4094 lines
139 KiB
Plaintext
4094 lines
139 KiB
Plaintext
SA Technical Pa
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evelopment and Validation iloted Simulation elicopter and
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External Sling Load
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J. D. Shaughnessy Langley Research Center, Hampton, Virginia Thomas N. Deaux Sperry Sapport Services, Hampton, Virginia Kenneth R. Yenni Langley Research Center, Nampton, Virginia
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National Aeronautics and Space Administration
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Scientific and Technical Jnformation Office
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1979
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CONTENTS
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SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1
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INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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1
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SYmOLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
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D
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EAACCEERFELLSCounxotuqooomaRtagstuotnedoedoIioartrP-nlmrdrtsGnaTSeioipaagoSIrunlOhtoleDnysai-ueNSpsscLytnrAtyeenoideOFosnceaamStFmrslfdeM CoyiimiogMMdscooAntyh.AsndeoneTtemttaS..arHliaCnooymsEc.nd.d.MsotiytcnA..Me.Gn..sTtomao.rI..d.Cm..oveA..eli..l.L..crS..sn...M.y..o..sO..r..t...De..M ..E.m...L...o.....d.M ....e....l..o......d....e.......l..............................................................................................................................................................................................................
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. .
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.
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. .
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.
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12 12 13 16 17 18 25 26 28 28 30 33
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. . . . . . . APPLICATION TO U.S. ARMY CH-54 HELICOPTER AND CARGO CONTAINER
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35
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S
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I
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MULATION Computer Cockpit Simulati Visual L Load/Lan Trim Cal
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o.aHDnn.EadSSri.dCnowgfR.taIwDPr.Teai Isr.Oe.pN.l.a..y....S..y..s.t...e.m.............. . . . . . . . . . d i n g Z o n e V i s u a l D i s p l a y
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culations
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.......
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.......
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...........................................................................
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.......
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......................................r~..
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39 39 40 42 44 44 46
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VESM PRiiIamFltIohuCtelA'amsTtIaiOCotiNoncmaAVlmNeeDMrniotVsfdAiecLl I.aDVtA.iaoTl.IniOd.N.a t...i o...n...................................................................................... . .
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47 47 47 50
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CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
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TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
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FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
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iii
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SUMMARY
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A generalized, real-time, p i l o t e d , visual simulation of a single-rotor helicopter, suspension system, and external load i s described and validated f o r t h e f u l l f l i g h t envelope o f t h e U.S. Army CH-54 h e l i c o p t e r and cargo c o n t a i n e r as an example. The mathematical model d e s c r i b e d u s e s modified n o n l i n e a r class i c a l rotor theory f o r both t h e main rotor and t a i l rotor, n o n l i n e a r f u s e l a g e aerodynamics, an elastic suspension system, nonlinear load aerodynamics, and a load-ground c o n t a c t model. The implementation of t h e mathematical model on a l a r g e d i g i t a l computing system i s d e s c r i b e d , and v a l i d a t i o n of the s i m u l a t i o n i s d i s c u s s e d . The mathematical model i s v a l i d a t e d by comparing measured f l i g h t data w i t h simulated d a t a , by comparing l i n e a r i z e d system matrices, e i g e n v a l u e s , and eigenvectors w i t h manufacturers' d a t a , and by t h e s u b j e c t i v e comparison of
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handling c h a r a c t e r i s t i c s by experienced p i l o t s . A v i s u a l l a n d i n g d i s p l a y syst e m f o r use i n simulation which g e n e r a t e s t h e p i l o t ' s forward-looking r e a l world d i s p l a y i s d i s c u s s e d , and a s p e c i a l head-up, down-looking l o a d / l a n d i n g zone d i s p l a y i s described.
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INTRODUCTION
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Simulation and a n a l y t i c a l research has been conducted a t the Langley Research Center (LaRC) t o compare various c o n t r o l system concepts f o r improving the handling q u a l i t i e s of single-rotor helicopters carrying relatively large e x t e r n a l s l i n g l o a d s . These c o n c e p t s i n c l u d e c o n t r o l jets a t t h e l o a d , a mova b l e c a b l e attachment p o i n t on t h e h e l i c o p t e r , and c a b l e a n g l e feedback i n t o the helieopter s t a b i l i t y augmentation system. It w a s believed t h a t the m o s t c o s t - e f f e c t i v e and s a f e way t o compare and s t u d y t h e s e systems w a s through t h e use of a p i l o t e d v i s u a l ' s i m u l a t i o n i n which wide v a r i a t i o n s i n parameters and concept o p t i m i z a t i o n could be e x p l o r e d e a s i l y and q u i c k l y .
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L i t e r a t u r e s e a r c h e s and d i s c u s s i o n s w i t h i n d u s t r y d i d n o t l o c a t e any simul a t i o n s f o r a h e l i c o p t e r s l i n g l o a d or any mathematical models having f u l l flight-envelope c a p a b i l i t y f o r a helicopter and load. Therefore such a m o d e l and simulation had t o be developed.
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The purpose o f t h i s r e p o r t i s t o d e s c r i b e t h e mathematical model of a h e l i copter and e x t e r n a l s l i n g load which w a s developed, to describe the implementat i o n o f t h e model t o o b t a i n a p i l o t e d v i s u a l s i m u l a t i o n , and t o d e s c r i b e the v a l i d a t i o n o f t h e model and s i m u l a t i o n through comparison of simulated d a t a w i t h a c t u a l f l i g h t d a t a by means o f a n a l y t i c a l t e c h n i q u e s and experienced p i l o t s ' evaluations.
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The o v e r a l l mathematical model i s made up o f numerous submodels t h a t d e s c r i b e v a r i o u s components of t h e t o t a l dynamic system. The scope of t h e s e submodels i s d e s c r i b e d i n g e n e r a l terms as f o l l o w s :
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Atmospheric model - The atmospheric model has v a r i a b l e a i r d e n s i t y ,
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winds with v a r i a b l e magnitude and d i r e c t i o n , and v a r i a b l e - i n t e n s i t y turbulence e
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C o n t r o l system model - The h e l i c o p t e r c o n t r o l system model c o n v e r t s
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p i l o t ' s cyclic-control-stick, collective-stick, and pedal inputs i n t o main- and t a i l - r o t o r c y c l i c and c o l l e c t i v e - p i t c h i n p u t s .
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- Rotor models Nonlinear models f o r t h e main and t a i l r o t o r s d e f i n e
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t h r u s t , d r a g , and s i d e f o r c e s as w e l l as hub and f o r c e moments r e p r e s e n t a t i v e of a r t i c u l a t e d rotors over a wide range of a i r s p e e d s from 100 knots through hover t o rearward and sideward f l i g h t t o a t l e a s t 20 k n o t s . The rotor models account f o r variable inflow velocity, variable rotor speed, blade t w i s t , t i p loss, b l a d e coning, b l a d e f l a p p i n g , a c t u a t o r dynamics, flapping-hinge o f f s e t , and tail-rotor flapping-hinge cant angle.
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- Automatic f l i g h t c o n t r o l system (AE'CS) model The h e l i c o p t e r AFCS
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model i s based on t h e system used i n t h e U.S. Army CH-54 h e l i c o p t e r . This AFCS p r o v i d e s h e l i c o p t e r r a t e and a t t i t u d e s t a b i l i z a t i o n i n roll, p i t c h , and yaw.
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Fuselage aerodynamics model - The f u s e l a g e aerodynamics model d e f i n e s
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nonlinear l i f t , drag, and s i d e f o r c e s as well as p i t c h i n g , r o l l i n g , and yawing moments i n terms of a wide range of f u s e l a g e a n g l e s of a t t a c k and s i d e s l i p , r o t o r downwash, body a n g u l a r r a t e s , and dynamic p r e s s u r e .
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E x t e r n a l - l o a d aerodynamics model - A n e x t e r n a l - l o a d aerodynamics
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model d e f i n e s n o n l i n e a r l i f t , drag, and s i d e f o r c e as w e l l a s p i t c h i n g , r o l l i n g , and yawing moments as a f u n c t i o n of a n g l e s o f a t t a c k and s i d e s l i p , dynamic p r e s s u r e , r o t o r downwash, and body a n g u l a r r a t e s .
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Load suspension model - A l o a d suspension model d e f i n e s c a b l e t e n s i o n
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i n one o r more c a b l e s and t h e r e s u l t i n g f o r c e s and moments a c t i n g on t h e h e l i c o p t e r and e x t e r n a l load.
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- Load-ground c o n t a c t model A load-ground c o n t a c t model determines
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t h e approximate f o r c e s and moments a c t i n g on t h e l o a d as it comes i n contact with the ground f o r pickup and landing.
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A general s e t of nonlinear, rigid-body equations of motion €or both t h e helicopter and external load determines the motion of each vehicle with respect t o a f l a t , n o n r o t a t i n g Earth. An algorithm determines t h e trimmed h e l i c o p t e r c o n t r o l p o s i t i o n s , h e l i c o p t e r a t t i t u d e , and load p o s i t i o n and a t t i t u d e so t h a t t h e e n t i r e dynamic system i s i n unaccelerated f l i g h t f o r a s p e c i f i e d i n i t i a l f l i g h t condition. Another algorithm o b t a i n s the equivalent l i n e a r system from t h e n o n l i n e a r model once t h e h e l i c o p t e r i s trimmed; t h e l i n e a r system i s used f o r v e r i f i c a t i o n and validation only.
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The mathematical model i s programed on a general-purpose, r e a l - t i m e d i g i t a l computer, w i t h d a t a f o r t h e U.S. Army CH-54 h e l i c o p t e r used as i n p u t s ; and appropriate outputs are fed t o a cockpit having a set of f l i g h t instruments. The computer o u t p u t s a l s o d r i v e a real-world, out-the-window v i s u a l d i s p l a y as
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well as a computer-generated l o a d / l a n d i n g zone d i s p l a y f o r p i l o t use. The research p i l o t i s a b l e t o c o n t r o l t h e simulated h e l i c o p t e r by making c y c l i c and c o l l e c t i v e - s t i c k and pedal i n p u t s i n t h e cockpit which generate electric a l s i g n a l s t h a t are transmitted t o t h e computer. Finally, provisions a r e m a d e f o r recording simulated f l i g h t data and f o r i n t e r a c t i n g with the simulation from a c o n t r o l console.
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U s e of t r a d e names o r names of manufacturers i n t h i s r e p o r t does n o t cons t i t u t e an o f f i c i a l endorsement of such products o r manufacturers, e i t h e r expressed o r implied, by t h e National Aeronautics and Space Administration.
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C o n t r i b u t i o n s t o t h i s work and a s s i s t a n c e t o t h e a u t h o r s w e r e provided by t h e f o l l o w i n g p e r s o n s : Dean E. Cooper, of Sikorsky A i r c r a f t D i v i s i o n of United Technologies Corporation; NASA t e s t p i l o t P e r r y L. Deal; L t . C o l . W. L. Welter, o f Langley Directorate, USAAMRDL; p i l o t s from Evergreen H e l i c o p t e r , Incorpor a t e d , McMinnville, O r e . , Colonial Helicopters, Incorporated, Norfolk, Va., and the 355th Aviation Company a t F o r t E u s t i s , V i r g i n i a ; W. F. L o v e l l , J. B. L e a v i t t , and L. E. Becker, of Sperry Support S e r v i c e s ; M. D. Pardue, g r a d u a t e s t u d e n t a t Old Dominion U n i v e r s i t y ; and Lawrence E. B a r k e r , Jr., Lemuel E. Meetze, and Richard E. Bardusch, of LaRC.
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SYMBOLS
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Measurements, c a l c u l a t i o n s , and programing w e r e made i n U.S. Customary Units. They are p r e s e n t e d h e r e i n t h e I n t e r n a t i o n a l System of U n i t s ( S I ) .
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A~~ B~~
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r o t o r l a t e r a l and l o n g i t u d i n a l c y c l i c c o n t r o l commands, defined by equations (121, rad
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AICafcs 1 'ICafcs
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r o t o r l a t e r a l and l o n g i t u d i n a l c y c l i c AFCS commands,
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defined by e q u a t i o n s (14) and (13) , r a d o r deg
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A;C B;C
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r o t o r l a t e r a l and longitudinal c y c l i c c o n t r o l displacements, defined by equations ( 2 3 ) , r a d
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a
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rotor blade lift-curve slope, per rad
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a'
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s m a l l angle t h a t d e f i n e s t h e r o t o r d r a g f o r c e , defined by
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equation (35), rad
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ax, htay,htaz,h
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h e l i c o p t e r body-axes a c c e l e r a t i o n s, m/sec2
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a0
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r o t o r coning angle given by equation ( 2 9 ) , rad
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a1'b l
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r o t o r longitudinal and lateral flapping angles with respect to c o n t r o l axes, defined by equations ( 3 2 ) , rad
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als'bls
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r o t o r longitudinal and lateral flapping angles with respect t o s h a f t axes, d e f i n e d by e q u a t i o n s (431, r a d o r deg
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B
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rotor-blade tip-loss constant
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3
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b
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number of b l a d e s per r o t o r
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h' "R
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Euler angle transformation matrix f o r helicopter and load,
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d e f i n e d by e q u a t i o n (1)
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Q '
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r o t o r torque c o e f f i c i e n t , d e f i n e d by equation (36)
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CT
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rotor t h r u s t coefficient, defined by equation (27)
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CY
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r o t o r side-force c o e f f i c i e n t , defined by equation ( 3 8 )
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C
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rotor blade chord, m
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dlc,eld2c,e rd3c ,e
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cable d i r e c t i o n c o s i n e s defined by equations (73)
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ekf e k t
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fuselage and t a i l angle-of-attack corrections due to rotor downwash, r a d
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emr
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r o t o r downwash f a c t o r , d e f i n e d by e q u a t i o n (521, rad
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e
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rotor f lapping-hinge o f f s e t, m
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CFxlh' CFy,h r CFz,h'
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CFxlRJFy, !LJFZ, R
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1 GB(3' GBql GBxrGA@
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GAP,GAX,GOt~lGOtr,
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GOch
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J
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f o r c e summations along h e l i c o p t e r and load body axes i n c l u d i n g a l l e x t e r n a l f o r c e s due t o r o t o r , body aerodynamics, ground contact, and suspension system, N
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AFCS feedback g a i n s (see t a b l e I f o r units)
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G ~ ~ ~ , K ~ ~ ~ ~ e,ngKine~/g~ov~ern, orK p,arameters (see table I f o r u n i t s )
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Gu1 Gv1 Gw
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g u s t v a r i a b l e s d e f i n e d by e q u a t i o n s (111, m / s e c 2
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9
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a c c e l e r a t i o n of g r a v i t y , m/sec2
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hhrh!L 'bmr 'bt
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helicopter and load a l t i t u d e , m main- and t a i l - r o t o r b l a d e f l a p p i n g moment of i n e r t i a , kg-m 2
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Imr
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main-rotor p o l a r moment of i n e r t i a , kg-mL
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IPt
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engine-power-turbine moment of i n e r t i a , kg-m2
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Ixx, h1Iyy, h r l z z ,h'
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I x x ,R I Iyy ,R 1 = z z ,R
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h e l i c o p t e r and l o a d m a s s moments o f i n e r t i a about
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body a x e s , kg-m2
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4
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'xz,h, Ixz,R
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h e l i c o p t e r and l o a d p r o d u c t s o f i n e r t i a , kg-m 2
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it
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flow i n c i d e n c e a t h e l i c o p t e r h o r i z o n t a l t a i l , d e f i n e d by
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equation (541, r a d or deg
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=to
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f i x e d incidence of h e l i c o p t e r h o r i z o n t a l t a i l , rad
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1 Kco Kcl Kc2 'Kc 3
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Kc4 Kc5 Kc6 %7
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control-system s t i c k gain, control mixing, and u n i t conversion constants (see table I f o r u n i t s )
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Kfe
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f u s e l a g e pitching-moment parameter due t o rotor t h r u s t used i n
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e q u a t i o n s (581, N-m
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%
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load-ground contact position force parameter used i n
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e q u a t i o n (61), N/m
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Ksc
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l o a d suspension system cable s p r i n g r a t e , N/m
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Kv
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load-ground c o n t a c t v e l o c i t y force parameter used i n equation (611,
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N/ ( m / s e c )
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Lc,RtMc,Q' Nc,R
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t o t a l load-ground c o n t a c t moments, d e f i n e d by e q u a t i o n s ( 6 6 ) , N-m
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Lei, R' M c i ,R rN c i ,R Ld,h' Md, h 'Nd,h
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l o a d moments due t o ground c o n t a c t a t p o i n t i , N-m
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h e l i c o p t e r body-axes moments due t o body a n g u l a r rates, d e f i n e d by e q u a t i o n s (891, N-m
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Ld, Rr'd, krNd,k
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l o a d moments due to l o a d a n g u l a r v e l o c i t i e s , d e f i n e d by e q u a t i o n s (951, N-m
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Lf,h'Mf,hlNf,h
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t o t a l moments a c t i n g on h e l i c o p t e r due t o fuselage aerodynamics, d e f i n e d by e q u a t i o n s ( 5 8 ) , N-m
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rijh I i;h Lhub, htMhub,h' Nhub,h
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h e l i c o p t e r fuselage l i f t , drag, and s i d e forces, N
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h e l i c o p t e r moments i n body axes due t o r o t o r moments t r a n s m i t t e d a t t h e hub, d e f i n e d by e q u a t i o n ( 4 5 ) , N-m
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Lhub,s,Mhub,s,Nhub,s
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h e l i c o p t e r moments i n s h a f t axes due t o r o t o r moments t r a n s m i t t e d a t t h e hub, defined by equations (42) and (44), N-m
|
||
|
||
t o t a l aerodynamic moments a c t i n g on t h e l o a d , d e f i n e d by e q u a t i o n s ( 9 6 ) , N-m
|
||
|
||
l i f t , drag, and s i d e f o r c e s a c t i n g on t h e load, defined by equations (921, N
|
||
|
||
5
|
||
|
||
Lr,h P M,rh‘ Nr,h
|
||
|
||
t o t a l body-axes moments a c t i n g on h e l i c o p t e r due t o
|
||
r o t o r f o r c e s and hub moments, d e f i n e d by e q u a t i o n (46) ,
|
||
N-m
|
||
|
||
Lt,h r M t ,h r N t ,h
|
||
|
||
body-axes moments a c t i n g on h e l i c o p t e r ‘due t o suspension c a b l e , d e f i n e d by e q u a t i o n s (751, N-m
|
||
|
||
Lt,!PM,tR, N t ,R
|
||
|
||
body-axes moments a c t i n g on t h e l o a d due t o suspension
|
||
cable, d e f i n e d by e q u a t i o n s (77) , N-m scales o f turbulence, d e f i n e d by equations ( 5 ) t o (7) , m
|
||
|
||
body-axes aerodynamic moments a c t i n g on f u s e l a g e , appearing i n e q u a t i o n s (581, N-m
|
||
|
||
e x t e r n a l moments, i n c l u d i n g main- and t a i l - r o t o r moments,
|
||
f u s e l a g e aerodynamic moments, and c a b l e suspension
|
||
moments, N-m
|
||
|
||
RC
|
||
|
||
suspension-system i n s t a n t a n e o u s c a b l e l e n g t h , d e f i n e d by
|
||
|
||
equation (69), m
|
||
|
||
Rc 0
|
||
|
||
suspension-system unstretched cable length, m
|
||
|
||
%?
|
||
|
||
m a s s moment of r o t o r blade a p p e a r i n g i n e q u a t i o n s (42), kg-m
|
||
|
||
mhrmR
|
||
|
||
h e l i c o p t e r and l o a d m a s s , kg
|
||
|
||
- n11n2,. * 1ng
|
||
|
||
white-noise signals used i n equations (10)
|
||
|
||
phl q h l ‘h 1PR ‘2 19%1
|
||
|
||
h e l i c o p t e r and l o a d a n g u l a r v e l o c i t y components i n body axes, rad/sec
|
||
|
||
Psr qs 1rs
|
||
|
||
h e l i c o p t e r angular v e l o c i t y components i n s h a f t
|
||
axes, rad/sec
|
||
|
||
Pwrqwl rw
|
||
|
||
h e l i c o p t e r angular v e l o c i t y components i n c o n t r o l
|
||
axes , rad/ s e c
|
||
|
||
Qam
|
||
|
||
aerodynamic t o r q u e a c t i n g on main r o t o r , p o s i t i v e i n d i r e c t i o n
|
||
|
||
o p p o s i t e t o r o t a t i o n , N-m
|
||
|
||
Qat
|
||
|
||
aerodynamic torque a c t i n g on t a i l rotor, p o s i t i v e i n d i r e c t i o n
|
||
o p p o s i t e t o r o t a t i o n , N-m
|
||
|
||
Qeng
|
||
|
||
s h a f t engine t o r q u e a c t i n g on r o t o r and f u s e l a g e ( p o s i t i v e v a l u e t e n d s t o accelerate r o t o r and cause f u s e l a g e t o yaw r i g h t ) , N-m
|
||
|
||
Qgen QS
|
||
|
||
gas-generator t o r q u e used i n e q u a t i o n s (481, N-m r e s u l t i n g main- ox t a i l - r o t o r s h a f t torque a c t i n g on f u s e l a g e , N-m
|
||
|
||
6
|
||
|
||
--
|
||
qhf qR
|
||
|
||
dynamic pressure a t f u s e l a g e and l o a d , given by e q u a t i o n s (50)
|
||
and (91) , N/m2
|
||
|
||
R
|
||
|
||
main- o r t a i l - r o t o r r a d i u s , m
|
||
|
||
S
|
||
|
||
s h a f t tilt transformation mafrix given by equation (18)
|
||
|
||
S
|
||
|
||
Laplace o p e r a t o r I sec-1
|
||
|
||
T,H, J
|
||
|
||
main- o r t a i l - r o t o r t h r u s t , d r a g , and s i d e f o r c e d e f i n e d by
|
||
, e q u a t i o n s ( 2 8 ) , ( 3 4 ) and ( 3 9 ) , N
|
||
|
||
%
|
||
|
||
suspension-system c a b l e tension, defined by equation (70) , N
|
||
|
||
Uas,h Vas,h t w a s ,h
|
||
|
||
h e l i c o p t e r body-axes components of v e l o c i t y , defined by
|
||
e q u a t i o n s (20) , m/sec
|
||
|
||
Uas,RfVas,QfWas,Q
|
||
|
||
load body-axes components of t o t a l a i r s p e e d , defined by
|
||
e q u a t i o n s (90) , m/sec
|
||
|
||
Ucg ,h vcg ,h wcg,h
|
||
|
||
body-axes components of i n e r t i a l v e l o c i t y of h e l i c o p t e r c.g., given by e q u a t i o n s ( 8 0 ) , m/sec
|
||
|
||
ucg ,R vcg ,R wcg,R
|
||
|
||
f
|
||
|
||
f
|
||
|
||
body-axes components o f i n e r t i a l v e l o c i t y of load
|
||
c.g., given by e q u a t i o n s (80) w i t h h replaced
|
||
by R, m / s e c
|
||
|
||
uc i ,e' vci, e w c i,e
|
||
|
||
Earth-axes components of i n e r t i a l v e l o c i t y of t h e i t h load-ground c o n t a c t p o i n t , defined by equation (601, m/sec
|
||
|
||
Uhcg, e' Vhcg,e ' whcg,e
|
||
|
||
Earth-axes components of i n e r t i a l v e l o c i t y of h e l i c o p t e r c.g., given by e q u a t i o n (841, m/sec
|
||
|
||
UQcgI e tVRcg WRcg,e
|
||
|
||
Earth-axes components of i n e r t i a l v e l o c i t y of load c.g., given by e q u a t i o n (84) w i t h h r e p l a c e d by 2, m/sec
|
||
|
||
Ugust,R V g u s t,R' W g u s,t R f
|
||
|
||
body-axes components of g u s t
|
||
velocity, given by equations (90) , m / s e c
|
||
|
||
ur,h vr,h 'wr,h
|
||
|
||
body-axes components o f t o t a l a i r s p e e d a t r o t o r hub, given by equations (191, m / s e c
|
||
|
||
shaft-axes components of t o t a l a i r s p e e d a t rotor hub, given by e q u a t i o n (171, m/sec
|
||
|
||
uwfvwf ww
|
||
|
||
control-axes components of t o t a l a i r s p e e d a t rotor hub, given by equations (221, m / s e c
|
||
|
||
%ind ,e Vwind,e Wwind,e
|
||
|
||
Earth-axes components of windspeed, given by equation (4) I m/sec
|
||
7
|
||
|
||
Uwind ,h Vwind,h' Wwind,h' Uwind ,R' Vwind,R' Wwind,
|
||
|
||
body-axes components of windspeed for h e l i c o p t e r
|
||
and l o a d , given by e q u a t i o n ( 4 ) , m/sec
|
||
|
||
'as, hl'as,
|
||
|
||
h e l i c o p t e r and load t o t a l airspeed defined by equat i o n s (51) and (911, m / s e c
|
||
|
||
'wind
|
||
VO
|
||
h
|
||
was,R
|
||
|
||
magnitude of wind v e c t o r , m / s e c
|
||
l o a d s l i d i n g v e l o c i t y beyond which s l i d i n g f r i c t i o n becomes independent of s l i d i n g v e l o c i t y , m/sec
|
||
l o a d body z-axis component of t o t a l a i r s p e e d w i t h c o n s t a n t added t o improve numerical s t a b i l i t y , m/sec
|
||
|
||
'ci ,e "ci ,e 1 'ci ,e
|
||
|
||
Earth-axes components of load-ground contact f o r c e s a t the i t h contact p o i n t , defined by equations (611,
|
||
(62) , and (631, N
|
||
|
||
Xci,R,Yci,R,Zci,R
|
||
|
||
load body-axes components of load-ground c o n t a c t f o r c e s a t t h e i t h c o n t a c t p o i n t , given by equation (641, N
|
||
|
||
Xc,RJCIR, Zc,R
|
||
|
||
load body-axes components of t o t a l load-ground contact f o r c e s , given by equations (661, N
|
||
|
||
Xf,hlYf,h'2f , h
|
||
|
||
h e l i c o p t e r body-axes components of fuselage l i f t , drag, and s i d e f o r c e , given by e q u a t i o n (571, N
|
||
|
||
XR' YR' 2%
|
||
r' ,h1'r1 h' zr ,h
|
||
|
||
l i f t , drag, and s i d e f o r c e s expressed i n load body axes (eq. ( 9 3 ) ) N
|
||
h e l i c o p t e r body-axes components o f r o t o r f o r c e s , given
|
||
by equation (411, N
|
||
|
||
'r, s,Yr,s,zrs,
|
||
|
||
shaft-axes components of r o t o r f o r c e s , defined by equations (401, N
|
||
|
||
't ,h t Y t,h r't ,h
|
||
|
||
h e l i c o p t e r body-axes components of cable t e n s i o n , given
|
||
by equation (74) , N
|
||
|
||
X,tR J t ,R J t , R
|
||
|
||
l o a d body-axes components of c a b l e t e n s i o n , given by
|
||
equation (76) , N
|
||
|
||
xa ,h 1ya ,h1za ,h
|
||
|
||
h e l i c o p t e r body-axes d i s t a n c e s from h e l i c o p t e r c.g. t o cable attachment point, m
|
||
|
||
xalR'Ya,R'Za, R
|
||
|
||
load body-axes d i s t a n c e s from load c.g. t o cable a t t a c h ment p o i n t , m
|
||
|
||
Xc i ,elYci ,e' z c i , e
|
||
|
||
Earth-axes coordinates of i t h ground contact p o i n t , m
|
||
|
||
8
|
||
|
||
Xc i , R' Y c i , R' 'ci ,R
|
||
Xc o l ' x l a t ' x l o n Xped
|
||
Xha ,e Yha,e' 'ha, e
|
||
Xhcg r e"hcg,e' Zhcg,e
|
||
|
||
Xkeg, e 'Ytcg, e ZRcg,e
|
||
|
||
Xkcg ,h' 'Reg ,h' 'Reg,h
|
||
|
||
XR p ,h'
|
||
|
||
h' 'Rp ,h
|
||
|
||
XLp ,R 'Y R p ,R
|
||
|
||
R
|
||
|
||
Xmr ,htYmr,h"mr, h'
|
||
X t rh, r Y t r, h t Z t r,h
|
||
Xp s , h r Y p s ,h"ps, h
|
||
|
||
Xscreen1 Yscreen
|
||
|
||
xv, e 1 Yv, e 1 zv, e
|
||
xv, h yv ,h zv, h Xw t , h l 'wt, h' 'wt ,h Xzp ,e, Yzp ,e ,'zp ,e
|
||
|
||
load body-axes d i s t a n c e s f r o m load c,g. t o i t h ground contact point, m
|
||
control displacements of collective s t i c k , l a t e r a l and longitudinal c y c l i c s t i c k , and pedals (positive displacements cause climb, r i g h t r o l l , p i t c h - u p , and yaw left, respectively), m
|
||
Earth-axes i n e r t i a l p o s i t i o n of h e l i c o p t e r c a b l e a t t a c h ment p o i n t , given by equation ( 6 7 ) , m
|
||
Earth-axes i n e r t i a l position of helicopter c.g., given by e q u a t i o n s (851, m
|
||
Earth-axes i n e r t i a l p o s i t i o n of load cable attachment
|
||
p o i n t , given by equation (68) , m
|
||
Earth-axes i n e r t i a l p o s i t i o n o f load c.g., given by
|
||
equations (85) with s u b s c r i p t h replaced by 2 , m
|
||
h e l i c o p t e r body-axes coordinates o f load c.g., given by equation (971, m
|
||
h e l i c o p t e r body-axes c o o r d i n a t e s of any p o i n t p on t h e load, given by equation (98), m
|
||
l o a d body-axes c o o r d i n a t e s of any p o i n t p on t h e load, m
|
||
h e l i c o p t e r body-axes c o o r d i n a t e s of main- and t a i l - r o t o r hub, m
|
||
h e l i c o p t e r body-axes coordinates of eye-level p o s i t i o n of p i l o t i n l e f t seat, m
|
||
nondimensional screen coordinates of any p o i n t p , used i n load/landing zone display defined by equat i o n s (1011, m
|
||
Earth-axes coordinates of helicopter viewpoint, given by e q u a t i o n (991, m
|
||
h e l i c o p t e r body-axes coordinates of down-looking viewpoint, m
|
||
h e l i c o p t e r body-axes coordinates o f wind-tunnel mounting point, m
|
||
Earth-axes i n e r t i a l p o s i t i o n of any p o i n t p f i x e d on the Earth, m
|
||
|
||
9
|
||
|
||
, , Xzp h 1 Yzp h 1 'zp ,h
|
||
|
||
h e l i c o p t e r body-axes coordinates of any p o i n t p on the Earth, m
|
||
|
||
ac ,e ,'c, e
|
||
|
||
cable angles with respect t o t h e v e r t i c a l , defined by equations (71)
|
||
and (72), rad
|
||
|
||
af 1 %
|
||
af R
|
||
B!L
|
||
P Y
|
||
|
||
fuselage angle of a t t a c k and s i d e s l i p , defined by equations (49) and (55), rad or deg
|
||
local fuselage angle of a t t a c k , defined by equation (53) , r a d or deg
|
||
l o a d a n g l e s of a t t a c k and s i d e s l i p , d e f i n e d by e q u a t i o n s (91), r a d
|
||
|
||
rotor orientation angle, rad
|
||
|
||
r o t o r Lock number,
|
||
|
||
pacR4 Rotor b l a d e f l a p p i n g moment of i n e r t i a
|
||
|
||
azlh1az2h
|
||
n'lwt n'2wt At
|
||
|
||
incremental fuselage l i f t , N i n c r e m e n t a l f u s e l a g e p i t c h i n g moment, N-m
|
||
simulation integration step size, sec
|
||
|
||
63,
|
||
|
||
tail-rotor flapping-hinge cant angle, rad
|
||
|
||
0ct
|
||
|
||
commanded v a l u e o f t a i l - r o t o r c o l l e c t i v e p i t c h given by
|
||
equations (12) , rad
|
||
|
||
@Om 00,
|
||
|
||
main-rotor c o l l e c t i v e p i t c h , given by e q u a t i o n s ( 1 2 ) , r a d o r deg
|
||
e f f e c t i v e value o f t a i l - r o t o r c o l l e c t i v e p i t c h , given by equation (471, rad o r deg
|
||
|
||
'mafcs, ' t a f c s
|
||
|
||
main- and t a i l - r o t o r AFCS c o l l e c t i v e p i t c h command, d e f i n e d by e q u a t i o n s (15) and (16), r a d
|
||
|
||
@S
|
||
|
||
l o n g i t u d i n a l s h a f t tilt angle, p o s i t i v e f o r t h r u s t vector t i l t e d
|
||
|
||
from -zh toward -xh, r a d
|
||
|
||
01 0 . 75
|
||
|
||
rotor blade t w i s t angle from r o o t t o t i p , r a d rotor c o l l e c t i v e p i t c h a t three-fourths radius, defined by
|
||
equation (33), rad
|
||
|
||
'h,$hf$h
|
||
|
||
h e l i c o p t e r p i t c h , r o l l , and yaw AFCS a t t i t u d e e r r o r s , r a d
|
||
|
||
Am, A t
|
||
Vf
|
||
|
||
main- and tail-rotor inflow r a t i o , defined by equation (25) c o e f f i c i e n t of s l i d i n g f r i c t i o n used i n load-ground c o n t a c t model
|
||
|
||
10
|
||
|
||
main- and t a i l - r o t o r t i p - s p e e d r a t i o , d e f i n e d by e q u a t i o n (24)
|
||
r o t o r induced inflow r a t i o , defined by equation (26)
|
||
atmospheric d e n s i t y g i v e n by e q u a t i o n ( 2 ) , kg/m 3
|
||
|
||
swashplate a c t u a t o r damping r a t i o
|
||
|
||
rotor s o l i d i t y , b-c 7TR
|
||
|
||
body-axes components of r m s g u s t i n t e n s i t y , m / s e c
|
||
|
||
engine t i m e c o n s t a n t , sec
|
||
|
||
t a i l - r o t o r ti,, t i m e c o n s t a n t , sec
|
||
|
||
r o t o r inflow t i m e c o n s t a n t , sec
|
||
|
||
white n o i s e power s p e c t r a l d e n s i t y , sec
|
||
|
||
@hlehl$h,$g,efi,$g
|
||
|
||
r o l l ($), p i t c h ( e ) , and yaw ($1 E u l e r a n g l e s o f
|
||
helicopter and load, rad
|
||
|
||
@S
|
||
|
||
lateral s h a f t tilt angle, p o s i t i v e f o r t h r u s t vector t i l t e d from
|
||
|
||
-zh toward +yh, r a d
|
||
|
||
@wind
|
||
|
||
wind a n g l e measured clockwise from t r u e n o r t h t h a t d e f i n e s t h e d i r e c t i o n from which t h e wind i s coming, r a d
|
||
|
||
@wt
|
||
R
|
||
|
||
wind-tunnel yaw a n g l e , r a d rotor angular velocity, rad/sec
|
||
|
||
QO
|
||
|
||
commanded r o t o r a n g u l a r v e l o c i t y , r a d / s e c
|
||
|
||
power-turbine angular v e l o c i t y , rad/sec QPt
|
||
|
||
wa
|
||
|
||
swashplate-actuator natural frequency, rad/sec
|
||
|
||
Abbreviations :
|
||
|
||
ADC
|
||
|
||
analog to d i g i t a l converter
|
||
|
||
AFCS
|
||
|
||
automatic f l i g h t control system
|
||
|
||
c.g.
|
||
|
||
center of gravity
|
||
|
||
DAC
|
||
|
||
d i g i t a l to analog converter
|
||
|
||
11
|
||
|
||
BLCG
|
||
|
||
buttock l i n e a t c,g.
|
||
|
||
FSCG
|
||
|
||
fuselage s t a t i o n a t c.g.
|
||
|
||
WLCG
|
||
|
||
w a t e r l i n e a t c.g.
|
||
|
||
RTS
|
||
|
||
real-time system
|
||
|
||
IXIS
|
||
|
||
r o o t mean squared
|
||
|
||
VLDS
|
||
|
||
visual landing display system
|
||
|
||
Dots o v e r a symbol denote d e r i v a t i v e s w i t h r e s p e c t t o t i m e .
|
||
|
||
I n i t i a l v a l u e s of v a r i a b l e s are denoted by (0) f o l l o w i n g t h e v a r i a b l e symbol.
|
||
|
||
Matrix t r a n s p o s e i s denoted by a s u p e r s c r i p t T.
|
||
|
||
DESCRIPTION O F MATHEMATICAL MODEL
|
||
The mathematical model f o r t h e s i m u l a t i o n of a s i n g l e - r o t o r h e l i c o p t e r and e x t e r n a l l o a d can be given i n terms o f submodels f o r t h e v a r i o u s components of t h e t o t a l dynamic system.
|
||
A block diagram f o r t h e o v e r a l l mathematical model i s given i n f i g u r e 1. This diagram together with the Contents should be useful i n understanding the i n t e r r e l a t i o n s h i p between t h e submodels. I n t h e following s e c t i o n s t h e mathematical model i s d e s c r i b e d i n approximately t h e o r d e r it would be executed i n t h e computer so t h a t t h e r e a d e r can w r i t e h i s own s i m u l a t i o n program more easily.
|
||
|
||
Coordinate Systems
|
||
The f o l l o w i n g right-hand o r t h o g o n a l a x i s systems are used i n t h i s r e p o r t :
|
||
(1) E a r t h a x e s ( s u b s c r i p t e ) : o r i g i n f i x e d on t h e E a r t h ' s s u r f a c e , xe-axis pointing north, ye-axis pointing east
|
||
( 2 ) H e l i c o p t e r body axes ( s u b s c r i p t h) : o r i g i n a t t h e h e l i c o p t e r c.g., xh-axis p o i n t i n g forward i n t h e p l a n e o f symmetry of t h e f u s e l a g e and p a r a l l e l t o t h e h e l i c o p t e r w a t e r l i n e , zh-axis p o i n t i n g downward away from t h e main r o t o r and i n t h e p l a n e o f symmetry (see f i g s . 2 and 3)
|
||
( 3 ) Shaft axes ( s u b s c r i p t s ) : o r i g i n a t the c e n t e r of the r o t o r hub, y,-axis r o t a t e d through the lateral s h a f t tilt angle $s about the xh-axis, xs-axis r o t a t e d through the longitudinal s h a f t tilt a n g l e 8, about t h e ys-axis, zs-axis c o i n c i d e n t w i t h t h e r o t o r s h a f t , a p p l i e s t o both t h e main r o t o r and t h e t a i l r o t o r (see f i g . 3)
|
||
12
|
||
|
||
(4) Control axes (subscript w ) : origin a t the center of the rotor hub,
|
||
- zw-axis d i r e c t e d toward t h e f u s e l a g e along t h e a x i s of no f e a t h e r -
|
||
ing (the physical axis of a pure flapping rotor a rotor with blades f i x e d i n p i t c h b u t free t o f l a p ) , %-axis chosen t o give no yw-component of v e l o c i t y r e l a t i v e t o t h e free-stream a i r ( t h e freestream a i r t o i n c l u d e t h e a i r motion from t u r b u l e n c e and s t e a d y winds), applies t o both r o t o r s (see f i g , 3)
|
||
(5) Wind-tunnel axes (subscript w t ) : o r i g i n a t t h e helicopter o r external-load wind-tunnel mounting point, s t - a x i s pointing i n t o t h e r e l a t i v e wind, zwt-axis p o i n t i n g downward and p e r p e n d i c u l a r t o the wind
|
||
(6) External-load body axes ( s u b s c r i p t R) : o r i g i n a t t h e load c.g.,
|
||
xR-axis p o i n t i n g forward i n t h e p l a n e of symmetry of t h e load, zR-axis p o i n t i n g downward i n t h e p l a n e of symmetry o f t h e l o a d
|
||
The Earth-to-body a x i s t r a n s f o r m a t i o n f o r t h e h e l i c o p t e r based on t h e s t a n d a r d yaw, p i t c h , and r o l l E u l e r a n g l e r o t a t i o n sequence shown i n f i g u r e 3 i s given i n m a t r i x form as
|
||
|
||
s i n 6, s i n $h cos $h
|
||
- cos $h s i n $h
|
||
s i n oh cos $h cos $h
|
||
L + s i n $h s i n $h
|
||
|
||
s i n 8, s i n $h s i n $h
|
||
+ cos @h cos $h s i n 6, cos $h s i n qh
|
||
- s i n @h cos $h
|
||
|
||
-sin 8h cos 8h s i n $h
|
||
cos 8, cos $h
|
||
|
||
The t r a n s f o r m a t i o n m a t r i x f o r t h e l o a d h a s t h e same form w i t h t h e s u b s c r i p t h replaced by s u b s c r i p t 2.
|
||
|
||
Atmospheric Mode1
|
||
The atmospheric model used allows f o r a i r - d e n s i t y v a r i a t i o n s with a l t i tude, v a r i a b l e wind d i r e c t i o n and magnitude, and v a r i a b l e - i n t e n s i t y atmospheric turbulence. The a i r d e n s i t y is c a l c u l a t e d according t o t h e polynomial i n h
|
||
|
||
- p = 1.2266 (1.176 X 10'4)h 4- (4.337 X 10-')h2 - (7.463 X 10'14)h3
|
||
|
||
- + (5.538 x 1 0 - - ~ ~ ) h * (9.357 x 1 0 - ~ ~ ) h ~
|
||
|
||
(2)
|
||
|
||
where h i s t h e h e l i c o p t e r o r external-load a l t i t u d e above sea l e v e l , i n meters, as determined from i n t e g r a t i n g t h e equations of motions discussed below.
|
||
13
|
||
|
||
Steady winds are s p e c i f i e d i n t e r m s of magnitude and d i r e c t i o n . The wind is expressed i n Earth axes by the r e l a t i o n s
|
||
|
||
%ind,e -- 'wind 'Os *wind
|
||
|
||
Vwind,e -- 'wind sin *wind
|
||
|
||
(3)
|
||
|
||
Wwind,e =
|
||
|
||
where *wind i s t h e a n g l e measured clockwise from t r u e n o r t h t h a t d e f i n e s t h e d i r e c t i o n from which t h e wind i s blowing. Steady v e r t i c a l winds are n o t simul a t e d . The components o f t h e s t e a d y winds a r e expressed i n h e l i c o p t e r body axes by using t h e t r a n s f o r m a t i o n
|
||
|
||
~ n d ,~~n d , ~
|
||
|
||
Vwind,h = ch Vwind,e
|
||
|
||
(4)
|
||
|
||
Wwind,h
|
||
|
||
Wwind,e
|
||
|
||
The components o f t h e s t e a d y winds are e x p r e s s e d i n l o a d body axes by u s i n g
|
||
e q u a t i o n (4) w i t h t h e s u b s c r i p t h r e p l a c e d by s u b s c r i p t R. The atmospheric t u r b u l e n c e mathematical model i s based on t h e Dryden spectrum o f t u r b u l e n c e as d i s c u s s e d i n r e f e r e n c e 1. This theory a l l o w s t h e s i m u l a t i o n of atmospheric turbulence by passing uncorrelated white noise through l i n e a r f i l t e r s to obtain g u s t components i n body axes.
|
||
The scales of t u r b u l e n c e f o r t h e h e l i c o p t e r and t h e l o a d are c a l c u l a t e d according t o the r e l a t i o n s shown f o r t h e h e l i c o p t e r
|
||
|
||
Lv,h = %,h
|
||
(762.0 14
|
||
|
||
(hh =< 762.0; Ou < 6.4)
|
||
|
||
(CTU => 6.4)
|
||
|
||
(7)
|
||
|
||
(hh > 762.0; Ou < 6.4) J
|
||
|
||
where 0, is t h e l o n g i t u d i n a l r m s g u s t i n t e n s i t y (assumed t o be t h e same f o r t h e h e l i c o p t e r and l o a d ) , The scales of t u r b u l e n c e f o r t h e load are c a l c u l a t e d by u s i n g e q u a t i o n s ( 5 ) (6) I and ( 7 ) with t h e s u b s c r i p t h r e p l a c e d by subscript A. The v e r t i c a l and l a t e r a l g u s t i n t e n s i t i e s f o r t h e h e l i c o p t e r a r e given by
|
||
0.03760,hh 1/3 and
|
||
av = au
|
||
The g u s t i n t e n s i t i e s f o r t h e l o a d are c a l c u l a t e d from e q u a t i o n s (8) with t h e
|
||
s u b s c r i p t h r e p l a c e d by subscript R. The white n o i s e power s p e c t r a l d e n s i t y
|
||
is given by
|
||
|
||
where A t i s t h e d i g i t a l simulation computation s t e p s i z e i n seconds.
|
||
The components of g u s t v e l o c i t y f o r t h e h e l i c o p t e r and l o a d i n body
|
||
. . axes are c a l c u l a t e d by p a s s i n g s i x u n c o r r e l a t e d white n o i s e s i g n a l s
|
||
nlr n2, , I n6 through l i n e a r f i l t e r s and a r e given a s follows f o r t h e helicopter:
|
||
|
||
Ugust,h --
|
||
|
||
s
|
||
|
||
Gulh
|
||
+ -'as,
|
||
|
||
h
|
||
|
||
nl
|
||
|
||
) .vIh(. + 'as,h
|
||
|
||
Vgust l h --
|
||
|
||
(. fi =v,h n2 +-)
|
||
|
||
"3
|
||
|
||
15
|
||
|
||
where
|
||
|
||
- m.1 Gu,h - 'u 'as,h (TQoLu,h
|
||
Gv,h = v' J3vas,h/(2'QoLv,h)
|
||
|
||
Gw,h = awJ3vas,h /(2'@o%?,h)
|
||
|
||
The g u s t components f o r t h e l o a d are computed i n a s i m i l a r manner. The f i l t e r s may be implemented d i g i t a l l y by using Z transform techniques.
|
||
I t was judged a f t e r d i s c u s s i o n with G. H. F i c h t l , of t h e NASA Marshall Space F l i g h t Center, t h a t f o r s l i n g - l o a d c a b l e l e n g t h s of approximately 30 meters, t h e g u s t s f o r t h e h e l i c o p t e r and t h e e x t e r n a l load w i l l be essent i a l l y u n c o r r e l a t e d . Thus two sets of u n c o r r e l a t e d white n o i s e s i g n a l s a r e used f o r the helicopter and t h e external load.
|
||
|
||
Control System
|
||
|
||
The f l i g h t c o n t r o l system mathematical model c o n v e r t s t h e p i l o t ' s c y c l i c -
|
||
|
||
s t i c k , pedal, and c o l l e c t i v e - s t i c k displacements and AFCS outputs t o equivalent
|
||
main-rotor and t a i l - r o t o r c o n t r o l i n p u t s . The main-rotor c o l l e c t i v e p i t c h eo,
|
||
|
||
longitudinal and l a t e r a l cyclic p i t c h BIC and ATC, and t a i l - r o t o r c o l l e c t i v e
|
||
|
||
eCt p i t c h
|
||
|
||
a r e given i n terms of c o l l e c t i v e , c y c l i c , and pedal displacements
|
||
|
||
and AFCS o u t p u t s by t h e following e x p r e s s i o n s o b t a i n e d from Sikorsky A i r c r a f t
|
||
|
||
Division of United Technologies Corporation:
|
||
|
||
K ~ O+ Kclxcol + 'mafcs
|
||
Kc2x10n BICafcs +
|
||
Kc3Xcol Kc4xlat + AICafcs +
|
||
Kc5 + Kc6xped + Kc7Xcol+ ' t a f c s
|
||
where xcol, xlon, xlat, and "ped are t h e p i l o t ' s c o n t r o l displacements w i t h r e s p e c t t o a f i x e d reference p o s i t i o n . The c o n s t a n t s KcO through Kc7 a r e used f o r s t i c k gain, control mixing, and u n i t conversions. Since control f e e l i s important t o p i l o t s , a programmable hydraulic c o n t r o l loader i s used f o r the cyclic control s t i c k and the pedals. Pertinent d e t a i l s of t h i s system are discussed i n the section "Simulation Description."
|
||
|
||
16
|
||
|
||
Automatic F l i g h t C o n t r o l System Model
|
||
The mathematical mode.1 of t h e automatic f l i g h t c o n t r o l system (AFCS) i s s i m i l a r t o t h a t of t h e a t t i t u d e command system employed i n t h e U.S. Army CH-54A h e l i c o p t e r , and w a s o b t a i n e d from unpublished S i k o r s k y A i r c r a f t d a t a . The p i t c h channel equation is given as
|
||
|
||
where and
|
||
|
||
A
|
||
|
||
h
|
||
|
||
BICafcs = GBeeh + GBqqh -k GB?lon
|
||
|
||
ehh = e, - eh(o)
|
||
|
||
(13)
|
||
|
||
The q u a n t i t i e s 8,,(0) and xlon(0) are t h e p r e c a l c u l a t e d i n i t i a l t r i m v a l u e s
|
||
|
||
eh of
|
||
|
||
and xlon d i s c u s s e d i n t h e s e c t i o n " T r i m C a l c u l a t i o n s . "
|
||
|
||
The r o l l e q u a t i o n is g i v e n s i m i l a r l y as
|
||
|
||
and
|
||
- h
|
||
Xl a t = xl a t xl a t ( 0 )
|
||
|
||
The yaw channel i s modeled by the f o l l o w i n g e q u a t i o n :
|
||
|
||
where
|
||
|
||
A
|
||
' t a f c s = G8t$*h + GOtrrh
|
||
|
||
17
|
||
|
||
The heading command $J0 i s i n i t i a l l y s e t t o t h e h e l i c o p t e r t r i m yaw angle.
|
||
|
||
During t h e simulation whenever t h e p i l o t a c t u a t e s e i t h e r microswitch l o c a t e d on
|
||
|
||
t h e s i m u l a t o r p e d a l s , t h e n $o i s s e t t o t h e c u r r e n t v a l u e of +ha When t h e
|
||
p i l o t releases t h e microswitches, q0 i s s e t t o t h e v a l u e of $h j u s t p r i o r
|
||
|
||
t o switch release. I f the heading hold f e a t u r e i s not desired, then a push
|
||
|
||
e b u t t o n d i s c r e t e i n t h e c o c k p i t w i l l s e t t h e g a i n G
|
||
|
||
t o zero.
|
||
|
||
t$
|
||
|
||
The a l t i t u d e channel i s modeled by u s i n g t h e f o l l o w i n g e q u a t i o n :
|
||
|
||
where
|
||
|
||
The a l t i t u d e command ho i s i n i t i a l l y s e t t o t h e h e l i c o p t e r a l t i t u d e . During t h e o p e r a t e mode, t h e p i l o t can r e s e t ho t o t h e c u r r e n t a l t i t u d e o r disable the a l t i t u d e hold f e a t u r e by using a push-button d i s c r e t e i n t h e cockpit,
|
||
R o t o r System
|
||
I n t h e i n t e r e s t of real-time pilot-in-the-loop computer simulation, every e f f o r t i s made t o keep t h e r o t o r mathematical model s i m p l e b u t adequate t o allow forward f l i g h t t o a t least 100 knots, rearward and sideward f l i g h t to 2 0 k n o t s , a u t o r o t a t i o n s , and l a r g e - a n g l e maneuvers. The f o r c e s and moments due t o t h e main and t a i l r o t o r s are c a l c u l a t e d by u s i n g a modified B a i l e y represent a t i o n d i s c u s s e d i n r e f e r e n c e s 2 t o 5.
|
||
The f o l l o w i n g d i s c u s s i o n of r o t o r modeling i s g e n e r a l and i s a p p l i c a b l e t o b o t h t h e main and t a i l rotors. Important l i m i t a t i o n s are given when necessary. Rotor v a r i a b l e s w i l l need "main ( m ) " o r " t a i l ( t ) "i d e n t i f i c a t i o n when i n c l u d e d i n a computer program.
|
||
The v e l o c i t y o f t h e f r e e stream a t t h e hub i s e x p r e s s e d i n s h a f t axes i n t e r m s o f i n e r t i a l v e l o c i t y o f t h e h e l i c o p t e r c e n t e r of g r a v i t y , body angular rates, s t e a d y winds, atmospheric g u s t s , and p o s i t i o n of t h e main- and t a i l r o t o r hubs by t h e following expression:
|
||
U S
|
||
(17)
|
||
vS
|
||
wS
|
||
18
|
||
|
||
where
|
||
|
||
cos e s sin Bs sin Qs sin 0, cos @s
|
||
|
||
s=
|
||
|
||
--sin 8,
|
||
|
||
cos 0, sin @s cos 0, cos Q S
|
||
|
||
and
|
||
|
||
- -
|
||
Ur,h - %s,h i- qhzr,h rhYr,h
|
||
|
||
- V r,h
|
||
|
||
=
|
||
|
||
v as,h
|
||
|
||
+
|
||
|
||
rhxr,h
|
||
|
||
‘hzr,h
|
||
|
||
Wr,h - Was,h
|
||
|
||
phyrIh - qhxr,h
|
||
|
||
+
|
||
|
||
and
|
||
|
||
Uas,h = ucg,h -I-Ugust,h + Uwind,h VasIh = Vcg,h + Vgust,h + vwind,h Waslh = wcg,h + - Wgust,h + Wwind,h
|
||
|
||
(19)
|
||
(20)
|
||
|
||
The rotor orientation angle B is defined by the relation
|
||
- B = tan-1 vs
|
||
US
|
||
and the velocity of the free stream at the hub is expressed in control axes by the approximation given in reference 2 (see fig. 3(c)) :
|
||
|
||
% = us cos B + vs sin B
|
||
|
||
vw = 0
|
||
|
||
(22)
|
||
|
||
- - wW = wS BiCUs AiCVs
|
||
|
||
19
|
||
|
||
B;. where
|
||
|
||
and A;C are t h e s h a f t r e l a t i v e c y c l i c c o n t r o l i n p u t s f o r t h e main
|
||
|
||
A;. r o t o r . For t h e t a i l r o t o r ,
|
||
|
||
and BiC are o f course zero.
|
||
|
||
Actuator dynamics are modeled by passing t h e c o n t r o l i n p u t s through secondorder f i l t e r s as
|
||
|
||
A;C
|
||
|
||
1 -
|
||
|
||
wa2
|
||
|
||
- s2 + 2pawas 4- wa 2 A I C
|
||
|
||
The f i l t e r s may be implemented by u s i n g Z t r a n s f o r m techniques. The c y c l i c c o n t r o l i n p u t s AIC and BIC are generated by p i l o t c y c l i c s t i c k motions and automatic c o n t r o l system o u t p u t given by equations ( 1 2 ) t o ( 1 4 ) .
|
||
The r o t o r f o r c e s and moments are f u n c t i o n s of t h e r o t o r t i p - s p e e d r a t i o and induced i n f l o w r a t i o , as d i s c u s s e d i n r e f e r e n c e s 2 , 4 , 6 , and 7. The t i p speed r a t i o JJ i s given by
|
||
|
||
J J = - uW
|
||
RR
|
||
where fi i s t h e r o t o r a n g u l a r v e l o c i t y , The i n f l o w r a t i o
|
||
the implicit equation
|
||
|
||
is calculated by
|
||
|
||
where t h e induced inflow r a t i o V i s determined from t h e d i f f e r e n t i a l equation
|
||
|
||
This method o f computing t h e inflow r a t i o
|
||
|
||
assumes t h a t t h e i n f l o w i s con-
|
||
|
||
s t a n t a c r o s s t h e r o t o r d i s k . The t h r u s t c o e f f i c i e n t CT i s c a l c u l a t e d below,
|
||
|
||
and a v a l u e of t h e t i m e c o n s t a n t T A o f approximately 0.1 sec i s chosen t o approximate t h e t i m e l a g associated with change i n rotor inflow. This tech-
|
||
|
||
nique of using a first-order d i f f e r e n t i a l equation t o calculate the induced
|
||
|
||
velocity ratio V i s superior t o algebraic calculation, because algebraic
|
||
|
||
methods were found t o be numerically u n s t a b l e i n d i g i t a l s i m u l a t i o n s ,
|
||
|
||
20
|
||
|
||
The r o t o r t h r u s t T and coning angle a. are c a l c u l a t e d t o t h e t h i r d power of t h e tip-speed r a t i o a c c o r d i n g t o t h e f o l l o w i n g r e l a t i o n s taken from r e f e r e n c e 4, where h i g h e r o r d e r terms have been n e g l e c t e d :
|
||
|
||
where 80 i s t h e e f f e c t i v e blade p i t c h angle a t t h e blade root and 81 i s t h e t w i s t of t h e blade. Then
|
||
|
||
and
|
||
|
||
The t e r m i n e q u a t i o n ( 2 2 ) i n r e f e r e n c e 4 i n v o l v i n g t h e b l a d e m a s s moment cont r i b u t e s less t h a n 0.5O, i s e s s e n t i a l l y c o n s t a n t , and is n e g l e c t e d here.
|
||
The f u s e l a g e a n g u l a r v e l o c i t y expressed i n c o n t r o l axes i s r e q u i r e d i n t h e c a l c u l a t i o n of c e r t a i n r o t o r f o r c e s and moments. T h i s q u a n t i t y i s o b t a i n e d by rotating the fuselage angular velocity expressed i n s h a f t axes through the
|
||
r o t o x o r i e n t a t i o n a n g l e 6, n e g l e c t i n g t h e small c y c l i c p i t c h a n g l e s AIC
|
||
and BIC. (See f i g . 3 ( c ) f o r c l a r i f i c a t i o n . )
|
||
|
||
1 pw = ps COS B + qs s i n B
|
||
qw -- -ps s i n B + q, COS 6
|
||
|
||
(30)
|
||
|
||
rw = rs
|
||
|
||
where
|
||
|
||
21
|
||
|
||
The f l a p p i n g a n g l e s al and bl are c a l c u l a t e d r e l a t i v e t o c o n t r o l axes by u s i n g t h e f o l l o w i n g formulas d e r i v e d f r o m r e f e r e n c e s 3 , 6, and 8 and unpublished data obtained from Sikorsky Aircraft Division of United Technologies Corporation:
|
||
|
||
al =
|
||
|
||
1
|
||
|
||
1 -- P2
|
||
|
||
2BZ
|
||
|
||
and
|
||
|
||
i
|
||
|
||
(32)
|
||
|
||
For a r o t o r b l a d e w i t h l i n e a r t w i s t and c o n s t a n t chord i t can be shown t h a t
|
||
replacing eo, t h e blade p i t c h a t the r o o t (appearing i n t h e r e f e r e n c e s ) , with
|
||
|
||
the p i t c h a t three-fourths radius, and dropping 8 1 w i l l have a negli-
|
||
|
||
g i b l e e f f e c t on t h e o v e r a l l s o l u t i o n , An e x p r e s s i o n f o r
|
||
|
||
i s given as
|
||
|
||
The downwind h o r i z o n t a l component o f t h e r o t o r force i n c o n t r o l axes i s expressed as
|
||
|
||
H = Ta'
|
||
|
||
(34)
|
||
|
||
where t h e small angle a ' i s a function of t h e u s e f u l and induced r o t o r dragl i f t power and inflow; however, it behaves s i m i l a r l y t o t h e l o n g i t u d i n a l f l a p p i n g a n g l e al. An e x p r e s s i o n f o r a' which i n c l u d e s t h e i n f l u e n c e due t o body rate, as d i s c u s s e d i n r e f e r e n c e 8 and i n unpublished Sikorsky A i r c r a f t data, is as follows:
|
||
|
||
aI =
|
||
|
||
1
|
||
|
||
1 - - L12
|
||
|
||
2BZ
|
||
|
||
(35)
|
||
|
||
The e x p r e s s i o n f o r t h e r o t o r torque which accounts f o r b o t h a c c e l e r a t i o n and d e c e l e r a t i o n t o r q u e s i s d e r i v e d from e q u a t i o n s (9) and (11) of r e f e r e n c e 4 and unpublished d a t a o b t a i n e d from S i k o r s k y A i r c r a f t . The t o r q u e c o e f f i c i e n t
|
||
may be e x p r e s s e d as a polynomial i n 1-1 times t h e major v a r i a b l e s a s
|
||
|
||
22
|
||
|
||
- - - - - cQ 0
|
||
|
||
=
|
||
|
||
(0.00io9
|
||
|
||
0.0036A 0 . 0 0 2 7 e . ~ ~ 1 . 1 0 ~ ~0 . 5 4 5 ~+ ~0 .~1 2 2 02. ~ ~ )
|
||
|
||
- - - - + (o.ooio9 0 . 0 0 2 7 e . ~ ~ 3 ~ 3 ~ 6.235~e.,, - - - 0 . 1 3 3 x e ~ ~3~+V( - 0 . 9 7 6 ~ ~ 6 . 3 8 ~ 5~.26e~:75)p4
|
||
|
||
(36)
|
||
|
||
Thus ,
|
||
|
||
The t o r q u e a c t i n g on t h e main r o t o r Q,
|
||
|
||
i s c a l c u l a t e d by using main-rotor
|
||
|
||
parameters i n e q u a t i o n s (36) and ( 3 7 ) . The r e a c t i o n t o r q u e on t h e f u s e l a g e ,
|
||
|
||
which i s a f u n c t i o n o f Q,, i s c a l c u l a t e d i n t h e engine dynamics and governor
|
||
|
||
model d i s c u s s e d i n t h e i s c a l c u l a t e d by using
|
||
|
||
next tail-
|
||
|
||
sect roto
|
||
|
||
io r
|
||
|
||
n. va
|
||
|
||
r
|
||
|
||
i
|
||
|
||
The t o ables
|
||
|
||
r i
|
||
|
||
que act n equat
|
||
|
||
i i
|
||
|
||
n o
|
||
|
||
g o ns
|
||
|
||
n th (36)
|
||
|
||
e ta and
|
||
|
||
i
|
||
|
||
l (
|
||
|
||
rot 37).
|
||
|
||
o
|
||
|
||
r I
|
||
|
||
t%1 st
|
||
|
||
assumed that t h e t a i l - r o t o r r e a c t i o n t o r q u e a c t s on the f u s e l a g e d i r e c t l y and
|
||
|
||
i s equal t o Qat.
|
||
|
||
The r o t o r s i d e f o r c e J i n c o n t r o l axes i s c a l c u l a t e d from t h e f o l l o w i n g
|
||
|
||
e x p r e s s i o n d e r i v e d from e q u a t i o n ( 3 ) i n r e f e r e n c e 3, assuming t h a t terms
|
||
|
||
el i n v o l v i n g p i t c h and r o l l r a t e may be n e g l e c t e d and t h a t t h e b l a d e p i t c h 8,
|
||
|
||
can be r e p l a c e d by 0.75 and t e r m s i n v o l v i n g
|
||
|
||
dropped:
|
||
|
||
CY
|
||
|
||
- - blX -23 a01.1x + 1 alblp a0a 1p2 + -61 aOal
|
||
|
||
- (i - 1 pao - bl
|
||
|
||
-12
|
||
|
||
2 bl)e.74
|
||
|
||
from which
|
||
|
||
The r o t o r f o r c e s i n c o n t r o l axes are r e s o l v e d i n t o s h a f t a x e s by assuming t h a t t h e components of t h r u s t a l o n g t h e xs- and ys-axes ( f i g . 3 (b) 1 are T B ~ ~ and TAiC, r e s p e c t i v e l y , and t h a t t h e components of drag H and s i d e f o r c e J
|
||
along t h e zs-axis are n e g l i g i b l e compared with t h e t h r u s t , so t h a t
|
||
|
||
' 1 - x = -H cos P J s i n P + mIC r,s
|
||
|
||
YT I S = -H s i n + J cos + T A ; ~
|
||
|
||
(40)
|
||
|
||
23
|
||
|
||
These f o r c e s are expressed i n h e l i c o p t e r body axes by using t h e transformation
|
||
|
||
The hub moments due t o f l a p p i n g h i n g e o f f s e t s are given i n s h a f t a x e s by t h e following approximate expressions derived f r o m reference 3, where higher order t e r m s have been neglected:
|
||
|
||
1 2Lhub,s = ebn V1s
|
||
|
||
(42)
|
||
|
||
where t h e c y c l i c f l a p p i n g a n g l e s r e l a t i v e t o s h a f t axes are given by
|
||
|
||
- a1s = al cos f3 + bl s i n f3 BIC
|
||
|
||
and
|
||
|
||
(43)
|
||
|
||
9 - bls = bl cos f3 al s i n f3 + AIC
|
||
|
||
The t o r q u e a b o u t t h e r o t o r s h a f t i s g i v e n by
|
||
|
||
Nhub,s = Qs
|
||
|
||
(44)
|
||
|
||
For t h e main r o t o r , Qs i s e q u a l t o Qeng, t h e engine t o r q u e computed i n t h e
|
||
|
||
s e c t i o n "Engine Dynamics and Governor Model." For t h e t a i l r o t o r , Qs i s
|
||
|
||
equal to t r a n s form
|
||
|
||
aQtBi otn
|
||
|
||
These hub moments a r e e x p r e s s e d i n h e l i c o p t e r body a x e s by t h e
|
||
|
||
24
|
||
|
||
The t o t a l moments a c t i n g on the f u s e l a g e due t o t h e main r o t o r and t a i l r o t o r are c a l c u l a t e d by using t h e rotor forces given by equation (41) and hub moments given by e q u a t i o n (45) as
|
||
|
||
The mathematical model developed h e r e assumes no 6,, h i n g e s on the main
|
||
|
||
r o t o r , t h a t is, blade-coning and lead-lag motion does n o t a f f e c t blade pitch.
|
||
|
||
I t i s assumed, however, t h a t t h e t a i l r o t o r h a s l a r g e values o f 63t; f o r example, i f 63t = 4501 t h e n lo o f i n c r e a s e d coning reduces t h e b l a d e p i t c h by
|
||
|
||
lo and conversely. T h i s e f f e c t i s modeled as f o l l o w s : t h e t a i l - r o t o r coning
|
||
|
||
angl tive
|
||
|
||
e t
|
||
|
||
a
|
||
|
||
ai lo-tr
|
||
|
||
o
|
||
|
||
is tor
|
||
|
||
c
|
||
|
||
a c
|
||
|
||
lc ol
|
||
|
||
ul le
|
||
|
||
a c
|
||
|
||
t t
|
||
|
||
ed us ive p
|
||
|
||
ing e itch
|
||
|
||
quat
|
||
Bot.
|
||
|
||
i
|
||
|
||
o
|
||
|
||
n (29) w The new
|
||
|
||
ith va
|
||
|
||
l
|
||
|
||
the c ue of
|
||
|
||
u
|
||
|
||
rren
|
||
Bot
|
||
|
||
t
|
||
|
||
value o f effeci s determined by
|
||
|
||
solving the first-order differential equation
|
||
|
||
eo, where
|
||
|
||
i s t h e c o l l e c t i v e p i t c h v a l u e commanded by t h e p i l o t ' s p e d a l s and
|
||
|
||
t h e automatic c o n t r o l system. The t i m e c o n s t a n t T63t i s t a k e n as s m a l l as
|
||
|
||
p o s s i b l e while maintaining a good margin of numerical s t a b i l i t y , A value
|
||
|
||
between 0.05 and 0.2 second i s t y p i c a l . This method i s s u p e r i o r t o a p u r e l y
|
||
|
||
eo, a l g e b r a i c c a l c u l a t i o n of
|
||
|
||
i n t h a t t h e algebraic method w a s found t o be
|
||
|
||
numerically unstable i n d i g i t a l simulations.
|
||
|
||
Engine Dynamics and Governor Model
|
||
The engine dynamics and governor model w a s adapted from one used by Boeing V e r t o l Company i n a s i m u l a t i o n o f a h e a v y - l i f t h e l i c o p t e r . This model i n c l u d e s the e f f e c t s o f a g a s g e n e r a t o r , a power t u r b i n e , r o t o r i n e r t i a , and s h a f t comp l i a n c e . The f o l l o w i n g d i f f e r e n t i a l e q u a t i o n s d e f i n e t h i s model:
|
||
k - - = [Qeng Qam + Kdgov(Qpt 'mj] k m r
|
||
|
||
25
|
||
|
||
The i n p u t variables t o t h e s e d i f f e r e n t i a l e q u a t i o n s are Ro, t h e r e f e r e n c e r o t o r
|
||
|
||
speed, and Qam, t h e aerodynamic t o r q u e a c t i n g on t h e main r o t o r , g i v e n by equa-
|
||
|
||
4 . t i o n ( 3 7 ) w i t h t h e a p p r o p r i a t e parameters f o r t h e main rotor. The o u t p u t s are
|
||
|
||
the and
|
||
|
||
rotor speed
|
||
|
||
and the
|
||
|
||
the gas-generator torque
|
||
|
||
engine Q
|
||
|
||
torque Qen are interna?
|
||
|
||
The power-turbine speed v a r i a b l e s . The c o n s t a n t
|
||
|
||
%R P t
|
||
|
||
r e p r e s e n t s t h e s h a f t compliancegenThe c o n s t a n t Kdgov i s needed f o r computa-
|
||
|
||
g?z t i o n a l s t a b i l i t y . The c o n s t a n t s K
|
||
|
||
and G
|
||
|
||
are the power-turbine and
|
||
|
||
gas sta tio
|
||
|
||
-g nt n
|
||
|
||
e . t
|
||
|
||
nerator speed governor g a i n sg',d: The aerodynamic t o r q u e Q,
|
||
o a l l o w the governor t o hold re
|
||
|
||
a p p eTaernsgi asonably
|
||
|
||
n c
|
||
|
||
the gas-gen
|
||
|
||
the onst
|
||
|
||
a
|
||
|
||
nQtgreon
|
||
|
||
t
|
||
|
||
d or
|
||
|
||
i
|
||
|
||
erator t i m e conf f e r e n t i a l equaspeed under wide
|
||
|
||
l
|
||
|
||
y
|
||
|
||
varying aerodynamic torques.
|
||
|
||
Fuse1age Aerodynamics
|
||
The h e l i c o p t e r f u s e l a g e f o r c e and moment data are assumed t o be g i v e n i n equation and table form i n wind-tunnel axes i n t e r m s of local angle o f a t t a c k , l o c a l angle of incidence a t t h e t a i l , angle of s i d e s l i p , body angular rates, and dynamic pressure.
|
||
The free-stream angle o f a t t a c k i s g i v e n by
|
||
|
||
- af = tan-' Was,h Uas,h
|
||
|
||
(-Tr
|
||
|
||
=< af
|
||
|
||
<
|
||
= Tr)
|
||
|
||
(49)
|
||
|
||
where t h e v e l o c i t y components are c a l c u l a t e d by u s i n g e q u a t i o n s ( 2 0 ) . The free-stream dynamic pressure i s given by
|
||
|
||
- -1 2
|
||
qh - pvas,h
|
||
|
||
(50)
|
||
|
||
where
|
||
|
||
'as, h = \I.:s,h -t- Vas,h + w a2 s , h
|
||
|
||
The e f f e c t o f t h e main-rotor downwash on t h e l o c a l a n g l e of a t t a c k i s accounted f o r by i n t r o d u c i n g a r o t o r downwash f a c t o r o b t a i n e d from unpublished Sikorsky A i r c r a f t data as
|
||
|
||
where hm and pm are t h e main-rotor inflow and t i p - s p e e d r a t i o s , respect i v e l y , and Cm i s t h e main-rotor t h r u s t c o e f f i c i e n t . The local a n g l e o f a t t a c k f o r t h e f u s e l a g e i s given by
|
||
26
|
||
|
||
ClfR - af
|
||
|
||
- emrekf
|
||
|
||
(-7r =< a f R=< T r )
|
||
|
||
and t h e l o c a l incidence a t t h e t a i l i s given by
|
||
|
||
(53)
|
||
|
||
where ekt and e are empirical c o n s t a n t s which have been determined b y Sikorsky A i r c r a f t $,om wind-tunnel and f l i g h t - t e s t correlation. The c o n s t a n t i t 0 i s t h e f i x e d incidence of the h o r i z o n t a l - t a i l surface.
|
||
The f u s e l a g e s i d e s l i p a n g l e i s g i v e n by
|
||
|
||
Bf = s i n-1 Vas,h
|
||
'as,h
|
||
|
||
(55)
|
||
|
||
and t h e wind-tunnel yaw a n g l e i s g i v e n by
|
||
|
||
+w=t 'Bf
|
||
Since wind-tunnel d a t a g e n e r a l l y do n o t cover the f u l l ranges of angle of a t t a c k and s i d e s l i p , i t i s assumed t h a t f o r c e and moment c o e f f i c i e n t s remain c o n s t a n t beyond t h e limits of t h e s e angles. This assumption i s based on t h e f a c t t h a t g e n e r a l l y when t h e s e a n g l e s are l a r g e , t h e a i r s p e e d i s low, so t h a t t h e f u s e l a g e f o r c e s and moments are r e l a t i v e l y s m a l l .
|
||
The f o r c e s i n wind-tunnel s t a b i l i t y axes axe transformed i n t o body a x e s by the relation
|
||
|
||
The b a s i c f u s e l a g e aerodynamic moments are assumed t o be g i v e n i n body axes, and t h e t o t a l f u s e l a g e aerodynamic moments, i n c l u d i n g t h e e f f e c t s of the 6.9. being o f f s e t from t h e wind-tunnel mounting p o i n t as w e l l as damping due t o a n g u l a r v e l o c i t y and r o t o r downwash, are o b t a i n e d as follows:
|
||
27
|
||
|
||
- L f , h = %t 'f,hYwt,h 'f,hzwt,h +
|
||
|
||
-
|
||
|
||
M f , h = %t + 'f,hzwt,h
|
||
|
||
'f,hxwt,h
|
||
|
||
+- Ld,h
|
||
|
||
Md,h KfeTm
|
||
|
||
+
|
||
|
||
+
|
||
|
||
- N f , h = N w t + 'f,hxwt,h
|
||
|
||
'f,hYwt,h + Nd,h
|
||
|
||
The l a s t tern i n t h e Mf,h e q u a t i o n r e p r e s e n t s the s t a t i c moment due t o mainr o t o r downwash a t t h e h o r i z o n t a l t a i l . The terms Ld,h, Ma,@, and Nd,h account f o r the aerodynamic moments due t o body a n g u l a r v e l o c i t i e s and are d i s cussed s u b s e q u e n t l y i n " A p p l i c a t i o n t o U,S. Army CH-54 H e l i c o p t e r and Cargo Container. I'
|
||
|
||
E x t e r n a l - Load Aerodynamics
|
||
The aerodynamic f o r c e s and moments a c t i n g on t h e e x t e r n a l l o a d are calcul a t e d i n e s s e n t i a l l y t h e s a m e way as t h e f u s e l a g e aerodynamics: i n t e r m s of dynamic p r e s s u r e , a n g l e s of a t t a c k and s i d e s l i p , and body a n g u l a r rates. The r o t o r downwash e f f e c t s are n o t considered i m p o r t a n t f o r l o n g c a b l e s as f a r as pendulum and r o c k i n g motions are concerned, b u t e x p e r i e n c e h a s shown t h a t some s i m u l a t e d downwash i s n e c e s s a r y t o provide aerodynamic damping of v e r t i c a l bounce-type o s c i l l a t i o n s near hover due t o cable e l a s t i c i t y . Generally force and moment d a t a are missing a t l a r g e a n g l e s o f a t t a c k , s o t h a t some t y p e of t r i g o n o m e t r i c f o r m u l a t i o n ' f o r forces and moments i s r e q u i r e d . Specific d e t a i l s of the aerodynamic c h a r a c t e r i s t i c s f o r a p a r t i c u l a r e x t e r n a l load are discussed subsequently i n the application section.
|
||
|
||
Load-Ground Contact Model
|
||
Since t h e pickup and release of s l i n g l o a d s are t o be s t u d i e d , a mathematical model of t h e load-ground c o n t a c t f o r c e s i s r e q u i r e d , This model i s d e r i v e d on t h e assumptions t h a t (1) t h e ground can be r e p r e s e n t e d by s p r i n g s and d a s h p o t s , so t h a t v e r t i c a l f o r c e s a c t on each c o r n e r of t h e base of t h e l o a d i n p r o p o r t i o n t o t h e d i s t a n c e t h a t t h e c o r n e r is below ground l e v e l , and (2) viscous s l i d i n g f r i c t i o n r e t a r d s t r a n s l a t i o n a l motion.
|
||
The i n e r t i a l p o s i t i o n of the i t h c o n t a c t p o i n t i s determined from t h e relations
|
||
|
||
28
|
||
|
||
where t h e f i r s t term on t h e right-hand s i d e d e f i n e s t h e i n e r t i a l p o s i t i o n of t h e l o a d c.g.; t h e second t e r m , t h e c o n t a c t p o i n t with r e s p e c t t o t h e c.g. The i n e r t i a l v e l o c i t i e s of t h i s load c o n t a c t p o i n t a r e given by
|
||
|
||
The v e r t i c a l ground c o n t a c t f o r c e s a r e computed f o r each c o r n e r o f t h e load by the equation
|
||
|
||
'ci e = -K p c i , e - K v w c i , e
|
||
|
||
(i = 1, 2 , 3, 4)
|
||
|
||
(61)
|
||
|
||
If Zcice > 0, then t h e load i s being pulled toward the Earth; therefore,
|
||
'ci ,e is set t o zero. The v i s c o u s s l i d i n g f o r c e s a r e then determined i n
|
||
terms of t h e v e r t i c a l force and t h e h o r i z o n t a l component of v e l o c i t y as
|
||
|
||
and
|
||
|
||
f o r i = I, 2 , 3, 4. This model assumes t h a t t h e s l i d i n g f o r c e i s propor-
|
||
|
||
tional to
|
||
vo = 0.31
|
||
|
||
the v e r t i c a l force Zci,e m/sec and p r o p o r t i o n a l
|
||
|
||
to
|
||
|
||
for the
|
||
|
||
sliding product
|
||
|
||
velocities greater than of v e r t i c a l f o r c e and
|
||
|
||
s l i d i n g v e l o c i t y f o r v e l o c i t i e s l e s s than t h i s value. The l o a d c o n t a c t
|
||
|
||
f o r c e s a t t h e i t h c o n t a c t p o i n t are transformed i n t o load body axes by t h e
|
||
|
||
transformation
|
||
|
||
29
|
||
|
||
'ci ,e 'ci,e .%ie,
|
||
|
||
(i = 1, 2, 3 , 4)
|
||
|
||
(64)
|
||
|
||
and t h e moments a c t i n g on t h e l o a d due t o ground c o n t a c t forces a t t h e i t h contact point are
|
||
|
||
The t o t a l f o r c e s and moments a c t i n g on t h e load a r e t h u s given by
|
||
|
||
and
|
||
|
||
( i = 1, 2 , 3, 4)
|
||
|
||
(66)
|
||
|
||
Load Suspension System
|
||
The mathematical model f o r t h e e x t e r n a l - l o a d suspension s y s t e m i s based on t h e assumption t h a t t h e cable(s) may be r e p r e s e n t e d by s p r i n g ( s 1 without damping. This assumption allows the cable tension t o be c a l c u l a t e d e a s i l y i n t e r m s of the cable spring constant and the vector d i s t a n c e between t h e cable attachment p o i n t s . With a d i g i t a l simulation t h e i n e r t i a l p o s i t i o n s of t h e cable attachment points are readily calculated, thus simplifying t h e calculat i o n o f the d i s t a n c e between t h e p o i n t s , I t w a s found by t r i a l and e r r o r t h a t
|
||
30
|
||
|
||
t h e simulated cable s p r i n g c o n s t a n t should be s e l e c t e d such that the cable v e r t i c a l bounce frequency i s n o t h i g h e r t h a n approximately 2 Hz, i n o r d e r t o maintain numerical s t a b i l i t y w i t h an i n t e g r a t i o n step s i z e of 1/32 second i n digital simulations.
|
||
The i n e r t i a l p o s i t i o n of the cable attachment p o i n t on t h e h e l i c o p t e r shown i n f i g u r e 4 i s c a l c u l a t e d i n terms of the i n e r t i a l p o s i t i o n of t h e h e l i copter 6.9. and t h e d i s t a n c e between t h i s p o s i t i o n and t h e attachment p o i n t as
|
||
|
||
The i n e r t i a l p o s i t i o n of t h e cable attachment p o i n t on t h e l o a d shown i n f i g u r e 4 i s c a l c u l a t e d s i m i l a r l y as
|
||
|
||
The c a b l e l e n g t h i s determined f r o m t h e s q u a r e r o o t of t h e sum o f the s q u a r e s of d i f f e r e n c e s i n i n e r t i a l coordinates of cable attachment p o i n t s as
|
||
|
||
J - - ' - RC = ( xha,e xRa,e)2 + (Yha,e y!La,e>2 ('ha,e
|
||
|
||
'Ra,e) 2
|
||
|
||
If t h e unstretched cable length i s Rco, then t h e cable tension is simply
|
||
|
||
where Ksc i s t h e cable s p r i n g c o n s t a n t . A t e s t on t h e sign o f Tc i s cont i n u o u s l y made t o i n s u r e t h a t t h e cable does n o t e x e r t a compression f o r c e .
|
||
- I f (Rc RcO) becomes n e g a t i v e , t h e n Tc i s set t o zero.
|
||
The cable t e n s i o n f o r c e must be e x p r e s s e d i n h e l i c o p t e r and l o a d body axes so t h a t i t s e f f e c t can be included i n t h e equations o f motion. Before t h e
|
||
31
|
||
|
||
- - t e n s i o n f o r c e can be expressed i n body axes, t h e i n e r t i a l o r i e n t a t i o n of t h e
|
||
cable assumed s t r a i g h t must be determined.
|
||
The a n g l e t h a t t h e cable makes w i t h t h e v e r t i c a l i n t h e n o r t h - v e r t i c a l p l a n e i s d e f i n e d i n f i g u r e 4 and i s given by
|
||
|
||
- = tm-1 XRa,e xha,e
|
||
|
||
Bc,e
|
||
|
||
'Ra,e - 2h a , e
|
||
|
||
The i n e r t i a l c a b l e angle i n t h e east-west d i r e c t i o n i s a l s o d e f i n e d i n f i g u r e 4 and i s given by
|
||
|
||
Three cable d i r e c t i o n cosines a r e defined with respect t o Earth axes by
|
||
|
||
- d l c , e
|
||
|
||
= sin
|
||
|
||
Bc , e
|
||
|
||
cos
|
||
|
||
ac , e
|
||
|
||
-
|
||
-
|
||
|
||
(XRa,e
|
||
|
||
Xha,e)/Rc
|
||
|
||
- -
|
||
d2c,e = -sin ac,e - (YRa,e Yha,e)/Rc
|
||
|
||
- d3c,e = cos 6C r e cos ac , e -- ('Ra,e
|
||
|
||
'ha,e)/'c
|
||
|
||
(73)
|
||
|
||
The t e n s i o n f o r c e i s r e s o l v e d i n t o h e l i c o p t e r body a x e s by t h e e x p r e s s i o n
|
||
|
||
The moments a c t i n g on t h e h e l i c o p t e r due t o t h e c a b l e t e n s i o n are computed according to
|
||
|
||
1- -
|
||
Lt , h - 't,hYaIh 't,hza,h
|
||
|
||
Mt,h = 't,hza,h Nt , h = 't,hxa,h
|
||
|
||
- 't,hxa,h - 't ,hya, h
|
||
|
||
32
|
||
|
||
The t e n s i o n f o r c e i s r e s o l v e d i n t o l o a d body a x e s by t h e expression and t h e moments a c t i n g on t h e l o a d due t o t h e cable t e n s i o n are given by
|
||
|
||
Equations of Motion
|
||
The e q u a t i o n s of motion f o r b o t h t h e h e l i c o p t e r and t h e e x t e r n a l s l i n g l o a d are developed i n body axes w i t h r e s p e c t t o a f l a t , n o n r o t a t i n g E a r t h . It i s assumed f o r convenience t h a t each body is r i g i d and t h a t t h e Xh'Zh plane and t h e XR-ZR p l a n e are planes of m a s s symmetry and t h a t gyroscopic e f f e c t s o f e n g i n e s a r e n e g l i g i b l e . The e q u a t i o n s o f motion f o r t h e h e l i c o p t e r are developed f i r s t .
|
||
The t r a n s l a t i o n a l motion e q u a t i o n s f o r t h e h e l i c o p t e r are g i v e n i n terms of body-axes components of angular v e l o c i t y , t r a n s l a t i o n a l v e l o c i t y , accelerat i o n s , and components of g r a v i t y as
|
||
|
||
where
|
||
|
||
ax,h -- CFx,h/mh
|
||
aYth = cFy,h/mh
|
||
az ,h - CFz,h/%
|
||
|
||
(79) 33
|
||
|
||
The summations i n c l u d e a l l e x t e r n a l f o r c e s : main- and t a i l - r o t o r f o r c e s , fusel a g e aerodynamic f o r c e s , and cable suspension f o r c e s . The l a s t terms on t h e right-hand s i d e of equations (78) give t h e a c c e l e r a t i o n components due t o g r a v i t y . The i n e r t i a l v e l o c i t y o f t h e h e l i c o p t e r i s g i v e n i n body a x e s by i n t e g r a t i n g e q u a t i o n s (78) as
|
||
|
||
=
|
||
Uc9,h
|
||
|
||
;cg,h
|
||
|
||
1 Vcg,h =
|
||
|
||
'cg,h
|
||
|
||
d t + ucg,h(')
|
||
} d t + vc9,h (0)
|
||
|
||
(80)
|
||
|
||
The e q u a t i o n s of r o t a t i o n a l motion a r e used i n t h e f o l l o w i n g form:
|
||
|
||
ph = k L h - ('zz,h - lyy,h)qhrh + 'xz,hphqh
|
||
|
||
7
|
||
|
||
+ h.'[
|
||
|
||
- ('yylh - 'xx,h)Phqh - ' x z l h ~ h r h'x]z~ )h/ ( ' x x l h - 'x2z,h/'zz,h)
|
||
zz,h
|
||
|
||
The body-axes components o f a n g u l a r v e l o c i t y a r e determined by i n t e g r a t i n g equations (81) as
|
||
sph = ph d t + Ph(O) sqh = Gh d t + qh ('1
|
||
1. r h = rh d t + r h (0)
|
||
The h e l i c o p t e r E u l e r a n g l e s shown i n f i g u r e 3 ( a ) are determined by integrating the following differential equations :
|
||
34
|
||
|
||
The i n e r t i a l v e l o c i t y of t h e h e l i c o p t e r c.g. expressed i n body axes i s given i n Earth coordinates by t h e transformation
|
||
The Earth-axes c o o r d i n a t e s of t h e h e l i c o p t e r c - g . are determined by i n t e g r a t i n g equation (84) to obtain
|
||
The e q u a t i o n s of motion f o r t h e e x t e r n a l l o a d may be o b t a i n e d by changing
|
||
a l l t h e s u b s c r i p t s h t o k i n e q u a t i o n s (78) t o ( 8 5 ) . The e x t e r n a l - l o a d
|
||
e q u a t i o n s of motion t h u s o b t a i n e d may then be s o l v e d t o g e t h e r w i t h t h e equations of motion f o r t h e helicopter to obtain load motions.
|
||
APPLICATION TO U.S. ARMY CH-54 HELICOPTER AND CARGO CONTAINER Rotor and f u s e l a g e d a t a f o r t h e U.S. Army CH-54 h e l i c o p t e r were o b t a i n e d from unpublished Sikorsky A i r c r a f t d a t a , f l i g h t tests a t Langley Research Center, and r e f e r e n c e 9. The f u s e l a g e and main- and t a i l - r o t o r d a t a used i n t h e s i m u l a t i o n are l i s t e d i n t a b l e I. The f u s e l a g e wind-tunnel d a t a are g i v e n i n f i g u r e s 5 t o 11. These c u r v e s are e n t e r e d w i t h l o c a l f u s e l a g e a n g l e o f
|
||
a t t a c k a f g l wind-tunnel yaw ( s i d e s l i p ) a n g l e $wt, l o c a l i n c i d e n c e a t t h e
|
||
t a i l it, and dynamic pressure Gh as determined from e q u a t i o n s (53) , (56) ,
|
||
(54), and ( 5 0 ) , r e s p e c t i v e l y . Values of ekt and ekf of 1.8 and 0 . 5 , respectively, w e r e used i n these equations t o determine fuselage l i f t , s i d e f o r c e , r o l l i n g moment, p i t c h i n g moment, and yawing moment.
|
||
35
|
||
|
||
The f u s e l a g e l i f t i s c a l c u l a t e d by u s i n g t h e d a t a from f i g u r e s 5 and 6 and the following equation :
|
||
|
||
The f u s e l a g e wind-tunnel p i t c h i n g moment i s c a l c u l a t e d by u s i n g t h e d a t a from f i g u r e s 9 and 10 and t h e following equation:
|
||
|
||
(87)
|
||
|
||
The f u s e l a g e d r a g i s c a l c u l a t e d a c c o r d i n g to t h e formula o b t a i n e d f r o m Sikorsky Aircraft
|
||
,.Dh = (7.25 -f- 2 . 4 a f R + 42.9af2R -f- 4 5 . 6 $21 ~ ~ ) : ~
|
||
|
||
where a f R and $wt are i n r a d i a n s .
|
||
The f u s e l a g e moments due t o body a n g u l a r rates a r e computed a c c o r d i n g t o t h e formulas obtained from unpublished Sikorsky A i r c r a f t d a t a a s
|
||
|
||
Ld,h = 95-6rhVas,h Md,h = -218qhvas,h Nd,h = -322rhVas,h
|
||
|
||
(89)
|
||
|
||
where Vas,h i s computed by u s i n g equation ( 5 1 ) , and rh and qh are i n
|
||
|
||
r a d i a n s p e r second. N o t e t h a t t h e r o l l i n g moment Ld,h i s a f u n c t i o n of rh
|
||
|
||
n o t ph. The f u s e l a g e aerodynamic f o r c e s and moments t h u s determined are used
|
||
|
||
i n equations (58). It is noted t h a t i n the transformation o f aerodynamic
|
||
|
||
f o r c e s from wind-tunnel t o body axes given by equation ( 5 7 ) , t h e s i d e s l i p
|
||
|
||
& a n g l e
|
||
|
||
w a s i n a d v e r t e n t l y set t o zero. The change i n h a n d l i n g q u a l i t i e s
|
||
|
||
caused by t h i s error i s considered t o be n e g l i g i b l e a t cruise c o n d i t i o n s and
|
||
|
||
nonexistent a t hover.
|
||
|
||
Mass d a t a , c a b l e attachment p o i n t c o o r d i n a t e s , ground c o n t a c t c o o r d i n a t e s and p a r a m e t e r s , and nominal c a b l e l e n g t h used f o r a 2.4-m by 2.4-m by 6.1-m c a r g o c o n t a i n e r are given i n t a b l e 11. Aerodynamic d a t a used f o r t h e c a r g o c o n t a i n e r are d e r i v e d below from d a t a given i n r e f e r e n c e s 10 and 11. Since l a r g e a n g l e s of s i d e s l i p and a n g l e s of a t t a c k w e r e expected during c r u i s e and
|
||
hover f l i g h t , t h e wind-tunnel d a t a - which ranged from -5O t o 45O i n p i t c h and
|
||
|
||
36
|
||
|
||
from Oo t o 95O i n yaw - had t o be modified t o a l l o w +_180° angle-of-attack v a r i a -
|
||
t i o n and +90° a n g l e - o f - s i d e s l i p v a r i a t i o n . This w a s accomplished by f i t t i n g t r i g o n o m e t r i c f u n c t i o n s t o t h e e x i s t i n g d a t a , as shown i n e q u a t i o n s (92) and (94).
|
||
|
||
The l o a d components of f r e e - s t r e a m v e l o c i t y uas,R' Vas,Rl and
|
||
|
||
are
|
||
|
||
obtained by adding steady-wind, g u s t , and i n e r t i a l components c a l c u l a t e d by
|
||
|
||
using the load version of equations (4), ( l o ) , and (80) as follows:
|
||
|
||
Uas,R = ucg,R + Ugust,R + Uwind,R
|
||
Vas,R = vc g , ~ V g u s t,R + Vwind,R +
|
||
|
||
Wa s , R =
|
||
|
||
W
|
||
|
||
c
|
||
|
||
g
|
||
|
||
r ~ Wg u s t , % +
|
||
|
||
-I-Wwind,R
|
||
|
||
Then t h e l o a d a n g l e s o f a t t a c k and s i d e s l i p and t h e dynamic p r e s s u r e a r e c a l c u l a t e d from t h e following expressions:
|
||
|
||
- CXR = tan- 1 Uas,R
|
||
|
||
62
|
||
|
||
=
|
||
|
||
s
|
||
|
||
i
|
||
|
||
-1 n
|
||
|
||
- V as,R
|
||
|
||
'as ,R
|
||
|
||
-
|
||
'as,&
|
||
|
||
2
|
||
|
||
2
|
||
|
||
A2
|
||
|
||
U as,R + Vas,R +
|
||
|
||
I
|
||
|
||
It w a s found i n s i m u l a t i o n t h a t d u r i n g hover w i t h no winds, d i v e r g e n t o s c i l l a t i o n s of load angular motions would occur. This w a s due t o t h e f a c t t h a t i n t h e zero-airspeed condition, load o s c i l l a t i o n s due to cable s t r e t c h w e r e essent i a l l y undamped and t h e s l i g h t phase s h i f t due t o t h e numerical i n t e g r a t i o n o f the equations of motion caused a numerical i n s t a b i l i t y . This i n s t a b i l i t y w a s e l i m i n a t e d by adding a c o n s t a n t " r o t o r downwash" v a l u e t o t h e 2%-component o f velocity as follows:
|
||
|
||
- A
|
||
Was,G = was,R
|
||
|
||
9.14
|
||
|
||
The c a r g o c o n t a i n e r l i f t , d r a g , and s i d e f o r c e s i n wind a x e s a t t h e l o a d geom e t r i c c e n t e r are c a l c u l a t e d from expressions derived from t h e d a t a i n r e f e r ence 10 as
|
||
37
|
||
|
||
..,
|
||
L~
|
||
|
||
=
|
||
|
||
(6.5
|
||
|
||
sin
|
||
|
||
2al
|
||
|
||
cos
|
||
|
||
$,)GR
|
||
|
||
- - = c20.9 7 . 6 6 ( 1 + cos 2 a ~cos BR)IGg
|
||
|
||
..,
|
||
yR = (-7.9 s i n 28, c o s 2aR);iR
|
||
|
||
(92)
|
||
|
||
These f o r c e s are expressed i n l o a d body axes by using t h e transformation
|
||
|
||
-cos aR c o s PR- -cos all s i n PR
|
||
|
||
-
|
||
s i n a1
|
||
|
||
- s i n a , cos BR - s i n a , s i n BR -cos a1
|
||
The cargo c o n t a i n e r aerodynamic moments are g i v e n below and are ased on t h e assumption t h a t t h e s t a t i c p i t c h i n g and r o l l i n g moments a r e n e g l i g i b l e i n comp a r i s o n w i t h t h e p i t c h i n g and r o l l i n g moments caused by t h e suspension system. The s t a t i c yawing moment was d e r i v e d from t h e d a t a i n r e f e r e n c e 10 a s
|
||
|
||
v e l o c i t i e s are assumed t o be p r o p o r t i o n a l t o t h e product o f a i r s p e e d and angul a r v e l o c i t y , as i n t h e c a s e of t h e f u s e l a g e moments given by e q u a t i o n s (891, and are given by
|
||
|
||
where pR, qRl and r, are i n r a d i a n s p e r second. The t o t a l aerodynamic moments a c t i n g on t h e l o a d are t h u s given by
|
||
38
|
||
|
||
SIMULATION DESCRIPTION
|
||
Computer Hardware
|
||
The mathematical model h a s been programed i n FORTRAN I V f o r o p e r a t i o n on t h e Langley real-time s i m u l a t i o n system u s i n g t h e Control D a t a CYBER 175 d i g i t a l computer system. The program a c c e p t s i n p u t s from t h e s i m u l a t i o n cockp i t through A D C ' s , and o u t p u t s v o l t a g e s t o t h e s i m u l a t o r through DAG'S. The program flow i s c o n t r o l l e d by a n o p e r a t o r through use of a s i m u l a t i o n c o n t r o l console (fig. 12).
|
||
The s i m u l a t i o n c o n t r o l c o n s o l e c o n s i s t s o f w h i t e i n d i c a t o r l i g h t s , r e d i n d i c a t o r l i g h t s , f u n c t i o n s e n s e s w i t c h e s , mode c o n t r o l s w i t c h e s , a d a t a e n t r y keyboard, d i g i t a l decimal d i s p l a y u n i t , and p o t e n t i o m e t e r s . The w h i t e i n d i c a t o r l i g h t s are used t o i n d i c a t e program s t a t u s o r d i a g n o s t i c s . The r e d i n d i c a t o r l i g h t s are used t o i n d i c a t e program d i a g n o s t i c s . The f u n c t i o n sense s w i t c h e s are used t o s e l e c t program o p t i o n s . The mode control s w i t c h e s shown i n f i g u r e s 13 and 14(a) are used t o c o n t r o l t h e running of t h e RTS computer program. Each s w i t c h (mode) i s b r i e f l y d e s c r i b e d as t o i t s use (mode nominally a c t i v e when s w i t c h d e p r e s s e d ) :
|
||
- OPER (OPERATE) begins u p d a t i n g time and i n t e g r a t i n g t h e d i f f e r e n t i a l
|
||
equations
|
||
HOLD - h o l d s i n t e g r a t e d v a r i a b l e s a t p r e v i o u s value
|
||
RESET - i n i t i a l i z e s program a t Time = 0
|
||
IDLE - i d l e s t h e computer (no computations)
|
||
CHANGE - changes program v a r i a b l e t o t h e new v a l u e e n t e r e d on t h e d a t a
|
||
entry keyboard
|
||
- SCAN s c a n s through tables and d i s p l a y s v a l u e s on t h e d i g i t a l decimal
|
||
display unit
|
||
RELEASE - releases CHANGE and SCAN modes
|
||
- E R ~ S E erases r e a l - t i m e d i s k f i l e
|
||
TERM (TERMINATE) - terminates program a t s i m u l a t i o n c o n t r o l console and
|
||
transfers control to the Tektronix terminal
|
||
READ - l o a d s r e a d o v e r l a y
|
||
- PRINT l o a d s p r i n t o v e r l a y
|
||
RELEASE - releases ERASE, TERM, READ, and PRINT modes
|
||
The d a t a e n t r y keyboard shown i n f i g u r e s 1 3 and 1 4 ( b ) i s used t o i n p u t new v a l u e s f o r program v a r i a b l e s . The keyboard i s used i n c o n j u n c t i o n w i t h t h e
|
||
39
|
||
|
||
d i g i t a l decimal d i s p l a y shown i n f i g u r e s 1 3 and 1 4 ( c ) . Any program v a r i a b l e can be changed w i t h t h e s e two u n i t s by f o l l o w i n g a simple procedure.
|
||
The p o t e n t i o m e t e r s are used t o i n p u t v a r i a b l e s ( t h r o u g h A D C ' s ) . They are mainly used f o r checkout,
|
||
The T e k t r o n i x t e r m i n a l i s used t o communicate i n t e r a c t i v e l y w i t h t h e CYBER 175. When t h e RTS program i s running, t h e t e r m i n a l i s used as an o u t p u t device, f o r example, f o r error messages,
|
||
Cockpit
|
||
The c o c k p i t , which i s l i n k e d t o t h e CYBER 175 computer f o r t h e s i m u l a t i o n , is shown i n f i g u r e s 15 t o 18, I t h a s s i m u l a t e d i n s t r u m e n t a t i o n , p i l o t c o n t r o l s , and a v i s u a l landing d i s p l a y system t o simulate a h e l i c o p t e r cockpit.
|
||
The c o c k p i t i n s t r u m e n t p a n e l i s shown i n f i g u r e 15. F i g u r e 16 shows t h e c o n t r o l s by which p i l o t i n p u t s are f e d i n t o t h e CYBER 175 computer. They include the standard helicopter controls: cyclic stick with t r i m release button and " c o o l i e h a t " t r i m c o n t r o l , c o l l e c t i v e s t i c k , and a n t i t o r q u e pedals.
|
||
The c y c l i c s t i c k i s o p e r a t e d by a t h r e e - a x i s h y d r a u l i c c o n t r o l l o a d e r which i s c o n t r o l l e d by t h e a n a l o g computer shown i n f i g u r e 19. S t i c k t r a v e l a t t h e c e n t e r o f t h e hand g r i p i s l i m i t e d by mechanical s t o p s t o 2 1 2 . 7 cm i n t h e l a t e r a l d i r e c t i o n and t14.0 cm i n t h e l o n g i t u d i n a l d i r e c t i o n . The s t i c k dynamics are modeled on t h e analog computer as second-order systems with t h e damping chosen by t h e p i l o t . The s t i c k f o r c e g r a d i e n t used i s 4.4 N/cm i n t h e l o n g i t u d i n a l a x i s and 8.9 N/cm i n t h e l a t e r a l a x i s and w a s o b t a i n e d from r e f e r e n c e 9. The f o r c e t h e p i l o t a p p l i e s t o t h e s t i c k i s opposed by t h e h y d r a u l i c c o n t r o l l o a d e r and measured by f o r c e t r a n s d u c e r s . The f o r c e t r a n s d u c e r s i g n a l s are f e d i n t o t h e a n a l o g computer and t h e s t i c k a c c e l e r a t i o n i s c a l c u l a t e d . The a c c e l e r a t i o n s i g n a l i s processed together with t h e a c t u a l s t i c k p o s i t i o n and a p o s i t i o n error s i g n a l i s formed. This e r r o r s i g n a l i s then s e n t t o t h e c o n t r o l l o a d e r s e r v o which moves t h e s t i c k . The new s t i c k p o s i t i o n i s f e d through an ADC t o t h e CYBER 175 computer a s t h e p i l o t ' s c y c l i c s t i c k i n p u t . The l a t e r a l p o s i t i o n of t h e s t i c k i s t h e i n p u t xlat i n equations ( 1 2 ) and t h e l o n g i t u d i n a l p o s i t i o n i s t h e i n p u t xlon i n e q u a t i o n s ( 1 2 ) .
|
||
I n t h e trimming mode, t h e CYBER 175 computer uses t h e t r i m a l g o r i t h m s d i s cussed subsequently i n the section "Trim Calculations" t o obtain the t r i m posit i o n of t h e c y c l i c s t i c k . T h i s p o s i t i o n i s f e d through a DAC t o t h e c o n t r o l l o a d e r analog computer as a command t o d r i v e t h e s t i c k t o t h e t r i m p o s i t i o n .
|
||
A c t i v a t i n g t h e t r i m release b u t t o n on t h e c y c l i c s t i c k o r s t i c k t r i m t o g g l e s w i t c h shown i n f i g u r e s 16 and 18 removes t h e t r i m f o r c e . The s t i c k position at the instant the p i l o t releases the button or turns the stick t r i m t o g g l e on becomes t h e new t r i m p o s i t i o n . The t r i m p o s i t i o n may also b e moved by t h e f o u r - p o s i t i o n c o o l i e h a t mentioned p r e v i o u s l y . By moving t h e c o o l i e h a t
|
||
40
|
||
|
||
i n a c e r t a i n d i r e c t i o n , t h e s t i c k ' s z e r o f o r c e p o s i t i o n i s moved i n t h a t d i r e c t i o n , The t r i m release b u t t o n , t h e s t i c k t r i m t o g g l e , and t h e c o o l i e h a t are d i s c r e t e i n p u t s t o t h e CYBER 175 computer.
|
||
|
||
t
|
||
|
||
i
|
||
|
||
o
|
||
|
||
n
|
||
|
||
The s (1
|
||
|
||
a 2)
|
||
|
||
nalog
|
||
, is f
|
||
|
||
ou ed
|
||
|
||
t p u t from t h e c through an ADC
|
||
|
||
olle to
|
||
|
||
ct th
|
||
|
||
iv e
|
||
|
||
e stic CYBER
|
||
|
||
k, t 175
|
||
|
||
he quanti computer.
|
||
|
||
t
|
||
|
||
y xcol The s t
|
||
|
||
i
|
||
|
||
c
|
||
|
||
in k
|
||
|
||
t
|
||
|
||
equaravel
|
||
|
||
i s l i m i t e d by mechanical s t o p s t o 35.6 cm. A f r i c t i o n c o l l a r can be a d j u s t e d
|
||
|
||
t o v a r y t h e s t i c k f r i c t i o n . The t r i m a l g o r i t h m c a l c u l a t e s t h e c o l l e c t i v e - s t i c k
|
||
|
||
t r i m p o s i t i o n . The p i l o t must then p l a c e t h e c o l l e c t i v e s t i c k i n i t s t r i m
|
||
|
||
position, which i s evidenced by t h e t u r n i n g o f f of t h e c o l l e c t i v e t r i m l i g h t
|
||
|
||
shown i n f i g u r e 18.
|
||
|
||
The p e d a l s are d r i v e n by t h e s a m e t h r e e - a x i s h y d r a u l i c c o n t r o l l o a d e r syst e m which d r i v e s t h e c y c l i c s t i c k ; however, t h e response c h a r a c t e r i s t i c s are modeled on t h e CYBER 175 computer because t h e frequency response of t h e p e d a l s i s n o t as high as t h a t o f t h e c y c l i c s t i c k . The pedal t r a v e l i s l i m i t e d by mechanical stops t o approximately 10 cm. The p e d a l dynamics are second o r d e r w i t h a f o r c e g r a d i e n t o f 62.2 N/cm, as o b t a i n e d from r e f e r e n c e 9. The p e d a l damping w a s chosen by t h e p i l o t . The o p e r a t i o n of the p e d a l c o n t r o l 1oad.er is i d e n t i c a l w i t h t h a t of t h e c y c l i c s t i c k . Microswitches l o c a t e d on each p e d a l have t h e s a m e f u n c t i o n as t h e t r i m r e l e a s e push b u t t o n l o c a t e d on t h e c y c l i c s t i c k . I n t h e trimming mode, t h e t r i m a l g o r i t h m c a l c u l a t e s the t r i m p o s i t i o n f o r t h e p e d a l s . These p o s i t i o n commands are f e d through DAC's t o d r i v e t h e pedals to their t r i m position,
|
||
|
||
The remaining p i l o t c o n t r o l s i n t h e c o c k p i t are d i s c r e t e i n p u t s t o t h e CYBER 175 computer. They are
|
||
Winch c o n t r o l - t h r e e - p o s i t i o n t o g g l e s w i t c h t o l e n g t h e n o r s h o r t e n t h e
|
||
load cable
|
||
Mode c o n t r o l b u t t o n s - shown i n f i g u r e 18; s e l e c t one o f t h e f o l l o w i n g
|
||
modes of o p e r a t i o n :
|
||
|
||
RESET
|
||
|
||
resets to i n i t i a l f l i g h t conditions
|
||
|
||
HOLD
|
||
|
||
holds present flight conditions
|
||
|
||
OPERATE
|
||
|
||
starts simulation
|
||
|
||
AE'CS s e l e c t o r b u t t o n s - shown i n f i g u r e 18; s e l e c t t h e f o l l o w i n g o p t i o n s :
|
||
|
||
AFCS
|
||
|
||
automatic f l i g h t c o n t r o l system on
|
||
|
||
YAW
|
||
|
||
heading h o l d on
|
||
|
||
ALT
|
||
|
||
a l t i t u d e h o l d on
|
||
|
||
HOVER
|
||
|
||
hover hold on
|
||
|
||
41
|
||
|
||
- S t i c k t r i m s w i t c h two-position t o g g l e switch t o t u r n c y c l i c - s t i c k - f o r c e
|
||
t r i m system on and o f f ; shown i n f i g u r e 18
|
||
Load release b u t t o n - l o c a t e d on t h e c y c l i c s t i c k ; when p r e s s e d , e x t e r n a l
|
||
load is released
|
||
Several additional features are included i n the cockpit.
|
||
The p i l o t views a v i s u a l t e r r a i n scene provided by t h e v i s u a l l a n d i n g d i s p l a y system (VLDS), and a computer-generated l o a d / l a n d i n g zone scene. P i l o t s ' comments d u r i n g checkout i n d i c a t e d t h a t a s e p a r a t e and independent computerg e n e r a t e d video d i s p l a y of t h e s l i n g l o a d and l a n d i n g zone as viewed by a downlooking TV camera a t t a c h e d t o t h e h e l i c o p t e r a t t h e p i l o t ' s l o c a t i o n is unaccepta b l e . Many hours o f s i m u l a t i o n experience w i t h NASA p i l o t s and p i l o t s f r o m i n d u s t r y have shown t h a t an a c c e p t a b l e s i m u l a t i o n s l i n g l o a d d i s p l a y can be made by e l e c t r o n i c a l l y combining t h e v i s u a l t e r r a i n scene w i t h t h e computerg e n e r a t e d scene. The r e s u l t i n g image i s t h e n d i s p l a y e d on t h e video monitor p l a c e d i n t h e normal e y e - l e v e l p o s i t i o n . F i g u r e 1 7 shows t h e v i r t u a l image l e n s system through which t h e p i l o t views t h e c o l o r monitor which d i s p l a y s t h e v i s u a l t e r r a i n scene e l e c t r o n i c a l l y mixed w i t h t h e down-looking l o a d scene. The v i r t u a l image l e n s c a u s e s t h e p i l o t ' s e y e s t o be focused a t i n f i n i t y . A l s o , shown i n f i g u r e 1 7 i s a s m a l l b l a c k and white monitor which shows t h e same d i s p l a y s a s t h e p i l o t ' s c o l o r monitor. The b l a c k and white monitor i s used by t h e researcher s i t t i n g i n the r i g h t s e a t of the cockpit.
|
||
A n audio generator c r e a t e s cockpit n o i s e , with one component having a frequency e q u a l t o 6 t i m e s r o t o r speed ( i n rpm) and t h e o t h e r component having
|
||
white n o i s e w i t h magnitude p r o p o r t i o n a l t o t h e q u a n t i t y (VaS,h + 24.4) m/sec
|
||
t o r e p r e s e n t wind n o i s e . These audio s i g n a l s are o u t p u t on a speaker i n t h e c o c k p i t w i t h volume l e v e l based on p i l o t comments.
|
||
Simulation Software
|
||
The s i m u l a t i o n s o f t w a r e i s w r i t t e n i n FORTRAN, w i t h some assembly language. It i s broken down i n t o primary and secondary o v e r l a y s w i t h many s u b r o u t i n e s and general-purpose functions.
|
||
Figure 20 shows t h e c e n t r a l memory l a y o u t w i t h t h e v a r i o u s o v e r l a y s . The l a r g e block l a b e l e d ( 0 , O ) r e p r e s e n t s t h e base o v e r l a y , which r e q u i r e s 40 0008 s t o r a g e l o c a t i o n s . It c o n t a i n s a l l v a r i a b l e s which must be communicated between o v e r l a y s , s u b r o u t i n e s r e q u i r e d by more than one o v e r l a y , and some r e a l t i m e system software.
|
||
The primary l e v e l o v e r l a y s (l,O), ( 2 , 0 ) , ( 3 , 0 ) , and ( 4 , O ) s h a r e t h e same memory l o c a t i o n s . T h e i r f u n c t i o n s a r e n e c e s s a r i l y mutually e x c l u s i v e , Overl a y (1,O) i n i t i a l i z e s program v a r i a b l e s and i n i t i a l i z e s t h e r e a l - t i m e system. Overlay ( 2 , O ) p r i n t s t r i m sheets o r t i m e h i s t o r i e s . Overlay (3,O) reads i n d a t a f o r v a r i o u s l o a d s . Overlay ( 4 , O ) i s t h e main o v e r l a y and c o n t a i n s t h e real-time loop. I t i s f u r t h e r described below and i n f i g u r e 2 1 ( a ) , Secondary l e v e l overlays ( 4 , l ) t o ( 4 , l O ) are o p t i o n a l l y executed by overlay ( 4 , O ) .
|
||
42
|
||
|
||
The secondary o v e r l a y s s h a r e t h e same memory l o c a t i o n s . Overlay ( 4 , l ) executes s t a t i c checks; ( 4 , 2 ) c o n t a i n s t h e load/landing zone d i s p l a y e q u a t i o n s ; (4,3) contains the t r i m algorithm and logic; (4,4) contains preprocessing equat i o n s , i.e., c a l c u l a t i o n s which can be done o u t o f t h e real-time loop f o r a given run; (4,5) checks and p r i n t s o u t function data; (4,6) c a l c u l a t e s stab i l i t y d e r i v a t i v e s ; (4,7) p r i n t s error messages t o t h e console operator; (4,101 c a l c u l a t e s l i n e a r i z a t i o n d e r i v a t i v e s . Of t h e s e e i g h t f u n c t i o n s , o n l y t h e load/landing zone d i s p l a y e q u a t i o n s are needed i n t h e real-time loop. The others are brought i n as necessary between runs.
|
||
The real-time o v e r l a y ( o v e r l a y ( 4 , O ) ) i s t h e main loop, w i t h a l l t h e o t h e r o v e r l a y s s u p p o r t i n g it. A g e n e r a l flow diagram o f t h e main l o o p i s shown i n figure 2 1 ( a ) . This real-time loop c o n s i s t s of three separate loops: r e s e t , hold, and o p e r a t e . The r e s e t l o o p i s c y c l e d through a t T i m e = 0. The h o l d loop i s s e l e c t e d a t any t i m e t o h o l d a l l s i m u l a t i o n v a r i a b l e s f i x e d . The operate loop begins the simulation, calculating and i n t e g r a t i n g the equations of motion and updating t h e independent v a r i a b l e t i m e i n synchronization w i t h real t i m e , with a s t e p s i z e At of 1/32 sec. This r a t e w a s s e l e c t e d a s t h e l a r g e s t t i m e i n t e r v a l allowed by t h e real-time system which g i v e s a c c u r a t e r e s u l t s and updates c o c k p i t i n s t r u m e n t s w i t h no v i s i b l e jumps.
|
||
The block i n f i g u r e 2 1 ( a ) l a b e l e d (A) r e p r e s e n t s t h e s e c t i o n of t h e reset loop i n which various secondary o v e r l a y s can be s e l e c t e d and executed. For example, when t h e c o n s o l e o p e r a t o r d e p r e s s e s t h e t r i m b u t t o n , o v e r l a y ( 4 , 4 ) i s executed t o c a l c u l a t e preprocessing equations, and then overlay ( 4 , 3 ) is loaded t o execute t h e t r i m algorithm. Overlay ( 4 , 3 ) w i l l s t a y i n memory u n t i l another option is selected.
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Blocks (B) t o ( E ) are cycled through i n b o t h h o l d and reset modes. Block (B) r e p r e s e n t s t h e sampling of 5 analog s i g n a l s ( v i a A D C ' s ) and 2 7 d i s c r e t e i n p u t s from t h e cockpit. These voltages are scaled and t h e r e s u l t i n g parameters (e.g., s t i c k inputs) saved f o r later use.
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Block (C) r e p r e s e n t s a l l t h e c a l c u l a t i o n s necessary t o compute t h e equations of motion f o r the helicopter and, optionally, f o r the load. This block i s broken down i n f i g u r e 2 1 ( b ) , where each b l o c k r e f e r s t o a p o r t i o n of t h e p r e v i o u s l y developed mathematical model. Some o f t h e general-purpose a l g o rithms used i n t h i s s e c t i o n a r e a c o n v o l u t i o n i n t e g r a t i o n scheme used t o repres e n t f i r s t - and second-order f i l t e r s , a l i n e a r i n t e r p o l a t i o n scheme f o r funct i o n d a t a t a b l e look-ups f o r f u n c t i o n s of one o r two v a r i a b l e s , and an E u l e r i n t e g r a t o r f o r u s e when speed i s d e s i r a b l e and accuracy n o t c r i t i c a l .
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Block ( D ) r e p r e s e n t s t h e c a l c u l a t i o n s f o r t h e VLDS and Adage d i s p l a y s . The VLDS d r i v e e q u a t i o n s are computed, 19 a n a l o g s i g n a l s are o u t p u t , and 11 a n a l o g e r r o r s i g n a l s are f e d back. The Adage d i s p l a y e q u a t i o n s are comp u t e d , and t h e d a t a are t r a n s m i t t e d i n d i g i t a l form t o t h e Adage Graphics Terminal (AGT 1 3 0 ) . F u r t h e r d e s c r i p t i o n s o f t h e VLDS and Adage d i s p l a y s are given be l o w .)
|
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43
|
||
|
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Block (E) represents t h e s c a l i n g of program v a r i a b l e s and the o u t p u t t i n g of those v a r i a b l e s v i a DAC’s and d i s c r e t e channels. Twenty-nine voltages and 12 discrete outputs are trunked t o the simulator cockpit.
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Blocks (F) and ( G ) are o n l y c y c l e d through i n t h e o p e r a t e mode. D a t a f o r
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t h e t i m e - h i s t o r y p r i n t o u t are recorded i n b l o c k (F), e v e r y s p e c i f i e d number of
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i t e r a t i o n s . These d a t a can be p r i n t e d later a t t h e r e s e a r c h e r ’ s option.
|
||
Block ( G ) r e p r e s e n t s t h e i n t e g r a t i o n o f t h e e q u a t i o n s o f motion. The real-time loop i s designed t o be as f a s t a$ p o s s i b l e , w h i l e m a i n t a i n i n g good
|
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accuracy. The Adams-Bashforth second-order (AB-2) , one-pass scheme i s very
|
||
f a s t , and i s a c c u r a t e enough f o r t h i s p a r t i c u l a r s i m u l a t i o n , as w a s shown i n t h e comparison of t i m e - h i s t o r y p l o t s w i t h t h e independent check program. The AB-2 i n t e g r a t i o n scheme i s f u l l y d e s c r i b e d i n r e f e r e n c e 1 2 .
|
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The complete real-time l o o p r e q u i r e s a minimum of 2.5 m s e c ( i n reset) and a maximum o f 6.2 msec ( i n o p e r a t e ) . The 2.5-msec f i g u r e i n c l u d e s o n l y t h e h e l i c o p t e r with AFCS, whereas t h e 6.2-msec f i g u r e i n c l u d e s t h e 2.4-m by 2.4-m by 6.1-m l o a d , winds, g u s t , and so f o r t h . Table I11 shows a complete breakdown of the required t i m e .
|
||
Visual Landing Display System
|
||
The v i s u a l l a n d i n g d i s p l a y system (VLDS) c o n s i s t s of a f i x e d , coloredt e r r a i n board system and a movable camera t r a n s p o r t and i s designed f o r use with a monitor and v i r t u a l image l e n s system f o r d i s p l a y i n g an “out-the-window” scene i n a s i m u l a t e d c o c k p i t . A b r i e f d e s c r i p t i o n follows. A more d e t a i l e d description i s given i n reference 13.
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The 7.3-m by 18.3-m t e r r a i n model board of t h e VLDS i n c l u d e s two a i r p o r t s and surrounding t e r r a i n , one a t 750/1 s c a l e and t h e o t h e r a t 1500/1 s c a l e , and i s shown i n f i g u r e 22. There are a t o t a l o f f i v e paved runways, from 0.6 km t o 3.5 km i n l e n g t h . A h e l i p a d i s l o c a t e d on t h e 750/1 a i r p o r t and i s shown i n f i g u r e 23. I t c o n s i s t s of a Maltese c r o s s w i t h a 45-m by 45-m b o r d e r . The t e r r a i n i s g e n e r a l l y f l a t , and p r o v i s i o n i s made f o r variable v i s i b i l i t y , v a r i a b l e cloud-base heights, and day, dusk, and n i g h t scenes.
|
||
The camera system has a f i e l d of view 48O wide and 36O h i g h and u s e s a 525-line color video raster system. This system provides nominal resolution on t h e o r d e r of 9 minutes of a r c . The p i l o t ’ s eye p o s i t i o n and t h e o r i e n t a t i o n of t h e p i l o t ’ s l i n e of s i g h t o u t t h e forward window are b o t h c a l c u l a t e d w i t h r e s p e c t t o t h e simulated runway. These p o s i t i o n s and o r i e n t a t i o n a n g l e s (and t h e i r r a t e s ) are used t o d r i v e t h e camera system. The dynamic c h a r a c t e r i s t i c s of t h e VLDS t r a n s p o r t system are given i n table IV.
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Load/Landing Zone V i s u a l Display
|
||
The s i m u l a t i o n i s i n t e n d e d t o be used by p i l o t s t o e v a l u a t e s l i n g l o a d s t a b i l i z a t i o n systems, and since s l i n g load p i l o t i n g i s a v i s u a l t a s k , a
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||
44
|
||
|
||
r e a l i s t i c d i s p l a y of load motions and landing zone p o s i t i o n must be a v a i l a b l e i n t h e s i m u l a t e d c o c k p i t . P r e l i m i n a r y work with p i l o t s d e f i n e d t h e format of t h e s i m u l a t i o n d i s p l a y as follows. The d i s p l a y should show i n p e r s p e c t i v e t h e three-dimensional o u t l i n e of the external load, the c a b l e ( s ) , and the Earthf i x e d f e a t u r e s such as t h e l a n d i n g zone and l e a d - i n d i s t a n c e marks. The c e n t e r l i n e of t h e d i s p l a y should be l o c a t e d a t t h e cable attachment p o i n t on t h e h e l i copter and t h e view should be s t a b i l i z e d i n p i t c h and r o l l ; t h a t i s , t h e v i e w should always be v e r t i c a l l y o r i e n t e d . Load a l t i t u d e above ground l e v e l should be presented i n analog form by a p o i n t e r and a l t i t u d e scale, and h e l i c o p t e r p i t c h and r o l l a t t i t u d e bars should be generated t o provide the p i l o t p r e c i s e a t t i t u d e information needed while hovering. A sketch of the desired load/ landing zone d i s p l a y i s given i n f i g u r e 24.
|
||
The l o a d / l a n d i n g zone computer g r a p h i c d i s p l a y i s d e f i n e d by v e c t o r end p o i n t s . These end p o i n t s are computed by using t h e formulas developed i n equations (97) t o (101).
|
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The c o o r d i n a t e s o f t h e l o a d c.g. are given w i t h r e s p e c t t o h e l i c o p t e r body axes by
|
||
The c o o r d i n a t e s o f any p o i n t p on t h e l o a d expressed i n h e l i c o p t e r body a x e s are thus given by
|
||
The c o o r d i n a t e s o f t h e h e l i c o p t e r viewpoint e x p r e s s e d i n E a r t h axes are g i v e n by
|
||
45
|
||
|
||
where X v l h l y v l h r Zv,h are t h e c o o r d i n a t e s o f t h e viewpoint i n h e l i c o p t e r axes. Thus, t h e c o o r d i n a t e s o f any p o i n t p on t h e E a r t h w i t h r e s p e c t t o t h e viewpoint are given i n helicopter axes by
|
||
|
||
where xzp,el Yzp,el zzp,e are t h e c o o r d i n a t e s of any p o i n t p i n E a r t h axes. S i n c e t h e l o a d / l a n d i n g zone d i s p l a y w i l l be shown on a s c r e e n , t h e s e p o i n t s must be e x p r e s s e d i n t h e c o o r d i n a t e system of t h e s c r e e n . The f o l l o w i n g equat i o n s are used t o transform t h e s e p o i n t s t o screen coordinates and t o add perspective :
|
||
Xs c r e e n = "p , h p p , h
|
||
J Yscreen - yp,h/Zp,h
|
||
|
||
where %,h' 'plhr 'plh are t h e coordinates a t any p o i n t p i n h e l i c o p t e r axes. The h e l i c o p t e r a t t i t u d e b a r s a r e g e n e r a t e d d i r e c t l y i n s c r e e n c o o r d i n a t e s . The d a t a d e f i n e d i n s c r e e n c o o r d i n a t e s must be c l i p p e d a t t h e s c r e e n boundary. The c l i p p i n g a l g o r i t h m employed i s d e s c r i b e d i n r e f e r e n c e 14.
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||
The l o a d / l a n d i n g zone d i s p l a y requirements are m e t by t h e Adage Graphics Terminal i n c o n j u n c t i o n w i t h t h e CYBER 175 computer. The Adage i s an independent, d i g i t a l , g r a p h i c s computer w i t h an o p e r a t o r console shown i n f i g u r e 25. Computations r e q u i r e d f o r t h e d i s p l a y are performed on t h e CYBER 175 computer and d a t a are t r a n s m i t t e d t o t h e Adage, which g e n e r a t e s t h e d i s p l a y . Sample d i s p l a y s are shown i n f i g u r e s 26 and 27.
|
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|
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Trim Calculations
|
||
|
||
I n order f o r the simulation t o s t a r t i n an unaccelerated f l i g h t condition,
|
||
|
||
it is r e q u i r e d t h a t an algorithm t h a t renders c e r t a i n mathematical model t i m e
|
||
|
||
d e r i v a t i v e s z e r o be a v a i l a b l e f o r determining t h e h e l i c o p t e r a t t i t u d e and con-
|
||
|
||
t r o l positions and the load a t t i t u d e and position with respect to the h e l i -
|
||
|
||
copter. The a l g o r i t h m used i s based on t h e s o - c a l l e d method of s e c a n t s and i s
|
||
|
||
d e s c r i b e d i n appendix D o f r e f e r e n c e 15. The a l g o r i t h m determines t h e v a l u e s
|
||
|
||
of t h e f o l l o w i n g independent v a r i a b l e s : xlon1 xlat1 xcol, xped1 etfl ohl ohl
|
||
|
||
Vml V t t
|
||
|
||
e t ~ t$21 O R , X g c g l e 1 ~
|
||
|
||
g Z R ~~ ~SO ,~t h~a t t h, e foll~owing ~dependent
|
||
|
||
46
|
||
|
||
. v a r i a b l e s are approximately zero:
|
||
*m, v t , g o t ' 'cg,R, ;cg,Rp ;cg,R,
|
||
|
||
. 6 cg,h'
|
||
|
||
Vcg,h'
|
||
|
||
*
|
||
Wcg,h' phr qh'
|
||
|
||
rh'
|
||
|
||
Whcg,e'
|
||
|
||
42,
|
||
|
||
F o r t h e s i m u l a t i o n of t h e CH-54 h e l i c o p t e r and cargo c o n t a i n e r t h e algorithm t r i m s a t any s p e c i f i e d a i r s p e e d from -20 t o 100 k n o t s i n approximately 1 sec. Values o f t h e major h e l i c o p t e r v a r i a b l e s i n t r i m a t 0.1, 30, 60, and 90 k n o t s are given i n t a b l e V. The use of 0 . 1 k n o t w a s t o p r e v e n t s i n g u l a r i t i e s t h a t would occur a t e x a c t l y z e r o a i r s p e e d .
|
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|
||
VERIFICATION AND VALIDATION
|
||
Simulation Verification
|
||
The s i m u l a t i o n software v e r i f i c a t i o n w a s accomplished w i t h an independent check program. The check program w a s w r i t t e n i n FORTRAN and w a s designed t o run i n a batch environment. I t w a s developed from t h e mathematical model independently of the real-time program. A s the independent check program i s n o t r e q u i r e d t o run i n r e a l t i m e , a m o r e a c c u r a t e i n t e g r a t i o n a l g o r i t h m t h a n AB-2 w a s selected f o r t h i s use. This procedure provided a verification of both the programing of t h e mathematical model and t h e accuracy of t h e numerical solut i o n . A Runge-Kutta seventh-order, 13-pass i n t e g r a t i o n algorithm with v a r i able s t e p s i z e was used i n t h e independent check program. T h i s a l g o r i t h m and i t s accuracy a r e described i n reference 16.
|
||
The check c a s e s e l e c t e d c o n s i s t e d of a 30-sec run, d u r i n g which t h e f o u r c o n t r o l i n p u t s w e r e disturbed independently with a half-cycle sine-wave forcing f u n c t i o n . The AFCS w a s o f f f o r t h e f i r s t 3 s e c , and w a s c u t on and o f f i n 3-sec i n t e r v a l s during the run. This allowed f o r large, b u t reasonable, pert u r b a t i o n s i n t h e s t a t e v a r i a b l e s . The check case w a s run f o r t h e h e l i c o p t e r alone a t hover and a t 60 knots and f o r the h e l i c o p t e r with s l i n g load a t hover and a t 60 knots. The time h i s t o r i e s of t h e s t a t e v a r i a b l e s showed e x c e l l e n t agreement with those from t h e real-time program, and f u r t h e r a n a l y s i s proved t h a t t h e n e g l i g i b l e d i f f e r e n c e s w e r e due t o i n t e g r a t i o n e r r o r s . These e r r o r s were s m a l l enough t o v e r i f y t h a t t h e AB-2 i n t e g r a t i o n scheme w a s s u f f i c i e n t l y accurate for the simulation.
|
||
Hardware v e r i f i c a t i o n c o n s i s t s of a s t a t i c check performed b e f o r e each real-time s e s s i o n . The i n s t r u m e n t s are checked v i s u a l l y f o r conformity w i t h s t a t i c check v a l u e s . A l l t h e c o n t r o l i n p u t s are d e f l e c t e d t o t h e i r maximum and minimum p o s i t i o n s while t h e console o p e r a t o r monitors t h e v o l t a g e s . Finally, a l l the discrete inputs are activated while the console operator monitors them.
|
||
|
||
Mathematical Model V a l i d a t i o n
|
||
The h e l i c o p t e r p o r t i o n o f t h e p r e v i o u s l y d e s c r i b e d mathematical model w a s v a l i d a t e d by comparison of simulated t i m e h i s t o r i e s with f l i g h t d a t a , a n a l y s i s of eigenvalues and eigenvectors, and by p i l o t evaluation.
|
||
|
||
47
|
||
|
||
Eleven s i m u l a t i o n s w e r e made f o r comparison w i t h f l i g h t t i m e h i s t o r i e s , and t h e r e s u l t s from two of t h e s e are shown i n f i g u r e s 28 and 29. I n a l l cases the simulated helicopter m a s s characteristics were set equal to those of the h e l i c o p t e r t h a t generated t h e f l i g h t t i m e h i s t o r i e s . (These f l i g h t s were conducted a t Langley i n 1972 i n an u n r e l a t e d s l t n g l o a d p r o j e c t r e p o r t e d i n r e f . 17.) Table I gives the m a s s c h a r a c t e r i s t i c s and o t h e r d a t a used i n t h e s i m u l a t i o n . The AFCS w a s o f f i n a l l cases. When reviewing f i g u r e s 28 and 29, t h e r e a d e r should keep i n mind t h a t t h e b a s i c h e l i c o p t e r is u n s t a b l e a b o u t each a x i s , so t h a t any perturbation from t r i m w i l l r e s u l t i n divergent r o l l , p i t c h , and yaw motion because of t h e dynamic c r o s s coupling. T h i s divergence t e n d s t o amplify d i f f e r e n c e s between f l i g h t and s i m u l a t i o n as t i m e i n c r e a s e s . I t was the manufacturer's opinion t h a t about 2 o r 3 sec of close agreement between simulation and f l i g h t d a t a would be a l l t h a t should be expected.
|
||
Figure 28 shows t h e d a t a f o r a run i n which t h e h e l i c o p t e r alone w a s hovering and t h e p i l o t made a l o n g i t u d i n a l c y c l i c s t e p i n p u t of about 3 c m f o r approximately 2 s e c while h o l d i n g t h e o t h e r c o n t r o l s approximately f i x e d . The s i m u l a t i o n w a s trimmed a t hover and t h e c o n t r o l p o s i t i o n changes made i n f l i g h t w e r e d u p l i c a t e d i n t h e s i m u l a t i o n by u s i n g t h e recorded c o n t r o l i n p u t d a t a . The upper two p l o t s i n f i g u r e 28 show t h e l o n g i t u d i n a l and l a t e r a l c y c l i c s t i c k motion f o r t h e f i r s t 5 s e c of t h i s case. The p e d a l s moved less than 0.05 cm d u r i n g t h i s run and t h e c o l l e c t i v e s t i c k moved l e s s than 0.09 cm a t t h e g r i p . The d i f f e r e n c e s i n E u l e r a n g l e s and body r a t e s between f l i g h t and s i m u l a t i o n a t t i m e zero noted i n t h e f i g u r e w e r e due t o t r i m and f l i g h t d a t a b i a s and should be d i s r e g a r d e d throughout t h e run when comparing t h e s e d a t a . Except f o r t h e s l i g h t r o l l acceleration reversal noted i n the figure a t about 3 sec, the data f o r a t t i t u d e and a n g u l a r r a t e s show very c l o s e agreement. The h e l i c o p t e r a l t i tude d a t a agreed c l o s e l y between s i m u l a t i o n and f l i g h t and showed a d e c r e a s e of about 1.5 m d u r i n g t h e 5-sec p e r i o d .
|
||
F i g u r e 29 shows t h e d a t a f o r a run i n which t h e h e l i c o p t e r was f l y i n g s t r a i g h t and l e v e l a t approximately 38 k n o t s and t h e p i l o t made a l o n g i t u d i n a l c y c l i c s t e p i n p u t o f about 2 cm f o r s e v e r a l seconds followed by a p e d a l i n p u t of a b o u t 1 cm and a l a t e r a l c y c l i c i n p u t of approximately 2 cm. The same t r i m a i r s p e e d w a s used i n t h e s i m u l a t i o n , and t h e c o n t r o l p o s i t i o n changes made i n f l i g h t w e r e d u p l i c a t e d i n t h e s i m u l a t i o n as b e f o r e . The upper t h r e e p l o t s i n f i g u r e 29 show t h e t i m e h i s t o r i e s of t h e f l i g h t and s i m u l a t i o n c o n t r o l i n p u t s f o r t h e f i r s t 7 sec of t h i s run. The c o l l e c t i v e s t i c k w a s n o t moved d u r i n g t h e 7-sec p e r i o d shown. The t i m e h i s t o r i e s of h e l i c o p t e r a l t i t u d e and a i r s p e e d are given i n t h e f o u r t h and f i f t h p l o t s , where good agreement i s noted between f l i g h t and simulation. A s f o r the hover run, the differences i n Euler angles and body a n g u l a r rates a t t i m e z e r o should be d i s r e g a r d e d throughout t h e run when comparing t h e d a t a . Here t h e agreement i n p i t c h and yaw d a t a i s c o n s i d e r e d e x c e l l e n t , whereas t h e agreement i n r o l l d a t a i s o n l y f a i r . The remaining n i n e comparison c a s e s between f l i g h t d a t a and s i m u l a t i o n d a t a showed e x c e l l e n t agreement f o r t h e f i r s t few seconds i n each c a s e . I n some c a s e s t h e agreement remained good f o r s e v e r a l more seconds; i n o t h e r s t h e agreement degraded s l i g h t l y , as i n t h e examples shown i n f i g u r e s 28 and 29. I n g e n e r a l , t h e agreement between simulation d a t a and f l i g h t d a t a w a s believed t o i n d i c a t e t h a t t h e simulation mathematical model i s adequate f o r s t u d y i n g h e l i c o p t e r s l i n g load control systems.
|
||
48
|
||
|
||
The h e l i c o p t e r w a s trimmed a t 0.1, 30, 60, and 90 k n o t s and t h e l i n e a r i z a t i o n algorithm described i n reference 19 w a s applied t o determine the l i n e a r system d e r i v a t i v e matrices A and B defined i n reference 19 and the system eigenvalues and eigenvectors. I n order t h a t t h e time-varying rotor inflow r a t i o s Vm and V t and t h e t a i l - r o t o r e f f e c t i v e p i t c h a n g l e OOt would n o t appear as variables i n t h e l i n e a r system, 30 i t e r a t i o n s w i t h t h e Vm, Vt,
|
||
and. eo, d i f f e r e n t i a l e q u a t i o n s (eqs. (26) and ( 4 7 ) ) w e r e performed a f t e r each
|
||
s t a t e v a r i a b l e p e r t u r b a t i o n w a s made so t h a t t h e s e t h r e e v a r i a b l e s would r e a c h semi-steady-state b e f o r e t h e l i n e a r system d e r i v a t i v e s were c a l c u l a t e d . The A and B l i n e a r system matrices are given i n table V I f o r t h e f o u r airspeeds.
|
||
Unpublished d e r i v a t i v e s obtained from Sikorsky A i r c r a f t , d e r i v a t i v e s c a l c u l a t e d by methods given i n r e f e r e n c e 7, and d e r i v a t i v e s given i n r e f e r e n c e 18 w e r e compared w i t h t h o s e i n t h e t a b l e and g e n e r a l l y good agreement w a s found.
|
||
The e i g e n v a l u e s and e i g e n v e c t o r s f o r t h e system A matrix w e r e c a l c u l a t e d and are a l s o given i n t a b l e V I . The upper h a l f - p l a n e of t h e l o c i of e i g e n v a l u e s a t the f o u r a i r s p e e d s i s shown i n f i g u r e 30. The e i g e n v e c t o r s were used t o i d e n t i f y t h e e i g e n v a l u e s w i t h r e s p e c t t o t h e h e l i c o p t e r modes of motion. The i d e n t i f i c a t i o n i s noted on t h e f i g u r e . The r e a l r o o t s r a n g i n g from -0.85 t o -1.0 are a s s o c i a t e d w i t h r o l l i n g v e l o c i t y and v e r t i c a l v e l o c i t y . The z’ero a t t h e o r i g i n corresponds t o t h e heading a n g l e $h. The root l o c i were compared with unpublished Sikorsky A i r c r a f t d a t a f o r a CH-53 h e l i c o p t e r , which i s s i m i l a r t o t h e CH-54, and w i t h d a t a a t 60 k n o t s g i v e n i n r e f e r e n c e 18. I n general, the l o c i trends w e r e found to be s i m i l a r b u t the agreement i n magnitudes was only fair.
|
||
The comparison o f t h e l i n e a r system m a t r i c e s and t h e e i g e n v a l u e s and e i g e n v e c t o r s o b t a i n e d from t h e n o n l i n e a r mathematical model w i t h d a t a from o t h e r s o u r c e s i n d i c a t e s t h a t t h e mathematical model does r e p r e s e n t t h e dynamics of a CH-54 h e l i c o p t e r f a i r l y w e l l .
|
||
The s l i n g l o a d p o r t i o n o f t h e mathematical model w a s v a l i d a t e d by compari n g measured frequencies of simulated pendulum, rocking, and bounce motions w i t h t h e o r e t i c a l v a l u e s and by p i l o t e v a l u a t i o n . The t h e o r e t i c a l and measured f r e q u e n c i e s o f t h e s e modes a r e g i v e n i n t a b l e V I I . I n each case t h e t h e o r e t i c a l values are based on the assumptions t h a t the helicopter attachment p o i n t i s f i x e d i n space and t h a t t h e cable i s i n e l a s t i c e x c e p t i n t h e bounce mode. I n each mode t h e measured f r e q u e n c i e s are s l i g h t l y h i g h e r t h a n t h e t h e o r e t i c a l values. This discrepancy i s believed t o be due t o the motion of the h e l i c o p t e r attachment p o i n t and t h e i n t e r a c t i o n between t h e bounce mode and t h e r o c k i n g modes. The agreement i s c o n s i d e r e d adequate.
|
||
As mentioned e a r l i e r , t h e suspension system c a b l e s p r i n g rate Ksc w a s c r i t i c a l i n t e r m s o f numerical s t a b i l i t y . T r i a l and e r r o r showed t h a t t h e s p r i n g r a t e had to be s e l e c t e d so t h a t t h e f r e q u e n c i e s a s s o c i a t e d w i t h t h e
|
||
c a b l e s t r e t c h would be no h i g h e r t h a n 2 Hz. A v a l u e of Ksc = 1.8 X l o 5 N/m
|
||
w a s used w i t h t h e 4536-kg l o a d , g i v i n g a t h e o r e t i c a l bounce n a t u r a l frequency of 1 Hz.
|
||
49
|
||
|
||
P i l o t ' s Comments
|
||
The p r o j e c t t e s t p i l o t a c q u i r e d e x p e r i e n c e i n t h e Army CH-54 h e l i c o p t e r during the f l i g h t tests reported i n reference 17. This p i l o t also received additional f l i g h t training with long-line s l i n g loads i n connection with the p r e s e n t r e p o r t . Numerous s i m u l a t e d f l i g h t s b o t h with and w i t h o u t a s i m u l a t e d s l i n g l o a d a t t a c h e d were performed f o r t h e purpose of v a l i d a t i n g t h e s i m u l a t i o n mathematical model.
|
||
Several combinations of simulated c y c l i c s t i c k and pedal force g r a d i e n t s and dynamic c h a r a c t e r i s t i c s w e r e considered. The s e t used i n t h i s r e p o r t repres e n t a u s a b l e set f o r t h e s i m u l a t i o n . The VLDS and l o a d / l a n d i n g zone v i s u a l display system described earlier i s considered t o be marginally adequate f o r t h e s i m u l a t i o n of h e l i c o p t e r s l i n g l o a d o p e r a t i o n s . The l a c k of p e r i p h e r a l v i s u a l cues i n t h e h o r i z o n t a l and v e r t i c a l p l a n e s makes hover and t r a n s i t i o n s t o hover e s p e c i a l l y d i f f i c u l t . The computer-generated l o a d / l a n d i n g zone d i s -
|
||
. p l a y and t h e VLDS a l s o l a c k t h e d e p t h and n a t u r a l cues t h a t are so u s e f u l i n
|
||
a c t u a l f 1i g h t
|
||
The s i m u l a t e d h e l i c o p t e r a l o n e with and w i t h o u t winds and t u r b u l e n c e seemed l i k e a l a r g e h e l i c o p t e r i n a l l f l i g h t regimes. I t seemed underdamped i n yaw motions when approaching hover, and i t s v e r t i c a l motions seemed much more sens i t i v e t o c o l l e c t i v e movements t h a n t h o s e f o r t h e a c t u a l h e l i c o p t e r . The simul a t e d h e l i c o p t e r seemed slower than t h e a c t u a l h e l i c o p t e r t o respond t o c y c l i c step and pulse i n p u t s . Autorotation w a s simulated and seemed r e a l i s t i c t o touchdown.
|
||
The s i m u l a t i o n w i t h t h e e x t e r n a l l o a d seemed r e a l i s t i c i n s p i t e of t h e visual display shortcomings. Simulated f l i g h t s with the external load w e r e performed over t h e e n t i r e speed range and t h e ensuing load motions w e r e observed on t h e load/landing zone d i s p l a y . In a l l cases t h e load motions appeared r e a l i s t i c . The h e l i c o p t e r motions d e f i n i t e l y w e r e a f f e c t e d by l o a d motions, and hovering over a s p o t w a s very d i f f i c u l t , as it i s i n a c t u a l f l i g h t . A l l normal s l i n g load o p e r a t i o n s were t r i e d with and without winds and turbulence and were found t o be p o s s i b l e t o e x e c u t e b u t w i t h s l i g h t l y h i g h e r work l o a d t h a n i n a c t u a l f l i g h t . Simulator motion validation w a s not necessary since i t w a s thought t h a t f o r s t u d i e s o f s l i n g l o a d s t a b i l i z a t i o n and c o n t r o l system comp a r i s o n , simulator motion would n o t be required.
|
||
It is thought t h a t the simulation described i n the report can be used t o compare v a r i o u s systems f o r s t a b i l i z i n g h e l i c o p t e r s l i n g loads and improving helicopter sling load handling qualities.
|
||
CONCLUDING REMARKS
|
||
A generalized, full-flight envelope, real-time, piloted visual simulation of a single-rotor h e l i c o p t e r , suspension system, and e x t e r n a l load i s described and v a l i d a t e d f o r t h e f u l l f l i g h t envelope of t h e U.S. Army CH-54 h e l i c o p t e r
|
||
50
|
||
|
||
and c a r g o c o n t a i n e r as an example. The mathematical model d e s c r i b e d uses modif i e d nonlinear c l a s s i c a l r o t o r theory f o r both t h e main rotor and t a i l rotor, nonlinear fuselage aerodynamics, an elastic suspension system, nonlinear load aerodynamics, and a load-ground c o n t a c t model. The implementation of t h e mathematical model on a l a r g e d i g i t a l computing system i s d e s c r i b e d , and v a l i d a t i o n of t h e s i m u l a t i o n is d i s c u s s e d . The mathematical model i s v a l i d a t e d by (1) comparison of f l i g h t d a t a w i t h simulated d a t a ; ( 2 ) comparison of l i n e a r i z e d system c o e f f i c i e n t matrices, eigenvalues, and eigenvectors with c a l c u l a t e d values, manufacturer's d a t a , and d a t a obtained from f l i g h t tests; and (3) by p i l o t evaluation. A visual landing display system t h a t generates the p i l o t ' s forward-looking real-world d i s p l a y i s d i s c u s s e d , and a s p e c i a l head-up, downlooking load/landing zone d i s p l a y i s described. I t w a s the test p i l o t ' s opinion t h a t t h e s i m u l a t i o n d e s c r i b e d i n t h i s r e p o r t can be used t o compare various systems f o r s t a b i l i z i n g helicopter s l i n g loads and improving helicopter sling load handling qualities. Langley Research Center National Aeronautics and Space Administration
|
||
Hampton , VA 2 3665
|
||
October 23, 1978
|
||
51
|
||
|
||
REFERENCES
|
||
1. D a n i e l s , Glenn E . , e d . : T e r r e s t r i a l Environment ( C l i m a t i c ) C r i t e r i a Guidel i n e s f o r U s e i n Aerospace Vehicle Development, 1973 Revision. NASA TM X-64757, 1973.
|
||
2. Wilcock, T.; and Thorpe, Ann C.: F l i g h t S i m u l a t i o n of a Wessex H e l i c o p t e r -
|
||
A Validation Exercise. C.P. No. 1299, B r i t i s h A.R.C., 1974.
|
||
3, Seckel, Edward; and C u r t i s s , H. C., Jr.: Aerodynamic C h a r a c t e r i s t i c s of H e l i c o p t e r Rotors. Rep. No. 659, D e p . Aerosp. Mech. S c i . , P r i n c e t o n Univ., D e c . 1963.
|
||
4. B a i l e y , F. J., Jr.: A S i m p l i f i e d T h e o r e t i c a l Method o f Determining t h e C h a r a c t e r i s t i c s o f a L i f t i n g Rotor i n Forward F l i g h t . NACA Rep. 716, 1941.
|
||
5 . Amer, Kenneth B.; and Gustafson, F. B.: C h a r t s f o r E s t i m a t i o n o f L o n g i t u d i n a l - S t a b i l i t y Derivatives f o r a Helicopter Rotor i n Forward F l i g h t . NACA TN 2309, 1951.
|
||
6. Gessow, A l f r e d ; and Myers, Garry C . , Jr.: Aerodynamics of t h e H e l i c o p t e r . Macmillan Co., c.1952. (Republished 1967 by F r e d e r i c k Ungar Pub. Co.)
|
||
7. S e c k e l , Edward: S t a b i l i t y and Control of A i r p l a n e s and H e l i c o p t e r s . Academic P r e s s , I n c . , c.1964.
|
||
8. Amer, Kenneth B.: Theory of H e l i c o p t e r Damping i n P i t c h o r Roll and a Comparison With F l i g h t Measurements. NACA TN 2136, 1950.
|
||
- 9. Bailes, Edward E.; Diekmann, Vernon L.; W a t t s , Joseph C.; and Henderson, John C.: Instrument-Flight-Rules C a p a b i l i t y E v a l u a t i o n CH-54B (TARHE) H e l i c o p t e r . USAASTA Pro]. No. 71-01, U.S. Army, D e c . 1972. ( A v a i l a b l e from DDC as AD 908 656.)
|
||
10. Laub, Georgene H.; and Kodani, H i f u M.: Wind Tunnel I n v e s t i g a t i o n of Aerodynamic C h a r a c t e r i s t i c s of S c a l e Models of Three Rectangular Shaped Cargo C o n t a i n e r s . NASA TM X-62,169, 1972.
|
||
11. Liu, David T.: I n - F l i g h t S t a b i l i z a t i o n o f E x t e r n a l l y Slung H e l i c o p t e r Loads. USAAMRDL Tech. Rep. 73-5, U.S. Army, 1973.
|
||
1 2 . Wilson, John W.; and Steinmetz, George C. (With Appendix A by Roland L. Bowles) : Analysis o f Numerical I n t e g r a t i o n Techniques f o r R e a l - T i m e D i g i t a l F l i g h t Simulation. NASA TN D-4900, 1968.
|
||
13. P a r r i s h , R. V.; R o l l i n s , J. D.; and Martin, Dennis J., Jr.: Visual/Motion Simulation of CTOL F l a r e and Touchdown Comparing D a t a Obtained From Two Model Board Display Systems. AIAA Paper 76-1709, A p r . 1976.
|
||
52
|
||
|
||
14. Newman, W i l l i a m M. ; and S p r o u l l , Robert F. : P r i n c i p l e s o f I n t e r a c t i v e
|
||
, Computer Graphics. M c G r a w - H i l l Book Co. 1973, pp. 123-124.
|
||
15. Houck, Jacob A.; Gibson, L u c i l l e H.; and Steinmetz, George G , : A R e a l - T i m e D i g i t a l Computer Program f o r t h e Simulation of a Single-Rotor H e l i c o p t e r . NASA TM X-2872, 1974.
|
||
16. Fehlberg, Erwin: C l a s s i c a l F i f t h - , Sixth-, Seventh-, and Eighth-Order Runge-Kutta Formulas With S t e p s i z e Control. NASA TR R-287, 1968,
|
||
17. D i C a r l o , Daniel J.; Kelley, Henry L.; and Yenni, Kenneth R.: An E x p l o r a t o r y F l i g h t I n v e s t i g a t i o n of Helicopter Sling-Load Placements Using a ClosedC i r c u i t T e l e v i s i o n as a P i l o t Aid. NASA TN D-7776, 1974.
|
||
18. Tomaine, Robert L.: F l i g h t D a t a I d e n t i f i c a t i o n of S i x Degree-of-Freedom S t a b i l i t y and C o n t r o l D e r i v a t i v e s of a Large "Crane" Type H e l i c o p t e r . NASA TM X-73958, 1976.
|
||
19. Dieudonne, J a m e s E. : D e s c r i p t i o n of a Computer Program and Numerical Techn i q u e f o r Developing L i n e a r P e r t u r b a t i o n Models From Nonlinear Systems Simulation. NASA TM-78710, 1978.
|
||
53
|
||
|
||
TABLE I.- VALUES OF PARAMETERS FOR CH-54 HELICOPTER
|
||
|
||
[Subscripts m and t denote main and t a i l rotor]
|
||
|
||
Xmr,hr m
|
||
ymlh1m
|
||
|
||
............................... ...............................
|
||
|
||
-0.33 0
|
||
|
||
Zmrlhr m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2.26
|
||
|
||
Xtr,hr m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -13.74
|
||
|
||
ytrlh1m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.84 ztrlh,rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -2.22
|
||
|
||
Xwt,hr m yWtlhlm
|
||
|
||
............................... ...............................
|
||
|
||
-0.51 0
|
||
|
||
zwt,h1m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
-0.37
|
||
|
||
Xp s , h l m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
5.77
|
||
|
||
ypslh1m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
-0.53
|
||
|
||
Zp s , h l m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.11
|
||
|
||
F S C G , m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.20
|
||
|
||
WLCG,m...............
|
||
|
||
. . . . . . . . . . . . . . . . . 4.28
|
||
|
||
BLCG,m... ............................. 0
|
||
|
||
x a l h l m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.33
|
||
|
||
yalh,m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0
|
||
|
||
zalh,m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.24
|
||
|
||
Ixxlh1kg-m 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
39 800
|
||
|
||
Iyy,h,kg-m 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
2.04X1o5
|
||
|
||
kg-m 2 'z.z1h1 I x z l h lkg-m 2
|
||
|
||
........................... .............................
|
||
|
||
1.78 x lo5
|
||
11 400
|
||
|
||
em,m.................................
|
||
|
||
0.610
|
||
|
||
Ibmlkg-m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.75 X lo3
|
||
|
||
Glkg-m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.0
|
||
|
||
&,m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.97
|
||
|
||
~ ~ ~ , .s .e .c. . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.20
|
||
|
||
63m,rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
|
||
|
||
elm, rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.183
|
||
|
||
Om . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.115
|
||
|
||
54
|
||
|
||
TABLE I.- Continued
|
||
|
||
'sm r rad $)smrrad
|
||
|
||
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-0.0524 ............................... 0
|
||
|
||
R,. rpm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.5
|
||
|
||
Ggov. N-m/(rad/sec) . . . . . . . . . . . . . . . . . . . . . . . . . . 85 160
|
||
|
||
Kdgov. N-m/(rad/sec) . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
1.32 x 105
|
||
|
||
&. N-m/(rad/sec) . . . . . . . . . . . . . . . . . . . . . . . . . 1.572 X 106
|
||
|
||
Kgovr N-m/(rad/sec)
|
||
. . . IP t ' kg-m2 . . . Imr. kg-m2
|
||
|
||
.... ..... ......
|
||
|
||
. . .
|
||
|
||
. . .
|
||
|
||
. . .
|
||
|
||
...... ...... .......
|
||
|
||
. . .
|
||
|
||
. . .
|
||
|
||
. . .
|
||
|
||
...... ...... .......
|
||
|
||
. . .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
833.3 4325
|
||
3 1 310
|
||
|
||
Teng. sec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.50
|
||
|
||
GBe. rad/rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.281
|
||
|
||
GA+. rad/rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.133
|
||
|
||
GBxlon. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.363
|
||
|
||
GAxlat. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.475
|
||
|
||
Gech. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.00037
|
||
|
||
G rad/(rad/sec) . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0. 727
|
||
|
||
Bq' GAP. r a d / ( r a d / s e c )
|
||
|
||
. . . . . . . . . . . . . . . . . . . . . . . . . . -0.096
|
||
|
||
Getr. rad/(rad/sec) . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.335
|
||
|
||
Get@' rad/rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.133
|
||
|
||
KcO. rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.128
|
||
|
||
Kcl. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.955
|
||
|
||
Kc2. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.361
|
||
|
||
KC3. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.096
|
||
|
||
K,.,rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.824
|
||
|
||
Kc5. rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0494
|
||
|
||
Kc6. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.64
|
||
|
||
Kc7. rad/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.09 Kfe. N-m/N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0243
|
||
|
||
KSc. N/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
1.8X105
|
||
|
||
mhrkg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13610
|
||
|
||
at. per rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.73
|
||
|
||
55
|
||
|
||
TABLE I.- Concluded
|
||
|
||
B t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.92
|
||
|
||
bt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
|
||
|
||
c t . m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.343
|
||
|
||
et.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.127
|
||
|
||
-Ibtl
|
||
\t.k
|
||
|
||
kg-m2 g-m
|
||
|
||
.
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
..... ......
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
..... ......
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
. .
|
||
|
||
.... ....
|
||
|
||
.
|
||
|
||
.
|
||
|
||
13.88 11.84
|
||
|
||
T ~ s~ec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.20
|
||
|
||
T A ~ ~se,c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.20
|
||
|
||
elt1rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -0.140
|
||
|
||
s l m .................................
|
||
|
||
2.44
|
||
|
||
CTt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.179
|
||
|
||
est. rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0
|
||
|
||
(Pstlrad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
1.57
|
||
|
||
63t. rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.78
|
||
|
||
Bm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.97
|
||
|
||
,b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
6
|
||
|
||
cm.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.661
|
||
|
||
aml per rad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
5.73
|
||
|
||
ua1 rad/sec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
14.0
|
||
|
||
pa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
1.0
|
||
|
||
ek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
1.8
|
||
|
||
ekf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0.5
|
||
|
||
it- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0
|
||
|
||
56
|
||
|
||
. TABLE I1 .VALUES O F PARAMETERS FOR 2.4-m BY 2.4-m BY 6.1-m
|
||
|
||
CARGO CONTAINER
|
||
|
||
Ixxg. kg.m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1124
|
||
|
||
IyV%. kg.m2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 610
|
||
|
||
I z z ~ . kgm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 610
|
||
|
||
I x z g , k g-m 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
0
|
||
|
||
mR. kg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
4536
|
||
|
||
Xa.R. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
|
||
|
||
yaIR. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0
|
||
|
||
Za.R.m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -6.1
|
||
|
||
x ~ ~ ,rn ~ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
3.05
|
||
|
||
Y , ~ . ~ .rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1.22
|
||
|
||
Zcl.R. rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.22
|
||
|
||
x ~ ~ .m~ .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
3.05
|
||
|
||
yC2.%. rn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.22
|
||
|
||
zc2.$. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.22
|
||
|
||
x ~ ~ m. ~. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -3.05
|
||
|
||
yc3.g. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.22
|
||
|
||
2C3'R' m
|
||
xc4.%. m
|
||
|
||
............................... ...............................
|
||
|
||
1.22 -3.05
|
||
|
||
yc4.g. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -1.22
|
||
|
||
Zc4. G' m Vo. rn/sec
|
||
|
||
............................. ...............................
|
||
|
||
.
|
||
|
||
.
|
||
|
||
1.22 0.305
|
||
|
||
Vf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.25
|
||
|
||
%. N/m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 000
|
||
|
||
G. N/(m/sec) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
7100
|
||
|
||
RcO. m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
|
||
|
||
30.5
|
||
|
||
57
|
||
|
||
TABLE 111.- REQUIRED COMPUTER TIMES
|
||
|
||
calculation
|
||
Helicopter only Cockpit interface Winds and g u s t s Visual landing
|
||
display system Load/suspension
|
||
system Load l a n d i n g zone
|
||
visual display T o t a l simulation
|
||
|
||
- Computer t i m e , m s e c , f o r mode
|
||
|
||
Reset
|
||
|
||
Hold
|
||
|
||
Operate
|
||
|
||
2.5
|
||
|
||
1.7
|
||
|
||
2.0
|
||
|
||
.3
|
||
|
||
.2
|
||
|
||
.3
|
||
|
||
.o
|
||
|
||
.1
|
||
|
||
.2
|
||
|
||
.7
|
||
|
||
.7
|
||
|
||
.8
|
||
|
||
.9
|
||
|
||
09
|
||
|
||
1.0
|
||
|
||
1.5
|
||
|
||
1.4
|
||
|
||
1.9
|
||
|
||
5.9
|
||
|
||
5 .O
|
||
|
||
6.2
|
||
|
||
TABLE 1V.- DYNAMIC CHARACTERISTICS OF VLDS
|
||
|
||
Drive
|
||
A 1t i t u d e Lateral Longitudinal Roll Pitch Yaw
|
||
|
||
Frequency, rad/sec 27.9 24.1 22.8 18.6 24.3 22.6
|
||
|
||
Damping ratio
|
||
|
||
0.64
|
||
|
||
.6
|
||
|
||
I
|
||
|
||
.3
|
||
|
||
.7
|
||
|
||
.7
|
||
|
||
.7
|
||
|
||
58
|
||
|
||
TABLE V.- TRIMMED VALUES OF MAJOR VARIABLES AT FOUR AIRSPEEDS [Subscripts m and t denote main and t a i l r o t o 4
|
||
|
||
Variable
|
||
|
||
V a l u e a t airspeed. knots. of .
|
||
|
||
0.1
|
||
|
||
30
|
||
|
||
60
|
||
|
||
90
|
||
|
||
. . . . . . Xlon ' c m
|
||
. . . . . . xlat. c m
|
||
|
||
-5.48 -0.12
|
||
|
||
-3.98 -1.09
|
||
|
||
-2.55 -1.79
|
||
|
||
-1.10
|
||
-2.79
|
||
|
||
2.04
|
||
|
||
. . . . . . XPed' cm * = *
|
||
xcol. c m
|
||
|
||
16.4
|
||
|
||
. . . . . . AiC. deg
|
||
|
||
-0.95
|
||
|
||
. . . . . . BiC. deg
|
||
|
||
-4.27
|
||
|
||
eOm. deg . . . . . . 16.3
|
||
|
||
Oat, deg . . . . . . 15.2
|
||
|
||
. . . . Uas.h. m / s e c
|
||
|
||
0.05
|
||
|
||
. . . . m / s e c
|
||
|
||
0
|
||
|
||
. . . . was.h. m / s e c
|
||
|
||
-0.001
|
||
|
||
. . . . . . @h. deg
|
||
|
||
-2.8
|
||
|
||
. . . . 0h. deg
|
||
|
||
-1.3
|
||
|
||
. . . . . . af. deg
|
||
|
||
-29.9
|
||
|
||
Bf. deg . . . . . . 0
|
||
|
||
. . . . m / s e c
|
||
|
||
0.05
|
||
|
||
. . . . . alsm. deg
|
||
|
||
4.3
|
||
|
||
. . . . . blsm. deg
|
||
|
||
-0.95
|
||
|
||
. . . . . aOsm. deg
|
||
|
||
5.82
|
||
|
||
. . . . . alst. deg
|
||
|
||
0.004
|
||
|
||
. . . . . blst. deg
|
||
|
||
0.001
|
||
|
||
. . . . . aOst. deg
|
||
|
||
2.14
|
||
|
||
. . . . . . 'mr. h. N . . . . . . Ym,.h. N
|
||
|
||
-2947 -2204
|
||
|
||
. . . . . . 'mr. ht N
|
||
. . . . . 'mu. h. N-m
|
||
|
||
-1.33 x 105 -1.93 X 104
|
||
|
||
1.05 13.7 -1.27 -3.10 14.9 12.0 15.4 0 -0.45 -2.2 -1.7 -15.0 0 15.4 4.1 -0.73 5.59 0.83 0.18 1.57 -2605 -1831 -1.34 x 105 -1.53 x 104
|
||
|
||
0.06 11.9 -1.50 -1.99 13.8 9.3 30.9 0 -1.46 -1.6 -2.7 -6.9 0 30.9 3.8 -0.49 5.31 0.96 0.26 1.09 -1828 -1796 -1.34 x 105 -1.21 x 104
|
||
|
||
-0.48 13.1 -2.03 -0.86 14.5 8.8 46.2 0 -4.06 -1.7 -5.0 -6.9 0 46.3 3.7 -0.53 5.35 1.33 0.44 1.14 -1635 -1955 -1.34 x 105
|
||
-1.33 X 104
|
||
|
||
59
|
||
|
||
TABLE V.- Continued
|
||
|
||
Variable
|
||
|
||
- V a l u e a t airspeed, knots, of
|
||
|
||
0.1
|
||
|
||
30
|
||
|
||
60
|
||
|
||
90
|
||
|
||
. . . . . Mmr,hr N-m
|
||
|
||
-939
|
||
|
||
- - Nmr,hi N-m
|
||
|
||
e
|
||
|
||
1.20 x lo5
|
||
|
||
-3420
|
||
9.44 X l o 4
|
||
|
||
-7734
|
||
7.54 X l o 4
|
||
|
||
-8927
|
||
8.37 X l o 4
|
||
|
||
. - X t r , h , N
|
||
|
||
.
|
||
|
||
-0.62
|
||
|
||
. Y t r , h l N
|
||
|
||
. 8699
|
||
|
||
Ztr,h, N
|
||
|
||
. . 0.17
|
||
|
||
. . . . . L ~ ~ N-,m ~ ,
|
||
|
||
1.93 x lo4
|
||
|
||
. . . M t r , h , N-m
|
||
|
||
-2288
|
||
|
||
. . . . . Ntrlh, N-m
|
||
|
||
-1.20 x lo5
|
||
|
||
. . . X f , h , N
|
||
|
||
-0.010
|
||
|
||
. Y f , h # N
|
||
|
||
. O
|
||
|
||
. . . . 'f ,h' N
|
||
|
||
. . -0.018
|
||
|
||
-99.6 6868 25.3 1.53 x 104 -721
|
||
-9.4 X l o 4
|
||
-1161 0 1046
|
||
|
||
-91.4 5414 19.4 1.21 x 104 -254
|
||
-7.4 X l o 4
|
||
-4401 0 376.5
|
||
|
||
-138.4 5912 29.5 1.33 x 104 59.2
|
||
-8.09 X l o 4
|
||
-9904 0 865.3
|
||
|
||
Lf ,h' N-m
|
||
|
||
0
|
||
|
||
. . . Mf ,hr N-m
|
||
|
||
. . 3227
|
||
|
||
. . . . . N f , h , N-m
|
||
|
||
-0.003
|
||
|
||
. hhr m . . . . .. 30.5
|
||
|
||
. . . . . . P, kg/m3
|
||
|
||
1.23
|
||
|
||
s l N/m2 . . . . . . 0.0016
|
||
|
||
. . . . . Qml r p m
|
||
|
||
.
|
||
|
||
184.5
|
||
|
||
Cm
|
||
|
||
. - . 0.00640
|
||
|
||
Pm . . . . . . . . . 2.42 X
|
||
|
||
. . . Vm . . . . . . 0.0566
|
||
|
||
. - - Am
|
||
|
||
0
|
||
|
||
. 0
|
||
|
||
-0.057
|
||
|
||
. . . . . . earn,N-m
|
||
|
||
1.19 x lo5
|
||
|
||
0 4142 -340.1 30.5 1.23 145.6 184.5 0.00646 0.0726 0.0388 -0.041 9.43 x 104
|
||
|
||
0 7988 -1252 30.5 1.23 582.3 184.5 0.00642 0.145 0.0217 -0.031 7.51 x 104
|
||
|
||
0 886 8 -2824 30.5 1.23 1310 184.5 0.00643 0.216 0.0146 -0.042 8.33 x 104
|
||
|
||
60
|
||
|
||
TABLE V. Concluded
|
||
|
||
Value a t airspeed. knots. of .
|
||
|
||
Variable
|
||
|
||
.0.1
|
||
.,T N . . . . . . . 1.33 lo5
|
||
|
||
H,. N . . . . . . . 89.9
|
||
|
||
.,J N . . . . . . . 5.04
|
||
|
||
. . . . . . Qt. r p m
|
||
|
||
835.6
|
||
|
||
.30
|
||
1.34 lo5
|
||
2381 1135 835.6
|
||
|
||
.60
|
||
1.33 4190 1683 835.6
|
||
|
||
.90
|
||
1-33 105
|
||
6628 2775 835.6
|
||
|
||
61
|
||
|
||
TABLE VI.- HELICOPTER LINEAR SYSTEM MATRICES, EIGENVALUES, AND EIGENVECTORS
|
||
|
||
( a ) V a l u e s a t 0 . 1 knot
|
||
|
||
TRINMED V E L O C I T Y =
|
||
|
||
-1 KNOTS
|
||
|
||
7 POINT F O P N U L A
|
||
|
||
30 ITERATIONS
|
||
|
||
INDEPENDEW VARIABLE TOTAL INCRENENTS
|
||
|
||
m3048E-01 -3048E-01
|
||
.304U€-Ol -1745E-02 -1745E-02 -1745E-02 -1745E-02 ~ 1 754E-02
|
||
*1745€-02
|
||
|
||
.i745c-n2 1745E-02
|
||
.1745E-C2 1 7 4 5F-02
|
||
|
||
ucg, h
|
||
-.1396E-01 s7121E-02
|
||
-.OZO+E-OZ .1361C-O1 .527ZE-02 .1061E-02
|
||
0. 0. 0.
|
||
|
||
"cg.h
|
||
-.73271-02 -.2995E-01 -.5904~-02 -.3444E-01
|
||
e2554E-02 +1585E-G1 0. C. 0.
|
||
|
||
A mmix
|
||
|
||
"c8.h
|
||
-.83046-02 -.5138E-C>2 -.3337~+00 -.3684€-02 -.6207E-02
|
||
m8314E-02 C. 0. C.
|
||
|
||
h '
|
||
-116471-01 .1519E+00
|
||
-.i7n8~-oi -.7563%+00
|
||
.1254E*00 -.ZZG9E-01
|
||
.1000E+01 0. 0.
|
||
|
||
qh
|
||
.2527E+00 -.7543i+OO -.3789~-01 -.126ZE+O1 -.2170i+00 -.6732€-01
|
||
.1377€-02 .9988€+00 -.4872%-01
|
||
|
||
r
|
||
m1701E-02 e1966E400 -.1012E-01 -7811E-01 -.5994€-02 -.2458E+00 -.2209E-01 .4571E-01 .9991E+00
|
||
|
||
h '
|
||
-1824E-09
|
||
.9792 E +o1
|
||
.4775E+00 -e53671106
|
||
.3961E-07 -1178E-05 0. 0. 0.
|
||
|
||
h '
|
||
-.9804€+01 -.1056E-01
|
||
.2165E+00 -.50826-20 0. -.1+91E-18 0. 0. 0.
|
||
|
||
*h
|
||
-.lZ7€-18 .1487E-18
|
||
-.7667€-17 -.50828-20 0. -.1491t-l8 0. U.
|
||
0.
|
||
|
||
8 HATRIX
|
||
|
||
.9754i+Ol .2823€-03
|
||
--...5282E*00 .1965E-03 3857f+01
|
||
12451-03 0. 0.
|
||
0.
|
||
|
||
..
|
||
~7238E-13 .9767E+01 -.7667E-17 .2015E+Ot
|
||
-.8009E-l0 1191E+Ol
|
||
c.
|
||
0.
|
||
0.
|
||
|
||
Born
|
||
-.2019E+Gl -.1508E+01 -.9098E+OL -.7471E+00 -.1554E+01
|
||
.7@57€+01
|
||
0. 0.
|
||
0.
|
||
|
||
8ct -.54(r9E-03
|
||
4165 E + O l 1 378E-03
|
||
-..1941E+01
|
||
-.9576E-01 42 bOi+Ol
|
||
0.
|
||
0.
|
||
0.
|
||
|
||
P E A L PARTS O F EIGENVALIJES
|
||
|
||
ROLL@.)
|
||
|
||
SHORT PERIOD(SP)
|
||
|
||
-.8493EE*JO
|
||
|
||
-.63450E+OO -.33748E+CC
|
||
|
||
I R A G PARTS OF LIGENVALUES
|
||
|
||
0.
|
||
|
||
0.
|
||
|
||
0.
|
||
|
||
EIGENVECTORS
|
||
%.h
|
||
|
||
"cg,h
|
||
|
||
"cg. h
|
||
|
||
R .3003tE+00
|
||
|
||
.9430RE+Ot
|
||
|
||
-81523E-01
|
||
|
||
S P I F a L (S) -.ZC704E+OC 0.
|
||
'h -68313E-01
|
||
|
||
HEADING (HI -.22678E-17 0.
|
||
h ' -.19306E-01
|
||
|
||
PHUGOID(P)
|
||
|
||
.lO13OC+I)O
|
||
|
||
.lGl30€+OC
|
||
|
||
h ' -.26074F-01
|
||
|
||
h ' -+5108bE-01
|
||
|
||
DUTCH ROLL(DR)
|
||
|
||
.114511+00
|
||
|
||
.11451t+00
|
||
|
||
h ' -24199E-01
|
||
|
||
*h ~29564E-01
|
||
|
||
'-.58@93t+!lU
|
||
sp J
|
||
\-.69560E+30
|
||
|
||
-.79722€+0C -.12582E*00
|
||
|
||
-.86512E-01
|
||
|
||
-+31491E-01
|
||
|
||
-.6473@Et00
|
||
|
||
.11696E-G2
|
||
|
||
.21029E-01 -30674E-02
|
||
|
||
.378228-01 .91051E-01
|
||
|
||
.5091ZE-01 .24837E-02
|
||
|
||
-.3600bE-01 -.222196-01
|
||
|
||
-.57939E-01 -.26910€+00
|
||
|
||
.17156E+OO -.12123€-01
|
||
|
||
-.57536t-02
|
||
|
||
-.82955€+00
|
||
|
||
-39610E-19
|
||
|
||
.10000E+Ol
|
||
|
||
62
|
||
|
||
TABLE VI.- Continued
|
||
|
||
&g,h
|
||
ecg ,h
|
||
*cg,h
|
||
Ph
|
||
t9h
|
||
|
||
(b) Values at 30 k n o t s
|
||
|
||
- TRIMMFO VELOCITY
|
||
|
||
30.0 KNOTS
|
||
|
||
7 POINT FOhtJULA
|
||
|
||
30 ITERATlONS
|
||
|
||
INOEPENOENT VARIABLE
|
||
|
||
__ _-
|
||
|
||
-._>g,h
|
||
|
||
-3048E-01
|
||
|
||
-..wcg,h - .3OIB€-Ol
|
||
|
||
--.Bcg,h . .3048€-01
|
||
|
||
=-h-.1745E-02
|
||
|
||
h '
|
||
|
||
117456-02
|
||
|
||
ph
|
||
|
||
.1745E-O2
|
||
|
||
h
|
||
|
||
-1745E-02
|
||
|
||
.1?45€-02
|
||
|
||
_h
|
||
|
||
-17456-02
|
||
|
||
TlTAL
|
||
|
||
INCREMENTC
|
||
|
||
%,h
|
||
-.ZRO~E-~I .1Z65E-Ol
|
||
-.2238€+00 -1642E-01 -172OE-02
|
||
-.9055E-OP 0. 0.
|
||
0.
|
||
|
||
'c&h
|
||
-.6359~-0~ -.6052€-01 -.1553E-01 -.1596E-01
|
||
-5378E-03 .2371E-01 0. 0. 0.
|
||
|
||
A MbTRIX
|
||
|
||
-. "cg,h 1Z Z I E-C 1
|
||
-.9035€-02 -.5558E+00 -.97016-03 -.8478€-02
|
||
-5737E-02
|
||
0. 0.
|
||
0.
|
||
|
||
h '
|
||
-.-.1199E-01
|
||
-.4713E+00 33341-01
|
||
-.BBO8E+OO .12ZZE+OO
|
||
-.74251-02 .1000E+Ol
|
||
0. 0.
|
||
|
||
h '
|
||
.8423E+00 -.84638+00
|
||
.1580t+02 -.1324€+01 -.Z409E+00 -.+336€-01
|
||
.1095€-02 .9993€+00 -137796-01
|
||
|
||
h '
|
||
U 2 +OE-03 -.1508E+OZ -.SCO9€-02
|
||
.1562E+OO -.2646E-02 -.3949E+00 -.2897€-01
|
||
,37778-01 .9997E+OO
|
||
|
||
'h
|
||
- 2 675 E-0 7 .9795€+01 .3702E+00 -t1655E-06 -1255E-07 -3567E-06 0. 0. 01
|
||
|
||
-. *h 9802 E +01
|
||
-.1073E-01 .2840E+00 a3970t-21
|
||
-.97ClE-20 -.3812E-20 0. 0. 0.
|
||
|
||
*h
|
||
908 BE-19 .187Zt-ZO rZ324E-20 .3970€-21 -.97*1€-2(1 -.3812€-20 0. 0. 0.
|
||
|
||
B;C .1005E+02 .1351E+00 .83646+01
|
||
.1314E-01 -.3750E+01 -.88491-01 0. 0. 0.
|
||
|
||
4c
|
||
.6138E-O7 r9050E+01 .309kE-05
|
||
.2021 E+OZ ~37 4 1E-07 .1193E+01
|
||
0.
|
||
0. 0.
|
||
|
||
.1162E+Ol -.9385E+QO
|
||
.6510E+Ol
|
||
0. 0. 0.
|
||
|
||
B MATRIX
|
||
-.1902€-01 -.3890€+01 0. 0. 0.
|
||
|
||
REAL PARTS O F EIGENWALUFS
|
||
|
||
ROLLCR)
|
||
|
||
SPIRAL(S)
|
||
|
||
-.89431E+00
|
||
|
||
-.51224E-01
|
||
|
||
I M A G PARTS OF EIGENVhLUES
|
||
|
||
0.
|
||
|
||
0.
|
||
|
||
EIGEUVECTORS
|
||
|
||
Ucg,h
|
||
|
||
"cg,h
|
||
|
||
R -.16631E+00
|
||
|
||
-.66433E+00
|
||
|
||
HWING(H) .1127OE-lR
|
||
0.
|
||
|
||
PHUGOIDD(P)
|
||
|
||
e62776E-01
|
||
|
||
-627768-61
|
||
|
||
DUTCH ROLL(DR) -r12986E+00 -.12986E+00
|
||
|
||
.28606€+00 -.28606E+00
|
||
|
||
.66800E+00 -.66800f+OO
|
||
|
||
SHORT PERIOD(SP1
|
||
|
||
-.54060€+00
|
||
|
||
-.54060E+00
|
||
|
||
wcg,h -.71209E+OO
|
||
|
||
h ' -.95506E-01
|
||
|
||
h ' e97492E-02
|
||
|
||
I .36125F-01
|
||
|
||
h ' .10795€+0O
|
||
|
||
Oh -.12419E-01
|
||
|
||
*h -.399718-01
|
||
|
||
S .71857€-01 -.57018E+00
|
||
|
||
H e1290PE-17
|
||
|
||
~26637E-17 -rSPSC7€-18
|
||
|
||
.32664€-20
|
||
|
||
-.425k9E-25
|
||
|
||
.11257E-10
|
||
|
||
.1871SE-18
|
||
|
||
.42116€-20
|
||
|
||
*10000E+01
|
||
|
||
.98380€-01
|
||
|
||
-3969kE-02 -.69572E-02
|
||
|
||
-.76027E-02
|
||
|
||
-.63714E-02
|
||
|
||
-.113C7€-01
|
||
|
||
-.56697E-02
|
||
|
||
.2281?€-01
|
||
|
||
.24407€-01
|
||
|
||
.17297€-02
|
||
|
||
-.11951€-01
|
||
|
||
-4979CL-01 -.18702E-02
|
||
|
||
.Zl2791-02
|
||
|
||
-.247hlE-01
|
||
|
||
e23334E-01
|
||
|
||
.28407E+CO -.24127€-01
|
||
|
||
e17039E-01
|
||
|
||
.108985-01
|
||
|
||
e39045E-01
|
||
|
||
-.69323E+00
|
||
|
||
.1284ZE-01
|
||
|
||
.14830€-UE
|
||
|
||
.21678C-01
|
||
|
||
.78622€-02
|
||
|
||
63
|
||
|
||
TABLE VI.- Continued
|
||
|
||
(c) Values a t 60 k n o t s
|
||
|
||
- T R I M M E D VtLLlCITY
|
||
|
||
60.0 KNOTS
|
||
|
||
7 POINT FOPIIULA
|
||
|
||
30 ITERATIONS
|
||
|
||
INOEPENOENT YAPIA8LE TOTAL INCRCqENTS
|
||
|
||
~304EE-Gl a304EE-01
|
||
~3048E-01 -1745E-02 a1745E-02
|
||
.1745E-02 41745E-02 e1745E-02 .IW~E-OZ
|
||
|
||
5~
|
||
AIC
|
||
eom
|
||
t
|
||
|
||
.1745E-02 .1745€-02 .1745E-02 t 1 7 4 5 f -02
|
||
|
||
%,h "cg,h *cg,h Fh sh fh
|
||
|
||
A MATRIX
|
||
|
||
Ucg,h -.3330€-01
|
||
.6410€-02 -.1251€+00
|
||
.1269E-01 -3674E-02 -.5580E-02 0.
|
||
0. 0.
|
||
|
||
"eg,h -.47928-02 -.9340t-01 -.2696E-01
|
||
m4809E-03 -.1469E-02
|
||
-3119E-01
|
||
0.
|
||
0. 0.
|
||
|
||
"c8.h -.1466E-C.1 -.1445€-01 -.7800E+OO
|
||
,50336-02 -.1098E-01
|
||
nlE71E-OZ 0.
|
||
(1.
|
||
0.
|
||
|
||
h ' -.8590E-OZ -r1637E+01 -.5264€-01 -.9786E+00
|
||
.1196E+00 .lZEBE-Ol *1000E+01
|
||
0.
|
||
0.
|
||
|
||
h ' .1939E+01 -.8464E+00 .3092E+02 -.1317E+01 -.2723E+00 -.5417E-Ol e1289E-02 .9996€+00 -.2719E-01
|
||
|
||
h ' .2016€-02 -.3037E+OZ -.1117€-02 .2433E*OO .1300E-03 -.5570E+GO -.4743F-01 .2716€-01 .1001E*01
|
||
|
||
h ' ,27141-07 .9792E+Ol .2661E+00 .llOZE-06 .1770E-08 -.2561E-06 0. 0. 0.
|
||
|
||
h ' -.9795E+01 -.lZbZE-Ol
|
||
.4646E+00 -.741ZE-21 -.1959E-20
|
||
.1059€-19 0. 0.
|
||
0.
|
||
|
||
.h' 1.33561-20 -.9036€-21 -.Z582E-19 -.7+1ZE-Zl -.1959€-2U
|
||
.1059E-19 0. 0. 0.
|
||
|
||
e.h cg,h
|
||
*cg,h ph ?h h ' h eh *h
|
||
|
||
E MATRIX
|
||
|
||
BIC
|
||
.103@Ei02 .4378E+00 .Z248E+02 -.1322€+00 -.3564E+U1 .1022E-01 0. 0. 0.
|
||
|
||
4C
|
||
e5083E-05 .9800E+01 ,1866E-03 .2017E+02 .2530€-05 .1192€+01 0. 0. I..
|
||
|
||
eom
|
||
-.4717E+01 -.1391E+00 -.lU34€+03
|
||
.2833E+Ol -.6393E+GO
|
||
.5376€+01 0.
|
||
0. 0.
|
||
|
||
ect
|
||
-.1668E+00 .44781+01 e3579E-01 -2117E101 .2769E-01
|
||
-.4560E+01 0. 0. 0.
|
||
|
||
RF.AL PARTS O F EIGENVALUES
|
||
|
||
ROLL00
|
||
|
||
HEADING(H)
|
||
|
||
-.95639€+00
|
||
|
||
-.68986E-20
|
||
|
||
IPAG PARTS OF EIGENVALUES
|
||
|
||
0.
|
||
|
||
0.
|
||
|
||
. EIGENVECTORS "cg h
|
||
|
||
"c%,h
|
||
|
||
R -.74926E-01
|
||
|
||
-.3342RE+00
|
||
|
||
SPIW(S) e56569E-01
|
||
0.
|
||
|
||
PHUGOID(P)
|
||
|
||
.27343E-01
|
||
|
||
a27343E-01
|
||
|
||
SHORT PERIOD(SP)
|
||
|
||
-.h0458€+00
|
||
|
||
-.60458€+00
|
||
|
||
.27284E+00 -.27284E+00
|
||
|
||
.57861E+00 -.57861E+00
|
||
|
||
DUTCH ROLL(DR)
|
||
|
||
-.33015E+OO
|
||
|
||
-a33015€+00
|
||
|
||
a98819Et00 -.96819E+00
|
||
|
||
"cg,h -.925\)9E+tO
|
||
|
||
h ' -.10735E+OU
|
||
|
||
h ' .35915E-02
|
||
|
||
h ' .3333@€-01
|
||
|
||
h ' .11390E+00
|
||
|
||
h ' -.47007E-O2
|
||
|
||
h ' -.34782€-01
|
||
|
||
64
|
||
|
||
TABLE VI.- Concluded
|
||
|
||
(d) V a l u e s a t 90 k n o t s
|
||
|
||
. TRlHflEO V E L O C I T Y
|
||
|
||
90.0 KNOTS
|
||
|
||
7 POINT FORMULA
|
||
|
||
30 ITERATIONS
|
||
|
||
INDEPENOENT VARIABLE TOTAL 1NCREMENTS
|
||
|
||
.3048€-01
|
||
30rBE-01 .304BE-01 a 1 7 45E-U2 .174SE-(rZ .1745E-O2 m1745E-02 -1745E-02 .1745€-(12
|
||
|
||
m1745E-02 .1745f-02 47456-02 .17458-02
|
||
|
||
A MATRXX
|
||
|
||
Ucg.h
|
||
-.-.4276E-01 -5430E-02 7655i-0 1
|
||
|
||
-. "cg.h
|
||
-.5663E-02
|
||
1 2 3 3 E +00 -.4154t-01
|
||
|
||
. i i s a ~ - i ~ i .15*6--Ul
|
||
|
||
.3325--72
|
||
|
||
-.3643 .--de
|
||
|
||
-.4 397- -02
|
||
|
||
.3452f-<l
|
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65
|
||
|
||
.- TABLE V I 1 THEORETICAL AND MEASURED FREQUENCIES
|
||
OF LOAD MOTIONS
|
||
|
||
Mode
|
||
Vertical bounce Longitudinal pendulum L a t e r a l pendulum Longitudinal rocking Lateral rocking
|
||
|
||
Frequency
|
||
|
||
Theoretical, Hz
|
||
|
||
Measured,
|
||
KZ
|
||
|
||
1.0
|
||
|
||
1.2
|
||
|
||
.083
|
||
|
||
.097
|
||
|
||
-083
|
||
|
||
.091
|
||
|
||
.58
|
||
|
||
* 74
|
||
|
||
1.1
|
||
|
||
1.4
|
||
|
||
66
|
||
|
||
k naJ
|
||
67
|
||
|
||
$4
|
||
a,
|
||
U
|
||
a
|
||
0 v
|
||
ad
|
||
d
|
||
ca,
|
||
$4
|
||
u 0
|
||
68
|
||
|
||
Manual and automatic c o n t r o l system equations (12) to (16)
|
||
(c) Control system model. F i g u r e 1.- Continued.
|
||
69
|
||
|
||
W
|
||
cg,h
|
||
|
||
U gust,h
|
||
).
|
||
V gust,h
|
||
I_.___)
|
||
W gust,h *
|
||
|
||
Uwind,h +
|
||
Vwind,h *
|
||
w
|
||
wind,h *
|
||
|
||
Rotor equations (17) to ( 4 6 ) with
|
||
|
||
main-rotor parameters
|
||
|
||
- xr,hm
|
||
r' ,hm
|
||
_____)
|
||
- r' ,hm
|
||
______)
|
||
r' ,hm
|
||
M r,hm
|
||
____)
|
||
- Nr,hm
|
||
P
|
||
U as,h
|
||
|
||
V as,h
|
||
_____)
|
||
A Was h
|
||
|
||
'Tm
|
||
_____)
|
||
Tm
|
||
_.___)
|
||
x
|
||
m
|
||
_____)
|
||
m '
|
||
_____)
|
||
|
||
( d ) Main-rotor (subscript m) m o d e l . Figure 1.- Continued.
|
||
|
||
70
|
||
|
||
"c5z.h
|
||
|
||
Ugust,h
|
||
|
||
V gust,h
|
||
c
|
||
W
|
||
gust,h
|
||
- U wind, h
|
||
- V
|
||
- wind,h
|
||
|
||
Rotor equations
|
||
(17) to ( 4 7 )
|
||
with tail-rotor parameters
|
||
|
||
'I-. ht
|
||
-
|
||
'r.ht L r ,ht
|
||
|
||
- _W_wi_n_d,_h _, h '
|
||
|
||
3r,ht
|
||
_____)
|
||
Nr,ht
|
||
|
||
h ' r
|
||
h
|
||
|
||
(e) Tail-rotor (subscript t) model. F i g u r e 1.- Continued.
|
||
71
|
||
|
||
(f) Engine dynamics and governor model.
|
||
- Figure 1. Continued.
|
||
72
|
||
|
||
U
|
||
as.h
|
||
|
||
u was h
|
||
|
||
Fuselage
|
||
|
||
aerodynamics
|
||
|
||
.-
|
||
Ah
|
||
_______+
|
||
|
||
equations (49) to (58), (86) t o (89);
|
||
|
||
figures
|
||
|
||
(5) t o (11)
|
||
|
||
(9) Fuselage aerodynamics model.
|
||
- Figure 1. Continued.
|
||
|
||
73
|
||
|
||
Ug u s t , &
|
||
|
||
Load
|
||
|
||
xR
|
||
|
||
___.____)
|
||
|
||
aerodynamics
|
||
|
||
V
|
||
gust,%
|
||
|
||
equations
|
||
|
||
W
|
||
gust,R
|
||
|
||
(90) t o (96)
|
||
|
||
-. Uwind, R
|
||
_______)
|
||
Vwind, R
|
||
Wwind R PR
|
||
|
||
N"
|
||
|
||
c
|
||
|
||
( h ) Load aerodynamics model. F i g u r e 1.- Continued.
|
||
|
||
74
|
||
|
||
Loadground contact equations
|
||
to (66)
|
||
|
||
__I___)
|
||
ZC,R
|
||
MC.R NC,R
|
||
|
||
( i )Load-ground c o n t a c t model. F i g u r e 1.- Continued,
|
||
|
||
75
|
||
|
||
Load suspension
|
||
system equations (67) t o (77)
|
||
-
|
||
‘h
|
||
|
||
M t,h
|
||
N t,h
|
||
|
||
‘t,Q
|
||
|
||
(j) Load suspension model.
|
||
- Figure 1. Continued.
|
||
|
||
76
|
||
|
||
zLh CMh CNh
|
||
|
||
Equations of motion with helicopter parameters (78) t o (85)
|
||
|
||
fk) Helicopter e q u a t i o n s of motion. F i g u r e 1.- Continued.
|
||
|
||
77
|
||
|
||
CFx.Q
|
||
CFY, Q CF
|
||
z,Q
|
||
______+
|
||
C=R
|
||
|
||
Equations of motion with load parameters (78) to (85)
|
||
|
||
( 2 ) Load e q u a t i o n s of motion. Figure 1.- Concluded.
|
||
|
||
78
|
||
|
||
k
|
||
al
|
||
79
|
||
|
||
(a) Body axes.
|
||
X W
|
||
|
||
(b) Shaft axes.
|
||
|
||
(c) Control axes.
|
||
|
||
(d) Flapping angles.
|
||
|
||
F i g u r e 3.- H e l i c o p t e r body axes, s h a f t axes, c o n t r o l axes, and flapping aogle definitions.
|
||
|
||
80
|
||
|
||
\Helicopter cable attachment point
|
||
(*haye’’ha, e’ =ha, e I
|
||
Z e (Down) Figure 4.- Load suspension cable a n g l e d e f i n i t i o n s .
|
||
81
|
||
|
||
7.5
|
||
s .o
|
||
2.5
|
||
D
|
||
-2.5
|
||
-5 .o
|
||
-7.5 -10.0
|
||
Figure 5.- Fuselage incremental lift as a function of a n g l e o f attack.
|
||
82
|
||
|
||
I
|
||
|
||
-2
|
||
|
||
I x 10'
|
||
|
||
F i g u r e 6.- Fuselage i n c r e m e n t a l l i f t as a f u n c t i o n of s i d e s l i p angle.
|
||
|
||
83
|
||
|
||
7-
|
||
|
||
~-I N 6
|
||
|
||
-8
|
||
|
||
i”
|
||
e L -12
|
||
|
||
-16
|
||
|
||
-1
|
||
|
||
-9
|
||
|
||
x 10‘
|
||
|
||
Figure 7.- Fuselage s i d e f o r c e as a f u n c t i o n of s i d e s l i p angle.
|
||
|
||
84
|
||
|
||
I x LO’ F i g u r e 8,- Fuselage r o l l i n g moment as a f u n c t i o n of s i d e s l i p angle.
|
||
85
|
||
|
||
m E
|
||
|
||
-6
|
||
|
||
I
|
||
|
||
!I-
|
||
|
||
-24
|
||
|
||
-30
|
||
|
||
-32
|
||
|
||
-24
|
||
|
||
A -8
|
||
|
||
8
|
||
|
||
16
|
||
|
||
24
|
||
|
||
Figure 9.- Fuselage incremental p i t c h i n g moment as a f u n c t i o n of angle of a t t a c k f o r d i f f e r e n t v a l u e s of incidence a t t h e t a i l .
|
||
|
||
86
|
||
|
||
F i g u r e 10.- Fuselage incremental p i t c h i n g moment as a function of s i d e s l i p angle.
|
||
87
|
||
|
||
h
|
||
|
||
L
|
||
|
||
0
|
||
|
||
1 x 10'
|
||
|
||
Figure 11.- Fuselage yawing moment as a f u n c t i o n o f s i d e s l i p a n g l e f o r d i f f e r e n t v a l u e s of a n g l e of attack,
|
||
|
||
88
|
||
|
||
89
|
||
|
||
trl
|
||
In
|
||
0 rl I
|
||
a,
|
||
u) I
|
||
4
|
||
4
|
||
I a,
|
||
[o
|
||
0 4 V a,
|
||
rl
|
||
0
|
||
;
|
||
0
|
||
V
|
||
rl
|
||
0 k 4J
|
||
d
|
||
8
|
||
90
|
||
|
||
RESET
|
||
|
||
IDLE
|
||
|
||
RELEASE ERASE
|
||
|
||
PRINT RELEASE
|
||
|
||
( a ) Mode c o n t r o l switches.
|
||
|
||
I DECIMAL (-) 1 POINT
|
||
|
||
(b) Data e n t r y keyboard.
|
||
|
||
(Address f i e l d )
|
||
|
||
(Magnitude f i e l d )
|
||
|
||
(Exponent f i e l d )
|
||
|
||
( e ) D i g i t a l decimal display. Figure 14.- Mode c o n t r o l , d a t a e n t r y , and d i g i t a l d i s p l a y
|
||
systems on s i m u l a t i o n control console.
|
||
91
|
||
|
||
92
|
||
|
||
93
|
||
|
||
94
|
||
|
||
95
|
||
|
||
Figure 19.- Simulator c o n t r o l system analog computer (on the l e f t ) .
|
||
96
|
||
|