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Msc-e0126SUPPLEMENT 2

00/99

MANNED SPACECRAFT CENTERHOUSTON,TEXAS

NOVEMBER 1969

APOLLO 10 MISSION REPORT

SUPPLEMENT 2

GUIDANCE, NAVIGATION, AND CONTROL

SYSTEMS PERFORMANCE ANALYSIS

:::::::::::::::::::::::

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MSC-00126Supplement 2

APOLLO 10 MISSION REPORT

SUPPLEMENT 2

GUIDANCE, NAVIGATION, AND CONTROL

SYSTEMS PERFORMANCE ANALYSIS

PREPARED BY

TRW Systems Group

APPROVED BY

James A. McDivittApollo Spacecraft Program

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

MANNED SPACECRAFT CENTER

HOUSTON, TEXAS

November 1969

11176-H386-RO-OO

PROJECT TECHNICAL REPORTTASK E-38C

APOLLO X GUIDANCE, NAVIGATION AND CONTROLSYSTEMS PERFORMANCE ANALYSIS REPORT

NAS 9-8166 31 OCTOBER 1969

Prepared forNA TlONAL AERONAUTICS AND SPACE ADMINISTRATION

MANNED SPACECRAFT CENTERHOUSTON, TEXAS

Prepared ByGuidance and Control Systems Department

Approved by \ \ ~~J. E. AI exander, ManagerGuidance and ControlSystems Department

TRW.vsr.... _

AGSAPSASABET

BMAGCDHCDUCEScgCM

CMCCSICSMDAPDOlDPSFCIFOAlGDAGETGN&CHOPEIMUISSIU

LGCLMLOI 1

LOI 2

LOSLRMCCPGNCS

NOMENCLATURE

Abort Guidance SystemAscent Propulsion SystemAbort Sensor AssemblyBest Estimate TrajectoryBody Mounted Attitude GyroConcentric Delta HeightCoupling Data UnitControl Electronics SectionCenter of gravityCommand ModuleCommand Module ComputerConcentric Sequence InitiationCommand & Service ModuleDigital AutopilotDescent Orbit InsertionDescent Propulsion SystemFlight Control IntegrationFlight Director Attitude IndicatorGimbal Drive ActuatorGround Elapsed Time (from liftoff)Guidance, Navigation &ControlHouston Operations Predictor EstimatorInertial Measurement UnitInertial SubsystemInstrumentation Unit (Saturn S-IVB)Lunar Module Guidance ComputerLunar ModuleLunar Orbit Insertion #1Lunar Orbit Insertion #2 (circularization)Line-of-sightLanding RadarMidcourse CorrectionPrimary Guidance Navigation &Control System I

iii

PTCRCSREFSMMATRRRTCCsICSPSSXTTIETElTEVENTTHCTILTLI

TMTPITVCVgVHF

Passive Thermal ControlReaction Control SystemReference to Stable Member MatrixRendezvous RadarReal Time Computer ComplexSpacecraftService Propulsion SystemSextantTransearthTransearth InjectionComputer Stored Time of Discrete EventTranslation Hand ControllerTranslunarTranslunar InsertionTelemetryTerminal Phase InitiationThrust Vector ControlVelocity-To-Be-GainedVery High Frequency

iv

-,

,

TABLE OF CONTENTS

Page

1.0 INTRODUCTION 1-1

1.1 General 1-1

2.0 SUMMARY 2-1

• 3.0 CSM IMU PERFORMANCE 3-1

3.1 ISS Errors 3-3

4.0 CSM DIGITAL AUTOPILOT 4-1

4.1 RCS DAP Performance 4-1

4.1.1 Attitude Maneuvers 4-1

4.1. 2 Attitude Hold 4-2

4.1.3 Attitude Hold During RCS Translation 4-3

4.2 TVC DAP

4.2.1 Engine Transients and Gimbal PositioningErrors 4-4

4.2.2 Propellant Slosh and SIC Body Bending 4-4

4.2.3 LOI 1 4-5

4.2.4 LOI 2 4-6

.. 4.2.5 TEl 4-6

4.3 Entry DAP 4-7

4.3.1 Roll Control 4-7

4.3.2 Pitch and Yaw Control 4-8

5.0 LM DIGITAL AUTOPILOT 5-1

v

Table of Contents (Continued)

Page

5. 1 Descent Configuration 5-1

5.1.1 Attitude Hold for Heavy Descent Configuration 5-1

5.1.2 Automatic Maneuver to 001 Attitude 5-2

5.1.3 DPS Phasing Burn 5-2

5.2 Ascent Configuration 5-3

5.2.1 APS Insertion Burn 5-3

5.2.2 Attitude Hold for Heavy Ascent Configuration 5-5

5.2.3 Automatic Maneuvers to CSI Burn Attitude 5-5

5.2.4 Automatic Maneuver to TPI Burn Attitude 5-5

5.2.5 Terminal Phase Initiation (TPI) 5-5

5.2.6 Attitude Hold for Lightest Ascent 5-6

6.0 AGS ANALYSIS 6-1

6. 1 Overall System Performance Summary 6-1

6.1.1 Velocity-To-Be-Gained Residual Comparisons 6-2

6.1.2 PGNCS/AGS Alignment Accuracy 6-3

6.1.3 Environment 6-3

6.2 Sensor Performance ,6.2. 1 Coasting Flight Analysis 6-4

6.2.2 APS Burn to Depletion Analysis 6-5

6.2.3 Comparison of Sensor Analysis Results toAGS Error Models 6-8

vi

Table of Contents (Continued)

6.2.4 Analysis Accuracy

7.0 OPTICS NAVIGATION SIGHTINGS

7.1 Star-Horizon SXT Sightings

7.2 Landmark Tracking

8.0 RENDEZVOUS NAVIGATION

8.1 Onboard Navigation

8.2 Rendezvous Targeting

9.0 LANDING RADAR VELOCITY AND ALTITUDE MEASUREMENTS

9.1 Results

9.2 Data Processing

10.0 CES PERFORMANCE

10.1 APS Depletion Burn

10.2 Coasting Flight

REFERENCES

APPENDIX A - AGS ANALYSIS METHODS

vii

Page

6-10

7-1

7-1

7-2

8-1

8-1

8-1

9-1

9-1

9-1

10-1

10-1

10-2

R-1

TABLES

3-1 CSM IMU System Errors

3-2 IMU Error Sources

4-1 Apollo 10 Post-Burn Vg Components

6-1 Ve1ocity-To-Be-Gained Residual Magnitudes

6-2 PGNCS/AGS Alignment Accuracy

6-3 Gyro Static Drift Measurements (Deg/Hr)

6-4 Accelerometer Static Bias Measurements

6-5 Error Set #1 - APS Burn to Depletion

6-6 Error Set #2 - APS Burn to Depletion

6-7 Performance Summary

6-8 Equivalent Accelerometer Bias Errors (APSBurn-To-Dep1etion) , ~g

6-9 Equivalent Gyro Bias Errors (APS Burn-ToDepletion), Deg/Hr

6-10 Standard Deviation of Accelerometer Biases

6-11 Accelerometer Bias Time Stability (Average of10-Free-F1ight Measurements Differenced withPIC Values)

6-12 Gyro Bias Repeatability

6-13 Gyro Bias Time Stability

6-14 Uncertainty In Sensor Performance Measurements

7-1 SXT Lines-of-Sight Relative to Sun Line

8-1 Rendezvous Targeting Summary

8-2 Rendezvous Targeting Solutions

Page

3-5

3-7

4-10

6-13

6-14

6-15

6-16

6-17

6-18

6-19

6-20

6-21

6-22

6-22

6-23

6-23

(30) 6-24

7-4

8-2

8-3

ILLUSTRATIONS

3-1 Uncompensated Ascent Velocity Comparison(G&N - S-IVB)



3-4 Uncompensated TLI Velocity Comparison(G&N - S-IVB)



3-7 Compensated Ascent Velocity Comparison(G&N - S-IVB)



3-10 Compensated TLI Velocity Comparison(G&N - S-IVB)



4-1 CSM/LM Maneuver to Evasive Burn Attitude

4-2 CSM Maneuver to T/E MCC Attitude

4-3a CSM/LM X-Axis Attitude Hold

4-3b CSM/LM V-axis Attitude Hold

XI

Page

3-8

3-9

3-10

3-11

3-12

3-13

3-14

3-15

3-16

3-17

3-18

3-19

4-11

4-12

4-13

4-14

Illustrations (Continued)

4-3c CSM/LM Z-Axis Attitude Hold

4-4a CSM X-Axis Attitude Hold

4-4b CSM Y-Axis Attitude Hold

4-4c CSM Z-Axis Attitude Hold

4-5 CSM/LM Attitude Hold During LOI 2 Ullage

4-6a CSM X-Axis Attitude Hold During T/E MCC

4-6b CSM Y-Axis Attitude Hold During T/E MCC

4-6c CSMZ-Axis Attitude Hold During T/E MCC

4-7 Spacecraft Dynamics During Evasive Maneuver

4-8 Spacecraft Dynamics During MCC2 Maneuver

4-9 Spacecraft Dynamics During Lunar Orbit Insertion

4-10 Spacecraft During Lunar Orbit Circularization

4-11 Spacecraft Dynamics During Transearth Injection

4-12 Pitch Engine Angle During LOI 2

4-13 Yaw Engine Angle During LOI 2

4-14 FDAI Body Pitch Rate During LOI 2

4-15 FDAI Body Yaw Rate During LOI 2

4-16 LOll Pitch and Yaw Attitude Errors

4-17 LOll Engine Trim Estimates

4-18 LOll Cross-Axis Velocity

4-19 LOll Roll Attitude Error

4-20 LOI 2 Burn Parameters

xii

Page

4-15

4-16

4-17

4-18

4-19

4-20

4-21

4-22

4-23

4-24

4-25

4-27

4-29

4-31

4-32

4-33

4-34

4-36

4-37

4-38

4-39

4-40


4-21 TEl Pitch and Yaw Attitude Errors

4-22 TEl Engine Trim Estimates

4-23 TEl Cross-Axis Velocity

4-24 TEl Roll Attitude Error

4-25 Entry Roll Command/Bank Angle Histories

4-26 Entry Pitch Jets Activity

4-27 Entry Yaw Jets Activity

4-28 Entry Fuel Consumption Per Axes

4-29 Entry Pitch Rate Damping

5-1 Attitude Hold Prior to Automatic Maneuver to001 Attitude

5-2 Attitude Hold Prior to Automatic Maneuver to001 Attitude

5-3 Automatic Maneuver to 001 Attitude



5-6 DPS Phasing Burn and Attitude Hold



5-9 APS Insertion Burn




xiii

Page

4-41

4-42

4-43

4-44

4-45

4-46

4-50

4-54

4-55

5-7

5-8

5-9

5-10

5-11

5-12

5-13

5-14

5-15

5-16

5-17

5-18




5-15 P-Axis Phase Plane Attitude Hold Prior to APSInsertion Burn

5-16 U-Axis Phase Plane Attitude Hold Prior to APSInsertion Burn

5-17 V-Axis Phase Plane Attitude Hold Prior to APSInsertion Burn

5-18 Automatic Maneuver to CSI Attitude Desired andActual Rates Vs. Time P-Axis

5-19 Automatic Maneuver to CSI Attitude Desired andActual Rates Vs. Time U-Axis

5-20 Automatic Maneuver to CSI Attitude Desired andActual Rates Vs. Time V-Axis

5-21 Automatic Maneuver to CSI Attitude CDU Angles

5-22 Automatic Maneuver to TPI Attitude Desired andActual Rates Vs. Time U-Axis

5-23 Automatic Maneuver to TPI Attitude Desired andActual Rates Vs. Time V-Axis

5-24 Automatic Maneuver to TPI Attitude CDU Angles

5-25 TPI Burn P-Axis Phase Plane

5-26 TPI Burn U-Axis Phase Plane

5-27 TPI Burn V-Axis Phase Plane

5-28a Attitude Hold After APS Burn to Depletion

5-28b Attitude Hold After APS Burn to Depletion

xiv

Page

5-19

5-20

5-21

5-22

5-23

5-24

5-25

5-26

5-27

5-28

5-29

5-30

5-31

5-32

5-33

5-34

5-35






6-1 AGS Ve1ocity-To-Be-Gained Magnitude; APSBurn to Depletion

6-2 Body Rate Data Derived From Changing AGSDirection Cosines

6-3 AGS/PGNCS X Axis Integrated Body Rate Differences; Coasting Flight and APS Burn toDepletion

6-4 AGS/PGNCS YAxis Integrated Body Rate Differences; Coasting Flight and APS Burn toDepletion

6-5 AGS/PGNCS Z Axis Integrated Body Rate Differences; Coasting Flight and APS Burn toDepletion

6-6 X Body Rate - APS Burn to Depletion

6-7 Y Body Rate - APS Burn to Depletion

6-8 Z Body Rate - APS Burn to Depletion

6-9 XAxis Sensed Acceleration - APS Burn toDepletion

6-10 X Axis Sensed Velocity - APS Burn to Depletion

6-11 YAxis Sensed Velocity - APS Burn to Depletion

6-12 Z Axis Sensed Velocity - APS Burn to Depletion

6-13 Uncompensated Sensed X-Axis Velocity DifferencePGNCS Gimbal Angles Used for Transform - APS Burnto Depletion

xv

Page

5-36

5-37

5-38

5-39

6-27

6-29

6-31

6-33

6-35

6-36

6-37

6-38

6-39

6-40

6-41

6-42


Page

6-14 Uncompensated Sensed V-Axis Velocity Difference;PGNCS Gimbal Angles Used for Transform - APS Burnto Dep1 etion 6-43

6-15 Uncompensated Sensed Z-Axis Velocity Difference;PGNCS Gimbal Angles Used for Transform - APS Burnto Dep1 etion 6-44

6-16 Compensated Sensed X-Axis Velocity Difference;PGNCS Gimbal Angles Used for Transform - APS Burnto Depletion 6-45

6-17 Compensated Sensed V-Axis Velocity Difference;PGNCS Gimbal Angles Used for Transform - APS Burnto Dep1 etion 6-46

6-18 Compensated Sensed Z-Axis Velocity Difference;PGNCS Gimbal Angles Used for Transform - APS Burnto Dep1 etion 6-47

6-19 Uncompensated Sensed X-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS Burnto Depletion 6-48

6-20 Uncompensated Sensed V-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS Burnto Depletion

6-21 Uncompensated Sensed Z-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS Burnto Depletion

6-22 Compensated Sensed X-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS BurnTo Depletion

6-23 Compensated Sensed V-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS BurnTo Depletion

6-24 Compensated Sensed Z-Axis Velocity Difference;AGS Direction Cosines Used for Transform - APS Burnto Depletion

xvi

6-49

6-50

6-51

6-52

6-53


Page

8-1 Comparison of CSM VHF Range &LM RR Rangewith BET Range 8-4

8-2 Comparison of LM Range Rate With BET RangeRate 8-5

8-3 Comparison of LGC &CMC Range &Range RateData During Rendezvous 8-6

9-1 LR Velocity Minus G&N Velocity (X Component) 9-3

9-2 LR Velocity Minus G&N Velocity (Y Component) 9-4

9-3 LR Velocity Minus G&N Velocity (Z Component) 9-5

9-4 Comparison of LR Measured Altitude and BETAltitude 9-6

9-5 Lunar Surface Profile Measured by LandingRadar 9-7

10-1 Pulse Ratio Modulator Characteristics 10-3

xvii

1.0 INTRODUCTION

1.1 GENERAL

This report presents the conclusions of the analyses of the inflightperformance of the Apollo 10 mission (AS-505/CSM-106/LM-4) guidance,navigation and control equipment and is intended to supplement the Apollo10 mission report (Reference 1). The report was prepared and sub-mitted under MSC/TRW Task E-38C, "G&C Test Analysis. 1I Results reportedherein reflect a working interface between Task E-38C, MSC/TRW TaskA-50, IITrajectory Reconstruction ll and MSC/TRW Task E-728, IIG&C SystemAnalysis. 11 These tasks are highly interdependent and the cooperationand support of the A-50 and E-72 task personnel are gratefully acknowledged.

1-1

2.0 SUMMARY

CSM IMU performance was near nominal based on error separationstudies conducted for the boost and TLI phases. A set of error termsfor each phase was derived, each set compatible with the other, whichprovided a satisfactory fit to the observed system errors. During thetranslunar and transearth coast the IMU remained powered up and considerable data were obtained on IMU freeflight drift characteristics andPIPA bias stability.

The performance of theCSM DAP was satisfactory. The peak attitudeerrors during the DAP controlled SPS burns were 0.5 deg or less. TheRCS DAP performance during attitude hold, automatic maneuvers, ullage,a~d RCS translation burns were satisfactory. The entry DAP performednominally with 33.0 lbs of RCS propellant used.

SXT midcourse navigation sightings performed during translunarand transearth flight were evaluated. The trunnion bias and noisevalues obtained were comparable with previous flights but unusuallywide variations in earth horizon bias (0.82 to 20.6 nm) were observedon this flight in comparisons to previous missions. Cause for thiswide variation could not be correlated with the latitude of the pointof tangency or sun angles relative to the two lines-of-sight.

LM IMU performance was acceptable based on the near nominal execution of the LM orbital maneuvers. No error separation studies wereconducted due to the short durations and low accelerations of the LMburns. Some question did arise on Apollo 10 as to the integrity ofthe X IMU gyro. One of the AOT alignments yielded a X sm torquing anglewhich corresponded to a gyro drift of 14 meru. One sigma drift uncertainty is 2 meru. Numerous procedural, hardware and systematicproblems were considered which would cause the large drift or wouldyield a false torquing angle. Due to the good hardware performanceboth before and after the problem occurred,a probable hardware failuremode was not evident. Procedures were thoroughly reviewed and no

2-1

procedural anomaly was apparent. A systematic error was dismissedsince one of the earlier alignments was checked against an independentCSM IMU alignment and the errors were acceptable. Another possible causeis an error in one of the sighting vectors. Confidence in the sightingdata is normally based on a star angle difference check which is acomparison of.the calculated subtended angle between the two AOT sightingvectors with the theoretical angle between the two stars. A good checkcan be obtained however, in the presence of a significant sightingerror, if the two stars lie in a plane which contains two of the platformaxes. This was the case for this alignment and it's most probable thata sighting error caused an erroneous torquing angle.

Performance of the LM DAP during coasting and powered flight appearednominal. Automatic attitude hold and automatic maneuvers at 2 deg/secin the descent configuration were performed in accordance with thesoftware design. Automatic attitude hold of the ascent configurationfor both the wide and narrow deadbands was quite satisfactory.

Landing Radar data obtained during the first pass through perigee(6.65 nm altitude) after the 001 maneuver indicated the radar wasfunctioning properly and accurately measuring the LM relative velocityand altitude above the surface. Considerable confidence in the LRsystem for the lunar landing mission was gained from the data.

The LM active rendezvous was conducted without incident and thetotal 6V required to perform the LM maneuvers was within one percentof the nominal 6V. All of the burn solutions were solved for by the LGCbased solely on rendezvous radar data to correct for any trajectorydispersions.

Overall performance of the Abort Guidance System (AGS) was excellent.State vector initializations and PGNCS/AGS alignments were smoothlyaccomplished within expected accuracies. An Abort Sensor Assembly (ASA)lerror separation study for the APS burn to depletion yielded instrumenterrors well within the 30 AGS capability estimates. In general theASA performed with high accuracy and the gyro bias stability was exceptionally good.

2-2

3.0 CSM IMU PERFORMANCE

Apollo 10 CSM IMU performance analysis was based upon velocitycomparisons for the boost and TLI thrusting periods.

The uncompensated velocity (no error compensation) differencesappear in Figures 3-1 through 3-6. The compensated (velocity residualsresulting from a comparison of the Apo110 G&N data, corrected for abest fit set of errors, compared to the S-IVB IU data) velocity comparisons are shown in Figures 3-7 through 3-12. Derived error sets tofit boost and TLI are presented in Table 3-1. The error sources considered and their respective definitions are presented in Table 3-2.Any errors in the booster data are included in the Apollo G&N data.Sensed velocity errors at insertion (approximately 703 seconds GET).. .were -2.82, -29.11, and -5.08 ft/sec for the X, Y, and Z axes. Thedifference is derived by taking Apollo G&N minus external reference.At the completion of TLI (approximately 9550 seconds GET), the velocityerrors accrued during TLI were 15.11,4.79, and -3.19 ft/sec for the.. .X, Y, and Z axes. These sensed boos t and TLI errors may also beobserved from their corresponding uncompensated plot.

The maximum deviation between any set of corresponding errorsources was 0.850. In total, 34 error sources were derived for boostand 34 for TLI. Satisfactory ISS performance has been establishedusing the generalized approach set forth in paragraph 3.1 of thisanalysis. Evaluating the 34 error sources individually (as opposedto the relative basis between boost and TLI) reveals the ADSRAY (Yaccelerometer drift due to acceleration along the spin axis) andADIAX (X acceleration drift due to acceleration along the input axis)and ADIAZ (Z acceleration drift due to acceleration along the inputaxis) slightly exceeded the 10 instrument stability estimate duringboost and TLI. These are discussed in the ISS Errors Paragraph 3.1.1.

3-1

It is worthy of noting that the X, V, and Z velocity offsets forboost and TLI (VOX, VOV, and VOZ) were difficult to obtain for each fitbecause of the unrealistic data available at the start of boost and TLIburns. For example the Xacceleration measured by the S-IVB indicateda step change from -0.5 ft/sec 2 for the first two seconds of data to+0.5 ft/sec for the next 2 seconds. The Apollo G&N measured -0.1 ft/sec 2

for the total 4 seconds. As a result the first 4 seconds of S-IVB datawas edited out and an X offset was formed based on the subsequent data.

The Apollo 11 G&C system accuracy analysis was based on the determination of a common set of errors which resulted in small residuals forboth the boost to orbit phase and the translunar insertion phase. Atthe same time, several constraints were imposed on the errors used. Thebias values for accelerometers and gyros were forced to be in close agreement with inflight determined values and other error terms which werepreflight calibrated were chosen to agree favorably with calibrationhistories. Due to various physical factors such as actual accelerationsensitive parameter shifts during the boost phase and degradation of thereference data between the two flight phases (2.6 hours of drift betweenascent and TLI) it was again recognized that all of the above conditionscould not be met at all times. Based on engineering judgement, theapproach pursued was to determine two sets of error sources with minimumvariations (~la) between the two flight phases. The error terms derivedfrom the analyses are presented in Table 3.1, and using these values,the G&N corrected trajectories fit the respective external measurementtrajectories. The maximum deviation between the derived ascent and TLIerror sources was 0.85a.

For each of the two flight phases, two trajectories were generatedby MSFC as a basis for comparison. One boost/TLI trajectory was the"Edited S-IVBIUTM" trajectory and the other was the "Final S-IVBObserved Mass Point Trajectory" (OMPT). The trajectory designated"Final S-IVB OMPT" is normally considered the best estimate trajectoryfor the boost and TLI phases but was again rejected due to inconsistencies

3-2

in the trajectory characteristics throughout the boost phase and TLIphases. Similar problems have been encountered with the OMPT on previousflights and in all cases no reasonable set of error sources could befound which effected a good boost and TLI comparison (Reference 2 and 3).The "Edited S-IVBIUTW trajectory was again accepted as most realistic.It should be pointed out that the first 4 seconds of IU Boost data issuspect due to the high vibration levels during this time. For thisreason, the velocity offset values are chosen to ootimize the "fit. 1I

These velocity offsets will cause considerable vertical curve shiftssince their corresponding partial derivatives are unity. Consequently,values are chosen that more realistically follow the data trends after. .the first 4 seconds for each of the X, Y, and Z axes.

The major difference between the OMPT and IIEdited S-IVBIUTW isthat the OMPT has been corrected for booster guidance errors. Noallowance has been made for these errors; any that exist are includedin the Apollo G&N errors. Analysis has shown, however, that theseerrors have less effect on the indicated performance of the ApolloG&N than the II correct ions" inc1uded in the OMPT (Reference 3) .

3.1 ISS ERRORS

It is worthy of noting that, even though the derived boost and TLIerrors were within 0.850 of each other for the evaluation of theseflight phases, the ADSRAY (Y accelerometer drift due to accelerationalong the spin axis) error source derived for ascent was 1.980 and1.120 for TLI. The derived ADSRAY value was -9.91 meru/g for ascentand -5.67 meru/g for TLI. These values were within 1.890 and .80 ofthe a priori ADSRAY error estimates for boost and TLI. There was nothingin the preflight test history which would explain the large errorsrequired to make the fit. Although no explanation based on preflightdata exists for the large ADSRAY term reasonable confidence in the valueremains due to the consistent requirement for this value to obtaina good fit and due to the close agreement with the value obtained for

the TLI phase.

3-3

The derived ADIAX (X acceleration drift due to acceleration alongthe input axis) values were 1.080 for boost and 1.160 for TLI. Basedupon the initial error estimates at start of boost and TLI, the derivedADIAX error values were within the 10 performance criteria. Using theinitial estimates as a reference for comparison the derived valueswere .90 for boost and .20 for TLI.

The derived ADIAZ (Z acceleration drift due to acceleration alongthe input axis) values were -9.86 meru/g for boost and -13.8 meru/gfor TLI. Preflight test history data trends indicated the value wasmoving toward negative. Preflight test history of ADIAZ for the timeinterval 24 February 69 to 3 April 69, shows a negative trend from 12.75meru!g to 8.75 meruig. For prelaunch load on 18 Maya value of 11 meru/gwas inserted into the CMC for ADIAZ compensation. An initial errorestimate of -2.4 meru/g existed before liftoff. The determined valueswere within .90 and .50 of the initial ADIAZ error estimates. There isalso reasonable confidence in the ADIAZ values due to the consistentrequirement of these values to obtain a good "fit. 1I

Reviewing the three relatively large ISS errors, ADSRAY, ADIAXand ADIAZ, it is worthy of noting that ADSRAY was the. only error thatexceeded the 10 instrument stability estimate when the derived valuesare compared with an initial error estimate based on preflight data.

3-4

Comments

between ascent and TLI.

Output error values

measurements

~ot comparable due to

state vector update

established from inf1ight

I,(Ascent Output \ (TlI Output )Error Value, -- Error Value

TlI OutputError Value

Ascent OutputError Value

Preflight Expected 10 B~unds

Maximum MinimumStandard·Deviation

ExpectedError· 1/

NA NA NA NA NA NA I0.2p9 - 0.523

Flight Load

NA

Pref11glltData MeanError Source

VOY (ft/sec) NA NA NA NA NA NA _ 0.999 _ 0.013 NA

VOX (ft/sec)

_A_C_BX_(_cm_/_se_c-:-2_) ---.:-=--..:Ol!.-'.~065~ ..:-~0!.:.~27!.._ __.:-~0~.2~0~5 0_._20 0~.405 __"0_'_.O:...:0...:..5 -_0.03:._.:.0 ---_0~.0.:..:3_2 NA_N 1ACBY (cm/sec:) - 0.055 - 0.07 0.015 0.20 0.215 _ 0.185 _ 0.088 _ 0.089 NA

ACSl (cm/sec") . _ 0.05 0.20 0.205 - 0.195 0.110 0.114 --------N-A------- 0.045· 0.005

VOl (ft/sec) NA NA NA NA NA NA 06 0.621 NA________________-----------'----'-- --=- 0 .•..:.7..:=. ---=-:..::..::..:....- --

DT (sec) NA NA NA NA NA NA NA0.007 0.0004

SFEX (ppm)-178.250 -10e - 78.25 116 37.75 -194.25 19.34 19.2 O.Olu

SFEY (ppm)-237 -230 - 7 116 109 -123 10.72 35.6 0.200 Insensitive in ascent

SFEl (ppm) -129 - 80 - 49 116 67 -165 80.14 -17.2 0.840"

MXAl (arc sec) NA NA NA 20 20 - 20 - 0.2 3.6 0.190

IUAY (IrC sec) NA NA NA 20 20 - 20 - 19.7 - 13.2 0.3300

MYAl (arc sec) NA NA NA 20 20 - 20 o 5.1 0.260'

MYAX (arc sec) NA NA NA 20 20 - 20 15.6 18.1 O.l3<T

MlAY (arc sec) NA NA NA 20 20 - 20 _ 13.5 - 20.9 0.3700

- 1.7 - 1.7 .. JMlAX (arc sec)

NBDX (meru)

NBDY (meru)

NBDZ (meru)

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Output error values

established from inf1ight

measurements

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ADIAY (meru/g) 8.7.00 . 13.0 - 4.3 8 3.7 12.3 - 1.66 0.8 0.31'1' Insensitive in ascent

ADIAZ (meru/g) 8.600 11.0 2.4 8 5.6 - 10.4 - 9.86 - 13.8 0.490·

ADSRAX (meru/g) 9.800 10.0 - 0.2 5.0 4.8 - 5.2 - 0.113 1.11 0.240" Insensitive in TLI

ADSRAY (meru/g) 3.400 3.0 0.4 5.0 5.4 - 4.6 - 9.91 - 5.66 0.850"

ADSRAl (meru/g)

ADOAX (meru/g)0.9·

3.27

7.0NA

- 6.1

3.27

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) )

8.27

- 11.1

- 1.73

- 6.37 - 5.93

- 3.85 - 3.57

0.090"

0.060'

Insensitive in ascent

AOOAY (meru/g) - 0.275 NA - 0.275 2-5** 4.725 - 5.276 4.43 4.13 0.060'

ADOAZ (meru/g) 0.825 NA 0.825 2-5** 5.825 - 4.175 - 3.13 - 3.0 0.03t'r

MlMX (arc sec)

MLMY (arc sec)

MlMZ (arc sec)

NA

NA

NA

NA

NA

NA

NA

NA

NA

50***

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50***

50***

50***

50***

- 50***

- 50***

Not comparable. TLIvalues based on platformmisalignments and 2.5 hoursdrift before TLI.

• Data mean minus flight load.

** Recent unofficial measurements by MIT.

*** Boost Phase only.

NA = Not applicable

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Figure 3-1 Uncompensated Ascent VelocityComparison (G&N - S-IVB)

3-8

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3-9

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3-11

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3-12

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3-13

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3-14

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3-17

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Figure 3-12 Compensated TLI VelocityComparison (G&N - S-IVB)

3-19

4.0 CSM DIGITAL AUTOPILOT

CMC control of the SIC was employed extensively during this missionand all three autopilots performed nominally. Because only minor changesare to be made to the CSM flight program for subsequent missions, theexcellent performance of the DAP's during the mission adds to an alreadyhigh confidence level in the CSM program for upcoming lunar landingmissions.

4.1 RCS DAP PERFORMANCE

Extensive use was made of the RCS DAP for maneuvering to desiredattitudes for SPS burns, PTC initialization, or navigation sightings.All PTC periods were implemented under CMC control. Periods of RCS DAPperformance during attitude maneuvers, attitude hold, attitude hold duringRCS translation, and passive thermal control were analyzed and are discussed in subsequent paragraphs.

4.1.1 Attitude Maneuvers

Following LM withdrawal from the S-IVB, the docked CSM/LM performedan evasive maneuver to avoid recontact. The docked SIC during thismaneuver was heavy, approximately 94,150 lbs. SIC roll, pitch, and yaw,gimbal angles at attitude maneuver initiation were -54, -37 and -48deg, respectively. The final desired gimbal angles were 61, -105 and -2deg. A maneuver rate of .2 deglsec was employed, with the desiredrotation rates being .158, -.107 and .060 deglsec about the vehicle X,Y, and Z axes. Figure 4-1 presents time history plots of DAP-measuredSIC body rates during the first 4 minutes of this automatic maneuver.The actual rates converged to the desired values with overshoots of .02deglsec or less in all axes.

Figure 4-2 presents time histories of DAP-computed body rates duringan RCS-controlled automatic maneuver to the TIE MCC attitude. The SIC

4-1

weight was a light 25,500 lbs. Initial roll, pitch, and yaw gimbalangles were -93, -152, and -12 deg and the desired final values were0, 129, and 0 deg. Figure 4-2 shows that the actual body rates duringthis maneuver did not converge to the desired rates as well as duringthe maneuver to evasive burn attitude. This occurred because of thelower vehicle weight and inertia values, which resulted in largerrotation accelerations from RCS firings and increased cross-axiscoupling effects.

4.1.2 Attitude Hold

Three minutes of attitude hold immediately following the maneuverto the CSM/LM evasive burn attitude are illustrated in the phase planeplots of Figures 4-3a to 4-3c. The phase planes of Figures 4-4a to4-4c contain 6 minutes of CSM-alone attitude hold immediately followingthe maneuver to T/E MCC attitude. Narrow (.5 deg) attitude error deadbands were employed during both periods. These figures do not preciselyrepresent the RCS attitude plotted at 2 second intervals, which is thedownlink frequency of the phase plane attitude errors. Also, thedownlinked rates are 20 words apart (.4 sec) from the attitude errors;therefore, the rate/error data are only approximately time homogeneous.However, they are close enough to give a general picture of RCS DAPperformance during these attitude hold periods. One must allow someleeway when viewing these plots, e.g., not all jet firings will appearto be initiated just after crossing the phase plane deadbands (dashedlines in the figures).

In general, the motions of the rate/error points in Figures 4-3ato 4-3c appear nominal and in accord with the phase plane attitude holdlogic. The only anomalous-looking motion occurs near the +.5 degattitude error deadband in Figure 4-3a where the measured rate changessign several times with no roll jets being fired. However, the ratesinvolved are quite low (less than .01 deg/sec in magnitude) and the sign

4-2

changes can be attributed to cross-axis coupling, since, during this timeperiod, there is necessarily frequent pitch jet activity as the pitchphase plane point "wa lks" up the left-hand deadband boundary of Figure4-3b.

Much more cross-axis coupling is evident in Figures 4-4a to 4-4c forthe period of CSM-alone attitude hold. In particular, the anomalouslooking roll rate reversal (Figure 4-4a) coming just before 188:19:09GET and the confusing phase plane histories near the left-hand pitch andyaw deadband boundaries (Figures 4-4b and 4-4c) are good examples of theeffects of cross-axis coupling on a light S/C, especially when bothpitch and yaw errors are near the deadbands at the same time.

The limit cycle set up in Figure 4-4a is of minimum impulse typewith a 2-jet pair of minimum impulse roll firings causing a rate changeof approximately .07 deg/sec. The rate change produced by the minimumimpulse firing for the CSM/LM configuration seen in Figure 4-3a is downby a factor of four from this value. This is consistent with thereciprocal roll moments of inertia, which are also down by the samefactor.

4.1.3 Attitude Hold During RCS Translation

The lunar orbit circularization burn (LOI 2) was preceded by a2-jet ullage of 16 seconds duration using quads A/C. During this periodthe RCS DAP maintained S/C attitude errors within the narrow attitudehold deadbands. Figure 4-5 illustrates RCS DAP performance during thisullage period. All attitude errors at ignition (80:25:08 GET) were ofmagnitude .6 deg or less. Comparable attitude hold performance was also

observed during ullage preceding TEl.

Only one T/E MCC was required during Apollo 10. Figures 4-6a to4-6c plot the attitude hold phase planes during this RCS translation.Initial rate excursions which result from +X translation, are negativein all axes. The positive rate excursions that follow result from asmall +Z translation input. Figures 4-6a to 4-6c verify that the RCS

4-3

DAP correctly implemented THC inputs during this MCC. Post burn velocityto-be-gained (vg) components were only 0, -.1, and -.1 ftlsec in theSIC X, V, and Z direction, respectively.

4.2 TVC DAP

Five SPS burns were made during Apollo 10. They consisted of adocked evasive maneuver from the vicinity of the S-IVB, TIL MCC, lunarorbit insertion (LOll), lunar orbit circularization (LOI 2), andtransearth injection (TEl). Figures 4-7, 4-8, 4-9, 4-10 and 4-11 showthe spacecraft dynamics during the five burns. Table 4-1 shows the postburn Vg components displayed on the DSKV via Noun 85 before and afterRCS residuals nulling. In Table 4-1, the only post-burn ~V componentthat seems out of line is the V-axis Vg value after TEl. As discussedbelow, this is attributable to the TVC DAP cg tracker loop not being ableto adequately follow the rapidly moving SIC cg at this light vehicleweight. Table 4-1 also shows that TVC performance generally improvedwith increased burn time.

4.2.1 Engine Transients and Gimbal Positioning Errors

Figures 4-12 and 4-13 are plots of time histories of pitch and yawengine gimbal positions for the entire LOI 2 burn. Also included, atthe downlink frequency of once per second, are values of pitch and yawengine commands. For this burn, the peak-to-peak engine gimbal transientsat ignition were quite small, .5 deg in pitch and +.2 deg in yaw. Theseerrors decreased practically to zero after SPS cutoff. Largely similarignition transients and steady state gimbal positioning errors wereobserved during LOll and TEl.

4.2.2 Propellant Slosh and SIC Body Bending

Propellant slosh and body bending effects were detected during thevarious burns by examining FDAI body rates. These rates are the outputvalues of caged BMAG's, sampled once every 10 msec. Figures 4-14 and4-15 present FDAI pitch and yaw body rates during LOI 2. This partic

ular burn was chosen for plotting purposes because it was short enoughlto make a detailed plot feasible and because it exhibits both slosh and

bending effects. 4-4

Eight or nine cycles of body bending can be detected in pitch atthe beginning of Figure 4-14. The bending frequency is approximately2.785 Hz. Propellant slosh at a frequency of approximately 0.469 Hzcan be seen in the yaw rate plot of Figure 4-15. Although roll rate isnot plotted, it also exhibited sloshing effects of approximately thissame frequency.

During LOll, propellant slosh effects were not seen in pitch oryaw. They were observed in roll at approximately 0.350 Hz, persistingfor about the first minute and 15 seconds of the burn. Body bending ofapproximately 2.466 Hz was noted in pitch and yaw, lasting for sevencycles or less.

No bending effects were observed during the undocked TEl burn. Propellant slosh at a frequency of 0.652 Hz was noted in all three axes.The pitch oscillations were damped out after 70 seconds while the rolland yaw oscillations persisted for almost the entire burn time. However,these slosh oscillations never appeared to diverge and represented nostability problems.

Comparing data from the various burns, it is seen that propellantslosh and body bending frequencies both increased with decreasing vehicleweight. This trend is consistent with preflight simulations.

4.2.3 LOll

Figures 4-16 through 4-19 present burn parameters for LOll. Thepitch and yaw attitude error histories of Figure 4-16 are impressivelysmall, approximately .1 to .2 deg. In Figure 4-17 the estimated pitchengine trim angle became asymptotic one minute before SPS cutoff. Theyaw trim estimate never became asymptotic but the total cg change wasonly .6 deg over a 6 minute period, so the TVC cg tracker loop had nodifficulty in following its motion. Cross-axis velocities plotted inFigure 4-18 are oscillatory because the granularity of the Vg data fromwhich these values were calculated is .25 ft/sec in all axes, which isof the same order of magnitude as the cross-axis velocity values being

4-5

computed. However, a trend from approximately .35 ft/sec shortly afterignition to .12 ft/sec at engine cutoff is observable. Figure 4-19presents a time history of TVC roll DAP attitude error during LOll.The behavior observed is similar to that noted during previous flights,where an external torque causes the roll error to bounce off thenegative deadband limit, rather than traverse from minus to plus, etc.However, only four roll firings were required during the entire 6minute burn.

4.2.4 LaI 2

Figure 4-20 presents time histories of DAP pitch and yaw attitudeerrors, roll gimbal angle error, pitch and yaw engine trim estimates(PACTOFF and YACTOFF), and cross-axis velocity component during LOI 2.The peak attitude error magnitudes were .4 deg in pitch and .2 deg inyaw. The cross-axis velocity values were computed from downlinked Vg'swhich are available every two seconds, or once per average G cycle.The value plotted in the figure is the component of Vg normal to thepreburn Vg vector. The peak cross-axis velocity mangitude during LOI 2was 1.2 ft/sec, decreasing to .45 ft/sec at SPS engine cutoff.

4.2.5 TEl

TEl burn parameters are presented in Figures 4-21 through 4-24.The peak pitch attitude error magnitude was .6 deg while the yaw errorgrew slowly during the burn to a final value of .35 deg. This steadybuildup occurred because the yaw cg tracker could not adequately followthe rapidly moving cg of this lightweight vehicle. As seen in Figure4-22, the yaw cg trim estimate changed by 1.8 deg during the 2 minuteand 45 second burn. Contrasting this with yaw cg motion during LOll,it is seen that the travel rate during TEl was approximately 6.5 timesas fast as during LOll. This inability to follow the cq trim

position caused the 1.6 ft/sec Y-axis ~V error seen in Table 4-1.Figure 4-23 implies that practically all of this 1.6 ft/sec Vg

'consisted of cross-axis velocity error. The peak cross axis velocity

4-6

was 3.6 ftlsec, occurring 20 seconds after ignition. In contrast toLOll, the outer gimbal angle error during TEl (Figure 4-24) traveledback and forth between the positive and negative deadband limits.

4.3 ENTRY DAP

A few seconds before entry communications blackout, control of thecommand module was handed over to the CMC. For the next 20 seconds, theexoatmospheric entry DAP maintained the desired entry orientation (roll,pitch, and yaw gimbal angles equal to 0,153 and 1 deg) using the .1second attitude hold phase plane for pitch and yaw control and the2-second predictive DAP in roll. After the vehicle drag level reached.05 G, the atmospheric entry DAP assumed control of the SIC and remainedin command for the duration of the entry phase. The atmospheric DAPconsists of the 2-second predictor logic in roll and rate damping inpitch and yaw. The RCS system A thruster ring was employed during theentire period of CMC entry DAP control.

4.3.1 Roll Control

Control of the CM bank angle was maintained by the 2-second predictive DAP, which performs the function of driving the SIC bank anglein response to roll commands issued every 2 seconds by entry guidance.Figure 4-25 presents time histories of commanded and actual SIC rollangles. The entry roll DAP closely followed the commands issued by entryguidance. Performance of the roll DAP was consistent with preflightsimulations and results of previous missions.

Entry guidance commanded a typical roll-down maneuver after theCMC assumed control and DAP succeeded in driving the SIC bank angle tolift down (180 deg roll angle) within a time lapse of 14 seconds. TheDAP required only 11 seconds for the roll-up maneuver initiated 30seconds later. The time difference arose primarily because the roll-downcommand sequence included 6 seconds worth of 80-90 deg bank angle commands,thus limiting the peal roll rate attained. The roll-up commands sequenced directly from full lift down to full lift-up.

4-7

4.3.2 Pitch and Yaw Control

For 20 seconds after initiation of CMC entry DAP control (before.05 G), the pitch and yaw DAP functions consisted of attitude hold aboutthe desired entry attitude. After .05 G, the pitch and yaw functionswere changed to rate damping with the pitch rate nominally being con~

trolled to 0~2 deg/sec and the yaw rate to within ~ 2 deg/sec of p tan ~.

p is the SIC roll rate and tan ~ is the tangent of the angle of attack.These rate damping functions are required in order to maintain a stateof coordinated SIC roll. In CMC program Comanche 45, the value usedfor tan ~ was a constant, equal to -.34202, which is approximatelythe tangent of -20 deg, the expected hypersonic trim angle of attackfor a vehicle LID ratio of 0.3.

For the majority of the entry phase, the SIC was so stable that veryfew pitch or yaw jet firings were required and these were usually neededonly during periods of large roll maneuvers. Figures 4-26 and 4-27present complete summaries of post-.05 G pitch and yaw jet activity.Dramatic increases in jet activity are seen during the last 2 minutesbefore drogue chutes deployment. Similar behavior has been notedduring previous missions. It is largely attributable to rapidly changingvehicle aerodynamics as the SIC velocity approaches the transonic region.This increase is also seen in Figure 4-28, which presents time historiesof entry fuel usage per axes. Thirty-three 1bs of RCS propellant wererequired for the entry of Apollo 10 (after .05 G). The table belowbreaks down this propellant usage on a per axes basis and contrasts

4-8

the total amounts used with the consumption during the final 2 minutesof entry.

Total Fuel Total During FinalJet ( 1bs) 2 Minutes (lbs)

+p 1.00 0.72-p 3.90 3.66+y 2.26 1.81-y 1.98 1.85+R 8.88 2.67-R 14.98 3.92

TOTAL 33.00

All pitch and yaw rate damping firings occurred nominally, i.e.,only when the respective measured rates fell outside the 2 deg/sec ratedeadband. Figure 4-24 illustrates a short (9-second) period of pitch jetactivity, along with values of DAP-computed pitch rate every 200 msec.DAP rates are actually computed every 100 msec, but only half of themare downlinked; therefore, not every pitch firing can be directly verified. However, as seen in Figure 4-29, every downlinked pitch ratevalue falling outside the ~ 2 deg/sec deadbands correctly resulted ina pitch jet firing in the proper direction. All other pitch and yawjet activity, for which corresponding rate data were available, wassimilarly verified.

Table 4-1 APOLLO 10 POST-BURN Vg COMPONENTS

Noun 85 6V Residuals (ft/sec)

Before ReS Nulling After RCS Nulling

Maneuver X Y Z X y Z

Evasive 1.0 0.3 0.7

T/L MCC -.9 -0.1 0.3 -0.2 0.0 0.3

LOI 1 0.0 -0.2 0.0

LOI 2 0.5 . -0.4 -0.4

TEl 0.3 1.6 -0.1 0.2 1.6 -0.2

- Means no RCS nulling was attempted

4-10

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4-13

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4-15

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4-16

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4-17

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4-18

\-----

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4-19

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4-20

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4-21

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4-22

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4-23

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4-24

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Figure 4-9 SPACECRAFT DYNAMICS DURINGLUNAR ORBIT INSERTION

4-25

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Figure 4-10 SPACECRAFT DURING LUNARORBIT CIRCULARIZATION

4-27

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Figure 4-11 SPACECRAFT DYNAMICS DURINGTRANSEARTH INJECTION

4-29

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4-33,

Figure 4-15 FOAl BODY YAW RATE DURING LOI 2

4-34

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4-35

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4-36

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4-37

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4-38

Figure 4-19 LOI 1 ROLL ATTITUDE ERROR

4-39

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4-40

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4-41

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4-42

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4-43

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4-44

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4-45

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Figure 4-26 ENTRY PITCH JETS ACTIVITY

4-46

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4-47

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4-48

Figure 4-26 ENTRY PITCH JETS ACTIVITY (CONCLUDED)

4-49

Figure 4-27 ENTRY YAW JETS ACTIVITY

4-50

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4-51

Fi gure 4- 27 ENTRY YAW JETS ACTIVITY (CONT.)

4-52

Figure 4- 27 ENTRY YAW JETS ACTIVITY (CONCLUDED)

4-53

Figure 4-28 ENTRY FUEL CONSUMPTION PER AXES

4-54

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5.0 LM DIGITAL AUTOPILOT

The LM DAP controlled two distinct configurations during the mission:Descent and Ascent.

The LM DAP was not used for control purposes during periods whenthe configuration consisted of LM/CSM docked. Periods of attitude hold,automatic maneuvers, and PGNCS controlled burns were analyzed. Basedon the data reviewed DAP performance was excellent.

5.1 DESCENT CONFIGURATION

There were two burns performed in the descent configuration underPGNCS control; Descent Orbit Insertion and Phasing. 001 was behindthe moon and no TM data were available.

5.1.1 Attitude Hold for Heavy Descent Configuration

Figures 5-1 and 5-2 show phase plane plots for a period of attitudehold prior to the automatic maneuver to 001 attitude. The time rangefor the U and V-axes phase planes is 99:06:32 to 99:07:24 GET.This period of attitude hold is for the heaviest descent configuration.A phase plane plot was not included for the P axis since the attitudeerrors were less than 0.05 deg and the magnitude of the P-axis rateerror was less than 0.006 deg/sec. A single +U jet firing occurredduring the time period used for the U-axis phase plane shown in Figure 5-1.Minimum deadband (0.3 deg) was set. The V-axis phase plane shown inFigure 5-2 required two -V jet firings. The V-axis attitude error wasapproximately equal to 0.4 deg when the second -V firing occurred whichis in accordance with the phase plane logic (Reference 4). The firingcan not occur when the rate error is zero, allowing larger attitudeerrors to be attained. However, a jet firing will occur when the rateerror becomes non-zero.

5-1

5.1.2 Automatic Maneuver to 001 Attitude

An automatic maneuver to 001 attitude started at 99:07:34.425 GET.The P, U, and V-axis rate responses are shown in Figures 5-3, 5-4, and5-5. The maneuver rate was 2.0 deg/sec with commanded rates about all3 axes. The estimated rates followed the desired rates well. The complete automatic maneuver is not shown because a data dropout occurredbefore the maneuver was completed. At the time of this data dropoutthe CDUls were approximately 6.5 deg, 16 deg, and 4.8 deg from the finaldesired CDUls for the X, Y, and Z axes. Actual and desired rates aboutthe U and V-axes were approximately equal when the data dropout occurred.

5.1.3 DPS Phasing Burn

Jets 6 and 14 were used for a 2-jet ullage prior to the burnstarting at 100:58:18.495. Jet 14 was toggled during the ullage tomaintain attitude control. The maximum attitude errors during ullagewere -0.55, +1.87 and +1.00 deg for the P, U, and V axes, respectively.Ullage ended at 100:58:26.675. Data showed the DPS on at 100:58:26.573with a burn duration of 40 seconds. Throttle up from 11.9% to 92.5%occurred at 100:58:51.938. No difficulty with the ~V monitor was encountered since the ~V threshold limit of 36 cm/sec was exceeded at thetime of the second sampling of the PIPA counts (approximately 4 secondsafter ignition). The thrust remained well above the threshold limitthroughout the burn.

A gimbal fail indication occurred at 100:58:38.425 approximately12 seconds after ignition. This indication of a gimbal fail was removed at 100:59:06.425. The GOAls appear to have worked nominallyin steering and tracking the cg. The alarm occurred during a periodof time when the GOAls were reversing directions and is believed tohave been caused by coasting. It was known prior to the flight thatthis alarm would probably occur.

During Apollo 10, the GOA drive rates exceeded the maximum specification value of 0.0662 in/sec +10% (Reference 3) as was observedon Apollo 9. This factor does not influence the controllability of

5-2

. ,

the DAP during the burn, but would lead to errors in positioning theengine bell prior to a burn.

Figures 5-6, 5-7, and 5-8 show phase plane plots for the DPSphasing burn with brief periods of attitude hold before and after theburn. Numerous jet firings occurred throughout the burn and the ullageperiod as required by the phase plane logic for attitude control. Thepeak angular rates about the U and V axes were -1.22 deg/sec and -0.78deg/sec, respectively. The peak attitude errors for both axes wereless than 1.75 deg. The burn deadband was one deg. The deadband forthe attitude hold before and after the burn was 0.3 degree. The phaseplane plots cover the period of both deadbands during the time rangefrom 100:57:08.425 to 100:59:09.425 GET. In general, the maximumattitude errors and attitude errors at maximum thrust for this burn werecomparable to the preflight simulation results. The estimated ratesfor the simulation results were also comparable to the actual ratesduring the burn. The actual burn used approximately 6.67 lbs of RCSfuel, whereas 7.73 1bs of RCS fuel were required in the preflight simulation test. This was nominal behavior since the actual burn startedfrom an assumed trimmed-up position and the simulation run had an initial3a mistrim.

5.2 ASCENT CONFIGURATION

After staging the APS Insertion Burn was performed under PGNCScontrol followed by CSI, an AGS controlled CDH, PGNCS controlled TPI,CSM active docking, LM jettison, and CSM active separation. The finalburn was the APS Burn-to-Dep1etion

5.2.1 APS Insertion Burn

Ullage for the APS Insertion burn was initiated at 102:54:58.685and terminated at 102:55:02.795. Jets 2, 6, 10 and 14 were used for the4-jet ullage with jets 6 and 10 toggling to maintain attitude control.The maximum attitude errors during ullage were -0.48, -1.16 and +1.08deg for P, U, and Vaxes, respectively. The DAP DATA LOAD ROUTINE (R03)

5-3

was executed after entering P42. This resulted in the deadband forthe burn being changed to 0.3 deg rather than the usual one degreedeadband. The R03 execution also commanded a 4-jet ullage rather thana 2-jet ullage due to the data previously loaded into R03. Ignitionwas at 102:55:01.40 (TEVENT Data) with cutoff at 102:55:16.95 GET.Burn performance was nominal for the minimum deadband. The LGCestimate of LM mass decreased 176.4 1bs during the burn. No difficultywith the ~V monitor was encountered since the ~V threshold of 308em/sec was exceeded at the time of the second sampling of the PIPAcounts (approximately 4 seconds after ignition). The thrust remainedwell above the threshold limit throughout the burn.

Figures 5-9, 5-10 and 5-11 show the P, U, and V axes attitude errorsversus time for the APS Insertion burn. The maximum attitude errorsnear the start of the burn. were -0.48, 1.18, and -2.30 deg for the P,U, and V axes, respectively. The jet firing logic was effective inrapidly reducing the errors to maintain the 0.3 deg deadband. A plotof P, U, and Vaxes rate errors versus time is shown in Figures 5-12,5-13 and 5-14. The maximum rate errors during the APS Insertion burnwere -1.17, +2.51, and -2.16 deg/sec for the P, U, and V axes, respectively.Some P-axis jet firings were required to maintain attitude control. Themajority of the jet firings were -U and +V. The cg offset apparentlycaused predominantly positive U-axis errors and negative V-axis errors.Some +U and -V jet firings were also required. In general, the maximumattitude errors were less than the errors observed in preflight simulation. More ReS activity was required than predicted by preflight tests.The preflight simulation results required 6.19 1bs of RCS fuel and theactual flight required 10.47 1bs of RCS fuel. These results were expected since the preflight tests used one deg deadband for the burn,whereas the APS Insertion burn during Apollo 10 used a 0.3 deg dead-band and a 4-jet rather than a 2-jet ullage.

5-4

5.2.2 Attitude Hold for Heavy Ascent Configuration

P, U, and V axes phase plane plots are shown in Figures 5-15,5-16, and 5-17 for a period of attitude hold prior to the APS Insertionburn. The time range used was 102:53:18.425 to 102:54:29.425 GET.The phase plane logic maintained a good limit cycle for this heavyascent configuration with a 0.3 deg deadband desired.

5.2.3 Automatic Maneuvers to CSI Burn Attitude

An automatic maneuver to CSI attitude was initiated at 103:01:13.425GET. The maneuver rate was 2 deg/sec with commanded rates about all3 axes. Figures 5-18, 5-19, and 5-20 show. the rate response for the P,U, and V axes during the automatic maneuver. Figure 5-21 shows thechange in the actual CDU angles during the automatic maneuver. Onlyeight readable data points were available and no attempt was made toevaluate the maneuver.

5.2.4 Automatic Manevuer to TPI Burn Attitude

An automatic maneuver to TPI attitude was initiated at 105:18:02.425GET. The maneuver rate was 2.0 deg/sec with rates commanded about theU and V axes. Figures 5-22 and 5-23 show the U and V axes rate responsesduring the automatic maneuver. Figure 5-24 shows the change in the CDUangles during the automatic maneuver.

5.2.5 Terminal Phase Initiation (TPI)

TPI was a 4-jet RCS burn beginning at 105:22:55.575. Jets 2, 6,10, and 14 were used during the burn with jets 6 and 10 toggling to maintain attitude control. The maximum attitude errors during the burnwere +0.68, -1.27, and +1.33 deg for the P, U, and V axes. The maximumrate errors during the burn were -0.38, +0.59, and -1.10 deg/sec for theP, U, and Vaxes, respectively. Figures 5-25, 5-26 and 5-27 presentphase plane plots for the P, U, and Vaxes during the burn. Numerous+U and -V jet firings were required during the burn to maintain attitudecontrol. These firings were achieved when jets 10 and 6 were turnedoff with jets 2 and 14 remaining on. Some P jet couples were also

5-5

required by the phase plane logic. Due to the position of the cg, theU and V attitude error remained near the deadband limit for the durationof the burn. The cg position of the cg, the U and V attitude errorremained near the deadband limit for the duration of the burn. Thecg position had a tendency to produce -U and +V attitude errors duringthis Res burn.

5.2.6 Attitude Hold for Lightest Ascent

Figure 5-28a shows a P axis phase plane plot for a period of attitudehold after the APS burn to depletion. The time period covered is116:15:53.445 to 116:16:54.445 GET. The deadband was initially 0.3deg and then it was changed to 5 deg. The change in deadband was verysmooth. Figure 5-28b shows the P axis phase plane with 5 deg deadbandfrom 116:16:54.445 to 116:21:41.445 GET. Figure 5-29a shows the U axisphase plane (116:15:53.445 to 116:16:49.445) with narrow deadband andthe U-axis phase plane with wide deadband is shown in Figure 5-29b(116:16:49.445 to 116:21:39.445). Figure 5-30a shows the V-axis phaseplane (116:15:53.445 to 116:16:54.445) with narrow deadband. TheV-axis phase plane (116:16:54.445 to 116:21:35.445) with wide deadbandis shown in Figure 5-30b. The phase plane logic maintained a gooddeadband for this light ascent configuration.

5-6

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5-23

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5-24

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5-25

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5-26

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5-28

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5-29

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5-33

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5-34

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5-39

6.0 AGS ANALYSIS

AGS performance was excellent. Overall AGS performance data arepresent in the Apollo 10 Mission Report (Reference 1). Apollo 10 AGSaccuracy analysis was based primarily on comparisons of the AGS sensedvelocity during the APS burn to depletion with PGNCS sensed velocity.Section 6.2 contains the results of an error separation study for thatburn.

6.1 OVERALL SYSTEM PERFORMANCE SUMMARY

The AGS provided LM control for the CDH burn and the APS burn todepletion and provided a backup capability during the PGNCS controlled001, phasing, insertion and TPI maneuvers.

One AGS inf1ight calibration was scheduled shortly before undockingbut was not performed due to lack of time as the result of a tunnelventing problem which occurred during the preparation for undocking.Accelerometer bias and gyro drift were calculated from the availabledownlink data and the instrument values were very close to the prelaunch flight load. Therefore, omission of the calibration procedureswas of no serious consequence. On a lunar landing mission an inf1ightcalibration should be perfonmed or the mission objectives could becompromised.

In accordance with preflight planning, no AGS radar updates wereincorporated during the rendezvous sequence.

During the LM staging operation the LM vehicle experienced highrotational body rates and for the Z body axis, the input rate causedthe output of the Z gyro to be saturated for 3 seconds. SubsequentAGS operation was nominal indicating the system was not permanentlydegraded as a result of the high input rate.

Improved system performance data, formulated after the publicationof the Apollo 10 Mission Report, are presented in the following sections.

6-1

6.1.1 Velocity-To-Be-Gained Residual Comparisons

The differences between PGNCS and AGS velocity-to-be-gained atthe end of LM burns with telemetry coverage are shown in Table 6-1.

The residual Vg comparisons show that the overall AGS performanceduring the burns was well within the accuracy required for it to havesuccessfully guided the LM through the burns.

The Vg data is also of value in illustrating the behavior of thesteering loop during an AGS controlled burn. Figure 6-1 shows theVg magnitude for the APS burn to depletion. The smooth approach towardzero indicates that the AGS steering was functioning correctly. Thevector never attained zero on this burn since the Vg was set largeknowing that propellant depletion would occur before the Vg was reducedto zero.

6-2

6.1.2 PGNCS/AGS Alignment Accuracy

The AGS inertial reference was aligned to the PGNCS inertial reference at least ten times during the flight. Differences between thePGNCS gimbal angles and those calculated from the AGS direction cosinesfor the cases in which telemetry data were available shortly after thealignment are listed in Table 6-2. All differences are within the.067 degree specification.

6.1.3 Environment

During the LM staging operation (initiated at 102:45:16.9 GET) theLM experienced high rotational body rates, apparently the result ofmisplaced mode control switches. A discussion of the problem and theprobable cause is presented in the Apollo 10 Mission Report (Reference 1).As a result of the problem the Z gyro axis input rate exceeded the AGSdesign limit. The maximum observed body rates based on rate gyroassembly (RGA) data were:

X (Yaw) = 25 deg/sec

Y (Pitch) = 17 deg/sec

Z (Roll) - 25 deg/sec

A precise yaw and roll rate cannot be established since the instrumentation range was ~25 deg/sec and the signals were limited during thestaging. The AGS sensed body rates derived from changing AGS directioncosines are plotted in Figure 6-2. In the figures, it can be seen thatduring a period of high angular acceleration the Z body rate suddenlyflattened for 3 seconds. During the same 3 second period the Z gyro20 ms pulse accumulation (sampled each second for telemetry) was 580counts, which is the maximum possible pulse count over a 20 ms interval.Therefore the gyro was apparently saturated (i.e., the input was greaterthan 25.347 deg/sec). The X and Y gyros did not indicate saturation.Approximately 3 minutes later the AGS was realigned to the PGNCSinertial reference. Corrections of 0.23, -0.39, and 1.18 deg forX, Y, and Z, respectively, were required to update the AGS to PGNCS.

6-3

SUbsequent AGS operation was nominal, indicating the system was notpermanently degraded as a result of the high rate.

6.2 SENSOR PERFORMANCE

AGS sensor performance was determined from studying several periodsof coasting flight and the APS burn to depletion. The coasting flightintervals were used to determine static accelerometer bias and gyrodrift. Data taken during the APS burn to depletion were used in estimating misalignments, scale factor errors, dynamic accelerometer bias,and dynamic gyro drift. Two sets of errors were derived, both of whichwhen used to correct the AGS data will result in a fit of AGS sensedvelocity to the PGNCS data. Two error sets are presented becauseaccelerometer dynamic bias is inseperable from accelerometer scalefactor error and/or misalignment due to the characteristics of the burnanalyzed. The methodology used for the powered flight error separationis presented in Appendix A. A compilation of sensor performance duringcoasting and powered flight is presented in Section 6.2.1 and 6.2.2;comparisons of these results with the AGS error model are presented inSection 6.2.3.

6.2.1 Coasting Flight Analysis

Gyro drift and accelerometer bias data were obtainable from theavailable telemetry data during the coasting flight.

Gyro drift was determined during three periods of coast. The inflight drifts and time intervals are listed in Table 6-3. Also listedare the final pre-installation calibration (PIC) values (which were theflight compensation values) and the final earth prelaunch calibration(EPC) values. The inflight drifts were obtained by least square fittingthe PGNCS/AGS integrated body rate differences. The flight load compensation was removed to obtain total drift. The differences over thelast period of free flight listed in Table 6-3 and through the APSburn to depletion (from tags = 67925 through 68175) are plotted inFigures 6-3, 6-4 and 6-5.

6-4

Static accelerometer biases were determined over ten periods ofcoasting flight; the data are listed in Table 6-4. The numbers werecalculated by differencing the sensed velocities accumulated over themeasurement period, and dividing by the time intervals. The flightcompensation was then removed to obtain total bias.

6.2.2 APS Burn to Depletion Analysis

The APS burn to depletion was used since it was the only LM thrusting maneuver on Apollo 10 which was of sufficient duration and acceleration to permit estimation of other than static sensor errors. The highfrequency and amplitude of spacecraft motion (peak-to-peak rates of10 deg/sec; period of 2-3 sec) during the Apollo 9 mission APS depletionburn (PGNCS controlled) precluded the data's use for sensor errordetermination. However, because of the tighter deadband for the AGS/CEScontrolled Apollo 10 burn (0.37 deg pitch and roll, 0.47 deg yaw),the data was suitable for analysis. Peak body rates during the burnwere about 0.3 deg/sec (Figures 6-6, 6-7, and 6-8).

Velocity Differences

The X body axis acceleration over the burn is plotted in Figure6-9. The length of the burn was about 210 seconds; the total bodyaxis ~VIS were 3837 fps in X, -2.4 fps in Y, and 92.2 fps in Z (Figures6-10,6-11, and 6-12). The uncompensated PGNCS/AGS sensed velocitydifferences at the end of the burn (Figures 6-19, 6-20, and 6-21). . .were: ~X = -0.96 fps; ~Y = -24.6 fps; ~Z = 18.1 fps. In comparisonthe next largest burn, the APS insertion burn, produced a ~V of about220 fps and PGNCS/AGS velocity residuals of less than 0.20 fps.

When AGS minus PGNCS differences were first calculated, the 90hour 0 minute 3 second Kfactor (constant which when added to AGSclock time yields an equivalent PGNCS clock time) stored in the LGCwas used. The differences, particularly along the X (thrust) axis,followed the acceleration profile, indicative of a data timing error.The error in time appeared to be 2.1 seconds. Further investigationrevealed that the true Kfactor was 90 hours 00 minutes 0.87 seconds

6-5

rather than the value stored in the LGC. Nominally Kwould have beenan even 90 hours, however, a nominal time synchronization is not alwaysobtainable. RTCC determines the true Kfactor in near real time andsends an update to the LGC. For this update the value was determinederroneously. The problem was of no consequence to this portion of themission, since no real time velocity comparisons (PGNCS versus AGS)were required. All velocity comparisons used in this analysis weremade using the true Kfactor to relate PGNCS time to AGS time.

Accelerometer Errors

In Figures 6-13 through 6-15, the PGNCS IMU gimbal angles wereused to transform the PGNCS velocities to body coordinates beforedifferencing. Since the gimbal angles are a measure of the orientationof the body axes relative to the PGNCS platform the velocity differencesare independent of the AGS attitude reference. Therefore no gyro errorsappear in this comparison. The comparison is, however, AGS relative toPGNCS, and thus contains PGNCS accelerometer errors, gimbal angle misalignment and quantization errors as well as the AGS accelerometererrors.

The cause of the +0.25 fps step change in the Z velocity differences(Figure 6-15) at ignition has not been established. It is thought tohave occurred in processing the data, and is not considered indicativeof hardware error.

The accelerometer errors chiefly responsible for the residuals aredynamic bias, static bias and scale factor error in X, and dynamic bias,static bias and misalignment in Y and Z. Separations of the effectsof dynamic bias from scale factor error effects and from accelerometermisalignment effects cannot be accurately made using data from thisburn because of insufficient variation in acceleration. Using theData Comparison program and LM Error Analysis program as discussed inAppendix A, two sets of accelerometer errors sufficient to null the

6-6

residuals were determined: static bias plus dynamic bias (Table 6-5)and static bias plus scale factor error in X and misalignment in Yand Z (Table 6-6). No X accelerometer misalignment and no Y or Zaccelerometer scale factor errors could be determined since theseerrors were insensitive during the APS engine burn (majority of thrustwas along the X axis). The static bias listed in Table 6-5 and 6-6 isthat measured during a period of coasting flight just before the burn(the bias remaining after compensation). The dynamic bias listed wasfound by subtracting the AGS static bias and PGNCS static bias fromthe total bias necessary to null the residuals during the burn. Thisis actually the difference between AGS dynamic bias and PGNCS dynamicbias. The compensated velocity differences appear in Figures 6-16,6-17 and 6-18.

Attitude Reference Misalignment and Gyro Drift

Figures 6-19, 6-20, and 6-21 are the PGNCS/AGS velocity differences produced after transforming the PGNCS velocities to bodycoordinates using the AGS direction cosine matrix. These differencesare due to the accelerometer errors discussed above plus all gyroerrors and initial misalignment of AGS attitude reference relativeto PGNCS. The initial misalignment is due to AGS/PGNCS alignmentcomputational errors, PGNCS gimbal angle quantization, and accumulatedAGS/PGNCS relative drift since the time of the last alignment.

The values of initial attitude reference misalignment used werefound by differencing the PGNCS gimbal angles and the Euler anglescalculated from the AGS direction cosine matrix near the beginningof the burn. These values are listed as misalignments about platformaxes in Tables 6-5 and 6-6. They account for all but one foot per secondor less of the residuals and are primarily due to gyro drifts accumulatedover a period of about l! hours since an alignment.

The gyro drifts listed were calculated as the slopes of straightlines fit by the method of least squares to the integrated PGNCS/AGSbody rate differences during the burn (Figures 6-3, 6-4, and 6-5).

6-7

They are listed in Tables 6-5 and 6-6 and include the effects of AGSstatic and dynamic gyro biases, AGS X-gyro spin axis mass unbalance,and all PGNCS gyro errors.

Having determined the gyro drift and initial attitude referencemisalignment and having found the accelerometer errors, the AGS velocitydata were corrected for these errors and compared with the PGNCS data.The compensated velocity differences (using AGS direction cosines forthe platform to body coordinate transformation) are plotted in Figures6-22, 6-23 and 6-24. All residuals (except the 0.25 fps processing caused step change in the Z residuals) were reduced to less than 0.10fps.

6.2.3 Comparison of Sensor Analysis Results to AGS Error Models

The estimates of the sensor errors that were derived from theinflight data are all within the 3cr ranges expected, based on the AGScapability estimate, and are all within the AGS error budget. Theratio of ASA 016 parameter values to one sigma values from the capabilityestimate or ASA 016 preflight performance estimate are given in Table6-7. These data show the AGS performance in terms of expected standarddeviation and as a whole show excellent corroboration of the a priorisystem error modeling. The general conclusion is that ASA 016 performed with high accuracy, well within that required for the mission,and the gyro bias stability was exceptional.

Error Model Comparison

Tables 6-8 and 6-9 present the inflight error estimates from Section6.2.2 in the form of the error model used in the AGS Capability Estimate(Reference 7).

Two comparison models are listed. The first is an estimate of ASA016 performance prepared for the FP5 FRR. The second comparison modelis the Error Budget from the AGS capability estimate (Reference 7) which

6-8

is a breakdown of the specification numbers in the current versions ofthe AGS Performance and Interface Specification (Reference 8). Inaddition to the terms listed in Tables 6-8 and 6-9 the Apollo 10 missionyielded data on gyro and accelerometer long term stability and short termrepeatability, which are compared with the capability estimates inTables 6~10 through 6-13.

Accelerometer Bias Repeatability

The standard deviations of accelerometer biases over a l2-hourflight interval were computed from the data in Table 6-4 and are givenin Table 6-10. The standard deviations compare well with the ErrorBudget value for acceleromater bias repeatability, which is 20 ~g.

Accelerometer Time Stability

Accelerometer instrument biases were derived from the free flightdata by determining the apparent bias from velocity data and addingthe flight compensation value. The inflight ~ias values are differencedfrom the preflight bias values measured in the laboratory 59 days earlier.The average of these deltas are presented in Table 6-11 along with thecapability estimate and error budget from Reference 7. These dataindicate good accelerometer bias time stability.

The gyro inflight bias repeatabilities over a period of 12 hours arepresented in Table 6-12 below, along with the capability estimate anderror budget values from Reference 7.

These data are well within the Error Budget and capability estimatelimits, and indicate excellent short term gyro bias stability for thismission.

Gyro Bias Time Stability

The gyro bias shifts from Earth Prelaunch Gyro Calibration (EPC)to free flight measurements are presented in Table 6-13 along with thecapability estimate and error budget from Reference 7. The maximum

6-9

observed shift was +0.11 deg/hr., which is well within the capabilityand error budget limits.

6.2.4 Analysis Accuracy

The estimation of the modeled sensor errors (accelerometer biases,gyro drifts and inertial reference misalignments) is subject to anumber of errors. These include errors caused by the following effects.

o Data readout quantization.

o PGNCS errors.

o AEA Computational Errors

o Sampling and Processing Errors

These are discussed below.

Quantization

On Apollo Flight 10 the AGS sensed body axis accumulated velocities(Vdx ' Vdy ' Vdz ) were quantized at 0.0625 ft/sec. Assuming! 0.03125ft/sec as the limits of a uniform distribution, the 30 uncertaintyin the accelerometer biases calculated from the differences of thesevelocities is + .03125~/6 ft/sec 2 , where t is the bias measurement

t

interval. This uncertainty is very small in the measurement of staticbias because of the long time periods used. For example, for the biasmeasured over a 1510 second period just before the APS burn to depletion(Table 6-4), the error is about + 1.5 ~g. Even for measurements oftotal dynamic drift during the burn, this error contributes only! 11 ~g

The velocity quantization also causes uncertainties in determinationof accelerometer misalignment and scale factor error. For Y and Zaccelerometer misalignment and X accelerometer scale factor, themeasurement uncertainties are both approximately + .03125\1:3 , where

AVxAVx is the total X velocity change over the burn. For the APS depletionburn, these uncertainties are about 3 sec in misalignment and 14 ppmin scale factor error.

6-10

'"'The PGNCS gimbal angle CDU readouts are quantized at 40 sec. Theseare the source of PGNCS angular measurements and are responsible for30 uncertaintie~f !. 20 -/3 sec in the estimates of initial misalignment and!. 20 -y 3/t deg/hr in the estimates of gyro bi as, where tisthe analysis interval in seconds. For the shortest coasting flightinterval used to measure static gyro bias, this uncertainty is !. .04deg/hr; for bias measured during the APS burn to depletion, it is + 0.16deg/hr.

PGNCS Errors

All AGS errors derived from the PGNCS/AGS velocity differences arethose relative to PGNCS; i.e., they contain both PGNCS and AGS errors.PGNCS gyro drifts as determined inflight were sam11 enough relative tothe AGS drifts that their effects may be neglected. PGNCS accelerometerbiases are significant and were measured inflight as -50 ~g in X, -160~g in Y, and 30 ~g in Z, (in body coordinates: +47 ~g in X, -155 ~g

in Y, and +50 ~g in Z). These biases are accounted for in the analysis.

AEA Computational Error

The AEA computational error in the attitude reference (directioncosine) data due to truncation, roundoff and algorithm errors can beas large as 0.14 deg/hr (Reference 9).

Sampling and Processing Errors

The effects of the low (1 sample per second) telemetry sampling rateand PGNCS to AGS data time interpolation produce errors which are afunction of the vehicle oscillatory motion as described in Section 2.4-3of Reference 9.

The limit cycling experienced in the APS burn to depletion wason the order of 0.2 deg/sec p-p at 0.1 to 0.2 cps and the same estimateof sampling and processing errors is used as for Apollo 9; i.e., 0.2deg/hr gyro drift uncertainty and 25 ~g .accelerometer bias uncertainty.

During coasting (free) flight these same error sources contributeapproximately 0.10 deg/hr gyro fixed drift uncertainty and ~'102 + C~0)2!'fl9

6-11

accelerometer bias uncertainty, where t is the analysis measurementinterval in minutes.

6-12

Table 6-1 VELOCITY-TO-BE-GAINEDRESIDUAL MAGNITUDES

Vg Magnitude - FpsBurn AGS PGNCS

PhasingInsertionCDHTPIAPS DEPLETION*

2.191.250.502.25

762

1. 74

1. 170.542.26

765

*The targeted value of Vg was larger thancould be attained with the fuel onboard.

6-13

Table 6-2 PGNCS/AGS ALIGNMENT ACCURACY

CDU - AEA Angular DifferenceAlignment Time X Y Z

(Deg) (Deg) (Deg)

97: 29 :1898:57:58

100:52:25102:48:18104:36:48105:09:45

0.006-0.020.005

-0.007-0.05-0.03

0.0030.030.0010.02

-0.02-0.04

-0.0020.030.001

0.04

*-0.04

*Data quality is not sufficient to establish an accuratevalue; however, the difference appears to be less than0.067 degree.

6-14

Tab

le6-

3GY

ROST

ATIC

DRIF

TM

EASU

REM

ENTS

(DEG

/HR)

O'l I .......

(J'l

Axi

s

x y Z

INFL

IGHT

MEA

SURE

MEN

TS*

(With

Com

pens

atio

nRe

mov

ed)

97:0

6:2Q

-+10

2:27

:35-

+10

8:24

:53

Fina

lPI

CEIP

C97

:19:

5510

2:44

:56

108:

50:0

1

-0.

11-

0.28

-0.

17-

0.12

-0.

20

-0.

41-

0.61

-0.

65-

0.58

-0.

61

-0.

44-

0.62

-0.

64-

0.60

-0.

69

*All~

0.17

deg/

hr.

Table 6-4 ACCELEROMETER STATIC BIAS MEASUREMENTS

BIAS (lJg)*X Y Z

FINAl CALIBRATION 59 - 107 17

FLIGHT LOAD 47 - 119 24

INFLIGHT MEASUREMENTS(WITH FLIGHT LOAD REMOVED)

From To At(sec)

96:58: 15 97:08:13 598 - 5 - 106 - 67

98:08:13 98:33:07 1494 + 4 - 113 - 80

98:51:11 99:00:43 572 - 8 - 119 - 85

100:36:22 100:56:24 1202 - 18 - 119 - 93

101:02:26 101: 16: 24 838 - 9 - 110 - 96

102:28:04 102:43:52 948 - 19 - 119 - 99

102:47:16 102:54:29- 433 - 7 - 101 - 84

104:35:41 104:43: 15 454 - 21 - 102 - 78

104:43:57 105:01:23 1046 - 35 - 126 - 95

108:24:53 108: 50:01 1508 - 25 - 114 - 84

*Measurement Error =~ 11 lJg

6-16

Tab

le6-

5ER

ROR

SET

#1-

APS

BURN

TODE

PLET

ION

Init

ial

Att

itud

eA

ccel

erom

eter

Acc

eler

omet

erT

otal

Ref

eren

ceM

isal

ignm

ent

Axi

sS

tati

cB

ias

Dyn

amic

Bia

sG

yro

Bi~s

(Abo

utP

latf

orm

Axe

s)(ll

g)(ll

g)(d

eg/h

r)_

(sec)

X-

72+

11+

50+

29-

0.22

±.0.

28-

1400

+32

O'l

5+

11-

0.26

.:t.0.

2895

6+

32I

Y+

+6

+29

+--0 ......,

Z-

108

.:t.11

+84

.:t.

29-

0.08

.:t.0.

28-

130

+32

Tab

le6-

6ER

ROR

SET

#2-

APS

BURN

TODE

PLET

ION

m I -'

00

Axi

s

x y z

Init

ial

Att

itud

eA

ccel

erom

eter

Acc

eler

omet

erA

ccel

erom

eter

Tot

alR

efer

ence

Mis

alig

nmen

tS

tati

cB

ias

Mis

alig

nmen

tS

cale

Fac

tor

Gyr

oB

ias

(Abo

utP

latf

orm

Axe

s)(11

g)(s

ec)

Err

or(P

PM)

(Deg

/Hr)

(Sec

)

-72

+11

*+

115

+44

-0.

22+

0.28

-14

00+

32

+5

+11

+3

+9

*-

0.25

+0.

28+

956

+32

-10

8+

11+

42+

9*

-0.

08+

0.28

-l3

0!.

32

*Err

oris

not

sens

itiv

eto

burn

anal

yzed

.

Tab1e 6-7 PERFORMANCE SUMMARY

Ratios of Parameter Value tothe Expected 10 Va1ues*

X y Z

Accelerometer Bias Repeat-ability 2.28 1.64 1.96

Accelerometer Bias TimeStability (60 days) 1.18 0.10 1.67

Accelerometer Dynamic Error* 0.99 0.40 0.79

Total Accelerometer PoweredFlight Error* 0.41:- 0.32 0.15

Gyro Bias Repeatability 0.81 0.81 1.04

Gyro Bias Time ~tabi1ity

(20 days) 0.61 0.00 . 0.11

Gyro Dynamic Error* 0.1l. ·1.23 0.81

Total Gyro Powered F1 ight0.40Error* 0.63 0.76

* From the AGS capability estimate or ASA 016 Performance Estimates.

6-19

Tab

le6-

8EQ

UIVA

LENT

ACCE

LERO

MET

ERBI

ASER

RORS

(APS

BURN

-TO-

DEPL

ETIO

N),~g

ASA

016

ASA

016

Pre

flig

ht(4

)E

rror

Bud

get

from

AGS

Inf1

ight

Est

imat

ePe

rfor

man

ceE

stim

ate

P&I

Spe

cifi

cati

onM

ean

30-

Mea

nG

auss

ian

30-

X-

72+

1119

147

9

Y+

5+

1117

947

9

Z-1

08+

1117

947

9

X+

50+

299

124

2715

9

Y+

6+

29+5

234

672

3

Z+

96+

29-

533

772

3

X-S

cale

Fac

tor

and

Dyn

amic

Err

ors

(2)

Yan

dZ

Dyn

amic

Err

ors,

ASA

Acc

el

erom

eter

Inte

rnal

Mis

alig

nmen

tan

dAS

Ato

IMU

Mou

ntin

gP

oint

sM

isal

ignm

ent

(2)

Acc

eler

omet

erB

ias

and

Non

line

arit

y(1

)

C'l I N o

Tot

al(lJ

g)(3

)X

-22

+27

922

827

Y+

11+

27+5

239

0Z

-24

+27

-5

382

.NOT

ES:

(1)

Inf1

ight

Est

imat

e:L

ast

Fre

e-F

ligh

tD

ata

Peri

od(2

)In

f1ig

htE

stim

ate:

Dif

fere

nce

betw

een

mea

sure

dto

tal

erro

ran

dm

easu

red

fixe

dbi

as.

(3)

Inf1

ight

Est

imat

e:D

eriv

edfr

omve

loci

tyco

mpa

riso

ns.

(4)

Dat

aar

efro

mR

efer

ence

3,

exce

pttim

est

abil

ity

and

acce

lero

met

erbi

asfro

mR

efer

ence

2w

ere

inco

rpor

ated

tom

ake

them

com

patib

lew

ithth

eac

tual

flig

ht

cond

itio

nsw

itho

utan

IFC

.Th

eal

ignm

ent

and

scal

efa

ctor

erro

rsin

this

tabl

eap

pear

diss

imil

arto

the

capa

bili

tyes

tim

ate

tabl

esbe

caus

eth

eyha

vebe

enco

nver

ted

toeq

uiva

lent

bias

erro

rsin

~gIS.

506

867

867

0"1 I N -'

Gyr

oFi

xed

Dri

ft(1

)

X-G

yro

Dyn

amic

Dri

ft(2

)(4

)X

-Gyr

oSp

inA

xis

Mas

sU

nbal

ance

(2)

Yan

dZ

Gyr

oD

ynam

icD

rift

(2)

(4)

Tot

al(d

eg/h

r)(3

)(5

)

Tab

le6·

·9EQ

UIVA

LENT

GYRO

BIAS

ERRO

RS(A

PSBU

RN-T

O-D

EPLE

TIO

N),

DEG/

HR

ASA

016

ASA

016

Pre

flig

ht

Err

orB

udge

tFr

omJn

f1ig

htE

stim

ate

Perf

orm

ance

Est

imat

eP&

IS

peci

fica

tion

~3a

..G

auss

ian

30

X-0

.09

+0.

200

0.75

.95

Y-0

.20

+0.

200

0.75

.94

Z-0

.25

!.0.

200

0.75

.94

X-0

.11

0.37

.77

-0.1

3+

0.34

X0

0.41

.58

Y-0

.06

+0.

34-0

.24

0.44

.69

Z+0

.17

+0.

34+0

.04

0.48

.90

--

X-0

.22

!.0.

29-0

.11

0.93

1.35

Y-0

.26

!.0.

29-0

.24

0.88

1.16

Z-0

.08

+0.

29+0

.04

0.90

1.30

(3)

(4)

NOTE

S:(l

)In

f1ig

htE

stim

ate:

Las

tF

ree-

Fli

ght

Dat

aP

erio

d.(2

)In

f1ig

htE

stim

ate:

Dif

fere

nce

betw

een

mea

sure

dto

tal

erro

ran

dm

easu

red

fixe

dbi

as.

Infl

igh

tE

stim

ate:

Der

ived

from

atti

tud

era

teco

mpa

riso

ns.

The

Err

orB

udge

tva

lues

wer

ede

rive

dfro

mth

eoG

SC

apab

ilit

yE

stim

ate

asfo

llow

s:M

ulti

ply

jfti

mes

unif

orm

erro

ran

dRS

Sth

ere

sult

with

the

Gau

ssia

n(3

0)er

rors

.(5

)Th

eE

rror

Bud

get

valu

esar

eth

eRS

Sof

the

abov

edy

nam

icer

rors

and

30fi

xed

dri

ft.

Table 6-10 STANDARD DEVIATION OF ACCELEROMETER BIASES

BA = 11.4 119X

BA = 8.~ 119Y

BA = 9.8 119Z

RMS = 9.9 llg(Standard Deviation)

Table 6-11 ACCELEROMETER BIAS TIME STABILITY(Averages of 10 Free-Flight Measurements Differenced with PICValues).

Channel t:,-Time t:,-Bias Ensemble* Error*(days) Capabity Estimate Budget

(60 days) (60 days)X 59 - 73 185 489

Y 59 - 6 185 489

Z 59 103 185 489

6-22

Table 6-12 GYRO BIAS REPEATABILITY

Standard Deviationof

Free Flight Capabil i ty ErrorMeas. Estimate (30) Budget

X 0.035 0.13 0.10Y 0.035 0.13 0.10Z 0.045 0.13 0.10

Table 6-13 GYRO BIAS TIME STABILITY

Mean ofInflight

Meas. Ensemble Error-EPC Capabil ity Budget

Axis (20 days) (18 days) (18 days)

X + 0.11 0.54 0.68

Y 0.00 0.54 0.68

Z + 0.02 0.54 0.68

6-23

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6-29

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6-31

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6-35

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6-38

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6-39

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6-40

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6-41

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6-42

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6-43

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6-44

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Figure 6-16 COMPENSATED SENSED X-AXIS VELOCITY DIFFERENCE;PGNCS GIMBAL ANGLES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-45

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Figure 6-17' COMPENSATED SENSED V-AXIS VELOCITV DIFFERENCE;PGNCS GIMBAL ANGLES USED FOR TRANSFORM - APSBURN TO DEPLETION .

6-46

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FiQure 6-18 COMPENSATED SENSED Z-AXIS VELOCITY DIFFERENCE;PGNCS GIMBAL ANGLES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-47

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Fiqure 6-19 _ UNCOMPENSATED SENSED X-AXIS VELOCITY DIFFERENCE;AGS DIRECTION COSINES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-48

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Fiqure 6-20. . ..

UNCOMPENSATED SENSED Y-AXIS VELOCITY DIFFERENCE;AGS-CIRECTION COSINES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-49

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Figure 6-21 - UNCOMPENSATED SENSED Z-AXIS VELOCITY DIFFERENCE;AGS DIRECTION COSINES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-50

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Figure 6-22 COMPENSATED SENSED X-AXIS VELOCITY DIFFERENCE;AGS DIRECTION COSINES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-51

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.,...Fi gure 6-23

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6-52

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Figure 6-24 COMPENSATED SENSED Z-AXIS VELOCITY DIFFERENCE;AGS DIRECTION COSINES USED FOR TRANSFORM - APSBURN TO DEPLETION

6-53

7.0 OPTICS NAVIGATION SIGHTINGS

7.1 STAR-HORIZON SXT SIGHTINGS

The star-horizon navigation data for Apollo 10 consisted of sixbatches or groups of sightings. The data were processed with the HOPEprogram. The results are summarized below for trunnion bias, standarddeviation and horizon bias by batch number. Each batch consists ofsightings taken on three different stars and using both near and farhorizon.

Batch

2

3

4

5

6

Trunnion Bias {i 9m) Horizon Bias(deg) deg (Km)

- .005 .004 33.4

- .005 .002 18.7

+ .004 .002 21.4

- .002 .002 23.6

- .003 .004 7.9

- .005 .003 14.5

The results for trunnion bias and standard deviation are comparablewith previous flights, but the wide variation in horizon bias is peculiarto Apollo 10. An effort was made to ascribe this variation to thelatitude of the sub-stellar tangent point and/or the angle between the1ines-of-sight and the sun direction. The conclusion is that there isno obvious correlation between the horizon bias variation and eitherof the above.

TRW program HOPE was used to determine the computed tangent pointfor each sighting and from this point the latitude was determined. Theresults indicate that the horizon bias altitude variation is not asimple function of latitude of the point of tangency of the line-of-sight.

7-1

The second approach was to calculate the sun line relative to eachSXT LOS. Using the down1inked computer words, REFSMMAT, CDU angles andshaft and trunnion angles, the landmark and star 1ines-of-sight werecomputed in body coordinates. An ephemeris tape plus computer valuesfor vehicle position were used to compute the sun direction in the samecoordinates. The angle between the sun direction and each 1ine-of-sightwas then computed. The results are contained in Table 7-1 •. Batch 3was not processed because of a tape problem. The individual horizonbiases were determined by computing the trunnion bias for each batchof sightings, then using the computed value of trunnion bias to determine the horizon bias for each star within that batch. In every casethe horizon bias was determined from three or more measurements.

Based on the two studies above, there is no obvious correlationbetween the horizon bias variation and latitude of the subste11arpoint or sun direction. No explanation presently exists for the largevariations in horizon bias.

A detailed evaluation of Apollo 10 midcourse navigation usingstar-horizon sightings will be reported separately.

7.2 LANDMARK TRACKING

Landmark tracking data from Apollo 10 were used in an effort toevaluate the optical subsystem accuracy. No conclusions concerning theperformance of the optical system were drawn for the following reason:

The trunnion/shaft biases and standard deviations were very largeas compared to previous flight results. A direct comparison wasmade between landmark tracking and star-horizon navigation for trun-nion bias and standard deviation, with the former much larger. Anattempt was made to isolate an error source which would consistentlyaccount for the difference. The error sources considered were landmarklocation, state vectors (in part and in whole), clock bias (or essentiallyposition along the pre-determined orbit) and initial state vector error.Failure to effectively reduce the residuals lead to the conclusion that some

7-2

other unmode1ed error source such as observer error was predominant andthat any attempt to evaluate the optical subsystem accuracy from thelandmark tracking data would be misleading.

A detailed evaluation of Apollo 10 orbital navigation using landmark tracking observations 'will be reported separately.

7-3

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8.0 RENDEZVOUS NAVIGATION

8.1 ON BOARD NAVIGATION

Rendezvous navigation performance was satisfactory based on the nearnominal rendezvous burn solutions and pilot reports on the minimal amountof corrective thrusting required during the final intercept trajectory.All of the LM executed solutions were solved for by the LGC based solelyon rendezvous radar data to correct for any trajectory dispersions asthe result of orbit integration and ISS errors. Figure 8-1 presentsa comparison of RR range data and and CSM VHF ranging data for intermittentperiods between phasing and TPI. The close agreement in these two completely independent measurement systems lends evidence to the validityof both data. Also presented on the same figure is the BET rangeestimate during the rendezvous period. Figure 8-2 shows the RR rangerate data and the BET range rate estimates. Satisfactory incorporationof these data into the respective computers is deduced based on thedata presented in Figure 8-3. The relative position and velocityvectors (CSM-LM) were derived based on the current state vectors inthe two computers during the rend~zvous period. The figure shows thatthe relative state vectors were being held in close agreement.

8.2 RENDEZVOUS TARGETING

Comparisons of all executed ~V solutions during the rendezvous withthe pre-mission nominal ~VIS are shown in Table 8-1. The total ~V

required to perform the LM maneuvers was within one percent (minus) of

the nominal ~V.

During the rendezvous sequence, various maneuver solutions wereavailable to the LM crew. Table 8-2 presents the available rendezvoustargeting solutions .. It should be noted that the out-of-plane velocitycomponent (Y) was calculated during CSI (P32) and CDH (P33), but wasnot used in the burn targeting. This accounts for the ~VY component

of -5.7 fps at TPI (would nominally be zero).

8-1

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9.0 LANDING RADAR VELOCITY AND ALTITUDE MEASUREMENTS

9.1 RESULTS

Based on data obtained during the first pass through perigee afterthe 001 burn, the LR was functioning properly and the measured altitudeand velocities agreed favorably with BET and guidance trajectory data.Also, terrain features measured by the LR altitude beam agreed with thelunar terrain along the flight path as determined from lunar maps.

The landing radar data was available on the LM downlink from100:32:22 GET to 100:50:34 GET. During this time, the radar antennawas in position 2. The data from 100:39:03 to 100:50:34 GET was notprocessed because of the intermittant data. 1 The landing radar measured velocity minus the G&N measured velocity are shown in Figures9-1 to 9-3. The out-of-plane ~V indicates a total misalignment ofthe LR antenna and the stable member of approximately 0.73 degrees.Total misalignments of this magnitude were expected on this mission.Figure 9-4 is a comparison of the computed landing radar altitude andthe BET. The divergence is the result of the radar measuring the lunarsurface below the mean lunar surface, as the radar gives an indicationof the surface features and is not an approximation. Figure 9-5 is aplot of the lunar surface profile from 100:32:24 to 100:39:08 GET and75.3 to 53.1 deg selenographic longitude.

9.2 DATA PROCESSING

The landing radar hardware for LM-4 was modified so that the individual frequency tracker outputs could be monitored rather than thecomposite velocity terms Vxa, Vya, and Vza; and the doppler compensationterm was removed from the slant range measurement. To obtain the radarantenna velocities and slant range, the following equations were used;

1 Problem was associated with the LM antenna position and ground trackduring perigee.

9-1

Vxa l = Vxa - O.37l5Vza (l)

Vzal = -Vya - 3.7627Vxa (2)Vzal = Vza - O.7l53Vya (3)Rs l = 7.854Vxa - 2.087Vya+Rs (4)

where Vxa, Vya, Vza and Rs are telemetry downlink words. These data andassociated time, CDU angles and position components were processed usingthe TRW landing radar program to obtain the lunar surface profile. Thegeneral equations used were:

T.... lSMNB] [A]....

Vsm = Vant (5)

lH beam sm) .....

Hmeas = Hslant Unit R (6)....

[ SMNB) T{ A] [H1beam ant (7)H beam sm =

H beam ant = [-C~S t ] (8)-slne-

Rm - Rm (anwg) - Hmeas = Lunar Surface Above or below (9)Mean Lunar Surface

where:-+Vsm = Velocity in stable member coordinatesSNMB = Stable member to navigation base matrixA = Matrix for radar antenna position 1 or 2-+Vant = Velocity in antenna coordinatesHmeas = Computed altitudeHslant = Rs'

-+unit R = Position ComponentsH beam ant = Range beam orientation angleRm = Distance from SC to moon's centerRm{anwg) = Radius of moon (5,702,395 ft).

9-2

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g 0 0 0 0 0 0 0 0 0 0 0 0 ·0 0 g 0 0 ~~~ ~

~ N 0 co -0 ~ N N ~ -0 co N ~N ..., I I I I 'I 'I

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Figure 9-2 LR VELOCITY MINUS GaN VELOCITY (Y COMPONENT)

9-4

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:.

r--.,.--..,-~--r---.,..--,.- .......,.......,.--..,....~--r-....,.--r-~~-0M

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Figure 9-3 LR VELOCITY MINUS G&N VELOCITY (Z COMPONENT)

9-5

coc:0(00(coc:~ •- z -25

~ z I) •w 0(... ....\I) •• \I)\I) •

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Figure 9-4 COMPARISON OF LR MEASURED ALTITUDE AND BET ALTITUDE

9-6

10,000

7,000

5,000

9,000

2,000

1,000

,000

3,000

4,000

...~6,000 ...

8,000

100:32-00100:33:00100:34:00100:35:00100:36:00

TIME (GET) HR:MIN:SEC

100:37:00100:38:00100:39:00

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Figure 9-5 LUNAR SURFACE PROFILEMEASURED BY LANDING RADAR

NASA-MSC

•

10.0 CES PERFORMANCE

Apollo 10 was the first opportunity to exercise the Control Electronics Section i1fonj unction with the Abort Guidance System during asimulated lunar ascent. The burn was conducted unmanned after conclusionof the rendezvous period. Data indicates the CES performed nominally.

10.1 APS DEPLETION BURN

A 2-jet ullage burn performed under PGNCS control was initiatedbetween 108:50:27 and 108:50:28 GET. (Time based on TLM sample rate.)The ullage duration was between 93 and 94 seconds. Before astronautexit from the LM the AGS was setup and targeted such that an lI eng ineon ll command was available at the nominal burn time. Between 108:52:04.3and 108:52:05.3 AGS control was selected by uplink. At 108:52:05.36(TLM sample rate 5/sec) the AGS started the APS engine. Fuel depletionoccurred at 108:56:14.36; yielding a burn duration of 4 minutes 9 seconds.

Items of significant interest appearing in the data that were investigated are discussed below:

1) Jet pulse duty ratio. The APS fixed engine thrustvector is nominally offset from the cg with nearfull tanks and this offset caused a moment of 717.5ft-lbs (3500 1bs x .205 ft) at APS ignition. Afterignition the thrust offset was balanced by thepulsed firings of jets (balanced couples) 1 and 4 Uand 2 and 3~. The pulse frequency was 9.5 Hz. Referring to Figure 10-1, one may observe that duringnominal operation the pulse duty ratio at 9.5 Hshould be 35%. Assuming nominal jet thrust andzatotal 4-jet moment of 2200 ft-1bs, a 35% duty ratiowould compensate for an APS thrust offset of 770ft-1bs (2200 ft-lbs x .35). (770/717.5 - 1) x 100 =7.31% error. This error is minimal and is consideredacceptable.

2) cg travel. As the burn progressed the cg movedtowards the thrust vector and was nearly coincidentwith the thrust vector at cutoff. At cutoff thepulse frequency was approximately 0.5 Hz' the pulse

10-1

duty ratio was about 5%, and the on times about 14milliseconds. Again these figures agree favorablywith the nominal design. Motion of the cg was aspredicted by the Grumman FCI simulation runs.

10.2 COASTING FLIGHT

Following the APS burn to depletion several tests were performedto obtain data on AGS/CES control modes in coasting flight. Vehicledynamics were observed with the CES in wide and narrow deadbandattitude hold. Satisfactory performance was observed.

10-2

•

l.LJl/)

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Vin VOLTS

760

720

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640

600

560

520

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:::: 440.......l/)

Cl"'- 4(\0Ul.LJl/)..... 36(\....J....J.....::E:

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200

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120

80

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Figure 10-1 PULSE RATIO MODULATOR CHARACTERISTICS

10-3

REFERENCES

1. MSC-00126, "Apollo 10 Mission Report," dated August, 1969.

2 TRW Report ll176-H095-RO-OO, "Apollo 7 Guidance, Navigation &Control Performance Analysis dated 20 December 1968.

3. TRW Report 05952-H546-RO-OO, "Apollo 6 Guidance and NavigationError Analysis - Final Report," dated 28 June 1968.

4. MIT/IL R-567, "Guidance System Operation Plan, Section 3," datedDecember, 1968.

5. NAS 9-4810, "LEM G&C Data Book," Revision 1,1 June 1968, Change A,1 December 1966, Submittal No. S-39.

6. NASA SNA-8-D-027 (I I) Rev. 1, "CSM/LM Spacecraft Operati ona1Data Book, Volume II - LM Data Book, Part I," Revision 1,dated 15 March 1969.

7. TRW Report 0 3358-6134-RO-OO, "LM AGS Capability Estimate,"dated 30 September 1968.

8. GAEC report LSP-500-1 ,.'Abort Guidance Section Software GFE Performance and Interface Specification"· dated August, 1966.

9. TRW Report 03358-6151-RO-00, "LM AGS Postflight Analysis Report(Apollo 9) ," dated June, 1969.

R-l

APPENDIX A

AGS ANALYSIS METHODS

1.1 DATA SOURCES

There are two possible sources of data for comparison with AGSdata; namely,

a) PGNCS acceleration and angle data.

b) Radar tracking data.

The data that has been used to measure AGS performance during theflight is the PGNCS data. The reasons for this are:

a) PGNCS, like AGS, is an inertial measurement unit andthus senses the same quantities, that is, acceleration,or velocity changes, and angular rotations.

b) PGNCS accuracy is high relative to the required AGSperformance levels.

c) Radar data does not measure LM attitude.

d) Radar velocity data, while very accurate when appropriatelysmoothed, does not provide as high a measurement accuracyof velocity transients as PGNCS.

e) Radar data, unlike PGNCS, would have to be corrected toeliminate gravity and geoidal effects.

The PGNCS data that are used in the postflight analysis consistof six quantities: three measured velocities and the three gimbalangles. The velocities each represent the accumulation of inertialvelocity during a two second interval along an inertial platform axis.The gimbal, or Euler, angles are a measure of the orientation of theLM body axes relative to the PGNCS platform.

1.2 ANALYSIS PERFORMED

The three basic errors discussed in this report are: accelerometerbias, gyro bias (or drift), and direction cosine misalignment. Accelero-

A-l

meter errors are modeled as biases. During non-thrusting intervalsthis bias quantity does, in fact, represent the accelerometer staticbias. During thrusting intervals this error (apparent bias) can beattributed to static bias, dynamic bias, accelerometer scale factor,or accelerometer misalignment. These effects are generally inseparable.

Gyro errors are also modeled as fixed drifts. These apparentfixed drifts include dynamic errors, g sensitive errors, scale factorand misalignment errors. The effects of Y and Z gyro drifts will beobserved in the velocity data across a burn as well as in the angulardata. X gyro drift is unobservable in the velocity domain because thevelocity change during the burn is along the X axis. Direction cosinemisalignment is modeled as a constant angular error initialized at thebeginning of each burn and includes the initial AGS direction cosinealignment errors and. the system drift between the time of alignmentand the start of the burn.

1.3 ANALYSIS COMPUTATIONS

Three computer programs are used to process the AGS data. TheAGS Edit Program (Figure A-l, Block 1) is used to edit the telemetrydata, merge and interpolate PGNCS gimbal angles with AGS data and computequantities including body thrust acceleration (AA) , direction cosinesfrom the gimbal angles (aG), body turning rates from both AGS andgimbal angle data (wA' wG)' and the integral of body rate differences!(wA' wG). This integral indicates the drift of each AGS gyro if noPGNCS drift error is present. Thus, gyro bias is computed from thisdata. Also, initial misalignment is computed by SUbtracting CDU anglesfrom equivalent angles computed from the AGS direction cosine matrixat the initial time.

The AGS Error Analysis Program (EAP Figure A-l, Block 3) computesthe partial derivatives of thrust velocity and accumulated angulardrift with respect to the modeled AGS errors. These partials multipliedby the calculated error coefficients of the modeled AGS errors (Ki)represent the velocity and angular drift errors accounted for by these

A-2

•

,

•

modeled errors. Hence, in Block 4 of Figure A-l the components of gyrobias (Kl avA/aGB), initial misalignment (K2 aVA/aIM), and accelerometerbias (K3 aVA/aAB) are subtracted from the AGS minus PGNCS velocityresiduals in order to check how much residual error is unaccounted forby the modeled errors.

The AGS Data Comparison Program computes AGS/PGNCS thrust velocityand angular differences in body coordinates. When PGNCS accelerometerdata is transformed through gimbal measured transformation (aG) no AGSor PGNCS gyro error is involved because the gimbals measure the orientation of the body axes relative to the PGNCS platform independent ofany gyro drift. Thus, the velocity residual is only due to accelerometerdifferences (Block 2). Accelerometer biases are therefore computedfrom this data. When PGNCS accelerometer data is transformed throughAGS direction cosines, AGS to PGNCS misalignment errors are presentin the velocity residuals. By removing the calculated gyro drift,initial misalignment and accelerometer errors (Block 4) the velocityresiduals should be nulled. Likewise, the angle residuals, ~(wA - wG),are compensated for by the calculated gyro drift and initial misalignment.They too should be nulled. This process should complete the fitting.Recycling through the process can be done if misfit residuals are seen.

A-3

AGS EDIT

INTERPOLATE PONCS TO AGSCOMPUTE AA eVA"G FROM V,

A _. 0W FROM aA , W FROM a O

(WA_WO )

t---. PLOT ! ( WA- W0)

SOLVE FOR 1<1 (G'iRO BlAS)

. -It---. COMPUTE (el A) laC;)

AT INITIAL TIMESOLVE FOR I<Z(INI71AL MISALIGNMENT)

Z

COMPUTE AV = VA - f "G Ap

AGS EAP

COMPUTE:

a VAa ERROR MODEL

3

a llwA-wOla ERROR MODEL

PLOT AVSOLVE FOR 1<3

(ACCELEROMETERBlAS)

DATA COMPARISON ..

COMPUTE:

AV=VA - !"'AAp-1<1 :c: -KZ M~--------~ -K3~

BA ANGLE = !(WA_WG) _ 1<1 8 !(WA_WOl

8GB

PLOT AV. A ANGLECHECK FOR NULL RESIDUALS

Figure A-l POSTFLIGHT ANALYSIS BLOCK DIAGRAM

A-4

TA = AOS Time

T p = PONCS Time

VA = AOS Body Thrult Accumulation

CiA = AOS Direction Co.• ine.

V Oimbal Angle.

AA = AOS Body Thrult Acceleration

GO Direction Cosinu (rom Oimbal Angle.

wA .Body Rates from AOS

f•Wo Body Rates from Oimbal Angles

J(wA -wO ) = Accumulated AGS Body Angular Difference

KI Oyro Bial Coefficients

Ap PONCS Platform Thrust Acceleration

VA - JGGAp = Velocity difference due to accelerometer errors

K3 Accelerometer Bias Coefficient

aVA iNA

=Velocity Difference due to K 1 units ofKI~ = K I x aGyro BiasB Gyro Bias.

Kl

aV AK l d'llJ'" =

avK3 x aX 1 A t B' = Velocity difference due to K3 unit.

cce erome er las of Accelerometer Bias

Direction COlines Milalignment Cooefficient.

aVAKl x = Velocity Difference Due to DirectionClMil!lalignment Cosine Milalignment.

•

•

f aVAVA- QAA p • KI ao::-

B

_ Kl aVA -K3 aVA =aIM aA B

Velocity Difference Compensated for all errors.

Body Coordinate Angular Difference. Due to Gyro Bias

Compensated body Coordinate Angular Difference.

Table A-l KEY TO ANALYSIS BLOCK DIAGRAM (Figure A-l)

A-5NASA-MSC

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