thrust uses

S I M U L A T I O N O F M A N N E D L U N A R L A N D I N G

1 2 3

E . M a r k s o n , J. B r y a n t and F . B e r g s t e n M a r t i n C o m p a n y , B a l t i m o r e 3, M a r y l a n d A B S T R A C T

A p r e d i c t i v e type of guidance s y s t e m f o r a m a n - i n - t h e - l o o p lunar landing is d e v e l o p e d w h i c h u s e s a n o v e l solution t o t h r e e - d i m e n s i o n a l p a r t i c l e m o t i o n f o r r e p e a t e d p r e d i c t i o n s of t r a j e c t o r y end c o n d i t i o n s . A n e f f i c i e n t E u l e r angle p r o g r a m and an a s s u m p t i o n of constant t r a n s l a t i o n a l thrust e n t e r into the p r e d i c t i o n t e c h n i q u e . T h e p r e d i c t e d end conditions a r e c o m p a r e d t o a set of d e s i r e d end c o n d i t i o n s , and a p p r o p r i a t e e r r o r s i g n a l s a r e g e n e r a t e d f o r p i l o t d i s p l a y and autopilot c o n t r o l s . A d i s c u s s i o n of the r e s u l t s of a s i m u l a t i o n p r o - g r a m using this s y s t e m i s g i v e n , c o v e r i n g the m e c h a n i z a t i o n , the d i s p l a y r e q u i r e m e n t s , and the e f f e c t s of "man in the l o o p . "

During manual o p e r a t i o n , the p i l o t l i t e r a l l y f l i e s the p r e d i c - tions t o the point w h e r e t e r m i n a l d i s p l a y s a r e a c t i v a t e d f o r the final pitchup and d e s c e n t m a n e u v e r o v e r the landing s i t e . A n " o u t - t h e - w i n d o w " a p p r o a c h to d i s p l a y s f o r lunar touch- down i s d i s c u s s e d .

I N T R O D U C T I O N

A n i n v e s t i g a t i o n w a s made of a m a n - i n - t h e - l o o p lunar landing, using a p r e d i c t i v e guidance t e c h n i q u e . T h e d y n a m i c a s p e c t s of the landing w e r e s i m u l a t e d . T h e s i m u l a t i o n w a s p e r f o r m e d w i t h a f i x e d b a s e s i m u l a t o r d e s i g n e d f o r o n e - m a n c o n t r o l .

T h e lunar landing m a n e u v e r i s d i v i d e d into f i v e sequential o p e r a t i o n a l p h a s e s : d e o r b i t , c o a s t i n g d e s c e n t , b r a k i n g , t e r - m i n a l m a n e u v e r and h o v e r t o touchdown. T h e s e p h a s e s a r e P r e s e n t e d at A R S L u n a r M i s s i o n s M e e t i n g , C l e v e l a n d , July

17-19, 1962.

"'"Engineering S p e c i a l i s t . 2

E n g i n e e r i n g S p e c i a l i s t .

^Senior E n g i n e e r .

MARKSON, BRYANT, A N D BERGSTEN

i l l u s t r a t e d in F i g . 1. T h e landing i s a s s u m e d t o take p l a c e after a d e o r b i t f r o m a 100-naut m i c i r c u l a r o r b i t a b o v e the m o o n¹ s s u r f a c e . F r e e c o a s t i s a s s u m e d f r o m the t i m e d e - o r b i t i s c o m p l e t e t o the point of thrust i n i t i a t i o n f o r the l a n d - ing m a n e u v e r .

Range a n g l e s f r o m 45° t o 180° a r e c o n s i d e r e d f o r the

c o a s t , r e s u l t i n g in i n i t i a l c o n d i t i o n s f o r the b r a k i n g m a n e u v e r as shown in F i g . 2. T h e b r a k i n g phase i s r e q u i r e d to r e - m o v e on the o r d e r of 98% of the t o t a l v e l o c i t y , ending n o m i - nally w i t h the v e h i c l e at 1000 ft a b o v e the s u r f a c e w i t h a v e l o c i t y l e s s than 150 f p s .

The t e r m i n a l m a n e u v e r i s s t a r t e d w h e r e the b r a k i n g m a - n e u v e r s t o p s . Due t o the flat c h a r a c t e r i s t i c s of landing t r a - j e c t o r i e s made f r o m a c i r c u l a r o r b i t , the thrust v e c t o r at the initiation of the t e r m i n a l phase i s g e n e r a l l y at an a n g l e l e s s than 30°, r e l a t i v e t o the h o r i z o n t a l . T h u s , the p r i m a r y p u r - p o s e of the t e r m i n a l m a n e u v e r i s t o null the l a t e r a l v e l o c i t i e s , w h i l e s m o o t h l y pitching the thrust v e c t o r o v e r t o a v e r t i c a l , or h o v e r i n g , attitude. T h e final d e s c e n t i s v e r t i c a l and i s made at v e l o c i t i e s r a n g i n g f r o m about 50 fps to a touchdown speed of a p p r o x i m a t e l y 6. 75 f p s .

The p o r t i o n of the lunar landing m a n e u v e r r e p o r t e d h e r e s t a r t s during the c o a s t i n g d e s c e n t phase 30 s e c b e f o r e the b r a k i n g thrust i s i n i t i a t e d . During the b r a k i n g m a n e u v e r , c o n t r o l i n f o r m a t i o n i s p r e s e n t e d to the p i l o t in the f o r m of p r e d i c t e d p o s i t i o n r e l a t i v e t o the t a r g e t . A n a c c e p t a b l e safe band of t e r m i n a l altitudes h^ and h ^ , defined by sinking speed o v e r the t a r g e t , p r o v i d e s the p r i m a r y pitch c o m m a n d . The p r e d i c t e d t e r m i n a l altitude h^, b a s e d on p r e s e n t E u l e r angle r a t e s that a r e a s s u m e d constant during a p r e d i c t i o n , p r o v i d e the p r i m a r y c o m m a n d f o r p i t c h r a t e . Y a w angle and yaw r a t e c o n t r o l s a r e b a s e d on p r e d i c t e d l a t e r a l r a n g e e r - r o r s . T h r o t t l i n g c o m m a n d s a r e made in r e s p o n s e t o d o w n - r a n g e e r r o r s .

A s i n g l e c o n t r o l , then, is p r o v i d e d f o r e a c h c o o r d i n a t e - - v e r t i c a l , longitudinal r a n g e and l a t e r a l r a n g e . T h e d i s p l a y s and c o c k p i t , as m e c h a n i z e d f o r the s i m u l a t i o n , a r e d e s c r i b e d in F i g s . 3 and 4.

T h r e e t y p e s of s t a b i l i z a t i o n and c o n t r o l s y s t e m s w e r e p r o v i d e d f o r the s i m u l a t i o n . T h e f i r s t w a s a p r o p o r t i o n a l damping c o n t r o l , w h i c h o p e r a t e d only when the p i l o t made an input c o m m a n d in pitch o r y a w . R o l l c o n t r o l w a s o v e r - damped with no p i l o t input and undamped w i t h p i l o t input.

T h e s e c o n d type of c o n t r o l p r o v i d e d a c o n v e n t i o n a l , c o n v e r - gent l i n e a r s y s t e m w i t h the p i l o t in the l o o p . T h e t h i r d w a s a c o n v e n t i o n a l c l o s e d l o o p f o r automatic c o n t r o l .

It w a s found that the p i l o t could p e r f o r m his a s s i g n e d task as w e l l as the autopilot s y s t e m , and his fuel usage w a s c o m - p e t i t i v e with the automatic s y s t e m . In g e n e r a l , the p i l o t i m - p r o v e d t o t a l s y s t e m p e r f o r m a n c e , in t h a t - - w i t h m a r g i n a l i n i - t i a l c o n d i t i o n s - - h e w a s able t o take c o m m a n d of the v e h i c l e and r e c o v e r f r o m a p o t e n t i a l i m p a c t .

G U I D A N C E D E V E L O P M E N T

The d e v e l o p m e n t of the guidance philosophy f o r this s i m u - lation w a s r o o t e d in the b e l i e f that man can a c c o m p l i s h a lunar landing if he i s g i v e n the r i g h t i n f o r m a t i o n , a p p r o p r i a t e l y d i s - p l a y e d . P a r t of the study, then, w a s d e v o t e d t o finding the r i g h t i n f o r m a t i o n . D i s p l a y o p t i m i z a t i o n w a s w e l l beyond the s c o p e of an e x p l o r a t o r y i n v e s t i g a t i o n of this t y p e .

B a s i c a l l y , t w o t y p e s of c o n t r o l i n f o r m a t i o n can be used t o guide the p i l o t¹ s inputs. T h e f i r s t i s t o fly a p r e d e t e r m i n e d , n o m i n a l flight path w i t h no f r e e d o m of c h o i c e . W i t h this t y p e of c o n t r o l i n f o r m a t i o n , the p i l o t i s a d e x t e r o u s " z e r o - m e t e r r e a d e r . ¹¹ T h e s e c o n d type of c o n t r o l i n f o r m a t i o n i s b a s e d on adaptive path c o n t r o l . C o n t r o l of t h i s type i s much m o r e

" f o r g i v i n g " than a d o w n - t h e - w i r e a p p r o a c h and is m o r e suited to manual o p e r a t i o n , p r o v i d i n g , as it d o e s , a w i d e band of conditions under w h i c h a safe landing can be a c c o m p l i s h e d .

The p r e s e n t study used a d a p t i v e path c o n t r o l as connoting the h i g h e s t p r o b a b i l i t y of e x p l o r i n g the r a n g e of f e a s i b l e i n i - t i a l conditions shown in F i g . 2.

B r a k i n g P h a s e

N o t i n g the s u c c e s s of a r e - e n t r y guidance technique using a p r e d i c t i o n a p p r o a c h , a n a l y s i s w a s initiated in S e p t e m b e r

1961 t o d e t e r m i n e the a p p l i c a b i l i t y of this a p p r o a c h t o the lunar landing. T w o p r o b l e m a r e a s r e q u i r e d r e s o l u t i o n b e f o r e definite c o n c l u s i o n s could be d r a w n . F i r s t , what thrust v e c - t o r c o n t r o l w a s m o s t suitable f o r manual o p e r a t i o n and, s e c - ond, what solution t o the equations of m o t i o n w a s a m e n a b l e t o r e p e t i t i v e solution with the s e l e c t e d flight path c o n t r o l .

T h r u s t V e c t o r C o n t r o l

The thrust v e c t o r must be c o n t r o l l e d in such a m a n n e r that the r a n g e and r a n g e r a t e go t o s p e c i f i c v a l u e s s i m u l t a n e o u s l y .

MARKSON, BRYANT, A N D BERGSTEN

The thrust magnitude should e x p e r i e n c e as s m a l l a v a r i a t i o n as is p r a c t i c a l to m i n i m i z e the r e q u i r e m e n t s f o r engine t h r o t t l i n g . T o c o m p l e t e the l i s t of r e q u i r e m e n t s , fuel c o n - sumption must not be p e n a l i z e d by the thrust v e c t o r c o n t r o l . In f a c t , it should be r e l a t i v e l y c l o s e to a m i n i m u m , so as t o make p o s s i b l e a r e a l i s t i c e v a l u a t i o n of the p e n a l t i e s i n c u r r e d by manual c o n t r o l .

T h e s e r e q u i r e m e n t s a r e not c o m p a t i b l e . F o r e x a m p l e , 4 m i n i m u m fuel consumption d i c t a t e s constant thrust ( 1 ) , but r a n g e c o n t r o l d i c t a t e s v a r i a b l e t h r u s t . A g a i n , m i n i m u m fuel consumption w i t h a r a n g e r e s t r a i n t d i c t a t e s a c o m p l i c a t e d thrust v e c t o r i n g s y s t e m , w h e r e a s the guidance i n f o r m a t i o n must be d i s p l a y e d s i m p l y and be instantaneously a s s i m i l a b l e by a human i n t e l l i g e n c e . T h e r e a r e other c o n f l i c t i n g r e q u i r e - m e n t s . A r e a s o n a b l e c o m p r o m i s e has b e e n a c h i e v e d and is h e r e d e s c r i b e d . L a w d e n ( 2 ) has noted that an e x t r e m u m of

s o m e payoff function i s obtainable f o r a point p a r t i c l e in a constant g f i e l d w i t h m a s s a function of t i m e , if the thrust v e c t o r d i r e c t i o n is r e p r e s e n t e d by a t i m e - d e p e n d e n t function of the f o r m

, ^Q a - bt

tan θ = ^{Τ Γ}

c - dt

w h e r e θ is the thrust v e c t o r angle in an i n e r t i a l t w o - d i m e n - sional a x i s s y s t e m . F r i e d ( 3 ) has shown that d = 0 f o r r a n g e u n r e s t r a i n e d , and P e r k i n s ( 4 ) has indicated that it i s a p p l i - cable to a b r a k i n g type of m a n e u v e r . It can be shown that a s i m i l a r f o r m is obtained when a t h r e e - d i m e n s i o n a l r e s o l u t i o n of the thrust v e c t o r i s m a d e .

A notable c h a r a c t e r i s t i c of solutions f o r a and b in this function is that the product ( b t ) is g e n e r a l l y s m a l l f o r b r a k i n g t r a j e c t o r i e s in s e l e n o c e n t r i c s p a c e - - a n d with i n i t i a l d e c e l e r a - tions g r e a t e r than 15 f p s / s e c . W i t h this o b s e r v a t i o n , it is p o s s i b l e to l i n e a r i z e and w r i t e

θ = θ + è t ο Ψ = Ψ⁰ + Ψ t

T h i s c o n c l u s i o n i s supported, in p a r t , by R e f . 5.

4 N u m b e r s in p a r e n t h e s e s indicate R e f e r e n c e s at end of p a p e r .

[1]

S u m m a r i z i n g the o b s e r v a t i o n s made a b o v e , the authors postulate that a E u l e r angle p r o g r a m having constant f i r s t d e r i v a t i v e s r e p r e s e n t s an e f f i c i e n t thrust v e c t o r c o n t r o l . F u r t h e r m o r e , the r e q u i r e m e n t that r a n g e and r a n g e r a t e be d r i v e n to a s p e c i f i e d value s i m u l t a n e o u s l y is s a t i s f i e d in t w o of the t h r e e d i m e n s i o n s . T h e t h i r d (longitudinal r a n g e ) i s s a t i s f i e d if the thrust magnitude and i g n i t i o n point a r e a l l o w e d to v a r y within s p e c i f i c bounds t o a c c o m m o d a t e e r r o r s in i g - nition t i m e and s y s t e m p e r f o r m a n c e . F i n a l l y , an E u l e r a n g l e p r o g r a m l i k e that g i v e n p r e v i o u s l y i s quickly a s s i m i l a t e d and understood by a human o b s e r v e r - o p e r a t o r .

P r e d i c t i o n Equations

Solution of the d i f f e r e n t i a l equations of m o t i o n f o r guidance p u r p o s e s needs t o be a p p r o x i m a t e o n l y , p r o v i d e d that a c o n - v e r g e n t a p p r o x i m a t i o n i s a c h i e v e d . That i s , as the v e h i c l e a p p r o a c h e s the t a r g e t , it b e c o m e s m o r e a c c u r a t e . It i s n e c e s s a r y that the i n i t i a l i n a c c u r a c i e s do not j e o p a r d i z e the l a t e r s t a g e s of the t r a j e c t o r y . In addition, the p r o p o s e d s y s - t e m e x h i b i t s a c l o s e d - l o o p r e s p o n s e , so that i n a c c u r a c i e s due t o constant e r r o r s o r computational roundoffs a r e d r i v e n to z e r o .

The d i f f e r e n t i a l equation of m o t i o n , in v e c t o r notation, is g i v e n by

d² r _ _ μ ^ . Τ

—Τ " " 3 " r + Ί Ξ d t r

F o r p r e s e n t p u r p o s e s , the f o l l o w i n g a p p r o x i m a t i o n s can be made: 1) constant thrust and m a s s f l o w ; 2) point p a r t i c l e and 3 ) the change in μ / r i s s m a l l when c o m p a r e d to F / m .

F o r t h e s e a s s u m p t i o n s , E q . 1 b e c o m e s

( D

+ ω

) Γ = ^ _

m^Q - m t w h e r e

3 ^{1 / 2}

co — (μ / R ) = constant

T h i s f o r m of d i f f e r e n t i a l equation in s c a l a r s i s a m e n a b l e to solution by the method of v a r i a t i o n of p a r a m e t e r s . It i s shown in R e f . 6, that this method m a y a l s o be a p p l i e d t o v e c t o r s . T h e solution i s obtained as

M A R K S O N , BRYANT, A N D BERGSTEN

r = (r - — \ — sinο ω J m cot d t ) cos ω τ ο τ

+ — ( r ^ + \ — cos cot d t ) sin ω τ

co Ο

Ο

τ

r = ( r + \ — cos ωΐο J m d t ) cos ω τ ο

τ _^

- (cor" - \ — sin cot d t ) sin ο J m

ο

F o r the case w h e r e burning t i m e s a r e b r i e f sin ω τ ~ ω τ

cos co τ -ν ¹ and Eq. 2 reduces to

τ

- - Γ r ^ r cos ω τ ο

ϊ Γ + \ — d t - (ν - \ ο J m \ ° J

F . . , \ 2

— t a t ω τ m /

[2]

[3]

Equations 3 satisfy the r e q u i r e m e n t s for the approximate prediction equations in X and Y . It is n e c e s s a r y , h o w e v e r ,

2

to retain s o m e second-order t e r m s (ω τ ) , in the Ζ d i r e c t i o n , indicated by the remaining cosine t e r m .

Solution f o r Euler A n g l e s and R a t e s

It is assumed that approximate initial values are a v a i l - able for θ^, ô^, and ψ^. A f i r s t p r e d i c t i o n f o r T a n d r i s made f r o m E q s . 3, using t h e s e v a l u e s . T h e d e s i r e d end c o n - ditions at the t a r g e t , r*j. and r£, a r e then c o m p a r e d with the p r e d i c t e d data; the E u l e r angle r a t e s e n s i t i v i t i e s a r e g e n e r a - ted, and the r a t e s a r e updated in the f o l l o w i n g manner:

θ = θ

C C n " ( n- 1 ) ⁺ 9 Ζ / 9 Θ Y^t - Y

V V l >

*

The c o m m a n d e d E u l e r angle r a t e s a r e i n t e g r a t e d w i t h r e s p e c t t o t i m e t o p r o v i d e updated v a l u e s f o r and ψ^. T h e c o m m a n d e d v a l u e s f o r the E u l e r a n g l e s p r o v i d e the inputs to the l i n e a r a u t o p i l o t , w h i c h g e n e r a t e the a p p r o p r i a t e e r r o r s i g n a l s f o r use in the automatic m o d e of f l i g h t .

During the manual m o d e , the p r e d i c t i o n s a r e a c t e d upon d i r e c t l y by t h e^#p i l o t . N o w , although he has not used the a n g l e s and θ^, he has s e e n the e f f e c t that his p r e s e n t body a n g l e s and body r a t e s w i l l have on his " b u r n o u t "⁵ c o n d i t i o n s . T h e n , using the a p p r o p r i a t e c o n t r o l , he adjusts his attitude until the p r e d i c t i o n i s f a v o r a b l e . In a s e n s e , the p i l o t is

s o l v i n g f o r the c o r r e c t attitude and attitude r a t e s w i t h his p r e d i c t i v e d i s p l a y s by t r i a l and e r r o r .

T h i s v o l u m e of t e c h n i c a l p a p e r s d o e s not p e r m i t sufficient space t o a l l o w p r e s e n t a t i o n of the final s y s t e m d e s i g n - - a n a n a l y t i c solution w h i c h d o e s not r e q u i r e high-speed i n t e g r a - tion t o s o l v e f o r the d i s p l a y inputs. See R e f . 6 f o r additional i n f o r m a t i o n .

Guidance Inputs f o r D i s p l a y

The guidance i n f o r m a t i o n d i s p l a y e d t o the p i l o t in this study w a s in the f o r m of (r" - r ^ ) . T h i s w a s a c h i e v e d f r o m Eq. 3 by f i r s t e s t i m a t i n g the p r o p e l l a n t r e q u i r e d to d r i v e the quantity |r~- t o z e r o . T h i s e s t i m a t e of p r o p e l l a n t m a s s a l l o w e d a p r e d i c t i o n of t i m e t o g o ( τ ) b a s e d on actual thrust l e v e l . T h i s v a l u e of τ w a s then used in E q . 3 t o p r o d u c e the p r e d i c t e d altitude h^., the p r e d i c t e d longitudinal d i s p l a c e m e n t f r o m the t a r g e t S^, and the p r e d i c t e d l a t e r a l d i s p l a c e m e n t L when the burnout condition i s r e a c h e d .

"Burnout" i s used throughout t o indicate the point in a phase of flight w h e r e c e r t a i n conditions have b e e n s a t i s f i e d . It d o e s not m e a n that the engine i s a c t u a l l y shut down.

M A R K S O N , BRYANT, A N D BERGSTEN

T h e s e s i g n a l s , h^., and L , w e r e d i s p l a y e d in the c o o r d i - nated p a t t e r n shown in F i g . 4b.

A second p r e d i c t i o n .for burnout altitude (denoted this t i m e as h ) w a s made using θ and the actual value of Θ, so

° ° ( n . - l )

that an u p - t o - d a t e value of θ could be obtained f r o m E q . 4.

η

T h i s w a s done e v e n when the a u t o m a t i c mode w a s i n a c t i v e and the manual m o d e in u s e . T h i s updated value f o r w a s u s e d , t o g e t h e r w i t h the actual value of Θ, t o make a p r e d i c t i o n f o r h^c, which is the r a t e of c l i m b at the end of burning f o r a t r a j e c t o r y flown with the c o r r e c t value of θ .

Since it i s d e s i r e d to have a z e r o , o r s l i g h t l y n e g a t i v e , r a t e of c l i m b at the end of burning, the p i l o t w a s g i v e n a p r e d i c t i o n of burnout altitude at w h i c h he would have s o m e p r e v i o u s l y s p e c i f i e d ( i . e . , n o m i n a l ) value of r a t e of c l i m b . T h e s p e c i f i e d v a l u e s w e r e +100 fps and -50 f p s , g i v e n by h^

and h , r e s p e c t i v e l y - - o b t a i n e d f r o m E q . 5 and d i s p l a y e d as

1_J

in F i g . 4b:

h = h + (100 + h )

u c ^x c

h^L= h ^c- ( 5 0 + h^c)

δ Ζ / θ θ δ Ζ / θ θ θ Ζ / δ θ δ Ζ / δ é

It w i l l be w e l l to pause here and consider the physical meaning of the altitude scale in F i g . 4b. The display indi- cates that the v e h i c l e w i l l end up at the altitude indicated by hj. and with a final rate of c l i m b between +100 fps and -50 fps. T h i s is a safe condition, if h^ is at the d e s i r e d altitude.

Suppose, h o w e v e r , that the h^ blip w e r e above ( o r b e l o w ) h^

(or h ^ ) . T h i s would indicate an a r r i v a l at h^ with a rate of c l i m b g r e a t e r than h (or l e s s than hT ) . T h i s is an unsafe

& u L

condition. Both of these e x a m p l e s assume that h and h^T u L are in the vicinity of the d e s i r e d burnout altitude. T h i s w i l l be so only if the actual body attitude is c o r r e c t . If the nose of the v e h i c l e is too low on the h o r i z o n , the predicted a l t i - tudes h^ and h ^ w i l l appear low on the display, and v i c e v e r s a for the nose-high condition.

The g e n e r a t i o n s of the s i g n a l s h,, L , h ^T and L ^T a r e b e s t suited t o e v a l u a t i o n by a b i n a r y c o m p u t e r . T h e s e d i s - p l a y s g e n e r a l l y should not be c o n s i d e r e d f o r analog s i m u l a - t i o n , unless h y b r i d computation i s a v a i l a b l e .

The manner in w h i c h this guidance i n f o r m a t i o n is used is d e s c r i b e d in d e t a i l under " D i s p l a y s D e s c r i p t i o n . " V e r y b r i e f l y , if the altitude b a r s , h^ and h ^ , a r e not at the d e - s i r e d t e r m i n a t i o n a l t i t u d e , the p i l o t must pitch the v e h i c l e up to b r i n g the b a r s up and p i t c h down t o l o w e r t h e m . A s he p e r f o r m s this pitchup o r pitchdown m a n e u v e r , he i s o v e r c o n - t r o l l i n g on h^., his p r e d i c t e d a l t i t u d e . T h e c o n t r o l on h^, of c o u r s e , i s v e r y s e n s i t i v e t o Θ, O v e r c o n t r o l l i n g in pitch o r yaw has a v i o l e n t r e a c t i o n on the altitude o r l a t e r a l r a n g e p r e d i c t i o n . H o w e v e r , this r e a c t i o n is a t r a n s i e n t e f f e c t and

s e t t l e s out once h^ and h ^ a r e p o s i t i o n e d .

In c o n t r o l l i n g the thrust l e v e l , the p i l o t d e t e r m i n e s the c o r r e c t t h r o t t l e setting by d r i v i n g the d i s p l a y e d e r r o r in r a n g e t o z e r o . F o r e x a m p l e , if the r a n g e is t o o g r e a t , a h i g h e r d e c e l e r a t i o n r a t e is n e e d e d , and the t h r o t t l e is m o v e d f o r w a r d t o i n c r e a s e the b r a k i n g t h r u s t .

T e r m i n a l P h a s e

B e c a u s e of the l o g i c a l a r r a n g e m e n t of o p e r a t i o n a l p h a s e s , it w a s p o s s i b l e t o t r e a t the t e r m i n a l phase s e p a r a t e l y - - a n a - l y t i c a l l y and p h y s i c a l l y . T h i s phase w a s a r b i t r a r i l y defined as b e i n g the point in the b r a k i n g t r a j e c t o r y w h e r e the h o r i - z o n t a l v e l o c i t y w a s r e d u c e d t o 150 f p s . N o t only d o e s this s i m p l i f y the m o t i o n e q u a t i o n s , but it a l l o w s the e n t i r e p r o b l e m to be r e s c a l e d t o l e v e l s that a r e m o s t a p p r o p r i a t e t o this phase of f l i g h t . T h i s i m p r o v e s a c c u r a c y t o the point w h e r e r e l i a b l e r e a d i n g s on v e l o c i t y at touchdown w e r e obtained and used as inputs f o r landing g e a r d e s i g n .

A s in the b r a k i n g p h a s e , p r o v i s i o n s w e r e made f o r both automatic and manual c o n t r o l . T h e automatic c o n t r o l i n f o r - mation w a s a l w a y s a v a i l a b l e t o the p i l o t , w h e t h e r he e l e c t e d to use it o r not. T h e guidance law w a s taken d i r e c t l y f r o m Ref. 7 and i s p r e s e n t e d h e r e f o r c o m p l e t e n e s s :

R (S -

s

)

T K¹ - K² S [ 6 ]

I R I (1 + h / h^Q)

MARKSON, BRYANT, A N D BERGSTEN

w h e r e K² / 0 f o r h > 200 ft and K² = 0 f or h < 200 f t . A U T O P I L O T D E S C R I P T I O N

T h r e e t y p e s of c o n t r o l w e r e p r o v i d e d f o r in the s i m u l a - t i o n . T h e f i r s t w a s a p r o p o r t i o n a l damping c o n t r o l that o p - e r a t e d only when the p i l o t i n s e r t e d a pitch o r y a w c o m m a n d . R o l l c o n t r o l w a s o v e r d a m p e d w i t h no p i l o t input and undamped with p i l o t input. Attitude c o n t r o l w a s a c h i e v e d , in pitch and y a w , by d i f f e r e n t i a l thrusting of v e r n i e r e n g i n e s canted at an angle with the longitudinal a x i s to i n c r e a s e the a v a i l a b l e m o m e n t a r m . R o l l c o n t r o l m o m e n t s w e r e a s s u m e d t o be p r o v i d e d by pulse modulation of c i r c u m f e r e n t i a l attitude j e t s . The second autopilot s y s t e m w a s p r o v i d e d by a c o n v e n t i o n a l , c o n v e r g e n t l i n e a r s y s t e m w i t h the p i l o t in the l o o p . T h e third s y s t e m w a s c l o s e d l o o p t o i m p l e m e n t the automatic c o n t r o l .

A d a p t i v e c o n t r o l s w e r e not c o n s i d e r e d f o r two r e a s o n s : f i r s t , equipment r e q u i r e m e n t s w e r e p r o h i b i t i v e ; and s e c o n d , the computations f o r m o m e n t adaption a r e difficult to p e r f o r m by analog c o m p u t e r . H y b r i d computation would h a v e made this c o n t r o l m o r e a t t r a c t i v e f o r study.

E s s e n t i a l l y , the p i l o t had t w o manual c o n t r o l m o d e s . T h e f i r s t , mentioned p r e v i o u s l y , w a s an " a c c e l e r a t i o n s t i c k " w i t h a b u i l t - i n l e a d on c o n t r o l r a t e s . T h e s e c o n d w a s a c o m p l e t e l y c o n v e n t i o n a l "position s t i c k , " w i t h r a t e

s t a b i l i z a t i o n . It is of distinct i n t e r e s t t o note that the p i l o t could d i s c e r n no distinguishable d i f f e r e n c e b e t w e e n c o n t r o l m o d e s during the b r a k i n g r u n s . T h i s w a s due e n t i r e l y , it is f e l t , to the l o w body r a t e s e x p e r i e n c e d during this phase of f l i g h t .

D I S P L A Y S D E S C R I P T I O N

T h e a c t i v e d i s p l a y c l u s t e r is outlined in F i g . 3. P r e - dominantly c e n t e r e d in the c l u s t e r i s the t e l e v i s i o n s c r e e n on which the c o o r d i n a t e d d i s p l a y s w e r e p r e s e n t e d . T h e use of the c l o s e d - c i r c u i t t e l e v i s i o n m a k e s p r a c t i c a l a w i d e v a r i a t i o n of e x p e r i m e n t a l d i s p l a y s w i t h a m i n i m u m of e q u i p - ment v a r i a t i o n s in the c o c k p i t . Sketches of the t w o f i n a l i z e d d i s p l a y s a r e shown in F i g . 4.

Surmounting the T V s c r e e n i s the t h r e e - a x i s attitude m e t e r . T h i s i n s t r u m e n t p r o v i d e s i n f o r m a t i o n on the i n e r t i a l attitude of the v e h i c l e r e f e r e n c e d t o an a x i s s y s t e m a l i g n e d with the l o c a l v e r t i c a l at the landing s i t e . Surrounding the attitude i n d i c a t o r a r e m e t e r s p r o v i d i n g component i n f o r m a -

t i o n on v e l o c i t y , g r o s s altitude and r o l l attitude. On the panel b e l o w the s c r e e n i s a p r e c i s i o n a l t i m e t e r , the i g n i t i o n s w i t c h and a r a n g e - t o - i g n i t i o n m e t e r - - w h i c h r e g i s t e r s p r e - i g n i t i o n v a l u e s of S^.

T h r o t t l e c o n t r o l s a r e on the l e f t . T h e l o w e r t h r o t t l e bar c o n t r o l s the m a i n t r a n s l a t i o n e n g i n e s w i t h a ± 10% v a r i a t i o n about t h e i r n o m i n a l thrust l e v e l . T h e s e c o n d , s m a l l e r t h r o t - tle in front of the m a i n one c o n t r o l s the mean thrust l e v e l of the v e r n i e r e n g i n e s . T o a s s i s t the r e a d e r in understanding the s e q u e n c e of e v e n t s as they o c c u r to the p i l o t , an a b b r e - v i a t e d f o r m of the flight p r o c e d u r e s and a b r i e f d e s c r i p t i o n of the p i l o t t a s k a r e p r e s e n t e d h e r e .

On e n t e r i n g the c o c k p i t , c h e c k i g n i t i o n s w i t c h t o c e n t e r p o s i t i o n , main t h r o t t l e to c e n t e r p o s i t i o n , v e r n i e r t h r o t t l e to off. C h e c k a l l w a r n i n g l i g h t s off. Signal to s t a r t p r o b l e m . C h e c k r a n g e - t o - i g n i t i o n m e t e r , o p e r a t i n g and a p p r o a c h i n g z e r o . F o c u s attention on the t h r e e - a x i s attitude m e t e r s . P i t c h e r r o r i s indicated by a d i s p l a c e m e n t of the h o r i z o n t a l b a r , and pitch r a t e e r r o r a p p e a r s on the left-hand v e r t i c a l m e t e r ( A P - t h e t a e r r o r ) . Y a w e r r o r is g i v e n by d i s p l a c e - ment of the v e r t i c a l b a r , and y a w r a t e e r r o r a p p e a r s on the l o w e r h o r i z o n t a l m e t e r ( s e e F i g . 4 ) .

T o c o r r e c t a n e g a t i v e e r r o r in Δ Θ , p l a c e the v e r t i c a l p o i n t e r o p p o s i t e the h o r i z o n t a l b a r by a p p l y i n g f o r w a r d p r e s -

s u r e on the attitude s t i c k . A s the b a r m o v e s t o w a r d the c e n t e r , apply back p r e s s u r e t o the attitude s t i c k t o keep the v e r t i c a l i n d i c a t o r o p p o s i t e the b a r . T h i s routine w i l l null both the angle and angle r a t e e r r o r s s i m u l t a n e o u s l y . A s i m i l a r e x e r c i s e i s a p p l i e d f o r y a w e r r o r s . F o r a p o s i t i v e e r r o r in Δ ψ , p l a c e the l o w e r h o r i z o n t a l i n d i c a t o r o p p o s i t e the v e r t i c a l bar by a p p l y i n g p r e s s u r e on the r i g h t p e d a l . Use left p e d a l t o keep the i n d i c a t o r o p p o s i t e the v e r t i c a l b a r .

The r a n g e - t o - i g n i t i o n m e t e r u n d e r g o e s a s c a l e change a u t o m a t i c a l l y , when S^ i s l e s s than 25, 000 ft. T h i s a l s o turns on the i g n i t i o n w a r n i n g l i g h t a b o v e the t h r e e - a x i s i n - d i c a t o r . W h e n the w a r n i n g l i g h t c o m e s on, turn on the v e r n i e r s t o 10% of full t h r u s t . Ignite the m a i n e n g i n e s when the r a n g e - t o - i g n i t i o n g o e s through z e r o .

A p p r o x i m a t e l y 1 s e c a f t e r i g n i t i o n , the T V d i s p l a y i s a c t i v a t e d and a p p e a r s r o u g h l y as sketched in the upper half of F i g . 4. If the altitude s c a l e on the r i g h t i s i g n o r e d , the S - L c o o r d i n a t e s m a y be c o n s i d e r e d as b e i n g an o v e r h e a d

MARKSON, BRYANT, A N D BERGSTEN

v i e w of the t a r g e t a r e a . T h e b l i p r e p r e s e n t s the p r e d i c t e d landing point ( P L P ) . If a map of the t e r r a i n surrounding the landing a r e a w e r e a v a i l a b l e , it would be p o s s i b l e t o s u p e r i m p o s e this i m a g e and c o m p l e t e the p i c t u r e .

Adjust the main engine t h r o t t l e so that the P L P i s c e n t e r e d in the S, o r d o w n r a n g e , d i r e c t i o n . If the P L P i s in the upper half of the d i s p l a y (the P L P i s l o n g ) , m o v e the t h r o t t l e f o r w a r d . If the P L P is in the l o w e r half of the d i s - p l a y , m o v e the t h r o t t l e aft. Do not t r y to c o r r e c t the l a t e r a l e r r o r y e t .

N e x t , o b s e r v e the altitude s c a l e . T h e b a r s , h and h^T ,

9 u L

a r e the d e s i r e d altitude at which the b r a k i n g m a n e u v e r is to be c o m p l e t e d and the t e r m i n a l m a n e u v e r s t a r t e d . A p p l y f o r - w a r d o r aft p r e s s u r e on the attitude s t i c k t o m o v e the b a r s down o r up, r e s p e c t i v e l y , until h ^ l i e s on the 1000-ft m a r k - e r . A f t e r doing t h i s , the b l i p on the h^. s c a l e , w h i c h i s highly s e n s i t i v e t o m o t i o n s of the attitude s t i c k , i s m o v e d into p o s i - tion to r e s t on the h ^ b a r . A g a i n , f o r w a r d p r e s s u r e on the attitude s t i c k m o v e s the b l i p down; aft p r e s s u r e m o v e s it up.

A p h y s i c a l i n t e r p r e t a t i o n of this d i s p l a y would be t o r e a d the h ^ bar in r e l a t i o n to the 1000-ft m a r k e r . If this is l o w , the nose of the ship is t o o l o w and back p r e s s u r e is r e q u i r e d to pull it up.

N o w , o b s e r v e the l a t e r a l d i s p l a c e m e n t of the P L P . If the P L P i s t o the r i g h t of the t a r g e t , apply r i g h t p e d a l , and v i c e v e r s a . T h e c o n t r o l s e q u e n c e - - t h r o t t l e , r o l l , p i t c h , y a w - - is r e p e a t e d c y c l i c a l l y , until the h o r i z o n t a l v e l o c i t y is r e - duced b e l o w 150 f p s . B e c a u s e of u n r e a l i s t i c s c a l i n g b e l o w this point in the t r a j e c t o r y , the b r a k i n g run w a s discontinued and the t e r m i n a l m a n e u v e r begun w i t h new s c a l i n g on a l l v a r i a b l e s .

The s c o p e d i s p l a y is no l o n g e r t a r g e t - c e n t e r e d - - b u t i s a s y m b o l i c b o d y - r e l a t i v e d i s p l a y such as might appear on an o p t i c a l s c o p e . T h e s t r a i g h t l i n e is the p r o j e c t i o n ( i . e . , s h a d o w ) of the longitudinal a x i s of the v e h i c l e on the ground b e l o w . T h i s d i s p l a y p r o v i d e s the p i l o t with the s a m e type of v i s u a l m o t i o n and p h y s i c a l o r i e n t a t i o n which would be obtained w i t h the sun d i r e c t l y o v e r h e a d and the t a r g e t in v i e w through an o p t i c a l d e v i c e .

T h e guidance i n f o r m a t i o n i s a l w a y s a v a i l a b l e through the attitude i n d i c a t o r , should the p i l o t e l e c t to land "blind. " T h e

b a s i c o b j e c t i v e of this p o r t i o n of the manual m a n e u v e r w a s not t o t e s t his a b i l i t y to f l y the attitude i n d i c a t o r but t o d e t e r - mine if he could p e r f o r m the t a s k without the guidance c o m - puter in the l o o p .

M E C H A N I Z A T I O N

The lunar landing s i m u l a t i o n w a s m e c h a n i z e d in a c c o r d - ance w i t h the b a s i c b l o c k d i a g r a m p r e s e n t e d in F i g . 5a. T h e only d e t a i l i n g included in the b a s i c b l o c k d i a g r a m is the c o n - necting link t o the p i l o t d i s p l a y s . T h e s e have b e e n expanded t o point out what i s f e l t t o be the m i n i m a l i n f o r m a t i o n r e q u i r e - ments f r o m the p i l o t¹ s point of v i e w . T h e s i m u l a t i o n r e - q u i r e d a t o t a l of 294 o p e r a t i o n a l a m p l i f i e r s , using four R e a c C - 4 0 0 ' s , t w o R e a c C - 1 0 0 ' s , and an expanded E A 231 R c o m - puter c a p a b l e of r e p e t i t i v e o p e r a t i o n . A n attempt w a s made to s e p a r a t e f o r c e , m o t i o n , g u i d a n c e , and d i s p l a y d r i v e r e - q u i r e m e n t s t o f a c i l i t a t e static and d y n a m i c c h e c k i n g .

Of p a r t i c u l a r i n t e r e s t in the m e c h a n i z a t i o n w a s the use of the E A 231 R c o m p u t e r , s i m u l a t i n g the onboard c o m p u t e r c a p a c i t y and computational function. T h e r e q u i r e d t o t a l s t o r a g e and computation is c o n s i d e r e d to be w e l l within the c a p a c i t y and c a p a b i l i t y of t o d a y¹ s s m a l l , l i g h t w e i g h t onboard c o m p u t e r s . T h e 231 R w a s used in the r e p e t i t i v e o p e r a t i o n m o d e , computing the e n t i r e t r a j e c t o r y at 500 t i m e s t r u e t i m e . T h e c o m p u t e r w a s d r i v e n in t h i s m o d e by an e x t e r n a l l y f u r - nished t r i a n g u l a r w a v e .

T h e w a v e , t r i g g e r points,and c o m p u t e r - s t o r e s e q u e n c e s a r e shown in F i g . 5b. T h e f i r s t h a l f - c y c l e w a s used t o compute the s u b s i d i a r y i n t e g r a l s and t o g e n e r a t e new v a l u e s f o r and h^.. A c t u a l r e a l t i m e v a l u e s f o r t h r u s t , fuel f l o w , E u l e r a n g l e s , and E u l e r angle r a t e s w e r e used in t h e s e c o m - putations. During the s e c o n d h a l f - c y c l e , the v a l u e s f o r h^.

and L w e r e computed a g a i n , using the l a s t known v a l u e s of the c o m m a n d r a t e s , θ and ψ , t o obtain h and L .

c( n - l ) ^C( n - 1 ) ^{c c}

T h e n the r a t e d e r i v a t i v e s w e r e obtained t o g e t h e r w i t h the d i s - play s i g n a l s , h^, h ^ and ti^c, a l l computed with the l a s t known v a l u e of the c o m m a n d r a t e . T h e c o m m a n d r a t e s a r e then up- dated.

T h i s a p p r o a c h r e s u l t e d in an e f f e c t i v e t i m e s h a r e r e - q u i r e m e n t of the c o m p u t a t i o n a l e q u i p m e n t , using the f i r s t h a l f - c y c l e to compute and s t o r e the v a l u e s of c o m m a n d g u i d - ance and the s e c o n d h a l f - c y c l e f o r d i s p l a y . T h e m i c r o s t o r e

MARKSON, BRYANT, A N D BERGSTEN

units of the 231 R w e r e used in conjunction w i t h m i c r o s e c o n d r e l a y s to e f f e c t the t i m e s h a r e of usable e q u i p m e n t .

A v a r i a t i o n of p r o g r a m m i n g and a change in the o r d e r and sequence of the s t o r e units had t o be made a f t e r e x p e r i m e n t a - t i o n w i t h the s y s t e m . F o r e x a m p l e , the i n i t i a l d i s p l a y v a l u e s of h , h , as they w e r e s t o r e d , had a tendency t o d r i f t o r

U L

p i c k up a b i a s v a l u e . D y n a m i c b a l a n c i n g of the c a p a c i t o r s did l i t t l e t o a l l e v i a t e this c o n d i t i o n . T h i s b i a s e d v a l u e w a s a c t e d upon, and an e r r a t i c d i v e r g e n t r e a c t i o n w a s o c c a s i o n e d in the c o n t r o l of the v e h i c l e .

P i l o t a c c e p t a n c e of this i n i t i a l e r r a t i c d i s p l a y b e h a v i o r and use of his a b i l i t y t o act as a s m o o t h i n g f i l t e r went a l o n g w a y in e f f e c t i n g an a c c e p t a b l e landing t r a j e c t o r y . During the final s t a g e s of the e x p e r i m e n t , a change w a s made t o the m i c r o - s t o r e s and the c o m p u t e - s t o r e t r i g g e r s i g n a l s . F l i p - f l o p s w e r e f i n a l l y used to a c t i v a t e and sequence the s t o r e units.

T h i s final change in the s y s t e m r e s u l t e d in s m o o t h e d , i n - t e l l i g e n t d i s p l a y s i g n a l s that enabled the p i l o t t o make a w e l l c o n t r o l l e d m a n e u v e r .

The a n t i c i p a t e d r e p e a t a b l e p r e c i s i o n l e v e l s f r o m the analog a r e on the o r d e r of ± 1 % . T h e s e a c c u r a c i e s a r e the b e s t that can be e x p e c t e d in the t i m e s c a l e and computation method that was u s e d .

S I M U L A T I O N R E S U L T S

A lunar landing c r a f t in the 100, 0 0 0 - l b c l a s s w a s u s e d . The i n i t i a l conditions w e r e s e l e c t e d t o c o r r e s p o n d w i t h the data shown in F i g . 2. T h i s landing t r a j e c t o r y is c h a r a c t e r i s - t i c a l l y flat and s t a r t s at v e l o c i t i e s n e a r c i r c u l a r s p e e d . Specific s e n s o r s used f o r guidance inputs w e r e outside the scope of the study but should in no w a y affect the r e s u l t s .

Sample t r a j e c t o r y data a r e p r e s e n t e d in F i g s . 7 - 1 1 . Both automatic and manual t r a j e c t o r i e s a r e p r e s e n t e d in the b r a k i n g p h a s e . A tabulation of v e l o c i t y c o m p o n e n t s at touchdown f r o m the t e r m i n a l phase f o r v a r i o u s runs i s g i v e n in T a b l e 1.

F u e l consumption during the manual b r a k i n g runs w a s g e n e r a l l y within 2% of the fuel consumption f o r an i d e n t i c a l automatic run. T h e c o m p a r a t i v e a c c u r a c i e s a r e s o m e w h a t questionable at the r e c o r d i n g l e v e l s used and disqualify a p r e c i s e e v a l u a t i o n of this p a r a m e t e r .

Body D y n a m i c s

T w o distinguishing a r e a s w e r e i n v e s t i g a t e d f o r thrust l e v e l e f f e c t s on p i l o t p e r f o r m a n c e and m i s s i o n a c c o m p l i s h m e n t . M o m e n t L e v e l s

A s e r i e s of b r a k i n g m a n e u v e r s w a s p e r f o r m e d , using v a r i o u s c o r r e c t i o n m o m e n t l e v e l s in the manual c o n t r o l m o d e . T h e s e m o m e n t l e v e l s p r o d u c e d m a x i m u m body a c c e l e r a t i o n

-2 2 -3 2 l e v e l s r a n g i n g f r o m 10 r a d / s e c t o 10 r a d / s e c . In a l l c a s e s , manual p e r f o r m a n c e w a s i m p r o v e d with the l o w e r c o r - r e c t i n g m o m e n t s for both the pitch and y a w a x e s . T h i s r e - q u i r e m e n t f o r a c o m p a r a t i v e l y l o w c o r r e c t i n g m o m e n t during the b r a k i n g phase must be made c o m p a t i b l e w i t h indicated r e - q u i r e m e n t s f o r the t e r m i n a l and h o v e r i n g p h a s e s .

, 2 A n g u l a r a c c e l e r a t i o n l e v e l s on the o r d e r of 0. 07 r a d / s e c w e r e found t o be n e c e s s a r y during the t e r m i n a l phase t o e n - s u r e an adequate c o n t r o l m a r g i n . T h i s d i s p a r i t y b e t w e e n c o n - t r o l r e q u i r e m e n t s f o r the t w o landing phases is due m a i n l y t o the h i g h e r angular r a t e s r e q u i r e d during the t e r m i n a l phase.

A n g u l a r r a t e s during the b r a k i n g phase w e r e a l w a y s l e s s than 1 d e g / s e c , w h e r e a s r a t e s as high as 7 d e g / s e c w e r e not un- usual during the t e r m i n a l p h a s e . T h i s can be s e e n quite e a s i l y in F i g . 10, which shows the pitch angle as a function of t i m e for s e v e r a l landing m a n e u v e r s .

The m a r k e d d i f f e r e n c e b e t w e e n the b r a k i n g and t e r m i n a l phase m o m e n t r e q u i r e m e n t s points to the n e c e s s i t y f o r one o r m o r e of the f o l l o w i n g d e s i g n f e a t u r e s :

1) A c o m p l e t e l y adaptive c o n t r o l s y s t e m capable of han- dling the r e q u i r e d r a n g e of gains a s s o c i a t e d with a l l phases of lunar landing.

2) A c o m p l e t e l y automatic landing s y s t e m , in c o m b i n a t i o n with a c a r e f u l l y s i z e d v e r n i e r engine attitude c o n t r o l s y s t e m . T h i s p r o v i s i o n would e l i m i n a t e the p i l o t e d manual c o n t r o l s e n - s i t i v i t y p r o b l e m , in that an automatic s y s t e m could be d e s i g n e d t o the r e q u i r e d s e n s i t i v i t y .

3) A c o n t r o l s t i c k s e n s i t i v i t y s e l e c t o r , which w i l l a l l o w the pilot t o manually change s e n s i t i v i t y in f l i g h t . T h i s has been shown t o be p r a c t i c a l in s u p e r s o n i c b o m b e r a p p l i c a t i o n s , w h i c h e x p e r i e n c e m o r e s e v e r e c o n t r o l disruption than is p r e s e n t l y under d i s c u s s i o n . H o w e v e r , p i l o t adaptation t o l a r g e , r a p i d changes in c o n t r o l s e n s i t i v i t y is a definite p r o b l e m . It has

MARKSON, BRYANT, A N D BERGSTEN

b e e n known t o cause s e v e r e d i s t u r b a n c e s in an o t h e r w i s e smooth o p e r a t i o n .

T r a n s l a t i o n a l T h r u s t L e v e l s

A v a r i e t y of thrust l e v e l s , w i t h a t h r o t t l i n g r a n g e of ± 1 0 % , w e r e included in the study of the manual c o n t r o l s y s t e m . N o p r o v i s i o n f o r t h r o t t l i n g w a s i n c o r p o r a t e d in the automatic s y s - t e m , although the " n o m i n a lⁿ thrust l e v e l s f o r c o m p a r a t i v e runs w e r e i d e n t i c a l . N o p r o b l e m w a s e n c o u n t e r e d , i n s o f a r as handling o r r e s p o n s e c h a r a c t e r i s t i c s w e r e c o n c e r n e d , f o r e i t h e r the automatic o r manual s y s t e m , in the r a n g e of thrust l e v e l s i n v e s t i g a t e d .

The m o s t s i g n i f i c a n t e f f e c t of thrust l e v e l on m i s s i o n p e r - f o r m a n c e w a s found to be f r o m the standpoint of m a n e u v e r a b i l - ity and fuel e c o n o m y . F u e l e c o n o m y w a s a o n e - w a y t r a d e , as shown in F i g . 7 by the m i n i m u m Δ ν l i n e . T h e h i g h e r thrust p r o v i d e s a c h e a p e r landing. M a n e u v e r a b i l i t y , on the other hand, p r e s e n t e d an a l t o g e t h e r d i f f e r e n t p i c t u r e . If the thrust l e v e l w a s t o o high, an insufficient amount of r a n g e c o n t r o l w a s a c h i e v e d , and flight t i m e s w e r e t o o s h o r t . F u r t h e r m o r e , ignition altitudes w e r e r e s t r i c t e d t o a r e l a t i v e l y s m a l l band for e f f i c i e n t o p e r a t i o n . On the other hand, t o o low a thrust l e v e l l e d to a l i m i t e d amount of thrust e x c e s s o v e r the g r a v i - tational a c c e l e r a t i o n . A l t h o u g h g r e a t e r r a n g e c o n t r o l w a s a c h i e v e d , ignition altitudes w e r e r e s t r i c t e d t o r e l a t i v e l y high l e v e l s a s s o c i a t e d with high g r a v i t a t i o n a l l o s s e s in p e r f o r m i n g the landing m a n e u v e r .

P i l o t C o n t r o l P i l o t d i s p l a y s

The d i s p l a y m e c h a n i z a t i o n p r e s e n t s a low l e v e l of c o n t r o l i n f o r m a t i o n to a v o i d saturating the o p e r a t o r w i t h superfluous data. It w a s r e a l i z e d , f r o m p r e v i o u s s t u d i e s , that the c o n t r o l of t h r e e a x e s c o m e s v e r y c l o s e t o e x c e e d i n g m a n ' s a b i l i t y to c o o r d i n a t e his a c t i o n s . It w a s n e c e s s a r y , t h e r e f o r e , t o m i n i - m i z e and s e p a r a t e t a s k r e s p o n s i b i l i t y by a s s i g n i n g a s i n g l e - channel, uncoupled conditioning t o a m i s s i o n w h i c h , in f a c t , w a s multichannel, w i t h a l l channels c o u p l e d .

It is w e l l known that d i f f i c u l t i e s i n v o l v e d with m o s t s y s t e m t a s k s can be o v e r c o m e if sufficient t i m e i s spent in t r a i n i n g t o d e v e l o p t e c h n i q u e s . T h e p r e d i c t i v e d i s p l a y p r o v i d e d f e e d - back i n f o r m a t i o n which e f f e c t i v e l y s h o r t - c i r c u i t e d a l a r g e p o r t i o n of the t r a i n i n g p e r i o d . T h e nature of the p r o b l e m a l -

l o w e d a t r a n s f e r of s k i l l s a c q u i r e d in other situations that used b a s i c flight i n s t r u m e n t a t i o n .

In m o s t c a s e s , a " s a f e " flight w a s flown on the second o r t h i r d a t t e m p t . Habit i n t e r f e r e n c e w a s encountered in one p a r t i c u l a r c a s e ; h o w e v e r , a highly s u c c e s s f u l run w a s made on the sixth flight and i s shown in F i g . 8.

A s i s mentioned in the s e c t i o n on " M e c h a n i z a t i o n , ^M the b e h a v i o r of d i s p l a y s i g n a l s h and h^T f o r the b r a k i n g m a n e u v e r

U LJ

was highly e r r a t i c throughout m o s t of the study. T h i s w a s un- fortunate in s e v e r a l r e s p e c t s , not the l e a s t of w h i c h w a s the p a r t i a l disruption of the p i l o t¹ s a b i l i t y t o d i s t r i b u t e his a t t e n - tion e v e n l y t o a l l the d i s p l a y s . T h i s highly a c t i v e , dancing s i g n a l a t t r a c t e d o v e r 70% of the attention of the s e v e r a l sub- j e c t s who flew the s i m u l a t o r . T h i s made p r e c i s i o n flight much m o r e difficult than it need have b e e n .

A m o r e r e c e n t s i m u l a t i o n done in August of 1962 m e c h a - n i z e d the final s y s t e m d e s i g n d i s c u s s e d in R e f . 6. T h e d i s - p l a y s w e r e s m o o t h and i n d i c a t e d an a c c e p t a b l e s i g n a l - t o - n o i s e r a t i o . A l l p i l o t s flew a c c e p t a b l e f l i g h t s on the f i r s t a t t e m p t .

E x p e r i e n c e with h^ and h ^ computation and d i s p l a y i n d i - c a t e s that future w o r k r e q u i r e s only a s i n g l e b a r i n d i c a t o r . A s i m i l a r b a r - t y p e i n d i c a t o r must a l s o be p r o v i d e d f o r l a t e r a l c o n t r o l .

P i l o t p e r f o r m a n c e

The p i l o t w a s able to p e r f o r m the r e q u i r e d c o n t r o l maneu- v e r s . H i s p e r f o r m a n c e w a s b e s t when augmenting the auto- m a t i c s y s t e m , and his i n c l u s i o n , in g e n e r a l , i m p r o v e d the t o t a l s y s t e m p e r f o r m a n c e . In s o m e c a s e s , w i t h m a r g i n a l i n i t i a l c o n d i t i o n s , the p i l o t w a s able to r e c o v e r c o n t r o l and s a v e the v e h i c l e in a situation in w h i c h the automatic s y s t e m i m p a c t e d .

T y p i c a l e r r o r d i s p e r s i o n s r e s u l t i n g f r o m manual c o n t r o l a r e shown in F i g . 6. T h e s e d i s p e r s i o n s , taken f r o m the l a t e r s i m u l a t i o n r e f e r r e d t o p r e v i o u s l y , w e r e obtained by f l y i n g a g r e a t many s i m u l a t e d runs w i t h the s a m e i n i t i a l c o n - ditions and the s a m e d e s i r e d end c o n d i t i o n s , but flown by s e v e n d i f f e r e n t p i l o t s . T h e s e data a r e c o n s i d e r e d t o be a v a l i d i n d i c a t i o n of the m a n - i n - t h e - l o o p p r e c i s i o n o b t a i n a b l e .

M A R K S O N , BRYANT, A N D BERGSTEN

Mane u v e r ab i l ity

The m a n e u v e r a b i l i t y of the v e h i c l e is used h e r e as the c o n t r o l l e d d e v i a t i o n f r o m a n o m i n a l t r a j e c t o r y . T h i s d e f i n i - tion is i l l u s t r a t e d g r a p h i c a l l y in F i g . 8, w h e r e s e v e r a l runs a r e r e c o r d e d , g i v i n g m a x i m u m , m i n i m u m , and n o m i n a l r a n g e c o n d i t i o n s . T h e s m a l l engine t h r o t t l i n g r a n g e p r o v i d e s an adequate c o n t r o l m a r g i n to a c c o m m o d a t e e r r o r s in thrust i n i t i a t i o n . T h e highest n o m i n a l thrust l e v e l i n v e s t i g a t e d p r o - v i d e d a r a n g e potential of 111, 000 ft. T h e l o w e s t l e v e l p r o - v i d e d a potential of 180, 000 ft. E x t r e m e s in l a t e r a l r a n g e c o n t r o l w e r e not obtained. H o w e v e r , it is felt that 70, 000 ft i s within r e a s o n f o r a n o - p e n a l t y fuel r e q u i r e m e n t .

Range c o n t r o l during the t e r m i n a l p h a s e - - a s distinguished f r o m the b r a k i n g p h a s e - - h a s b e e n shown t o be quite f e a s i b l e ( F i g . 11) but i s v e r y e x p e n s i v e in t e r m s of fuel consumption.

It i s the opinion of the authors that g r o s s r a n g e c o n t r o l should not be attempted during the t e r m i n a l m a n e u v e r - - o n l y v e r n i e r c o n t r o l of the touchdown point.

A s the m i s s i o n p r o g r e s s e s and e n t e r s into the final v e r t i c a l descent t o touchdown, the p i l o t tends t o b e c o m e o v e r c a u t i o u s . T o a v o i d e x c e s s i v e fuel consumption during the final maneu- v e r , he should be g i v e n a f i r m r a t e - o f - d e s c e n t p r o g r a m , which would be a m e m o r i z e d step function.

C O N C L U S I O N S

A d i s c u s s i o n has been p r e s e n t e d of a d y n a m i c s i m u l a t i o n of the manned lunar landing. It has b e e n found that the e n t i r e landing m a n e u v e r can be a c c o m p l i s h e d manually w i t h a g u i d - ance c o m p u t e r in the l o o p . A new method f o r adaptive flight c o n t r o l has been p r e s e n t e d , as w e l l as an analog m e c h a n i z a - t i o n , w i t h the r e q u i r e d mockup d i s p l a y s . T h e c o n t r o l t e c h - nique m a k e s it p o s s i b l e t o a c h i e v e a c o m p l e t e l y f l e x i b l e lunar m i s s i o n c a p a b i l i t y .

A C K N O W L E D G M E N T

The authors w i s h to e x p r e s s t h e i r a p p r e c i a t i o n to a l l those individuals of the M a r t i n Company and E l e c t r o n i c s A s s o c i a t e s , Inc., w h o s e outstanding e f f o r t s made the m e c h a n i z a t i o n of this p r o g r a m a r e a l i t y .

N O M E N C L A T U R E

—>

F = thrust v e c t o r

g r a v i t a t i o n a l a c c e l e r a t i o n at the s u r f a c e

p r e d i c t e d altitude at end of burning b a s e d on p r e s - ent thrust v e c t o r and its r a t e of change of o r i e n t a - t i o n

upper and l o w e r p r e d i c t e d a l t i t u d e s , at end of burning, at w h i c h a r a t e of c l i m b of +100 and -50 fps can be a c h i e v e d b a s e d on p r e s e n t thrust v e c t o r thrust s e n s i t i v i t y c o e f f i c i e n t s used in t e r m i n a l m a - n e u v e r . V a l u e s used in this e x p e r i m e n t w e r e Κ^χ = 0. 18 ( s e c "¹) and K² = 0. 001 ( s e c "²) l a t e r a l d i s p l a c e m e n t of P L P f r o m landing s i t e , b a s e d on p r e s e n t thrust v e c t o r and its r a t e of change of o r i e n t a t i o n

l a t e r a l d i s p l a c e m e n t of P L P at w h i c h a s p e c i f i e d l a t e r a l r a t e ( n o m i n a l l y z e r o ) can be a c h i e v e d b a s e d on p r e s e n t thrust v e c t o r

m a s s

c e n t r a l body r a d i u s v e c t o r t o landing site c e n t r a l body r a d i u s v e c t o r to v e h i c l e slant r a n g e v e c t o r f r o m t a r g e t t o v e h i c l e

longitudinal d i s p l a c e m e n t of P L P f r o m landing s i t e , b a s e d on p r e s e n t thrust v e c t o r and its r a t e of change of o r i e n t a t i o n

t i m e

i n e r t i a l , t a r g e t c e n t e r e d , C a r t e s i a n c o o r d i n a t e s y s t e m ( s e e F i g . 1)

c o - a n g l e b e t w e e n thrust v e c t o r and Z - a x i s 2

lunar g r a v i t a t i o n a l constant = g R t i m e - t o - g o

—>

angle b e t w e e n X - a x i s and p r o j e c t i o n of F in X - Y plane

MARKSON, BRYANT, A N D BERGSTEN

ω = mean m o t i o n

S u p e r s c r i p t s

C ) = d e r i v a t i v e with r e s p e c t to t i m e

= v e c t o r quantity S u b s c r i p t s

c = c o m m a n d value

η = value c o r r e s p o n d i n g to nth step ο = at t i m e z e r o

t = at landing site

R E F E R E N C E S

1 B e r m a n , L . J. , " O p t i m u m soft landing t r a j e c t o r i e s , P a r t 1, A n a l y s i s , " M a s s . Inst. T e c h . , A i r F o r c e Office Scientific R e s e a r c h , 519 ( M a r c h 1961).

2 L a w d e n , D. F . , " D y n a m i c p r o b l e m s of i n t e r p l a n e t a r y f l i g h t , " A e r o n a u t . Q u a r t e r l y , £, 165-180 ( 1 9 5 5 ) .

3 F r i e d , B . D . , " T r a j e c t o r y o p t i m i z a t i o n for p o w e r e d flight in t w o o r t h r e e d i m e n s i o n s , " Space T e c h n o l o g y (John W i l e y & Sons, Inc. , N e w Y o r k , 1959X

4 P e r k i n s , C . W . , "Optimum r e t r o - t h r u s t t r a j e c t o r i e s , "

M . S . T h e s i s , M a s s . Inst. T e c h . (June 1961).

5 P f e i f f e r , C . G. , " T h e o r y and a p p l i c a t i o n of the c r i t i c a l d i r e c t i o n method of t r a j e c t o r y o p t i m i z a t i o n , " I A S S y m p o s i u m on V e h i c l e S y s t e m s O p t i m i z a t i o n , G a r d e n C i t y , Ν . Υ . , ( N o - v e m b e r 1961),

6 M a r k s o n , Ε . E., Bryant, J., and B e r g s t e n , F . , " S i m - ulation of manned lunar landing, " A R S L u n a r M i s s i o n s M e e t - ing, C l e v e l a n d , P r e p r i n t N o . 2482-62 (July 1962).

7 M a r k s o n , Ε . Ε . , "Thrust p r o g r a m m i n g f o r t e r m i n a l m a n e u v e r s in s o a c e , " P r o c . of I A S M e e t i n g on A e r o s p a c e Support and O p e r a t i o n s , O r l a n d o , F l a . ( D e c e m b e r 1961).

Table 1 Representative touchdown conditions Terminal phase initial conditions Final conditions h, h, Vx, Vy, Θ, m, t, h, Vx, Vy, Θ, m. ft fps fps fps deg Ø slugs sec fps fps fps deg slugs 1000 -50 150 0 22.0 180 2155 38.36 -7.33 1.55 -0.15 85.5 2114 2000 -50 150 0 22.0 180 2155 82.76 -5.52 -0.64 -0.24 90.0 2076 3000 -50 150 0 22.0 180 2155 115.20 -5.44 -1.45 -0.06 90.0 2050 1000 +50 150 0 22.0 180 2155 160.00 -5.55 1.31 +0.02 87.8 2014 1000 +100 150 0 22.0 180 2155 203.00 -4.95 -0.28 0.01 90.0 1995 1000 +150 150 0 22.0 180 2155 229.00 -4.96 -0.66 -0.09 90.0 1978 1500 -100 150 0 22.0 180 2155 27.56 -12.72 8.09 -0.07 73.1 2117 2000 -100 150 0 22.0 180 2155 64.50 -4.96 -1.88 -0.16 90.0 2082 1000 -50 130 0 22.0 180 2155 41.05 -8.19 -3.15 -1.04 90.0 2110 1000 -50 75 75 22.0 180 2155 35.50 -8.95 0.16 0.10 85.5 2114 1000 -50 0 130 22.0 180 2155 36.60 -8.75 0.15 0.08 84.4 2105 1000 -50 -75 150 22.0 180 2155 42.70 -6.25 0.17 0.11 87.8 2102 1000 -50 -130 130 22.0 180 2155 42.10 -6.67 0.17 0.11 87.8 2102 1000 -50 -150 75 22.0 180 2155 41.50 -6.23 0.21 2.10 85.5 2105 1000 -50 150 0 22.0 165.7 2155 39.20 -6.69 0.15 0.53 90.0 2115

START OF

30-SEC FREE FALL

F i g . 1 O p e r a t i o n a l p h a s e s of flight

5800 r

5200 h

-5 -10 FLIGHT PATH ANGLE (DEGREES)

F i g . 2 Range of i n i t i a l c o n d i t i o n s

F i g . 3 L a y o u t of cockpit

M A R K S O N , BRYANT, A N D BERGSTEN

(a)

TARGET POSITION RELATIVE

\ Τ 0 PREDICTED LANDING POINT

(b)

_ TARGET POSITION IN BODY-RELATIVE

\ C O O R DINATES

Xb

±

SHADOW OF VEHICLE'S LONGITUDINAL AXIS

(c)

F i g . 4 Guidance d i s p l a y s g e n e r a t e d on C R T and t r a n s m i t t e d on c l o s e d c i r c u i t T V to mockup: a ) t h r e e - a x i s a t t i - tude m e t e r ; b ) f o r braking m a n e u v e r ; c ) f o r t e r m i n a l m a n e u v e r

ALTITUDE

RATE OF CLIMB