Document
NASA TM -73,262 CALCULATED DYNMXC CHARACEMSTICS OF A SOFT-II'dPLANF, HNGELESS ROTOR HELICOPTER Wayne Johnson h e s Research Center, NASA and h e s Directorate U S M R D L Ames Research Center Moffett Field, Cam. 94035 REPRODUCED BY. C U S Department of Commerce National Technical Information Service Springf~eld, V ~ r g ~ n ~ a 22161 r o t o r blade chord r o t o r t h r u s t c o e f f i c i e n t ( t h r u s t divided by g r ~ 2 ( ~ ) 2 ) , horizonLal tail l i f t - c u r v e slope divided by dynanic pressure r o t o r radius time t o half-amplitude ( t i n e t o double-amplitude when negative) period h e l i c o p t e r f o m a r d speed blade chordwise aerodynamic center p o s i t i o n , p o s i t i v e a f t of t h e p i t c h a x i s bla?.s chordwise center of g r a v i t y p o s i t i o n , p o s i t i v e a f t of t h e p i t c h a x i s main r o t o r trim e l a s t i c coning angle main r o t o r trh 1ongitud.inal t i p - p a t h plane tilt angle main r o t o r t r i m l a t e r a l tip-path plane tilt angle r o t o r blade Lock number damping r a t i o of an eigenvalue main r o t o r trim c o l l e c t i v e l a g angle h e l i c o p t e r trim p i t c h angle tail r o t o r c o l l e c t i v e p i t c h angle main r o t o r l a t e r a l c y c l i c p i t c h angle main r o t o r l o n g i t u d i n a l c y c l i c p i t c h angle main r o t o r c o l l e c t i v e p i t c h angle a t 75% r a d i u s r o t o r advance r a t i o ( h e l i c o p t e r forward speed divided by r o t o r t i p speed) blade r o t a t i n g f l a p mtu-ral frequency blade r o t a t i n g l a g natural frequency a i r d e n s i t y r o t o r s o l i d i t y r a t i o (blade a r e a dLvided by disk a r e a ) h e l i c o p t e r trim r o l l angle blade r i g i d p i t c h natxcal frequency blade e l a s t i c t o r s i o n n a t u r a l frequency r o t o r r o t a t i o n a l speed CALCULATED DYNA?,lIC CilAMCTEBISTICS GF A SGFT-ITPLAhTE HINGELESS 2GTCIR IBLIKiPTFR Wayne Johnson Ames Research Center - N A S A a nci.
Ames Directorate - USAAimCL
Koffett Fielc?, California Calculatefi dynamic c h a r a c t e r i s t i c s of a r e p r e s e n t a t i v e sof t-inplane The f l i g h t c7 ynanlics ap a function hingeless r o t o r h e l i c o p t e r a r e presented.
of speed and gross weight a r e given. 'i'he requirements f o r accurate a n a l y t i c a l modelling of t h i s helicopter a r e established. The influence of t h e horizontal tail s i z e , the r o t o r precone, t h e blade sweep, an6 t h e blade c e n t e r of gravity/ aeroclynanic center o f f s e t on t h e calculated f l i g h t dynamics and zeroe1;letic s t a b i l i t y a r e examined. The calculations show no evi&ence of a n a i r resonance s t a b i l i t y problem with t h i s a i r c r a f t .
The 80-105 h e l i c o p t e r is a production a i r c r a f t u t i l i z i n g a soft-inplane hingeless main r o t o r . A hingeless r o t o r has a major influence on t h e dynamic c h a r a c t e r i s t i c s of a h e l i c o p t e r , inclucing t h e f l i g h t dynamics and aeroeLss t i c s t a b i l i t y . Also, with a soft-inplane r o t o r t h e p o s s i b i l i t y of a n air resonance i n s t a b i l i t y is introduced. This r e p o r t presents the r e s u l t s of The investigation a t h e o r e t i c a l i n v e s t i g a t i o n of t h e BO-105 helicopter dynamics.
includes c a l c l ~ l a t i o n s of the f l i g h t dynamics and a i r resonance behavior; consiCeration of t h e a n a l y t i c a l modelling requirements; anr7 a n e ~ ~ i i ~ i n a t i o n of the influence of t h e r o t o r parameters, The p w p s e of t h i s work is f i r s t +a investigate t h e dynarriic c h a r a c t e r i s t i c s of t h i s r e p r e s e n t z t i v e hingeless r o b r h e l i c o p t e r , i n p a r t i c u l a r t h e influence of r o t o r parameters on t h e f l i g h t d-ynanics anfi a e r o e l a s t i c s t a b i l i t y ; an& secondly to demonstrate the a p p l i c z b i l i t g of the r o t o r c r a f t aeroelas t i c a n a l y s i s developed i n ref erence 1 ta hingeless r o t o r h e l i c o p t e r s .
The a n a l y s i s on which these calculations were based is described i n reference 1. The input d.ata describing t h e BG-105 h e l i c o p t e r were obtained from references 2 and 3.
' DESCRIPTION OF T H E KELICOPTER The BO-105 h e l i c o p t e r has a four-bladed hingeless r o t o r of r a d i u s R = : 4.9 m , operated a t a t i p speed of -bl~ = 218 m/sec, The r o t o r has a s o l i d i t y r a t i o of V- = 0.07, and the blade Lock number is d = 5.0 .
The calculated n a t u r a l frequencies of the r o t a t i n g blade a r e ? @ = la12/rev
f o r the fundamental f l a p mode, and ?$ = 0.?b/rev f o r t h e fundamental l a g
mode. The blade e l a s t i c t o r s i o n mode has a n a t u r a l frequency %, = 3.66/rev.
No information was a v a i l a b l e about the c o n t r o l system s t i f f n e s s , so it was assumed t h a t t h e blade r i g i d p i t c h motion has a n a t u r a l frequency of W a o = 5,8/rev f o r the c o l l e c t i v e mode, 5.3/rev f o r the c y c l i c modes, and 6.5/rev f o r the r e a c t i o n l e s s mode (giving a coupled r i g i d pitch/elas t i c tors ion n a t u r a l frequency of about 3 .&/rev).
The r o t o r hub has 2.5' of b u i l t - i n precone, and no b u i l t - i n droop o r sweep of the blade outboard of t h e p i t c h bearing. It is assumed t h a t the hub is r i g i d with no bending d e f l e c t i o n a t t h e p i t c h bearing, and s o there is no kinematic pitch/bending coupling. The blade s e c t i o n aerodynamic center and c e n t e r of g r a v i t y have no chordwise o f f s e t from the p i t c h a x i s . A s t r u c t u r a l damping l e v e l of 3% c r i t i c a l was used f o r the blade bending and t o r s i o n motions .
The a n a l y s i s included the following degrees of freedom: two bending modes (fundamental f l a p and l a g ) , r i g i d p i t c h , and e l a s t i c t o r s i o n f o r each blade; the s i x r i g i d body motions of the h e l i c o p t e r ; tail r o t o r flapping; and inflow perturbations f o r the tail r o t o r and main r o t o r . The inflow and tail r o t o r degrees of freedom were q u a s i s t a t i c ( s e e reference 1 ) . The r o t o r was assumed t o be operating a t constant r o t a t i o n a l speed.
S t a l l and compressibility e f f e c t s were included i n the r o t o r aerodynamics. HO t o ~ / % i l and r o t o r / r o t o r aerodynamic i n t e r f e r e n c e e f f e c t s were not considered! The constant c o e f f i c i e n t approximation was used t o evaluate t h e dynamic c h a r a c t e r i s t i c s i n forward f l i g h t .
The dymnic c h a r a c t e r i s t i c s were calculated f o r t h e h e l i c o p t e r I n l e v e l f l i g h t a t forward speeds from V = 0 t o 120 knots, corresponding
to a n advance r a t i o of )A = 0 t o 0.28 . The b a s i c operating con6Ltion
considered is a g o s s weight of 1800 kg, corresponding t o a t h r u s t c o e f f i c i e n t
to s o l i d i t y r a t i o of c T / r
= 0.0575; s e a l e v e l , standard day; o u t of ground e f f e c t ; and. mid c e n t e r of g r a v i t y position.
HELICOPTER m I P 4 Figures 1 to b present t h e calculated BC-105 trim f o r a gross weight of 1800 kg, a t forward speeds from hover to 120 knots. The c o n t r o l p o s i t i o n and fuselage a t t i t u d e given i n f i g u r e s I and 2 generally agree with t h e calculations and experimental r e s u l t s of reference 4 ( f i g u r e s 10 and ii) , except of c o m e f o r t h e l a t e r a l c y c l i c c o n t r o l 8,, ( t h e a n a l y s i s considered only a uniform induced v e l o c i t y ) . The information about t h e f l i g h t conditions of t h e t e s t r e s u l t s i n reference 4 is not s u f f i c i e n t to attempt a d e t a i l e d c o r r e l a t i o n with t h e present calculations. Figure 3 gives the calculated power required of the h e l i c o p t e r , and f i g u r e 4 gives the trlm f l a p and lag motion of the r o t o r . The c o l l e c t i v e lag angle E , v a r i e s a s the r o t o r potrer, The c y c l i c flapping angles ( l o n g i t u d i n a l and l a t e r a l t i p - p t h plane tilt, ) a r e small because the h e l i c o p t e r center of g r a v i t y is near
klc and (3
thw rotor shaft. ax& f o r the case m ~ s i d e r e d ~ There is a small amolmt o f negztive e l a s t i c coning of the r o t o r because t h e hub precone of 2.5 is i d e a l f o r a s l i g h t l y higher gross weight than t h e 1800 kg considered here* FLIGHT DYNAblICS Figures 5 to 7 present the calculated f l i g h t dynamics of the BO-105 helicopter a s a function of speed and gross weight. The hover longitudinal o s c i l l a t i o n is only moc-lerately unstable ( f i g u r e 5 ) , because of the high p i t c h damping of t h e hingeless r o t o r . A t high speeds the time t o double- amplitude of the l o n g i t u d i n a l o s c i l l a t i o n decreases due to t h e r o t o r a n g l e - o f - a t t a c k i n s t a b i l i t y . The tren?k o f t h e calculdter! period and time t o double-anplitude of t h e longituc?inal mode a r e confirmed by the theory znd experimental r e s u l t s o f r e f e r e n c e 4 ( f i g u r e 13), although a g a i n the i n f o r m t i o n a b o u t t h e t e s t f l i g h t c o n d i t i o n s is n o t s u f f i c i e n t f u r d e t a i l e d c o r r e l a t i o n s .
The l a t e r a l o s c i l l a t i o n becomes a highly-damped s h o r t perio?
mode 6lie t o t h e l a r g e d i r e c t i o n a l s t a b i l i t y c o n t r i b ~ r t ~ i o n of t h e titi1 r o t o r .
'The yaw/spiral mode time c o n s t a n t is l a r g e i n forwar6 f l i g h t ( f igirre 5 ) , in:! i c a t i n g t h a t as d e s i r e d t h e response t o l a t e r a l c y c l i c is a r o l l r a t e r a t h e r than a r o l l a t t i t u d e change. S e p a r a t e p i t c h and r o l l roots can be i G e n t i f i e d ( f i g u r e 6 ) , b u t b o t h of t h e s e modes a c t u a l l v invclve couple?
p i t c h anc?. r o l l . motion. '~%e p i t c h and r o l l mo6es a r e al:o h i g h l y coupled w i t r l the low frequency f l a p mode ( a n o s c i l l a t i o n w i t h a time to half-arnplitllde
cf t2 - 0.06 t o 0.07 s e c ) . The low frequenc:y l a g mode has a tlr?e to
G half-smplitucle o f t1 = 0.5 t o 0.8 s e c . The p r i n c i p a l e f f e c t of increa::lng gross weight shown i n f i g u r e 7 is a d e c r e a s e i n t h e time t o $ouble-3mplitu.le of t h e l o n g i t u ? i n a l o s c i l l a t o r y mode i n forward f l i g h t , ANALYTICAL MG DELLING REQUIREFIENTS Consider now what elements o f t h e a n a l y t i c a l mo2el a r e r e q u i r e d t o a c c u r a t e l y r e p r e s e n t t h e dynamics o f t h i s h i n g e l e s s r o t o r h e l i c o p t e r .
Fizure 8 sh3ws t h e i n f l u e n c e on t h e o s c i l l a t o r y modes of a decoupled r i g i d bo4 j r Jyngnic model, o r a q u a s i s t a t i c r o t o r model, I n t h e decoup1e:i dynamics T . O ' e l o n l y t h r e e rigid body degrees of freedom a r e included : l c n g i t u d i n a l v e l o c i t y , v e r t i c a l v e l o c i t y , and p i t c h f o r t h e l o n g i t u d i n a l dynamics; o r l z t e r a l v e l o c i t y , r o l l , and yaw f o r t h e l a t e m l dynamics. The im?lementat,ion o f t h e q u a s i s t a t i c r o t o r model, f o r which t h e r o t o r i n f l u e n c e is reduced t o simply s t a b i l i t y d e r i v s t i v e s , is discussed i n r e f e r e n c e 1, The v e r t i c a l and yaw modes ( n o t shown) a r e n o t a f f e c t e d much by e i t h e r of t h e s e modelling changes. The p i t c h and r o l l modes a r e h i g h e r frequency and involve couple4 l o n g i t u r ~ i n a l / l a t e r a l motion, hence a r e more s e n s i t i v e t o these changes, Generally t h e uncouplec? dynamics and q u a s i s t a t i c r o t o r approximations a r e a c c e p t a b l e i f a low o r d e r model is r e q u i r e + f o r t h e f l i g h t dynamics.
Figure 9 s h o i ~ s the e f f e c t on the calculated f l i g h t dynamics of success5.vely dropping from the a n a l y t i c a l model the r o t o r inflow -perturbation, t h e blar7.e t o r s i o n motion, and the blade l a g motion. For t h i s hingeless ro-tor h e l i c o p t e r a l l of these degrees of freedom a r e required i n order t o adequately nodel t h e f l i g h t dynamics.
A I R RESO HA NCE Figure 10 shows the damping r a t i o of the low frequency l a g mode a s a function of forward speed, inclurling t h e influence of the a n a l y t i c a l model.
The blade t o r s i o n dynamics a r e important t o the h e l i c o p t e r air resomnce behavior, b u t the influence is primarily a q u a s i s t a t i c pitch/benrling coupling. The theory and exgerimental r e s u l t s i n reference 5 ( f i g u r e 22) show a similar i n s e n s i t i v i t y of t h e air resonance s t a b i l i t y to speed, 'i%e calculations showed no evidence of a i r resonance problems with t h l s helicopter.
For some values of t h e r o t o r parameters (precone, sweep, o r droop) t h e r e can be a blade l a g i n s t a b i l i t y , which is not the same as an a i r resonance i n s t a b i l i t y . The former involes a l l the l a g modes of the r o t o r , while the l a t t e r involes only the 1o:a frequency l a g mode.
Also, a* resorance is p o t e n t i a l l y more d e s t r u c t i v e s i n c e the low frequency l a g mode produces a whirling motion of t h e r o t o r c e n t e r of g r a v i t y about t h e s h a f t .
HORIZCIJTAL TAIL IWLUENCE Figure 11 shows the calculated influence of increased horizontal tail effectiveness on the longitudinal o s c i l l a t o r y mode.
A mildly s t a b l e long period longitudinal o s c i l l a t i o n ( n o t shown i n f i g u r e 11 because t h e time t o half-amplituCe is very l a r g e ) is produced above about 70 knots ( t h r e e times t h e b a s e l i n e t a i l s i z e ) . Increase?
with (L, /q)HT = 9 m t a L l effectiveness a l s o produces a s h o r t period o s c i l l a t i o n from t h e v e r t i c a l and. p i t c h r o o t s above about 40 knots, with a perioc! of T = 2 t o an4 a time t o half-amplitude of around ti = 0.2 s e c a t high speed.
3 s e e , The calcu1ate:i r e s u l t s of reference 4 ( f i g u r e 16) agreee with these t r e n d s . However, aerodynamic i n t e r f e r e n c e , which has not been included.
i n t h e present model, would tend t o reduce the tail e f f i c i e n c y a t low and moderate forward. speeds by s ' t a l l i n g the tail and lowering the dynamic pressure.
INFLUENCE GP RCTOR PARAMETERS Figures 1 2 t o 16 present the influence of possible changes i n the r o t o r precone, sweep, center of g r a v i t y o f f s e t , and aerodynamic center o f f s e t on t h e calculated f l i g h t dynamics. A precone increase ( f i g u r e 12) degrades the hover longitudinal o s c i l l a t i o n , b u t improves the l a t e r a l o s c i l l a t i o n and the forward f l i g h t longitudinal o s c i l l a t i o n . A l a g i n s t a b i l i t y is predicted a t a precone angle of about 3.5' f o r t h i s gross weight; the combination of high precone and low gross weight produces l a r g e negative t r i m e l a s t i c coning of the blade, hence unfavorable pi tch/bend ing coupling.
precone is eelermined primarily by the steacly blade loads; The choice of f o r t u n a t e l y the id.eal value a l s o r e s u l t s i n the b e s t f l i g h t d-ynamics.
Aft sweep of the blade outboard of the p i t c h bearing improves the hover and forwarcl. f l i g h t l o n g i t u d i n a l o s c i l l a t i o n s , b u t degrades the l a t e r a l o s c i l l a t i o n ( f i g u r e 13). Similar r e s u l t s a r e given i n reference 5 ( f i g u r e 11). A l a g i n s t a b i l i t y is predicted f o r about lbO forward sweep, and a torsion i n s t a b i l i t y a t about 4' a f t sweep. Blade droop outboard of the p i t c h bearing was found t o have very l i t t l e e f f e c t on t h e calculated f l i g h t 6ynamics. A l a g T n s t a b i l i t y is precjicted f o r l a r g e down droop ( a t about 3.25' with a precone of 2.5 ) .
A forward s h i f t of the blade c e n t e r of g r a v i t y p o s i t i o n r e l a t i v e t o the p i t c h a x i s ( f i g u r e 14). o r an a f t s h i f t of the aerodynamic c e n t e r ( f i g u r e l j ) , improves the longitudinal o s c i l l a t i o n i n hover and forward f l i g h t , although t h e r e is some degrad-ation of the l a t e r a l o s c i l l a t i o n and v e r t i c a l damping.
Similar r e s u l t s a r e given i n reference 6 ( f i g u r e s 16, 17, and 21). Figures 14 and. 15 a r e nearly i d e n t i c a l , demonstrating t h a t the r e l e v z n t pzrameter is a c t u a l l y t h e chor6wise o f f s e t between t h e ih t e t h a t t h e l o n g i t ~ i ~ i m l c e n t e r L F g r z v i t y an:: aerodynamic c e n t e r ( xr - x a ) o s c i l l a t o r y mode i n f o ~ r a r d f l i g h t (100 k n o t s ) becomes tvo r e a l r o o t s a t zth3-lt 'X - x , ) / u = 0.03, one of which is v e r y u n s t a b l e . A t c r s i o n i n s u b i l i t y \ I A is p e d i c t e d f o r a b o u t x- - = 0.0I~c , Reference 7 d e s c r i b e s the pi-cch . L an: r o l l r a t e feedback r e s u l t i n g from a c e n t e r o f gravity/aerodymmic ,-~~.-l?,-r o f f s e t w i t h a torsionaaliy s o f t blacie, which produces t h e observer7 ~harlges i n t h e f l i g h t dymmlcs. F i g u r e 16 shc;:s t h e hover v e r t i c a l rnoc'e t h e t o rial:-zm~lituie v a r i a t i o n x i t h xI - x, . C f f s e t 0 : the c e l i t & r o f A g r ~ v i t y forxard o f t h e zeror'ynamic c e n t e r (an6 a l s c f o - d e ~ - ' sweer of t h e blade) r n d i ces t2 by t h e followfng m ~ c h ~ n i s m , An1 u p a r p velocS t y of the L.
h e l i c o p t e r produces z nose dcwn p i t c h of t h e b l a g e s Cue t o t h e i r i n e r t i 3 l re-ctiofi. Tnis b l a d e p i t c h change reduces the r o t o r t k f ~ ~ i . So t h e r e IF a f c r c e pro$uce+ opposing t h e h e l i c o p t e r motion, which i m p i i e s increased iianping, L 6 a m of t h e s e pzrarneters iizs found t o i n f l u e n c e s i g n i f i c a n t l y t h e novsr yaw r o o t o r t h e forwar? f l i g h t l a t e r a l o s c i l l a t i o n , which a r e c7eterriiinea y r l m o r i l y by t h e tail r o t o r .
The c a l c u l a t e 3 d.ynamic c h a r a c t e r f s t i c s of a r e p r e s e n t a t i v e s o f t - i n n l a n e h i n g e l e s s r o t o r h e l i c o p t e r have been examine&, i n c l u d i n g the f l i g h t dynamics and a i r resonance b e h a v i o r ; t h e a n a l y t i c a l model required. to a c c u r a t e l y r e p r e s e n t t h e dynamics o f t h i s h e l i c o p t e r ; and t h e i n f l u e n c e of t h e h o r i z o n A a l tail s i z e and v a r i o u s r ~ t o r parameters on t h e f l i g h t dynamics and a e r o r - l a s t i c c t a h i l i t y . The c a l c u l a t i o n s show no evid.ence o f a n air resonance p r c b l e z with t h i s a i r c r a f t . The r o t o r c r a f t a e r o e l a s t i c a n a l y s i s developed i n r e f e r e n c e 1 prove3 t o be a u s e f u l t o o l f o r t h i s i n v e s t i g a t i o n .
REFERENCES 1 Johnson, Wayne, " A e r o e l a s t i c Analysis f o r R o t o r c r a f t i n F l i g h t o r i n a Flint! Tunnel, " N A S A Ti4 D-8515, 1977 McLaughlin, J , J . , " S t a b i l i t y and Control Data f o r t h e RO-105 H e l i c o p t e r , " Boeing V e r t o l Report No. D212-10035-1, May 1975
3 S t a l e y , J , A * , "\'alid.ation of Rotorcraf t F l i g h t Simulation Program
Thro1:gh C o r r e l a t i o n w i t h F l i g h t Data f o r S o f t I n p l a n e Hingeless R o t o r s , " USAAFWDL T R 75-50, January 1976 4 R e i c h e r t , G . , and Oelker, P., "Handling Q u a l i t i e s w i t h t h e Bolkow R i g i d Rotor System, " American H e l i c o p t e r S o c i e t y Annual Iiational Forum, Washington, D.C,, May 1968 5 Huber, H.B., " E f f e c t o f Torsion-E'lap-Lag Coupling on Hingeless Rotor S t a b i l i t y , " American H e l i c o p t e r S o c i e t y Annual National F o r m , Washington, D . C . , May 1973 6 R e i c h e r t , G . , and Huber, H., "Influence o f E l a s t i c Coupling E f f e c t s AGASD on t h e Handling Q u a l i t i e s o f a Hingeless Rotor H e l i c o p t e r , " Conference Proceedings No, 121, Hampton, V i r g i n i a , September 1971 7 Mi-ller, R.H., "Helicopter Control and S t a b i l i t y i n Hovering F l i g h t , "
J o u r n a l o f t h e Aeronautical S c i e n c e s , 2, 8, August 1940
/
TAIL ROTOR V, knots Figure 3 BO-105 helicopter trim: power required.
T, sec LOMGHTUDlNAL OSCILLATION
--- LATERAL OSGl LLAJlON
V, knots Figure 5 BO-105 h e l i c o p t e r f l i g h t dynamics: l o n g i t u d i n a l and l a t e r a l o s c i l l a t o r y mode period and time t o half-amplitu2.e.
VERTICAL MODE YAWISPIRAL MODE PITCHIROLL MODES
-
-
-
ROLL
-
--,--- --------
I I I I I I
V, knots Figure 6 BO-105 h e l i c o p t e r f l i g h t dynamics : v e r t i c a l mode, yaw/spiral mod.e, p i t c h mode, and r o l l mode time to half-amplitude.
-
-
T, sec
-
I I I I I I
n HOVER LONGITUDINAL
--
HOVER LATERAL
-----
100 knots LONGITUDINAL
-20 I I I I 1
1500 2000 2508 3000 GROSS WEIGHT, kg Figure 7 BC-105 h e l i c o p t e r flight dynamics: i n f l u e n c e of gross weight on oscillatory modes i n hover and a t 100 knoA&.
-
-
T, sec COMPLETE MODEL
--
LONGITUDINAL DYNAMICS
----
QUASISTATIC ROTOR
I-
V, knots ( a ) Longitudinal o s c i l l a t o r y mode.
Figure 8 A n a l y t i c a l modelling requirements: i n f l u e n c e o f decoupled dynamics and. q u a s i s t a t i c r o t o r approximations on the G l c u l a ted. f l i g h t dynamics.
T, ssc COMPLETE MODEL
-- LATERAL DYD'AM1GS
---- QUASBSJATlC ROTOR
V, knots (b) L a t e r a l o s c i l l a t o r y mode.
Fig-e 8 Concluded.
k rc .rl 0 , 4-1 3 'd o'cdc cud a, k P +.'
cd t x l -rc
---
- 4
--
\- ---
T, sec COMPLETE MODEL
--
NO INFLOW
-----
NO INFLOW, NO TORSION
--- NO INFLOW, NO TORSiON, NO LAG
V, knots (b) Longitudinal o s c i l l a t o r y mode, Figure 9 Concluded.
COMPLETE MODEL
--
WITHOUT TORSION DYNAMICS
I )
QUASISTATIC TORSION DYNAMICS
V, knots
F i g u r e 10 BO-105 h e l i c o p t e r a i r resonance: damping r a t i o of t h e low frequency l a g m0d.e.
V, knots Figure 19 BC-105 h e l i c o p t e r c a l c u l a t e d f l i g h t dynamics: iidluence o f h o r i z o n t a l tail s i z e o n t h e l o n g i t u d i n a l o s c i l l a t o r y mode.
HOVER LONGITUDINAL
--
HOVERLATERAL
-
----
100 knots LONGITUDINAL , I / --/-
--
----------
-\ . A T, sec PRECONE, deg E'igure 12 BO-105 h e l i c o p t e r c a l c u l a t e d f l i g h t dynamics: i n f l u e n c e of hub precone a n g l e on t h e o s c i l l a t o r y nodes.
- 22-.
HOVER LONGITUDINAL
--
HOVER LATERAL ---- 108 knots LONGITUDINAL
- -
T , see I . ~ , SWEEP, deg Figure 13 BO-105 helicopter flight dynamics: influence of the blade sweep (positive aft) on the oscillatory modes.
- 23- T, s e c tlI2, s e c
-
HOVER LONGITUDINAL
-
--
HOVERLATERAL
--
- - 100 knots LONGITUDINAL
-
-40 -.05 0 .05 x,/c Figure 14 BO-105 h e l i c o p t e r calculated f l i g h t dynamics: influence of t h e blade chordwise center of g r a v i t y p o s i t i o n (xT p o s i t i v e a f t of the p i t c h axis) on the o s c i l l a t o r y modes.
- \
I \ \ I \ I \ \ I \
-
\ I \ \ I \ / T, sec \ /
'-'
\
tIl2, sec 0 -
-
- HOVER LONGITUDINAL -HOVER LATERAL -- -400 knots LONG1TUDINAL
-
-40 Figure 15 BO-105 h e l i c o p t e r calculated f l i g h t dynamics: influence
of t h e blade chorriise aerodynamic canter p o s i t i o n ( - xA
p o s i t i v e forward. of t h e p i t c h a x i s ) on the o s c i l l a t o r y modes.
t1/2f sec
-
DESIGN
VALUE
1 I
BO-105 h e l i c o p t e r calculated. f l i g h t dynamics : influence of the Figure 16 blade chord.wise c e n t e r of gravity/aerodynarnic center o f f s e t
(x, - xA p o s i t i v e f o r t h e CG a f t of t h e A C ) on the hover v e r t i c a l
mode.
1 Report No 2. Government Accarion No. 3. Recipient's Catalog No W- 73,262 4 Title and Subtltle 5. Report Date CALCULATED DYNAMIC CWCTERISTICS OF A SOFT-INPLANE 6. Performing Organization Code HINGELESS ROTOR HELICOPTER 8 . Performing Organization Report No.
7 Author(s1 Wayne Johnson A-7115 10. Work Unit No 9 Periorm~ng Organization Name and Address 505-10-22 Ames Research Center, N A S A and h e s D i r e c t o r a t e , 17. Contract o r Grant No.
USAAMPCDL, Ames Research Center, Moffett F i e l d , C a l i f . 94035 13. ~ y p e of Report and Period Covered 12. Sponsoring Agency Name and Address Technical Memorandun National Aeronautics and Space Administration 74. Sponsoring Agency Code Washington, D. C. 20546 and U.S. Army A i r PIobility RED Laboratory, Moffett F i e l d , CA 94035 15. Supplementary Notes 16 Abstract Calculated dynamic c h a r a c t e r i s t i c s of a r e p r e s e n t a t i v e sof t-inplane h i n g e l e s s r o r o r h e l i c o p t e r are presented.
The f l i g h t dynamics a s a f u n c t i o n of speed and g r o s s weight are given.
The requirements f o r a c c u r a t e a n a l y t i c a l modelling of t h i s h e l i c o p t e r a r e e s t a b l i s h e d .
The i n f l u e n c e of t h e h o r i z o n t a l t a i l s i z e , t h e r o t o r precone, t h e b l a d e sweep, and t h e b l a d e c e n t e r of gravity/aerodynamic c e n t e r o f f s e t on t h e c a l c u l a t e d f l i g h t dynamics and a e r o e l a s t i c s t a b i l i t y a r e examined.
The c a l c u l a t i o n s show no evidence of an a i r resonance s t a b i l i t y problem w i t h t h i s a i r c r a f t .
17 Key Words (Suggested by Author(s)l 18. Distribut~on Statement BO-105 h e l i c o p t e r Unlimited Helicopter a i r resonance Helicopter f l i g h t dynamics STAR Category - 0 1 27. No. of Pages 22. Price* 79. Security Classif. (of thls report) 20. Security Classif. (of this pasel Unclassified U n c l a s s i f i e d *For sale by the National Technical Information Service, Springfield, Virginia 221 61