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NASA Technical Memo1anfiPlrn81238
(NASA-TA-812 38) A HATHEXATICAL HODEL O f THE ca-53 HELICOPTER (NASA) 6 0 p HC ~ 0 4 A,O 1~
CSCL 0 1 C
G3/05
U n c las 29424
A Mathematical Model of the CH-53 Helicopter
William R. Sturgeon James D. Phillips, Ames Research Center, Moffett Field, California
I.la!ionaI Aeronautics and
S v x e Adrn~nistratior~
Ames Research Center M,)llott F~eidCaliforn~a34035
TABLE OF CONTENTS
SYMBOLS.................................
v
SUMMARY.................................
1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
. . . . MATHEMATICAL MODEL
. . . Coordinate Systems .
General Model Description
. . Fuselage Aerodynamics . . . . . . . Rotor Models
Engine and Governor Model
. . . . . . Control System . . . Equations of Motion
MODELVALIDATION . . . . . .
. . . . . Time History Comparisons
Pilot Comments
...
. . .
. . .
.. .
...
. . .
.
. .
. ..
...
...
...
.. .
.. .
...
...
.. .
...
.. .
...
...
...
. . .
19 19 20
CONCLUSIONS...............................
21
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
FIGURES.................................
27
iii
SYMBOLS
A,# B~ Alafcs~Blafcs
lateral and longitudinal cyclic control, swashplate angle, commands
lateral and longitudinal cyclic AFCS control, swashplate angle, commands
lateral and longitudinal cyclic control, swashplate angle, in shaft axes
rotor blade lift-curve slope small angle used to define rotor drag force coning angle longitudinal and lateral flapping angles in control axes longitudinal and lateral flapping angles in shaft axes lateral specific force, positive in direction of Yh rotor blade tip-loss constant number of blades per rotor transformation matrix from Euler angle rates to angular
velocity in body axes transformation matrix from shaft to control axes transformation matrix from Earth to body axes transformation matrix from wind tunnel to body axes torque coefficient transformation matrix from body to shaft axes thrust coefficient rotor side force coefficient blade chord fuselage drag in wind-tunnel axes flapping hinge offset
eki' ekt
'trim Ixlat
fuselage and t a i l angle-of-attack corrections due t o main r o t o r downwash
main r o t o r downwash f a c t o r gas generator governor gain acceleration of gravity rotor drag force altitude a l t i t u d e command i n t e g e r i n d i c a t i n g AFCS engaged integer indicating altitude-hold engaged b l a d e moment of i n e r t i a about f l a p p i n g a x i s i n e r t i a matrix of h e l i c o p t e r , i n body axes p o l a r moment of i n e r t i a of t h e main r o t o r integer indicating pilots feet off pedals moment of i n e r t i a of power t u r b i n e integer indicating turn coordination engaged integer indicating cyclic t r i m button released integer indicating l a t e r a l cyclic s t i c k displacement from
zero force t r i m position flow incidence a t the horizontal tail fixed i n c i d e n c e of t h e h o r i z o n t a l t a i l rotor side force rnain r o t o r s h a f t compliance main r o t o r s h a f t damping p i t c h i n g moment c o e f f i c i e n t due t o main r o t o r t h r u s t power t u r b i n e governor gain cctnst:ant g a i n s i n c o ~ t r o lsystem
Qeng
body axes soments due t o angular v e l o c i t y body a x e s moments due t o f u s e l a g e acrodynantics body a x e s moments due : < ) r o t o r moments t r a n s m i t t e d a t t h e
hub s h a f t a x e s rnonents 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 t o t a l body a x e s moment!, due t o t h e r o t o r
body axes aerodynamic moments a c t i n g on t h e f u s e l a g e fuselage l i f t i n wind-tuunel axes
mass moment of r o t o r b l a d e
h e l i c o p t e r mass angular velocities in control ases
angular v e l o c i t i e s i n body a s e s
angular vclucitics in shaft nscs
aerodynamic torque a c t i n g on mnin r o t o r , p o s i t i v e i n direction opposite to rotation
aerodynamic torque a c t i n g on t a i l r o t o r , p o s i t i v e i n direction opposite to rotation
engine torque a c t i n g on t h e mnin r o t o r s h a f t and fuselilgc, p o s i t i v e value tends t o a c c e l e r a t e main r o t o r acd carisc f u s e l a g e t o yaw r i g h t
gas generator torque
r o t o r s h a f t torque a c t i n g on the fuselage dynamic pressure
rotor radius
Laplace operator
thrust time delay in primary servo transfer function
t r u e a i r s p e e d of h e l i c o p t e r c.g. i n body a x e s
,e a i r s p e e d of r o t o r hub i n c o n t r o l a x e s
[ U BV B w] CSB e
,., [ua V a wICp,
i n e r t i a l velocity of helicopter c.g. i n Earth axes 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. i n body axes
l u s v b w 1 8 U S ~ , h gust v e l o c i t y i n body axes
[ U Sv. ~ 1 ,
t r u e airspeed of t h e r o t o r hub i n s h a f t axes
[ U *V B W1wind, h wind v e l o c i t y i n body axes total true airspeed
, IX, u, Z I f ,
p i l o t c o n t r o l displacements of c o l l e c t i v e s t i c k , 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 s t i c k , end pedals from nominal positions. (Positive displacements cause climb, r o l l right, p i t c h down, and yaw l e f t , r e s p e c t i v e l y . )
body a x i s f o r c e s due t o f u s e l a g e aerodynamics
[S, Y, Z ] r , h [s, Y, 21C6, 0
[ x * Y. Z I ~ h~ ,
body a x i s f o r c e s due t o t h e r o t o r inertial position in Earth axes p i l o t s eye l o c a t i o n i n body axes
Ix. Y s 21r, h
r o t o r hub l o c a t i o n i n body axes
Y, [ X I zlwt, h
Ywt
wind-tunnel mounting point i n body axes fuselage side force i n wind-tunnel axes fuselage angle of a t t a c k and s i d e s l i p
fuselage local angle of attack
rotor orientation angle
- r o t o r lock number, p a c ~ ' Ib
damping r a t i o i n primary servo t r a n s f e r function
t a i l r o t o r c o l l e c t i v e p i t c h command
tail rotor collective pitch
main r o t o r c o l l e c t i v e p i t c h AFCS command
main r o t o r c o l l e c t i v e p i t c h command
viii
'trim 's
['r 8 , $1,
main r o t o r c o l l e c t i v e p i t c h
e f f e c t i v e value of t a i l r o t o r coflective pitch
longitudinal shaft tilt angle
t a i l r o t o r c o l l e c t i v e p i t c h AFCS command
blade twist angle, from r o o t t o t i p
blade pitch a t 314 radius
i n f law r a t i o
tip-speed r a t i o
induced inflow r a t i o
atmospheric densiry
- r o t o r
solidity,
be
nR
time constant i n primary servo transfer function
engine time constant
time corstants i n control system
i n £low time constant
t r i m value of QI
lateral shaft tilt angle
Euler angles, r e l a t i n g body and Earth axes
trim value of $
wind-tunnel yaw angle
rotor angular velocity
power turbine angular v e l o c i t y
commanded r o t o r angular velc c i t y
natural frequency i n primary servo transfer function
Subscripte:
C
e
h m
8
t
wt Superscripts: T ('1
control axes Earb,.axes body axes nain rotor shaft axes tail rotor wind-tunnel axes
matrix transpose time derivative of ( )
.
I
h
.!
,
, i
/ -
A MATHEMATICAL MODEL OF THE CH-53 HELICOPTER
W i l l i a m R. Sturgeon and James D. P h i l l i p s
Ames Research Center
SUMMARY
A mathematical model s u i t a b l e f o r r e a l - t i m e s i m u l a t i o n of t h e CH-53 h e l i copter is presented. This model, which is based on modified nonlinear c l a s s i c a l r o t o r theory and nonlinear fuselage aerodynamics, w i l l be used t o support
terminal-area guidance and navigation s t u d i e s on a fixed-base simulator. V a l i d a t i m i s achieved by compering t h e model response with t h a t of a s i m i l a r a i r c r a f t and by a q u a l i t a t i v e comparison o f t h e h a n d l i n g c h a r a c t e r i s t i c s made by experienced p i l o t s .
INTRODUCTION
Terminal-area guidance and navigation helicopter research is t o be conducted a t Ames Research C e n t e r , P r i o r t o a c t u a l f l i g h t t e s t s , advanced concepts and procedures w i l l be evaluated using a piloted f l i g h t simulator. This simulator f a c i l i t y consists a£ a "fixed-base" cockpit, configared t o that of t h e CH-53 ( f i g . l ) , and a Sigma 9 C l g i t a l computer. O p e r a t i o n of t h i s simul a t o r r e q u i r e s t h e u s e of a CH-53 mathematical model t h a t can o p e r a t e i n r e a l time on t h e Sigma 9 h o s t computer.
Helicopter models range i n complexity from l i n e a r models, which a r e v a l i d near one particular f l i g h t condition, t o nonlinear blade-element models which account f o r complex r o t o r flow conditions and a r e used over the e n t i r e f l i g h t regime. A model of intermediate complexity, which meets simulation rcquirements f o r terminal-area guidance and navigation s t u d i e s , i s hased on quasis t a t i c r o t o r r e p r e s e n t a t i o n s . A CH-53 model of t h i s l a t t e r t y p e i s p r e s e n t e d .
The h e l p of t h e following persons i n o b t a i n i n g t h i s mathematical model is acknowledged: Dean E. C c ~ p e r ,Thomas H. Lawrence, and P h i l Gold of S i k o r s k y Aircraft Division of United Technologies, S t r a t f o r d , Connecticut; and J. D. Shaughnessy of Langley Research Center. The model was programmed on t h e Sigma 9 c o m p u ~ e rby B o r i s Voh of Computer S c i e n c e Corporation. V a l i d a t i o n was performed w i t h t h e h e l p of George Tucker and Ron Cerdes o i Ames Research C e n t e r .
PATHEMATICAL MODEL
The h e l i c o p t e r mathematical model i s d e f i n e d i n terms of submodels of t h e fuselage aerodynamics, rotor systems, engine and governor, and control systcm. The r e l a t i v e r e l a t i o n s h i p of t h e s e submodels is discussed i n t h e s e c t i o n e n t i t l e d "General Model D e s c r i p t i o n " which p r e c e d e s d e t a i l e d d e s c r i p t i o n s
each submodel. The submodela are d e f i n e d i n torma of f o r c e r , moments, and
motion expressed i n t h e following coordinate systems which a r e used i n the development of t h e mathematical model ( f i g . 2).
Coordinate Systems
1. Earth 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 a x i s p o i n t i n g n o r t h , ye p o i n t i n g e a s t ( f i g . 2 ( a ) ) .
2. Helicopter body axes, s u b s c r i p t h: O r i g i n a t t h e c e n t e r o f g r a v i t y
(c.g.), xh a x i s forward i n t h e plane of symmetry and p a r a l l e l t o t h e waterl i n e , zh a x i s down i n t h e plane of symmetry ( f i g . 2 ( a ) ) .
3, S h a f t a x e s , s u b s c r i p t s: O r i g i n a t t h e r o t o r hub, xs a x i s r o t a t e d
through t h e l o n g i t u d i n a l s h a f t t i l t a n g l e Bs about t h e yh a x i s , ys a x i s
rotated through the l a t e r a l shaft tilt angle
about the xs a x i s , zs
axis coincident with the rotor shaft (fig. 2(b)), This applies t o both the
main and t a i l r o t o r s .
4. Control axes, subscript c: Origin a t the rotor hub, zc a x i s directed toward t h e fuselage along t h e a x i s of no-feathering (an a x i s perpendicular t o t h e swashplate), xc a x i s p o i n t s i n t o t h e r e l a t i v e wind s o t h a t t h e y, component of t h e r e l a t i v e witld i s zero ( f i g . 2 ( c ) ) , T h i s a p p l i e s t o both t h e main and t a i l r o t o r s .
5. Wind-tunnel axes, subscript w t : Origin a t t h e wind-tunnel mounting
p o i n t , xwt a x i s p o i n t i n g i n t o t h e r e l a t i v e wind, zwt down and perpendicular t o t h e r e l a t i v e wind.
General Model D e s c r i p t i o n
The helicaptt!r model i s defined i n terms of t h e following submodels:
1. Fuselage aerodynamics model: The f u s e l a g e aerodynamics model d e f i n e s nonlinear l i f t , drag, and s i d e forces a s w e l l a s 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 angular v e l o c i t y , and dynamic pressure.
2. Rotor model: nonlinear models f o r t h e main r o t o r and t a i l r o t o r d e f i n e t h r u s t , drag, and s i d e f o r c e s a s w e l l a s hub f o r c e and moments representative of a r t i c u l a t e d rotors over a wide range of airspeeds through hover t o rearward and sideward f l i g h t . The r o t o r models account f o r v a r i a b l e inflow velocity, variable rotor speed, blade t w i s t , t i p loss, blade coning, blade f l a p p i n g , f lapping-hinge o f f set, and t a i l - r o t o r 6 h!-nge.
3. Engine model: An engine and governor model adapted from a heavy l i f t helicopter simulation provides a r e s t i s t i c time delay between aerodynamic rotor torque and t h e r e s u l t i n g r e a c t i o n torque a p p l i e d t o t h e fuselage. The model i n c l u d e s t h e e f f e c t s of gall t u r b i n e , 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 compliance.
4, Control 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
p i l o t ' s c y c l i c c o n t r o l , c o l l e c t i v e c o n t r o l , 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 . An automatic f l i g h t c o n t r o l system (AFCS) i s included which provides h e l i c o p t e r rate and a t t i t u d e s t a b i l i e a t i o n rn r o l l , p i t c h , and yaw.
Wind and gust i n p u t s t o t h e h e l i c o p - e r modal a r e provided, a s well a s t:: p i l o t c o n t r o l i n p u t s . A l l 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 a r e output8 of t h e f u s e l a g e aerodynamics and t h e r o t o r systems s ~ b m o z l e l s ~F u s r i . ~ g e f o r c e s and moments are c a l c u l a t e d i a wind-tunnel axes and transformed t o body axes. Rotor f o r c e s are c a l c u l a t e d i n c o n t r o l axes and transfonned t o body a x e s , and t h e r o t o r moments a r e c a l c u l a t e d i n s h a f i axes and transfo7med t o body axes.
The equations of motion use t h e t o t a l f o r c e s and moments, i n body a x e s , t o c a l c u l a t e t h e t r a n s l a t i o n a l and a n g u l a r body a x i s a c c e l e r a t i o n s . The t r a n s l a t i o n a l a c c e l e r a t i o n is i n t e g r a t e d t o give body i n e r t i a l v e l o c i t y which i 8 transformed t o Earth axes and i n t e g r a t e d t o o b t a i n h e l i c o p t e r p o s i t i o n . The angular a c c e l e r a t i o n is i n t e g r a t e d t o give body angular v e l o c i t y , which is transfonned t o Euler angular velocity and integrated t o obtain helicopter attitude.
The r e l a t i v e r e l a t i o n s h i p of t h e submodels i s shown i n Figure 3 ( a ) , and t h e i n p u t s and o u t p u t s of each submodel a r e shown i n f i g u r e s 3(b) through 3(g). The model parameters a r e given i n Table 1.
Fuselage Aerodynamics
The f u s e l a g e aerodynamic d a t a a r e given i n both equation and t a b u l a r form. The f o r c e s and moments a r e given i n wind-cunnel axes i n terms of l o c a l angle of a t t a c k , l o c a l a n g l e of i n c i d e n c e a t t h e t a i l , s i d e s l i p a n g l e , body angular v s l o c i t y , and dynamic pressure.
Airspeed i n body axes- The h e l ' c o p t e r a i r s p e e d is expressed i n terms of i t s i n e r t i a l v e l o c i t y and t h e wind v e l o c i t y a s
cg, h
gust, h
wind, h
The free-stream angle of a t t a c k and s i d e s l i p a n g l e a r e defined a s
and
r e s p e c t i v e l y , where
-h (Ju2 f v2 4 wZ)a e , h
and t h e free-stream d y n a ~ r i cp r e s s u r e i e
Main r o t o r downwash e f f e c t - The e f f e c t of t h e main r o t o r downwash on t h e l o c a l a n g l e o f a t t a c k is accounted f a r by t h e r o t o r downwash f a c t o r ( r e f . 1):
CTms A, and pm a r e r o t o r parameters defined i n t h e following s e c t i o n . The fuselage local angle of attack is
and the local incidence a t the t a i l is
where ekt and ekf a r e e m p i r i c a l constants. The wind-tunnel yaw a n g l e is
Fuselage f o r c e s and moments i n wind tunnel axes- The f u s e l a g e f o r c e s and moments i n wind-tunnel axca a r e provided through t h e wind-tunnel d a t a given i n f i g u r e s 4 through 13. These curves a r e e n t e r e d with t h e fuselage l o c a l angle of a t t a c k (eq. ( 7 ) ) , l o c a l i n c i d e n c e a t t h e t a i l (eq. (8)), wind-tunnel yaw angle (eq. ( 9 ) ) ' and dynamic pressure (eq. ( 5 ) ) a s determined from t h e equations noted.
Since the wind-tunnel data do not cover the f u l l range 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 v 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 l i m i t s of t h e s e angles f o r which d a t a a r e given. This assumption should not s i g n i f i c a n t l y degrade t h e model performance, f o r l a r g e v a l u e s of t h e above a n g l e s g e n e r a l l y occur a t low a i r s p e e d s where f u s c l s g e forces and moments a r e r e l a t i v e l y small.
The f u s e l a g e f o r c e s and moments a r e determined as follows:
where Also,
-- +it ADlwt )MI sin (ft2? Q
Transformation of fuselage aerodynamic forces to b?dy axes- The fuselage aerodynamic forces are transformed fromvind tunnel to body axes.
r f ufl cos a cos Bf -cos a sir^ Bf
f
-sin
Trclneformation of fuselage aerodynamic moments to body axes- The total fuselage aerodynamic moments include the basic wind-tunnel moments, additional moments due to the wind-tunnel mounting point being offset From the c.g., damping due to angular velocity, and rotor downwash on the tail. In body axes these moments are
where
....,
and Tm is t h e main r o t o r t h r u s t . Both t h e damping equation a..d r o t o t downwash moment c o e f f i c i e n t were obtained from a n unpublished- Sikorsky A i r c r a f t report,
The i n p u t s and o u t p u t s of t h e f u s e l a g e aerodynamic model a r e shorn i n figure 3(b).
Rotor Models
The r o t o r f o r c e s and moments a r e c a l c u l a t e d u s i n g nonlinear c l a s s i c a l rotor theory, specifically a modified Bailey representation used i n reference 1 and discussed i n r e f e r e n c e s 2 through 5. Important a s p e c t s of t h i s rocor model a r e
1. Uniform inflow over t h e r o t o r d i s k i s assumed
2. Compressibility ac:l
effects are neglected
3. Lagging motion of t h e r o t o r blades is neglected
4 . Only f i r s t harmonic motion of t h e r o t o r blades is considered
5 . The b l a d e coning and f l a p p i n g angles a r e assumed q u a s i - s t a t i c
This r e l a t i v e l y simple r o t o r model i s used t o f a c i l i t a t e i t s u s e i n a real-time simulation. This model i s v a l i d f o r forward f l i g h t t o about 120 knots, hover, rearward and sideward f l i g h t t o about 20 knots, a u t o r o t a t i o n s , and large-angle maneuvers. Although t h e model i s adequate f o r guidance and navigation s t u d i e s a t a i r s p e e d s g r e a t e r than 120 knots, i t s handling c h a r a c t e r i s t i c s f i d e l i t y is degraded due t o t h e increasing e f f e c t s of compress i b i l i t y and t h e r e v e r s e flow region.
The following d i s c u s s i o n a p p l i e s t o both t h e main and t a i l r o t o r s , except where noted. Specific application t o e i t h e r t h e main o r t a i l r o t o r i s indicated by t h e s u b s c r i p t s m o r t respectively.
Airrpeed of r o t o r hub i n c o n t r o l axes- The t o t a l a i r r p e e d of t h e r o t o r
hub, i n control axes, is required f o r calcolation of t h e moments, This airspeed i o i n i t i a l l y determined i n sbaf t
roto axee
r ,
forcee
using t
and he h
e
l
i
-
copter airopead end angular velocity, and then t r a n s f o m d t o control exes
wherr and
(13) as, h
cos 0,
6, s i n (s
+, 6, cos
0 cos 6, -sin +s
I-sin eS
cos 0, s i n 4,
cos os cos +S
is defined by equation (1). The airspeed a t the hub is t r a n s f e r r e d i n t o cont r o l axes using the rotor orientation angle
which is obtained using t h e d e f i n i t i o n of c o n t r o l axes, t h a t is
and using small angle approximations f o r t h e main r o t o r c y c l i c control inputs (swashplate angles), A: and B: (see f i g . 2 ( c ) ) ,
where
Cc1 s
cos B 0
sin B cos B
-A;
I B: cos 8 + A: s i n B
- A: cos 0 B: s i n B
1
7
Note t h a t the t a i l r o t o r does not have c y c l i c c o n t r o l r , and t h e r e f o r e t h e
correspondlug A: and Bi are zero. Rotor t i p speed and induced f l w r a t i o r - The rotor force8 and moments are
functions of t h e r o t o r t i p speed and induced inflow ratios, which a r e defined i n term of t h e hub airspeed i n c o n t r o l axes, a8
and
respectively. The induced inflow r a t i o v l a obtained by f i l t e r i n g t h e steady-state value of v. The r e s u l t i n g d i f f e r e n t i a l equation is
The time constant .rv is included t o account f o r t h e l a g associated with changes i n r o t o r inflow. Note t h a t t h e t h r u s t c o e f f i c i e n t CT, defined below, and inflow r a t i o h a r e functions of v, so t h a t equation (19) i s a f i r s t order nonlinear differential equation,
- Rotor t h r u s t and coning angle i n c o n t r o l axes- The r o t o r t h r u s t , i n con-
t r o l axes, and t h e 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 the. tip.-sp.eed r a t i r according- t o t h e following r e l a t i o n s obtained from r e f e r ences 1 and 4:
and where
and 8, i s the e f f e c t i v e blade p i t c h angle a t t h e root ( c o l l e c t i v e p i t c h
angle); and
is the blade t w i s t . Note t h a t a tenn involving the blade
mass moment i n equaticn (22) of reference 4 has been neglected i n equation (21)
above, f o r i t contributes l e a s than 0.5' and is essentiaLly constant (ref. 1).
8
Rotor f l a p p i n g angles i n c o n t r o l - axe%- The c a l c u l a t i o n of t h e r o t o r f l a p ping angles requires the fuselage angular velocity expressed i n control axes:
where t h e transformation matrices a r e defined by equations ( 1 4 ) and (16).
The f l a p p i n g a n g l e s a l and bl ( f i g , 2(d!) are c a l c u l a t e d i n c o n t r o l a x e s according t o formulas obtained from reference 1,
and
For a blade with 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 replac-
i n g the 8, appearing i n t h e references with t h e p i t c h a t 314 r a d i u s u ~ . , ~ ,
and dropping 0, w i l l have a negligible e f f e c t on t h e o v e r a l l solution ( r e f . 1 The p i t c h a t 314 r a d i u s is
Rotor drag f o r c e i n c o n t r o l axes- The downwind component of t h e r o t o r force, i n control axes, is
where t h e small angle a' i s a function of t h e u s e f u l and induced r a t o r drag-
l i f t power and inflow ( r e f . l ) , but 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 -
ping angle a l , An expression f o r a ' , which i n c l u d e s t h e e f f e c t s of f u s e l a g e
,
angular velocity (ref. l ) , is
I
Rotor s i d e f o r c e i n c o n t r o l axes- The r o t o r s i d e f o r c e , i n c o n t r o l axes is
2.nit equation, derived from equation (3) i n r e f e r e n c e 3, n e g l e c t s angular -relo i t y terms and u s e s t h e previous assumption involving t h e p i t c h a t 314 r e d i n s , go. 75.
Transformation of r o t o r f o r c e s t o body axes- The r o t o r f o r c e s i n c o n t r o l axes, given by equations (20), (27), and (?9), are transformed t o body axes,
~a'heret h e trclnsformation m a t r i c e s a r e defined by equations (14) and (16). Rotor torque i n s h a f t axes- The r o t o r aerodynamic torque equation ( r e f . 1 ) .
which-accounts f o r both 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 , i s
The aeroc:ynamic t -,-.n,uea c t i n g on t h e main r o t o r QamB i s c a l c u l a t e d using main r o t o r parameters i n (32) and (33). The torque applied t o t h e f u s e l a g e by t h e r ~ i nr o t o r t f u n c t i o n of ,Q and i s determined by t h e engine and governor modal :
. T , t h e main r o t o r , Q8 i s equal t o t h e engine torque Qen The t a i l r o t o r
torque Pat, calr llated using t a i l rotor parameters i n (327 and (33). is
assumed t o a c t d i r e c t l y on t h e f u s e l a g e s o t h a t Qs is equal t o Qat.
Rotor hub momenta j.n a h a f t axes- The hub momante due t o f l a p p i n g angle
of f a e t a a r e c a k u l a t a d i n s h a f t axes according t o formulae obtained from reference 1. These formulas r e s u l t from n e g l e c t i n g higher o r d e r terms i n equations presented i n r e f e r e n c e 3:
where
hub, e
B
are the flapping angles i n shaft axes.
Transformation of r o t o r moments t o body axes- The r o t o r moments i n s h a f t axes, given by equations (34) and (35). a r c transformed t o body axes:
hub, h
hub, s
The t o t a l moments applied t o t h e fuselage by t h e r o t o r i n c l u d e t b e hub mornents (37) and a d d i t i o n a l moments due t o t h e l o c a t i o n of t h e hub r e l a t i v e t o t h e helicopter c.g. :
hub, h
where t h e r o t o r f o r c e s are defined by equation (31).
Tail rotor
hinge e f f e c t - The above model r e p r e s e n t s a r o t o r without
a d e l t a - t h r e e (63) hinge, such a s t h e main r o t o r of a CH-53, However, t h e
t a i l r o t o r has a 69 hinge, so t h a t b l a d e coning and flapping a f f e c t blade
p i t c h ; t h e r e f o r e , t h e model i s madif i e d accordingly. Assw.ning t h e changes i n
blade p i t c h due t o flapping a r e small comparcd with those due t o coning,
- Oat = 8c t ao t t a n
where BCt is the value of Note t h a t t h e c m i n g angle
c o l l e c t i v e p i t c h cornmonded by t h e c o n t r o l system,
a,, equation (ill), i s n function of eo; a s a
result, equations simultaneously.
(21)
and
(39),
far
the
tail
rotor,
sh,ould
be
solved
The i n p u t 8 and o u t p u t s of t h e r o t o r modele trre shown i n f i g u r e 8 3kc) and 3(d).
Engine and Governor Modal
An engine and governor model is i n c l u d e d . t o provide a realistic time
delay between aerodynamic r o t o r torquu and the r e s u l t i n g reaction torque applied t o t h e fuselage. This model was adapted from one used by Boeing Vertol
( r e f . I ) ; although i t is nor a model of a CH-53 engine, it does provide t h e
desired effects. This model, which includea t h e eEfecta of a gas t u r b i n e , 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 compliance, uses t h e r e f e r e n c e r o t o r speed R, and
t h e main r o t o r aerodynamic torque Qaln (eq. (32)) t o c a l c u l a t e t h e angular v e l o c i t i e s of the main and t a i l r o t o r s and t h e engine torque. Note that t h e engine torque Qeng is equal t o t h e main r o t o r s h a f t torque Qs i n equst i o n (34).
The c o n s t a n t s Kc and Kd represent t h e meln r o t o r s h a f t complinr~ceand dampi n g , r e s p e c t i v e l y ; n o t e t h a t t h e l a t t e r Is required f o r computational s t a b i l f t y . The Q - , term i n the Qgen dfffr!rential equuti.on allows t h e model t o hold reason...~ l ycoirstant r o t o r a.peed under w l d d y varying aerodynamic torqucr3 (ref. 1).
The i n p u t s and outputs of t h e engine model a r e shown i n f i g u r e 3 ( e ) .
Control System The c o n t r o l system model, which includes t h e e f f e c t s of p i l o t i n p u t s , c o n t r o l c r o s s coupling, an automatic f l i g h t c o n r r o l system (AFCS), and servo a c t u a t o r s , dezines the main r o t o r colZective p i t c h Born, longitudinal and h t e r a l c y c l i c p i t c h B1 and A 1 , and t a i l r o t o r cclllective p i t c h command
Get. This model was obtained from an unpublished Sikorsky A i r c r a f t r e p o r t ,
where
- Xbol = xcol 2.54 cm
or equivalently
if Xcol > 2.54 cm
Xiol = X C o l g 1.0 in. or Xcol > 1.0 in.
or Xcol S 1.0 in.
and the term in parentheses is limited to the range of -0,0349 rad (-2.0") to M.419 red (+24.0°).
The pilot inputs, in equation (41), are the displacements of the pilot controls relative to a nomiaal position. These positions are shown in the
control rigging diagrams, figures l3(a)- 13(C) , as the zero displacement
positions. The force characteristics of the pilot controls are given in table 2.
AFCS inputs- The following features of the AFCS are not implemerted, directly, due to hardware limitations of the fixed-base simulator used in conjunction with this model:
1. Trim adjustments for various c. g. locations 2. Indicator of AFCS authority ueed
3. Supplemental controller which changes effective collective stick posit ion
4. "Open-loop" pedal spring
5. Lateral cyclic "stick pusher"
Effects of t h e m features t h a t are considered c r i t i c a l t o t h e anticipated flyi n g tasks are included by modifying t h e M C S model obtained fro;n Sikoreky
Aircraft.
The absence of t r i m adjustments is compansated f a r by placing t h e c.8. a t
fuselage s t a t i o n 332 s o t h a t t h e mathcrmatical model triats s t r a i g h t and l e v e l
, a t 90 knots, with miniopal AFCS contribution t o t h e longitudinal c y c l i c pitch;
that is BIaf
0, Probleras caused by t h e lack of information on AFCS
a u t h o r i t y u s d a r e a l l e v i a t e d by ( I ) increasing t h e l i m i t s on the AFCS c o n t r i -
bution t o t h e t a i l r o t o r p i t c h command Btafcs ( t a b l e 5); (2) removing Gtafcs
from t h e bracketed term i n equation (41), which i s limited; and (3) s e l e c t i o n
of t h e c.g. fuselage s t a t i o n discussed above. The e f f e c t s of t h e c o l l e c t i v e
s t i c k supplemental controller a r e not considered c r i t i c a l and, therefore, a r e
- not included. The "open-loop" pedal spring i s represented by the i n t e g r a l K23/ i n t h e Btafcs equation (62). The b a s i c C f f e c t s of t h e l a t e r a l cyclic "stfck pusher" a r e t o provide the p i l o t with a s t i c k force propartional
t o t h e deviation of r o l l a t t i t u d e from i t s t r i m value, and t o r e t u r n t h e
v e h i c l e t o i t s t r i m r o l l a t t i t u d e when t h e p i l o t r e l e a s e s t h e s t i c k . Since a
"control loader" is not a v a i l a b l e i n the fixed-base simulator, Implementat! on
of these e f f a t s required s e v e r a l changes t o t h e AFCS model; t h e changes a r e
described i n d e t a i l below.
I n t h e o r i g i n a l AFCS t h e r o l l t r i m r ~ f e r e n c ei s removed from t h e l a t e r a l channel, Alafcs i n equation (42), when t h e p i l o t places h i s f e e t on the pedals (activating a pressure s e n s i t i v e .-uiLch) p r i o r t o a l a t e r a l maneuver. I f t h e p i l o t r e l e a s e s l a t e r a l s t i c k pres-ure during t h e maneuver and keeps h i s
f e e t on the pedals, t h e " s t i c k pusher" moves t h e s t i c k so a s t o regain t h e r o l l trim reference a t t i t u d e . This c h a r a c t e r i s t i c i s obtained by removing t h e r o l l t r i m reference from Alafcs i n equation (42) only when t h e l a t e r a l s t i c k i s displaced 1.27 cm (0.5 i n , ) o r more from i t s zero f o r c e t r i m p o s i t i o n , Thus, t h e r o l l reference i s removed when t h e p i l o t , by d i s p l a c i n g t h e s t i c k l a t e r a l l y , i n d i c a t e s a d e s i r e t o maneuver; t h e reference i s regained when the pilot releases his control force, allowing the stick t o return t o its zero force position. The c o n t r o l forces provided by t h e " s t i c k pusher" during t h e maneuver a r e obtained by adding a b i a s proportional t o t h e r o l l deviation from
trim t o the l a t e r a l s t i c k displacement (see X i a t , eq, (42)). This causes the
steady-state r o l l a t t i t u d e deviation from trim t o be proportional t o l a t e r a l s t i c k displacement from t h e zero force t r i m p o s i t i o n and, t h e r e f o r e , proport i o n a l t o t h e c o n t r o l force required by t h e p i l o t . The b i a s gain, K21, i n equation (42) corresponds t o 0.14 N (0.08 l b ) of p i l o t f o r c e per degree change in roll attitude.
The c o n t r o l inputs from t h e modified AFCS model which contains a l t i t u d e hold, heading hold, and t u r n coordination modes, a r e
altitude hold
#
a
( fade in/out
+ fade in/out
no. 2 T s + 1 h c i r c u i t no.
][ 3 ~ 1
heading hold
( Y- altitude hold
A9+8 +
fade in/out
s)I(circuinto. 4 K1sltcPh + s
1 rh
turn coor-
L
L d inat ion
-l
-l
fade inlout
- $Ih
The fade i n l o u t c i r c u i t s are intended t o minimize t h e i n t r q d u c t i o n of l a r g e t r a n s i e n t s t o t h e f l i g h t c o n t r o l system due t o changes i n t h e AFCS apera t i n g mode. The g a i n of t h e s e c i r c u i t s v a r i e s between zero and u n i t y , accordi n g t o t h e t r a n s f e r f u n c t i o n s l i s t e d i n t a b l e 3. It should be noted t h a t t h e s a t r a n s f e r functions a r e only used t a determine gain values, and do not
represent actual filters.
AFCS modes- The o p e r a t i o n a l modes of t h e AFCS a r e c o n t r o l l e d by t h e f o l -
lowing variables, which appear i n equation ( 4 2 ) .
= 1
-Iah 9
- 1
- lafcs 0
--I ped
o 1
A l t i t u d e hold mode engaged A l t i t u d e hold mode disenganed
AFCS engaged AFCS disengaged
Pilot's feet off pedals ~ i l o' at f e e t on pedals
- Itrim= 01
Cyclic t r i m button released Cyclic t r i n button depressed
-- 1
Itc 0
-Ixtat 01
Above 60 knots and p i l o t ' s f e e t on pedals A t o r below 60 knot. o r p i l o t ' s f e e t o f f pedals
L a t e r a l s t i c k w i t h i n 0.5 i n . of z e r o f o r c e trim p o s i t i o n L a t e r a l s t i c k beyond 0.5 i n , of z e r o f o r c e trim potsition
The values of t h e r o l l and heading trim a n g l e s , $trim and $trim r e s p e c t i v e l y ,
a r e determined a s follows: $trim i s set e q u a l t o t h e c u r r e n t #h when t h e
c y c l i c trim button i s released; $trim i s set equal t o t h e c u r r e n t $h when
t h e p i l o t s f e e t move o f f t h e pedals.
.
The AFCS and t h e a l t i t u d e - h o l d mode a r e a c t i v a t e d by switches on t h e
instrument panel. The heading-hold and turn-coordination modes a r e c o n t r o l l e d
. by airspeed and l o c a t i o n of t h e p i l o t ' s f e e t ( e i t h e r on o r o f f t h e pedals).
The ading-hold mode i s engaged whenever t h e p i l o t ' s f e e t a r e o f f t h e pedals,
r e g a r d l e s s of a i r s p e e d . The turn-coordination mode i s engaged o n l y when t h e
p i l o t ' s f e e t a r e on the pedals
t h e a i r s p e e d i s g r e a t e r than 60 knots. The
o p e r a t i o n of t h e s e modes i s summarized i n t a b l e 4.
AFCS a u t h o r i t y l i m i t s - The a u t h o r i t y of t h e AFCS i s l i m i t e d s o t h a t i t can be overridden by t h e p i l o t . This is accomplished by l i m i t i n g t h e c o n t r o l i n p u t s from t h e AFCSI equation (42), t o t h e values shown i n t a b l e 5. I n t h e expressions f o r Alaf and Btafcs t h e l i m i t s a r e inposed p r i o r t o the addit i o n of the altitude-gold terms.
Servo a c t u a t o r s - The primary servo a c t u a t o r s transform t h e main r o t o r c o n t r o l commands, given i n equation (41), i n t o swashplate a n g l e s and b l a d e
. c a l l e c t i v e pitch. The following model of t h e s e servos was obtained from
Sikorsky Aircraft
A model of t h e t a i l r o t o r s e r v o was not obtained from Sikorsky; t h e r e f o r e , i t was assumed t h a t
Approximations f o r r e a l - t !.me simulation- During use of t h i s h e l i c o p t e r
- model i n real-time guidance and navigation s t u d i e s i t may be d e s i r a b l e t o
neglect some of t h e r e l a t i v e l y high-frequency dynamics s p e c i f i c a l l y , t h e r e l a t i v e l y small time c o n s t a n t s , T~ and T j r i n equation (42), and t h e s e r v o dynamics, equation (43).
The i n p u t s and o u ~ p u t sof t h e c o n t r o l system model a r e shown i n f i g ure 3(f).
Equations of Motion
The h e l i c o p t e r e q u a t i o n s of motion a r e given i n body axe8 w i t h r e r p e c t t o
- a f l a t , nonrotating Earth. The h e l i c o p t e r i s considered a r i g i d body w i t h
mas8 symmetry about t h e xh t h plane. The e f f e c t s due t o t h e engine angular momentum a r e neglected.
T r a n e l a t i o n a l a c c e l e r a t i o n - The t r a n s l a t i o n a l equation* of motion a r e
'h/. where
f, h
, cos 8 c o s JI
sin 9 sin 8 cos $
- c c s 9 s i n J1
cos 9 s i n 0 cos $
+ sin 9 sin Q
cos 9 s i n J!
cos 4 cos $
+ sin 4 sin 0 sin $
cos 4 s i n 8 s i n J1
- sin 4 cos $
- s i n t3 sin Q cos 6
cos 9 cos 0
and 9h, Oh, and $h a r e t h e Euler angles t h a t d e f i n e t h e o r i e n t a t i o n of the body a x i s systera (fig. 3 ) . The fuselage aerodynamic f o r c e s a r e given by equation ( l o ) , and t h e r o t o r f o r c e s , which include those due t o both main and t a i l r o t o r s , a r e given by equation (31). Equation (45) can be rearranged t o yield
L
f, h
cg, ?.
I n e r t i a l v e l o c i t y and position- The i n e r t i a l v e l o c i t y , i n body coordin a t e s , i s obtained by i n t e g r a t i n g equation (47), with respect t o time, subject t o a p p r o p r i a t e i n i t i a l conditions. The i n e r t i a l v e l o c i t y i n Earth axes i s
The p o s i t i o n of t h e h e l i c o p t e r , i n Earth coordinates, is determined by i n t e grating equation (48) with the appropriate i n i t i a l conditions.
Angular a c c e l e r a t i o n - The r o t a t i o n a l equations of motion are
where
The fusel.age aerod'.iaamic moments a r e given by equation (11). and t h e r o t o r moments, which i n c l u d e chose due t o both t h e main and t a i l r o t o r s , a r e given by equation (38). Equation (50) can be rearranged t o y i e l d
(51
f, h
r, h
Anguiar v e l o c i t y and o r i e n t a t i o n - The angular velocity, i n body axes, i s obtained by i n t e g r a t i n g equation ( S l ) , w i t h r e s p e c t t o time, s u b j e c t t o the appropriate i n i t i a l conditions.
The h e l i c o p t e r E u l ~ ra n g l e s are determined by i n t e g r a t i n g
where
-[ 0
c
cos 4
-sin 4
-sin 0
+ s i n cos
coe (J c o s
The i n p u t s and o u t p u t s of t h e equations of motion a r e s h o m ~i n f i g ure 3(g).
MODEL VALIDATION
The m t h a n a t i c a l m o d c l is v a l i d a t e d by comparing i t s reapanae t o t h a t of an a z t u r l h e l i c o p t e r and by a q u a l i t a t i ~ ecomparison of t h e h a d l i n g characterirtico uude by experienced p i l o t s .
Time Hirtory Conparisone
The moat r e a d i l y a v a i l a b l e f l i g h t d a t a were from an HH-53C, an A i r Force veraion of a CH-S3C, which has two e x t e r n a l f u e l tanks. Since t h e HH-53C response time histories given i n reference 6 were obtained with t h e s e taqks f u l l , t h e helicopter i n e r t i a s i n the model were modified accordingly i n order t o provide a more r e a l i e t i c compariron of responses, The following modified parameters were calc.ulsrtod using d a t a supplied by Sik:reky Aircraft ,
.I
- I
i . I I
The aerodynamics e f f e c t s of t h e e x t e r n a l tanks were not known and, theref o r e , not: incorporated i n t o t h e model. leference 6 contained HH-53C t i n e histories for pulse type inputs t o the longitudinal cyclic, lateral cyclic,
- 1 and pedals, a t t h e following f l i g h t condition with t h e AFCS both on and o f f . A i r speed 113 knots
A l t i t u d e 0 7C00 i t
Main r o t o r speed = 185 rpn
Gross weight = 41,000 lb
FSCG = 328
- 1 Atmoapherlc temperature -18' C
The response time h i s t o r y cf t h e CH-53 modal a t t h e above f l i g h t csndit i o n was obtained using a "dynamic check" routine. This r o u t i n e provided t h e w d e l with f l i g h t c o n t r o l i n p u t s t h a t approximated those of t h e HH-53C. Also, t h i s r o u t i n e was used t o c o n t r o l t h e o p e r a t i o n a l modes of t h e AFCS, as w i l l be discussed later. The time h i s t o r i e s of t h e CH-53 model ar.u t h e HH-53C a r e compared with t h e AFCS on; t h i s is done because t h e model w i l l normally be operated i n t h i s mode f o r terminal-area s t u d i e s .
A comparison of t h e .zsponses t o a forward longitudinal c y c l i c pulse, shown i n f i g u r e 14(a), i n d i c a t e s good agreement f o r t h c Euler t n g l e s and for
t h e body-axid angular v e l o c i t i e s .
Thi.
i
d
also
,"
thd' casz for
.the
re&onae6
to
(
a r i g h t l a t e r a l c y c l i c p u l s e , shown i n f i g u r e 14(b). Here,-it is,assumcd t h a t
t h e HH-53C response 'was. obtained with t h e c y c l i c , t r i m button depressed; si'nce
t h e r o l l a t t i t ~ d ed o e s - h o t return t o zero a f t e r . t h e p u l s e . . This .condStion was
simulated i n t h e model by u s i n g t h e dynamic check r o u t i n e t o set I t r b = 0 .. i n equatior-s (42). The responses t o n r i g h t . p e d ~ lp u l s e d i d not compare as'
w e l l -as those for.-t h e previous i n p u t s c. The model produced much l a r g e r a t t i -
tude excursions than indicated f o r thz ljH->3C.response, A reasonable corzpari-
s o n , s,hown i n f i g u r e 1 4 ( c ) , was o b t a i n e d by t a i s f n g t h e damping g a i n " Kr9 .' . .
-from 0.37'3 t o 1 . 5 0 .
. .-
: A
' . - P o s s i b l e sources of, t h e discrepancy are the- unmqdeled aerodynamtcs oE t h e
HH-53C e x t e r n a l f u e l t a n k s , and f e a t u r e s of t h e AFCS which were modified o r
not Lnc1uded:due t o l i q i t a r i o n s of t h e fixed-bage simulator. 'An attempt ,was
made t o .compensate f o r d i f f e r e n c e s between t h e a c t u a l and modeled AFCS by cox* - t r o l l i n g t h e mode: of t h e l a t t e r w i t h t h e dynamic check r o u t i n e . For ttre response to.. a pec.al p u l s e , . t h i s r o u t i n e simulated t h e AFCS transformation from
; t h e heading-hold mode:to*the t u r n t c o o r d i n a t i o n mode by s e t t i n g Ipcd = 0 and
Itrim= 0 i n equations ( 4 2 ) , L a t e r review indicated. hat t h i s is (I poor mqthod f o r s i m u l a t i n g t h e mode t r a n s f o r m a t i o n . . The above method completely - . r e m ~ v e st h e r o l l t d m r e f e r e n c e when t h e pedal p u l s e is i n i t i a t e d . Actually, ,
t h i s re-erence should fade out with a 1-sec time constant and,-therefore, a '
Icedniore r e a i i s t i c simulation would keep Itrim= 1 and s e t I,lat:= 0 and
. %
= 0 a t t h e beginning of t h e pulse. It may a l s o be d e s i r a b l e t o e l i m i n a t e
e f e c t s of tihe " s t i c k pusher" by s e t t i n g K2t, = 0 i n equation ( 4 2 ) . Because t h e me'thod used i n simulating t h e AFCS mode transformation served t o prema-
t u r e l y remove an a t i i t u d e e r r o r s i g n a l , i t probably increased t h e a t t i t u d e
~ s c u r s f o n sof t h e model and, t h e r e f c r e , may have c o n t r i b u t e d t o t h e response
discrepancy.
P il o t Comments
A q u a l i t a t i v e e v a l u a t i o n of t h e mathematic4'1 model was made by two p i l o t s
using a fixed-base simulator with v i s u a l scene. These e v a l u a t i o c s were t o bed
, made cstlsiderihg t h e intended use of t h e model, t h a t i s , terminal-area guidance
and navigation s t u d i e s .
. #
.,
. .
* '. The r o n t r o l f o r c e s a n d , g e n e r a l f e e l of t h e f l i g h t c o n t r o l s were s a t i s r ' a c -
t o r y , a l t h o u g h - t h e absence ofrbreakout and gradient f o r c e s , wirh t h e c y c l i c
t r i m button depressed, r e s u l t s i n stick-jump and a tendency t o overcontrol.
he absence of c y c l i c beeper trir! and c o l l e c t i v e and pedal. p a r a l l e l servos diC
. . not degrade t h e model f o r i t s i n t e l d . 4 use. The b a s i c AFCS f u n c t i o n s were
primarily evaluated i n forward f l i g h t a t approach speeds (90-120 KIAS). The
, r e t e n t i c i of trimmed a i r s p e e d and I ~ l . t c hand r o l l a t t i t u d e was e x c e l l e n t . The
XFCS modes, a l t i t u d e - h o l d , heading-hc'd , and turn-coordiuation operated s a t l s -
f a c t o r i l y . Also, t h e AFCS m o d i f i c a t i o n s , made ':o include e f f e c t s of a Icxer.11
. It sric!: pusher ,I1 provided responses t h a t were much more ~ h ~ ~ r a c t q irci sotf t h e a i r c r a f t . Although, not r e q u i r e d , low-speed f l i g h t and hover were a l s o ev.11-
uated. .The a t t i t u d e - and heading-hold f e a t u r e s operated very wcil d u r i n s
d e c e l e r a t i n g approaches t o a 50-ft hover. The c o l l e c t i v e i n c r e a s e s mcl nl\er\-
high a t t i t u d e s required d u r i n g deceleration were s i m i l a r t o those of t \ w Cti-5;
aircraft, Above 10 knot*, turns were eaeily coordinated with the pedals, At lowar aptredo, in forward and sideward f light and in hover, prociao hrrdina and h o v w control required much closer pilot atcention to the turn coordinator. Thir waa mainly duo to inrufficient motion curs from the v i r u r l ncene,
It was cancludad that rha flying qualitlm of this modol wbrr qualitatively rayreoentativa of the actual eircraft, within th* li~ltatlonsE a fixed-baaa airnulator,
C O N C t J S IONS
I . Schannamy, J. D. ; Deaux, Thomas N. ; and Yenni, Kenneth R. : The Development an3 Validation of a Piloted Simulation of a Helicopter and External Sling Load. NASA TP-1285, 1979,
2. Wilcock, T.; and Thorpe, Ann C.: Flight Siraulation of a Wassex Helicop-
ter - A Validation Ehrcise, C.P. No. 1299, British A.R.C., 1974.
. .
8
3. Seckel, Edward; and Curtis$, H. C . , Jr,: Aerodynwic Charactariaticq of
Helicopter Rotors. Report No. 659, Department of Aerospace and Mecheni-
cel Science, Princeton U,, Princaton, N.J., Dec. 1963.
4. Bailey, F, J., J r , : A Simplified Theoretical Method of Detemining the ' Characteristics of a Lifting Rotor in Forward Flight, NACA Rep. 716,
1941.
5 , h e r , Kennerh B.; and Gustafson, F. B.: Charts for Estiula~iona£ Longitudinal-Stability Darivatives for a Helicopter Rator in Forward Flight. NACA TK-2309, 1951.
6 Barbini, Wayne 3 , ; Balfe, P. J.; Lovrien, C. E., Jr.: Category 11 Performance and Flying Qualities Tests of the HH-53C Helicopter. AFFTC-TR70-8, Air Force Flight Test Center, Edwards AFB, Calif., Feb. 1970.
TABLE 1.- VALUES OF PARAMETERS FOP CH-53 HELICOPTER
[Subscripts m and t denote main and t a i l r o t o r . r e s p e c t i v e l y ]
% . p e r rad . . . . . . . . . . . . . . . . . 5.73 it,. rad (deg) . . . . . . . . . . . . 0.0524 (3.0)
. . . . . . . . . . . . . . . . . . . at. per rad . . . . . . . . . . . . . BLCG. m (in.)
5.73 Kc N-m/ (rad Isec) [f t-lb / (radlsec) ]
0.0 (0.3)
1572000 [1159209]
, B B,
. . . . . . . . . . . . . . . . . . . . . 0.97 . . . . . . . . . . . . . . . . . . . . . 0.97
. . Kd' N-m/ (radlsec) [ ft-lb/(rad/sec) 1
132000 [97338]
bm . . . . . . . . . . . . . . . . . . . . . . 6 K f Y m ( f t ) . . . . . . . . . . . . . 0.099 (0.327)
. bt . . . . . . . . . . . . . . . . . . . . . . 4 Kgovr N-m/(rad/sec) [ft-lb/(rad/sec)J .83 3.3 (614)
%. m ( f t ) . . . . . . . . . . . . . 0.66 (2.165) K,. rad (deg) . . . . . . . . . . . . . 0.0436 (2.5)
ct ' lekf
m
.
(ft)
...
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
. .
0.391 (1.284)
. . . . . 0.5
. . . . . . . . K,. . radlcm (deglin.)
0.00989 (1.44)
Ks. rad (deg) . . . . . . . . . . . . . 0.0524 (3.011
1 . . . . . . . . . . . . . lekt . . . . . . . . . . . . . . . . . . . . . 1.8 K. radlcm (deglin.)
. . . . . . . . . . . . . N em. m ( f t )
0.610 (2.0) K g rad (deg)
. . . . . . . . . . . . . e . rn ( f i )
0.122 (0.1) Kg. radlcm (deglin.)
. . . . . . . . 0.0146 (2.13)
.0.0175 (.1.0)
. . . . . . . . 0.00930 (1.35)
IFSCG. . . . . . . . . . . . . . . . . . . m (in )
8.433 (332.0) K,. radlcm (deglin.)
.0.000989 (-0.14b
. . Ggov. N-m/ (radlsec) [ f t - l b / ( r ~ d l s e c])
K,. rad (deg) . . . . . . . . . . . . . 0.0262 (1.5)
. . . . . . . . 85160 [62798] Kg. rad/cm (deg/in.)
0.0364 (5.30)
. . . . . . . . . . . . . . . . Ibm.kern2 (slug-it')
. . . . . . . . . . . . . . . . Ibt kg-m7 (slug-ft2)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imr kg- m2 (slug-f t 2 )
5489 (4046) K,,. 22.72 (16.75) K1, 43478 (29840) K12
radlcm (degjin.) rad/m (deglf t)
0.00989 (1.44) 0.000778 (0.5136)
0.60
. . . . . . . . . . . . . . . . . . . . . . . . . . . Iptskg-m2 (slug-ft2)
4325 (3188) K13. 8ec
. . . . . . . . . . . . . . In.h p kg-m2 (slug-ft2)
48891 (36041) K,,. rad/cm (deglin.)
. . . . . . . . . . . . . . . . . . . . . . . . Iwsh kg-m2 (slug-ft2)
239491 (176551) K15. s e c
0.32 0.00756 ( 1 . ' ~ )
-0.15
. . . . . . . . . . . . . . . . . . . . . . . Izz .h. kg-m2 (slug-f t2,
223361 (164660) K 1 6
. a m , . 0.24
. . . . . . . . . . . Ixz.hr kg-m2 (slug-£ t 2 )
22518 (16600) K17. radlm ( d e g l f t )
.0.0000778 (-0.001363
TABLE 1. Continued
K,,, sec . . . . . . . . . . . . . . . . . -0.081 ,K19,sec2 . . . . . . . . . . . . . . . . . 1.50
'3m* rad (deg) 6,t, rad (deg)
.. ..
..... .....
...... ......
0.0 (0.0) 0.78 (45)
K2, . . . . . . . . . . . . . . . . . . . . -0.216 c . . . . . . . . . . . . . . . . . . . . . . . .
0.2
. . . . . . . . . . . . . . K,,, rad/m/sec2 (deg/ft/sec2)
0.0162 (0.283) ,,8 rad (deg)
-0.0873 (-5.0)
. . . . . . . . . . . . . . . . . . . K,,, rad/m (deg/ft)
0.000778 (0.0136) OSt, rau (deg)
0.0 (0.0)
K23, sec-' . . . . . . . . . . . . . . . . 0.830 elm, rad (deg) . . . . . . . . . . . -0.105 (-6.0)
. . . . . . . . . . . . . . . . . . . . Kz,, m/rad (m/deg)
0.143 (0.0025) OLt, rad (deg)
-0.140 (-8)
. . . . . . . . . L,kg-m (slug-£2)
819 (184.1) I u
. . . . . . . . . . . . . . . . . . . . . 0.1145
Qt,
. . . . . . . . . kg-m (slug-ft)
18.76 (4.2)
at
. . . . . . . . . . . . . . . . . . . . .0.2042
%, kg (Ib) . . . . . . . . . . . 15,227 (33,500) T, sec . . . . . . . . . . . . . . . . . . . 0.012
%, m (ft) . . . . . . . . . . . . 11.01 (36.11) T ~ se~c .~. .,. . . . . . . . . . . . . . . . 0.50
Rt, m (ft) . . . . . . . . . . . . . . 2.44 (8.0)
sec . . . . . . . . . . . . . . . . . . . 0.20
to, sec . . . . . . . . . . . . . . . . . . . 0.02 rut, sec . . . . . . . . . . . . . . . . . . . 0.24
WLCG, rn (in.) . . . . . . . . . . . 4.149 (163.3) T,, see. . . . . . . . . . . . . . . . . . . 0.013
. . . . . . . . . . Xrm,h, u~ (ft)
-0.112 (-0.368)
T ~ ,sec.. . . . . . . . . . . . . . . . . . . 1.4
yrm,h, m (ft) . . . . . . . . . . . . . 0.0 (0.0) T ~ s,ec . . . . . . . . . . . . . . . . . . . 0.016
'rm,h, Xrt,h) yrt,h, m
(ft).
. (ft) . (ft)
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. -2.438 (-7.81) .-13.68 (-44.85)
-0.853 (-2.8)
I
I
T ~ s,ec . . . . . . . . . . . . . . . . . . . . T ~ ,sec.. . . . . . . . . . . . . . . . . . . T ~ s,ec.. . . . . . . . . . . . . . . . . . .
1.8 4.0 1.4
zrt ,h, m (ft) . . . . . . . . . . -2.819 (-9.06) T ~ ,sec.. . . . . . . . . . . . . . . . . . . 1.4
. U.t,h*
Ywt,hs zwt ,h m x ps,h, m
(ft) (ft) (ft) (ft)
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
-0.102 (-0.333)
. . . 0.0 (0.0) . 0.0584 (0.16) . 4.827 (15.8^)
sec . . . . . . . . . . . . . . . . . . . . 1.a
4sm, rad (deg) . . . . . . . . . . . . . . 0.0 (0.0) $st, rad (degj . . . . . . . . . . . . . 1.57 (90) Q,, rad/sec . . . . . . . . . . . . . . . . . 19.3
. Yps,h* m
zPS,~' m
(ft) (ft)
. .
. .
.. ..
.. ..
.. ..
. .
....
-0.2083
--- (---)
(-0.6833)
. . . . not, radjsec . . . . . . . . . . . . 82.9 wm radlsec . . . . . . . . . . . . . . . . . 95.0
1 I
TABLE 2.- FORCE CBABACTBRISTICS OF PILOT CONTROLS
,
pi'ot
i
Force
Breakout. N (lb) I GradientIN/an ( l b / h $
Longitudinal cyclic
8.9 (2,0)
2.3 (1 .-3)
Lateral c y c l i c
6.7 (1,,5)
1.4 (0.8)
Collective
20 (4.5)
0 (0)
Pedals
36 (8.0)
5.3 (3.0)
, TABLE 3.- GAINS OF FADE IN/OUT
C i r c u i t number
1
2 1 3
4
TABLE 4.- SUMMABY OF HEADING-HOLD AND TW-COOR1)INATION MODE LOGIC
Operating condition
Feedback information
Airspeed I P i l o t s f e e t Roll p o s . l ~ e a d i n gI Roll r a t e I Lat. acc.
Mode
I II
Above 60 knots On pedals
Off pedals
Below 60 knots On pedals
1
I
I
Off
Off
Off
Off
Off
Off
I Turn-coord.
Head. -hold
-.--
Off pedals On
On
Off
Off
Head. -hold
TABLE 5.- AUTHORITY LIMITS OF AF( AFCS input L i m i t s , rad (deg)
cs B,afcs
20.0227 rad, ('1.3) 20.0454, (22.6)
Alafcs f0.0209, (21.2)
'eafcs
20.0332, ( + I .')9
%his l i m i t increased t o 27' i n the simulation.
rr. xh NORTH
EAST
a} BODY AXES
b) SHAFT AXES
4
c) CON1ROL AXES
d) FLAPPING ANGLES
Figure 2 . - Helicopter body axes, shaft axes, control a x e s , and flapping angle definitions.
PILOT INPUTS
*
L
MA1N
C
I
ROTOR
-
CONTROL SYSTEM
C
ROTOR MODEL
1 " -t GOVERNOR
FUSELAGE AERODYNAMICS
I WIND, GUST INPUTS
-
-
EQUATIONS
b
OF
MOTION
1 TO SIMULATOR
(aj Helicopter simulation.
Figure 3.- Block diagram of helicopter model and input-output diagrams of individual component mode 1s.
[El *-jwind,h
FUSELAGE RODYNAMIC!
(b) Fuselage aerodynamics model. Figure 3.- Continued.
[El-
MAIN ROTOR MODEL
( c ) Eldin rotor ( s u b s c r i p t m) model.
- . Figure 3. Cont h u e d
[' h-j TAIL ROTOR
k!!%+q+[t]
hub,, h
(d) T a i l Rotor (subscript t) model. Figure 3.- Continued.
ENGINE AND
GOVERNOR MODEL
(el Engine and p v e r n o r model.
- . Figuie 3 . Continued
PI LOT
INPUTS
CONTROL SYSTEM
( f ) Control system.
- Figure 3. Conthued.
EQUATIONS OF MOTION
(g) Equations of motion. Figure 3.- Concluded.
Figure 4.- Fuselage incremental d r ~ . ?nu .I function o f m p l e ,>.ilet .I;;.
Figure 6.- Fuselage incremental l i f t a s a function of s i d e s l i p (wind tunnel yaw angle).
. Figure 7.- Fuselage sideforce a s a function of s i d e s l i p (wind tunnel yaw angle)
Figure 8.- Fuselage incremental rolling moment as a function of angle of attack.
Figure 9.- Fuselage incremental r o l l i n g mament as a function of sideslip (wind tunnel yaw a n g l e ) .
Figure 10.- Fuselage incremental pitching moment as a function of angle of attack and incidence at the tail.
. Figure 11.- Fuselage incremental pitching moment as a function of sideslip (wind tunnel yaw angle) 4 2
Figure 12.- Fuselage yawing moment a s a function of s i d e s l i p (wind tunnel yaw angle) and angle of rttack.
-DOWN
* UP
COLLECTIVE STICK DISPLACEMENT, XmI
(a) Collective
6
Figure 13.- Control rigging diagrams.
- -10.16 AFT
0
lO.'l6 FORWARD
203 cm
LONGITUDINAL CYCLIC STICK DISPLACEMENT, Xlo,
(b) Longitudinal cyclic Figure 13.- Continued.
tad 4eg
I" COLLECTIVE STICK DISPLACEMENT, XCOL
w
-
-4.435
-5
-4
-2
0
2
4
5 in.
LEFT
-RIGHT
LATERAL CYCLIC STICK DISPLACEMENT, Xlat
( c ) Lateral cyclic Figure 13.- Continued.
COLLECTIVE STICK ,DISPLACEMENT, Xcd
in.
-2.db in.
I
- L 1
-5.08 -2.64 RIGHT
1
0
1
1
2.W 5.08 ~m
- LEFT
PEDAL DISPLACEMENT, Xw
(d) Pedal Figure !3.- Concluded.
1 -20 PITCH ATTITUDE, drg
- --- FLIGHT~ E S T MATH MODEL
- '
I4 PITCH RATE, ~ W C
40 r
1ROLL ATTITUDE,
-20
[4 0 ROLL RATE, rlfg/mc
1 -40
LONGITUDINAL STICK,
- .
in.
01234
ELAPSED TIME, KC
1 -40 LONGITUDINAL STICK, in
l
I
1
'
I
01234
ELAPSED TIME, soc
(a) Longitudinal cyclic pulse.
Figure 14.- Flight test-math model comparisons.
-FLlOHT TEST
----MATH MODEL
WLATTITUDE. dm~
-20
-40L
'Or
LATERAL STICK. In.
UALJ
01234 ELAPSED TIME. IK:
ILATERAL STICK. In.
-4 -
r
a;zs4
ELAPSEDf M E , as
(b) Lateral c y c l i c pulse.
Figure 14.- Continued.
4 9
-FLIGHT TEST
+ -mL PITCH ATTITUDE.
-)o ROLL ATTITUDE, deg
.do. PITCH RATE, ckght?~
-
L -20 YAW ATTITUDE. dog
I
-40 1. Y A W RATE. c k g h t ~
L-4 RUDDERPEDAL POSITION, in.
L--.ILL---d
01234
ELAPSED TIME, sac
I-4 RUDDER PEDAL POSITION. In. L- L . -. I -I - 2 01234 ELAPSED TIME. sec