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GEORGE C , MARSHALL SPACE FLIGHT CENTER

I / NASA TM X-53,002 .

'' PERFORMANCE ANALYSIS O F CHEMICAL STAGES IN THE 300 TO 400 SECOND SPECIFIC IMPULSE RANGE -

FOR INTERPLANETARY MISSIONS

BY >/ J Walter H. Stafford and Carmen R. Catalfamo

ABSTRACT I -3-6 ;rj a:t,eJ

The purpose of this report is to present a procedure by which t r a j ec to ry pa rame te r s can be determined f o r escaping f rom, and braking into, an orb i t about the ea r th utilizing a single vehicle stage in the low specific impulse range.

The data a r e presented in two sections: Section A i s for escape f r o m a n ' o r b i t about the ea r th and Section B is f o r braking into an orbi t about the ear th .

The effect of thrust-to-weight ra t ios and specific impulses on t r a j e c t o r y pa rame te r s was investigated f o r hyperbolic velocit ies. F o r the escape t r a j ec to r i e s , the thrust vector was applied tangential to the flight path and in the direction of the velocity vec tor . F o r the braking t r a j e c t o r i e s , the th rus t vector was directed against the velocity vector . Specific impulses of 300 to 400 seconds and ea r th thrust-to-weight ra t ios of 0 .2 to 1.0 were used.

The approach used for the escape t r a j ec to r i e s was to determine the t r a j ec to ry pa rame te r s a t burnout, convert the cha rac t e r i s t i c velocity t o a hyperbolic excess velocity and then present the data graphically. The approach used for the braking t r a j ec to r i e s was to determine the a r r i v a l velocity f o r a given t ransfer t r a j ec to ry and initiate burning such that c i r cu la r orbi t conditions a r e attained a t burnout. t e r i s t ic velocity i s converted to a hyperbolic excess velocity and presented

The cha rac -

graphically. 7

GEORGE C. MARSHALL SPACE FLIGHT CENTER

NASA TM X-53,002

PERFORMANCE ANALYSIS O F CHEMICAL STAGES IN THE

FOR INTERPLANETARY MISSIONS 300 TO 400 SECOND SPECIFIC IMPULSE RANGE

Walter H. Stafford and C a r m e n R. Catalfamo

MISSION ANALYSIS GROUP ADVANCED STUDIES OFFICE

PROPULSION AND VEHICLE ENGINEERING LABORATORY

TABLE O F CONTENTS

.

SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

SECTION I . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . SECTION I1 . ASSUMPTIONS . . . . . . . . . . . . . . . . . . . . . . . SECTION 111 . ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . .

SECTION IV . DISCUSSION OF RESULTS . . . . . . . . . . . . . . .

SECTION V . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . .

SECTION VI . GRAPHIC PRESENTATION . . . . . . . . . . . . . .

A . DEPARTUREFROMEARTHORBIT . . . . . . . . . . . . .

B . BRAKE TO EARTH ORBIT . . . . . . . . . . . . . . . . . . . . BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page

1

1

2

2

7

7

8

9

3 1

55 .

c

.

iii

Figure

1

2

3

LIST O F ILLUSTRATIONS

Title Page

DEPARTURE FROM EARTH ORBIT

Character is t ic Velocity Versus Hyperbolic Excess Velocity with Thrust- to- Weight Ratio as a P a r a m e t e r f G r a Constant Specific Impulse of 300 Seconds

a. F o r Hyperbolic Excess Velocities of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 10

b . F o r Hyperbolic Excess Velocities of 4 . 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . . 11

c . F o r Hyperbolic Excess Velocities of 7 . 8 through 1 0 . 0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 12

c

Charac ter i s t ic Velocity Ver sus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r fo r a Constant Specific Impulse of 325 Seconds

a. F o r Hyperbolic Excess Velocities of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 13

b. F o r Hyperbolic Excess Velocities of 4 . 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . . 14

c . F o r Hyperbolic Excess Velocities of 7. 8 through 10 .0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 15

Charac te r i s t ic Velocity Ver sus Hyperbolic E x c e s s Velocity with Thrust- to- Weight Ratio as a P a r a m e t e r fo r a Constant Specific Impulse of 350 Seconds

a. F o r Hyperbolic Excess Velocities of 0. 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 16

i v

.

.

LIST OF ILLUSTRATIONS (Continued)

F igu re

4

5

6

Title Page

b. F o r Hyperbolic Excess Velocities of 4. 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . . 17

c . F o r Hyperbolic Excess Velocit ies of 7. 8 through 1 0 . 0 km/sec . . . . . . . . . . . . . . . . . . . . . 18

Charac te r i s t ic Velocity Versus Hyperbolic Excess Velocity with Thrus t - to- Weight-Ratio as a P a r a m e t e r fo r a Constant Specific Impulse of 375 Seconds

a. F o r Hyperbolic Excess Velocit ies of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 19

b. F o r Hyperbolic Excess Velocit ies of 4. 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . . 2 0

c . F o r Hyperbolic Excess Velocit ies of 7 . 8 through 1 0 . 0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 2 1

Charac te r i s t ic Velocity Ver sus Hyperbolic E x c e s s Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r for a Constant Specific Impulse of 400 Seconds

a . F o r Hyperbolic Excess Velocit ies of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 22

b. F o r Hyperbolic Excess Velocit ies of 4 . 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . . 23

c . F o r Hyperbolic E x c e s s Velocit ies of 7. 8 through 1 0 . 0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 24

Velocity Loss Due to Gravi ty Versus Thrust- to- Weight Ratio with Hyperbolic Excess Velocity as a P a r a m e t e r for a Constant Specific Impulse of 300 Seconds. . . . . . . . . . . . . . . . . . . . . . . . . . . 25

V

LIST OF ILLUSTRATIONS (Continued)

Title Page F igu re

7

8

9

10

11

1

Velocity Loss Due to Gravity Ver sus Thrus t - to- Weight Ratio with Hyperbolic Excess Velocity as a P a r a m e t e r fo r a Constant Specific Impulse of 400 Seconds. . . . . . . . . . . . . . . . . . . . . . . . . . .

Flight Pa th Angle Versus Hyperbolic Excess Velocity with Thrus t - to- Weight Ratio f o r Specific Impulses of 300, 350 and 400 Seconds a s a P a r a m e te r . . . . . . . . . . . . . . . . . . . . . . . . . . .

Change in Altitude Versus Hyperbolic Excess Velocity with Thrust.-to- Weight Ratio fo r Specific Impulses of 300, 350 and 400 Seconds a s a P a r a m e t e r . . . . . . . . . . . . . . . . . . . . . . . . . . .

Centra l Angle Ver sus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio fo r Specific Impulses of 300, 350 and 400 Seconds as a P a r a m e t e r . . . . .

Burning Time Versus Hyperbolic Excess Velocity with Thrust- to- Weight Ratio fo r Specific Impulses of 300, 350 and 400 Seconds as a P a r a m e t e r . . . . .

BRAKE TO EARTH ORBIT

Charac te r i s t ic Velocity Versus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio a s a P a r a m e t e r fo r a Constant Specific Impulse of 300 Seconds

a. F o r Hyperbolic Excess Velocit ies of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . .

b . F o r Hyperbolic Excess Velocit ies of 4 . 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . .

26

27

2 8

2 9

30

32

33

c . F o r Hyperbolic Excess Velocities of 7. 8 through 10 .0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 34

vi

.

.

LIST O F ILLUSTRATIONS (Continued)

F igu re

2

3

4

.

Title

Charac te r i s t ic Velocity Ver sus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r f o r a Constant Specific Impulse of 325 Seconds


b. F o r Hyperbolic Excess Velocit ies of 4 . 6 through 7 . 8 k m / s e c . . . . . . . . . . . . . . . . . . . . .

c. F o r Hyperbolic Excess Velocit ies of 7 . 8 through 10 .0 km.!sec. . . . . . . . . . . . . . . . . . . . .

Charac ter i s t ic Velocity Versus Hyperbolic E x c e s s Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r f o r a Constant Specific Impulse of 350 Seconds


b. F o r Hyperbolic Excess Velocit ies of 4 . 6 through 7 . 8 k m l s e c . . . . . . . . . . . . . . . . . . . . .

c . F o r Hyperbolic Excess Velocities of 7. 8 through 10.0 k m / s e c . . . . . . . . . . . . . . . . . . . . .

Charac ter i s t ic Velocity Ver sus Hyperbolic E x c e s s Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r fo r a Constant Specific Impulse of 375 Seconds

a. F o r Hyperbolic E x c e s s Velocit ies of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . .

Page

35

36

37

38

39

40

41


v i i

LIST O F ILLUSTRATIONS (Continued)

F igure

5

6

7

8

9

Title Page

c . F o r Hyperbolic Excess Velocit ies of 7 . 8 through 1 0 . 0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 43

Character is t ic Velocity Versus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio as a P a r a m e t e r for a Constant Specific Impulse of 400 Seconds

a . F o r Hyperbolic Excess Velocities of 0 . 0 through 4 . 6 k m / s e c . . . . . . . . . . . . . . . . . . . . . 44


c . F o r Hyperbolic Excess Velocit ies of 7 . 8 through 1 0 . 0 k m / s e c . . . . . . . . . . . . . . . . . . . . . 46

Velocity Loss Due to Gravity Ver sus Thrust- to- Weight Ratio with Hyperbolic Excess Velocity as a P a r a m e t e r for a Constant Specific Impulse of 300 Seconds. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Velocity Loss Due to Gravity Versus Thrus t - to- Weight Ratio with Hyperbolic Excess Velocity as a P a r a m e t e r fo r a Constant Specific Impulse of 400 Seconds. . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Flight Pa th Angle V- r sus Hyperbolic Excess Velocity with Thrust- to- Weight Ratio fo r Specific Impulses of 3 0 0 , 350 and 400 Seconds a s a P a r a m e t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

Change in Altitude Versus Hyperbolic Excess Velocity with Thrust- to- Weight Ratio fo r Specific Impulses fo 300 , 350 and 400 Seconds as a

. P a r a m e t e r . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

.

viii

Figure

10

11

12

13

LIST OF ILLUSTRATIONS (Concluded)

Title Page

Cen t ra l Angle Versus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio fo r Specific Impulses of 300, 350 and 400 Seconds as a P a r a m e t e r . . . . . 51

Burning Time Versus Hyperbolic Excess Velocity with Thrust-to-Weight Ratio fo r Specific Impulses of 300, 350 and 400 Seconds a s a P a r a m e t e r . . . . . 52

M a s s Ratio Versus Charac te r i s t ic Velocity with Specific Impulse as a P a r a m e t e r . . . . . . . . . . . . . 53

Payload Frac t ion and Stage Frac t ion Versus M a s s Ratio with Stage Mass Frac t ion a s a Pa.rarr,eter. . . 54

ix

Symbol

F

F / W o

f

g

H

h

Ah

I SP

m

r

R

r 0

tB

V

v 'P

VI

.L

vco

wA

W, L

DEFINITION O F SYMBOLS

Definition

Thrus t , N

Initial thrust-to-weight ra t io (based on weight a t ea r th sea level)

Stage mas s f ract ion, ( W p / WA)

Gravitational accelerat ion, m l sec'

Energy

Altitude, km

Altitude change, (h - ho), k m

Specific impulse, s ec

M a s s , kg

Radius, k m

Plane t rad ius , km

(ho -t R ) , k m

Burning t ime, sec

Velocity

Comparat ive velocity

Stage charac te r i s t ic velocity

Hyperbolic excess velocity

Stage weight, (Wo - WL), N

Payload weight, N

X

,

Symbol

wO

wP

X

cy

5

sp

tJ.

Subscripts

C

e s c

ex

f

id

K

0

P

DEFINTION OF SYMBOLS (Continued)

Definition

G r o s s weight, N

Propel lant weight, N

Range, km

Angle of attack (angle between velocity vec tor and th rus t vector) , deg

Propel lant m a s s f rac t ion , ( W p l Wo)

Fl ight path angle f r o m ver t ica l , deg

Gravitational constant

Cen t ra l angle, deg

B urn0 ut

Escape

Exhaust

F ina l

Ideal

C i rcu la r

Init ial

Propel lan t

xi

Symbol

Abbreviations

kg

km

m

s ec

N

DEFINITION O F SYMBOLS (Concluded)

De finit ion

Kilogram

Ki lome t e r

M e t e r

Second

Newton

xii

GEORGE C. MARSHALL SPACE FLIGHT CENTER

.

NASA TM X-53,002

PERFORMANCE ANALYSIS O F CHEMICAL STAGES IN THE

FOR INTERPLANETARY MISSIONS 300 TO 400 SECOND SPECIFIC IMPULSE RANGE

Walter H. Stafford and Carmen R. Catalfamo

The effect of thrust-to-weight ra t ios and specific impulses on t r a j ec to ry p a r a m e t e r s has been investigated f o r hyperbolic escape f r o m , and braking into, an orbi t about ear th . F o r the escape t r a j ec to r i e s , the th rus t vector was applied tangential to the flight path and in the direct ion of the velocity vector. F o r the braking-in t r a j ec to r i e s , the t h r u s t vector was directed against the velocity vec tor . Thrus t - to- weight ra t ios of 0 . 2 to 1. 0 and specific impulses of 300 to 400 seconds w e r e used.

The resu l t s of the study a r e presented graphically.

SECTION I. INTRODUCTION

A study of the t ra jec tory requirements is of fundamental impor tance in planning interplanetary round-tr ip miss ions . ana lys i s of the miss ion requi res a rapid method of sufficient accu racy f o r determining the t ra jec tory pa rame te r s . is dependent, to a la rge extent, on the velocity requi rements of the pa r tic u l a r t ra jec to r y c ho sen.

P re l imina ry

The sizing of boost vehicles

The purpose of this study is to present a method fo r determining the t r a j ec to ry p a r a m e t e r s and vehicle m a s s cha rac t e r i s t i c s fo r a specif ic miss ion , when the hyperbolic excess velocity is known.

2

The approach used for escape f r o m orb i t was to determine the t r a j ec to ry pa rame te r s at burnout, convert the cha rac t e r i s t i c velocity to a hyperbolic excess velocity, and then present the data graphically. The approach used f o r braking into orb i t was to de te rmine the a r r i v a l velocity for a given t r ans fe r t r a j ec to ry and init iate burning such that c i r c u l a r orbit conditions a r e attained a t burnout. The equations of motion were integrated on a digital computer , using a Runge-Kutta numer ica l integration procedure.

SECTION 11. ASSUMPTIONS

The following is a summary of the basic assumptions used in th i s study:

1 . F o r escape - - Accelerat ion of a single stage f rom a re ference orbi t about ea r th , using a constant th rus t directed along the velocity vector.

2 . F o r braking - - Deceleration of a single stage f r o m an in t e r - planetary t r ans fe r t ra jec tory to a re ference orbi t about ea r th , using a constant thrust directed against the velocity vector .

3 . Reference orb i t about the ea r th was c i r cu la r with a radius of 6556 km and a velocity of 7798 m f s e c .

4. Constant specific impulse values f rom 300 to 400 seconds.

5 . f r o m 0 .2 to 1 .0 .

The thrust-to-weight ra t ios used were var ied paramet r ica l ly

6 . Mean spher ica l earth:

p = 398606.6 km3/ sec'

R = 6371.27 km

SECTION 111. ANALYSIS

F o r interplanetary flight, the ideal") total energy that mus t be impar ted to the spacecraf t is the ideal energy required to escape the

~~ ~~ -

(1)The te rm "ideal" r e f e r s to an instantaneous change of energy.

3

gravitational field of the planet, plus the energy required to change i t s path about the Sun. a t t rac t ion of a planet can be determined f rom two-body mechanics to be He,, = p / r and the energy needed to a l t e r the flight path about the Sun, H,, is determined by the charac te r i s t ics of the interplanetary t r a j ec to ry .

The ideal energy requi red to escape the gravitational

F o r determining the vehicle s i ze necessa ry to inject the space- c r a f t into the interplanetary t ra jec tory , it is convenient to expres s the idea l total energy, H = He,, + H,, in t e r m s of a burnout velocity. produces equations of the following forms:

This

or

When considering finite vehicle sys t ems there is a n additional ene rgy requi rement , Hloss, which resu l t s f r o m expending the propellants at different energy-levels . Therefore , the total velocity increment for the injecting stage is now

where Vo is the init ial velocity. be determined f rom the equation

The vehicle m a s s cha rac t e r i s t i c s can

- ex V

= e wo

wc - (4)

. To accomplish this study, the two-degree -of - f reedom equations

of motion were numerical ly integrated.

4

Referring to the sketches, l'a'' f o r escaping f r o m and "b" fo r braking into, computations were made f o r a point m a s s moving in a plane using the following equations of motion:

* F cos CY v = - JL cos 9, 2 r m (5)

1: = V c o s & (7)

where

m = m t J m d t 0

and

F m = - - Vex

(9)

The velocity and flight path angle may be obtained by integrating the equations of motion

n .

V = V o t J V d t

The range and per icenter altitude can then be calculated by the r e la tions

t 13) R

X = Xo t J - V sin d d t r

h = h o t J k d t t 14)

The cent ra l angle i s

(15) t / ~ = $ ~ t J - d d t X

R

5

INITIAL VERTICAL

I

I LOCAL VERTIC

I

\

h

’

EARTH CENTER

SKETCH a. ESCAPE FROM ORBIT

LOCAL VERTICAL

A L

.

1 - SKETCH b. BRAKE TO ORBIT

6

The initial weight of the stage i s

The velocity expended by the stage is the cha rac t e r i s t i c velocity, o r

Then the velocity lo s ses a r e the difference between the cha rac - t e r i s t i c velocity and the change in comparat ive velocity, o r

where the comparative velocity i s

F o r ascent f rom r = ro to r = r f , the change in comparat ive velocity i s

and the velocity loss due to gravi ty i s

vloss = vexl"(+c) - [ 4-1 -vo] (21)

F o r descent f rom r = ro to r = rf, the change in comparat ive velocity i s

t

and the velocity loss due to gravity i s

= V 1n(rG)- 1 vloss ex

7

SECTION IV. DISCUSSION O F RESULTS

The r e su l t s of this investigation a r e presented grahical ly i n The F igu res 1 through 11 f o r each of the two a r e a s considered. (2)

s tage charac te r i s t ic velocity, V,, is plotted v e r s u s hyperbolic excess velocity, with thrust-to-weight ratios as a pa rame te r , i n F igu res 1 through 5.

F i g u r e s 6 and 7 show the velocity lo s ses , Vloss, due to gravi ty f o r specific impulse values of 300 seconds and 400 seconds, respect ively. The flight path angle at burnout for depar ture t r a j ec to r i e s and at initiation of burning f o r braking t ra jec tor ies , is shown v e r s u s hyperbolic excess velocity in F igu re 8.

F igu re 9 gives the change in altitude. This change is the difference h c t w e e ~ the altitude zf the refe+eiice orbi t about the pianet and the alt i tude at burnout f o r the depar ture t r a j ec to r i e s , and the difference between the altitude of the re ference orb i t and the altitude at initiation of burning f o r braking t ra jec tor ies . t r a j ec to ry p a r a m e t e r s is shown in F igu res 10 and 11.

The change in o ther

The vehicle mass charac te r i s t ics can be determined from F i g u r e s 12 and 13 in the Section entitled "Brake to E a r t h Orbit .

SECTION V. CONCLUSIONS

F r o m these paramet r ic analyses] sufficient data a r e provided to enable the designer to make a prel iminary design of a stage tha t will accompl ish any one of the mission a r e a s studied when that par t icu lar miss ion ' s requi rements are defined.

(2)Figure r e fe rences apply to each of the two a r e a s considered.

8

SECTION VI. GRAPHIC PRESENTATION

9

. DEPARTURE FROM EARTH ORBIT

10

cn v) w

9 * * d m m m m

,

E Y Y

HYPERBOLIC EXCESS VELOCITY, V, (km/sec)

FIGURE lb. CHARACTERISTIC VELOCITY, VI (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, Vm (km/sec), WITH THRUST-

SPECIFIC IMPULSE OF 300 SECONDS TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT

I

12

HYPERBOLIC EXCESS VELOCITY, V, (km/ sec)

FIGURE I C . CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


c

14

t


F I G U R E 2b. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec) , WITH THRUST-

TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT SPECIFIC IMPULSE OF 325 SECONDS


FIGURE 2c. CHARACTERISTIC VELOCITY, VI (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-

SPECIFIC IMPULSE O F 325 SECONDS TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT

7

HYPERBOLIC EXCESS VELOCITY, V, (km/ set)

FIGURE 3b. CHARACTERISTIC VELOCITY, VI (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, Va (km/sec), WITH THRUST-

TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT SPECIFIC IMPULSE O F 350 SECONDS

18

7.

7 .

7.

7.

7.

6 .

6 .

6 .

6 .

6 .

5 .

.

.

8.0 8.5 9.0 9 .5 10.0


FIGURE 3c. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


.

1 9

20


FIGURE 4b. CHARACTERISTIC VELOC'ITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, Vw (km/sec) , WITH THRUST-

SPECIFIC IMPULSE O F 375 SECONDS TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT

21

,

7. a

7.6

u 7.4 Q) II) \

E

> 7.2

.x Y - G E u 2 7.0

F 2 I? 6 . 8 p: W b u 2 6 . 6 4 z u W 9 6 . 4 b cn

6 . 2

6 . 0

5.8


FIGURE 4c. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (kmlsec), WITH THRUST-

TO-WEIGHT RATIO AS A PARAMETER FOR A CONSTANT SPECIFIC MPULSE OF 375 SECONDS

23

.

6 .

6 .

5 .

5 .

5 .

5.

5 .

4.

4.

4.

4.


FIGURE 5b. CHARACTERISTIC VELOCITY, VI (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec) , WITH THRUST-


24

7. a

7.6

h

v 7.4 a, v) \

E

$ 7.2

2

3 Y

* u 0 7.c J w > 2

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25

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BRAKE TO EARTH ORBIT

4

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4.

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5 . 0 5 . 5 6 .0 6.5 7.0 7.5 HYPERBOLIC EXCESS VELOCITY, V, (km/sec)

FIGURE lb. CHARACTERISTIC VELOCITY, VI (kmlsec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


34

7 .

7.

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z

2

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6 .

5.

8 . 0 8 . 5 9 .0 9 . 5 10.0 HYPERBOLIC EXCESS VELOCITY, V, (km/sec)

FIGURE IC. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


36

6 .

6 .

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$ 5.

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b

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4.

FIGURE 2b. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


.

37

7.1

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h

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39

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FIGURE 3b. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-



FIGURE 3c. CHARACTERISTIC VELOCITY, V, (km/sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


41

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$

u"

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FIGURE 4b. CHARACTERISTIC VELOCITY, V, (km/ s e c ) , VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/sec), WITH THRUST-


a

h


FIGURE 4c. CHARACTERISTIC VELOCITY, VI (km/ sec), VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/ sec), WITH THRUST-


44

t

d+ d+ w d+ m m m

Y

6

6

5

5

5

5

5

4.

4.

4.

4.


FIGURE 5b. CHARACTERISTIC VELOCITY, V1 (km/ sec), VERSUS HYPERBOLIC EXCESS VELOCITY, Vm (km/sec), WITH THRUST-


46


.

I

Y

FIGURE 5c. CHARACTERISTIC VELOCITY, V, (km/ sec) , VERSUS HYPERBOLIC EXCESS VELOCITY, V, (km/ sec) , WITH THRUST-


1

47

ssoTA 'SSO? ALLI3013A

- - _ _ _ _ _ _

HYPERBOLIC EXCESS VELOCITY, Voo (km/ sec)

FIGURE 9. CHANGE IN ALTITUDE (km) VERSUS HYPERBOLIC EXCESS VELOCITY (km/sec) WITH THRUST-TO-WEIGHT RATIO

AS A PARAMETER

I

52

0 0 0 0 0 0 0 0 0 0 0

N 0 co Q) a 0 N

0 0 0 0 0 0 9 * 2 4 4 4 4

I

1

0.0.

MASS RATIO, ( - )

FIGURE 13 . PAYLOAD FRACTION AND STAGE FRACTION VERSUS MASS RATIO WITH STAGE MASS FRACTION AS A PARA-METER

55

BIBLIOGRAPHY

?

0

0

c

Cavicchi, Richard H. and Mise r , J a m e s W . , Determination of Nuclear- Rocket Power Levels f o r Unmanned M a r s Vehicle Star t ing f r o m Orbi t About Ea r th . NASA TN D-474, January 1962.

C la rke , Victor C . , A Summary of the Charac t e r i s t i c s of Bal l is t ic Interplanetary Tra j ec to r i e s , 1962- 1977. J e t Propuls ion Laboratory, Cal i fornia Institute of Technology, Pasadena , Cal i fornia , Technical Repor t No. 32-209, NASA Contract No. 7-100, January 15, 1962.

Dobson, Wilbur F . , Mackay, John S. and Huff, Vea r l N . , Star t ing Conditions f o r Nonoscillatory Low -Thrus t P lane t -Escape Tra j ec to r i e s . NASA TN D-1410, August 1962.

Ehr i cke , Krafft A . , Space Flight Pr inc ip les of Guided Miss i le Design. (Edi ted by Grayson M e r r i l l ) , Princeton, New J e r s e y , D. Van Nosirand Company, Inc . , 1960.

F r i ed lande r , Alan L. , A Study of Guidance Sensit ivity f o r Various Low- T h r u s t T r a n s f e r s f rom E a r t h to M a r s . NASA TN s-1183, F e b r u a r y 1962.

F r i ed lande r , Alan L. and Harry , David P. 111, A Study of Stat is t ical Data-Adjustment'and Logic Techniques a s Applied to the Interplanetary Midcourse Guidance Problem. NASA TR R-113, 1961.

Knip, Gera ld , Jr. and Zola, Charles L . , Three-Dimensional Sphere- of-Influence Analysis of Interplanetary Tra j ec to r i e s to M a r s . TN D-1199, May 1962.

NASA

Knip, Gera ld , Jr. and Zola, Charles L. , Three-Dimensional T ra j ec to ry Analysis fo r Round-Trip Missions to M a r s . October 1962.

NASA TN D- 13 16,

Melbourne, W . G . , Richardson, D. E. and Saue r , C. G. , Interplanetary Tra j ec to ry Optimization with Power-Limited Propuls ion Sys tems. Propuls ion Laboratory, California Insti tute of Technology, Pasadena , Cal i fornia , Technical Report No. 32-173, NASA Contract No. NAS 7-100, F e b r u a r y 26, 1962.

J e t

Ross , S . , et . a l . , A Study of Interplanetary Transportat ion Sys tems. Lockheed Miss i les and Space Division, F ina l Report No. 3-17-62-1, Cont rac t NAS 8-2469, June 2 , 1962.

56

BIBLIOGRAPHY (Concluded)

Soviet P r e s s (February 12 - March 3 , 1961), Destination--Venus (Astronaut ics Information Translat ion No. 20) Compiled and Trans la ted

Labora tory , California Institute of Technology, Pasadena , California, Apr i l 1 , 1961.

' by Joseph L. Zygielbaum under NASA Contract NASw-6. Jet Propuls ion

Stafford, Walter H . , Harlin, Sam H. and Catalfamo, C a r m e n R . , Pe r fo rmance Analysis of High-Energy Chemical Stages fo r Interplanetary Miss ions . NASA T N D-1829, January 1964.

Stafford, Walter H. and Harlin, Sam H . , P a r a m e t r i c Pe r fo rmance Analysis for Interplanetary Missions Utilizing F i rs t -Genera t ion Nuclear S tages , P a r t I: Departure f rom E a r t h Orbit . MSFC Report MTP-P&VE-F-63-14 , August 26 , 1963.

Stafford, Walter H. and Harlin, Sam H . , P a r a m e t r i c Pe r fo rmance Analysis for Interplanetary Mis sions Utilizing F i r s t -Generation Nuclear S tages , Part 11: Brake to Venus Orbit . MSFC Report MTP-P&VE-F-63-15 ,

' September 1, 1963.

Stafford, Walter H. and Catalfamo, Carmen R . , P a r a m e t r i c Pe r fo rmance Analysis for Interplanetary Missions Utilizing F i rs t -Genera t ion Nuclear S tages , P a r t 111: Departure f rom M a r s Orbit . MSFC Report M T P -P&VE -F - 63 - 16, September 3 0 , 1 963.

i

I Stafford, Walter H. and Harlin, Sam H . , P a r a m e t r i c Per formance Analysis for Interplanetary Missions Utilizing Firs t -Generat ion Nuclear S tages , P a r t IV: Departure f rom Venus Orbit . MSFC Report MTP-P&VE-A-63-17, October 4, 1963.

Stafford, Walter H. and Catalfamo, C a r m e n R. , P a r a m e t r i c Pe r fo rmance Analysis for Interplanetary Missions Utilizing F i rs t -Genera t ion Nuclear S tages , P a r t V: Brake to M a r s Orbit . MSFC Report MTP-P&VE-A-63-18, October 25, 1963.

Zola, Char les L. and Knip, Gerald, Jr . , Three-Dimensional T ra j ec to ry Analysis for Round-Trip Missions to Venus. August 1962.

NASA TN D- 13 19,

1

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