THE TEMS APOLLO-SATURN V RESULTS … technical memorandum i nasa tm x- 53804 december 3, 1968 the tems apollo-saturn v results through the as-502 flight test by bobby junkin

N A S A TECHNICAL M E M O R A N D U M

I

NASA TM X- 53804

December 3, 1968

THE TEMS APOLLO-SATURN V RESULTS THROUGH THE AS-502 FLIGHT TEST

By Bobby Junkin Computation Laboratory

NASA

George C. MdrshdII Space Fkght Center

https://ntrs.nasa.gov/search.jsp?R=19690009613 2018-05-16T13:55:29+00:00Z

TECHNICAL MEMORANDUM X-53804


Bobby Junkin

George C. Marshall Space Flight Center Marshall Space Flight Center, Alabama 35812

ABSTRACT

Truncated tracker e r r o r models €or representing the systematic e r r o r s on the Apollo-Saturn AS-501 and AS-502 flight tests are presented. The TEMS method for determining the models involves establishing the tracker e r r o r s and then determining, in the least squares sense , functional expressions to describe the established er rors . Guidelines used in obtaining the truncated e r r o r models have resulted in generally acceptable models for the AS-501 and AS-502 data. Although C-band radar e r r o r models are used in the TEMS development , the method can be adapted to other types of tracking systems.

NASA-GEORGE C. MARSHALL SPACE FLIGHT CENTER

NASA-GEORGE C. MARSHALL SPACE FLIGHT CENTER



BY

Bobby Junkin

COMPUTATION LABORATORY RESEARCH AND DEVELOPMENT OPERATIONS

TABLE OF CONTENTS

Page

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SUMMARY i

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

SUMMARY OF APOLLO-SATURN V RESULTS THROUGH AS-502LAUNCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

APPENDIX A. THE C-BAND RADAR TRACKING SYSTEM ERROR MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

APPENDIX B. RESULTS FROM THE APOLLO-SATURN 501 VEHICLE FLIGHT TEST.. . . . . . . . . . . . . . . . . . . . 12

APPENDIX C. RESULTS FROM THE APOLLO-SATURN 502 VEHICLE FLIGHT TEST . . . . . . . . . . . . . . . . . . . . 39

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

iii

L I S T OF ILLUSTRATIONS

Figure

1.

2.

3.

4.

B-1.

B-2.

B-3.

B- 4.

B-5.

B-6.

B-7.

B-8.

B-9.

B-IO.

B-11.

B-12.

Title Page

Utilization of the TEMS and STEPRG Computer Programs . . 3

AS-502 Launch Phase Ground Track . . . . . . . . . . . . . . . . . 5

AS-502 Orbital Phase Ground Track . . . . . . . . . . . . . . . . . 5

TEMS AS-502 Tracking Data Utilization . . . . . . . . . . . . . . 7

Radar 0.18 Residuals on AS-501 First Burn Data . . . . . . . . 17

Radar 0.18 Range, Azimuth, and Elevation E r r o r s on AS-501 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 18

Radar 19.18 Residuals on AS-501 First Burn Data . . . . . . . 19

Radar 19. 18 Range, Azimuth, and Elevation E r r o r s on AS-501 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 20

Radar 3.18 Residuals on AS-501 First Burn Data . . . . . . . . 2 1

Radar 3.18 Range, Azimuth, and Elevation Errors on AS-501 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Radar 7.18 Residuals on AS-501 First Burn Data . . . . . . . . . 23

Radar 7.18 Range, Azimuth, and Elevation E r r o r s on AS-SO1 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 24

Radar 67.16 Residuals on AS-501 F i r s t Burn Data. . . . . . . . 25

Radar 67.16 Range, Azimuth, and Elevation E r r o r s on AS-501 First Burn Data ......................... 26

Radar 67.18 Residuals on AS-501 First Burn Data . . . . . . . 27

Radar 67.18 Range Azimuth and Elevation E r r o r s on AS-501 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 28

iv

L I S T OF ILLUSTRATIONS (Continued)

Figure

B.13 . B.14 .

B.15 . B.16 .

B.17 . B.18 .

B.19 . B.20 .

B-2 I . B.22 .

C.1 . c.2 .

c.3 . c.4 .

c.5 . C.6 .

Title Page

Radar 1.16 Residuals on AS-501 First Burn Data . . . . . . . . . 29

Radar I . 16 Range. Azimuth. and Elevation E r r o r s on AS-501 First Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 30

Radar 19.18 Residuals on AS-501 Second Burn Data . . . . . . . 31

Radar 19.18 Range. Azimuth. and Elevation E r r o r s on AS-501 Second Burn Data . . . . . . . . . . . . . . . . . . . . . . . . . 32

Radar 3.18 Residuals on AS-501 Second Burn Data . . . . . . . . 33


Radar 91.18Residuals on AS-501 Second Burn Data . . . . . . . 35

Radar 91.18 Range. Azimuth. and Elevation E r r o r s on AS-501 Second Burn Data . . . . . . . . . . . . . . . . . . . . . . . . 36

Radar 67.18 Residuals on AS-501 Second Burn Data . . . . . . . 37


Radar 19.18 Residuals on AS-502 Launch Phase Data . . . . . . 44

Radar 19.18 Range. Azimuth. and Elevation E r r o r s on AS-502 Launch Phase Data . . . . . . . . . . . . . . . . . . . . . . . . 45

Radar 0.18 Residuals on AS-502 Launch Phase Data . . . . . . . 46

Radar 0.18 Range. Azimuth. and Elevation E r r o r s on AS-502 Launch Phase Data ........................ 47

Radar 1 . 16 Residuals on AS-502 Launch Phase Data . . . . . . . 48

Radar 1.16 Range. Azimuth. and Elevation E r r o r s on AS-502 Launch Phase Data ........................ 49

V

Figure

c-7.

C- 8.

c-9.

c-IO.

c-11.

c-12.

C-13.

C-14.

C-15.

C-16.

L I S T OF ILLUSTRATIONS (Concluded)

Title Page

Radar 67.18 Residuals on AS-502 Launch Phase Data. . . . . . 50

Radar 67.18 Range, Azimuth, and Elevation E r r o r s on AS-502 Launch Phase Data . . . . . . . . . . . . . . . . . . . . . . . 51

Radar 3.18 Residuals on AS-502 Launch Phase Data . . . . . . 52

Radar 3.18 Range, Azimuth, and Elevation E r r o r s on AS-502 Launch Phase Data . . . . . . . . . . . . . . . . . . . . . . . 53

Radar 0.18 Residuals on AS-502 Orbital Phase (Rev. I) Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Radar 0.18 Range, Azimuth, and Elevation E r r o r s on AS-502 Orbital Phase (Rev. I) Data . . . . . . . . . . . . . . . . . 55

Radar 3.18 Residuals on AS-502 Orbital Phase (Rev. 1) Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Radar 3.18 Range, Azimuth, and Elevation E r r o r s on AS-502 Orbital Phase (Rev. I) Data . . . . . . . . . . . . . . . . . 57

Radar 19.18 Residuals on AS-502 Orbital Phase (Rev. I) Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Radar 19.18 Range Azimuth, and Elevation E r r o r s on AS-502 Orbital Phase (Rev. I) Data . . . . . . . . . . . . . . . . . 59

v i

LIST OF TABLES

Title Page Table

I.

111.

IV.

V.

B-I.

B-11.

B-111.

B-IV.

c -I.

c-11.

Location of Launch Site and C-Band Tracking Radars Used in TEMS AS-502 Reduction. . . . . . . . . . . . . . . . . . . . . 4

Truncated Radar Error Model Multiple Regression Results For First Burn Data on AS-501 and AS-502 Vehicle Flight Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Coefficient Standard Deviations For Truncated Radar Er ror Models For First Burn Data on AS-5Oi and AS-502 Vehicle Flight Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Truncated Radar Er ror Model Multiple Regression Results for Second Burn Data on AS-501 and Orbital Data on AS-502 Vehicle Flight Tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . i o

Coefficient Standard Deviations For Truncated Radar Error Models For Second Burn Data on AS-501 and Orbital Data on AS-502 Vehicle Flight Tests . . . . . . . . . . . . . . . . . . . . . i o

Stepwise Regression Analysis Results For AS-50i First Burn Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Stepwise Regression Analysis Results For AS-50i Second B u r n D a t a . . 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Coefficient Correlations For The Truncated AS-501 First Burn Radar Er ror Models . . . . . . . . . . . . . . . . . . . . . . . . . 15

Coefficient Correlations For The Truncated AS-501 Second Burn Radar Error Models . . . . . . . . . . . . . . . . . . . . . . . . . 16

Stepwise Regression Analysis Results Fo r AS-502 Launch Phase Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Stepwise Regression Analysis Results Fo r AS-502 Orbital Phase (Rev. i) Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

v ii

L I S T OF TABLES

Table Title

C-111. Coefficient Correlations For The

(Concluded)

Truncated AS-502 Launch

Page

Phase E r r o r Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

C-IV. Coefficient Correlations For The Truncated AS-502 Orbital Phase (Rev. I) E r r o r Models . . . . . . . . . . . . . . . . . . . . . . 43

viii

DEFINITION OF SYMBOLS

Symbol Definition

TEMS Acronym for - Tracking System - E r r o r - Model - Studies

AR, AA, AE Functional expressions for the systematic e r r o r s in range , azimuth, and eleva;tion,. respectively

ARO, AAO, A E O Observed tracking e r r o r s in range, azimuth , and elevation , respectively

vR> ’A, Residuals in range, azimuth, and elevation, respectively

Coefficient observational residuals

Coefficients in range e r r o r model

, . . . , V vco’ vci Fl2

co, 6 1 ,

Do, Dl, - - * Coefficients in azimuth e r r o r model

F,, Fl, e.. Coefficients in elevation e r r o r model

.. .. A , E

First derivatives of range, azimuth, and elevation, respectively, with respect to time

Second derivatives of azimuth and elevation, respectively, with respect to time

Reference position of vehicle in an earth-fixed ephemeris coordinate system with origin at the tracking site

cT2 cr2 Least square residual variances in range, azimuth, and elevation, respectively VR’O;VA’ VE

N N

co, ci, e.. Parameter approximation values

6C0, 6C1, ... Parameter corrections

0 3 0 0

co, CI Y * a * Parameter a priori values

Range, azimuth, and elevation e r r o r model factors, respectively

ix

DEFINITION OF SYMBOLS (Concluded)

Symbol Definition

F Level Ratio for determining the statistical significance of a regress ion equation

Standard deviation of the response variable Y (T

X



SUMMARY

Truncated t racker e r r o r models for representing the systematic e r r o r s on the Apollo-Saturn AS-501 and AS-502 flight tests are presented. Guidelines used in obtaining the truncated e r r o r models have resulted in generally acceptable models for the AS-501 and AS-502 data. the models involves establishing the tracker e r r o r s and then determining, in the least squares sense, functional expressions to describe the established e r ro r s . Although C-band radar e r r o r models a r e used in the TEMS development, the method can be adapted to other types of tracking systems.

The TEMS method for determining

INTRODUCTION

This report is one in a continuing series summarizing results from the evaluation of tracking system measurement e r r o r s on the Apollo-Saturn V flight tests. The basic concept in the evaluation process is given in the TEMS Multiple Regression Analysis Method [ I]. The method inyolves establishing the tracker e r r o r s and then determining, in the least squares sense, e r r o r model expressions to describe the established e r ro r s . equations in the method are given by:

The fundamental observational residual

vA - = A A O

- vE = A E O - - - Observational Observed Functional

Residuals Deltas Deltas

where:

AE = go + 6Fo + (Fi + 6Fi) el + ( F2 + 6F2) e2 + . . . + ( gm + 6F ) e m m

and rk, am , and e m measurements. The parameter ( o r coefficient) residual equations are given by:

a r e functions of the basic range, azimuth, and elevation

Parameter Corrections Coefficient A priori Residuals Approximations Coefficient

Values

W e then determine the corrections 6Co, 6Ci, . . . , 6Fm, in the least squares

sense, and adjust our initial approximations Co, Ci, . . . F N N N

by these amounts. m

The above TEMS method is used in conjunction with a stepwise regression procedure to obtain truncated tracker e r r o r models for representing the systematic e r rors . The stepwise regression procedure involves examining at every step the variables incorporated into the e r r o r model in previous steps. final regression model results in only the most significant variables being retained in the model. Detailed development information can be found in Reference 1.

The

The IBM 7094 and Univac 1108 computer programs for application of the TEMS method and the stepwise regression procedure are discussed in detail in Reference 1. The utilization of these two programs to obtain the final TEMS e r r o r models is summarized in Figure 1.

2

IBM 7094 T

IBM 7094

I TEMS EDIT PASS TO DETERMINE USABLE DATA r

TEMS PASS TO CREATE BINARY TAPE CONTAINING r, a, e ERROR MODEL FACTORS

I

G UNIVAC 1108l

STEPWISE REGRESSION I (STEPRG) ANALYSIS USING RESULTS FROM PREVIOUS BLOCK

INTERPRETATION AND ANALYSIS OF STEPWISE RESULTS TO DETERMINE VARIABLES TO CONSIDER FOR FINAI MODEL

1

IBM 7094

ITEMS FINAL PASS ( OR PASSES)

FIGURE I. UTILIZATION OF THE TEMS AND STEPRG COMPUTER PROGRAMS

3

SUMMARY OF APOLLO-SATURN V RESULTS THROUGH THE AS-402 LAUNCH

The Apollo-Saturn AS-502 vehicle was launched at 07:OO:Ol (AM) Eastern Standard Time on April 4, 1968 from Kennedy Space Center, Launch Complex 39, Pad A. Tracking data from five C-band radars providing coverage on the launch to orbital insertion phase and three providing coverage on the orbital phase (revolution 1) were used in the reduction.

The post flight reference trajectory used as the standard in the reduction is presented in Reference 2. The relation between the vehicle trajectory for the first phase of the launch and the various C-band radar tracking sites is shown in Figure 2. A similar summary for the orbital phase is given in Figure 3. Table I contains location data for the launch site and the various tracking stations.

TABLE I. LOCATION OF LAUNCH SITE AND C-BAND TRACKING RADARS USED IN TEMS AS-502 REDUCTION

Site

Launch Complex 39, Pad A

Patrick Radar (0. 18)

Merritt Island Radar ( 19.18)

Grand Bahama Radar ( 3.18)

67.18 (FPQ-6)

Cape Kennedy ( I. 16)

Latitude , deg

28.608422

28. 226553

28. 424862

26.636350

32.347964

28.481766

Longitude, deg

80.604133

80. 599293

80.664404

78.267708

64.653742

80.576515

a Height, m

b 116.04

19.92

16.39

16.29

19.03

18.78

a.

b.

Elevation above the Fischer Ellipsoid

Elevation of the C-band radar antenna above the Fischer Ellipsoid

4

FIGURE 2. AS-502 LAUNCH PHASE GROUND TRACK

100 80 60 40 20 0 20 40 60 80 100 120 140 160 180 160 140 120 100 80

LONGITUDE, DEGREES

FIGURE 3. AS-502 ORBITAL PHASE GROUND TRACK

5

The specific tracking data utilization for the launch and orbital phases is shown in Figure 4. These data were determined from an edit pass through the TEMS program. The preliminary edited data for all the radars were processed with the parameter weight matrix (%) and approximation matrix ( e) equal to zero. A priori estimates of zero for the e r r o r model coefficients were also entered into the final TEMS computer runs.

The general approach for obtaining truncated e r r o r models to describe the AS-501 and AS-502 range, azimuth, and elevation response variables is summarized in the following guidelines:

I) It was assumed that the survey te rms , rate bias te rm, and the azimuth and elevation velocity lag te rms were not essential in obtaining truncated e r r o r models to describe the response variables.

( 2) The first two variables entered in the stepwise regression (excluding those left out under the assumption in guideline I) were selected for considera- tion in the final TEMS e r r o r model.

( 3) A third variable w a s considered if an adequate description of the response variable w a s not obtained with the first two, or if a constraining condition required an additional variable in the model.

This approach actually results in entering the most significant variables into the e r r o r model. It should be pointed out that the third variable selected in guideline ( 3) often involved selecting one of two variables that represented borderline cases so far a s the order of entry in the stepwise regression w a s concerned; i. e. , the two variables had partial correlation coefficient values nearly equal.

The AS-501 and AS-502 truncated e r r o r model results obtained using guidelines ( I ) through (3 ) are presented in Tables I1 through V. observed and computed response variables and the least squares residuals for the truncated models are given in Appendixes B and C. are also presented.

Plots of the

Coefficient correlations

CONCLUS IONS

The TEMS Multiple Regression Analysis Method is used in conjunction with a stepwise regression procedure to obtain truncated tracker e r r o r models

6

ORBITAL PHASE

n m , 1 : I

I1 500 I1 550 I1 600 11 650 I1

TIME (sec)

0. 18

19.18

3.18

00

NOTE: THE DOTTED LINES INDICATE WHERE ONLY 1-3 DATA POINTS ARE LEFT OUT.

LAUNCH PHASE

1 : I 1 I

I I 1 I

I I 1

1 I

0 200 400 600 81

TIME ( s e c )

3, 18

1. 16

19. 18

57. 18

3. 18

1

FIGURE 4. TEMS AS-502 TRACKING DATA UTILIZATION

7

for representing the systematic e r r o r s on the Apollo-Saturn AS-501 and AS-502 flight tests. Guidelines used in pbtaining the truncated e r r o r models have resulted in generally acceptable models for the AS-501 and AS-502 data. Although C-band radar e r r o r models are used in the TEMS development, the method can be adapted to other types of tracking systems.

8

I

~ d

9 1 d

o m m a m m 0 0 0 0 . .

I I -.

I I qjf1 m

d +

- m m N O N N

w m m

d d d

0 0 c 4" 0 0 0 0

- 0 n N O w 4 . 4 0 0 0 0 d d d -- - 0 0 m c m 4 4 E:

m 0 m * b I $ p$ -E N m 4 *.- O N 0 0

0. d -

$ 1 d

-

w w m N my3 m r . . 0 0

- " * e N n O 0 0

d d - m 1 ;

-,I d

- -4 P-

- * T I I

m N

I 1

2% d d - r m m w Gn' m a

I 1 - W rl

< -

4 L u 0 0 m m

$ 2 T O ." d d

y 3 1 E l

m *

g g l d d

I

9

N e

e m m

- m v t - m

d d 0 0 0 0

- O d m m 0 0 0 0

d d

m m c : c d

- 0-8

- E l d

- m r l - 4 0 0.4 0 0

d d

~m m Nt-

- m w m r l 0.4 0 0

d d - moa m m 0 0 0 0

d d - w t - r l m Gcd - m m %/ N'

/ . I / I

- NOO

4 0 0 0

I I

m m

d d -

-

- m m N r l

rl I

m v dc.i

- -IC-

0 0 0 0 m~

d d - rlrl

w t - o r l 0 4

d d -

I I - w m v m . . m r l 0 t- - m rl

d -

.-IN 0 0 m m -

I I -

d

APPEND IX A

THE C-BAND RADAR TRACKING SYSTEM ERROR MODELS

The basic radar e r r o r models for describing the systematic e r r o r s in the range, azimuth, and elevation measurements are given by the following equations:

Range

AR = co + C ~ R + c2R + c3t + cq(-o. 022 cosec E)

Azimuth

AA = Do + DIA + D 3 i + D, tan E + D, sec E + D7 tan E sin A

sin A cos A $ ( sin A cos A ) +Dl0 - Y + D8 tan E cos A + D9(

(A-2) + ~~~i sec E

E levation

AE = Fo + FIE + FsE + F5(-sin A) + F, cos A

+ F7 [(E sin 022 E - cotan E] -t F9( -XF ')

The specific physical interpretation of the terms appearing in equations ( A-I) , (A-2) , and (A-3) are given in Reference 1. These equations require modifications, depending on the particular tracking system being considered and on the flight trajectory geometry. The IBM 7094 computer program was thus developed such that any combination of terms appearing in the e r r o r models can be retained in a given a d j u s b e n t through the use of appropriate program control matrices.

APPENDIX B

RESULTS FROM THE APOLLO-SATURN 501 VEH ICLE FLIGHT TEST

This appendix presents a summary of the results from the Apollo-Saturn 501 Vehicle Flight Test launched on November 9, 1967. The Stepwise Regres- sion Analysis results for the first and second burn data are presented in Tables B-I and B-11 respectively. Coefficient correlations for the truncated e r r o r models for the first and second burn data are given in Tables B-III and B-IV, respectively.

In the figures (B-1 through B-22) the tracking e r r o r s for the various radars are represented by dots. The description of these e r r o r s as obtained from the TEMS least squares adjustment program is represented by the solid computed curves.

The least squares residuals for the truncated e r r o r models presented in this appendix and in Appendix C can be thought of as being composed of random e r r o r s and unmodeled systematic errors. A high random e r r o r content in the data may prevent a systematic e r r o r of comparable magnitude from being determined. The latter errors are those that can be attributed to uncertainties in the standard used in establishing the tracking e r r o r s , unknown systematic e r r o r s not absorbed by those that are modeled, or to geometry limitations. presence of a significant unmodeled systematic e r r o r may prevent an adequate description of the data from being obtained.

The

12

TABLE B-I. STEPWISE REGRESSION ANALYSIS RESULTS FOR AS-501 FIRST BURN DATA

Equation I Variables in Regression

0.18 1 AR AA AE

19.18 1 AR AA AE

7.18 I AR AA AE

I 3. 18

AR AA AE

I 67.16

AR AA AE

I 67.18

AR AA AE

I. 16 I AR AA AE

Y (r

I. 7 1 0.0058 0.0060

2. 39 0.0042 0.0048

I. 13 0.0037 0.0158

I. 82 0.0024 0.0043

2.73 0.0072 0.0044

I. 95 0.0042 0.0034

4. 05 0.0102 0.0101

F Level

-0.10 6.6

-1.0

76.9 234.9

9. 5

15. 0 76.6 22.9

22. 8 35. 0 16. 8

7.5 3. 8

io. I

-0.80 5. 6 7. 9

-0.06 5. 9

<3.5

13

TABLE B-11. STEPWISE REGRESSION ANALYSIS RESULTS FOR AS-501 SECOND BURN DATA

Variables in Regression

3.37 0.0035 0.0048

22.3 -0.90

267.6

4. 12 153.8 0.0039 -1. 5 0.0062 -0.20

3. 85 0.0040 0.0053

28. 4 26. 9

1 43.0 1

14

TABLE B-111. COEFFICIENT CORRELATIONS FOR THE TRUNCATED AS-5Oi FIRST BURN RADAR ERROR MODELS

F3 I 1.00 I Radar 67.16

CO

Radar 7.18

CO

Co Cz C4 Do D3 Fo F3

CO

Radar 3.18

15

I I

a 0

d d I

Fyo

a"

a"

u"

r( u

w w w o o o o w o

I

d m o

. . d d d o 4

? a " 0 0 0

I

w m o o m 0

d d d d

. a " d 6 - I

" ? C Y

0

Fr

a3 d

c: CD k cd 3 P;

0 u

0 0 . - P d u 0

0 u

16

t L

I I

I C a I o U I L S

0 E c

FIGURE B-1. RADAR 0.18 RESIDUALS ON AS-501 FIRST BURN DATA

17

c L L 'I A 1 I 0 W

L I I 0 n 0 C c

A 2 I M

" E R R 0 R

0 E 6

R A M C E

r R R 0 R

M

1 C I I

r

TIME I SEC

FIGURE B-2. RADAR 0.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 FIRST BURN DATA

C L

0 C C

A I

I C 8 I 0 U A L s

0 C

I

I c 3 I O U A L s


19

c L c v I 1 I 0 Y

C I I 0 I

0 E C

A I I M U r n

E I I 0 I

D E C

I 1 M C L

r I ) I 0 I

M

1 C I L

r

100011 ooa OOJ

*e

-.**a

TIME I SEC

TIME , 5Ec

s

TIME , src


20

E L

c E S I D U A L 5

0 E C

T I M E , SEC

A 2

I .050

E 5 I D U A .o L 5

D

- .OS0

I i i i i i i i i i i i i i i i t i i i i i i i i i i i t t i - W t t t . L L l T ' r ~ f t t l - t ~ ~ E G

5

T I M E , SEC 100

TIME , SEC


21

f I t Y A I I 0 M

E C R '3 C

0 E C

A 2 I w U T n

E E E '3 c

0 E C

R A H C L

E R R 0 R

bl

E r f I $

TIME , SEC

71ME , I E C


22

1. L

a L 5 I D U A L s

0 L 5

A 2

0 L b

a b

I c 8 I D Y A L 8


23

L L c 1 A 1 1 0 m

L I I 0 I

D L

1 I I m U

II

C I I 0 I

0 c

r

0 1 il 6 C

c I I 0 I

m c 1 c I I

.e

- . n e

TIME , SEC

.*I.

.a

- . 111

FIGURE B-8. RADAR 7 .18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 FIRST BURN DATA

24

100011 0 0 1 0 0 1

I L

I C s I o U A L s

0 C 5

0 E C

n 5

I E s I 0 U A L 0

TIME I SEC


25

I L I I I 1 1 0 II

f. I I 0 n 0 c 6

A I I bl u T H

E R R 0 R

0 E c

R A ?I C E

E I R 0 I

I 4 C 1 C

3 a

003 ~ o o o a e 001

TIME I SEC

TIME , SEC IO0

100

*

TIME , SEC

FIGURE B-IO. RADAR 67.16 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 FIRST BURN DATA

26

1 ~ 0 0 1 2 001 001

C L

R C I I 0 U L L s

0 C c

A 2

I E

I 0 U A L s

a

0 C C

I

R C

I 0 U A L

a

a

W C 1 C I S

TIME , SEC


27

L L I V A 1 1

I4 0 .I1

t 1 1 0 I

0 -' L

TIUE , SEC

L I) I 0 R

0 L

n A I4

L

L I n 0 I

I 4 i I i I $

.os0

.e

-. -

t---- ~ 1, -

TlUE , SEC


28

... I

C L

I C e I D U A L a

0 C *

A 2

e I 8 I D U I L e

I I e

4 8 t w * il

ri

2 (I

1 .I


29

C L C 1 L I I 0 I

I

R 0 R

0 I I

n

A 2 1 m U 1 n

E I) R 0 R

0 I 6

I ooeor 008 OOJ

a 1 I) I E

# 8 8 0 a

I (I 7 I

I a

FIGURE B-14. RADAR I. 16 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 FIRST BURN DATA

30

t L

E 5 I O U I\ L 5

0 E C

A . I

E E 5 I 0 U A . L 5

0 E G

TIME SEC

TIME , SEC C

E c 5 I 0 U A

L 5

E 1 E i 5

TIYE , x c

FIGURE B-15. RADAR 19.18 RESIDUALS ON AS-501 SECOND BURN DATA

31

L L C 1 I 1 I

N

c

3 E G

U r

F A N G E

C

c

F

c I

C

5

T I M E , SEC

.os0

.a

-. O¶O

100 TIME , SEC

FIGURE B-16. RADAR 19.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-SO1 SECOND BURN DATA

32

to0032 OOL ooe

t L

I L 4 I D u- 1 L 8

0 t C

h z R t 8 I 0 U h L 4

0 t c

I c

I e 8 I D U A

TIME, SEC

.. 11

- -4s.

TIM€, SEC

TIME K C

FIGURE B-17. RADAR 3.18 RESIDUALS ON AS-501 SECOND BURN DATA

33

C L C 9 A

1 0

r

n e I I 0 I

- 180OIL 008 00)

D

c e

w

c

T I M I SEC

' A . 2

ll U 1 n

L I I 0 I

0 .C c

I A ll C E

I I I 0 a

m I 1 E I e

T I M t SEC

T I * , P C

FIGURE B-18. RADAR 3.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 SECOND BURN DATA

34

i a0011 001 001

C L

I L s I 0 U L L 3

D L C

T I E , 9Ec

A I

I L 8 I D U A L a

D C C

.. . -

T I E , SEC

FIGURE B-19. RADAR 91-18 RESIDUALS ON AS-501 SECOND BURN DATA

35

C

A 1 I 0 Y

L (L I 0 I

D E C

.os*

D . E

C

TIM€ , SEC I

TIME t SEC

E I I 0 I

Y c 1 E I S

FIGURE B-20. RADAR 91.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-501 SECOND BURN DATA

36

1#0081 oor ook

m

C L

I C 8 I D U A L L

0 C C

A z

0 C c

I C

1 L s

FIGURE B-2L RADAR 67.18 RESIDUALS ON AS-501 SECOND BURN DATA

37

I L

FIGURE B-22. RADAR 67.18 RANGE, AZIMUTH, AND ELEVATION ERROKS ON AS-501 SECOND BURN DATA

38

APPENDIX C

RESULTS FROM THE APOLLO-SATURN 502 VEHICLE FLIGHT TEST

This appendix presents a summary of the results from the Apollo-Saturn 502 Vehicle Flight Test launched on April 4, 1968. The Stepwise Regression Analysis results for the AS-502 data are given in Tables C-I and C-11. Coef- ficient correlations are given in Tables C-I11 and C-IV. deltas, computed deltas, and the least squares residuals are presented in Figures C-I through C-16. represented by dots in these figures. from the TEMS least squares adjustment program is represented by the solid computed curves.

Plots of the observed

The tracking e r r o r s fo r the various radars are The description of these e r r o r s a s obtained

39

TABLE C-I. STEPWISE REGRESSION ANALYSIS RESULTS FOR AS-502 LAUNCH PHASE DATA

40

TABLE C-11. STEPWISE REGRESSION ANALYSIS RESULTS FOR AS-502 ORBITAL PHASE (REV. I) DATA

41

TABLE C-III. COEFFICIENT CORRELATIONS FOR THE TRUNCATED AS-502 LAUNCH PHASE ERROR MODELS

-0.15

-0.08

-0.17

-0.21

0.33

-0.23

1.0

Fo

I. 0

D?

0.14

0.07

0.16

0.20

-0.30

0.22

-0.93

1.0

19.18

Co I. 0 -0.31 0.66 0.04 0.0 0.04 CO

I. 16

Cz 1.0 0.39 -0.14 0.0 0.03

0.0

0.01

, ~ I. 0

C4 1.0 -0.05 0.0 0.06

42

Do I. 0 0. 15 0.0

D, I. 0 0.0

Fg 1.0

Co 1.0

C i

-0.90 0.20 0.01 -0.03

1.0 -0.31 -0.01 0.04

Cz 1.0 0.04 -0.14

Do 1.0 0.18

D, 1.0

TABLE C-IV. COEFFICIENT CORRELATIONS FOR THE TRUNCATED AS-502 ORBITAL PHASE (REV. 1) ERROR MODELS

3. 18

DO I 1 .0 1-0.81 I 0.02 I I

1.0 1.0 -0.07 -0.20 -0.29

C2 1.0 -0.07 -0.20 -0.29 1

43

L L

L L 8 I 0 U 4 L a

0 t c

A 1

0 C 6

I 6

1*oosr 0 0 1 oor

.. - .OS0

I..

-1.

FIGURE C-I. RADAR 19.18 RESIDUALS ON AS-502 LAUNCH PHASE DATA

44

L L C 1 4 1 I 0 N

C I I 0 I

0 E c

I A n c L

E I

0 I

M C 1 L I J

n

.@SO

.e

-.OlO

I I I I I I

.OS0

.e

- . O S 0

50.

e

- 9 # .

FIGURE C-2. RADAR 19.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 LAUNCH PHASE DATA

45

C C

a C 8 I 0 U A L a

0 C b

A 2

I C

I 0 U A L a

a

0 E

I c

I C a I 0 U A L s

FIGURE C-3. RADAR 0.18 RESIDUALS ON AS-502 LAUNCH PHASE DATA

46

A 2 I bl U 1 n

C a I 0 a

0 L b

I A bl s L

C I

0 I

a L I L I s

1*00a1 O O I e08

r1nc I SfC

11ML , scc


47

L L

I E s I 0 U A L s

o L C

A 2

A L s

0 E C

R c

a L J I o U A L 5

#I E r E

s a

1b0011 001 0 0 1

.I

J " l l l l I 1 1 . 1 I I I I I I I I I I I I l l 1 I I I I I I I I I I I I I

I I I I I I 1 - 1 1 I I I I 1 I 1 I I I I I I I I I I I 1 1 I l l I I 1 -.a50 I I [ I 1 I 1 I 1 1 ,

-.

- mt-- I I I I I I I -

1 1 1 1 1 1 I t - 1 1 1 I I I I I I I I l l 1 1 I I I l . + I l l l I I ] l 1 l 1 1 1 1 I l

, , I I I , I , ! I I t L l I I I I 1 1 1 1 1 I 1 I I I I 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 1

T I M E I SEC

. O M

.a

- . O M

T I M E , SEE

40

ao

a

-48


L L L V A 1 I 0 N

E R I 0 I

D E c

I A N C L

L a I 0 1)

U E 1 E I s

FIGURE C-6. RADAR 1, 16 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 LAUNCH PHASE DATA

49

14008C 001 001

t L

I C s I D U 4 L s

0 C c

4 2

n L I I D U 4 L s

D c c

I) 6

I c s I 0 U 1 L s

m c 1 C I I

8


50

C L f. I L 1 I 0 n

C

I 0 I

0 C c

n

A 1 I Y U I n

C I I 0 I

0 C c

I 4 n c C

C

I 0

a

n n

r C

t I 1

.I@@

T I M E , SEC

T l Y E SEC

k


51

1 ~ 0 0 1 1 G G I GO2

. W O

.e

-.os0

T I M E I SEC

. O l O

..

- . O M

TIME I SEC

40

2 0

e

-10

-40

TIHE I SEC

L $

0 E 5

a c

R E


52

c 1 E Y I 1 I 0 N

E

R 0 I(

n

R I N C E

E

R 0 e

"

a

E

E s 5

r

.m

-.a10

TIME I SEC

TIME I SEC

FIGURE C-IO. RADAR 3.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 LAUNCH PHASE DATA

53

c L

L L

I 0 U h L

a

a

D c 6

I 2

I E s I D U I L a

D c c

I 6

L s

0 0 1 I600S1 001

11Wf , IEC

FIGURE C-I I . RADAR 0.18 RESIDUALS ON AS-502 ORBITAL PHASE (REV. I) DATA

54

E L c 1)

4 1 I 0 Y

c I I 0 I

0 E

A I I M U 1 n

E a I 0 R

0 c C

140011 OOJ a

TlWE I SEC

T I M E , SEC

IOJ

I 1 N C E

E R I 0 I

M E r C I 1

FIGURE C-12. RADAR 0.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 ORBITAL PHASE (REV. I) DATA

55

D L

A I

0 L

a TIME I SEC 4

I L 8 I D U 1 L 8

M c 7 c

S a,

FIGURE C-13. RADAR 3.18 RESIDUALS ON AS-502 ORBITAL PHASE (REV. 1) DATA

56

0 L c

I # O O I . OOJ OOJ

FIGURE C-14. RADAR 3.18 RANGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 ORBITAL PHASE (REV. I) DATA

57

L L

0 L C

L I

0 E C

R C

R C s I 0 U 1 L I

la0011 002 001

.a 11

-.OM

TIME , SEC

TlUE , SEC

-I#. I I I I I I I 1 I I 1 1 I I I I I I I I I I I I I I I I I I I I I 1 I I I I 1 t t t m t t t : 1lMC , I E C

FIGURE C-15. RADAR 19.18 RESIDUALS ON AS-502 ORBITAL PHASE (REV. I) DATA

58

c L C V A 7 I 0 n

E I I 0 I

O E

I A n

c

t I R 0 I

W L 1 E a 9

FIGURE C-16. RADAR 19.18 MNGE, AZIMUTH, AND ELEVATION ERRORS ON AS-502 ORBITAL PHASE (REV. 1) DATA

59

REFERENCES

1. Junkin, Bobby G. : R e g r e s s i o n Analys is P r o c e d u r e s F o r The NASA Evaluat ion of Tracking Sys tem M e a s u r e m e n t E r r o r s .

T N D-4826, D e c e m b e r 1968.

2. Apol lo /Sa turn V Pos t f l igh t T r a j e c t o r y AS-502. The Boeing Company Space Divis ion Document No. D5-15773, Ju ly 31, 1968.

60

APPROVAL TM-X 53804

THE TEMS APOLLO-SATURN V RESULTS

THROUGH THE AS-502 FLIGHT TEST

By Bobby G. Junkin

The informat ion in th i s r e p o r t h a s been reviewed f o r s e c u r i t y c lass i f ica t ion . Review of any informat ion concern ing Depar tment of Defense o r Atomic E n e r g y C o m m i s s i o n p r o g r a m s h a s been m a d e by the MSFC Secur i ty Class i f ica t ion Off icer . This r e p o r t , i n its en t i r e ty , h a s been de te rmined to be unc lass i f ied .

This document h a s a l s o been rev iewed and approved f o r technica l a c c u r a c y .

Roy f . Cochran Chief, Engineer ing Computation Division

c i i i e 4 D i r e c t o r , Computation Labora to ry

61

INTERNAL

DIR Dr. von Braun

DEP-T Dr. E. Rees

R-DIR Mr. H. Weidner

R-C OMP-DIR Dr. H. Hoelzer Mr. Car l Prince

R-COMP-D Mr. D. G. Aichele

R-COMP-RR Mr. R. J. Cochran

R-COMP-RRT Mr. R. H. Craf t Mr. B. G. Junkin (15)

R-COMP-RRM Mr. C. E. Houston

R-COMP-RRP Mr. P. R. Harness

R-COMP-RRV Mr. Jack A. Jones

R-C OMP-RRF Mr. R. L. Neece

R-COMP-RRG Mr. Paul 0. Hurst

DISTRIBUTION

R-COMP-S Mr. J. C. Lynn

R -A E RO-DIR Dr. E . Geissler

R-AERO-F Mr. J. P. Lindberg

NASA TM X-53804

R-AERO-FF Mr. C. C. Hagood Mr. John P. Sheats

R-AERO-F Mr. C. R. Fulmer

R-AERO-FT Mr. R. H. Benson

R-AERO-FFT Mr. J. B. Haussler

R-ASTR-DIR Dr. W. Haeussermann

R-SSL-DIR Dr. E. Stuhlinger

R-P&VE-DIR Dr. W. R. Lucas

R-ME-DIR Dr, Siebel

R-AS-DIR Mr. F. Williams

R-QUAL-DIR Mr. Grau

62

R-EO-DIR Mr. W. G. Johnson

I-DIR Gen. E. O'Connor Dr. W. A. Mrazek

I-V-MGR Col. James

I-MO-MGR Dr. F. A. Speer

I-I/IB-MGR Col. Teir

I-MO-0 Mr. Fletcher Kurtz Mr. MaxHorst

R-TEST-DIR Mr. K. L. Heimburg

MS-IL (8)

MS-IP (2)

MS-H

I-RM-M

PA T Mr. L. D. Wofford, Jr.

MS-T ( 6 )

EXTERNAL

Chrysler Corporation Space Division Department 2783 New Orleans, Louisiana 70129 Attn: Mr. J. Nichols (2)

The Boeing Company Huntsville Industrial Center Huntsvill-e, Alabama 35801 Attn: Dr. J. Liu

Manned Spacecraft Center National Aeronautics and Space

Houston, Texas 77058 Attn: Mr. J. Hanaway, ED

Administration

Mr. B. F. McCreary, FM-12 Mr. E. R. Schiesser, FM-4 Mr. W. M. Boyce, FM-4

John F. Kennedy Space Center National Aeronautics and Space

Kennedy Space Center, Florida 32899 Attn: Dr. 5, Debus, DIR

Dr. R. H. Bruns, K-ED Mr. Karl Sendler, K-E

Administration

Scientific and Technical Information

P. 0. Box 33 College Park, Maryland 20740 Attn: NASA Representative , S-AK/RKT

Facility (25)

Computer Sciences Corporation Huntsville, Alabama 35802 Attn: Mr. E. Clyde Anderson

63

DISTRIBUTION (Concluded) NASA TM x-53804

Philco , WDL 3875 Fabian Way Mail Stop 875 Palo Alto, California 94303 Attn: Mr. Jim Tyler

Lockheed Missiles and Space Company Huntsville Research and Engineering

4800 Bradford Drive Huntsville , Alabama 35806 Attn: Mr. Richard Hill, 54-30

Center

Goddard Space Flight Center National Aeronautics and Space

Greenbelt, Maryland 2007 1 Attn: Mr. W. D. Kahn, Code 507

Administration

Mr. P. G. Brumberg, Code 554 Mr. M. J. Keller, Code 554 Mr. P. E. Schmid, Code 551

TRW Sy s tem s Houston Operations Space Park Drive Houston, Texas 77058 Attn: Mr. Gerald Riddle ( 2 ) , H2-1080

Dr. D. D. Nadkarni, H2-1080d

RCA Performance Analysis Cocoa Beach Office Mail Unit 645 P. 0. Box 4036 Patrick Air Force Base, Florida 32925 Attn: Mr. E. A. Hoffman-Heyden

6 4

Documents

THE TEMS APOLLO-SATURN V RESULTS … technical memorandum i nasa tm x- 53804 december 3, 1968 the tems apollo-saturn v results through the as-502 flight test by bobby junkin