode does not become unstable at high collective where the induced drag dominates, o__ o l _EU_S v _wt, By the same consideration, the air-resonance Figure 17. Stability Characteristics with Sup- mode should become more stable in descent since during pression of Flap-Pitch Coupling Term descent, the induced drag acts toward the leading edge Due to Induced Drag producing a flap-pitch coupling of flap-up/pitch-nose- down sense, which is stabilizing.
Pitch-Flap-Lag Coupling Characteristics flexibility. Some of these design rules have already been applied to this model rotor design (low precone, aft For a complete understanding of the elastic- sweep, soft control systems).
coupling characteristics of a hingeless rotor with a pitch-flap-lag sequence of hinges, aH blade motions Parametric Sensitivities must be considered together. For this purpose it is in- structive to analyze a simple cyclic-pitch case in hover.
The following paragraphs describe the air- In Figure 18 the elastic flap, lead-lag, and pitch mo- resonance mode stability sensitivities obtained from the tions are shown over one rotor revolution. It can he model test.
seen clearly that the flap and lag motions are accom- panied by an elastic pitch torsion, the resultant coupling Climb and Descent being in the sense of flap up/lead forward/pitch nose- down. For a clear understanding this complex coupling Figure 19 shows the sensitivity with lg climb and can be divided into two distinct coupling phenomena: the descent at a scaled airspeed of 80 knots. With normal one equivalent to a negative pitch-flap coupling (flap up/ control system stiffness (90 in.-lb/rad), descent sta- pitch nosedown), the other equivalent to a positive pitch- bilizes the mode as discussed in the previous section; lag coupling (lead forward/pitch nosedown). The cou- conversely, climb has a destabilizing effect.
pling factors are 0.4 degree pitch per degree flap and 0.6 degree pitch per degree lag• PRECONE ffi0 DEGREES SWEEP = 2.5 DEGREES AFT _M CONTROL STIFFNESS = 90 IN.-LB/RAD t3 z_ _z
e _-_
-40 -30 -20 -x0 0 10 20 30 !
CLIM_ I DESCENT
ROTOR ANGLE OF ATTACK - DEGREES l z Figure 19.
Effects of Climb, Descent, and Control o H System Stiffness on Air-Resonance Stability u Control System Stiffness Also sho_m in Figure 19 are the test data obtained with the control system stiffness seven times stiffer than normal. The effect of climb and descent almost . PITCH -2 disappeared. Since the stability is affected by the pitch- TORSION flap-lag coupling, a stiff control system minimizes the coupling effect, be it favorable or unfavorable.
-4 • . . | • • • . . . • , . • . , • • • • Preeone 0 90 180 270 360 Precone of the pitch axis directly alters the pitch- AZIMUTH ANGLE - DEGREES flap-lag coupling. The beneficial effect of lower precone has been evaluated many times. 1,2,7 Figure 20 shows the test confirmation of the favorable effect of the low Figure 18. Blade Elastic Coupling precone.
Cyclic Trim Besides the well-known stabilizing effect of pitch- flap coupling, the pitch-lag part of the total coupling is An evaluation of the cyclic trim on the air- of utmost importance for the in-plane motions of the resonance stability was accomplished by varying the blade. Positive pitch-lag coupling (decrease of pitch as angle of incidence of the tail. The tail incidence angle the blade leads forward, increase of pitch as the blade was varied from 2 degrees through 45 degrees. As lags back) has a highly stabilizing effect on the lead-lag shown in Figure 21, the stability is insensitive to the oscillations. Recent investigstionsl, 2 have shown that range of cyclic-trim variation at constant thrust. This these coupling characteristics can be influenced by sev- suggests that the steady 1/rev cyclic-pitch variation in eral hub and blade parameters, for example, by feather- forward flight can be ignored with respect to the air resonance.
ing axis precone, blade sweep, and control system SYMBOL THRUST 3.0 V = 150 KNOTS | V = 150 KNOTS ig THRUST AT HOVER NNO R = i00 PERCENT NNO R = i00 PERCENT O 92 PERCENT
o_
/k 116 PERCENT SYMBOL PRECONE -- _ 0 DEGREES D 139 PERCENT 2.0 162 PERCENT 0 1.5 DEGREES Z_9 '_C9 1.0 _ I.
ZH 0 50 i00 150 20q
_ o 1o 20 30 40 so
COLLECTIVE PITCH _ PERCENT Ow _ STABILIZER ANGLE - DEGREES HOVER ig COLLECTIVE PITCH Effect of the Tncidence Angle of the Figure 21.
Figure 20. Effect of Blade Precone on Air- Horizontal Tail on Air-Resonance Resonance Stability Stability References Conclusions 1. Burkam, J.E., and Miao, W., EXPLORATION OF 1. The air-resonance mode stability is sensitive AEROELASTIC STABILITY BOUNDARIES WITH A to collective pitch (thrust}.
SOFT-IN-PLANE HINGELESS-ROTOR MODEL, Preprint No. 610, 28th Annual National Forum of 2. Air-resonance mode stability is also sensitive the American Helicopter Society, Washington, D.C., to climb and descent; that is, descent is stabilizing while climb is destabilizing. May 1972.
2. Huber, H.B., EFFECT OF TORSION-FLAP-LAG 3. The prime coupling term in the rotor system COUPLING ON HINGELESS ROTOR STABILITY, which causes the degradation of stability at high thrust Preprfnt No. 731, 29th Annual National Forum of is the induced drag. This coupling also provides the the American Helicopter Society, Washington, D.C., trend versus climb and descent.
May 1973.
4. Air-resonance mode stability in lg level flight 3. Gabel, R., and Capurso, V., EXACT MECHANI- shows the rotor-power-curve trend with highly stable CAL INSTABILITY BOUNDARIES AS DETERMINED characteristics at high speed.
FROM THE COLEMAN EQUATION, Journal of the American Helicopter Society, January 1962.
5. The elastic-coupling behavior of the model rotor with normal control system stiffness is charac- 4. Lytwyn, R.T., Miao, W., and Woitsch, W., AIR- terized by a pitch-flap coupling (0.4 degree pitch per BORNE AND GROUND RESONANCE OF HINGE- degree flap} and a pitch-lag coupling (0.6 degree pitch LESS ROTORS, Preprint No. 414, 26th Annual per degree lag}. National Forum of the American Helicopter Society, Washington, D.C., June 1970.
6. High control system stiffness minimizes the 5. Donham, R.E., Cardinale, S.V., and Sachs, I.B., flap-pitch coupling effectiveness and reduces the sensi- GROUND AND AIR RESONANCE CHARACTERIS- tivity of the air-resonance stability to design parameters TICS OF A SOFT INPLANE RIGID ROTOR which are otherwise influential.
SYSTEM, Journal of the American Helicopter Society, October 1969.
7. Less precone is stabilizing for a soft-in-plane hingeless-rotor system with an equivalent hinge sequence 6. Woitsch, W., and Weiss, H., DYNAMIC BEHAVIOR of pitch-flap-lag from inboard to outboard.
OF A HINGELESS FIBERGLASS ROTOR, AIAA/ AHS VTOL Research, Design, and Operations 8. Variation in cyclic trim does not affect air- Meeting, Atlanta, Georgia, February 1969.
resonance stability.
7. Hodges, D.H., and Ormiston, R.A., STABILITY 9. The testing technique to define air-resonance OF ELASTIC BENDING AND TORSION OF UNI- modal damping discretely at many operational conditions FORM CANTILEVERED ROTOR BLADES IN proved highly successful. Use of these methods to define HOVER, AIAA/ASME/SAE 14th Structures, Struc- modal damping, rather than defining only the boundaries, allows for a more definitive view of an aircraft's stability tural Dynamics, and Materials Conference, Williamsburg, Virginia, March 1973.
characteristics.