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A LGUIDANCE AND NAVIGATION

Approved: . -,:_ ",' , /L. Date: .'_ __ _1

JOHN M. DAHLEN, DIRECTOR, SYSTEM ENGINEERINGAPOLLO GUIDANCE AND NAVIGATION PROGRAM

Approved: __.'1_-_\ _ _.,-_.. Date: '' ]",1" ,/

RICHARDH. BATTIN,DIRECTOR,MISSIONDEVEL.APOLLOGUIDANCEANDNAV,GATIONPROGRA_

Approved:' _,//'/"f'/__C'L_ D.at e ..,_, CuL¢ 7

DAVIDG: .OAG.-_,_ECTOR$7APOLLOGUmANCE"ANDNArrATION PROCRAM

Approved: ,; _La_.'Z: . _, , "(,._,_ .__DEPUTJ_IRECTOR_, Date: ,'/-_" ,, _,RALPH R. RABAN.

INSTRUM ENTATION LA BORA TORY

R-527 (Rev. 2) *.'_.:.,'-.,

GUIDANCE SYSTEM OPERATIONS PLAN _ _lec__:-' :z* yea_a_FOR UNMANNED LM EARTH ORBITAL MISSIONSUSING

PROGRAM SUNBURST

SECTION 7 G&N ERROR ANALYSES

DECEMBER 1967

| __ $ 5 _ . . tit '_..'-'.=," . ."_T'C__0TI_ _ I_ K ..... r _*:_- ,,,'-' •

pIOHiSII_-D 6¥ LAW. "_k

CAMBRIDGE

INSTRUMENTATION

,,, ,,.,,.¢.u,..,,, L A B O R AT O R Y

ACKNOW LEDGEM ENT

This report was prepared under DSR Project 55 23850, sponsored by the Manned

Spacecraft Center of the National Aeronautics and Space Administration through

Contract NAS 9-4065 with the Instrumentation Laboratory, Massachusetts Institute

of Technology, Cambridge, Mass.

This document, ontains informati affecting the

national defens, the Unite, within the

meaning of the Esp Title 18, U.S.C.o

Sections 793 and e transmission or the

revelation of manner to an

unauthorized person is d by law.

• 4b

The publication of thi§._eport does not constitute approval by the National• 1 ' ,, . ,

Aeronautics and _pace Administration of the findings or the conclusions contained

therein. It is published only for the exchange and stimulation of ideas.

R-527(Rev.II)

GUIDANCE ANDNAVIGATIONSYSTEMOPERATIONSPLAN

MISSIONAS-204/LM - 1G&NERRORANALYSIS

ABSTRACT

The purpose of this document is to present a performance summary of

the Guidance and Navigation System in LM-1 and to compare this performance

with the requirements of Mission 204/LM-1. The calculated G&N errors

are based upon system performance as of November 26, 1967. More recent

data through December 1967 is included. This includes both IMU S/N 11 and

S_6. (The updated performance uncertainties derived using data up to this

time period, are shown for certain parameters. Other parameters could not

be derived because of system history and the lack of a large enough data

sample). The system performance of all the major components are shown.

The chapter contains an alignment summary of the G&N System. The one

sigma standard deviation for the accelerometer and gyro performance para-

meters are calculated. These uncertainties are utilized to calculate the

error in position and velocity. As a comparison, the Block II Performance

Specifications in the Master End Item (MEI) are also utilized to calculate

the mission position and velocity uncertainties. Utilizing those uncertainties

from the Block II Specifications show that updating before DPS 1 burn does

not reduce the perigee uncertainty in coast after APS 2 burn; in fact, it is

less with no update. With an update before the second APS burn, the perigee

uncertainty is slightly less than with no update.

December 1967

°..iii

7.0 G&N ERROR ANALYSIS

The Guidance System Operations Plan is published as seven separate

volumes (sections) as listed below:

Section 1 Pre-Launch

Section 2 Data Links

Section 3 Digital Auto Pilots

Section 4 Operational Modes

Section 5 Guidance Equations

Section 6 Control Data

Section 7 Error Analyses

This volume, Section 7 of the Guidance System Operations Plan, G&N Error

Analyses for Unmanned LM Earth Orbital Mission using Program SUNBURST was

based on the LM-1 missions.

The content

of this volume is arranged:

Introduction

Important Results of Error Study

Effectiveness of Navigational Update

Navigational Update Uncertainties

IMU Errors and Uncertainties

Accelerometer Error Coefficients

Gyro Drift Coefficients and S.M. Drift RateEquations

Stable Member Axes and Component OrientationRelative to S.M. Axes

Orientation of Stable Member Axes

Stable Member Pre-Launch Alignment Uncer°ta_nties

Effect of Stable Member Orientation on FlightUnc ertaintie s

PIPA Saturation Effects

Trajectory Data for Error Studies

Error Computation Procedures

Error Table Definitions

77 Hardware Data

7.1 IntroductionThe results of anerror study of the effectsof IMU componenterrors on LM

guidanceandnavigationfor the LM-1 mission are givenhere. Three navigationalor state vector updateswere considered. Thesewere:

a) No on-board (R, V) navigationalupdatethroughoutthe flight.b) Navigational updatejust before DPSIburn.c) Navigational updatejust before APS2burn.

The error studiesinclude the effectsof tracking uncertainties on the statevector updates. Updatingdid not apply to the alignmentof the IMU StableMember,sincethis is not realigned during the LM-1 flight.

The orientation of the StableMember, relative to inertial axes, assumedforthe error studies is obtained(seeFig. 7_l) by rotating:

40 deg.aboutXi, then-30 deg.aboutZSM

This sameorientation wasassumedfor the previous error study(Rev. 1 - Jan. 1967).This was chosento prevent the middle gimbal anglemagnitudefrom exceeding50degreesduring the mission.

The present error study is basedona mission plan providing for two DPSandtwo APSburns. The previous error studyhad assumedshort 3rd and4th APSburns.Thesehavenowbeenomitted from the mission plan.

This error studywas carried out for two different sets of IMU uncertainties.Theseare:

a) Block II IMU uncertainties (seeTable 7.5)b) IMU uncertainties basedon mostrecent systemtest measurementsand

compensationvalues(seeTable 7.5a)

Both sets as listed in the tables are onesigmauncertainties.

7.2 Important Resultsof Error StudyOneimportant purposefor the error studywas to determine the actual perigee

altitudes for the coastsfollowing the DPSand APSburns assumingG&Nguidanceof the burns with adversethree-sigma andone-sigma IMU uncertainties. Tables 7. 1and 7.2 summarizethe datafor Block II IMU uncertainties. Tables 7. la and 7.2asummarize the datafor most recently measuredIMU uncertainties. The dataforcoast following SIVBcutoff are, for the normal mission, indication uncertainties,since the LM G&Nonly monitors the launchto earth orbit trajectory. However, seesection 7.3a for the contingencycasewhereSIVBthrust fails. Thefollowing com-ments canbe made.

Horizontal planeat launchinstant

XSC(OGA)

TX I (along local vertical

at launch instant)

"\\_ ZS_VI_ YSM (I_A)

AXI shown positive

AZSIVl shown negative

XI" YI" ZI

Xc*_VI_ YSM, ZSM

XSC' YSC' ZSC

Launch Inertial Axes

IMU Stable Member Axes

Spacecraft Axes

NOTES: Orientation angles for Stable Member are AXI, AZSM

To align SM to the desired orientation, the SM axes are

initially set colinear with launch inertial axes. The SM

is then rotated about X I through the angle, AXI. Then it

is rotated about ZSM through the angle, AZSM.

For the error study AXI = 40 ° and AZSM -30 °

were assumed. AlsoAZ = 72 ° was assumed to be the

launch azimuth.

Fig. 7.1 Coordinate axes for 206 Launch Configuration

(This Page is UNCLASSIFIED)

IA XSM IA

Ifm___.OA

Z ,IA IA

OA ZSM

IA _/2_RA _AIA

Seconds of Arc

BDX 1 meru

BDY 1 meru

BDZ 1 meru

A DSRAX 1 meru

ADSRAZ 1 meru

ADIAX 1 meru

ADIAY 1 meru

ASF/SFX 10 3 PPM

ASF/SFY 103 PPM

ASF/SFZ 103 PPM

7XZ 1 sec

7Xy 1 sec

7yz 1 sec

?YX I sec

7Z X 1 sec

7Zy 1 sec

ABX 1 cm/sec 2

ABY 1 cm/sec 2

ABZ i cm/sec 2

_XZ 1 sec

ayz 1 sec

aZX 1 sec

-100.7

-53• 8

-25. 7

-44. 7

a = PIPA IA Misalignment

_' = IRIG IA Misalignment

• 04

wl _ w m_ -in

(This Pageis UNCLASSIFIED )

With three-sigma Block II IMU uncertainties, dangerously low perigee altitudes

(less than 65 n. miles) occur only after the 2rid APS burn and only for the naviga-

tional update before DPS1 burn case. Here the perigee altitude is 36 n. miles.

With no update the perigee altitude for the coast following the 2nd APS burn is

75 n. miles, while with update before this burn the perigee altitude is 76 n. miles.

With one-sigma Block II IMU uncertainties no dangerously low perigee altitudes

occur. The lowest perigee altitudes all occur after the 2nd APS burn and is lowest

(100 n. miles) for the update before DPS1 burn case. The prime contributors to

altitude uncertainties at this perigee are the Y and Z gyro bias drift uncertainties

as Table 7.32 shows. For the no update and the update before APS2 burn cases the

ADIAX and ADIAY drift uncertainties are also important contributors to lowering of

perigee altitude as Table 7.29 and Table 7.37 show. In all cases the accelerometer

uncertainties have a secondary effect on altitude uncertainties.

Tables 7.8, 7. 9, and 7.10 give detailed summary data, with Block II IMU un-

certainties, respectively, on uncertainties with no update, with update before DPS1

burn, and with update before APS2 burn.

At the end of this section will be found computer printed error tables. Tables 7.17

through 7. 37 are with Block II IMU uncertainties. Tables 7. 38 through 7.51 are

with most recently measured IMU uncertainties.

7.3 Effectiveness of Navigational Update

Table 7.1 and Table 7.2 using Block II IMU uncertainties, show that updating

before the DPS1 burn produces lower perigee altitudes than no updating for the

coasts following the DPS2/APS1 burns and the APS2 burn. Further, these tables

also show that updating before the APS2 burn produces perigee altitudes roughly

the same as those obtained for the no update case.

Table 7.1

Altitude Uncertainties and Perigee Altitude due to 3a

IMU Uncertainties for LM-1 Mission

(AXI = 40 °, AYIP = 0 °, AZSM = -30 ° )

with Block II IMU uncertainties

Mission

Launch

SIVB Cutoff

Cutoff

At Perigeein

FollowingCoast

C uto ff

At Perigeein

FollowingCoast

Update ?

Bef. DPS 1

Bef. DPSI

Bef. APS2

Bef. DPSI

Bef. APS2

Nominal

PerigeeAltitude

for FollowingCoast

n. miles

127. 7

Altitude

Adverse

Altitude

Uncert.

n. miles

105, 9

Altitude

Uncertainties

at Event

n. mile s

Altitude Uncertainties

n. miles

Max. In

FollowingCoast

Min. In

FollowingCoast

The principal reasons why updating fails to reduce altitude uncertainties

more are:

1) Large drift angles due to gyro bias drift since launch generates velocity

uncertainties during the APS2/APS1 and the APS2 burns considerably greater

than those generated during the earth launch to orbit trajectory.

2) Initial Stable Member azimuth misaIignments due primarily to the gyro

acceleration sensitive drift undertainties, ADIAY and ADIAX, cause large

altitude uncertainties after the DPS2/APS1 and APS2 burns. This is due to

the fact that the thrust direction for these burns is approximately normal to

the orbital plane. The initial azimuth misalignment causes the accelerome-

ters to sense incorrectly accelerations in the orbital plane thus contributing

to velocity uncertainties in the altitude-range plane.

More detailed comments on the effect of updating on altitude uncertainties

follow. The principal contributors to the altitude uncertainties at perigee in coasts

following APS1 and APS2 cutoffs are for all cases: NBDZ, NBDY, ADIAY and ADIAX

with NBDZ as the prime contributor. (These are respectively the Z and Y gyro bias

drift, and the Y and X gyro input axis accelerationsensitive drift uncertainties.) In

general the in-flight effect of the NBDZ and NBDY terms is considerably greater

than the initial misalignment effect. However, for the ADIAY and ADIAX terms the

initial azimuth misalignment effect is at least an order of magnitude greater than

the inflight effect.

Table 7.3 gives position and velocity uncertainties due to NBDZ for all update

cases. The drift angle due to NBDZ of 2 meru is 0.09 milliradian (mr.) at SIV_

cutoff, while it is about 2.5 mr. for the DPS2/APS! burns, and 3.3 mr. for the AP_2

burn. The velocity uncertainty in the altitude-range plane was 2. 1 ft/sec, at SIVB

cutoff. However, the velocity uncertainty increase due to the DPS2/APS1 burns was

16. 6 ft/sec., and the increase due to the APS2 burn was 19 ft/sec, in the same

plane. The effectively large Stable Member mi_alignment due to driftduring these

burns accounts for the large increase in velocity uncertainty during these burns in

the altitude-range plane and for the large increase in altitude uncertainty at perigee

in the following coasts. For the update before DPS1 burn case the velocity uncertainties

generated during the APS2 burn are added effectively to those generated in the DPS2/

APS1 burns with the result that the altitude uncertainty gets large at perigee after the

APS2 burn. However, for the no update case, the velocity uncertainties generated

during the DPS2/APS1 burns tend to cancel the uncertainties existing at burn ignition

with the result that altitude uncertainties at following perigees are not as large as

for the first update case.

Table 7. la

Altitude Uncertainties and Perigee Altitude due to 3_

(AXI = 40 ° , AYIP = 0 °, AZSM = -30 ° )

with most recently measured IMU uncertainties

Mission

Launch

SIVB Cutoff

Cutoff

At Perigeein

FollowingCoast

Cutoff

At Perigeein

FollowingCoast

Update ?

Def. DPSI

Def. DPS 1

Def. DPSI

Def. DPS1

Def. APS2

Def. DPSI

Def. APS2

Nominal

PerigeeAltitude

for followingCoast

n. miles

Altitude

Adverse

Altitude

Uncert.

n. miles

Altitude

Uncertainties

at Event

n. miles

Max. In

Follow ingCoa st

Min. In

FollowingCoast

Table 7. 2

Altitude Uncertainties and Perigee Altitudes due to I_

IMU Uncertainties for LM-I Mission

(AXI = 40 ° , AYIP = 0 °, AZSM = -30 °)

with Block II IMU Uncertainties

Mi s sion

Launch

SIVB Cutoff

Cutoff

At Perigee

Following

Cutoff

At Perigee

Following

Update ?

Bef. DPSI

Bef. APS2

Bef. DPSI

Bef. APS2

Nominal

PerigeeAltitude

for FollowingCoast

n. mile s

Altitude

Adverse

Alt it ude

Unce ft.

n. miles

Altitude

Unc ert aintie s

at Event

n. miles

Max. In

F ollowingCoast

Min. In

FollowingCoast

x m_upn P_l_LI imAIIC Ira, .... _ _T__ ____._

Table 7.2a

Altitude Uncertainties and Perigee Altitude due to 1_

(AXI = 40 ° , AYIP = 0°, AZSM = -30 ° )

with most recently measured IMU Uncertainties

Mission

La un ch

SIVB Cutoff

Cutoff

At Perigeein

FollowingCoast

Cutoff

At Perigeein

FollowingCoast

Update ?

Def. DPSl

Def. DPS1

Def. DPSI

Def. APS2

Def. DPS 1Def. APS2

Nominal

PerigeeAltitude

for FollowingCoast

n. miles

Altitudewith

Adversela

AltitudeUncert.

n. miles

110. 599.1

AltitudeUncertainties

at EventTime

n. miles

17.731.218.1

n. miles

Max. in

FollowingCoast

19.333.919.7

Min. in

Follow ingCoast

2.60.50.01

n dpumnl_:nnpnnm_, .... • I

Table 7. 3

Uncertainties Due to NBDZ = 2 meru

{Combined effects of uncertainties caused by initial S.M. mis-

alignment due to NBDZ and in-flight effect are given here}

La unc h

SIVB Cutoff

Cutoff

Ignition

Cutoff

At Perigee

in Follow-

ing Coast

Ignition

Cutoff

At Perigee

In Follow-

ing Coast

Update ?

Bef. DPSI

Bef. DPS1

Bef. APS2

Bef. DPSI

Bef. APS2

Bef. DPS1

Bef. APS2

l_'osition

Uncertainties - n. milesL ,-

Alt. Track Range

0.04 1.19 0.05

0. 18"

10. 66*

- 5.42

- 9.43

- 0.08

II. 51

- 8.81

- 2.56

- 30.67

- 40.03

- 28.24

- 37.30

- 60.28

- 78.31

- 26.81

Velocity

Uncertainties- ft/sec

Alt.0 Track0 i Range0

1.76 28.02 1.14

- 5.54

- 3.71

- 18.18

- 2.06

- 5.08

-1, 12

22. 77

- 44.53

- 5.46

- 2.18

-20.61

-51.86

-81.91

-55.52

*Initial misalignment and in-flight effects tend to cancel here.

Table 7.4

Uncertainties Dueto Initial StableMemberAzimuth MisalignmentAboutXI of 50Seconds

Launch

SIVBCutoff

DPS1Cutoff

Ignition

APS1Cutoff

At PerigeeIn Follow-ing CoastAPS2

Ignition

Cutoff

At Perigee

In Follow-

Update ?

Bef. DPS1

Bef. DPSI

Bef. APS2

Bef. DPSI

Bef. APS2

Bef. DPSI

Bef. APS2

Position

Uncertainties - feet

3, 076

-4,720

-1,978

Alt. Track

-1,471

1,190 -2,137

-1,609

802 -1,691

-3,582 - 137

1,241 - 18

91 - 72

573 - 26

-1,046 4,376

- 292 - 18

I, 023

-4,508

15,680

14, 490

13,372

13,341

4, 803

7, 52 9

18, 173

6, 905

1 7, 496

5, 42 4

41,871

11,387

Ve loc ity

Uncertainties ft/sec

Track Range

-5.66 -0.30

3.07 0. 97

0.03 0

-5.37 -1.19

-0.03 0

-3.92 -0.53

-0.15 -0.30

-3.88 -0. 50

0.06 3.03

-4.34 -0.88

-0.1 7 -0.79

-4.39 0.28

-I. 47 -0.18

-0.09 -0.34

4.27 -2.69

0.16 i 4.20

0.09 i 1.65k

_* -.._b_,_,i,.,i'll_l I1_,11II,.,ilP=,..-un-. • mnmr

• <D

{_11_ "I¥_)I.LITYN) }10}1}1_ :K_rlIlllY 3301}1_d

_A& n IPmil IP_, P &.J mr it _ .i. _

L,_ ...... . a I el 'lUll-

The ADIAY and ADIAX terms are important contributors almost entirely through

their effect on initial Stable Member misalignments. Table 7.11 with Block II un-

certainties shows that the azimuth alignment uncertainty is 3. 3 mr. (690 secs) for

both these terms, and that they are the dominant contributors. The effect of the

azimuth misalignments on altitude uncertainty may be explained with recourse to

Table 7.4, which gives uncertainties due to an initial Stable Member misalignment

about azimuth of 50 secs. For the update before DPS1 burn case this table shows

that, while track uncertainties dominate for the DPS1 burn, the dominant uncertain-

ties for the DPS2/APS1 burns are in the altitude-range plane. The reason for this

phenomenon is as follows: The thrust direction for the DPS2/APS1 burns and for

the APS2 burn are approximately normal to the orbital plane. (For the DPS1 burn

the thrust is in the orbital plane. ) This is shown in Table 7.16 which gives data on

the AV components (integral of thrust acceleration) in and perpendicular to the

orbital plane. With the thrust normal to the orbital plane the azimuth misalignment

of the Stable Member causes the accelerometers to sense or pickup accelerations

in the orbital plane contributing to velocity and position uncertainties in the altitude-

range plane. For the no-update case the uncertainties generated in the DPS2/APS1

and APS2 tend to cancel partially the uncertainties existing prior to the DPS2 burn

as Table 7.4 indicates.

Figure 7. 3 shows the effect of initial Stable Member azimuth error on perigee

altitude error for the coast following the APS2 burn for the no update and the two up-

date conditons. These curves show that for a given azimuth error the perigee error

is greater with update before DPS1 burn than with no update.

Figure 7.4 shows the effect of Stable Member drift angle due to the three gyro

bias drift terms on perigee altitude error for the coast following the APS2 burn for

the no update and the two update cases. The Block II bias drift rate uncertainty is

2 meru or 0.03 deg. per hour. At APS2 cutoff the accumulated drift angle about each

S.M. axis is 3.3 mr. or 0.2 deg. Figure 7.4 shows that the Y and Z gyro drift terms

have a much greater affect on perigee error than the X gyro. It also shows that the

perigee error is greater with update before DPS1 burn than with no update for all gyro

drift terms.

7.3a Errors in Perigee Following SIVB Cutoff

For the contingency where the Saturn SIVB stage fails to perform correctly,

it is planned that the LM-1 will be able to perform the orbit insertion maneuver.

Here IMU uncertainties will directly affect uncertainties in perigee for coast follow-

ing LM-1 orbit insertion cutoff. Table 7.14 gives data on perigee uncertainties

due to Block II uncertainties. This table also gives the IMU error values required

to produce a 1 n. mile perigee altitude error.

7.3b Errors in Perigee for Premature Cutoff of APS2 Burn

During the APS2 burn the instantaneous perigee (the perigee associated

with the free-fall coast if cutoff occurred at that instant} declines to the

critically low figure of 54 n. miles before rising again to the value of 128 n. miles

at normal cutoff. It is important to knc,w how large altitude uncertainties would

be at perigee if premature cutoff took place at the point where instantaneous

perigee is lowest. This occurs at 2?0 secs after ignition and ,157 secs

before normal cutoff. Tabley 7. 14a gives data on perigee uncertainty with

Block II IMU uncertainties for the critical premature cutoff time for the no

update and the two update cases.

7.4 Navigational Update Uncertainties

Navigational or state vector updates of the CSM computer's data on spacecraft

position and velocity have been proposed prior to the first DPS burn and also prior to

the second APS burn. These updates would be made on the basis of observations

made by the radar tracking stations of the Manned Space Flight Network (MSFN).

Uncertainties in the tracking data exist because of the presence of radar noise, bias,

uncertainties in station location and in the knowledge of earth gravitational constant.

The covariance matrices (one sigma) for the tracking uncertainties existing prior to

the above burns were obtained from "Error Analysis of MSFN Tracking Data for

AS-206A" by P.T. Pixley and D.H. Fessenden (MSC Internal Note No. 66-FM-60,

June 22, 1966, MSC, Houston, Texas).

The one sigma position and velocity uncertainties, derived from the diagonal

terms of the covariance matrices, are glen in the following table relative to local

vertical axes at burn ignition. The propagated tracking update uncertainties are

given near the bottom of all relevant error tables.

APS2 iPosition ncerttlVelocity ncertAlt. I Track Range Alt. Track

181 t 155 1,840, 2.18 0.31

5471411 2,102 I 2.15 0.40

Update Uncertainties at Burn Ignition

(ft/sec)I

Range I

0.88 I

0.49 J

7.5 IMU Errors and Uncertainties

IMU errors can classed into two groups. These are: (1) those errors that

the LGC (lunar module guidance computer) can provide compensation for, and

(2) those errors for which there is no compensation.

IMU errors are compensated as follows. The average error for the particu-

lar IMU component is first determined on the basis of system tests extending over

many months. The negative of the computed average error is then stored in the

LGC shortly before earth launch. Pre-launch and in-flight compensation is then

effected by means of stored programs in the LGC. The rms IMU component un-

certainties are then the unpredictable deviations of the actual instantaneous error

from the assumed average error.

Table 7.5 lists the Block II one-sigma IMU error uncertainties that were

assumed for the error studies in this chapter. These are the same as those given

on p. 3-25 of MEI No. 2015000, Part I, which lists Block II specifications for the

Apollo Command Module.

Table 7.5a lists the one-sigma IMU error uncertainties computed on the

basis of the most recent system test measurements.

The following IMU errors are errors that the guidance computer is equipped

to compensate for:

1) Accelerometer bias error

2) Accelerometer scale factor error

3) Gyro bias drift

4) Gyro input axis accel, sens. drift

5) Gyro spin ref. axis accel, sens. drift

These are defined and discussed in some detail in subsections 7.6 and 7.7.

The computer does not provide compensation for the following IMU errors:

1) Stable Member initial misalignment_ (those that are uncorrelated with

gyro drift)

2) Accelerometer input axis misalignments

3) Accelerometer acceleration-squared indication uncertainties

4) Gyro output axis acceleration sensitive drift

5) Gyro acceleration-squared sensitive drift

6) Gyro input axis misalignments

The subject of Stable Member initial misalignments will be covered in Section

7.10. It should be noted that those sources of initial S.M. alignment errors directly

due to gyro bias drift, to acceleration sensitive drift, and to accelerometer bias will,

of course, be compensated for.

Accelerometer input axis misalignments will be covered in the next subsection.

Table 7.5

Block II One-Sigma IMU Error Uncertainties

Accelerometer Errors

Bias Error ACB Yes

S.F. Error SFE Yes

Accel. Sqd. Ind. Error NC No

Input Axis Misalignment a No

G.yro Errors

Bias Drift NBD Yes

IA Accel. Sens. Drift ADIA Yes

SRA Accel. Sens. Drift ADSRA Yes

OA Accel. Sens. Drift ADOA No

IA Misalign. about SPA "YSRA No

IA Misalign. about OA 7OA No

Stable Member Alignment Errors

Prelaunch Azimuth .... No

Vertical .... No

Free-Fall All Axes .... No

RMS Uncertainty(after compen-

Error Compen- sation whenSymbol sated ? applicable)

ErrorUnits

0.20 am/sea 2

11 6 ppm

10 U g/g2

20 seas.

2 meru

8 meru/g

5 meru/g

1" meru/g

50 $ seas.

50 _ secs.

50"* seas.

5** sees.

20 secs.

IAsted value for ADOA is not a Block II uncertainty.value used for the error studies.

It represents a reasonable

The error values listed for S.M. prelaunch azimuth and vertical alignments are notthose listed in MEI No. 2015000. They represent present estimates for these mis-alignments.

NOTE: 2 meru = 0.03 deg/hour

0.2 cm/sec 2 = 0. 00656 ft/sec 2 = 2.04 (10 -4 ) g

50 seas = 0.242 mi_iradian = 0.242 (10 -3 ) radian

Table 7.5a

Most Recently Computed One-Sigma IMU Error Uncertainties

Accelerometer Errors

Bias Error

Scale Factor Error

Accel. Sqd. Ind. Error

Input Axis Misalignment

Gyro Errors

Bias Drift

IA Accel. Sens. Drift

SRA Accel. Sens. Drift*

OA Accel. Sens. Drift

Input Axis Misalignment

Stable Member Alignm. Errors

Prelaunch Azimuth

Prelaunch Vertical

ComputedError 1_

Symbol Uncertainties

Input Axes

A DSRA

0.08 0.06 0. i0

92 45 76

02 0.2 0.2

About Y About Z About X

About Z

About X

Input Axes

1.3 2.3

5.1 6.0

2.2 2.7

About Y About Z

About Y

About X

-19.2 +19.4 -115

About Z About X About Y

2cm/sec

meru/g

-128.0 +87 secs

Launch Inertial Axes

XI YI ZI

50 ........ secs

.... 5 5 secs

*Denotes that listed uncertainty value is based on present estimates and not on system

test measurements.

**Prelaunch azimuth alignment uncertainty of 50 secs is based on rss estimate related

to specifications, since gyro IA misalignment data was incomplete at time of table

preparation.

NOTE: Computed uncertainty data for accelerometers were based on compilation period,

June 27 - Nov. 26, 1967. Uncertainty data for gyros were based on compilation

period, June 14 - Nov. 26, 1967.

CO: tam'm--P::=:==

Both aceelerometer acceleration-squared indication and uncertainty and gyro

acceleration-squared sensitive drift are difficult and time-consuming to measure.

For this reason and because their effects on trajectory uncertainties are secondary,

they are not compensated for. The effects of vibrations operating through these un-

certainties and through rectification effects may well have a greater effect than that

produced by burn thrust or reentry drag accelerations. However, no attempt was

made to study vibration effects in this chapter.

Gyro output axis acceleration sensitive drift (ADOA) is a relatively difficult

error to measure. The value of 1 meru/g for ADOA is a reasonable estimate for this

uncertainty.

Gyro input axis misalignments affect trajectory uncertainties only in their

effect on Stable Member azimuth misalignment prior to earth launch alignment when

gyro compassing is used for azimuth alignment. They are the prime contributors to

the pre-launch azimuth alignment uncertainty (uncorrelated) of 50 secs.

Since none of the above IMU errors are compensated for, uncertainties are the

same as errors for this group.

7.6 Accelerometer Error Coefficients

Accelerometer bias (ACB) is defined as the indicated acceleration of the

accelerometer with zero input acceleration. Bias is positive when the indicated accel-

eration is positive. This bias is due to torques about the output axis of the PIPA.

Accelerometer scale factor error (SFE) is defined as the deviation in the actual

PIPA scale factor from the nominal scale factor divided by the nominal scale factor.

The scale factor itself is conventionally defined as a given number of cm/sec 2 per

pulse/sec, delivered to the computer. The scale factor error is positive when the

mesaured scale factor (in cm/sec 2 per pulse/sec or cm/sec per pulse) is greater

than the nominal. However, it should be carefully noted that when scale factor error

is thought of as the deviation of indicated acceleration from the input acceleration

divided by the input acceleration (where ideal scale factor would then be unity), the

above definition of positive scale factor error corresponds to an indicated accelera-

tion less than the input acceleration.

Aeeelerometer input axis misalignments are not compensated for. A positive

misalignment is a positive rotation of the input axis about the appropriate S.M. axis.

There are two misalignments associated with each accelerometer. The misalignment

of the Z accelerometer input axis about YSM is nominally zero by definition. (See

definition of Stable Member axes in Section 7.8) However, for earth prelaunch align-

ment of the Stable Member the alignment of the accelerometer, whose input axis is

in the horizontal plane, is considered to be perfect relative to the horizontal plane.

This, of course, assumes a zero bias accelerometer.

For the LM-1 earth launch Stable Member orientation (AXI = 40 °, AYIP = 0 °,

AZSM = -30 ° ) this means that, since ZIA is ideally horizontal (see Fig. 7.1), the

misalignments of ZIA about XSM and about YSM are both zero. The Block II rms

alignment uncertainty for each aceelerometer input axis is 20 seconds. Since the

misalignment of ZIA about YSM is zero, the misalignment of XIA about YSM must

be 28.3 secs. (That is, 28.3 secs. is the rss of the nominal misalignments of 20

secs. of ZIA and XIA about YSM.) Likewise, the misalignment of YIA about XSM

must be 28.3 secs, since misalignment of ZIA about XSM is zero. The misalign-

merits of XIA and of YIA about ZSM are computed on the basis of the following

equations:

Mlm. XIA about ZSM = 28.3 cos 2 (AZSM)

Mlm. YIA about ZSM = 28.3 sin 2 (AZSM)

where 28.3 is the rss of the nominal XIA and YIA misalignments about ZSM. Note

that if AZSM is zero (YIA horizontal), the first misalignment is 28.3 secs. and the

second is zero.

7.7 Gyro Drift Coefficients and S.M. Drift Rate Equations

Definitions for the gyro drift coefficients, NBD, ADIA, ADSRA, and ADOA

are given here. It is assumed in the following that the gyro is servo-controlled to

maintain the error signal at null.

NBD The normal excitation bias drift. It is non-acceleration sensi-

tive. NBD is positive when the S.M. drift rate is about the

positive gyro input axis (IA). A positive NBD is due to a nega-

tive torque about the output axis. The term BD is used to

designate gyro bias drift due to mechanical torques present prior

to gyro electrical excitation.

ADIA The acceleration sensitive drift rate due to gyro case

acceleration of one gravity along the input axis. It is positive

when the S.M. drift rate is about the positive gyro input axis

in response to a positive acceleration along the positive gyro

input axis. It will cause a negative torque about the output

axis. Internally this term is caused by a displacement of the

center of gravity with respect to the center of buoyancy of the

float along the positive SRA.

ADSRA The acceleration sensitive drift rate due to a gyro case accel-

eration of one gravity along the spin reference axis. It is

positive when the S. M. drift rate is about the positive gyro

input axis in response to a positive acceleration along the

positive gyro SRA. It will cause a negativetorque abouttheoutputaxis. Internally this term is causedby a displacementof the center of gravity with respect to the center of buoyancyof the float alongtheminus 1A.

AI_A The acceleration sensitivedrift rate dueto a gyro caseaccel-eration of one gravity along the outputaxis. It is positivewhenthe S.M. drift rate is aboutthe positive gyro input axisin responseto a positive acceleration alongthe positive gyroOA. TheADOAdrift coefficient is generally small relativeto the other drift coefficients. There is no computer compen-sation for the ADOAterms.

The following table gives the drift rates, WXSM, WysM, WZSM abouttheStableMember axes, XSM, YSM, ZSM, respectively, dueto the various gyro driftcoefficients. Figure 7.4 in the next sectionshowsthe orientation of the Block IIgyro axes relative to the StableMemberaxes. (Block I gyro axeshavethe sameorientation with the oneexceptionthat the Z gyro IA is along+ZsM.) The accel-eration components,AXSM, Ays M, AZSM, are positive with reference to S.M.axes. It is of interest to note that the correspondingdrift rate equationsforBlock I IMUs havethe samesigns with theexceptionthat NBDZcarries aplussign.

Drift Rate Gyro Drift Coefficientsabout

S.M. Axes NBD ADIA ADSRA ADOA

WXSM = NBDX +ADIAX(AxsM) -ADSRAX(AysM) +AIX)AX(AzsM)

Wys M = NBDY +ADIAY(AysM) -ADSRAY(AzsM) +ADOAY(AxsM)

WZS M = -NBDZ +ADIAZ(Azs M) +ADSRAZ(Ays M) +ADOAZ(Azs M)

7.8 Stable Member Axes and Component Orientation Relative to S.M. Axes

IMU Stable Member axes are defined by the following equations:

YSM = unit (IGA)

ZSM = unit (component of ZIA in plane normal to YSM)

XSM = unit (YSM x ZSM)

In words YSM is identical with the direction of the IMU Inner Gimbal axis.

ZSM is defined by that component of the Z PIPA input axis which lies in the plane per-

pendicular to YSM.

The orientation of the three S.M. gyros (size - 25 IRIGs) for the Block II IMU

system are shown in Figure 7.4 relative to the positive Stable Member axes, XSM,

YSM, ZSM.

OAy XSM

SRA y _gyro

_.____ S RA X

X gyro

Z gyro

axe s.

Block IIIMU Gyro Axes Relative to S.M. Axes

Figure 7.4

The following table gives the orientation of gyro axes relative to Stable Member

YSM -ZSM XSM

Z -ZSM -YSM XSM

The input axes of the X, Y, Z accelerometers (PIPAs) lie respectively along the

positive XSM, YSM, ZSM axes

7.9 Orientation of Stable Member Axes

The orientation fo the IMU Stable Member axes (XSM, YSM, ZSM) relative to

launch inertial axes are shown in Fig. 7.1. The launch inertial axes, X I and ZI,

define the initial reference trajectory plane as well as the initial pitch plane. The

axis, Z I, is in the horizontal plane at launch instant and oriented to the nominal

launch azimuth of 72 ° from north.

The orientation of the StableMemberrelative to launch inertial axesis mostconvenientlydescribedby the Euler rotation angles, AXI, AYIP, andAZSM. (See

Fig. 7.1) To reach the desired orientationthe S.M. is first rotatedaboutXI throughthe angle, AXI. ThenaboutYI (prime) throughthe angle,AYII:', andfinally aboutZSMthroughthe angle, AZSM. For the presenterror studythe StableMemberorien-tationangles assumedwere:

AXI = 40 ° , AYIP = 0°0 AZSM = -30 °

The corresponding IMU gimbal angles at launch were:

Aig = 0°, Amg = 30 ° , Aog = 140 °

7.10 Stable Member Pre-Launch Alignment Unce rtainties

The principal contributors to Stable Member pre-launch alignment uncertain-

ties are:

1) Effects of gyro IA alignment uncertainty on S.M. azimuth alignment.

(Called S.M. misalignment (uncorrelated) in error tables. )

2) Effects of gyro drift rate uncertainties on azimuth alignment of the Stable

Member. (Gyrocompassing to align the S.M. about azimuth is assumed.)

3) Effects of accelerometer bias and scale factor uncertainties on vertical

erection of the Stable Member.

The ways in which IMU component uncertainties contribute to pre-launch align-

ment uncertainty are described by the alignment error equations given in Table 7.6.

They are grouped under: 1) gyrocompassing errors, and 2) vertical erection errors.

The symbol, 4, is used to denote the Stable Member misalignment about the inertial

vector indicated by the subscript. For example, _XI is the S.M. misalignment about

X I. Note that misalignment about azimuth = -_XI" Second order terms are omitted

in these equations. These assume that AYIP = 0 and that Block II IMUs are used.

Table 7.11 gives data on initial azimuth alignment uncertainties due to gyro

drift uncertainties.for several different Stable Member orientations. The data were

computed, of course, from the equations of Table 7.6. Table 7.11 shows how

markedly the azimuth misalignment increases as AZSM goes from zero to -30 degrees

due to the effect of the gyro acceleration sensitive drift terms.

7.11 Effect of Stable Member Orientation on Flight Uncertainties

Table 7.12 for position and velocity uncertainties at SIVB cutoff shows how

the track uncertainty is more than doubled as AZSM goes from zero to -30 degrees

due to the effect on azimuth misalignment.

Table 7.6

Initial Stable Member Alignment Errors

G_yro-Compas sing Errors

X gyro drift effects

_Xl = NBDX sin (AZSM) cos (AZ - AXI)/Wh

+ADIAX(g) sin (AZSM) cos (AZSM) cos (AZ - AXI)/Wh

+ADSRAX (g) sin 2 (AZSM) cos (AZ - AXI)/Wh

Y gyro drift effects

_XI = NBDY cos (AZSM) cos (AZ - AXI)/Wh

-ADIAY (g) sin (AZSM) cos (AZSM) cos (AZ - AXI)/Wh

+ ADOAY (g) cos 2 (AZSM) cos (AZ - AXI)Wh

Z gyro drift effects

_XI = -NBDZ sin (AZ - AXI)/Wh

-ADSRAZ (g) sin (AZSM) sin (AZ - AXI)/Wh

-ADOAZ (g) cos (AZSM) sin (AZ - AXI)/Wh

Vertical Erection Errors

_YI = -ACBZ/g (cos (AXI) + sin (AZSM) sin (AXD)

-ACBY/g cos (AZSM) sin (AXI)

-(SFEY + SFEX) (sin (AZSM) cos (AZSM) sin (AXI))

_ZI = -ACBZ/g (sin (AX[) - sin (AZSM)cos (AXI))

+ACBY/g cos (AZSM) cos (AXI)

-(SFEY- SFEX) (sin (AZSM) cos (AZSM) cos (AXI))

where Wh = WIE cos (Lat) (earth's rate horizontal component)

AZ = azimuth angle of Z[ from north

g = acceleration due to gravity

NOTE: Aximuth alignment errors due to vertical gyro drift rate effect are not

included in above equations.

'I_ • --- ---- --. I • ilrll_- --

Table 7. 13 gives summary data on S.M. drifts and misalignments for various

event times throughout the LM-1 flight.

7.12 PIPA Saturation Effects

Because of the possibility that one of the IMU accelerometers (PIPAs) might

saturate during the earth launch trajectory, a special study was made of this problem.

For the S.M. orientation of AXI = 40 ° and AZSM = -30 ° the maximum accelera-

tion sensed during earth boost was 3.06 g's by the Y PIPA. This is sensed shortly

before S1B cutoff. Since the PIPA does not saturate unless the input acceleration

exceeds 3.3 g's, it is clear that under nominal conditions there will be no PIPA

saturation. However, with non-nominal conditions or with other Stable Member orien-

tation, the peak acceleration input could well exceed the PIPA saturation level. This

is indicated by the fact that the maximum vector acceleration reached during boost is

4.2 g's.

Although the Y PIPA will not saturate with the above S.M. orientation, a study

was made with the assumption that the Y PIPA had actually saturated at 2.82 g's.

This was 85% of its nominal saturation level (3.3 g's) and 92% of the peak acceleration

(3.06 g's) sensed by the Y PIPA. With this saturation level the AV lost by the Y

PIPA was 15.1 ft/sec.

Table 7.15 gives the indication uncertainties at SIVB cutoff and subsequent

events due to this particular AV loss. Comparison of these uncertainties with the

position and velocity uncertainties due to one-sigma IMU uncertainties given in Table

7.7 shows that a AV loss exceeding 15 ft/sec cannot be tolerated. Table 7.15 was

prepared for an earlier revision of this chapterp hence the slight discrepancies in

trajectory event times.

7.13 Trajectory Data for Error Studies

Error studies were made on the basis of trajectory data furnished in Volumes

I and II of "Apollo Mission AS-206 Spacecraft Operational Trajectory" prepared for

MSC-Houston by TRW Systems, (Vol. I date was Feb. 1967, Vol. II date was April

1967.)

Table 7.16 summarizes the trajectory data significant from the error study

point of view. Delta V (AV) is the integral of thrust acceleration.

7.14 Error Computation Procedure

The position, velocity and other uncertainties given in the error tables were

computed as follows. Approximate error equations describing the effect of IMU

component errors on acceleration indication error were incorporated in a computer

program. These equations included the effect of the position error on the computa-

tion of gravity. Through two successive integrations, errors in indicated trajectory

position and velocity could be obtained. The assumptions underlying the use of tbese

equations were (I) the errors were small relative to the parameters being measured,

and (2) the IMU component errors were statistically independent of each other.

Computation of the above errors required as inputs to the main computation

program two sets of vectors, one for spacecraft acceleration and the other for its

position. These were generated in a separate program where a nominal trajectory

was simulated. At significant events, such as powered trajectory cutoff, detailed

error printouts were made.

Perigee altitudes were computed as follows. For different points in coast

following burn cutoff the rss of the altitude uncertainties due to IMU uncertainties

propagated to that point in orbit was subtracted from the nominal orbit altitude to

obtain the altitude with adverse rss uncertainties. The point in orbit where this alti-

tude was at minimum was termed the altitude of closest approach or the perigee

altitude with i_ uncertainties. A spherical earth was assumed. The same proce-

dure was followed with 3_ uncertainties.

7.1 5 Error Table Definitions

Definitions of Local Vertical Axes - Most of the error tables give position and

velocity uncertainties relative to actual local vertical axes at nominal event time.

(Indicated local vertical axes are used at SIVB cutoff and in following coast.) Note

that actual local vertical axes are displaced from nominal local axes by the angle sub-

tended by the range error. (In previous reports the uncertainty tables were given

relative to nominal local vertical axes. For large range uncertainty the altitude rate

uncertainty also becomes large when expressed relative to nominal local axes.)

Altitude Outward along R at event time

Track Along V × R

Range Along Altitude × Track

Symbols for IMU Uncertainties

Accelerometer Bias Uncertainty

ACBX X accelerometer bias, etc.

CM/S. SQ. centimeters/see 2

Aeeelerometer Scale Factor Uncertainty

SFUX X aecelerometer scale factor uncertainty, etc.

PPM parts per million

Accelerometer Acceleration-Squared Indication Uncertainty

NCXX X accelerometer accel, squared indic,uncert., etc.

MG/GSQ micro-gs/g squared

Gyro Bias DriftNBDXINITNBDXFLGTNBDXCOMBMERU

Effect on initial S.M. misalignmentEffect of X gyrodrift during burnTotal or combinedeffects of K gyro bias driftMilli-earth rate unit = 0.015deg/hour

Gyro Acceleration SensitiveDriftADX-Terms RSSof uncertaintiesdueto X gyro's ADIAX, ADSRAX,

andADOAXdrift uncertainties. Uncertainty values for

ADIAX and ADSRAX are given in position and velocity

uncertainty tables. (See Section 7.6 for gyro drift rate

definitions. )

MERU/G Milli-earth rate unit/g = 0. 015 deg/hour/g

Gyro Acceleration Squared Sensitive Drift

ADIXX X gyro accelerationsquared sensitive drift due to

acceleration along its input axis

ADSYY Y gyro accelerationsquared sensitive drift due to accel-

eration along its spin reference axis

ADIZZ Z gyro acceleration-squared sensitive drift due to accel-

eration along its input axis

MERU/GSQ Milli-earth rate unit/g 2 = 0.01 5 deg/hour/g 2

Table 7. 7LM-1 Mission Uncertainty Summarywith Block II IMU Uncertainties

Launch

SIVBCutoff

Cutoff

Ignition

Cutoff

At Perigee

in FollowingCoast

Ignition

Cutoff

At Perigee

in Following

Update ?

Bef. DPS1

Bef. DPSI

Bef. DPS1

Bef. APS2

Bef. DPS1

Bef. APS2

Bef. DPSI

Bef. APS2

RSS Position

Uncertaintyn. miles

Track Range

23.8 213.9

0.2 66.0

RSS Velocity

Un certainty

ft/sec

0.4 5.6

3.7 16.6

0.03 0.03

5.6 8.2

0.6 0. i

4.4 7.0

2.9 0.6

4.3 7.3

16.7 1.0

6.0 5.4

1.1 0.5

0.1 0.1

3.8 12.9

4.2 23. O

1.3 O.2

17.4 i0. 1

Track Range

125 I 33

104 32

123 31

136 93

12 173

Launch

Table 7.8

LM-1 Flight Uncertainties With No Navigation Update

with Block I! IMU Uncertainties

Launch

Altitude RSS Position

above earth Uncertainties

with ad- n._ milesverse rss --I

uncertain- AI_. i_a_ Rangeties

n. miles I,|

0 --- 0 0 0 0 0 0

RSS Velocity]

Uncertainties:

ft/sec

Alt. Track Range

SIVB Cutoff 591 87.7 0.4 5.6 0.4 10 132 9

At perigee

DPS1 ignit.

DPS1 cutoff

591 87.7 0.4 5.6 0.4 10 132 9

14,394 112.6 3.8 16.1: 68.8 14 77 31

14,440 112.1 3.7 16.6 69.2 18 72 29

DPS2 ignit.

DPS2 cutoff

16,606 164.0 5.6 8,2 64.2 9 125 33

17,334 163.0 4.4 7.1 57.6 38 99 28

APS1 cutoff

At perigee

APS2 ignit.

APS2 cutoff

At perigee

17,340 163.0 4.4 7.0 57.6 38 99 27

17,361 162.9 4.3 7.3 57.4 38 98 27

22,412 163.8 6.0 5.4 64.3 29 104 32

22,843 165.9 3.8:12.9! 59.0 82 123 31

25,774 108.8 17.4 10.1123.8 85 136 93

Other RSS

Uncertainties*

(u) V (U)7 (U) rNCft/sec ideg. deg.

i i ,.

9.0 0.02 0.31

:31. 1 0.03 0. 31

:29. 3 0.04 0.31

33.2 0.02 0.31

27.6 0.08 0.25

27. 5 0.09 0.25

26. q 0.09 0.25

32.0 0.07 0.25

31.5 0. 19 0. 35

93. 1 0. 19 0.35

_(U)V - uncertainty in inertial velocity magnitude

(U)7 - uncertainty in inertial flight path angle

(U)INC - uncertainty in orbit inclination

Table 7.9

LM-1 Flight Uncertainties With Navigation Update

Just Before DPSI Ignition with Block II IMU Uncertainties

Altitudeabove earth RSS Position RSS Velocity

Time with ad- Uncertainties I Uncertaintiesfrom verse rss n. miles ft/secLaunch uncertain-

secs. tiesn. miles Alt. TrackRange Alt. rracl Knge

Other RSSUncertainties_, -"

(U)V (U)_ (U)_NC

Launch

SIVB cutoff 591 (See Table 7.8)

At perigee 591

DPSI ignit.

DPS1 zutoff

DPS2 ignit.

DPS2 cutoff

14,394 116.4 0.031 0.03 0.30 2.2 0.3

14,440 115.9 0.03 0.03 0.31 2.2 1.0

16,606 168.9 0.56 0.08 0.64 1.2 0.8

17,334 164.6 2.84 0.591 2.09 54.9 6.6

0.9 0.9 .005 .001

2.8 2.8 .003 .002

20.6 20.6 .13 .017

APS1 cutoff

At perigee

APS2 ignit.

APS2 cutoff

At perigee

17,340 164.5 2.89 0.60 2.10 55.5 6.7

18,586 153.2 16.67 1.0120.13 59.7] 3.5

22,412 168.7 1.05 0.48 96.07 31.9 7.6

22,843 165.3 4.2222.9691.48 116.7_.5

25,774 99.8 29.9523.7721& 9 105.611.7

20.6 20.6 .13 .017

82.4 82.4 .14 .017

25.6 25.6 .07 .019

35.0 35.0 .25 .381

173.11172.9 .24 .381

(U)rNC

- uncertainty in inertial velocity magnitude

- uncertainty in inertial flight path angle

- uncertainty in orbit inclination

Launch

SIVB cutoff

At perigee

DPS 1 ignit.

DPS1 cutoff

DPS2 ignit

DPS2 cutoff

!APS1 cutoff

!At perigee

APS2 ignit.

APS2 cutoff

At perigee

TimefromLaunch

14, 394

14, 440

16,606

17, 334

17, 340

17, 361

22,412

22,843

25,588

Table 7.10

LM-I Flight Uncertainties With Navigation UpdateJust Before APS2 Ignition with Block IIIMU Uncertainties

Altitude

above earth RSS Velocitywith ad- Uncertainties

verse rss ft/secuncertainties

n. miles Alt. Tra Rnge

RSS PositionUn ce rtaintie s

n. miles

Alt. rrad_ Rang_

Other RSSUncertainties*

(u)v (u)_ DINC

(See Table 7.8)

169.7 0.09 0.07 0.35 2.1 0.4 0.5 0.5 .001 .001

168.4 1.31 0.22 0.9146.5 5.0 25.825.8 .ii .012

110.7 16.6 0.25!66.0 51.9 5.088.388.3 .12 .012

(U)INC

uncertainty in inertial velocity magnitude

uncertainty in inertial flight path angle

uncertainty in orbit inclination

Table 7.11

Initial Azimuth Alignment Uncertainties Due to Gyro DriftRate Uncertainties For Different Stable Member Orientations

Source

ADSRAX

A DOAX

A DIAY

ADSRAY

A DOAY

ADSRAZ

One SigmaUncert.

2 meru

8 meru/g

5 meru/g

1 meru/g

8 meru/g

5 meru/g

1 meru/g

8 meru/g

5 meru/g

1 meru/g

S. M. AnglesAXI =

AZSM =

Alighment Uncertainty about Azimuth -millirad.

0.146 2. 162

0.702 0.702

-2. 162 0.146

0. 583 0

0 -i. 081

0 1.756

O. 351 0

0 -0. 583

-i. 081 0

2. 623 3. 137

-1.205

0. 583

-0.602

-0.351

-2.162

-1.217

0. 439

1. 217

0. 263

2. 702

-0. 936

40o-30 °

-0.964

-1.205

-3.339

0. 723

-0.522

NOTE: I. The assumed drift rate uncertainties are Block If.

2. These alignment uncertainties do not include the vertical gyrodrift rate effect.

0_-_ c_ c_ c3 c3 c_

0 "'_ 0 _I

_ _ _'_ O0

_._ _ o _ o _0._ ¢j "_ c_1 c.D c_1 _t _ _0

_ _ c3 _ _3 c3

o_ --_

_ 0 0 0 0 0

_o.._O

r--'+<_r_

tmm 0e'J

_ F.,;.I_.+.,

_ t_'_ lJ_

0 "_ _ L+'"

d d ,q d

_ d d d

d d _4 d

r/l _,1 ,-..i ._ u'_

_ d _4 d _4

,,.a _ o o oB ++B _ _ -"-'• ,,.-4

_ m m m

d _,i ,d ,d

M _ _ d

d d d _"

d d d d

,_ d d d

d d d d

p.+.,-4

o ._ _

_ m m m

Table 7.14

Perigee Errors in Coast Following Earth Orbit

Insertion with Active (Contingency Case) LM-1 Guidance

ResultingAssumed Perigee

IMU Error Value ErrorError (Block II) (feet)

MLMXI 50 secs 35

MLMYI 5 secs -107

MLMZI 5 secs -3

MXAY** 28.3 secs -470

MXAZ 21.2 secs 469

MYAX 28.3 secs 487

MYAZ 7.1 secs -61

ACBX 0.2 cm/sec 2 602

ACBY 0.2 cm/sec 2 1,353

ACBZ 0.2 cm/sec 2 1,033

SFEX 116 PPM -99

SFEY 116 PPM -640

SFEZ 116 PPM -139

NBDX 2 meru -58

NBDY 2 meru 174

MBDZ 2 meru -262

ADIAX 8 meru/g -180

ADIAY 8 meru/g 207

ADIAZ 8 meru/g 332

ADSRAX 5 meru/g 8

ADSRAY 5 meru/g 212

ADSRAZ 5 meru/g 516

IMU Errorthat results in a

1 n. mile Perigee Error

284 secs

366 secs

274 secs

353 secs

706 secs

2.0 cm/sec 2

O. 9 cm/sec 2

1.2 cm/sec 2

7, 130 PPM

1, 100 PPM

5, 060 PPM

208 meru

70 meru

46 meru

270 meru/g

235 meru/g

147 meru/g

3, 900 meru/g

143 meru/g

39 meru/g

_'MLMXI denotes S.M. misalignment about XI, etc.

**MXAY denotes X accelerom. IA misalignment about YSM.

Given errors are for combined initial MLM and in-flight effects.

__ ....... ImImI | I_

Table 14a

Instantaneous Perigee Uncertainties for Premature APS2 BurnCutoff with 1 _ Block II IMU Uncertainties for No Update, andfor Updates before DPS1 Burn and before APS2 Burn.

Time fromAPS2 Burn

Ignitionsecs

NominalInstantaneousPerigeeAltituden. miles

107, 7

Attitude Uncertainty atInstantaneous Nominal Perigee in n. miles

No Update

With Update BeforeDPS1 Burn Ign.

With Update BeforeAPS2 Burn Ign.

Note: Altitude uncertainties are computed for nominal perigee location in orbit.Computations are approximate in that the effect of altitude uncertainties on perigeelocation were not considered as they were in Tables 7.1 and 7.2.

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Error Tables with Block II IMU Uncertainties

Table 7. 17

Table 7. 18

Table 7.19

Table 7.20

Table 7.21

Table 7.22

Table 7.23

Table 7.24

Table 7.25

Table 7. 26

Table 7.27

Table 7.28

Table 7.29

Table 7. 30

Table 7.31

Table 7.32

Table 7.33

Table 7.34

Table 7. 35

Table 7. 36

Table 7. 37

SIVB Cutoff Indication Uncertainties

SIVB Cutoff Indication Uncertainties (AD Terms)

IMU S.M. Misalignments and Drift Angles at SIVB Cutoff

Flight Uncertainties at APS1 Cutoff-No Update

Flight Uncertainties at

Flight Uncertainties at(AD Terms)

Flight Uncertainties atBefore DPS1 Burn

Flight Uncertainties atBefore DPS1 Burn (AD

Flight Uncertainties atTerms)

Flight Uncertainties at(AD Terms)

Flight Uncertainties atBefore DPS1 Burn

APS1 Cutoff-No Update (AD Terms)

APS1 Cutoff with Update Before DPS1 Burn

Perigee After APS1 Cutoff with Update

Perigee After APS1 Cutoff with UpdateTerms)

APS2 Cutoff-No Update

APS2 Cutoff-No Update (AD Terms)

Perigee After APS2 Cutoff-No Update

Perigee After APS2 Cutoff-No Update (AD

APS2 Cutoff with Update Before DPS1 Burn

APS2 Cutoff With Update Before DPS1 Burn

Perigee After APS2 Cutoff With Update

Perigee After APS2 Cutoff With UpdateBefore DPS1 Burn (AD Terms)

Flight Unce rtainties at APS2 Cutoff with Update Before APS2 Burn

Flight Uncertainties at APS2 Cutoff With Update Before APS2 Burn(AD Terms)

Flight Uncertainties atBefore APS2 Burn

Flight Uncertainties atBefore APS2 Burn (AD

Perigee After APS2 Cutoff With Update

Perigee After APS2 Cutoff With UpdateTerms)

Error Tables With Latest Measured IMU Uncertainties

Table 7.38

Table 7.39a

Table 7.39b

Table 7.40

Table 7.41

Table 7.42

Table 7.43

Table 7.44

Table 7.45

Table 7.46

Table 7.47

Table 7.48

Table 7.49

Table 7.50

Table 7.51

SIVB Cutoff Indication Uncertainties

IMU S.M. Misalignments and Drift Angles at SIVB Cutoff

IMU S. M. Misalignments and Drift Angles at SIVB Cutoff

Flight Uncertainties at APS1 Cutoff - No Update

Flight Uncertainties at APS1 Cutoff With Update Before DPS1 Burn

Flight Uncertainties at Perigee after APS1 Cutoff with UpdateBefore DPS1 Burn

Flight Uncertainties at APS2 Cutoff - No Update

Flight Uncertainties at Perigee After APS2 Cutoff - No Update

Flight Uncertainties at Perigee After APS2 Cutoff - No Update(AD Terms)

Flight Uncertainties at APS2 Cutoff with Update Before DPS1 Burn

Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore DPS1 Burn

Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore DPS1 Burn (AD Terms)

Flight Uncertainties at APS2 Cutoff with Update Before APS2 Burn

Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore APS2 Burn

Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore APS2 Burn (AD Terms)

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_ I I I II

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I I I I I

leo ell

III III II III

-_ ._ _ _ _;2 -_

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( This Page I._I_CLAS_'! FI_rlT)

• /,_ I, II

• • l

LAUNCH VERTICALI

Z_V : 1.50 FT/SEC

AT : 37 SEC

APOGEE CHANGE, IN PLANE BURN

ULLAGE 8SEC

TIG N : 4HR IMIN

LAUNCHVERTICAL

ULLAGE 8 SEC

TIG N : 4 HR 43 MIN

L_V : 7000

AT : 720SEC

&V = 59 FT/SEC

AT : 5. SEC

.... ,_ I ULLAGE 13SEC

TIG N : 6HR 13MIN

VERTICAL /

AV : 6650 FT/SEC

AT : 435 SEC

Fig. 7-6 Apollo 5 LM Orbit and Burn Sequence

--=Ak |m=LgnLiqp| & • -- .4

ayzayx

X PIPA

Y PIPA

Z PIPA

PIPA ORIENTATIONS

DEFINITION OF POSITIVE SENSE

PIPA INPUT-AXIS MISALIGNMENTS

with respect to

IDEAL STABLE MEMBER AXES

Fig. 7-7

.,ty2- .... -::--,_

IIDF_,,Ar_,IjlHIO in i I i IA,_u_.

PIPA Misalignments from Ideal Stable Member Axes (See Fig. 7-7 for Definition

of Positive Sense)

Angle in Sec

Term IMU 6 IMU 11

_XY +3 +37

aXZ -6 +36

_YZ - 10 +7

_YX -4 -22

_ZX +20 -20

c FL Z

DEFINITION OF" Pr}SITIVE SENSE

GIMBA 1, AXIS "_RTIIr)(Ir)NA I.ITY

OUTER GIMBAL AI,IGNMI-TNq"

with respect ICASE Mc)I:NTING ,kI,I(;N.MENI

Fig. 7-8

_%__ , ,wa_ll-_R_ll I/'111,,.

Gimbal Axis Orthogonality Errors and Outer Gimbal Misalignment from Case-

Mounting Axes (See Fig. 7-8 for Definition of Positive Sense)

Angle in Sec

Term IMU 6 IMU 11

• IGA +23 +21

• MGA +5 - 2

CFL Y +28 +3

CFL Z -2 +5

X IRIG

Y IRIG +YsM -ZsM

Z IRIG -ZsM +XsM -YsM

IRIG ORIENTATION

Block II G&N

DF_II_I/_!QN Ota PO._ITI_E ,SENSE

IRIGi INP U_]-AX_S _I I]_ LIGNM_ENtTSwith respect to

IDEAL STABLE MEMBER AXESJ

Fig. 7-9

_L mnmiz_._L nqllm i _rmr--

"lw_II[-----;-I-1 I I,l"l, I--

IRIG Misalignments from Ideal Stable Member Axes (See Fig. 7-9 for Definition

of Positive Sense)

Angle in Sec

Term IMU 6

"YXY - 19

'xz -5o

_'YZ +19

_YX - 12 8

7ZX - 115

_ZY +87

IMU 11

J.A., n n.l hp, L LTi Al .......*_,,%_i _ u .......

G&N 603

IMU S/N 6

2AP168

2AP163

2AP213

IMU S/N 11

2AP196

2AP249

3AP301

A n --m

Dictionary of Terms

AV ACC

IG CDU PROBLEM

PRE ACC

RESIS CHG

s/cSCK

SF, SFA

Acceptance of Data

After Cooldown

Acceleration Sensitive Drift Due to Acceleration along the OA

Average of Acceptance Data

Average of Retest Data

12 Day Storage

Bia_ Adjusted

Binary Current Switch

Component Re qualification

Post Cooldown

Component Verification

Degaussed IRIG

Degaussed

Guidance & Navigation System Measurement

Gaussed PIPAs

Hi Buss Voltage

Inspection and Acceptance

Inner Gimbal CDU Problem

Kennedy Space Ccntcr

Lo Buss Voltage

I_op Not Open

North American Aviation

Nominal Buss Voltage

Out of Spec

Pre Acceptance Data

Resistor Changed

Rete st

Spacecraft

ISS Check

Scale,Factor, Scale Factor Adjusted

ISS Post Vibration

ISS Pre Vibration

ISS Post Visual/Mechanical Inspection

After Vibration

Recheck After Welding Calibration Module

5 Point Test

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t,_ 00 <

...... _- _-_9_g,_,_,4 d d d d -dddd! o _ r !

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V&V_ V_i

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.,-4_u

STANDARDDEVIATION(I_) OF THE IRIGANDPIPAPARAMETERUNCERTAINTIESUSEDFOR

MISSIONPERFORMANCESUMMARY(Corrected for ADOA)

IMU S/N 6

PARAMETER

IMU Axis PIPAsDataCompilationPeriodAccelerometer Bias (era/see2)

Scale Factor (ASF/SF ppm)

(6/26-i 1/26/67) (6/26- 11/26/67) (6/26-11/26/67)

+.08 +.06 +.10

(2/3/67-11/26/67)

92 45 76

IMU Axis IRIGs

Data Compilation Period

Bias Drift (MERU)

ADSRA (MERU/g)

ADIA (MERU/g)

(6/14-11/26/67) (6/14-11/26/67) (6/12-11/26/67)

1.3 2.3 2.4

2.2 2.7 1.2

5.1 6.0 5.8

Data is based uponperformance in,the IMU. Point-to-point stability in operation

is much better than the above data. The error computation for Mission 204 uses the

above data.

Accelerometer data taken prior to degaussing following incorrect procedures

has been excluded.

Current (11/26/67) Inertial Compensation Parameters are corrected for ADOA

and tablutated:

PARAMETER

Accelerometer Bias (cm/sec 2) +. 21

Scale Factor (ASF/SF ppm) -237

Bias Drift (MERU) -4.9

ADSRA (MERU/g) +5.7

ADIA (MERU/g} -35.6

Gyro data is the average of all KSC data.

degauss at KSC.

IMU AXIS

.10 +.08

-229 -444

-4. 7 -3.8

+0. 5 -1.0

-20.0 -1.6

PIP data the averages after last

2 _W i_ w

CORRECTIONS FOR THE ADOA DRIFT TERM

A drift term proportional to the acceleration along the output axis {ADOA}

is evident in the Apollo Gyro.

Due to the mechanization of G&N and spacecraft tests a factor times this

term is included in the NBD, ADSRA, and ADIA measurements. Table 7-52 gives

the drift values measured for each test configuration.

The Gyro data tabulation shown on pages 7-87, 88, 90, 92 and 93 include

the ADOA errors in each test configuration Table 7-52 shows. The Gyro curves

on pages 7-89, 91, and 94 and the standard deviation calculated for page 7-124

have been corrected for these ADOA errors.

A tabulation for the ADOA releases are given on page 7-127.

7 -125

Table 7-52

ERROR IN GYRO DRIFT TEST DUE TO ADOA TERM

FOR VARIOUS TEST CONFIGURATIONS

Drift TermMea sure d

ISS Test G&N Test Spacecraft

NBD X NBD x + ADOA X NBD X + ADOA X

NBDy NBDy + ADOAy NBDy + ADOAy

NBD Z NBD Z - ADOA Z NBD Z - ADOA Z

ADSRAx ADSRA X - ADOA X ADSRA X + 0. 414 ADOA x

ADSRAy ADSRAy - ADOAy ADSRAy - ADOAy

ADSRAz ADSRA Z - ADOA Z ADSRA Z - 2. 414 ADOA Z

ADIA ADIA x ADIA x + ADOA x ADIA x + ADOA X

ADIAy ADIAy + ADOAy ADIAy + 2 ADOAx- 0. 414 ADOAy

ADIA Z ADIA Z _ ADOA Z ADIA Z + ADOA Z

Table 7-53

The ADOA data included in the G&N NBD measurements are tabulated below:

IMU S/N 6

, 12113166 1/17/67 2/5/67 3/11/67 AverageX

0.89 I. 52 1.31 0.46 I. 0

Y7/17/67 7/31/67

I. 57 0.89 1.23

Z12/28/66 1/17/67 2/5/67 3/ii/67

2.24 0.93 0.73 i. 24 1.28

_'7A97 had ADOA of 1.60 meru on 12/13/66 for calculation of correction toS/C ADIA on 1/17/67.

_ _Lmmm-mlm,,Lpm. ,mm._..... lnbwi.,_T- _"- .w

(This Page is UNCLASSIFIED )

:7 (,_.

7 -128

: ] i i _ i --I", . _, , r :,_TT ....

_I_::':I _! I ¸ _-_T,i!i _ ::_, ! _ : i : I

:;l:!, ...........i i ....t +---1,-

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T _TTT?: I_-,1- ii _:..: :2.2

222 :2": .... :..

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_:I'. = Ti:-i!_:=:]]

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,' " ill!fiLL! -L::Z2 i!;2

iIiii! T21!iiI ii_ ...._"_I : . _ .2221-22 _ . : 22

::: Utiliiil :':::,; IH_I]!_!

_ _ii_ _iiiili:.i_..

;:: !i:Ti!: T ::;:

........ 'i:::: !::i _:"

i:: :il !11',ii _:i i:i

"' 'i I :_:I::: I_!i !:! iiiliii:_

:.! _ii ii;i iili i::

_22 ::2 i!!_

ill! ............,__ :_Ji ltI! _ti;l_tI',

_ii ;j'_ iii!|!!i!.....:I:_i LUt _ 512't

i i 'i i

i!:i LL

ili: !!!

i!i n. tl;i :_ !it

n:.::_!:_!_ii:iZ Ii:.!

;;: 121,: :!:

i:ii _iiI:!: _::i _]::. :_!::_: :!![!! !:{.}I_{[]}i

-- I ......

.,,:;!T

Internal

R. Battin

G. Cherry (2)

E. Copps

W. Cooper

J. Dahlen

J. Dunbar

G. Edmonds

P. Felleman

J. Fleming

E. Gardner

L. Gediman

R. Gilbert

K. Greene

F. Grant

J. Hand

P. Heinemann

Letter of transmittal only

R-527 SUNBURST

Section 7

D. Hoag

M. Johnston

* J. Kingston

A. Klumpp

W. Kupfer (2)

A. Laats

L. Larson

R. Larson (3)

J. Lawrence

D. Lic k.ly

H. Little

R. Lones

F. Martin

G. Mayo

R. McKern

J. S. Miller

J. E. Miller (25)

R. Morth

J. Nevins

P. Philliou

R. Ragan

N. Sears

J. Shillingford

G. Stubbs

M. Sullivan

J. Suthe rland

W. Tempelman

R. Tinkham

J. Vittek

R. White

W. Widnall (3)

R. Weatherbee

Apollo Library (2)

MIT/IL Library (6)

Rev. 2 -12/67

MIT Instrumentation Laboratoryc/o North American Aviation, Inc.Space and Information Division12214 Lakewood BouIevardDowney, California 90241Attn: Mr. Thomas A. Hemker

MIT Instrumentation LaboratoryG&N Systems Laboratoryc/o Grumman Aircraft Engineering Corp.

LM Project - Plant 25Bethpage, Long Island, New YorkAttn: (TOD)

MIT Instrumentation LaboratoryP.O. Box 21025Kennedy Space Center, Florida 32815Attn: (TOD)

MIT Instrumentation LaboratoryCode EG/MIT Building 1 6NASA Manned Spacecraft CenterHouston, Texas 77058Attn: (TOD)

John F. Kennedy Space CenterNASA MSC HWBldg. M7 - 409FloridaAttn: Frank Hughes

Mr. A. Metzger (NASA/RASPO at MIT/IL)

AC Electronics DivisionGeneral Motors CorporationMilwaukee, WisconsinAttn: Mr. J. Stridde, Dept. 32-21Attn: Mr. Reino K arell

(13)(2)

Kollsman Instrument Corp.575 Underhill Boulevard

Syosset, Long IslandAttn: Mr. F. McCoy

Raytheon CompanyBoston Post RoadSudbury, Massachusetts 01 776Attn: Mr. C. Bradshaw

NASA/RASPO /NAA

National Aeronautics and Space AdministrationResident Apollo Spacecraft Program OfficeNorth American Aviation, Inc.Space & Information Systems Division12214 Lakewood BoulevardDowney, California

National Aeronautics and Space AdministrationJohn F. Kennedy Space CenterJ. F. Kennedy Space Center, Florida 32899Attn: Technical Document Control Office

HDQ NASA Headquarters600 Independence Ave. SWWashington, D.C. 20546Attn: MAP-2 (4)Attn: Mission Director, Code MA (1)Attn: Robert Aller, Code MAO (1)

AMES: National Aeronautics and Space AdministrationAmes Research CenterMoffett Field, CaliforniaAttn: Library

LEWIS: National Aeronautics and Space AdministrationLewis Research CenterCleveland, OhioAttn: Library

FRC: National Aeronautics and Space AdministrationFlight Research CenterEdwards AFB, CaliforniaAttn: Research Library

LRC: National Aeronautics and Space AdministrationLangley Research CenterLangley AFB, VirginiaAttn: Mr. A. T. Mattson

GSFC: National Aeronautics and Space AdministrationGoddard Space Flight CenterGreenbelt, MarylandAttn: Mr. Paul Pashby, Code 554

ERC: National Aeronautics and Space AdministrationElectronics Research Center575 Technology SquareCambridge, MassachusettsAttn: Mr. R. Hayes/Mr. A. Colella

GAEC: Grumman Aircraft Engineering CorporationBethpage, Long Island, New YorkAttn: Mr. C. Brown (10)

Mr. R. Adarnato (3)Mr. B. Sidor (1)Mr. H. Sherman (3)Mr. E. Stern (1R)Mr. R. Fleisig (I)Mr. G. Smith (I)Mr. R. Pratt (4)

(23 + 1R)

NAA North American Aviation, Inc.Space & Information Systems Division12214 Lakewood Boulevard

Downey, California 90241Attn: Apollo Data Requirements

Dept. 096-340Building 3, CA 99

(1 + IR)

NASA/RASPO/National Aeronautics and Space Administration

GAEC Resident Apollo Spacecraft Program Officer

Grumman Aircraft Engineering Corporation

Bethpage, Long Island, New York

NASA/ RA SPO/ACED

National Aeronautics and Space Administration

Resident Apollo Spacccraft Program Officer

Department 32-31AC Electronics Division of General Motors

Milwaukee, Wisconsin 53201

Attn: Mr. W. Swingle

WSMR: National Aeronautics and Space AdministrationPost Office Drawer MM

Las Cruces, New Mexico

Attn: RH4 Documentation

MSFC: National Aeronautics and Space Administration

George C. Marshall Space Flight CenterHuntsville, Alabama

Attn: J. Mack R-ASTR- 5 (1)

H. Ledford R-AERO-P (2)

L. McNair R-AERO-P (1)

T. Telfer R-AERO-DA (2)

E. Deaton R-AERO-DA (1)

J. Cremin R-AERO-DAP (i)

L. Stone R-AERO-F (1)

C. Hagood R-AERO-F (I)

O. Hardage R-AERO-FM (I)F. Moore R-ASTR-N (1)

S. Seltzer R-ASTR-NG (5)

H. Hosenthien R-ASTR-F (i)

A. McNair I-MO-R (l)

D. Germany I-I/IB-E (1)R. Barraza I-V-E (I)

W. Chubb R-ASTR/NG (I)

J. McCullough I-VE/T (1)

BELLCOM M:

National Aeronautics and Space Administration

Manned Spacecraft Center

Apollo Document Control Group (PA 2)

Houston, Texas 77058

Attn: A. Alber, FS5 (letter of transmittal only)

(Above includes information copy for PD-6;letter PP7-66-775)

Bellcomm, Inc.11 00 17th Street N. W.

Washington, D.C. 20036

Attn: Info. Analysis Section

LINK : Link Div. of GPI

Hillcrest

Bingham, New YorkAttn: Mr. Fred Martikan

TRW: TRW Systems

1 Space ParkRedondo Beach, California

Attn: Mr. R. A. Evans, Bldg. 2Room 2044

I00 +2R)

copy °'---- : co. zes - ibiblio · 2009-09-06 · this report was prepared under dsr project...

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