TM X 53398 Saturn Block Guidance Summary Report Chapman

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SATURN I BLOCK II GUIDANCE SUM MARY REPORT

B y R . A . CH APM AN

A e r o - A s t r o d y n a m i c s L a b o r a t o r y

N A S A

George C. MarsballSpace Flight Center,

Hantsuille, A l a b m a



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rlorral defmse of the

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TECHN ICAL MEMORANDUM X - 53398

SATURN I BLOCK I I GUIDANCE SUMMARY REPORT

BY

R. A . Chapman

George C. Marshal l Space Fl i g h t Center

Hu nt sv il le,Alabama

e BSTRACT

One of th e missions ass igned t o th e Saturn I Block I I veh ic le s wasf l i g h t tes t i ng the ST-124 in er t i a l guidance system.an al yt i c r ep or t o f t he ST-124 pla t fo rms and associated hardware f lownon t he s i x Sa t u rn I Block I I vehic les, S A - 5 through SA-IO.

T h i s i s an

This rep or t presents fo r each vehi c le th e ve lo c i ty component er r or sversus t ime fo r the t o t a l powered f l ight , combinat ions of p la t formsystem er ro rs th a t would p roduce the v e l oc i t y e r ro r p r o f i l es , and theveloci ty component error corresponding t o each plat form system error.

NASA - GEORGE C. MARSHALL SPACE FLIGHT CENTER



,

NASA - GEORGE C, MARSHALL SPACE FLIGHT CENTER

TECHNICAL MEMORANDUM x-53398

F e b r u a r y 2 3 , 1966


BY

R. A. Chapman

AERO-ASTRODYNAMICS LABORATORY

RESEARCH AND DEVELOPMENT OPERATIONS



)I TABLE OF CONTENTS

Page

I O INTRODUCTION ............................................ 2

2.0 SATURN I BLOCK I I GUIDANCE SYSTEMS h ..................... 1-3

3.0 DESCRl PT lO N OF THE ST-I 24 PLATFORM SYSTEM a.............. 5

4.0 ERROR ANALYSES (6......................................... 5 - 7

4.1 GUIDANCE VELOCITY COMPARISONS ( ........................... 8 , 17

4 .2

4.3

ST -1 24 PLATFORM SYSTEM ERRORS (a ......................... 17-20, 29

CORRELAT ION BETWEEN GU IDANCE ERRORS (6 .................... 29

5.0 CONCLUSIONS w.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9-30

iii



(U ) L I S T OF ILLUSTRATION%

Figure

3- I

4- I

4-2

4-3

4-4

4- 5

4 -6

4-7

4-8

4-9

4-10

4-1 I

4-12

5- I

5-2

5-3

5-4

T,i t e Page

ST-124 Plat for m Schematic......,......,.......... 4

Iner t ia l Ve loc i ty Compar isons S A - 5* #

11(Telemetered,minus Trackin g) ...................

12nertia4 Velocity Comparisons SA-6

(Telemetered minus Tracking) ...................rr'

I n e r t i a l V e l o c i t y C parisons SA-7

In e r t i I Ve Ioc i y m a pa r i ons SA-9

i? 13

14

(Telemetered minu Tra cki ng) ...................

(Telemetered. minus Tracking) ...................1

Inert ial Velocity Comparisons SA-8(Telemetered minus Tracking).. ... &:.. 15

Iner t ia l Ve loc i ty Compar isons S A - I O16(Telemetered minus Tracking) ..................

Guidance Hardware Er r or Co nt r i bu ti on (SA-5)..... 22

Guidance Hardware Er r or C on tr ib ut i on (SA-6)..... 23

Guidance Hardware Error Co nt ri bu ti on (SA-7)... .. 24

Guidance Hardware Error Contribution (SA-9)... . . 25

Guidance Hardware Er r or C on tr ib ut io n (SA-8)..... 26

Guidance Hardware Error Con t r i bu t i on ( S A - I O ) . . . . 27

Guidance Accelerometer and I n i t i a l Alignment32Errors..............,,.....,.........,........

33Gyro D r i f t Rates.,.......,......................

Guidance Error Comparisons (A na ly si s minus 34Predicted)....................................

35uidance Error Comparisons (A na ly si s minusPredicted)....................................

iv



Tab I e

2-

4-

4-1

4-1 I4-IV

5-

(U ) L I ST OF TABLES

T i t l e P a g e

Saturn I Block I1 Platform Systems .........,..... 3

I n e r t i a l Ve l oc i ty Comparisons .................... 9

Space-Fixed Ve lo ci ty Comparisons a t Or b i t alInsertion...............................,...... 10

ST-124 Pl a t f o r m System Errors.,.................. 21

Correlation Coefficients..... . . . . . . . . . . . . . . . . . . . . 28

Guidance Error Comparisons.......... ..,.......... 31

V



Symbo

B

MP9

X,YS

( U ) D EFIN IT ION OF SYMBOLS

Definition

iAcceleration bias

Misalignment of the sensitive axis of the pthaccelerometer about the qth xis.

Initial platform leveling error In yaw

Initial azimuth error

Initial platform leveling error In pitch

Constant drift rate of X,Y,Z gyros re pectlvely.3

I1 11 -

gsensitive drift due to mass unbalance along

the spin reference axis (X and Y gyros respectively).

Drift due to end plate "g"-sensItive turbinetorque (X,Y,Z gyros respectively).

11 11 -

g sensitive drift due to mass unbalance along

input axis o f Z gyro

Schle factor error of range and altitudeaccelerometers respectively.

Refers to ith row

Refers to j t h column

'vi



TECHN ICAL MEMORANDUM X- 53i98


SUMMARY

Th is repor t p resen ts an e r ro r ana lys is of the ST-124 i n e r t i a l p l a t f o r msystems flown on the Saturn I Block I I f l ig h t s . F ina l data f rom pre-c i s i on t ra ck in g were used f o r comparisons w it h t he te lemetered guidanceve lo ci t i es . These di f f er en ce s were input t o a weighted Least SquaresProgram t o determine the most probable sets of pl a t f or m system error s.The e r r o r so lu t ion s were ve r i f i ed by ad jus t ing the te lemete red ve lo c i t i esand computing a cont inuous tra je ct or y comparable t o the reference tr a j ec to r yand sa t i s f y i ng t he o rb i t a l i n se r t i on cond i ti ons .

Although some pla tf or m system er r or s were la rg er than desi red fo r ap rec i s ion f l i gh t , averages f o r t he s i x Sa tu rn I Block I I f l i g h t s i n d i c a t e don ly the "g" -sensi t ive gyro d r i f t s were g rea te r than the 3a va lue spec i f i -cat ions.0.05 deg/hr/g. However, si xte en o f twenty- four "g" -sen sit i ve d r i f t termswere pred ic ted greater than the err or ana lys is ind icated.

The average error was 0.07 deg/hr /g compared t o a 3a va lue of

The f l i g h t te st s indi cate d each guidance system performed t o ahigh degree of accuracy.



J), I .O INTRODUCTION

One of the missions assigned t o t he Saturn I Block I I vehicles wasf l i g h t te st in g th e ST-124 i n e r t i a l guidance system.re po rt o f the ST-124 st ab le p lat for ms and assoc iated hardware f lown on

s i x Saturn I Block I I vehicles, Saturn S A - 5 through S A - I O .

T h is i s an a n a l y t i c

The analyses presented i n t h i s repor4 re based on comparisons o f

the te lemete red gu idance da ta w i t h f i na l t ra ck i ng inc l ud ing estab l i shedo r b i t a l i n se r t i on cond i ti ons . F ina l t rack ing f o r most f l i g h t s was no trece ived i n t ime t o be used f o r the "Test F l i gh t Resu l ts" analyses;therefore , in termedia te t r ac k i ng data were used t o i so la te any s i g n i f i -cant guidance system error greater than predict ions based on laboratorytests o f the hardware.

The general phi losophy fo l lowed f o r t he evalu at io n r ep or ts was t o

assume the error predict ions were known error terms and then solve for

a minimum of add i t i ona l va lues requ i red t o approx imate the v e l oc i t y er ro rp ro ' f i les . For t h i s repor t , the e r ro r p red i c t ion s were used as "a p r io r i "estimates and a more complete guidance error model was used with thebest t rack ing data ava i l ab le f o r each veh i c le f l i g h t . A lt hough t he f i na lres u l t s a re very s im i l a r , they a re no t necessar i l y iden t ica l t o thoseshown i n rep ort s, "Resu lts of the Saturn I Launch Vehicle Test Fl ight",publ ished soon a f t er each veh ic l e f l i g h t . (See References)

Th is report presents for each veh ic le the ve loc i ty component errorsversus t ime f or the t o t a l powered f l i g h t , combinations o f p la t fo rm systemer ro r s t ha t would p roduce t he ve loc i t y e r r o r p ro f i l e s , and t he ve loc i t ycomponent error corresponding t o each pl at fo rm system err or .

( U ) 2.0 SATURN I BLOCK I I GUIDANCE SYSTEMS

The platform systems flown on the Saturn I Block I I vehicles andt he fun cti on o f each system are shown i n Table 2-1.

Although two pre vio us veh icl es, SA-3 and SA-4, c a r r i e d proto typ es oft h e ST-124 pl atf orm , Satur n SA-5 was t h e f i r s t v e h i c l e t o carry the com-p l e t e ST-124 guidance system. In er t i a l ve lo c i t i es and veh ic l e a t t i tu de sref ere nced t o th e ST-124 p l a t f o r m were fed i n t o an ASC-15 guidance com-pu te r fo r computations o f "Path Adaptive" guidance commands and t o i n i t i a t edi s cr ee t sig nal s. The guidance was i n open loop.

An ST-90-S p l a t f o r m system was al s o c a r r i e d on t h e SA-5 v eh i c l e andused as a reference f o r at t i tu d e co nt ro l . The ST-90-S pl at fo rm was amodi f ica t ion o f th e ST-90 system f lown on th e Ju p i te r f l i gh ts . The mod-i f i c a t i o n c on si st ed o f an extended azimuth drive t o permit a programmedr o l l maneuver t o t u rn t he veh i c le f rom a 90 degree launch azimuth t o th edesi red f l i g h t az imuth.

2



Saturn SA-6 a ls o ca rr ie d two p l a t f o r m systems. The ST-90-S systemgenerated signals t o t u r n t he vehi c le i n t o t he des ired f l igh t az imuth andserved as a reference fo r a t t i t u d e c on t r o l o f t h e S - l stage. A t about14 sec a f t e r S - I / S - I V separat ion, a t t i tu de er ro r s igna ls were swi tchedfrom t h e ST-90-S t o t he ST-124 pl at fo rm .

the guidance loop was closed and the vehicle f lew a guided tra jectory,"Path Adaptive" i n the p i t c h p lane and "De lta Minimum" i n t h e yaw plane,referenced t o t he ST-124 platform system.

A t about 168 sec of f l i g h t ,

Vehicle

SA-5

Satu rn SA-7 and subsequent Sa turn I Block I t vehic les ca r r l ed on l yth e ST-124 pl at fo rm systems which generated sig nal s t o tu r n t he v ehic lesin to the desi red f l i g h t az imuth and served as re ference fo r a t t l t ud e con-t r o l o f t h e s - l stages. The guidance loop was cl ose d i n t h e S - I V stageof each veh i Ie. SA-7 u t i ed the "Path Adapt 1vel' and "De I a M i n imum"guidance mode fo r p i t c h and yaw, re sp ect ive ly . SA-9, SA-8, and S A - I O

veh ic les u t i 1 zed the " I te ra t i ve " guidance mode ( I GM ) and "Delta Minimum"fo r p i t c h and yaw, res pec tiv ely .

Pl at fo rm System Funct ion

ST-90-S I n i t i a l r o l l maneuver and at t i tude control

ST-I24 Passenger

reference en t i re powered f I g h t

The S - I V stage of each of the guided Saturn 1 Block I I vehicles wasguided t o s a t i s f a c t o r y o r b i t a l i nse r t lon cond i t ions .

ST-90-S

ST- I24

TABLE 2-18 ATURN I BLOCK I I PLATFORM SYSTEMS

I n i t i a l ro l l maneuver and at t i tude controlreference S - l stageAt t i tu de con tr ol and closed loop "PathAdaptive" guidance reference S - I V stage

SA - 8

SA-6

S i - I24 A t t i tu de con t r o l and c losed loop " I te r a t iv e "guidance referenc e e nt i r e powered f I g h t

SA-7

ST- I24

IA - I O Att i tude cont ro l and c losed loop " I t e r a t i v e "

guidance re ference e nt i r e powered f l i g h t

ST- I24 At t i tu de co nt ro l and closed loop "PathAdapt ive" guldance reference ent irepowered f l i g h t

SA-9 ST- I24 t t i tude cont ro l and c losed l o o p " I t e r a t i v e "guidance reference e n t i r e powered f l i g h ti

I 1

3



\\\

I

4



0 ) .0 DESCRIPTION OF THE ST-124 PLATFORM SYSTEM

The ST-124 platform i s a four-gimbal system which perm its f u l l free -dom about a l l t hr ee ve hi cl e axes. The gimbal ord er from t h e v e hi cl e t oth e inner gimbal i s pi tc h redundant, yaw, p i t c h l im it ed , and r o l l . The

p i t c h redundant gimbal i s pos i t ioned from a p i t c h command reso lv er anda gimbal re so lv er ope rat in g in t o an associat ed gimbal servo. The p i t c hl im i t e d gimbal i s c o n t r o l l e d t o essent ia l ly zero (s teady s ta te) .

Three pendulous in t e g r a t i n g gyro accelerometers (AMAB-3-K4) ar emounted on t h e ST-124 s t a b i l i z e d element. The range and cr os s rangeaccelerometers are normal t o each o ther i n th e loca l hor izonta l p lane a tlaunch w i t h t h e range accelerometer di re ct ed down range. Cross rangeoutput i s po s i t i ve r i g h t w i th observer fac ing down range. The a l t i tu deaccelerometer i s di re ct ed up and normal t o the launch hor izontal plane.

The ST-124 pl at fo rm i s sta bi l iz ed by t hr ee (AB-5-K3-P) a i r bearing,

single-degree-of-freedom gyros mounted wi th th e se ns i t i ve axes mut ual lyperpendicular. The gyro axes (s en si t i ve o r input , output , sp in reference)are or iented such that some of t h e " g" -s en si ti ve d r i f t s and a l l t h e"g2"-sensi t ive d r i f t s are ef fe c t i ve l y zero or , i n any case, a minimum. A

schematic o f t h e ST-124 pl at fo rm system i s shown i n Figur e 3-1.

4.0 ERROR ANALYSES

The e r r o r analyses o f t h e ST-124 guidance pl a t f o r m system are basedon comparisons o f t he te lemete red gu idance ve l oc i t i es w i t h f i na l t r ack in gdata f o r each vehic le. Although the re su l t s are very s i mi la r , they areno t necessa r i l y i d en t i c a l t o those presented i n "Test F l i g h t Resul ts"

pub l ished soon a f t e r each veh ic le f l i g h t (see References).

The guidance error model used f o r the analyses has been simpli f ied bycombining er ro r terms th a t produce l i k e ve lo c i t y e r r or p ro f i le s andel im in at in g e r r o r terms th at are general ly considered negl ig ib le . Becauseo f t he a l ignment o f t he p la t fo rm a t launch with respect t o the p lane conta ining th e th ru st vector , some of the d r i f t s caused by mass unbalance anda l l o f t h e an i so e la s t i c d r i f t s are n e gl i g ib l e.

The p la t f o rm i s leve led i n the hor izont a l p lane a t launch w i t h thecross range accelerometer e le c t ro ni ca l l y a l i gned i n az imuth. Since t h e

cross range accelerat ion i s essen t ia l l y ze ro du r ing f l gh t , an e r ro r com-

ponent picked up by either the range or a l t i tude acce lerometers ro ta tedi n t o cross range would be ne gl ig ib le f o r small angle rot at i ons . Thus,the a l t i t ud e accelerometer e r ro r i n t he p i t ch p lane usua l l y i s t he on lynonorthogonali ty error considered. A t o t a l of eighteen platform systeme r r o r terms has been considered i n t h e analyses. The e r r o r term con-s idered are:

5



a.b.

C.

d.

e.

f .

h.

.:*I '

Bias error for each o f the three acce lerometers.Sca le fac to r er ro r f o r range and a l t i tu de acce lerometers.Scale fa c t o r e r ro r f o r c ross range i s n e g l i g i b le .Nonor thogonal i t y o f .a I t i t ud e accelerometer i n the p i t c h p lane.I n i t i a l p l a t f orm a l ignment er ro rs i n p i tc h , yaw,and azimuth.

Constan t d r i f t o f the p la t fo rm abou t the inpu t axes of +heth ree s tab i l i z i ng gy ros .

reference axes of the yaw ( X I and ro l l ( Y ) gyros."g"-sens i t ive d r i f t due t o mass unbalance a long the inpu ta x i s o f t h e p i t c h ( Z ) gyro.End p l a t e "g"-sensi t ive tu rb in e torque fo r each of t h e t h r e es tab i I z ing gyros.

11 11-

g sens i t i ve d r i f t due t o mass unbalance along the spin

The guidance pla t f or m e r r o r model i s described by the fo l l ow in gequat ion :

- - - -Ai =

B t S Xm [Mpq] [SI Xm

where B = accelerometer b ias error.

S = acce lerometer sca le fa ct or err or .c

Subscript m = denotes an ideal measuring system.

[M ]P9

= 3 X 3 mat r i x de f i n in g t he m isal ignmen t o f t he sens i t i veaxis o f the p th acce lerometer about the q th ax is .

[SI = 3 X 3 matr ix def in ing the instantaneous a l ignment o fthe p la t f o rm wi t h respect t o the idea l al ignment. Th isinc ludes t he e f f e c t s o f a l l d r i f t terms.

Measurements made by t h e guidanc e acc ele rom ete rs ar e re fe renced t oa po in t i n in e r t i a l space. Th is po i n t co incides w i t h the launch s i t ea t t im e of "Guidance Release" which occurs a t o r j u s t p r i o r t o l i f t o f f ofthe veh ic le .are mounted remains f i xe d i n in e r t i a l space throughout f l i g h t . Errorsmade i n the v el o c i t y measurements r e s u l t from imperfec t accelerometersand non ideal a l ignment o f th e s t ab l e p l a t f orm a t any t ime a f t e r gu idancerelease.present during a veh ic le f l i gh t , the measured ve lo c i t i es a re re fe rencedaga ins t a se t o f data th a t descr ibes the t ra je c t o r y o f t h e p a r t i c u l a r f l i g h t .

Idea l ly , the s ta b i l i zed p la t fo rm on which the accele romete rs

I n order t o determine th e p l a t f orm system err or s t ha t were

6



The referenc e data used i n these analyses vary from f l i g h t t o

f l i g h t a cc or di ng t o t h e a v a i l a b i l i t y of prec is ion t rack ing da ta .case th e establ ished in se rt io n condit i ons were considered t o be moreaccurate than data f rom any in di vi dua l t r ac ki ng system.

In each

Tracking data, inc lud ing establ ished in se r t io n po in ts , are convertedt o t h e guidance coor dina te system and compared w it h t he guidance accelero-meter outp uts (guidance minus tr ac ki ng ) t o e s t a b l i s h t h e v e hi c l e e r r o rp r o f i l e s .ing system, on l y random noi se i s considered i n the covar iance matr ix usedi n th e guidance er r or anal ysis . The tra ck in g data have been processedt o eli mi nat e, t o some ext ent , known e r r o r s bef or e comparisons ar e madewith guidance.

A lthough t rac k in g da ta con ta in e r r o rs pecu l i a r t o each t rack -

The guidance ve lo ci ty er r or model i s f i t t e d t o t h e v e l o c i t y e r r o r p r o -f i l e s by a double pr ec is io n weighted "Least Squares" method t o determinea set o f gu idance system errors that would produce the 've loc i ty dev ia-

t i o n s (r es id ua ls ) between th e measured guidance data and tra ck in g.

The general equation fo r th e "Least Squares" so lu ti on i s

- = cw, + PTWP1" Cw-u, t PTW R-J

-where U

P

Superscr ip t T

Superscr ip t - I

W

w0

-!?

0U

v v

pla t fo rm system err or s (n x I )

3 X n mat r ix of p a r t i a l d e r iv a tt v es r e l a t i n gt h e v e l o c i t y e r r o r t o the p la t fo rm systeme r r o r s ,

denoted matrix transpose.

denotes matr ix inverse.

3 xres

n X

Pia

3 x

3 covariance matrduals.

x associa ted wi th the

n covariance r n a t r x associated with theform system error terms.

! m a t r i x c f residuals !Gulbance iii:niis

Tracking).

n X I mat r i x of ''a p r i o r i " es t ima tes of t h eplat form system error terms.

7



4 .1 GUIDANCE VELOCITY COMPAR SONS

The re fer enc e data used f o r guidance compar sons va r i ed betweenf l i g h t s . For t h e f i r s t t h r e e S at ur n I Block I I (SA-5, SA-6, SA-7) f l i g h t sno tr ac ki ng system adequately covered t he major po r t i on of t h e f l i g h t .

There fo re , f i na l po s t f l ig h t t ra j ec t o r ies , based on va r ious t ra ck i ng andin ser t i on data, were used fo r est ab l ish lng the guidance ve lo c i ty e rr orp r o f i l e s . MISTRAM, t i e d t o cl os e- in t r a c k i ng from Cape Kennedy, andi n s er t i o n data were used as refe ren ce data f o r ve hi cl es SA-9 and SA-8.The analysis fo r S A - I O was based on ODOP t r a c k i n g and in se rt io n data.The qu al i t y o f th e tr ac ki ng from th e i nd iv id ua l systems used fo r SA-9,SA-8, and S A - I O was ver i f ied by adjust ing the measured guidance veloci t iesf o r er ro rs corresponding t o th e analyses made and comput ing tr a j ec t or i est h a t s a t i s f i e d co nd i ti o ns e st ab li sh ed f o r o r b i t a l i n s e r t i o n of eachvehic le . The ve lo c i ty cond i t ion s were complete ly sa t i s f ie d and po si t i ond i f fe r enc es were wi th in t he accurac ies associated wi th t he in se r t io n data .

The comparisons of t he v e l o c i t y components ar e shown, p l o t t e d versusrange t ime, i n Figures 4-1 through 4-6 . The so l i d l i nes rep resen t thecomparisons between guidance velocit ies and range tracking o r ( f o rveh ic le SA-5, SA-6, SA-7) f in a l po st f l i gh t t r a j ec to ry . The c i r c le d po i n tsrepresent ve l oc i t y d i f fe r enc es associa ted w i t h th e gu idance system err or sdetermined from th e analyses. The comparisons di t h establ is hed in se rt io nv e l o c i t i e s are shown enclosed i n squares.

The in er t ia l ve lo c i ty components and t o t a l ve lo c i t i es a t c u t o f f o ft h e S - l stage and or b i t a l in se r t io n are shown f or each veh i c le i n Table4-1 . Predic ted, tr ac k in g, and telem etered valu es are shown fo r com-par ison. S ince the Saturn veh ic les ar e not const ra ined t o a predeter-mined powered trajectory and the programmed S - I V c u t o f f v el o c i ty i s i na space- f ixed ( inc ludes the e f fe c t o f g r av i t y ) p lumbl ine coordina tesystems, the te lemetered i n er t i a l ve lo c i t i es are not .necessar i1y c loset o pred icted values. The ve loc i t y d i f fe re nces re f l ec t the nons tandardperformance o f the t o t a l veh ic le system i n add i t i on t o any guidancee r ro rs .

The vel oc i t y d i f fer en ce s between te lemetr y and tr ac ki ng r e f l e c t t heer ro rs of t he guidance system. Although tr ac ki ng does cont ain erro rs,the values i n Table 4-1 should be va l id espec i a l l y a t o r b i t a l i n s e r t i o n .

The i ne r t i a l ve lo c i ty outputs o f th e gu idance accelerometers wereconverted t o space-f ixed values by th e onboard (ASC-15) guidance computerfo r use i n path guidance computations. Table 4-11 shows the space-fixedvelocit ies telemetered from the guidance computer compared with pre-ca lcu la ted and o rb i ta l t rack ing a t t ime o f o r b i t a l i n se r t i on . S ince SA-5

was f l own wit h open loop guidance, t h i s ve hi cl e was no t included.



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The precalculated velocity vecl;or.at S - I V cu to f f was presef i n theguidance computer and cuto f f s i gna l "&s"#&&4iitwhen t h e onboard measure-ment equaled th e preset value. Or bi ta l in se rt io n occurred I O sec a f terS-IV cu to f f . Fo r SA-6 t he p recal cula ted ve loc i t y vec to r a t i n se r t i onwas erroneously p rese t i n the guidance computer as cu to f f ve lo ci ty which

explains most of t he 6 . 2 m/s v e l o c i t y d i f f e r e n c e a t i nse r t i on .veh ic les SA-6 and SA-7 th e t ime delay between c ut o f f s ignal and actual

cu to f f was not inc luded i n computations o f ve lo c i ty increase due t o th ru st

decay.th e te iemetered and precalculat ed ve lo ci ty vectors was wi th in -O , I m/s

a t o r b t a i ser t on.

For

Th is was i ncl uded f o r subsequent vehicles and the deviation between

The differences between the telemetered guidance values and orbitalt r a c ki n g r e f l e c t t h e e r r o rs of th e guidance system and er ro rs i n th egr av it y p r of i l e s based on the measured guidance ve lo ci t i es .

4.2 ST-124 PLATFORM SYSTEM ERRORS

The phi losophy fo l low ed f o r the f i n a l analyses was th at th e mostprobable set of guidance errors would represent ad justments t o t hete lemete red ve loc i t ies necessary to s imu la te the veh ic le t ra jec to ry w i thspecial emphasis on the o r b i t a l i nse r t ion condi t ions . D i f fe r en tphi losophi es concerning conf idence i n p r e f l ig h t es t ima tes and p red ic tedperformance can vary solutions using the same data and method.may be verif ied by comparing error solutions shown i n Tab le 4-111.Es sen t i a l l y , t h e same method, weigh ted "Least Squares", was used f o r t h epo st f l i gh t eva luat ion r epor ts( 1) as was used fo r the f i na l ana lys is . Thef i na l t ra ck i ng data was a lso ava i lab le fo r S A - 8 and S A - I O veh ic les beforethe p os t f l i gh t eva lua ti on repo r t s were published.i n these reports , the p r e f l ig h t est imates were considered genera l lyaccurate and weighted accordingly. A minimum amount of f l e x i b i l i t y waspermi t ted t o g ive a so lu t ion t ha t would f i t he end point and given ane r r or p r o f i l e s i m i l ar t o the observed ve lo ci ty d i f ference s. The so lu t i on swere const rained t o the pr e f l i gh t est imates wi t h i n the data no ise leve lpermitt ing a minimum of terms t o exceed the pre f l igh t est imates.

Th is

For the analyses used

The procedure used fo r th e f i na l analyses als o u t i l i z e s a weighted"Least Squares" approach.terms were used as ' la priori" estimates f o r a f i r s t pass a t f i t t i n g t h e

heavier than +3 u l i m i t s were th e angular e r ro rs made i n mounting th eaccelerometer? on th e pl atf orm (general l y 0. I t imes 3a values).

a re re fe r red t o as nonorthogonal i ty of the individual accelerometerse nsi t i ve ax is wi t h respect t o another accelerometer. Const ra in ts werep laced on the so lu t ion t o insure a curve f i t o f t he res idua l s t o f a l l w i t h i nth e nois e lev el of the data used. Completely w i l d d a t a o r d ata gaps wereweighted out of t he so lut i on. O rb i t a l insert ion data were heavi ly weighted.

However, pref I i gh t es t imates o f t he e r r o r

established velocity 8 r rO r p ro f i l e s . The m l y p r e f l i g h t BTTOTS weigh+ed

These

( I ) Reports published by F l i g h t Evaluati on Group (See References).

17



Successive cases were computed, i t e r a t i n g around t he pr evi ous case t o

el im in at e unnecessary compensating e r r o r terms, u n t i l a s e t of guidancee r r o r terms was d eri ved w i t h a minimum number exceeding th e magnitude

o f th e "a p r i o r i " es t ima tes and 'ye t f i t the observed v e lo c i t y e r ro rcurves. The so lu t i on s were v e r i f i e d as reasonable by ad ju st in g th emeasured guidance veloci t ies by the error solut ions and comput ingt ra jec to r i es t h a t compared ve ry f avo rab l y w i t h t he po s t f l i g h t t r a je c t o r i esand sa t is f i ed the in se r t io n ve lo c i ty components wi t h i n +0.1 m/s andp o s i t o ns t o w i t h i the accuracies quoted f o r t h e 1nserFion parameterso lu t ions.

Table 4-111 p resents t he f i na l p la t f o r m system e r r o r so lu t i ons f o reach of the Saturn I Block I I veh ic les . Als o shown fo r each veh ic le arethe p re f l ig h t es timates o f the e r ro r s and the va lues p resen ted I n theind iv i dua l eva luat ion reports . The er ro rs are l is te d under seven major

types. Three types of erro rs, b ias, scale fa ct or , and nonorthogonal i ty,p e r t a i n t o the accelerometers. Two types, p l at fo rm lev el in g i n p i t c h andyaw and azimir-bh al ignment, p e r t a i n t o t h e o r i e n t a t i o n of the measuringd i r e c t i o n s a t launch. Two types o f d r i f t , constant and "g"-sensi t ive .p e r t a i n t o t he s tab i l i z i ng gy ros .a re known t o ex i s t , they a re e i th e r in s i gn i f i c an t or cannot be dist inguishedfrom some one of t he l i s t ed te rms.

A lthough e r r o rs o the r than those l i s t ed

S ince the accele ra t ion i n the c ross range d i r ec t i on i s ve ry sma ll o ressen t i a l l y ze ro fo r the ma jo r po r t i on of powered f l i g h t , th e sca lef a c t o r e r r o r s of the cross range accelerometer and the nonorthogonalityof the range and a l t i t ud e sens i t i ve axes w i t h respect t o the c ross

range di r ec t i on were assumed t o be as predicted. Any p o s t f l i g h t solu-t ion for these errors would be h igh ly quest ionab le .one "g"-sensi t ive d r i f t te rm f o r each gyro and a l l a n i s o e l a s t i c d r i f t swere not considered.

For the same reason

The f in a l po s t f l ig h t ana lyses ind ica ted the acce le romete r b ias e r ro rswere general ly c lose t o t h e p r e f l i g h t e st im at e,accelerometers f o r each o f s i x vehi cles ) fourteen were equal i n s i gn o r

ess en t i a l ly zero. Only two accelerometers, range and a l t i t u d e fo r SA-5and S A - I O respec t ive l y, expe rienced b ias e r ro r s s i gn i f i c an t l y g rea te rthan the 3a value of 0.5 X 10-3 m/sec2.

O f eighteen va lues ( thr ee

The scale f ac to r err or s were ess en t i a l ly as pred ic ted except fo r SA-9.The po st f l ig h t so l u t ions showed four va lues o f d i f f e r en t s igns but es sen t i a l lythe same magnitude as predicted.t o i n t e r p r e t a t i o n of t e s t data. The sca le fac to r er ro rs shown fo r SA-9could be due t o approximately 4 degree lower tha n normal gimbal temper-at ur e th a t was experience estimates were assumedfor the cross range acceler

This discrepancy could very well be due

18



The p l a t f o rm i s o r i en ted so t h a t t he sensi-hye axes of the range andcross range accelerometers are i n the hori zon tal &ane wi th the cro ssrange a xi s more accurat ely a l igned.and az imuth errors leav ing the nonorthogonal i ty o f the a l t i tude acce lero-meter wi th respect t o range d , i- rec t ion the on ly e f fe c t iv e e r ro r i n mount-ing the acce le romete rs . A lthough the po s t f l ig h t so lu t ions ind ica ted thep r e f l i g h t measurements were h ig hl y accurate ( l es s than 2 sec of arcexcept fo r SA-6 which was o n l y 6.8 a r c sec.), th e accelerometer mountingwas ra th er poor fo r SA -5 and SA-6. SA-7 was much more accurately assembled,bu t subsequent ve hi cl es show t h a t t he acceler ometers can be mounted t o ah igh degree o f prec is ion.

This procedure minimizes th e range

The ra t he r la rge l eve l i ng and azimuth e r r o rs noted on the f i r s t th r eeSaturn I Block I I veh ic les were ev iden t ly due t o v ib r a t i ons dur ing t h r us tbu i ldup.l i f t o f f sig nal. When th e plat form became space-f ixed a t l i f t o f f , th ep o s i t i o n of th e p l a t f orm became th e gyro nu l l pos i t i on .s t a b i l i z e d t h e p l a t f o r m t o t h e l i f t o f f p o s i t i o n. B egi nn in g w i t h SA-9,th e pl at fo rm was space-fiwed p r i o r t o i g n i t i o n and t h e i n i t i a l e r r o r swere reduced t o less than 3a values i n each case except fo r p i t c h l e v h l i n gon S A - I O which was only 0.007 deg compared t o the 3a value of 0.005 deg.Level ing and azimuth pref l ight est imates shown are 3a values.

The pl at f or m was torque d t o compensate fo r e a rt h ' s r o t a t i o n u n t i l

The gyros

Wi th one excep tion the d i re c t i ons assigned t o the p r e f l i gh t es t ima tesof t h e guidance e r r o r terms shown i n Table 4-111 were taken f r m memorandapub l i shed p r i o r t o launch o f each ve hi cl e. I n these memoranda nonorthogona-I i t y was defi ned as po s i t i v e when the angle between th e measur ng di r ec ti on sof two accelerometers was greater than 90 degrees. I n th e ana y s i sprogram the o r th ogo nal i ty er ro r i s considered as an angular ro a t i o n o fth e measur ing d i re ct io n about an ax is and pos i t iv e fo r a r i g h t hand ro ta -t on.

A p o s i t i v e b i a s o t sca le fac tor e rr or ind icates an accelerometer out -put greater than the abso lu te va lue.gyro d r i f t e r r o r pe rmi ts the p la t f o rm t o move i n a r ight -handed senseabout the idea l axes and the veh ic le fo l lows the p la t form.

A pos i t i v e p la t f o rm a li gnment o r

The p red ic t ions o f the magnitude o f the cons tan t gy ro d r i f t te rmswere r e l a t i v e l y c o n si s te n t w i t h t h e p o s t f l i g h t r e s u l t s .terms iii and Y g ym s f ~ rA-5 and Y gyro fo r SA-6)were s ig n i f i ca n t lygreater than predicted and one o f the th ree ( X gyro S A - 5 ) was essent ia l lya 3a va lue o f 0.075 deg/hr.

Only three

Gyro d r i f t s r e f e r r e d t o as " g "- s en si ti ve d r i f t s ar e due t o mass un-balance along th e inp ut and spin-refe rence axes and end pl a t e mi sal ig n-ment producing a torque proport ional t o a c ce l er a ti o n p a r a l l e l t o t h e o ut -

pu t ax i s . S ince e i t he r t he i npu t o r spin -reference ax i s i s i n t he crossrange d i rec t ion f o r eachgyr o, were considered. No pd r i f t s on v eh ic le s SA -5 and

i t i v e t erms f o r eachions were pub1 ished f o r the "g"-sens t i v e

19



Several t e st s are made i n th e aboratory t o approxlmate the "g"-s e n s i t i v e g y r o d r i f t s .t he p re f l i gh t es t ima te .accurate of the predicted hardware errors due t o inconsistency (non-r e p e a t a b i l i t y ) of day t o day la bo ra to ry measurements. However, t h i s should

no t be in te rp re ted as a re f l ec t i on on the qua l i t y o f the gyros used w i thth e ST-124 pl at fo rm system. The d r i f t s determined i n th e lab oratoryo r f rom pos t f l igh t ana lyses a re p robab ly w i th in the accuracy o f themeasurements of ot he r types o f gyr os t h a t a re less accurate but sa id t obe more predictable.

An average o f these t e s t re su l t s i s publ ished asThese estimates are believed t o be t he l eas t

The "g"-sensi t ive d r i f t s determined from t he pos t f l i gh t ana l ysesc lo se l y agreed i n magni tude w i t h p red ic t ion s fo r eighteen of th e twenty-four terms shown. O f the rema in ing s i x te rms th a t were s i gn i f i c an t l yd i f f e r e n t i n magnitude, fo ur were much small er.

The s ign i f icance o f t he computed guidance er r o r terms shown i n Table4-111 Is presented i n Figure s 4-7 through 4-12.t r i b u t i o n fo r each hardware er r o r was computed by m ul t i p l i c at i o n oft he respec ti ve pa r t i a l de r i va t i ves times t he e r r o r so lut i ons . De l t ave lo c i t i es are shown a t outboard eng ine cu to f f , 3 5 0 sec, and S - I V stagecu to f f f o r each veh ic le . The t ime of 350 seconds was chosen f o r con-venience as an approximate midpoin t t o g ive an ind i ca t ion o f the ve lo c i t yer r or bui ldup. Tota l v e l oc i t y erro rs shown f or each po in t correspondt o re spect ive p oi nt s on curves presented i n Figure 4-1 through 4-6.

The ve loc i ty error con-

Figures 4-7, 4-8, and 4-9 ar e o f somewhat spec ial i nt e r e s t . TheseFigures show the ef fects of t h e e r r o r s o l u t i o n s f o r SA-5, S A - 6 , and SA-7,respec t ive ly ,p rox ima te t he ve loc i t y e r ro r p ro f i l e , as was done i n t h e Eva lu ati onReports, wi th onl y one er r or exceeding th e predi cted values.t i o n from t he observed v e l o c i t y e r r o r p r o f i l e c ou ld be w i t h i n t h e da tano ise level esp eci a l l y f o r pre l i min ary data . However, it would seemmore re a l i s t i c , when using f i n a l comparison data, t o perm it more fre e-dome o f e r r o r d i s t r i bu t i on and f i t t he es tabl i shed e r r o r p ro f i l e s . Theso lu ti on s shown i n Table 4-111 fo r the f inal analyses would produceth e observed ve lo ci ty er r or p r o f i l e s as shown i n Figures 4-1 through 4-6.

For veh ic les SA-5 and SA-6 it was n ot d i f f i c u l t t o ap-

Any devia-

Fi gu re 4-9 shows fo r SA-7 th e ve lo c i ty er ro rs associa ted wi th th e hard-ware error so lu t ion.smal ler than fo r th e two previous f l i g h t s . However, t h i s was not th ecase. A l l attempts t o ge t an unbiased po s t f l i g h t e r ro r so lu t i on i nd i ca t -ed ra th er large lev el in g and azimuth er ro r. Eventual ly, these misa l ign -ment err or s were found t o be due t o v i br a t i ons dur ing t hr us t bu i ldupcausing the p la t fo rm t o be s t ab i l i ze d a t an e rroneous p os i t i on a t l i f t o f fsignal when It became space-fixed. As a re su l t , f o r subsequent veh ic lesth e pl at fo rm was space-f ixed p r i o r t o i g n i t i o n and any movement due t o

vi br at io ns was sensed by the s t a b i l i z i n g gyros and correct ed.

SA-7 ve l o ci ty e r r or s were expected t o be much

20



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Figures 4-10 through 4-12 show the associated ve l oc i ty er ro rs r epre-sent ing error ana lyses f o r veh ic les SA-9, SA-8, and S A - I O , respec t ive ly .

(a .3 CORRELAT ION BETWEEN GU IDANCE ERRORS

Table 4- I -V shows a typical se t o f co r re la t ion coe f f i c ien ts be tween thevarious guidance system errors. The va lues a r e given t o the f i r s t decimaland were computed using the equation:

= a /a.a' i j i j I j

where : u represents th e e lements o f th e covar iance mat r ix associa t -ing v el oc i t y component e rr or s t o t he guidance systeme r r o r s .

i r e f e r s t o th e i t h row and j r e f e r s t o the j t h column.

Although .these values may vary between vehicles and also between computerruns due t o weight ing factors, th ree pa i r s of e r ro r t erms a re cons i s ten t l yh i g h l y ( p 10.75) cor re la ted , ( 1 ) b i a s i n X and sca le fact or i n X , ( 2 ) con-s t a n t d r i f t of X gyro and "g" d r i f t propor t iona l t o X, ( 3 ) c on st ant d r i f tof Z gyro and "g" d r i f t propor t iona l t o X.

5.0 CONCLUSIONS

.The purpose of a po s t f l ig h t ana lys is o f the gu idance system i s t o

es tabl i s h the conf idence I n p re f 1 ight error measurements and point out

areas where improvements may be made. The pr edi c te d and p o s t f l i g h tanalysis platform system errors are shown i n bar graph form i n F igures

5-1 and 5-2. The as te r isks over the pa r t i c u l a r e r ro rs in d ica t e th a tp red ic ted and ana lys is e r r o rs a re opposi te i n s ign .

Pla t form le ve l i ng and azimuth er ro rs were pred i c ted t o be wi t h i n 3a

t o erances of 0.005 and 0 ,O degrees, respect i e Iy .values observed on SA - 5 , SA-6, and SA-7 ar e bel ie ve d t o be r e s u l t s o fvi br at i on s durt ng t h r u s t buil dup. The plat for ms, which became space-f i x e d a t l i f t o f f s ign al, probably had moved due t o v ib ra t ions and the

gyro n u l l pos i t i ons were e r roneous ly o r ie n ted &a t l i f b f f . Beginningwi th SA-9 t he plat forms were.space-fixed p r i o r t o igni t ion and any torque

appl ied t o t h e pl at fo rm durin g th r u s t bui,ldup was sensed by th e gyrosand a torque equal and opposite i n s ig n was generated thus s t ab i l iz in g

th e pla tfo rm . The le v el i n g and azimuth e r r o r s shown f o r SA-9, SA-8 andS A - I O a r e w e ll w i t h i n t h e 3a to lerances.

The re'l a t i e Iarge

Fi gur es 5-3 and 5-4 show th e di f f e r enc es between computed and pre -d ic te d p la t f o rm sys tem.e r ro rs .d i f f e rence va lue i s re l a t i v e l y l arge , t he ana lys i s i nd i ca ted an e r ro r

In pr ac t i c a l l y every case where th e

29



.

o pp os it e i n s i gn t o t h e p r e d i c t i o n .good and especially good i f the s ign convent lon Is disregarded.magnitudes of the er ro rs determined from the post f l igh t and lyses weregenera l ly very c lose t o pred ic t idns .

The comparisons i n general ar e veryThe

Considerat ions have been give n t o inco rpor at in g guidance e r r or correc-t i on s ' in the f l i g h t equa t ions t o compensate f o r pref l ight measurments.Based on the results of the Saturn I Block I 1 guldance error analyses, it

I s f e l t th at e f f ec t i ve ly la rge accelerometer er ro rs cou ld be compensatedf o r i n the f l i g h t equat ions. However, gyro d r i f t rate compensation wouldbe quest ionab le unt i l some addi t i on al analyses are made using th e f l i g h tdata from vehicles carrying the ST-124 M p la t fo rms.

Table 5-1 shows the averages of th e guidance e r r or comparisons (a na ly si sThese averages fo r the accelerometer error measurements,inus pred ic t ion) .

b i as and scale fa ctor , show th a t p r e f l i g h t est imates were general i y good.

T h e i n i t i a l p l a t f o r m a lignment e r r o rs f o r th e la s t th re e vehic les werehe ld w i t h in t he 3a tolerances with an average value of -0.31 X I O - *

degrees.

The average difference of the constant d r i f t e r r o rs was s l i gh t l y l e ssthan the 30 value of 0.75 deg/hr.s e n s i t i v e d r i f t s was 0.07 deg/hr/g compared t o a,3a va lue o f 0.05 deg/hr/g.However, if he sign convent ion i s d isregarded, ..the averages of th edi ff er en ce i n magnitude would be 0.034 deg/hr and 0.038 deg/hr/g forconstant and "g"-sensi t ive d r i f t s , respect i ve ly .

The average d i f fe re nc e I n th e "g"-

The missions o f the Saturn I Block I I veh ic les d i d not r equ i re more

accu ra te guidance hardware. Howdver, based on t h e comparisons shownprev ious ly , th e use o f advanced qu a l i t y cont ro l techn iques i n se l ect ingt he in di v id ua l components o f t h e guidance system hardware alr ead y de-signed would insu re t he f u l f i l men t o f t he t erm ina l cond i t i ons t o h ighdegree o f accuracy. Cor rect ions f o r accelerometer er r or s coul d be pro-grammed i n t h e f l i g h t computer. Programming of c o r r e c t i on s f o r g yr od r i f t s would be somewhat quest ionable u n t i l t es t s show th a t ' 'g"-sensi-t i v e d r i f t s a re more repea table.

30



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1 .

2.

3.

4.

5 .

6.

Q)) REFERENCES

MPR-SAT-FE-64-15, A D r i l I . 1964. Results o f The F i f t h Sa tu rn ILaunch Vehi c le Test ' FI i g h t (W, -Sa tur n F I ig ht Evalu at ion Working

Group.

MPR-SAT-FE-64-16, August 7, 1964, Results o f The Sixth Saturn ILaunch Vehic le Test Fl ight @ , Saturn F l i g h t E valua t ion Work ingGroup.

MPR-SAT-FE-64-17, November 25, 1964, Results o f The Seventh Saturn ILaunch Vehic le Test F l ight m), aturn F l i g h t E valua t ion WorkingGroup.

MPR-SAT-FE-65-6, A p r i lLaunch Veh ic Ie Test F I

Group.

MPR-SAT-FE-65-6, J u l yLaunch Vehicle Test FIGroup.

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27, 1965, Results o f The N

g h t m, Saturn FI ig ht Eva

ghth Saturn Iua t on Working

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MPR-SAT-FE-65,14, September 4, 1965, Resu l ts o f The Tenth Saturn ILaunch Vehic le Test Fl ight 1, Saturn F l i g h t Eva lua t ion Work ingGroup. a

36



APPROVAL TM X-53338

SATURN I BLOCK - I I GU IDANCE SUMMARY REPORT

By R. A. Chapman

The inf ormat ion i n t h i s r epo rt has been reviewed fo r s e c u r i t yc lass i f ica t ion . Rev iew o f any in for mat io n concerning Department o fDefense o r Atomic Energy Commission programs has been made by t h e MSFC

Secur i t y C la ss i f i ca t io n O f f i ce r . The h ighest c la ss i f i c a t io n has beendetermined t o be Conf iden t ia l .

Th is r ep or t has been reviewed and approved f o r te ch ni ca l accuracy.

A k d ACar los C. HaafaodChie f , F I igh i Evaluat ion Branch

Operat ions Studies Div is ion

Director, Aero-AstrodynamicsLaboratory

37



D I STR IBUT ION

D r . Rees, DEP-T

I

Col. James, I-I/IB-MGR

D r . Speer, I-MO-MGR

-

RAD

M r . Weidner, R-DIR-

R-AERO

D r . Geiss le r , R-AERO-DIR

M r . Jean, R-AERO-DIR

M r . Lindberg, R-AERO-F

,h-. Hagood, R-AERO-FFM r . Stone, R-AERO-FMM r . McNa i r, R-AERO-PM r . W inch, R-AERO-DA

Mrs. Chandler, R-AERO-DAG

M r . Sheats, R-AERO-FFRM r . Chapman, R-AERO-FFR ( I O )

M r . Horn, R-AERO-DM r . Hart , R-AERO- G

M r . Baker, R-AERO-G

R-ASTR

D r . Haeusserman, R-ASTR-DIRM r . Fe r re l , R-ASTR-GSAM r . Nicaise, R-ASTR-NGIM r . Mandel, R-ASTR-G

M r . Mack, R-ASTR-SM r . D i gesu, R-ASTR-AM r . H. Thomason, R-ASTR-GM r . Moore, R-ASTR-N

M r . S . Seltzer, R-ASTR-NG

R-COMPM r . Houston, R-COMP-RRM ( 2 )

M S C

M r . Henson, MSC-EG-

EXTERNA LInternat ional Business MachinesSystem Design, Dep t. 229150 Sparkman Drive NW

Huntsvil le, Alabama 35808A t t n : R. E. Poupard ( 2 )

cc-PI-RM-M

MS-H

MS-IPMS-IL (8 )

MS-T

M r . Bland ( 5 )

M r . Sulette

Scientific and Technical Information Fac ility (25)

Attn: NASA Represe ntat ive (S-AK/ RKT)

P. 0. Box 33

College Park, Maryland 20740

C . A . Cassoly

Pro ject s Aeronautical Material Laboratory

N a v a l Aeronautical Engineering Center

Philadelphia 12, Pa.

Documents

TM X 53398 Saturn Block Guidance Summary Report Chapman