NASA TECHNICAL MEMORANDUM

i l- a

A MATHEMATICAL FORCE AND MOMENT MODEL OF A UH-1H

HELICOPTER FOR FLIGHT DYNAMICS SIMULATIONS

Peter D. Talbot and Lloyd D. Corliss

Ames Research Center, NASA

and

Ames Directorate, USAAMRDL, AVRADCOM Ames Research Center Moffett Field, Calif. 94035

NASA TM-73,254 (Rcvis ed 8 ,' 30 / 7 8 )

June 1977

https://ntrs.nasa.gov/search.jsp?R=19770024231 2020-05-08T17:55:51+00:00Z

NOTATION

a

a 0

a1 9%

a lsSbls

a

A

1 s w

A X , Y , Z

A1 c

A1 C L

A1 s

Ai CB

CP

1 sw b

B I C

B I C L

BICP

BIS

B I C B

c 6 , c7

main r o t o r 1 i f . t curve s l o p e , p e r r a d i a n

main r o t o r coning, r a d

f i r s t harmonic va lues of main r o t o r b l a d e f l a p p i n g wi th r e s p e c t t o c o n t r o l a x i s , r ad

f i r s t harmonic va lues of main r o t o r b l a d e f l a p p i n g w i t h r e s p e c t t o s h a f t a x i s , r a d

l o n g i t u d i n a l component of c o n t r o l a x i s p o s i t i o n , r a d

r o t o r d i s k area, nR2, f t 2 , m2

body axis a c c e l e r a t i o n s , f t / s e c 2 , m/sec2

l a t e r a l swashplate c o n t r o l i n p u t , r ad

l a t e r a l c y c l i c p i t c h c o n t r i b u t i o n of s t a b i l i z e r b a r , r a d

l a t e r a l swashplate c o n t r o l b i a s r i g g i n g term, r ad

l a t e r a l p i l o t c o n t r o l i n p u t , r a d

l a t e ra l c o n t r o l a x i s command p o s i t i o n wi th r e s p e c t t o s h a f t , rad

l a t e ra l component of c o n t r o l a x i s p o s i t i o n , r a d

l o n g i t u d i n a l swashpla te c o n t r o l i n p u t , r a d

l o n g i t u d i n a l c y c l i c p i t c h c o n t r i b u t i o n of s t a b i l i z e r b a r , r a d

l o n g i t u d i n a l swashplate c o n t r o l b i a s r i g g i n g t e r m , r a d

l o n g i t u d i n a l p i l o t c o n t r o l i n p u t , r ad

l o n g i t u d i n a l c o n t r o l axis command p o s i t i o n w i t h r e s p e c t t o s h a f t , r a d

c o n s t a n t s i n l i nkage equa t ions , c y c l i c s t i c k t o swashpla te motion, r a d / i n . , rad/cm

cons tan t i n l inkage equa t ion , c o l l e c t i v e p i t c h t o c o l l e c t i v e s t i c k motion, r a d / i n . , rad/cm

c o n s t a n t s i n l i nkage equa t ion , t a i l r o t o r c o l l e c t i v e p i t c h t o peda l motion, r a d / i n . , rad/cm

i

f e , f e , f e 1 2 3

F 1

G1

i

h~~

H

main r o t o r d iameter , f t , m

c o n s t a n t s i n f u s e l a g e drag f o r c e e q u a t i o n s , l b / ( f t / s e c ) 2 , N/ (m/sec> 2

drag areas of f u s e l a g e , f t 2 , m2

v e r t i c a l f i n drag c o n s t a n t , l b / ( f t / s e c ) 2 , N / ( m / . ~ e c > ~

cons tan t used i n ground e f f e c t computation

h e l i c o p t e r rate of climb

h e i g h t of t a i l r o t o r above c . g . , f t , m

r o t o r H-force i n c o n t r o l axis - wind system, l b , N

c o n s t a n t s i n h o r i z o n t a l s t a b i l i z e r aerodynamic f o r c e s , l b / ( f t / s e c I 2 , N/(m/sec)2

I , I , I i n e r t i a s i n body axis I X X , yy zz xz

k, * k2 c o n s t a n t s i n v e r t i c a l f i n aerodynamic f o r c e s , l b / ( f t / s e c ) 2 , N / (m/sec>2

numerator t e r m , combining l i n k a g e and damping c o n s t a n t s , of s t a b i l i z e r b a r input t o c y c l i c p i t c h , sec 53

c o n s t a n t i n X equat ion r e p r e s e n t i n g ground e f f e c t

w a t e r l i n e displacement of r o t o r hub from a i r c r a f t c e n t e r of

KG

‘H g r a v i t y , f t , m

‘HS l o n g i t u d i n a l displacement of h o r i z o n t a l s t a b i l i z e r

aerodynamic c e n t e r from a i r c r a f t c e n t e r of g r a v i t y , f t , m

l o n g i t u d i n a l displacement of t a i l r o t o r hub from a i r c r a f t c e n t e r of g r a v i t y , f t , m ‘TR

w a t e r l i n e displacement of v e r t i c a l f i n aerodynamic c e n t e r from a i r c r a f t c e n t e r of g r a v i t y , f t , m ‘VF

cons tan t i n f u s e l a g e aerodynamic f o r c e c o n t r i b u t i o n , l b / ( f t / s e c ) 2 , N / (m/sec>2 ,

L1

body a x i s r o l l i n g moment, due t o main r o t o r , f t - l b , J

body a x i s r o l l i n g moment, due t o t a i l r o t o r , f t - l b , J

LR

L~~

,

M 1

cons tan t i n f u s e l a g e aerodynamic p i t c h i n g moment, f t - l b / (f t / s e c ) 2 , J / ( f t / s e c ) 2

ii

body a x i s p i t ch ing moment, due t o f u s e l a g e , f t - l b , J % body a x i s p i t ch ing moment, due t o h o r i z o n t a l s t a b i l i z e r ,

f t - l b , J

body a x i s p i t ch ing moment, due t o main r o t o r , f t - l b , J % N l cons tan t i n fuse lage aerodynamic yawing moment , f t - l b / ( f t / s e c ) ,

J/ (m/sec12

body a x i s yawing moment, due t o f u s e l a g e , f t - l b , J NF

NR

N~~

NVF

PB

PC

Q

qB

4C

B r

R

S

T

T~~

body a x i s yawing moment, due t o main r o t o r , f t - l b , J

body axis yawing moment, due t o t a i l r o t o r , f t - l b , J

body a x i s yawing moment, due t o v e r t i c a l f i n , f t - l b , J

body a x i s r o l l r a t e , r a d / s e c

main r o t o r s h a f t r o l l rate, wind-control a x i s system, r a d / s e c

main r o t o r to rque , f t - l b , J

body a x i s p i t c h r a t e , r a d / s e c

main r o t o r s h a f t p i t c h rate, wind-control a x i s system, r a d / s e c

body a x i s yaw r a t e , r a d / s e c

r o t o r r a d i u s , f t , m

c o n s t a n t s i n main r o t o r f o r c e equat ions , t a b l e 3

Laplace o p e r a t o r

area of aerodynamic s u r f a c e , f t 2 , m2

main r o t o r t h r u s t , lb, N

c o n s t a n t s i n ta i l r o t o r f o r c e equa t ions , t a b l e 3

t a i l r o t o r t h r u s t , l b , N

x-body a x i s relative v e l o c i t y , f t / s e c , m/sec

l o n g i t u d i n a l component of re la t ive wind i n wind c o n t r o l a x i s

B

C

U

system, f t / s e c , m/sec U

component of r e l a t i v e wind i n equa t ions f o r ve r t i ca l f i n aerodynamic force , f t l s e c , m/sec F U

iii

H U

B

C

V

V

F V

T

B

C

V

W

W

component of re la t ive wind i n equat ions f o r h o r i z o n t a l s t a b i l i z e r aerodynamic f o r c e , f t / s e c , m/sec

y-body a x i s re lat ive v e l o c i t y , f t / s e c , m/sec

l a t e r a l component of re la t ive wind i n wind-control axis system, f t / s e c , m/sec

component of re la t ive wind i n equat ions f o r v e r t i c a l f i n aerodynamic f o r c e , f t / s e c , m/sec

re la t ive wind normal t o p l ane of t a i l r o t o r , f t / s e c , m/sec

z-body a x i s r t r a t l v e v e l o c i t y , f t / s e c , m/sec

ver t ica l component of r e l a t i v e wind i n wind-control a x i s s y s t e m , f t / s e c , m/sec

xC

XF XR

c.g. X

Y

yC

yF

yR

'TR

'VF

Z

zc

zF

component of r e l a t i v e wind i n equat ions f o r h o r i z o n t a l s t a b i l i z e r aerodynamic f o r c e , f t l s e c , m/sec

main r o t o r f o r c e i n c o n t r o l a x i s system, l b , N

l o n g i t u d i n a l x-body f o r c e , due t o f u s e l a g e , l b , N

l o n g i t u d i n a l x-body f o r c e , due t o main r o t o r , l b , N

l o n g i t u d i n a l d i s t a n c e of a i rcraf t c e n t e r of g r a v i t y forward of main r o t o r s h a f t hub, f t , m

r o t o r Y-force i n wind c o n t r o l axis system, l b , N

cons t an t i n f u s e l a g e aerodynamic f o r c e c o n t r i b u t i o n , l b , N

main r o t o r f o r c e i n c o n t r o l a x i s system, l b , N

l a t e r a l y-body f o r c e , due t o f u s e l a g e , l b , N

l a t e r a l y-body f o r c e , due t o main r o t o r , l b , N

l a t e r a l y-body f o r c e due t o t a i l r o t o r , l b , N

l a t e r a l y-body f o r c e , due t o v e r t i c a l f i n , l b , N

r o t o r he igh t above ground p lane , f t , m

main r o t o r f o r c e i n c o n t r o l a x i s s y s t e m , l b , N

v e r t i c a l z-body f o r c e , due t o f u s e l a g e , l b , N

i v

zH

zR

F ci

HS ci

'm

Y

6

6 0 9 6 2

'1BY62B

a 6

6 C

e

P

6

6

6 S

0 e

'TR A

B

R

T

T

9

v e r t i c a l z-body fo rce , due t o h o r i z o n t a l s t a b i l i z e r , l b , N

v e r t i c a l z-body fo rce , due t o main r o t o r , l b , N

v e r t i c a l f i n angle of att&k'; rad

h o r i z o n t a l s t a b i l i z e r ang le of a t t a c k , r a d

maximum f l a p p i n g ampli tude of main r o t o r w i th r e s p e c t t o

aCR4 r o t o r Lock number f o r one b l ade , p - r o t o r mean b lade drag c o e f f i c i e n t

s h a f t , r a d

I B

c o n s t a n t s i n r o t o r d rag equat ion

s t a b i l i z e r ba r f l app ing c o n s t a n t s , r a d

p i l o t ' s l a t e r a l s t i c k displacement , i n . , cm

p i l o t ' s c o l l e c t i v e s t i c k d isp lacement , i n . , c m

p i l o t ' s l o n g i t u d i n a l s t i c k displacement , i n . , cm

p i l o t ' s peda l displacement , i n . , cm

h o r i z o n t a l s t a b i l i z e r i nc idence a n g l e , rad

a i r c r a f t p i t c h a t t i t u d e Euler ang le , deg, r a d

main r o t o r c o l l e c t i v e p i t c h

t a i l r o t o r c o l l e c t i v e p i t c h , rad

main r o t o r in f low r a t i o

main r o t o r advance r a t i o

sea leve l a i r dens i ty , s l u g s / f t 3 , kg/m3

r o t o r s o l i d i t y

s t a b i l i z e r b a r time c o n s t a n t , s e c

c o n t r o l a x i s response t i m e cons t an t , sec

a i r c r a f t r o l l a t t i t u d e , r ad

ampli tude of t o t a l c y c l i c p i t c h c o n t r o l i n p u t , r ad

phase angle of c y c l i c r i g g i n g , deg

V

phase (with r e s p e c t t o body a x i s ) of t o t a l c y c l i c p i t c h c o n t r o l i n p u t , r a d

I

1cI

n

S u b s c r i p t s

TR

VF

HS

IC

m

a i r c r a f t heading, r a d

r o t o r r a t i o n a l speed, r a d / s e c

t a i l r o t o r

v e r t i c a l f i n

h o r i z o n t a l s t a b i l i z e r

i n i t i a l c o n d i t i o n s - trimmed c o n d i t i o n s f o r t h e h e l i c o p t e r

model

v i

A MATHEMATICAL FORCE AND MOMENT MODEL OF A UH-1H

HELICOPTER FOR FLIGHT DYNAMICS SIMULATIONS

P e t e r D. Talbot and Lloyd D. C o r l i s s

Ames Research Center, NASA and

Ames Di rec to ra t e , USAAMRDL, AVRADCOM

SUMMARY

A model of a Bell UH-1H h e l i c o p t e r w a s developed t o suppor t s e v e r a l s imula t ions a t Ames Research Center and w a s used a l s o f o r development work on an a v i o n i c s system known as t h e V/STOLAND system a t Sperry F l i g h t Systems. This r e p o r t p r e s e n t s t h e complete equat ions and numerical v a l u e s of c o n s t a n t s used t o r e p r e s e n t t h e h e l i c o p t e r .

Responses t o s t e p i n p u t s of the c y c l i c and c o l l e c t i v e c o n t r o l s are shown and compared wi th f l i g h t test d a t a f o r a UH-1H. The model c o e f f i c i e n t s w e r e a d j u s t e d i n an a t t empt t o g e t a c o n s i s t e n t match wi th t h e f l i g h t t i m e h i s t o r i e s a t hover and 60 knots . F a i r l y good response matching w a s ob ta ined a t 60 kno t s , b u t t h e matching a t hover w a s no t as success fu l . P i l o t evalua- t i o n s of t h e model, bo th f i x e d and moving base , were made.

INTRODUCTION

The mathematical f o r c e and moment model descr ibed w a s developed t o s a t i s f y t h e need f o r r e p r e s e n t i n g t h e dynamics of a UH-1H h e l i c o p t e r f o r p i l o t e d s imula t ion . dynamics i n v e s t i g a t i o n s and f o r s imula t ion of terminal-area guidance and nav iga t ion t a s k s . It has been used i n s imula t ions f o r t h e development of so f tware f o r t h e nav iga t ion and guidance programs of an a v i o n i c s system known as V/STOLAND and f o r t h e i n v e s t i g a t i o n of t h e e f f e c t s of f a i l u r e s of s t a b i l i t y augmentation elements of t he c o n t r o l system (see r e f . 1).

The model w a s developed s p e c i f i c a l l y f o r u s e i n f l i g h t

The equat ions , r ep resen t ing the non l inea r c o n t r i b u t i o n s of t h e components of t h e h e l i c o p t e r t o the f o r c e and moments were assembled from many sources . The equa t ions are i n gene ra l form so t h a t changes can be made t o r e p r e s e n t h e l i c o p t e r s o the r t han t h e UH-1H. r o t o r r e p r e s e n t a t i o n , uniform inflow over t h e r o t o r d i s c , and s imple expres s ions f o r t h e c o n t r i b u t i o n s of t h e t a i l r o t o r , f u s e l a g e , and empennage. No i n t e r f e r e n c e e f f e c t s between components were modelled. I n t h e s imula t ion , the equa t ions were used i n a s tandard d i g i t a l program, p a r t i a l l y desc r ibed i n r e f e r e n c e 2 which i n c o r p o r a t e s t h e equa t ions of motion, v a r i a t i o n s i n t h e atmosphere, and r o u t i n e s f o r i n t e r f a c i n g wi th ana log equipment f o r

The model employs a q u a s i - s t a t i c main

d r i v i n g ins t ruments , p rovid ing c o n t r o l f o r c e s , e tc . S imula t ions have been conducted w i t h an EA1 8400 computer.

The model was eva lua ted by. comparing i t s response t o s t e p i n p u t s w i t h t h o s e obta ined i n f l i g h t on a UH-1H h e l i c o p t e r , and s u b j e c t i v e p i l o t assess- ments. s imula t ions .

The p i l o t e v a l u a t i o n s were obta ined dur ing both f i x e d and moving-base

HELICOPTER FORCE AND MOMENT EQUATIONS

The q u a s i - s t a t i c main r o t o r e q u a t i o n s were adapted from r e f e r e n c e 3 . The e q u a t i o n s f o r the aerodynamic f o r c e s of t h e f u s e l a g e and empennage were s e p a r a t e l y der ived , based e i t h e r on a v a i l a b l e wind t u n n e l d a t a of r e f e r e n c e 4 o r s tandard textbook wing theory , modified t o approximate s t a l l e d c o n d i t i o n s . An approximate r e p r e s e n t a t i o n f o r t h e t a i l r o t o r w a s d e r i v e d ; however, i n i t s o r i g i n a l form i t d i d n o t c o r r e c t l y p r e d i c t t a i l r o t o r damping. t h e e q u a t i o n s was r e t a i n e d w i t h a d j u s t e d c o n s t a n t v a l u e s used t o match t h e apparent t a i l r o t o r damping seen i n t h e f l i g h t t es t d a t a yaw responses .

The form of

The equat ions r e p r e s e n t aerodynamic f o r c e s and moments c o n t r i b u t e d by each component of t h e h e l i c o p t e r . The n e t r e s u l t s are t h r e e aerodynamic f o r c e s and t h r e e aerodynamic moments a p p l i e d i n a body-axis system. The o r i g i n of t h e body system is t h e h e l i c o p t e r c .g . frame w a s t a k e n t o be p a r a l l e l t o t h e main r o t o r s h a f t , p o s i t i v e d i r e c t i o n down, as i n f i g u r e 1.

The z axis of t h e r e f e r e n c e

The c o n s t a n t v a l u e s used f o r t h e c o e f f i c i e n t s i n t h e e q u a t i o n s are presented i n t ab l e s 1 and 2. It may b e noted t h a t t h e c h a r a c t e r i s t i c l e n g t h s used t o compute moments are based on d a t a r e f e r e n c e d t o t h e water- l i n e - b u t t l i n e - s t a t i o n system of t h e h e l i c o p t e r , r a t h e r than t h e axis system def ined above. S ince t h e UH-1H h a s a 5" forward mast t i l t , s l i g h t d i s c r e p - a n c i e s a re introduced by us ing r a w s t a t i o n and w a t e r l i n e v a l u e s t o l o c a t e components of t h e model. These are thought t o b e i n s i g n i f i c a n t .

Main Rotor Forces a t t h e Rotor Hub

a p ub - - 3 A u 2 ( 1 + 3 . 3 3 ~ ) - a. (+ - e) - RqqC ($ + G) 8

2

Main Rotor Torque

uAal w o b l +-I 3 - -

2

This expression was obtained from reference 5, equation (441, Po 195.

Flapping Coefficients

a = 0.048 0

( 4 )

Advance Ratio

Mean Blade Drag Coefficient

6 = 6 0 + 6,T2 (9)

Inflow Ratio

This expression is an implicit function and required an iterative solution in the computer program.

X = - R W 7 C - (p2 + ~ 2 1 1 1 2 KG (10)

3

The KG f a c t o r is a ground e f f e c t t e r m and r e p r e s e n t s a r e d u c t i o n i n inf low v e l o c i t y i n ground e f f e c t . The va lue G, (below) '

match performance d a t a presented i n r e f e r e n c e 61

Wind Components a t t h e Rotor Hub

u = - u - w B C B B 1 s + ~ B ~ H

C B B 1s - PB'H v = - v - w A

was a d j u s t e d t o

( l o a )

w C = -WB + B ~ ~ ( U ~ - qBgH> + A ~ ~ ( v ~ + pBtH) (13:

Rotor Forces and Moments Resolved I n t o Body Axes

(a) Forces i n c o n t r o l ax is system

C Yv + HUC xc =

Zc = -T

(b) Main r o t o r f o r c e s i n body axes

XR = Xc - ZCBIS

Y R = Y c - Z A c 1s

Z R = Z c + X c B 1s + YCAIS

4

(c) Main r o t o r moments i n body axes

% - XRRH + R c.g.

NR = Q - YRXc

P i l o t t o Swashplate Cont ro l Equat ions

B = C16, 1 CP

I n t h i s form, no cross-coupling is shown corresponding t o c o n t r o l r i gg ing . I n t h e most gene ra l form,

AICp = C,6, cos 4p - (216, s i n 9,

BICp = C46, s i n 4p -k C16e COS $ J ~

For t h e UH-1H I # I ~ i s a c t u a l l y 5". For t h e s imula t ion @,= 0" w a s used.

, . Main and Tai l Rotor C o l l e c t i v e P i t c h

The f i r s t o r d e r l a g r e p r e s e n t a t i o n w a s used t o match more c l o s e l y t h e a a c c e l e r a t i o n d a t a obta ined from t h e f l i g h t t es t r e s u l t s .

2

S t a b i l i z e r Bar Trans fe r Funct ions

The B e l l s t ab i l izer b a r can be r ep resen ted by a s imple t r a n s f e r f u n c t i o n It which d e s c r i b e s i t s p a r a l l e l i npu t t o t h e c y c l i c p i t c h of t h e main r o t o r .

is c h a r a c t e r i z e d by a ga in KB and a t i m e c o n s t a n t , TB, which r e f l e c t

5

r e s p e c t i v e l y t h e mechanical mixing r a t i o and t h e mechanical damper charac te r - i s t i c of t h e shaft-mounted ba r .

p (SI -5

AICB(S) = -rBS + 1 B

The b a r has a pronounced e f f e c t on t h e s t a b i l i t y and t i c s of t h e h e l i c o p t e r . Values of t h e b a r c o n s t a n t s were t a t i o n w i t h B e l l H e l i c o p t e r Company.

Cont ro l I n p u t s t o Cycl ic P i t c h

c o n t r o l c h a r a c t e r i s - ob ta ined by consul-

The c o n t r o l i n p u t s t o t h e r o t o r c y c l i c p i t c h are represented as t h e sum of t h o s e due t o t h e p i l o t , s t a b i l i z e r bar and r i g g i n g of t h e c o n t r o l system.

( 3 1 ) - B i C - BICP + BICB + BICL

Rotor Control Axis Response t o Cycl ic P i t c h

I n t h i s r e p r e s e n t a t i o n , A I C and B I C are regarded as i n p u t s t o t h e r o t o r c y c l i c p i t c h . wi th a l a g r e l a t e d t o t h e r o t o r Lock number. The t e r m s A I S and B1S repre- s e n t t h e ins tan taneous o r i e n t a t i o n of t h e c o n t r o l a x i s w i t h r e s p e c t t o t h e f u s e l a g e body a x i s system ( i n t h i s case, t h e main r o t o r s h a f t a x i s ) .

The c o n t r o l a x i s of t h e h e l i c o p t e r is then allowed t o fo l low

AIC(S)

‘cRS + 1

I n s t e a d y s t a t e , B I S = B I C and A I S - - A I C ’

( 3 4 )

Thrus t T i s o r i e n t e d along t h e c o n t r o l a x i s and t h e H and Y f o r c e s are or thogonal t o T and each o t h e r . Forces H and Y may b e viewed approximately as components of t h e r o t o r f o r c e normal t o t h e t i p p a t h p lane a r i s i n g from r o t o r t i p p a t h p lane excurs ions from t h e commanded c o n t r o l a x i s

6

p o s i t i o n (as i n r e f . 7) o r as unique f o r c e s de r ived i n a c o n s i s t e n t wind- c o n t r o l a x i s system as i n r e fe rence 3. I n t h i s r e p r e s e n t a t i o n , r e f e r e n c e 3 w a s fol lowed. Equat ions 1 4 through 19 r e s o l v e t h e T , H and Y f o r c e s i n t o body axes.

Cont ro l Axis P i t c h and R o l l Rates

I n equat ions (1) through (7) t he t e r m s qc and pc are used t o denote p i t c h and r o l l rates of t h e c o n t r o l axis i n t h e c o n t r o l axis-wind system. They are r e l a t e d t o t h e body p i t c h and r o l l rates by t h e fo l lowing two equat ions :

T a i l Rotor Thrus t

where

e2 = leTR[ , eTR > 0.0873

e 2 = 0.0873 , eTR 5 0.0873

Due t o memory de r ived as an i s o l a t e d t a i l

l i m i t a t i o n s i n t h e computer, t h e s e equa t ions were o r i g i n a l l y economical approximation t o t h e t a i l r o t o r t h r u s t of an r o t o r . (The equat ions do n o t i n c o r p o r a t e t h e v o r t e x r i n g

o p e r a t i n g s t a t e of t h e t a i l r o t o r or f i n i n t e r f e r e n c e e f f e c t s . ) t h e main i n f l u e n c e s of in f low and c o l l e c t i v e p i t c h on t a i l r o t o r t h r u s t . It w a s found t h a t t h e d e r i v a t i o n on which t h e t a i l r o t o r damping c o n t r i b u t i o n t o N r . It w a s necessary , t h e r e f o r e , t o a d j u s t t h e cons t an t e m p i r i c a l l y t o match t h e f l i g h t test r e s u l t s .

They r e f l e c t

was based, g r o s s l y underpredic ted T,,

7

T a i l Rotor Con t r ibu t ion t o Body Forces and Moments

- 'TR - T~~

L~~ TR TR = Y h

NTR = -Y k TR TR

Fuselage Aerodynamics

N = - N v u F 1 B B

Vertical F i n Aerodynamics

u = u F B

B + ' V F ~ B v = -v F

s i n a = v /(uG + v;)1/2

= K V U + F v I v I

F F

'VF I F F 1 F F

YVF = k2u; + F v Iv I I F F

= - k u 2 + F v I V I 'VF 2 F 1 F F

NVF = -Y R VF VF

-20" 5 aF 5 20"

160" 5 aF 5 200"

20" < aF < 160'

200" < aF < 340"

8

Horizonta l S t a b i l i z e r Aerodynamics

( 5 4 ) A w = w + - + u 6 + k q H B R, B S H S B + " C

u = u ( 5 5 ) H B

The h o r i z o n t a l s t a b i l i z e r of t h e h e l i c o p t e r is connected t o t h e 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 and v a r i e s i n a non l inea r manner wi th l o n g i t u d i n a l c y c l i c s t i c k p o s i t i o n ( t a b l e 1 ) .

At t h e t i m e t h e s e equat ions were developed, d a t a f o r t h e UH-1H s t a b i l i z e r i nc idence schedule were n o t a v a i l a b l e . S ince t h e UH-1B s t a b i l i z e r is l inked i n a s i m i l a r manner to t h e c y c l i c c o n t r o l s , and t a b l e 1 v a l u e s were a v a i l a b l e , they were used i n l i e u of UH-1H va lues .

H W s i n aHS =

x B = x R + s (61)

YB = Y + Y + Y 4- YVF ( 6 2 )

z B = z + z + Z H (63)

R TR F

R F

The form of t h e equat ions f o r t h e f u s e l

T o t a l Body Forces and Moments

LB = LR + LTR

M B = % + % + %

NB = NR + NTR + N + NvF F

g e , h o r i z o n t a l s t a b i l i z e r nd v e r t i c a l f i n aerodynamics r e s u l t s from us ing t r igonomet r i c f u n c t i o n s t o approximate t h e l i f t and d rag curves i n wind axes , and then r e s o l v i n g t h e s e f o r c e s and r e l a t i v e wind i n t o body axes .

Estimation of Rotor F lapping w i t h Respect t o t h e S h a f t

The t i p path p lane o r i e n t a t i o n w i t h r e s p e c t t o t h e c o n t r o l a x i s i s r e p r e s e n t e d by t h e v a l u e s of t h e f l a p p i n g c o e f f i c i e n t s approximation t o t h e a c t u a l r o t o r f l a p p i n g a n g l e w i t h r e s p e c t t o t h e s h a f t a iS and blS, t h e fol lowing e q u a t i o n s were used. of t h e cyc l ic c o n t r o l i n p u t s

a l and b, . A s an

They r e f l e c t t h e i n f l u e n c e s A I C and B I C and t h e computed f l a p p i n g a m p l i -

convent ion of r e f e r e n c e 5 i s fol lowed. t u d e s a i and b l . The s i g n

bl s w a = a - 1s 1

b l s = b , + a 1 s w

a = 4, cos 4 1 s w t

4, = C O S - ~ ( C O S A I C c o s B ) 1c

t a n A

s i n B

The maximum f lapping ampli tude is g iven by

(72 )

where Bm The or thogonal components of f l a p p i n g i n t h e wind-shaft a x i s system are a l s and b ls , and phase of t h e c y c l i c i n p u t , r e s p e c t i v e l y .

is the maximum t e e t e r i n g a n g l e w i t h r e s p e c t t o t h e r o t o r mast.

4c and + t are t h e ampli tude of t h e c y c l i c i n p u t and t h e

COMPARISON OF HELICOPTER FLIGHT DYNAMICS WITH MATH MODEL DYNAMICS

A Bell UH-1H h e l i c o p t e r w a s instrumented and flown a t Crows Landing NAS November 12 , 1974 f o r t h e purpose o f o b t a i n i n g f l i g h t r e c o r d s a g a i n s t which t h e s i m u l a t o r model could be compared.

10

I n t h i s s e c t i o n , t h e he l i cop te r responses t o s t e p c o n t r o l i n p u t s are compared d i r e c t l y wi th t h e math model responses t o t h e same i n p u t s .

F l igh t Condi t ions

Two f l i g h t cond i t ions are shown: hover ou t of ground e f f e c t and 60 k n o t s level f l i g h t . no-wfnd cond i t ions . cond i t ions .

The f l i g h t tests were made a t nominally sea l e v e l The s imula to r model i s shown a t s t anda rd day, sea level

Control I n p u t s

S tep c o n t r o l i n p u t s of from k1.25 cm t o k2.5 cm (k1/2 i n . t o k 1 i n . ) were made i n c o l l e c t i v e , p i t c h , r o l l , and yaw c o n t r o l s . The p i l o t w a s i n s t r u c t e d t o e s t a b l i s h a s t eady f l i g h t cond i t ion (zero r a t e of c l imb, p i t c h , r o l l , and yaw) and then t o inpu t and hold t h e a p p r o p r i a t e c o n t r o l f o r as long a pe r iod as p o s s i b l e be fo re i n i t i a t i n g a recovery. These i n p u t s are simu- l a t e d as t r u e s t e p s i n t h e s imula tor t i m e h i s t o r y comparisons. Amplitudes f o r t h e s imula to r i n p u t s are adjus ted t o conform as c l o s e l y as p o s s i b l e t o t h e f l i g h t v a l u e s f o r l i n e a r displacements a t t h e p i l o t ' s hand o r f o o t .

Aircraft Conf igura t ion

The a i r c r a f t f lown, and t h e s imula tor model, r e p r e s e n t s a s t anda rd UH-1H (wi th s t a b i l i z e r b a r ) weighing 2800 kg (6158 l b ) . e s t ima ted i n i t i a l g ros s weight of t h e h e l i c o p t e r a t t h e commencement of t h e tests. a p r e - f l i g h t weight and ba lance of t h e h e l i c o p t e r , fol lowed by ad jus tments f o r f u e l burnoff and personnel t r a n s f e r s p r i o r t o t h e test runs .

This weight i s t h e

Both t h e weight and l o n g i t u d i n a l c e n t e r of g r a v i t y were de r ived from

The i n e r t i a v a l u e s used f o r the s imula to r model are r e p r e s e n t a t i v e va lues ob ta ined from unpublished B e l l Hel icopter Company da ta .

The ver t ical c e n t e r of g r a v i t y of t h e h e l i c o p t e r w a s no t known. The c h a r a c t e r i s t i c l e n g t h s used i n t h e model r e f l e c t on ly a reasonable estimate of i ts va lue .

Aircraft On-Board Sensors

The s e n s o r s on t h e a i r c r a f t were:

1. Body angu la r rate gyros sensing roll r a t e , p i t c h ra te and yaw rate,

2. Vertical gyro sens ing Euler a t t i t u d e s of t h e a i r c r a f t i n r o l l , p i t c h , and heading,

3 . Body acce lerometers measuring body axis a c c e l e r a t i o n s ,

11

4 . Airspeed i n d i c a t o r ,

5 . Ins tan taneous v e r t i c a l speed i n d i c a t o r (IVSI), i . e . , rate-of-climb p r e s s u r e instrument ,

6. Sensors f o r measuring c o n t r o l displacements a t t h e p i l o t ' s hand o r f o o t : 6, ( c o l l e c t i v e p i t c h s t i c k ) , 6, ( l o n g i t u d i n a l c y c l i c s t i c k ) , 6, ( l a t e r a l c y c l i c s t i c k ) , and 6 p (peda l , o r 8TR p i t c h i n p u t ) .

T i m e H i s t o r y Comparisons

The a i r c r a f t and model angular ra te and a t t i t u d e responses t o t h e s t e p c o n t r o l i n p u t s a r e shown o p p o s i t e each o t h e r i n f i g u r e s 2 through 9 . Fig- u r e s 2 through 5 a re responses t o i n p u t s i n i t i a t e d from a s t e a d y 60 knot trimmed forward f l i g h t condi t ion . F igures 6 through 9 are responses t o i n p u t s s t a r t i n g from an i n i t i a l trimmed hover condi t ion .

The format f o r each f i g u r e i s t h e same. The f i r s t page c o n s i s t s of p ~ , qB and r B page. The second page shows t h e displacement a n g l e s 0, 8 and + and t h e ve r t i ca l a c c e l e r a t i o n A, f o r t h e same c o n t r o l i n p u t . Vert ical l i n e s on t h e f l i g h t d a t a denote t h e beginning and end of t h e c o n t r o l i n p u t . Tick marks on t h e model d a t a i n d i c a t e c o n t r o l i n p u t . A l l pens are zeroed a t t h e end of t h e c o n t r o l s t e p on t h e model d a t a .

versus t i m e f o r t h e c o n t r o l i n p u t shown a t t h e bottom of t h e

The a i rcraf t A, is included o n l y f o r a g e n e r a l t r e n d comparison s i n c e t h e f i l t e r i n g of t h i s s i g n a l was subsequent ly found t o be q u e s t i o n a b l e . The a i r c r a f t IVSI was suspec ted of having a l a r g e l a g s i n c e r a d a r h e i g h t p o s i t i o n data d i d n o t compare w e l l w i t h i n t e g r a t e d i n s t a n t a n e o u s v e r t i c a l speed i n d i - c a t o r (IVSI) readings. Consequently, a comparison of rate-of-climb response t o c o l l e c t i v e p i t c h i s n o t shown. Comparison w i t h r a d a r h e i g h t d a t a i n hover d i d show t h a t the rate-of-climb response i s a f i r s t o r d e r type of heave

response (h = Kh6c(l - e 'ITA)) and t h a t bo th t h e t i m e c o n s t a n t and s t e a d y s t a t e va lues were w e l l modeled by t h e equat ions .

-

A d i r e c t comparison of t h e r e c o r d s a t 60 k n o t s shows t h a t t h e primary responses t o t h e c o n t r o l i n p u t s are reasonably w e l l modeled: p i t c h ra te t o longi tudimal c y c l i c , r o l l rate t o la teral c y c l i c and yaw rate t o a p e d a l s t e p . The coupled responses t o t h e s e same s t e p s show s i g n d i f f e r e n c e s i n some cases, b u t t h e a b s o l u t e magnitudes of t h e responses are s m a l l . For t h e peda l s t e p and t h e c o l l e c t i v e s t e p , where t h e coupled responses are l a r g e r , t h e magni- t u d e s and s i g n s of t h e coupled responses appear t o be p r o p e r l y r e p r e s e n t e d .

Attempts t o d u p l i c a t e f l i g h t responses i n hover were n o t as s u c c e s s f u l . The primary responses are s u f f i c i e n t l y w e l l modeled so t h a t t h e p i l o t w a s g iven proper cues i n t h e f i r s t one t o two seconds fo l lowing a s e r v o f a i l u r e . The long term response i n p i t c h ra te i s exaggerated and t h e long term response i n r o l l rate i s underpredic ted by t h e model. p i t c h coupl ing i s e v i d e n t i n t h e f l i g h t r e c o r d s f o r b o t h t h e l a t e r a l s t e p

I n a d d i t i o n , s t r o n g

12

i npu t and t h e peda l s t e p i n p u t , a phenomenon not p r e s e n t i n t h e model. p h y s i c a l r eason f o r t h e s e coupled responses w a s no t understood.

The

The primary yaw ra te response i n hover i s good. The coupled yaw responses t o l a t e ra l c y c l i c p i t c h and t o c o l l e c t i v e p i t c h are s a t i s f a c t o r y .

The v a l i d a t i o n e f f o r t w a s stopped a t t h i s po in t because f u r t h e r a t t empt s t o improve t h e hover responses were n o t s u c c e s s f u l , o r i t changed t h e model adve r se ly a t 60 knots . Without more i n s i g h t i n t o t h e b a s i c aerodynamics of t h e a i r c r a f t i n hover , i t w a s a l s o d i f f i c u l t t o understand how t o al ter t h e equa t ions t o o b t a i n t h e d e s i r e d r e s u l t s ,

The i n i t i a l responses t o servo hardovers were be l i eved rea l i s t ic enough t o p rov ide t h e p i l o t w i th t h e appropr i a t e cues t o i n i t i a t e recovery. The o v e r a l l dynamics appeared t o be adequate t o g i v e a r easonab le estimate of a i r c r a f t excurs ions du r ing t h e recovery from a f a i l u r e .

P i l o t Evalua t ions

I n a d d i t i o n t o comparing t h e model w i t h f l i g h t t i m e h i s t o r i e s , t h e model w a s opera ted b o t h i n a f ixed-base s imula to r and i n a six-degree-of- freedom moving-base s imula to r ( 6 DOF). motion washout i n hover , and wi th motion washout a t 60 knots . The f l i g h t s wi thout washout w e r e made wi th open cab and wi th real outside-world r e f e r e n c e s . r e f e r e n c e provided by a t e r r a i n model.

The model w a s flown wi th and wi thout

The f l i g h t s w i th washout, and f i x e d base , were made w i t h v i s u a l

The model w a s judged t o be real is t ic a t 60 knots by t h e r e s e a r c h pilots who f l ew t h e s imula t ion . However, t he model w a s judged t o b e d i f f i c u l t t o f l y normally i n hover by every p i l o t who f lew i t . P r e c i s e hover and p r e c i s e maneuvers around hover a t low speeds , i nc lud ing qu ick s t o p s and la teral t r a n s l a t i o n s , were more d i f f i c u l t w i th t h e s imula ted model than wi th t h e a c t u a l h e l i c o p t e r . change t h e p i l o t ' s eva lua t ions .

Motion cues provided b y . t h e 6 DOF s imula to r d i d no t

I n s p i t e of t h i s , a l l p i l o t s were a b l e t o adapt themselves t o t h e s imula to r and f l y q u i t e p r e c i s e l y a f te r a l e a r n i n g pe r iod . i n t h e 6 DOF s imula to r wi th open cab and no motion washout w a s p o s s i b l e . I n a d d i t i o n t o t h i s , r e c o v e r i e s from r o l l and p i t c h s e r v o hardovers were accomplished, and a p r e c i s i o n hover r e e s t a b l i s h e d w i t h i n t h e 5.5 m2 of p o s s i b l e s imula to r travel.

P r e c i s i o n hover

This model was used i n a f l i g h t c o n t r o l s imula t ion desc r ibed i n r e f - e rence 1.

13

CONCLUDING REMARKS

The mathematical model 0 f . a UH-1H h e l i c o p t e r descr ibed i n t h i s r e p o r t w a s developed f o r rea l t i m e p i l o t e d s i m u l a t i o n . The model w a s eva lua ted by comparing i t s dynamics o b j e c t i v e l y w i t h f l i g h t test r e s u l t s and subjec- t i v e l y w i t h p i l o t e v a l u a t i o n s . The model appears t o b e s a t i s f a c t o r y f o r f l y i n g q u a l i t i e s i n v e s t i g a t i o n s a t forward speeds and u s a b l e , bu t less r e a l - i s t i c , f o r hover. The reasons f o r t h e d i s c r e p a n c i e s between f l i g h t and s i m u l a t i o n have n o t y e t been determined.

It i s be l ieved t h a t enough informat ion has been provided h e r e t o e n a b l e a p o t e n t i a l user t o d e c i d e whether t h e model i s s u i t a b l e f o r h i s a p p l i c a t i o n .

REFERENCES

1. C o r l i s s , Lloyd C . ; and Talbot , P . D . : A F a i l u r e E f f e c t s S imula t ion of a Low Authori ty F l i g h t Control Augmentation System on a UH-1H H e l i c o p t e r . NASA TM-73,258, 1977.

2. McFarland, R. F.: A Standard Kinematic Model f o r F l i g h t S imula t ion a t NASA-Ames. NASA CR-2497, 1975.

3. Seckel , Edward; and C u r t i s , H. C . , Jr.: Aerodynamic C h a r a c t e r i s t i c s of Hel icopter Rotors. Rotor C o n t r i b u t i o n s t o H e l i c o p t e r S t a b i l i t y Parameters. P r i n c e t o n U n i v e r s i t y Report , 1963.

4. Biggers , J. C . ; McCloud, 3. L . , 111; and P a t t e r a k i s , P e t e r : Wind Tunnel Tests of Two F u l l Scale H e l i c o p t e r Fuse lages . NASA TN D-1548, 1962.

5. Gessow, A . ; and Myers, G. C . , Jr . : Aerodynamics of t h e H e l i c o p t e r , Macmillan, 1952.

6. F lan igen and P o r t e r : Category I1 Performance Tests of t h e YUH-1D w i t h a 48-foot Rotor. AFFTC TDR 64-27, Nov. 1964.

7 . Wilcock, T . ; and Thorpe, A. C . : F l i g h t S imula t ion of a Wessex H e l i c o p t e r : A V a l i d a t i o n Exerc ise . RAE TR 73096, Sept . 1973.

8. McCloud, J. L . , 111; Biggers , J. C . ; and S t roub , R. H . : An I n v e s t i g a t i o n of F u l l Scale H e l i c o p t e r Rotors a t High Advance R a t i o s and Advancing Tip Mach Numbers. NASA TN D-4632, 1968.

9. F innes tead , R. L . ; and Graham, W. A , : T a i l Rotor Performance and T r a n s l a t i o n a l F l i g h t Handling Q u a l i t i e s Tests of t h e UH-1H H e l i c o p t e r . USAASTA Proj ect #71-18 , Jan. 1972.

14

TABLE 1.- VARIATION OF HORIZONTAL STmILIZER INCIDENCE

WITH LONGITUDINAL STICK POSITION

6e CIU in.

6s rad

16.38

15.25

12.7

10.16

7.62

5.08

2.54

0

2.54

5.08

7.62

10.16

12.7

15.25

16.38

-6.45

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0

1.00

2.00

3.00

4.00

5.00

6.00

6.45

0.0224

.0174

0

-. 0192

-. 0384

-. 0541

-. 0690

-. 0820

-. 0850

-. 0803

-. 0628

-. 0300

.0035

.0593

.0942

15

TABLE 2.- SUMMARY OF UH-1H PHYSICAL CONSTANTS Engl i sh Metric

2.75 deg 24.13 f t 7.35 m

1.75 f t .53 m 760 f t / s e c 231.6 m/sec 133.5 136.5

.046

Main r o t o r Hub precone a n g l e Radius Chord Tip speed (RR) Hub s t a t i o n Hub w a t e r l i n e S o l i d i t y

T a i l r o t o r Radius Chord Tip speed S h a f t s t a t i o n S h a f t w a t e r l i n e S o l i d i t y

Center of g r a v i t y Most forward Most a f t Vertical

H o r i z o n t a l s t a b i l i z e r Area Span 1 f 4 c s t a t i o n

Area Span 114 c s t a t i o n a. c . , w a t e r l i n e

Vertical f i n

Fuse lage

inc ludes s t a b . ) Cma ( inc ludes s t a b . ) C L ~ (no ho r i z . s t a b . ) Cma (no ho r i z . s t a b . ) S r ef g ref Mast t i l t

Cont ro l t ravels ( f u l l throw) C o l l e c t i v e s t i c k Longi tudinal s t i c k Lateral s t i c k Pedals

L a t e r a l c y c l i c r i g g i n g

Longi tudina l c y c l i c p i t c h Lateral c y c l i c p i t c h T a i l r o t o r c o l l e c t i v e p i t c h

F u l l 1. pedal F u l l r . p e d a l

fe1 CLa (

4.25 f t .70 f t

740 f t / s e c 479.4 137.5

,105

s ta . 130 s t a . 144 w . 1 . 55

16.4 f t 2 8 .75 f t

380

12 f t 2 4.5 f t

460 112

19 .2 f t 2 .036/deg

.02/deg 7 . 5 ~ 1 0 - ~ / d e g 48 f t 2 39 f t +5 deg fwd.

0

11 i n . 12.9 i n . 12.6 i n .

6.9 i n .

2' l e f t

+12' +go t o -11'

18 O

- loo

1.29 m 21.33 c m

225.5 m/sec

1.52 m2 2.67 m

1.11 m2 1 .37 m

1 .78 m2

4.46 m2 3.62 m

27.9 c m 32.8 c m 32.0 c m 17.5 c m

1 6

a, 1 rl (d 3

d u (d rl

7.1 m e3

a, u k 1 0 cn

c -4 M .rl k 0 \ c 0 *rl U

U c (d u 2 0 u

u .rl k

i

2 d rl M c w

z 0 rl X rl

h rl

Ln

5 Ln 0 rl X U 03

m

m

w 2

N n

v

d :IN

Q

d

p:

V a, m

m I 0 rl X h m h

V a, cn

m I 0 rl X h m h

m

w 2

C U \ rl

nl I 0 4 X 0 h

03

m

w a, p:

(d

hl \ rl

p:"

V a, cn

nl I 0 rl X m m e4

nl I 0 rl X \D m U

m

w a, Pi

(d

U \ rl

Ln p:

u al 111

* * I i

E 1 u a, m m I 0 rl X 0 0

U

U w \ u a, cn

m I 0 rl X hl hl

rl

m

w a, p:

p: C \ rl

co 0 rl X m m hl rl

P rl I U w

0 rl X h 0 rl

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co

v)

w 2

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nl

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nl P rl \ rl d

d

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0 hl 0 03

rl

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a (d k

03 U 0

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03

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cn (d

a a,

0 9 arb rl M C k ( d o a, c a , 0 1 u r l a,(d k ? a

C arb

w

2 2

0 (d

17

a 3 U . 2 N N m m . .

5 \ a (d Li co m 0 0

C .I4 \ a (d k

u) N 0

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ru 2

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c .rl

Li aJ a

5 u .rl a aJ 3 .rl u u a,& r l u rl .rl o u urn

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a3

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m

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a

do

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18

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I

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w aJ

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k .rl o u u o O E k

rl r l a *rl a (d a , Bca

3

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m k

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n n u u a J a J z p z p 5 5

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m hl n u aJ

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I

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x x3 24

20

aJ U & 7 0 m

c *ri M .a . . k 0 \ d 0 -r( u (d 1 m w

U c rd u (0 d - 0 u

hl

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Ad

m m b m

N u w

I M 7 rl m 0 0 W -4

k aJ U a 0 U .ri r l c d aJu x ( d

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H

hl

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m

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21

Figure 1.

4 +XCG

L

XB

b

H U B FORCES AND MOMENTS T - ALONG CONTROL AXIS H - NORMAL TO CONTROL AXIS IN PLANE OF RELATIVE WIND

NORMAL TO T, H AND CONTROL AXIS

Y -

\ "I\ LA

Q ;> kT H U B + \4

1'1,

SHAFT AXIS

VIEW LOOKING AFT

NOTE: BODY Z AXIS IS PARALLEL TO MAIN ROTOR SHAFT

, - C h a r a c t e r i s t i c l e n g t h s and s i g n convent ions used f o r f o r c e s , moments and c o n t r o l displacements .

22

AIRCRAFT LJH-1H SN AAB-11519 CONTROL INPUT Fwd. long. s t e p FLIGHT CONDITION 60 knots GROS S WE I GHT LONGITUDINAL CG.

29,371 N (6158 lb) I

I - 8 '

i ! I MoncL

(a) Rate response .

F igu re 2.- Forward cycl ic s t e p i n p u t .

23 .

60 KNOTS CONTROL INPUT Fwd. long. s t e p

MW€L

e-

-

0 I . , t I 4 I I I t 8 I I scc t I / z l I

( b ) A t t i t u d e r e s p o n s e .

F i g u r e 2 . - C o n c l u d e d .

24

CONTROL INPUT L a t . cycl ic s t e p v

I I I MODEL f

(a> Rate response .

Figure 3 . - Lateral s t e p input .

25

60 KNOTS CONTROL INPUT L a t . c y c l i c s t e p k

MODEL

I v ) I

I

i -180

I I - (b) A t t i t u d e response.

F igu re 3.- Concluded.

26

60 KNOTS CONTROL INPUT R. peda l s t e p w

i MODCL I I I

(a ) Rate response .

F igu re 4.- Pedal s t e p i n p u t .

27

60 KNOTS

Q R

I .s-

. -

I . .

I I

CONTROL INPUT R. p e d a l s t e p

MCWEL

I

(b) A t t i t u d e response.

Figure 4 . - Concluded.

28

60 KNOTS

I 25

I

i L!! i 2 5 -

0-

26.6cm (10.5 in.)

I . -.A

CONTROL INPUT UP c o l l e c t i v e

AqODCL

!

(a) Rate response.

F igure 5.- Col l ec t ive s t e p i n p u t .

29

60 KNOTS CONTROL INPUT U P c o l l e c t i v e

(b) A t t i t u d e response .

Figure 5.- Concluded.

30

. 25

- to

, 20 -

25 - 16 cm (6.33 in.).

0- 9Y

-16cm ,

(-6.33 in.)

-_

I

AIRCRAFT UH-1H SN AAB-11519 CONTROL INPUT Fwd. long. s t e p FLIGHT CONDITION Hover GROSS WEIGHT LONGITUDINAL CG.

29 ,371 N (6158 lb)

I I A q O D E t

(a) Rate response.

F igure 6 . - Forward c y c l i c s t e p i n p u t .

31

' - 4 5 - L - ' I

8 1; R

I * 4 5 -

- 45 - 3 D' ' 4 r

!e 0 0

I / 0--- - 1 7

c

--

/

------y-

1 / e 5 -I I

I - I I n I 1 I I

CONTROL INPUT Fwd. long,. s t e p

- 4 . - / , . . I I , I . . 8 , I , I I I

! . , ! I t-~! . ,. . .~., . _ ~ I ..+. . . . . , . . .

(b) A t t i t u d e response .

F igure 6 . - Concluded.

32

HOVER

I I

1 2 0 -

I p i I ! 2 5 - -1 5.9 crn (-6.25 in.) I

I L 1

I 0- I

R I w ! i lhacm 1(6.25 in.)' -

. I , . - . i I i t . . . . . . . . ..

! I 1 , , . . I ' I

CONTROL INPUT Lat . c y c l i c s t e p

AqODEL I

(a) Rate response.

F igure 7.- L a t e r a l c y c l i c s t e p inpu t .

33

- ~ ..- ' I

. I

/-- - I - - 180

I

CONTROL INPUT L a t . c y c l i c s t e p

MW€L

. (b) A t t i t u d e response.

F igu re 7.- Concluded.

34

HOVER - i -

-25

1 I 25 L 1 - 2 0 -

I 2 0 - I-zs-

8 2 5 cm ! (3.25 in.)

CONTROL INPUT R. pedal s t ep

I A?10DEL

(a) Rate response.

Figure 8 . - Pedal s t e p input.

35

HOVER CONTROL I N P U T R. peda l s t e p I I

(b) A t t i t u d e response .

F igu re 8.- Concluded.

36

.

HOVER Y

' i i 25

I

I ' -i- --____

- . . 1 - I

I I 1

I 4 8 src. IZ

26.6 cm (10.5 in.)

CONTROL INPUT UP c o l l e c t i v e

AqODEf-

-I I I I I I

! ! I i

I

0 1' B 5EC I2

(a) Rate response .

F igu re 9.- Collective s t e p i n p u t .

37

I

! ! I 1 -180 - -

I I

.

(b) A t t i t u d e response .

F i g u r e 9.- Concluded.

38

I . Report No. TM- 73 , 254

8. Performing Organization Report No. 7. Author(s1 A-7080 Peter D. Talbot and Lloyd D. C o r l i s s

10. Work Unit No.

505-10-23 9. Performing Organization Name and Address

3. Recipient's Catalog No. 2. Government Accession No.

Ames Research Center , NASA and Ames D i r e c t o r a t e , 11. Contract or Grant No. USAAMRDL, AVRADCOM, Ames Research Center

4. Title and Subtitle

A MATHEMATICAL FORCE AND MOMENT MODEL OF A UH-1H HELICOPTER FOR FLIGHT DYNAMICS SIMULATIONS

5. Report Date

6. Performing Organization Code

Moffe t t F i e l d , CA 94035 S nsorin Agency Name and Address

'kaflona? Aeronaut ics and Space Adminis t ra t ion

16. Abstract

13. Typa of Report and Period Covered Technica l Memorandum

A model of a B e l l UH-1H h e l i c o p t e r w a s developed t o suppor t s e v e r a l s imula t ions a t Ames Research Center and w a s used a l s o f o r development work on an a v i o n i c s system known as t h e V/STOLAND system a t Sper ry F l i g h t Systems. This r e p o r t p r e s e n t s t h e complete equat ions and numerical v a l u e s of c o n s t a n t s used t o r e p r e s e n t t h e h e l i c o p t e r .

Responses t o s t e p i n p u t s of t he c y c l i c and c o l l e c t i v e c o n t r o l s are shown and compared w i t h f l i g h t test d a t a f o r a UH-1H. a d j u s t e d i n an a t tempt t o g e t a c o n s i s t e n t match wi th t h e f l i g h t t i m e h i s t o r i e s a t hover and 60 knots . a t 60 kno t s , bu t t h e matching a t hover w a s no t as s u c c e s s f u l . e v a l u a t i o n s of t h e model, bo th f ixed and moving base , were made.

The model c o e f f i c i e n t s were

F a i r l y good response matching w a s ob ta ined P i l o t

Washington, D. C. RfiD Laboratory, Moffe t t F i e l d , CA 94035

20546 and U. S. Army A i r Mobi l i ty

17. Key Words (Suggested by Author(s1)

UH-lfi h e l i c o p t e r f l i g h t dynamics S imula t ion Fixed base and comparison with f l i g h t

test

14. Agency code

18. Distribution Statement

Unlimited

STAR Category - 08 ~ ~~

~

19. Security Classif. (of this report) 20. Security Classif. (of this pagel

U n c l a s s i f i e d Unclass i f ied

21. No. of Pages 22. Price'

45 $3.75