NASA TECHNICAL NOTE N A S A TN D-2504 C-L- - - - - c> /

A SIMPLIFIED GUIDANCE SCHEME FOR ABORTING LUNAR LANDINGS

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I ‘7 Langley Research Center by G. Kimball Miller, Jr.

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1 - l I Langley Station,

I NATIONAL AERONAUTICS A N D w

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Hampton, Va.

SPACE A D M I N I S T R A T I O N WASHINGTON, D. C. DECEMBER 1964

- 31

TECH LIBRARY KAFB. NM

1 A SIMPLIFIED GUIDANCE SCHEME FOR ABORTING LUNAR LANDINGS

I By G. Kimball Mil ler , Jr.

Langley Research Center Langley Station, Hampton, Va.

N A T I O N A L AERONAUTICS AND SPACE ADMINISTRATION

For sa le by the Off ice of Technical Services, Department of Commerce, Washington, D.C. 20230 -- Price $1.00

i

A SLMPLIFIED GUTDANCE SCHEME FOR ABORTING LUNAR I;ANDINGS

By G. Kimball Miller, Jr. Langley Research Center

SUMMARY

An analytical investigation has been made of a technique to abort the landing phase of the lunar mission. The abort technique requires only a stop- watch and an optical device for measuring the angle between the vehicle thrust axis and the line of sight to the orbiting command module. The results of the investigation indicated that the abort maneuver placed the ferry vehicle in a safe orbit that would provide rendezvous capability during the first orbital period. Thrust-angle errors of k0.5' were permissible if the landing trajec- tory was chosen so that the lunar surface in the region of the landing site contained no features that exceeded an altitude of 20,000 feet.

INTRODUCTION

The capability of aborting the landing phase of the lunar mission is a

Alternately, necessary requirement for insuring the astronauts' safety. Onboard automatic systems may be used to provide control during the abort mode. simplified guidance techniques can be used to develop a manual procedure that is independent of automatic systems. These manual procedures can serve as a backup guidance mode o r if sufficiently precise might be considered as primary control modes. equipment. command module as a reference for thrust vector orientation and requires the pilots' use of line-of-sight measurements and a timing device.

Such abort, procedures should be simple and require a minimum of The procedure investigated in the present paper uses the orbiting

SYMBOLS

.

F

Qe

Any consistent set of units may be used. In this report it is assumed that

1 international foot = 0.3048 meter

1 international mile = 1.852 kilometers

thrust, lb

acceleration at surface of earth due to gravitational attraction, 32.2 ft/sec2

l l l l 1 1 1 l l l l l l l I l I l l l l I l l I1 I

acceleration a t lunar surface due t o grav i ta t iona l a t t rac t ion , 5.32 f t / sec 2 Qm

h a l t i t u d e above lunar surface, f t

hmin minimum a l t i t u d e reached during thrus t ing phase of abort maneuver, f t 5

ISP specif ic impulse, 303 sec

K angle between th rus t vector and l i n e of s igh t t o orbi t ing command module (f ig . l), deg

i

m mass of f e r ry vehicle, slugs

P period of o r b i t established by abort maneuver, sec

r r ad ia l distance f r o m center of moon, f t

rm radius of moon, 5,702,000 f t

t time, sec

elapsed time between abort i n i t i a t i o n and abort termination, sec t A

elapsed time between landing i n i t i a t i o n and abort i n i t i a t i o n , sec t L

charac te r i s t ic velocity, geIsp loge m, my f t / s ec V

W weight of f e r ry vehicle on earth, l b

w angular veloci ty of command module about moon, 0.048947, deg/sec

B angle between l o c a l v e r t i c a l of command module and l i n e of s ight f r o m f e r ry vehicle t o orb i t ing command module, radians o r deg

e range angle between pericynthion of o r b i t established by abort maneu- ver and nominal landing s i t e (posi t ive values indicate a pericynthion located downrange from the nominal landing s i t e ) , radians o r deg

range angle by which the f e r ry vehicle leads the command module, radians o r deg

82

k i n range angle between minimum a l t i t u d e reached during thrust ing and the nominal landing s i t e (posi t ive values correspond t o a minimum a l t i - tude t h a t i s located downrange from nominal landing s i te ) , radians o r deg I

'e angular t r a v e l over lunar surface, radians !

2

Subscripts:

a apocynthion conditions

n nominal abort conditions

0 initial conditions

P pericynthion conditions

1 conditions during initial phase of abort maneuver .

2 conditions during second phase of abort maneuver

I conditions at first intersection of orbit established by abort maneuver with orbit of command module

I1 conditions at second intersection of orbit established by abort maneuver with orbit of command module

Dots over symbols denote differentiation with respect to time.

A A preceding a parameter indicates a change in that parameter from the nominal; for example, Ah = h - %.

ANALYSIS

For the purpose of this investigation, the command module and ferry vehicle combination is assumed to have been injected into a circular orbit about the moon at an altitude of 80 nautical miles. The ferry vehicle is subsequently detached from the command module and placed in a synchronous orbit with a peri- cynthion altitude of 50,000 feet located approximately Po downrange from injec- tion. The nominal landing trajectory used in this study consists of applying constant thrust at the pericynthion of the synchronous orbit and performing a gravity-turn descent to a point about 5,500 feet above the lunar surface. At this point the ferry vehicle has approxFmately zero velocity. The trajectory characteristics of the nominal gravity-turn maneuver are presented in figure 2. The remainder of the descent is not considered in the present study.

. Preliminary investigation indicated that after about the first 60 seconds of a gravity-turn lunar take-off, the angle between the thrust vector and the line of sight to the orbiting command module (fig. 1) remained very nearly con- stant. In addition, the end conditions of the initial 60-second segment of the lunar take-off could be approximated by maintaining a constant thrust angle with respect to the command module. Since the launch phase is about the same as an abort f r o m the final portion of the landing maneuver, it appeared possible to develop an abort procedure for the entire landing maneuver, based on using two constant thrust angles with respect to the command module.

3

I

Equations of Motion

The computations f o r t h i s investigation were made f o r a point mass moving The general equations of motion of a point i n a plane about a spherical moon.

mass i n spherical coordinates a re derived i n a straightforward manner i n ref- erence 1. tu t ing the appropriate angles of f igure 1 in to the general spherical equations. The resu l t ing equations a re presented f o r reference a s follows:

The equations of motion used i n t h i s study may be obtained by substi-

where

and

s i n 82

6.188 x lo6 - cos e 2 p = tan-1

r

Assumed Vehicle Parameters

It was assumed tha t t he vehicle w a s fully staged a t abort i n i t i a t i o n and t h a t t he abort maneuver was made by using the ferry-vehicle ascent engine. was also assumed that the rotat ion of t he vehicle from landing-trajectory orien- t a t i o n t o abort or ientat ion occurred instantaneously. The values of F/Wo used f o r the descent and ascent stages were 0.483 and 0.436, respectively.

It

1 Abort Maneuver

The equations of motion were solved on an electronic d i g i t a l computer t o develop an abort procedure based upon two periods of constant th rus t angle with respect t o the orb i t ing command module. The i n i t i a l t h rus t angle and time of thrust ing a t t h a t angle were determined by an i t e r a t i o n process, the only c r i - t e r i a being that the pericynthion a l t i t udes resu l t ing from the abort maneuver be greater than 20,000 fee t . Pericynthion a l t i t udes of this magnitude were considered safe providedtha t pericynthion occurs within close proximity of t he I

4

t

nominal landing s i t e . The i n i t i a l thrust angle and the time it i s t o be main- tained are presented i n f igure 3 and are given i n the following equations as l inear functions of t he elapsed time between landing i n i t i a t i o n and abort i n i t i - ation:

K 1 = 160 - 0 . 3 3 t ~ tA,l = o.30tL

(7)

where K1 i s expressed i n degrees and t A , 1 i n seconds.

The second thrust angle w a s chosen so t h a t the radial velocity component w a s zero when the tangent ia l veloci ty component became equal t o t h a t a t peri- cynthion of t h e synchronous o r b i t a t which t i m e thrust w68 terminated. T h i s procedure should result i n t h e establishment of safe o rb i t s t h a t are very simi- lar t o the synchronous o r b i t used during landing. It w a s necessary t o change the thrust ing time given by t h i s method f o r aborts that a re i n i t i a t e d later than about 204 seconds after landing in i t i a t ion . T h i s change w a s made i n order t o formulate an abort procedure which, i n addition t o establishing safe orb i t s , provided the capabili ty of rendezvousing with the command module during the f irst o r b i t a l period. The second thrus t angle and the t i m e of thrust ing a t t h a t angle a re given i n f igure 4 as functions of t he elapsed time between landing i n i t i a t i o n and abort i n i t i a t ion . It should be noted t h a t t he discon- t i n u i t y i n tA,2 a t a . t L of 204 seconds p’roduced s i m i l a r d iscont inui t ies i n the o r b i t a l parameters of t he o r b i t s established by the abort maneuver.

The abort maneuver i s predicated on the assumption tha t . t h e p i l o t has avail- able a timing device and an op t i ca l device f o r measuring t h e angle between ferry vehicle t h rus t axis and t h e l i n e of sight t o the command module. The p i l o t would a l so have avai lable a family of char ts corresponding t o figures 3 and 4. The p i lo t ing procedure f o r t h e abort maneuver i s given as follows f o r reference.

The timing device i s started a t landing i n i t i a t i o n and i s stopped a t tha t point during the landing where an abort i s deemed necessary. The p i l o t then enters a chart similar t o f igure 3 (instantaneous staging and rotat ion t o abort a t t i t ude i s assumed i n the present study) and obtains t h e value of

t A , 1 staged, releasing t h a t portion that i s necessary only for landing, and i s rotated t o the proper th rus t angle proper time t A , 1 . obtains those values of $ and t t ia t ion . The ferry vehicle i s then rotated t o K2 which is maintained u n t i l th rus t termination a t tA,2. places the f e r ry vehicle i n close proximity t o t h e command module during the first o r b i t a l period.

K1 and t h a t i s appropriate for the t i m e of abort i n i t i a t ion . The vehicle i s then

K1. Thrust i s then applied and maintained f o r t h e The p i l o t then enters a chart similar t o f igure 4 and

corresponding t o the t i m e of abort i n i - AJ2

This procedure should r e su l t i n a safe o rb i t which

5

DISCUSSION O F RESULTS

The abort maneuver r e su l t s i n the establishment of o r b i t s with pericynthion a l t i t udes tha t exceed 24,000 f e e t and are located within approximately ?80 of the nominal landing s i te ( f ig . 5) f o r aborts from any point along the nominal landing t ra jectory. t u re s (ref. 2) which are located primarily i n t h e polar regions of the moon. The choice of t he nominal landing s i te i s v i r t u a l l y unres t r ic ted f o r near equa- t o r i a l o rb i t s . b

Thus, pericynthion exceeds a l l but the highest lunar fea- 1

The a l t i t u d e at pericynthion of the resu l t ing o r b i t i s not the minimum a l t i t u d e reached during the abort maneuver. during the i n i t i a l phase of t he abort a t point of landing i n i t i a t i o n and the nominal landing s i t e ( f ig . 6) and thus should not cons t i tu te a problem.

The minimum a l t i t ude , which occurs Kl, is i n general located between the

The e l l i p t i c o r b i t s established by the abort maneuver exceed 486,000 f e e t a t apocynthion ( f ig . 7) and thus in te rsec t t he c i r cu la r o r b i t of the command module. by 3 O t o lrp, but at the second intersect ion the f e r r y vehicle lead angle i s between 2' and -2'. t i c a l miles of t he command module a t the second o r b i t a l in te rsec t ion which should be close enough t o permit rendezvous. period of t he f e r ry vehicle i s l e s s than t h a t of the command module ( f ig . 9) and the lead angle of the f e r ry vehicle increases with each revolution by as much as 13.5'. ver i s 6,000 f e e t per second or less.

A t t he first intersect ion the ferry vehicle leads the command module

(See f ig . 8.) Thus, the f e r ry vehicle i s within k36 nau-

(See re fs . 3 and 4.) The o r b i t a l

The charac te r i s t ic veloci ty required t o perform the abort maneu- (See f i g . 10.)

An er ror analysis i s included i n t h e appendix which considers the e f fec t of The e r ror anal- various e r rors on the o r b i t s established by the abort maneuver.

y s i s indicated t h a t t h rus t angle e r rors of kO.5O a r e permissible and t h a t abort thrust ing time must be maintained very accurately i f the abort maneuver i s t o provide rendezvous capabi l i ty during the f irst o rb i t .

CONCLUDING REMARKS

An analy t ica l investigation has been made of an abort technique which requires only a timing device t o measure the elapsed time between landing i n i t i a - t i on and abort i n i t i a t i o n and an op t i ca l device t o measure the angle between the thrus t axis of the f e r ry vehicle and the l i n e of s igh t t o the orbi t ing command module. The landing t ra jec tory from which aborts were considered was a gravity- turn descent t o 5,500 f ee t from the 5O,OOO-foot pericynthion a l t i t ude of an equiperiod t ransfer o r b i t from the command module.

The abort maneuver was i n i t i a t e d by applying thrus t a t some angle with respect t o the l i n e of s ight t o the command module f o r a given time where both the thrus t angle and the thrust ing time a re l i nea r functions of the elapsed time between landing i n i t i a t i o n and abort i n i t i a t ion . rotated t o a second thrus t angle with respect t o the command module, and t h i s

The ferry vehicle was then

6

angle was maintained until thrust termination at a given time. Both the thrust angle and thrusting time are functions of the elapsed time between landing ini- tiation and abort initiation. It was found that the abort maneuver resulted in the establishment of nonimpacting orbits for aborts from any point along the landing trajectory. In addition, the orbits established by the abort maneuver resulted in placing the ferry vehicle within rendezvous range of the command module. having altitudes at pericynthion that are greater than 20,000 feet.

Thrust-angle errors of k0.5' are permissible, the resulting orbits t

Langley Research Center, National Aeronautics and Space Administration,

Langley Station, Hampton, Va., September 4, 1964.

7

ERROR ANALYSIS

The ef fec t of errors i n ferry vehicle t h rus t angle on several pertinent o r b i t a l parameters i s presented i n figure 11. ment of o rb i t s with pericynthion a l t i t udes that are too low t o be considered safe, t he nominal t h rus t angle of the abort maneuver must be maintained t o with- i n 0.5'. I n addition, the ferry vehicle lead angle a t t he second o r b i t a l inter- section can change by as much as about 3 O per degree e r ro r i n thrus t angle. (See f i g . l l ( c ) . ) The e f fec t of th rus t angle e r rors on the other o r b i t a l param- eters considered are re la t ive ly insignif icant .

I I n order t o avoid the establish-

*

Several additional e r rors including errors i n t o t a l abort thrust ing t i m e and errors i n veloci ty and a l t i t ude a t abort i n i t i a t i o n were considered. For the sake of brevity, only a s ingle time of abort i n i t i a t i o n along the landing t ra jec tory w a s considered f o r t h i s portion of t he e r ror analysis. chosen, 204' seconds af ter landing i n i t i a t i o n very nearly corresponds t o tha t point along the landing t ra jec tory f o r which the pericynthion a l t i t ude of t he o rb i t s established by the abort maneuver i s a minimum.

The t i m e

(See f i g . 5 . )

The ef fec t of f a i l i n g t o terminate abort th rus t a t the proper time i s pre- sented i n f igure 12. on pericynthion a l t i t ude and location. (See f igs . E ( a ) and l2 (b ) . ) However, there i s a significant e f fec t on apocynthion a l t i t ude ( f ig . = ( e ) ) and, conse- quently, on the ferry vehicle lead angle a t t'. second o r b i t a l intersect ion (f ig . l 2 (e ) ) . The f e r ry vehicle lead angle changes by about 4' per second er ror i n time of th rus t termination. very accurately i f t he abort maneuver i s t o provide rendezvous capabili ty during the first o r b i t a l period.

Errors i n time of t hn i s t termination have l i t t l e e f fec t

Thus, abort thrust ing t i m e should be maintained

The abort maneuver assumes that the landing vehicle has a specif ic velocity-alt i tude combination a t a given point along the landing t ra jectory. Consequently, errors i n velocity and a l t i t ude a t abort i n i t i a t i o n resu l t i n t he establishment of o rb i t s t h a t d i f f e r from those nominally expected. The e f f ec t s of such er rors on several pertinent o r b i t a l parameters are presented i n f igures 13 t o 13. tude and location (f igs . l3(a) and l3 (b ) ) , with l i t t l e e f fec t on apocynthion a l t i t ude (f ig . l 3 ( c ) ) and ferry vehicle lead angle a t the second o r b i t a l in te r - section (f ig . l3 (e) ) . Errors i n tangential veloci ty have some ef fec t on peri- cynthion a l t i t ude and location (f igs . 14(a) and 14(b)) but primarily a f f ec t apo- cynthion a l t i t ude (f ig . 14(c)) and hence the f e r ry vehicle lead angle a t the second o r b i t a l intersect ion (f ig . 14(e) ) . Errors i n a l t i t ude have some ef fec t on pericynthion a l t i t ude (f ig . l'J(a)) and prac t ica l ly no e f fec t on apocynthion a l t i t ude ( f i g . 15(c) ) and fe r ry vehicle lead angle a t t he second o r b i t a l intersection.

Errors i n r ad ia l velocity primarily a f fec t pericynthion a l t i -

8

1. Nelson, Richard D.: Effects of Flight Conditions a t Booster Separation on Payload Weight i n O r b i t . NASA TN D-1069, 1961.

2. Kopal, Zdengk: Topography of t he Moon. Physics and Astronolqy of t he Moon, 9 Zdengk Kopal, ed., Academic Press, 1962, pp. 231-282.

3. Brissenden, Roy F.; Burton, B e r t B.; Foudriat, Edwin C . ; and Whitten, James B.: Analog Simulation of a Pilot-Controlled Rendezvous. NASA TN D-747, 1961.

4. Uneberry, Edgar C. , Jr. ; Brissenden, Roy F. ; and Kurbjun, Max C. : Analytical

NASA and Preliminary Simulation Study of a P i l o t ' s Abil i ty To Control the Term- i n a l Phase of a Rendezvous With Simple Optical Devices and a Timer . mD-965, 1961.

9

Figure 1.- I l lu s t r a t ion of abort maneuver.

-

b

I O X 105 -I-- ----------- \ 1 \ 5 0 ~ IO3 4-

Time from l a n d i n g in i t ia t ion , t, sec

(a) Altitude and range.

Figure 2.- Trajectory characteristics of nominal gravity-turn landing trajectory.

.a ---------- -480-

I \

40 80 I20 I60 200 240 I\-- 280 320 0 ---------- - 5600- Time from landing initiation, t, sec

(b) Velocity components.

Figure 2.- Concluded.

Elapsed time between landing initiation and abort initiation, t,, sec

Figure 3. - Thrust angle and thrusting time used during i n i t i a l phase of the abort maneuver as functions of elapsed time between landing in i t i a t ion and abort in i t ia t ion .

P w

0, a, 73

c rrl

Y

c

a, 0 C 0

cn 3 L r

-

c

I-

0 a, cn c

N c

+a E c

Q)

.- c

IT c c cn 3 c L t-

'\ / 30- ---------- - ----. 0 40 80 I20 I60 200 240 280 . 320

Elapsed t i m e between landing in i t iat ion and abort in i t iat ion, t,, sec

0

Figure 4.- Thrust angle and thms t ing time used during second phase of the abort maneuver as functions of elapsed time between landing i n i t i a t i o n and abort i n i t i a t ion .

Elapsed time between landing initiation and abort initiation, t,, sec

Figure 5.- Pericynthion a l t i tude and location of pericynthion of orb i t s established by abort maneuver.

t y. c

to ----i__--L__---pp---.- OO 40 80 I20 I60 200 240 280 320

Elapsed time between landing initiation and abort initiation, tL, sec

Figure 6 . - Minimum a l t i tude reached during t h s t i n g phase of abort maneuver and i t s location with respect t o nominal landing s i t e .

I60 200 240 280 320

Elapsed time between landing initiation and abort ini t iat ion, tL, sec

Figure 7.- Apocynthion al t i tude of orbi ts established by abort maneuver.

- 4 L i I L i I L L L L L 1 1 1 1 1 1 80 I20 I60 200 240 2 80 320 0 40

Elapsed time between landing initiation and abort initiation, t,, sec

Figure 8.- Angle by which the f e r ry vehicle leads the command module at the two intersections of the orb i t established by the abort maneuver with the orb i t of the command module.

73801 I I I - - - .

80 n. mi. circular orbit

I

40

1. 1

.. .

\

'\

I \ \

80 .I 20 I60 200 240 Elapsed time between landing initiation and abort initiation, t,, sec

Figure 9.- Period of o r b i t s established by abort maneuver. ,

6x IO3

5 I I*-- J

/’ 40 80 I 2 0 I60 200 240 280 Elapsed time between landing initiation and abort init iation, t,, sec

320

Figure 10.- Characterist ic velocity required by abort maneuver.

8 x IO3

/

'--

40 E lap

e .5

.5

'4.0

80

#$

L.

\

\

'\

I20

-.5 - 1.0

.5

1.0

:d time ,etween land..tg initiation and abort initiation, t,, sec

( a ) Effect on pericynthion a l t i t ude and locat ion.

Figure 11.- Effect of e r ro r s i n thrust angle on o rb i t s established by abort maneuver.

21

I20 I 24 0 280

1.0

.5

-. 5

-1.0

Elapsed time b - tween landing initialmua. and abort initiation, tL, sec 3

(b) Effect on apocynthion a l t i t ude and o r b i t a l period.

Figure 11.- Continued.

22

P

0“ #- O r z

-_ c-- -- -IO/-’-- ‘\ -

\ ’ -.5 / /

a : -4-

U c .- C G

co E

--

- 1-1.0 I ~+++#

e

(c ) Effect on m i n i m a l t i t u d e reached during thrust ing and Its location, and on the f e r r y vehicle lead angle a t t h e two o r b i t a l intersect ions.

Figure 11.- Concluded.

23

2

0 a, v)

Q - 0 ti

-20 -10 --2--

I L

'I 0

2

0 (u v)

- 0 a 3

- 2-

10

Y

I I I

, I I I

A h p , f t

2

o a, v)

i o 3

-2

(a) Effect on pericynthion a l t i t u d e .

i i - ,' I 1

I 1 I

20

r

(b) Effect on pericynthion locat ion.

-32 -24 - I 6 -8 0 8

Ah,, f t

.4

16

30

i

.6

( c ) Effect on apocynthion a l t i t u d e .

F i w e 12.- Effect of e r rors i n abort thrust ing time on o r b i t s established by abort maneuver.

24

- 2. -.6

y\

- .4

--I--- 72 0

+ .2 4

. .6

. : .8 (a ) Effect on f e r r y vehicle lead angle a t first o r b i t a l intersect ion.

2

0 W ln

- c a 2l

c - L - I

I

Y\ -8 -4

i

12 1 16

(e ) Effect on ferry- vehicle lead angle a t second o r b i t a l intersect ion.

-160 -80 0 80

AP, sec

/ I

I60 1 -

240 I 3 20

( f ) Effect on o r b i t a l period.

Figure 12.- Concluded.

25

I 20

0 aJ 5 Y-

- 0 .LO Q

-20 /'.

Ahp, f t

(a) Effect on pericynthion a l t i t ude .

I I / ' I 1

! ! - .

/

6

20.

0 al s - 0 .c

.Lo Q

-20

Ae, deg

(b) Effect on pericynthion locat ion.

\

. .. 1

x 103

(c ) Effect on apocynthion location.

Figure 13.- Effect of e r ro r s i n r ad ia l ve loc i ty a t abort i n i t i a t i o n on o rb i t s established by abort maneuver.

26

L

Q

-20 -1.6 -1.2

i\

-.8

\

\

4 \

.8 1.2

( a ) Effect on f e r ry vehicle lead angle a t first o r b i t a l intersect ion.

-2 a -. 8

( e ) Effect on f e r r y vehicle lead angle a t second o rb i t a l intersect ion.

-.I6

I I IC ir

-I 2 -8 -4 0 4 8 12x102

- . I 2 -.08 -.04 * 0 .04 .08 .I2 Ahmin, f t

A h i n , deg

( f ) Effect on m i n i m a l t i t ude reached during tbrust ing and on i t s location.

Figure 13.- Concluded.

27

-I

/

I ---I- . .

0 Ahp, f t

( a ) Effect on pericynthion a l t i t u d e .

\

--P

-2

i i i

i i r \ / / I [y\i 0 2

AB, deg

(b) Effect on pericynthion location.

/ /

0

/

1

I

\ I \1 - 1 r 0

deg

1 1.2 \ 0 Y- -20 - 1.6

\

\ \ \

-. 8 .8 -1.2

( a ) Effect on f e r r y vehicle lead angle a t f i r s t o r b i t a l intersect ion.

\ i

-6

\ i r i y\

\ \

- 4 4 6

(e ) Effect on f e r r y vehicle lead angle a t second orb i ta l Lntersection.

i

-120

i

I, -80 - 40 0 40

AP, sec 80 120

( f ) Effect on o r b i t a l period.

Figure 14.- Concluded.

29

2000

z 6 0 z

Ahp, f t

(a ) Effect on pericynthion a l t i t u d e

,’ I l l I l l 111 2 3 x IO3

AB, deg

(b) Effect on pericynthion location.

Ah,, ft

(c) Effect on apocynthion a l t i tude .

Figure l5-- Effect of e r rors i n a l t i t u d e a t abort i n i t i a t i o n on orb i t s established by abort maneuver.

200c

e -I-

.. 0 0 c a

(a) Effect on f e r ry vehicle lead angle a t f i r s t o rb i t a l intersect ion.

\

\

c c

0

-2000. -.I6

I I I I I I I I - 2000

-.I 2 -.08

--'\..

( e ) Effect on f e r ry vehicle

.O.q

-2wc I

e -I-

2 0 - i -4

i

-3

i

c -2

lead

/

angle a t second o r b i t a l intersect ion.

i i I / / 1(1

I I I 2 3 x lo3

( f ) Effect on minimum a l t i t ude reached during thrust ing.

Figure 15.- Concluded.

NASA-Langley, 1964 L-4185

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