a method for calculating transient thrust and flow-rate

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

Technical Memorandum 33-604

A Method for Calculating Transient Thrust and

Flow-Rate Levels for Mariner Type Attitude

Control Nitrogen Gas Jets

John D. Ferrera

J E T P R O P U L S I O N L A B O R A T O R Y

C A L I F O R N I A I N S T I T U T E O F T E C H N O L O G Y

P A S A D E N A , C A L I F O R N I A

January 1, 1972

PREFACE

The work described in this report was performed by the Guidance

and Control Division of the Jet Propulsion Laboratory.

JPL Technical Memorandum 33-604 iii

CONTENTS

I. Introduction 1

II. Flow Analysis 2

III. Digital Computer Solutions 7

IV. Conclusions 8

References 10

TABLES

1. Summary of computer equations 11

2. Jet valve characteristics (computer input cards) 12

3. MM'71 jet valve parameters (fixed) 13

4. Computer program results 14

FIGURES

1. MM'71 jet valve model 15

2. Typical valve chamber pressure profile 15

3. Typical valve electrical and pneumatic characteristics:(a) voltage to valve, (b) valve coil current, (c) valvechamber pressure , (d) valve orifice area 15

4. Computer program flow chart 16

5. Computer list printout of steady-state and transientthrust prediction program 17

6. Steady-state printout: (a) MM'71 pitch/yaw,(b) MM'71 roll, (c) MM'64 pitch/yaw, (d) MM«64 roll 22

7. MM'71 pitch/yaw valve parameters as a function oftime: (a) chamber pressure, (b) total mass, nozzle,(c) total mass, chamber, (d) total mass, valve,(e) nozzle flow rate, (f) chamber flow rate, (g) valveflow rate, (h) total impulse, (i) chamber pressurederivative 23

8. MM'71 roll valve parameters as a function of time:(a) chamber pressure , (b) total mass, nozzle,(c) total mass, chamber, (d) total mass, valve,(e) nozzle flow rate, (f) chamber flow rate,(g) valve flow rate, (h) total impulse, (i) chamberpressure derivative 32

JPL, Technical Memorandum 33-604

CONTENTS (contd)

FIGURES (contd)

9. MM164 pitch/yaw valve parameters as a function oftime: (a) chamber pressure, (b) total mass, nozzle,(c) total mass, chamber, (d) total mass, valve,(e) nozzle flow rate, (f) chamber flow rate, (g) valveflow rate, (h) total impulse, (i) chamber pressurederivative 41

10. MM'64 roll valve parameters as a function of time:(a) chamber pressure, (b) total mass, nozzle,(c) total mass, chamber, (d) total mass, valve,(e) nozzle flow rate, (f) chamber flow rate, (g) valveflow rate, (h) total impulse, (i) chamber pressurederivative 50

vi JPL Technical Memorandum 33-604

ABSTRACT

The purpose of this report is to define and program the transient

pneumatic flow equations necessary to determine, for a given set of condi-

tions (geometry, pressures, temperatures, valve on time, etc. ), the total

nitrogen impulse and mass flow per pulse for the single pulsing of a

Mariner type reaction control assembly valve. The rates of opening and

closing of the valves are modeled, and electrical pulse durations of from

20 to 100 ms are investigated. In developing the transient flow analysis,

maximum use was made of the steady-state analysis undertaken in Ref. 1.

The impulse results are also compared to an equivalent "square-wave"

impulse for both the Mariner Mars 1971 (MM1 71) and Mariner Mars 1964

(MM1 64) systems. It is demonstrated that, whereas in the MM' 64 system,

the actual impulse was as much as 56% higher than an assumed impulse

(which is the product of the steady-state thrust and value on time -- i. e. ,

the square -wave), in the MM1 71 system, these two values were in error in

the same direction by only approximately 4% because of the larger nozzle

areas and shorter valve stroke used.

JPL Technical Memorandum 33-604 vii

I. INTRODUCTION

This memorandum is a supplement to Technical Report 32-1353 (Ref. 1]

and is intended to be used in conjunction with it. The work presented in that

report is limited to steady-state thrust and flow-rate determinations vs.

varying design parameters for the Mariner type ball valve/nozzle configura-

tion, in which a subsonic orifice is in series with a sonic nozzle throat

separated by a chamber volume of approximately 0.2 cm . Design variables4 5 2investigated include inlet pressures of 6. 9 x 10 to 2. 1 x 10 N/m (10 to

-4 2 -630 psi), ambient pressure of 1 x 10 N/m (1 x 10 torr) , inlet tem-

peratures of -100 to 150°C, valve orifice areas of 0.32 to 2.6 mm-4 -4 2(5 x 10 to 40 x 10 in. ), nozzle throat diameters of 0. 13 to 1.3 mm- 3 - 3

(5 x 10 to 50 x 10 in. ), nozzle geometric area ratios of 25 to 275, and

nozzle cone half-angles of 15 to 40 deg. The thrust levels considered are in

the millinewton range, and the propellant is cold nitrogen gas. The equa-

tions used to determine nozzle losses are based on flat-plate analogies.

The work described here extends the analysis and computer program

presented in Ref. 1 (using the same ranges of parameters) to include an

investigation of the transient thrust and flow-rate effects for both the

Mariner Mars 1964 and 1971 cases. Of particular concern was the total

quantity of gas consumed in the firing of each axis of the MM'71 reaction

control assembly. The results -were used in the Mariner Mars 1971 program

to aid in the flight analysis of total gas consumption, and tended to correlate

with in-flight data. The resulting Univac 1108 program can easily be

modified to investigate other valve geometries and conditions.

*The dimensions in the equations are in English units to correspond to thecomputer program on which they are based.

JPL Technical Memorandum 33-604

II. FLOW ANALYSIS

The model used to represent the MM '71 RCA jet valve is shown in

Fig. 1, where the subscripts 0, c, and N refer to conditions at the jet valve

orifice, in the plenum chamber between the jet valve orifice and nozzle,

and in the nozzle throat, respectively.

For this model, the -weight of gas in the thrust chamber W at any

time t is assumed to be given by the perfect gas law,

Wc = PcVc =

•where p is the gas density, V is the chamber volume, R is the gas constant,

T is the gas temperature, and P is the chamber pressure. For an adiabatic

process, the change in weight is proportional to the change in pressure, or

9W V 8P_ c ___ c _ c ,_.

at ~ RT at ( '

For the case to be considered in this report, at t = 0 (i. e. , imme-

diately prior to the initiation of valve opening), P_ equals the supply pres-5 2sure of 1. 0 x 10 N/m (15. 0 psia), and the chamber pressure P and

ambient pressure P equal zero (i. e. , vacuum condition). Between the timecl

the valve starts to open and the time that the chamber pressure reaches a

steady-state level (see Fig. 2), there is a difference in flow rates between

the solenoid valve orifice W_ and the nozzle W,,. This flow-rate difference

causes an accumulation of gas in the chamber, thereby building up the

chamber pressure. The differential equation of the rate of gas accumula-

tion is

dW— - w - W (3)

dt 0 N ( '


Because the local ambient is vacuum, the flow rate through the nozzle is

always sonic and is given by

J_2

N 'DN N c _ RT \y + 1

Y - I(4)

n T is the nozzle discharge coefficient, and A~, is the nozzlewhere

cross-sectional area.

The flow rate through the valve orifice W~ is sonic initially, since

P /P0 < 0. 528. During this period (0 < P /P_ < 0. 528, 0 < t < t , from

Fig. 2), the sonic orifice flow rate is given by

W, CDvVt)P0 . RT \Y + 1

(+1

(5)

where A n ( t ) is the valve orifice area as a function of time, and £-„.., is the

valve discharge coefficient. During the subsequent period, when the pres-

sure ratio P /P« is greater than 0.528 (t . <t <t 7), the flow rate throughc \j r i r £the orifice is subsonic and is given by the following equation:

RT Y - 11 -

1X 2

(6!

where a'1' is the characteristic sonic velocity (equal to /g_YRT) . At a

time t = t ?, the rate of pressure buildup in the chamber becomes zero

(i. e. , chamber pressure is constant), and the flow through the orifice equals

the flow out of the nozzle until such time t,, as the valve starts to close.

This is the steady-state thrust case and is described in detail, along with

performance losses, in Ref. 1, where

dPW = W

N 0' = 0


From the time ( t 2 ) t h e valve starts to close until the time ( to)when it is

fully closed, the flow through the valve orifice is subsonic and is given by

Eq. (6) . For t >^ t.,, the valve is fully closed (W_ = 0), and the gas accumu-

lated in the chamber is discharged by an isentropic process through the

nozzle (W = ~^n^ The density ratio for isentropic expansion is

P3(7)

where the subscript 3 refers to conditions at t = t, and p is the gas density.

Using Eq. (1) for the initial weight of gas trapped in the chamber, Eq. (7)

becomes

(8)wU N

V P. C C3" RT 1

C3Mpj

Differentiating P with respect to time, and substituting Eq. (4) and theC

equation

TC ' " ' (9)T

C3

into the results and then integrating from t_ to any time t > t_ gives the

following equation for decay pressure as a function of time:

Jl_(1 - Y) A (t - t )| 1-Y

P (t) = P |1 -^ ^-1 (10)c c3

•where A? is defined in Table 1.


Equations (5) and (6) require that the valve area as a function of time,

A (t), be known. Appendix A of Ref. 1 details the derivation of the steady-

state (valve full open) valve orifice effective area (A_ ). This value as0- s s

a function of valve ball travel T and for a ball radius of 0. 24 cm (0. 094D

in. ) and a seat radius of 0. 17 cm (0. 066 in. ) (MM'71 data) is (Eq. A-11

of Ref. 1) .

( 0 . 2 0 7 3 ) ( T B ) ( 0 . 134

° [o. 008836 + T f i(0. 134 1/2

Since it can be demonstrated (Ref. 2) that the particular solenoid valve will

open (t ) and close (t., - t?) in both cases in less than 1 ms, and since the

total on time t is 20 ms or greater, it is a reasonable approximation thatL*

the ball opening and closing is a linear function of time. Figures 3a-c

demonstrate the typical electrical and pneumatic properties of the valve

under study as afunction of time. Figure 3d is, therefore, the mathematical

representation of the valve orifice area as a function of time as developed

from Fig. 3c. With reference to Fig. 3d, the following equations for

A (t) can be developed:

(A ) ( t )A0 ( t ) = ~liT) 0 < t < t x ( l l a )

AQ(t) = AQ tj < t < t2 ( l i b )

(A )(t - t)A0< t } = (t" - t,) t 2 < t < t 3 ( l i e )

AQ( t ) = 0 t > t 3 (Hd)

For this study, the values of t , t?, t., which represent the MM1 71 flight

data are taken from Ref. 2 and tabulated in Table 2. In this table, the

appropriate values for the MM'64 valves are also tabulated such that the

computer program results for the two flight programs can be compared.


With the value for A«( t ) thus determined, the chamber pressure P (t)

and the flow rates W (t), W _ ( t ) , and W (t) c,an be calculated using the appro-

priate equations previously defined. With the flow rates known, the accumu-

lated mass (rnn, mTvr> or rn ) is determined by solving the integral

with the appropriate flow rate equation over the appropriate time interval.

The total effective impulse I is given by the integral

1 =

t=co

(13;

where, from Ref. 1,

4-net^ipU- 1 U + 1 /

and thus,

t=00

I = K I Pc(t) dt

where

K = A tCDN(l- - losses)V -

111

The thrust losses are taken into account in Eq. (14). These losses, derived

and explained in Ref. 1, are assumed here to be a constant as a function of


time. It is also assumed that both the inlet pressure P. and the inlet

temperature T stay constant as a function of time. The actual specific

impulse I for nitrogen at ambient temperature T is

Reference 3 gives an estimated temperature profile for the entire

MM1 71 mission, including Mars occultation. If the specific impulse at any

other temperature T is desired, the following equation can be used:

However, it should be remembered that the total impulse I does not change,

since I oc V T and m oc 1 /^~T (see Eq. 15).S jp U

For the purposes of this report, an "effective" valve on time will be

defined as

e steady- state thrust

Furthermore, an equivalent "tailoff" on time, t _, will be defined as

t = At - (actual valve on time)u \J C

(17)

The use of the two time values, A, and t _, in the sizing of a gas system

for attitude control system application is explained in Ref. 2.

III. DIGITAL COMPUTER SOLUTIONS

With all the relevant equations available, a number of methods may

be used to obtain the sought after solutions. Reference 4, from which much


of the above discussion is abstracted, details a solution assuming a constant

flow density. Reference 5 describes a solution that can readily be imple-

mented on an analog computer. The solution method used in this study

involves numerical differentiation and integration programmed for a Univac

1108 computer using in part the existing program for the steady-state analy-

sis discussed in Ref. 1. The computer flowchart for the steady-state portion

of this analysis is given in Ref. 1, along with a list of nomenclature. For

the transient analysis, which is the principal concern here, the equations

previously derived must be written in the appropriate computer format for

numerical differentiation and integration. This has been done for all the

equations and is summarized in Table 1. The computer flow diagram for

the transient analysis is given in Fig. 4. The transient analysis is added

onto the end of the steady-state analysis program and is called up at state-

ment number 600 in the main program, as can be seen by the list-print

(Fig. 5). The input to the entire program is via a single read card (the

variable NZ controls the number of possible read cards) which uses a

7F10. 5 format to read in the seven variables on a single horizontal line in

Table 2. All other data, including those in Table 3, are fixed and already

in the program for this study.

In addition to the steady-state printout shown in Fig. 6, the program

is also set up to print out in tabular form, in 0. 1-ms intervals, the values

of the following variables: t, AQ(t) , Mc(t), MQ(t) , MN> Pc(t), AP/AT, I(t),

W (t), W _ ( t ) , and W (t). The program also plots out the last nine of these

variables as a function of time (see Figs. 7-10).

IV. CONCLUSIONS

Figures 7-10 show the plots for the four cases (defined in Table 2)

studied for this report. Table 4 summarizes these plots. From the table,

a number of conclusions can be drawn.

(1) On the MM' 64 pitch and yaw valves, the area ratio (ratio of

valve seat area to nozzle throat area) was 24. 5:1. As a result,

the transient flow rate for a short period of time is greater than

15 times the steady-state flow, with a 56% increase in impluse

per pulse for a nominal 20-ms valve on time.


The equivalent area ratios for the MM'71 pitch/yaw and roll

valves are 6. 24 and 2.38, respectively. With these much lower

ratios, the resulting increase in impulse per pulse is only

4 and 3%, respectively, for a nominal 79.5- and 27.3-ms value

on time. Note that the 4% figure would have increased only

slightly had the nominal on time been closer to 20 ms.

From these test points, it is concluded that for area ratios of

less than 10:1, the impulse per pulse (and gas consumed per

pulse) calculated by the much simpler steady-state approach

would be in error on the low side by less than 10%.

(2) As expected, the gas vacuum specific impulse is the same

(within 4%) when calculated by either the transient or steady-

state approach.

(3) All computer runs were made assuming a local ambient tem-

perature of 25°C. No attempt was made to determine an in-flight

ambient or gas temperature, although this could be done.

(4) The shortest electrical valve on time assumed was 20 ms.

Since pressure and flow rate build up to their steady-state value

in a short period of time (usually less than 2. 0 ms), steady-state

approximations for value times of somewhat less than 20 ms

should be valid.

(5) For this study, it was assumed that the discharge coefficients

(losses) stay constant over the relatively short transient flow

periods.


REFERENCES

1. Ferrera, J. D. , and McKown, P. M. , A Method for Calculating Steady-State Thrust and Flow-Rate Levels for Mariner IV Type Attitude ControlNitrogen Gas Jets. Technical Report 32-1353, Jet Propulsion Laboratory,Pasadena, Calif., Dec. 1, 1968.

2. Edmunds, R. S. , Investigation of the Mariner 9 Cold Gas System andAssociated Electronics (Attachment 2 to EM 344-352), EM 344-353,Jet Propulsion Laboratory, Pasadena, Calif. , July 26, 1971 (JPLinternal document).

3. Nordwall, H. , Attitude Control Jet and Acquisition Sun Sensor Temper-ature, Solar Panel Thermal Shock Test, Interoffice Memorandum,Jet Propulsion Laboratory, Pasadena, Calif. , June 24, 1969 (JPLinternal document).

4. Greer, H. , Analytical Investigation of Nitrogen Jet Reaction ControlSystems. TDR-469(5560-30)-1, Aerospace Corporation, El Segundo,Calif. , Nov. 30, 1964.

5. Bouvier, H. K. , MC-3 Altitude Control Gas Valve Performance, IOM344-390, Jet Propulsion Laboratory, Pasadena, Calif. , Feb. 2, 1965(JPL internal document).

10 JPL Technical Memorandum 33-604

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JPL Technical Memorandum 33-604 11

Table 2. Jet valve characteristics (computer input cards)

Mission

MM' 71

MM1 71

MM '64

MM '64

Axis

Pitch/yaw

Roll

Pitch/yaw

Roll

PO,N/m 2 (psi)

1.0 X 105

(15)

1.0 X 105

(15)

1. 0 X 105

(15)

1.0 X 105

(15)

°C

25

25

25

25

mm (in. )

0.513(0. 0202)

0.831(0. 0327)

0. 290(0.0114)

0.374(0. 0147)

T

mm (in. )

0. 173(0. 0068)

0. 173(0. 0068)

0.216(0. 0085)

0. 216(0. 0085)

V sb

0. 001

0. 001

0. 001

0. 001

bV s

0.0795

0.0273

0.020C

0.020C

bto , S

0. 0805

0. 0283

0. 021C

0.021C

Nozzle throat diameter.

See Fig. 3 for definition.

Estimate.


Table 3. MM1 71 jet valve parameters (fixed)

Parameter Value

Nozzle discharge coefficient C,_

Valve discharge coefficient C

Ambient temperature T_, °C

Valve ball diameter, cm (in. )

Valve seat diameter, cm (in. )

Nozzle geometric area ratio

Nozzle exit geometry half-angle, deg

Ratio of specific heats (nitrogen)

Nitrogen gas constant, N-m/kg K(ft- lbf/ lbm °R)

Ambient pres sure, N/m (psi)

Valve inlet pressure P~, N/m (psi)

Valve chamber volume V_,, cm (in. )^

Time differential, s (BELT)

1. 0

0. 63

25

0.478 (0. 188)

0. 335 (0. 132)

250:1

25

1. 4

2. 967 X 102 (55. 16)

0

1. 0 X 105 (15. 0)

7. 48 X 102 (0. 0116)

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FLOW .

VALVE NOZZLE

,/WN

1AN

VALVE CH AMBER -

Fig. 1. MM'7l jet valve model

c CHAMBER PRESSURE

Fig. 2. Typical valve chamber pressureprofile

VOLTAGETO VALVE, V

3224

1680

_ W

—-_

10 10

I I I30 / 50

(b)

TIME, s

Fig. 3. Typical valve electrical andpneumatic characteristics:(a) voltage to valve, (b) valvecoil current, (c) valvechamber pressure, (d) valveorifice area


YES

j 530

NO

P(N)*WC(N)WO(N)WN(N)DPDT(h

(3a)= (= (

^P(

Sa)5a)4)(2°)

N-

1

) > 0.52

r<^NO/\

WC(N) = (6b)WO(N) = (5b)WN(N) = (4)

,>*j

J

P(N) - (3b)

520

DPDT(N) =(2b)

*

*

s <

P(N) > PCSS

K =K +

).ooo5y^

. Y E

NC

5.

1

_S ^

P(N) =DPDT(SWC(N)WO(N)WN(N)

525

(3c)) = (2c)= (6c)

= (4)

P(N) =DPDT(^WC(N)WO(N)WN(N)

)/ r -. , \ YES

(30 pccc = F

= (4)̂ M = M

_

* NO.

I ,AT = T2 - T(N)

MC(N) - (9e)MO(N) - (8e)

t 550

MC(N) = (9f)MO(N) = (8f)MN(N) = (7f)l(N) = (10f)PCC(N) = (11 f)

MN(N) = (7e)PCC(N) = ( l l e )I(N) = (lOe)T(N) = T2

PRINT

N =N +1

NOTE: SEE TABLE 1 FOR EQUATIONSDENOTED BY ROW NUMBERS ANDCOLUMN LETTERS IN PARENTHESES

Fig. 4. Computer program flow chart


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.ISA PJ=_i,_l1_ll17 . 5 0 = 3 9 6 . 0 6 7 7 3

ASA B_=EA.US.2.19* P»-0.2 0 . C M N I T : 6 . C21. 0 3 = 0 . 1 3 3

_22A D_SJLC..L3i2 3 . » R ( 3 £ 0 = 2 5 C . a

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-tfl*. 2l_»C:.»CJL4 1 . 2 2 PRINT 2 3 . P G

12 • .... 2.3 F.CRjit.llJLd-Liixlldlblut-LEfitiSilBi-JliF.Z .̂Jj-lllii.alS/JN.J J.LM3. 2U P9 INT 2 5 . C C V J _ ' 1<< i4» 25 F CKK IF <5X 3 7H«"«LVt "cfi'JF^icY""i51 s'cViR 5E~ C C E F F ICIENl = • F 7 . <* )15. ?6 P R I N T 2 7.T 3us« 2? F C R K O T I S X ms'iLU'TRVi/ET ='F~V.'sViViiViYN> )i<7. 23 P9 INT 2 9 t « R T 3 £ QU S . 2 5 F C R M » T ( 5 X Z 5 H N C Z ? L E 3 t O « E T h I C ; 4f iE» R A T I O = . F 6 . 3 )1(3. 30 P R I N T 3 1 , < S I 3 Q E 35(1. 31 F C R M S T 1 5 X I S H N O Z Z L E H » L F - » N G L t = iF 5 . 1 . I X 5H ( CE 3 ) )5 1 * 3 2 PRINT 3 3 . 1 052. 33 F C R K 1 T I 5X t S H I N L E T 3CS It MF ER & f I! 5E = • F c . I . 1 X 7 •< I DE5 C ) )5 3 « 3 M P R I N T 3 551 . 35 FORMHiX i ' 3 H N I T R O S E N P S O P L L L ' N T I5 5 « 3 6 PRINT 3 7 . A O56. 37 F O R K A U 5 X H - H V A L V E O R I F I C E E F F E C T I V E « R t * : iF 7 . : • 1 » 5 ̂ { I N2 I >5 7 « 3 3 P 3 I N T 3 3 . A O X _5E« 39 F C R K A T t 5X 1?-U*L VE S E « T »RE« = . F 7 . 5 . IX 5 - ( I N 2 > / / I59* in P R I N T '•! I ; [6ti* «1 F e R K « I I 5 ~ X ~ i t ^ N E T T -RU 5 T . I 1 X6 ̂ OZ ZL E . 7 X 5 - V ft LV E . 3 X 6 H 1 iVl} S T. I C X6 H kE IS -61* I T . 3 X 3 - K X I.T.__M*>_HJE 2 « U P R I N T I I53* 11 F O R M 4 T ( 7 X . = HJ.L3.5J.1 J.ftAS .11 HRQ.» T_i.§_X.| H_P9JuS_S-JJltj. 7 _X_S HL QS S E 3 • 3X6 1 * 1 9 X E H M P 3 E K )55. 15 PRINT '476t» 1? F C P M «I t Z S X ? - I C I * M E T E R i 7XMCf i OP« 7X I C-I ( P E 5 C E \ T ) . 7X 3 H (LB S/SE C I >67. 13 PRINT 13 .. '.68« 15 F O R M A T ( 2 7 X 1 H ( I-N) . £ X 9 - f L B S / I N 2 1 />63» RT = 3I/2,.7P* 5 I « T i P I ' R I . S T71- 52 AirAST3£fl.«-iI72. 53 DE :Sl iRT ( > i . » 4 E / P I >

Fig. 5. Computer list printout of steady-state and transient thrustprediction program


7 3 *7 M *7 5 *76*77 .7e*7 9 *S C *S I *9 2 *3 3 *S M *3 5 *B 6 »9 7 *5E *39.

. SC*91 *2 2 *3 3 *91*9 5 *96*3 7 *3 6 *3 3 -

i re*1C I »1 C 2 *103*iru.105*I C E *1 C 7 *i t s *I C 3 «1 1 C > «1 1 1 *1 1 2 *113*I 11.II 5*l i e *11 7.1 IS*119*I 2G*1 2 1 *1 22*1 2 3 *1 2 « *1 25 •1 26*1 2 7 *.LLS*129*

5M RE:0£/2 .5 5 S I 3 K A : ( S I 2 D E 3 / 3 6 C . I * J . * P I56 SL = I 31-« I.I. *.COi. J.SUiM.4 J7-S-La57 F 3 A r * : ( S A H ^ A * 1 . ) / ( 3 A N M A - I . )

5°. PC; PC i MI. i_ :5 5 C F C : l t 3 A M C A - l . > / 2 . > » l t « T * C O N / < A O * C D « ) > * * 2 . > « ( ( 2 . / ( 2 A M K A » l . ) ) * * F 3 A K

1 I _ _ _ .f C I K I : 1

1 I I - C F CS 3 O F O C ; ( ( | 2 . - ( ? . « 5 A q > 1 A ) l / 5 A , < H A I « ( P O « » ( t ( 2 . » 3 A M H A ) - 2 . ) / 3 A H . H A l > . ( J C « « (

2 A) I .( = C • • U_U-_l_2_,E E P C N = P C - ( F F C / C F P C I57 . IF( T £ S T ,JS.£-t-J-l,.3C-_IC_-J?.lES PRIM E-B. FPC .O rPC .PC!\ • IMS3 F Q 3 M A T 1 2X5 HFPC - , £ 1 S. 3. 5 Xe HOF PC r . El S . 3 . 5X 5 HPCN :. E 1 5 . 3 . Sx I 0-I I T£ 31

1PC ) = .14 )

T i I F ( A S S ( P C N - P C I - E F S 1 1 7 5 . 7 5 . 7 373 P C ^ P C M •_ t

7 < t I r e i > - a x l - I N l ) 7 5 . 7 5 r E l75 P * I N T 75 ,.?_£.76 F C R M A T t Z X i s u l T E R A T ION L I M I T £ X .CT t CED . 5 X 54 FC I CI V I : . £ 1 5 . 6 )77 30 TO 1.7.5 -7 8 P : - P C f.73 0£LP:?f l -PC -5C T R ; ( 3 . . T O 1 /5 . » H ? 1 .E2 ^_si WOCOT- i "o *cav " *p "o» (Tp~c"/"p"b~i"»* f F ."V S~A M~H Vi i « S S R T " ( ( 2 , * 3 o / ( s *TR)T*T34M,MA/ "

33 W T C O T = C C N * P C * A T « S 3 R T l ( 3A~MMA* GO/ ( K * T R ) ) ' « l ( 2 . / ( 3 * N H A » i . l ) • « ( 13AHM»V"11.) / ( 3 A M H O - 1 . 1 1 ) 1

3 5 A R T £ S O : . 5 * A R T 3 E O» E C N : C M M T _9 7 I N 3 : l= £ I N 2 : C _ :

33 Cl = ( j * M M A * I . )M 2.* ( 3A M M A - 1 .)>9 tl C 2 - (3 A MM A -I. 1 /2 . ; '

93 O F C N : C 3 * (2 . * C 2 * C N * CN* (- C II « ( ( 1 . • I C 2* CN* CM ) «* I - C 1- 1 . ) i« 1C 1 . » r C 2 VCN"1 * C N ) ) «*.l..7C_mj

35 C N N ^ C N - ( F C ' 4 / C F C N )36 IK2HN2* !37 I F | T £ S T ".",•<£. II 30 Tu ICO58 PRIM i S ^ F t N ^ C _ F C N I _ C N ^39 FO*N*'f('YxV^FCN" :7n 5Vr."5XS7oFCN iVtVs . 3 . 5~X 5~Vc NNi '=i Erl" 5. 9 I

ICC I F I A B S (CKN-CN; > - E F S2JI CE • 105_._1CJ1C1 CN=CNN ~

1U3 PRINT 1 0 4 . C N1 0 1 .P.CR_K A It 2.X.JL4_H T.ER.A.I-lCA.J.IitIJ..t.X.C.E.£iEJ_..5.X_S_sxt,.Uiy).. : .

30 TO 175

1C? UP : 12.; 7 C E - D 3 > « I T S » » l 3 . / 2 . » / I T i ; » 1 5 S . o l1CB RENOJ -( CM/ JO ) 'SORI (G SMMA/ t ( 3 A MM A- I . ) *C V *T f! ) I « I T

_1£.»W5A.-. J.̂ lAJ.»-LitJJly.T,B.trj.«JLii.£.l.y-lIJl«-L3in RENO = i2 . * R = ; N O U * S L « P C

«« ( ( -2 . ) /(

1 3 1 *

]J2_«-1 3 3 *L3_<i*._1 3 5 *f26_*1 3 7 *US*139*J.1.C*-1 X 1 *J_4.i_* .1 4 3 *1 4_M*.

12 IF( CN-5.5) I 13i It 3i 1 IS_L3.

1- . 3 0 3 7 5 * C N * » 2 » . 5 9 2 3 C* CN* 2 . 2 3 3 2 4 )15 SC TO -1Z3IS IF< C N - 7 . 5 1 1 1 7 . 1 1 7 . 1 1 51 ? DELSTq^LkllL.Jji^.^^A.jil13 30 TO 123IE TF I CN- S. D I I?C . I ~n. 1? ;20 Q E L S i a r O E L T « * C IC . -9*CN-38 .4 I2.1 ̂ .C._TC..JZ322 C E L S T R i O E L T«»M0.3«CN-<I1.<I I

1 2 J RE E.FFASt-rJliLSJ-R

Fig. 5 (contd)


115. I 2 ! < IF( R ^ - . f F n 29. I ?9i 1 25JJLL*. I?S a R I T E R i l R E - F F . R T E ' - F l / 1 K T . S T 11 < < 7 » 126 IF (43S ( AS T E 3 C - 4R ITE3 )- EPS 31 1 33. 1 3 3. 127J-1S.»,. 1 2.1 - l_F..LKAJli.--IA.3J-l.il..iJ_:LUJ.Z.L1M9. 123 IN3=IN3* I1_5C_«_ l2.i.»BJ£Bi:_L*AI£J3fl.»^AU.EJLiy.2J.^151* 1 3 C 3 C T O 3 3I =?. 1*1 PPTM n ? . t R T T F p

153. 132 F 0 3 M 4 T I 2 X 2 ' - H I T £ R 4 T I0.\ L IMIT E X C E E C t O i 5 X 1 H » S T £ 3 0 C O I V I = • £ ! = . 3)J_S!L». £C .10—U.5155. 1 3 3 S I 3 £ F F = 4 T 4 M ( R I E F . - / S L IJ.Sfc.%-- 12 !i157. 1351 5 9 « 13c C E ^ S S K T ( j C » ' S 4 " ( K 4 V K V l t " ) " "153. 1 3 7 V i = C r « C N1 cC* 1 3 S V E F H I C / 1 2 .161. 1 3 3 : F P : p ; « 4 R I T E a . 3 0 . J r / t M O S O T « ) ) £ l162. lit* FP : ( l.-Ys'.Tl . .COS ( S 13 EFF I I I / I I . «CFp )I i3» I tl F-C£L = 2. » (S i - ( . 3 | k ! A ^ - < i . ' - - l A * _ O t X ! A ^ - L l - l ' - E r - Q £ ) _ . . . . . .I£i4. 112 F M 4 X :P C» 4 T * S Q « f I I .. i4 HM4~. 34 MM4 « ( ( 2 . / ( 34 KM4 . 1 . | ) * »F5 4 H I / ( E»MI«» - U

165. 1)16b> ni C F : S G P I II (2. « 3 f t K K <• 3 4 v ! K 4 )/ C-4MM4- 1 . ) 1 .( ( 2 ./ (3 »MM4 .1 . ) ) . .F34M )«( 1167. 1- { I P i /PC l » » t ( 3 4 M H a - l . l / 3 4 M M 4 ) l ) > * ( ( P £ - P 4 ) * 4 R I I £ R / P C Ilee. I IE FTHEC 'R :CF"» "P 'C»«T169. II 7 FNr ( FM4 X -F MECJRJ./fJlAX. _1 7 0 » 1"E F L T O I : 1.-I I 1 .-FP) . ( 1 ,-FCES.I « 11 .-FM )171. 1«9 FLTOTPrFLTO_T« .LgC. , _1 7 2 * 1 5 C F N E I : F M * X . ( 1 , - F L T C I )173 . 151 PSINI 1 5 2 t F N E T . D T i 3 E L P i F L T Q I P i i n Q G O T . C N I17M. 15i F OR M 4 T ( Z X . C 1 5 . B . 7 X . F S . 5 t 5 X t F 7 . « . S X . F 6 . Z i 6 X . E TS ". S . E"X-I F E . 3 •175. PRINT 1531 7E. 153 F O R M 4 ! t InM177. IF( T EST .NE_.J_)..30_.T_0___o_CC_1 7 B « 151 P R I N T 15 5 . w"fc"o"f Vl N~2179. 155 F O R H 4 T ( 2X7 H W T O O T - . El 5. 3 . 5 X 1C -IIT ES C M£l I.miI S C * 1 5 E P R I N T 1 5 7 . f t R T E R O . 4 R I I E R .IN3191. 157 F Q 3 M 4 T I 2 X I 3.-«4i.̂ AIJ-ll!liIJ..j:tA.l5-«3.t5AlJli*i/.*J-ll.t£H ) -' £ l..;.,-3 j.5tl£LdJLti1 6 2 « 11 EL) :.I1)1 3 3 « 15* PRINT I.BO.._?..!Lt?_i_f_T!i££_!.X.EF_ _ISU. IEC F C R K 4 T . ( 2 X " n P C - i i. I E . E • 5 X H -P i = • E 1 5 . E t S X i| H I £ : •£ I 5 . E • 5 X 4-iC E :.E15.13.5» . - - . 1 .5X 5 H V £ F : . EIS. 911SE. I E 2 P R I N T t £ 3 . T R 4 T . U C . 3 E N O U . R E N O137.. . 163 FORM4Tt2X&.HlSAI--;j_£.liJ^3.iJJtJLiWiJjJJ--;jLEJ-5-».3j-S«-l.C--ia£aUil.'lua--;j-£i5^SiJJI B S * l 6 - i R £ N C : . E I 5 . e >139. 165 PSINI 1 66j.iD£LJ-4jJ2£i_SJLBj^££££I S O * 16c F C R K 4 T C 2 X ? H C E L T 4 : .E 15 .» . ?X 1 3-lD EL T 4 (S T «R I : • E 1 5 .3 . '. X 7 - REE FF :,E1191. 1 5 . 3 )I 5 2 « l c£ P P I N T 169 > r T ^ O R . F » 4 »193* 163 F O S M 4 T J1 2 M « I 7 f . P R I N T 17 1 ,FP ,FOEL .FN .r LTO I135. 1 71 F O S M 4 T 11 5E» IE 15 .5)197. 5PP Q l M g N ^ TI S E * 1 ) > . N ( 9 5 C ) . P C C l S l L M . T l S E U I i X | 5 5 C ) . r ( b 5 C ) . E f P ( 6 5 C )199. »:52 C O « P C S S = F C / P C2C1. 0£LT:O.OOai2 T 2 * T t l ) : C .2G 3 . P( 1 ) =£_,2C«. C F D T ( i ) : C .2C5« K:l2C6 . N:22H7. Z C ( 1 ) : C .2C.8« Z C ( l ) = C .2C9« ZN(1)=Q. .2 IP. E f P ( I ) :tl.211. V C ^ O . C I J5J.35.2 1 2 « , & S T 4 R : S Q R T < 3 C « ^ f l M » ' 4 . h » T R )213. 41;C3V.4SJ_t«.«iSDjiJjL2L»T/J21«4 . 4 2 : C C N « A S T 4 R . » T / ( V C « C 3 )21 5. »3:COV«4ST~4¥/Vv:>:~3l216« « » : V C / ( R » IR I

Fig. 5 (contd)


2 1 7 * A5 = SQ«iT (30 * 3 A M M A / ( S * T H ) I / : 32 1 J » _A_E : ( 1 . - F L I O T > « A T » S A M r ' A / I C i « S C R T I C 2 > >2 1 3 * 5DC" T I N ) r K . M - l > » C E L T2 2 C * _ _ . . . I F ( I (is I ._3_E_._T_L>__ EO _10 5C5_2 2 1 * AOT = AO* HN 177 12 2 2 « . 30 TG 5l_5 __2 2 3 * 505 I F l I ( N I . 3 1 . 1 2 1 30 1C 51C2 2 " « « A Q T i t C2 2 5 * 30 TO "Yl 52.26* 5 1C .15. IJ ( N > ._S_E.t T_2J__SO...T.Q__5_3_52 2 7 * A O T = A C * ( I . - I I ( N ) - T 2 I / ( T 3 - 1 2 ) )2 2 9 * . . . . 3 . 0 T O 5 3 02 2 3 * 5 1 5 I F ( P I N - I I . G E . P C S S ) 3 0 T O 5 2 52 3 C * _ IF ( F ( K - I ) . 5 E . C . 5 2 8 I SO TO 52 P2 3 1 * O P 3 M N I : « 3 « » O T - 4 2 . P ( N - l I2.3.2*.... . P.iN.i;-c-(KT.LL».£p_a.Li_8a*.iiE.Li2 3 3 « y C ( N ) = 4 i « * C P O T ( N I *FO231« W C ( M : 4.5 • CSV.t A.QJA F.C235* U M N l : 4 5 « C O N « 4 T « P ( N ) » P O

.2_3.e.« S_0__LC ._5.5_G2 3 7 » 5 2 0 D P D T ( N ) = 6 1 « 4 0 T • ( P ( N - 1 ) • • ( 1 . / 3 » M M « ) I . S 3 R I 1 1 . - P ( N - l ) • • ( ( 3 » M M « - 1 . ) / 3 «2.35A233*

.?J»D.«...2 i « l » I F ( P J N ) . S L . P C 5 S I 3 0 ! 0 5 2 5.2_12« WC 1M = * 1 » D P O T I I < ) « F C2 ^ 3 * W O ( N ) = C O V * 4 0 T * P O * ( P ( S I * « ( l . / 3 * M H * ) > * S 3 l ? I ( 2 . * 5 0 * 5 t M M A * ( l . - P ( N ) * * C ( 52.«t •»_•_. L&r.M»-_l_..»_/i4mi«-LJ-aA«_L8_'_2 M 5 > W M N I = 4 5 » C C N « 4 T « P ( N I « P O

.2J46... 5.C _IC^;.5_C .2 " ) 7 « 5 2 5 y C l N C C .

_<_!i«_ P. iM ^ P. C SI2 M 9 «2.5CL«...2 5 I • W O ( N ) 1 U N ( N )2 .52V 1^ lK.St...5..l_5.C..lCL.5_tl2 5 3 « K : K « 5z s u « _s_c_i_t__=5j:2 5 5 « 5 2 7 D E L T 1 : T 2 - I ( N l2.5E_« -ZCtH)_:2rtJs.-JLl2 5 7 « Z O I N ) = Z O ( N - 1 I » W O ( M » O c L T 12.5 9 « . . . _ . ZN(M:Z\(ArJLl_«_«K.(.iLl»^.EO_IJ2 5 3 « £ M P ( N I = £ M P ( N - l ) * A c > P ( N I * P O * 0 £ I . T l2 E C » P C C ( N > : P ( M « P C2 6 1 » T ( M r T 22 6 2 * 3 C T C S.5.1

26 3 • 53C OP ;3 II Nil =41 • 40 T » ( P ( N - I )«« II . / 3 A MM A) I .S33t (1 . -PI N - l ) ••( (3 A . M M 4-1. I / GA2_f *.» 1 HP A_n.- »i*AlfirJLl2 6 5 * P I N l : P ( N _ | ) , 3 p n j ( f 4 j , 3 £ L I2_66_« U C ( N I : > M « C P D T ( N l » F O2 6 7 * H 3 ( N ) = C O V * » O r * P O « ( P ( . \ l » * ( l . / 5 « . M > i l > l * S 3 , ? J ( 2 . * 3 C * 3 A M M A * ( l . - P < N I * * ( « 32.6 8 •. 1 A C M A - I . l../iAM.M_A.».J./iJl».Ta».15.A!UlA.-J^IJ-L -— --26 9 * UN I N ) = l 5 * C ON.» A T * P I N ) • PC27l>.. .3.0 T C . . 5 5 D . _

' 2 7 1 * 535 IF( H,-.F. . 1C I 3i'. TO 5J4P2 7 2 * P C C C = P I M - " i ' ) " ""2 7 3 * » i : M « i n2 7 < » * E " * C P (N ) r P C C C * ( I .-~('U-~3A> y'iV* 4~2 • I T I~N l~: VH'l / <"."»"•'<• It . »E » «!H A / ( I . - 5 A H M AT) )2 7 5 * C P C T ( . V | : ( P ( N I - P ( N - 1 ) W J £ L T2 76* AC T i c . "2 7 7 * r i C ( N I = C .2 7 3 * W M M r A 5 » ' C S " N « " A T » P I N T * P C2 7 3 * W C ( N l : - W N ( N l28ii* iFCPtNi .LE. 'bYcTdT'sb" TO lYn2 3 1 * 5 s c Z C I N I - z c ( N - i I * W C I M I . » O ; L T2 9 2 * Z C I N I : 2 0 ( K - 1 I » W C ( \ I » : £ L T233* Z N ( N l : Z N ( " w - l l _ » _ ^ N t M *0£L T2 9 < » * E K P ( M : E M K N - 1 iVilip"^ r*P"c"«"CcL i2 3 5 * P C C I N » = P(N I«_PO _ _2 6 6 * b5l P R I M ICO C .N iT(N T'^iY TTz C VN ) Vz 0 IN r«?N"(^ i. FC C IN I 16 FC T t N I • E PP ( N I • bC (2 3 7 * I N I i W U C N I t W N ( N I2 8 6 * 1 C C C > C R M » T l Y x . m i I I E 1 1. ' .I

Fig. 5 (contd)


299. N = N + 1~2~90~«~ " 5C I C " 5 C O291* 17M L = N-12 S 2 « DIP ENSIGN II ILL! I » > • >N »K~ETf "Tfi V N « K i t 1C > • YNt fu I 1C) tVMK2~( 1 C )•2 9 3 » l l O I » » N ' 4 K 5 l l O l t i r N 4 M 5 ( l G ) . Y . ' . i 4 M 7 < l C I ) t Y N 4 M 9 l i q i i Y N i > l 9 l l C l . ; ! O U l ( 2 l l l2 3 M « RE »L R C W 2 ( 1 )295 . DMA .11.I.L£..7.I2 9 6 « . • /297.. D.» T.»...XN_»M£_./_;2 9 B » . • /239. D A T A Y N t m /' C H 4 M 3 ~ 3ire. . •/301. D M 4 T N 4 M £ y J-fll « . L _ S .3 C 2 * . ' /30_ 3 » . „ 3 » T » ..» N.»«.«„_/! IfiJAI BASS.-£J AlitR.-Li3C1* . •/30 5 » _ C.4_T .4 TJiA.1S_/J T O T A L H 4 S S - V 4 L V E - L 33C£. " . •/307. DM4 Y N 4 M 5 _/_! fJÔX8AIc.-fH.QZ_Zl.E.r.L3/_S.E.Csee"."" . •/30 9« 0 4 I » Y N » M S . / ' _ EkOW_8AL£.T.5J*-?13i.8.-L3-^3AS-3 1C* . •/31 1 « _ CM 4 J T N 4 M 7 /' F L O w a 4 T E - V 4 L V £ - L 3 / S £ :312." . •/3 1 3 . DM 4 r>4M3 /• _ t_a! 4L. IAPyj.S_£.rJL3__Si:_C311. . •/3 1 5 * 0414 rN 4M9._./« C_H*_M3_£S__P_S_ES_SJ_aE__0£3_lyAIJ.y.£316." . •/317. OAT A ROW I / ' '_/jTe"»"" " D 4 T 4 tii'-Ji / c . /31 9. I N I E R P r l :

3 2 0 » C C S C C J M I . L3 2 1 « . X( N) = T C N ! . « . LCCC_.3 2 2 « V I K) : P C C(M323 . . 30n. C.ON'T.I.«iy.t3 2 M . C 4 L L E Z P L C f (X ft iL i U T E R P • 11 H.E t XN« CE • » N» >• 1 •'»OK 1 .R0» 2 i C J3_25_.____ DO .9C.L.H=^tl -3 2 6 « » f ^ ) : ^ ^ ( N )3JL7.*-. . - 9f!l CONTINUE _3 2 S » C1LL E i F L C T (_X_ _'_r_ •!• •IA!J1:P • T! iLt t X N 4 J^t t V Nt|»2 • ROW 1 .f if lwr iC I329. DO 802 MfiL"33U. V IM :2 : iN )331. 3C2 CONI INOc33 j« C A L L E ? P L C T ix .Y .L I INTESP t IIILE: » x s 4 f E > Y ^ ^ . l » 3 1 ROH i t R Q » 2 t C >3 3 3 « 00 303 N = l .L3 3M. Y I N | : Z C ( N _ )3 3 5 . 303 COMINJE3 3 6 . C 'LL £ Z F L C ! (X iY iL_i I_N_!J RP 1 H Ik^ • *_Na A£ • » N * f. t • SO* 1 • RC» t• C I3 3 7 . oo act NÎ .L " "3 3 B * V ( K :) : » N IN )

333. Sn^ C O N T I N U E ~"3"4C. C « L L C Z P L C T _ !.*___•_* JLl • IN 'E RP.l MJJÊ • X.N4_»<E i Y _M P S . f?OW l . R O k 5 _ i C )3t I > 00 3U5 ,M = 1 it3 < t 2 » Y ( N ) = W C ( N )313. ' J05 CONTINUE3Mt|. C 4 L L E Z P L C T (X .t »L • IN T E EP i 1 I 1 LE . X N4 f.j , Y M Kc t RQI. 1 , R Q f c ; , 0 )3 M 5 . DC 305 N:"liL3 MB. r (M i t !C(NI3« ?'» 4C£ C O N T I N U E3 t8 . C»LL E 2 F L C I (X ,< . L . IN IE SP f J I Tj.E i XN 6j<E • Y N4 c ? . ROW I . ROK 2 t 0 I3 M 9 . 00 307 N = l t L350. "^> :E.KPUJ351. 3C7 C O N T I N U E3 5 2 « C4LL E Z P L C T (X , Y_ t LiJ_N_ If_EP t.T i Tj_E.» XA^J" E L»A4f 9 • ROW 1 • RO-> 2 t C 13 5 3 * DC 903 Nrl .L3514. Y (N ) =GFO.T.(.NJ355. 303 CONTINUE '35E. C»LL EZPLCI IX tY i n I M E H P i T I I L E i X N 4 y £ t Y N a E 5 t R O K I »RQ«Z,C 1357. I 75 CONTINUE.3.5.6*. . . END

ENO OF COMP-IL 4 TIONt . N_0_ SJL»_S.NOSJ_I C.S.

Fig. 5 (contd)


INLET P R E S S U R E = I 5 . C C C ( L 3 S / I N 2 )V A L VE OR IFIC E G IS C H A it G E " CO'EFF I"C I ENl" Y"B A L L T R A V E L ; .ooeec UNINOZZLE G E O M E T R I C A R E A R A T l ' 6 " " = 2 5 U ~ . Q O C ~N O Z Z L E H A L F - A N S L E : 25.0 J DEJJJINLET GAS T E M P E R A T U R E - 2 5 . 0 (DE3 C)N I T R O G E N P R O P E L L A N T

.5300

VALVE ORIflCE EFFECTIVE A R E A - .00200 (IN2IV A L V E S E A T A R E A = .CIJ68 I I N 2 I

NET THRUST(L3S)

.76137258-02

NCZ2LETHR04T

DI'AME'T'ER"( I N )

. C 2 0 2 D

V A L V E_ PRESSURE

D ROP"ILflS/ IN2I

T H R U S TLOSS_ES___

(PER C E N T l

11 .19

W E I G H T_Fj.Q>!.RATE_._

( L B S / S E C I

, 1 0 6 5 2 0 3 5 - 0 3

E X I T W A C H

E . 3 7 B

INLET P R E S S U R E : l 5-o n o "-3S_/I_N2_I_V A L V E ^ O R I F I C E "DISCH»Ri3'E" CC"EFFI"CI"ENT~: "".6"2tr6"B»LL T R A V E L : .00690 (INI

• ' N O Z Z L E ' G E O M E T R I C A R E A R»iTc :" jsoVccfc ~ "NOZZLE eULFr'NSLE I Z S . O ( O E S IINLET 'GAS" fEHPERAt "uRE : " 25 .0 ( D E E ClNITROGEN P R O P E L L A N TVALVE:""b"R I FiCE " E F P E C l i v t "A R'EA "= . 7d tTfoY ~f IN'Z")V A L V E S E A T ARJH : . 01 353 (IN2I

NE f"" t hTRlFs f" "' ~~N 0^2 ZL E V A L V E T H R U S T H E I S HT E X I T M A C H• ( L B S 1 T H R O A T : F R E E S _ U R E _ __ _ L C S S E S _ F L Q W R A T E N_UJ1B_E.R

DIAMETER" " DROP IPER" CENT") ( L S S / S E C I.(I.N_I_ <_L3|j(.Il*.2_l

.1 961 S O M O - 0 1 . 0 3 2 7 0 I . Ml 95 3.83 ii.515. 'I2 7-£3 7 .085

(c) ' ~ ~~ " ' "'INLET P R E S S U R E - 1 = . C C L I L S S / I N 2 )V A L V E ORIFiCE 'Di'SCHA33'r "C"6~EF~Fi~ci"EN~ry ".630iSB A L L T R A V E L : . O O B 5 C (IN)NOz 'zLE"GEOMETRIC A R E A RYtTo'V 250.000N_czzL_E_ H A L F - A N G L E - 25 .o ICEGI .INLET GAS fEMPcRATuRE :" 25.0 ( O E 3 C)NITROGEN P R Q P E L L A K T

"v""A"LV"E"b"RIFi"CE""EFFECT"l"v"E""AR"E"A":" . QOTHTTi N2lV A L V E S E A T A R E A : • C 1 3 6 8 IIN2I

N E T ~f HR U'ST ~~Sf0 2 Z LE V A L V E T -iRUS 1 H E I G H T E X I T K A C H( L 3 S ) I J ? ? _ A T ^ P R E S S U R E _ LOSSES F_L_oy_RATE NUMBER_ _c.--_---„-. o---.- (-_----c-,^ t ^ -_ _ _ L _ S _ _ ^ _ _ _ : _ - .

( INI ( _ L 3 _ S / I N 2 I

. 2 3 7 6 1 7 3 9 - C 2 . C l l i » 0 _ .0 11 7 It. 13 .J<4 E 3 1 B tC_-^l_ t .565

INLET P R E S S U R E = i s . c c c ILBS/ INJ) •V A L V E ORIFICE D I S C H A R G E CO EFF 'lcTEN"f":""7S3'o6B A L L T R A V E L = . 0 0 6 5 0 ( IN)NOZZLE G E O M E T R I C A R E A RAT 10 "= 2507000NCZZLE_ H A L F - A N 3 L E = 25.0JPEJL!TNLET " G A S T E M P E R A T U R E ' : " 25 .0 ( O E G Cl "N I T R O G E N P P O P E L L A N T

' ORIFICE:" E F F E C T I V E AS ;E A V "Vdb"2 SO" ( I~N2T. . . . . — S E * T. *"?* "^PI3^?..i5.N21_

NET""THRUST " KTZZLE" "" V A L V E T H R U S T ' "ii'Eisn't" E X I T M A C H(LBSI T H R O A T PHESSUR_E _ L O S S _ E _ S _ _ F L O W R A T E NUMBER. _ _

D I A M E T E R bfiO"p" (PE"lT"CENf) ' it BS / 'SEC)

. X C 1 S 2 7 E 3 - 0 2 . C l < 4 ? 0 .010E 1 2 . 6 5 .5 7 32 3 6 71-C1 E . 7 1 0

Fig. 6. Steady-state printout: (a) MM'71 pitch/yaw, (b) MM«71 roll,(c) MM«64 pitch/yaw, (d) MM»64 roll


(a)

CHA

IR

PR

IPS

A

60. 80.

TIME,MILLISECONDS

Fig. 7. MM'71 pitch/yaw valve parameters as a function of time:(a) chamber pressure, (b) total mass, nozzle, (c) totalmass, chamber, (d) total mass, valve, (e) nozzle flowrate, (f) chamber flow rate, (g) valve flow rate, (h) totalimpulse, (i) chamber pressure derivative


».-06(b)

AL

MA

N0

k

40.

TIME. MILLISECONDS

Fig. 7 (contd)


(c)

HA

A 2.0n

!J.5-O7

*o. 4O.

TIHEiMILLISiCQNDS

Fig. 7 (contd)


».-06

AL

MA

A

V

60.

TIME, MILLISECONDS

Fig. 7 (contd)

too.


(e)

bWRA

E

60.

TIMEiMILLISECONOS

Fig. 7 (contd)


(f)

3.3-O4

3.O-O4

F

0 «.„

RA

- 1.3

cHA

I s.o-05

0.0

-3.0-03

60.

TIME.MILL I SECONDS

Fig. 7 (contd)


(g)

4 .0-04

J.5-O4

3.O-O4

L0URA 2. 5^O4

"*T

E

VA

yE

kB/ 1 . S-O4

rc

|

1

0. 2O. 40. CO. «0. tOO. ICO.

TIME.MILL I SECONDS

Fig. 7 (contd)

JPL. Technical Memorandum 33-604 29

(h)

• .-04

9AL

IHPU

b

•0.

T I M E . M I L L I SECONDS

Fig. 7 (contd)

30 JPL, Technical Memorandum 33-604

•00.

HAH

PR

II

1

•00.

to. 40. 60.

TI Kin ILL I SECONDS

Fig. 7 (contd)

•o.


15. K>. IS.

TIME, MILL I SECONDS

JO.

Fig. 8. MM!71 roll valve parameters as a function of time: (a) chamberpressure, (b) total mass, nozzle, (c) total mass, chamber,(d) total mass, valve, (e) nozzle flow rate, (f) chamber flowrate, (g) valve flow rate, (h) total impulse, (i) chamberpressure derivative


(b)

9A

HA

b

03. IS. 30. 35.

TIMEi MILLISECONDS

Fig. 8 (contd)


4.S-O7(c)

4.0.07

3.91.07

9AL

nA

f.S-07

HAn

b

s.Q-oa

to. is. to.**•

35. 40.


Fig. 8 (contd)

34 JPL. Technical Memorandum 33-604

».-oe

9AL

NA

VA

V

b

is. to. *»•

TI ME. MILL(SECONDS

Fig. 8 (contd)

3D. 39.


2.0-04

b

A

E

N0

L

3.O-03

0.019. W. 3D. 33. 40.

TIME. MILL I SECONDS

Fig. 8 (contd)


4. -04

F

bWR

HAn

5. 10. CO. 3d. IS.

TIMEi MILL(SECONDS

Fig. 8 (contd)


4.S-O4(g)

9.O-O4

F

0

A *-s-04

E

VA

b/ 1.3-04

I.O-O4

0. 13. K. tS.

TIME •MILLISECONDS

Fig. 8 (contd)

33.


5.. 04

AL

IHP 3.-O4

UL

b

S Z.-04

Ec

15. 20. IS.

TIME.MILL I SECONDS

Fig. 8 (contd)

IS.


HAH

pR

UR

IV

1

eoo.

40O,

200.

O.

-ZOO.

-400.

-too.13. K. if.

TIME. MILLISECONDS

Fig. 8 (contd)

JO.


19.(a)

CD. 3d. 40. SO.

TIME»MILLISECONDS

Fig. 9. MM'64 pitch/yaw valve parameters as a function of time:(a) chamber pressure, (b) total mass, nozzle, (c) totalmass, chamber, (d) total mass, valve, (e) nozzle flowrate, (f) chamber flow rate, (g) valve flow rate, (h) totalimpulse, (i) chamber pressure derivative


(b)

1,O-O«

9AL

NA

- 4.0-07

JO. 60.

TIMEi MILL I SECONDS

Fig. 9 (contd)

»0. to.


S.O-OT

J.O-O7AL

nA

HA Z.O-O7

3D. 40. 50.

TI ME • MILL I SECONDS

Fig. 9 (contd)

TO. »O.


AL

HA

VAL

40. SO.

TIME • MILL I SECONDS

Fig. 9 (contd)

jo. ao.


(e)

F

bWP Z.O-Q3

A

E

H

4 1.5-O5

L

SO. 40.

T I M E i M I L L I SECONDS

Fig. 9 (contd)

f- -t T »

ao. M>.

JPL, Technical Memorandum 33-604 45

• .-04

bwRA

E

CHAn

b

10. to. 30. 40. so. go. jo. »o.

TIME.MILLISECONDS

Fig. 9 (contd)


(9)

b

VA

/ Z.-04

a. 10. to. Jo. 40. so. ao.


Fig. 9 (contd)


(h)

7.-QS

AL

Inpu

4. -05

3.-OS

s

I.-OS

30. 40. 30. 60. TO. ra.

TIME*MILL I SECONDS

Fig. 9 (contd)


HAn

pR

0

I

V

TIME, MILLISECONDS

Fig. 9 (contd)


(a);

- f t

HAn

pR

PS

tO. 30. 40.


LLTO.

Fig. 10. MM'64 roll valve parameters as a function of time: (a) chamberpressure, (b) total mass, nozzle, (c) total mass, chamber,(d\ total mass, valve, (e) nozzle flow rate, (f) chamber flowrate, (g) valve flow rate, (h) total impulse, (i) chamberpressure derivative


(b)

AL

HA

M

f ».0-OT

l.O-OT

0.0 tO. 30. 40.

TI ME. MILL I SECONDS

Fig. 10 (contd)


30. 40.

TIME.MILL I SECONDS

Fig. 10 (contd)


t .4-06

T

AL

nA

syA

o.o

11

/

1

/1

1

1t

1t

1f111

1f

f

11

f' •

' i

i ! i

1

i

i

i

;i

i

I

i!

j

1i

\

30. 40.

TIME*MILL I SECONDS

Fig. 10 (contd)


b8A

E

.,.., t.«-.-(-t • + • •

tO. 30. 40.

TIMEtMILLISECONDS

Fig. 10 (contd)


bA

E

HAHB

R

r

10. 40.

TIME. MILLISECONDS

Fig. 10 (contd)

-i *


buRA

_

VA

.-04(g)

5.-04

*.-<M

J.-04

+4-

W. SO. 40.


Fig. 10 (contd)

so. •o.


(h)

1.0-04

•,0-OS

9KL

•.0-09

0.0JO, 40.

TI Ml. M I L L I SECONDS

Fig. 10 (contd)

JPL, Technical Memorandum 33-604 57

»MO.

HAH

IPR

jf

IVA

1QOO.

10. 40.


so.

Fig. 10 (contd)

58 JPL Technical Memorandum 33-604NASA — JPl — Coml., L.A., Calif.

a method for calculating transient thrust and flow-rate

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