Skip to main content

Full text of "Guidance, navigation, and control systems performance analysis: Apollo 13 mission report"

See other formats


^m 



I & 



• ^ 










^ 



I-tSC-026QC 
Sutclenent 1 



APOLLO 13 ^CSSION REPORT 



SUPPLEMEN"^ 1 



GUIDANCE, NAVIGATIOK, AND CONTROL SYSTEMS PERFORMANCE 



PREPARED BY 
TRW Systems 




APPROVED BY 



/^v^ 



S5«r 



James A. McDivitt 
Colonel, USAF 
lager, Apollo Spacecraft Program 



NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

MANNED SPACECRAFT CENTER 

HOUSTON, TEXAS 

September 1970 




V 



11176-H586-R0-00 



PROJECT TECHNICAL REPORT 
TASK E - 38D 



APOLLO XIII GUIDANCE, NAVIGATION, AND CONTROL 
SYSTEMS PERFORMANCE ANALYSIS REPORT 



NAS 9-8166 



24 JULY 1970 






Prepared for 

^4ATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

MANNED SPACECRAFT CENTER 

HOUSTON, TEXAS 



Prepored by 
Guidonce ond Control Systems Deportment 



Approved by . 



JUE. Alexander, Manager 
Guidance and Control Systems 
Department 



TRW 







W 



CONTENTS 



Page 



1.0 INTRODUCTION 1-1 

2.0 SUMMARY 2-1 

3.0 CM SYSTEMS 3-1 

3.1 CM Inertial Measurement Unit 3-1 

3.1.1 Velocity Comparisons During Ascent and TLI 3-1 

3.1.2 Ascent and TLI Error Determination 3-2 

3.1.3 Quick Look Evaluation 3-3 

3.1.4 Impact of Power Supply Degradation on CM 3-4 
PIPA Behavior 

3.2 CM Optical Navigation 3-5 
4.0 LM SYSTEMS 4-1 

4.1 LM Inertial Measurement Unit 4-1 

4.1.1 Transearth Injection Burn: Cut-Off 4-1 
Velocity Errors 

4.1.1.1 Velocity Errors 4-1 

4.1.1.2 Error Sources 4-2 

4.1.2 IMU Misalignments at time of TEI Burn 4-3 

4.1.2.1 Sun Check 4-3 

4.1.2.2 Drift Check 4-3 

4.1.2.3 Velocity Error Check 4-4 

4.1.3 PIPA Bias and IRIG Drift 4-5 

4.2 LM Digital Autopilot 4-6 




~-. 



Ill 



V 



Contents (Continued) 



Page 



4.2.1 MCC 2 DPS Free Return Maneuver Analysis 

4.2.2 TEI DPS Maneuver Analysis 

4.2.3 Maneuver to PTC Attitude 

4.2.4 DAP Control of the LM/CSM Configuration 

4.2.5 DAP Control of the LM/CM Configuration 

4.3 LM Abort Guidance System 

4.3.1 Burn Analysis 

4.3.2 Sensor Performance 

4.3.2.1 Accel erometer Errors 
4.3.2.2 Gyro Errors 

4.4 LM Optical Alignment Checks 

4.4.1 Sun Check for TEI Alignment 

4.4.2 Sun/Moon Alignment Star Angle Difference 
S.O SEPARATION 

5.1 SM Separation from the LM/CM 

5.2 LM Separation from the CM 
5.1.2 LM aV 

5.2.2 CM aV 
REFERENCES 



4-6 

4-7 

4-9 

4-12 

4-12 

4-13 

4-13 

4-15 

4-15 

4-16 

4-17 

4-17 

4-19 

5-1 

5-1 

5-1 

5-2 

5-2 

5-4 







1v 



* m 




TABLES 



Page 



3.1 IMU Error Sources - Acronym Definitions 

3.2 IMU Errors for Ascent and TLI (Derived from 
Sensed Velocity Comparisons) 

3.3 CM IMU PIPA Biases 

3.4 Apollo 13 P23 Cislunar Navigation Sighting 
Marks Batch 1 

Apollo 13 P23 Cislunar Navigation Sighting 
Marks Batch 2 

3.5 Combined Results of Processing Batches 1 and 
2 of P23 Data 

4.1 TEI Ignition and Cutoff Vectors 

4.2 LM IMU Predicted Misalignments (Degrees) 

4.3 Maximum Body Rates (MCC 2 Burn) 

4.4 DAP Control Axes Attitude Errors and Rate Errors 
(rice 2 Burn) 

4.5 RCS Fuel Consumption Required to Maintain Attitude 
Control 

4.6 Maxiiman Body Rates (TEI Burn) 

4.7 DAP Control Axes Attitude Errors and Rate Errors 
(TEI Bum) 

4.8 Body Torques Created by Translational Policies 
Defined in GSOP (Reference 4) 

4.9 Body Torques Created by Rotational Policies 
Defined in GSOP (Reference 4) 

4.10 Body Torques Created by Possi.ie Pitch Roll 
Rotational Policies 



3-7 
3-9 

3-11 
3-12 

3-13 

3-14 

4-21 
4-22 
4-23 
4-23 

4-24 

4-25 
4-26 

4-27 

4-29 

4-31 




\ 



«* 



Tables (Continued) 



4.11 AGS Accel erometer Biases 

4.12 AGS Gyro Errors (ASA 023) 



Page 

4-32 
4-32 



^ i 
i 



^ V 












l^j^ 



4 






r- 



v1 



«t^ 



ILLUSTRATIONS 






3-1 Uncompensated Ascent Velocity Comparison 
(6N-SIVB), Delta Vj^ 

3-2 Uncompensated Ascent Velocity Comparisons 
(SN-SIVB), Delta Vy 

3-3 Uncompensated Ascent Velocity Comparisons 
(GN-SIVB), Delta V^ 

3-4 Uncompensated TLI Velocity Comparison 
(GN-SIVB). Delta V^ 

3-5 Uncompensated TLI Velocity Comparison 
(GN-SIVB). Delta Vy 

3-6 Uncompensated TLI Velocity Comparison 
(GN-SIVB), Delta Vj 

3-7 Compensated Ascent Velocity Comparison 
(GN-SIVB), Delta \l^ 

3-8 Compensated Ascent Velocity Comparison 
(GN-SIVB), Delta Vy 

3-9 Compensated Ascent Velocity Comparison 
(GN-SIVB), Delta V^ 

3-10 Compensated TLI Velocity Comparison 
(GN>SIVB), Delta V^ 

3-11 Compensated TLI Velocity Comparison 
(GN-SIVB), Delta Vy 

3-12 Compensated TLI Velocity Comparison 
(GN-SIVB), Delta V^ 

3-13 CM PIPA Power Supply Voltages 

3-14 PIPA Outputs and MSFN Ooppler Data After 
SM LOX Tank Incident 



Page 

3-15 

3-16 

3-17 

3-18 

3-19 

3-20 

3-21 

3-22 

3-23 

3-24 

3-25 

3-26 

3-27 
3-29 



t 







I> ,^ 



Vl1 



.t •«ki 



<% 





1 
f 

5 




i 

i 4-1 




4-2 


•i 


4-3 


-"^ 


4-4 




4-5 


&. 


4-6 


\ 




v" .. 


4-7 


> 


4-8 




4-9 

4-10 

4-11 




4-12 




4-13 


i 


4-14 


, 




' 1 


4-15 




4-16 



Illustrations (Continuec*) 



MCC 2 Burn/P-Axis Phase Plane Plot 

MCC 2 Burn/U-Axis Phase Plane Plot 

MCC 2 Burn/V-axis Phase Plane Plot 

MCC 2 Burn/Pitch 6DA Position 

MCC 2 4 Burn/Roll GDA Position 

TEI Burn (Pre-Burn Initiation Through Throttle-Up) 
P-Axis Phase Plane Plot 

TEI Burn (Pre-Burn Initiation Through Throttle-Up) 
U-Axis Phase Plane Plot 

TEI Burn (Pre-Burn Initiation Through Throttle-Up) 
V-Axis Phase Plane Plot 

TEI Burn/Pitch GDA Position Through Throttle-Up 

TEI Burn/Roll GDA Position Through Throttle-Up 

LM/CSM Configuration Auto Maneuver and Attitude 
Hold P-Ax1s Phase Plane Plot 

LM/CSM Configuration Auto Maneuver and Attitude 
Hold U-Axis Phaso Plane Plot 

LM/CSM Configurat1on^\uto Maneuver and Attitude 
Hold V-Axis Phase Plane 1>lot 

LM/CSM Configuration Auto Maneuver P-Axis Phase 
Plane Plot 

LM/CSM Configuration Auto Maneuver U-AxIs Phase 
Plane Plot 

LM/CSM Configuration Auto Maneuver V-Axis Phase 
Plane Plot 



vlil 



Page 

4-37 
4-39 
4-41 
4-43 
4-45 
4-47 

4-49 

4-51 

4-53 
4-55 
4-57 

4-59 

4-61 

4-63 

4-65 

4-67 



•* > 








Illustrations (Continued) 



4-17 LM/CSM Configuration Attitude Hold 
P-Axis Phase Plane Plot 

4-18 LM/CSM Configuration Attitude Hold 
U-Axis Phase Plane Plot 

4-19 LM/CSM Configuration Attitude Hold 
V-Axis Phase Plane Plot 

4-20 LM/CM Configuration Manual Maneuver 

and Attitude Hold P-AxIs Phase Plane Plot 

4-21 LM/CM Configuration Manual Maneuver and 
Attitude Hold U-AxIs Phase Plane Plot 

4-22 LM/CM Configuration Manual Maneuver and 
Attitude Hold V-AxIs Phase Plane Plot 

4-23 AGS/PGNCS Sensed Velocity Comparison 
During TEI Burn 

4-24 AGS Sensed Velocity Along Body Axes 
During MCC 3 Burn 

4-25 Roll Kate and Attitude Error During 
MCC 3 (AGS Controlled) 

4-26 Pitch Rate and Attitude Error During 
MCC 3 (AGS Controlled) 

4-27 Yaw Rate and Attitude Error During 
MCC 3 (AGS Controlled) 

4-28 AGS Sensed Velocity Along Body Axes 
During MCC 4 Bum 

4-29 Acquisition of Yaw Attitude for MCC 4 
Burn 

4-30 Acquisition of Pitch Attitude for MCC 4 
Burn 



Page 
4-69 
4-71 
4-73 
4-75 
4-77 
4-79 
4-81 
4-82 
4-83 
4-84 
4-85 
4-86 
4-87 
4-88 









1x 



"S*. 






mustrations (Continued) 



y^ji 






4-31 Acquisition of Roll Attitude for MCC 4 
Burn 

4-32 Spacecraft Attitude During MCC 4 Burn 
(AGS Euler Angles) 

4-33 Accumulated X-Axis Sensed Velocity 

4-34 Accumulated Y-Axis Sensed Velocity 

4-35 Accumulated Z-Axis Sensed Velocity 

4-36 X-Axis Velocity Differences (No AGS 
Compensation) 

4-37 Y-Axis Velocity Differences (No AGS 
Compensation) 

4-38 Z-Axis Velocity Differences (No AGS 
Compensation) 

4-39 X-Axis Velocity Differences (Compensated 
for AGS Accel erometer Errors) 

1-40 Y-Axis Velocity Differences (Compensated 
for AGS Accel erometer Errors) 

4-41 Z-Axis Velocity Differences (Con^ensated 
for AGS Accel erometer Errors) 

4-42 AGS/PGNCS Angular Drift - "X" Body 

4-43 AGS/PGNCS Angular Drift - "Y" Body 

4-44 AGS/PGNCS Angular Drift - "Z" Body 



Page 

4-89 

4-90 

4-91 
4-92 
4-93 
4-94 

4-95 

4-96 

4-97 

4-98 

4-99 

4-100 
4-101 
4-102 



m 

n^.'- 






1 



I 



>. 



«% 



I . 



NOMENCLATURE 






ACA 

ACB (X, Y, Z) 

ADSRA (X, Y, Z) 

ADIA (X, Y, Z) 

AGS 

AOT 

APS 

ASA 

BDA 

CDU 

COAS 

CM 

CMC 

DAP 

DEDA 

DPS 

DSKY 

EPC 

FDAI 

GOA 

GDS 

GET 

G&N 

GSOP 

HOPE 

IFC 

IMU 

IRIG 

JPL 



Attitude Controller Assembly 

Accel erometer bias (channels X, Y, Z) 

Gyro drift due to acceleration along the 
sp!n reference axis (Channels X, Y, Z) 

Gyro drift du«» to acceleration along the 
input axis (Channels X, Y, Z) 

Abort Guidance System 

Alignment Optical Telescope 

Ascent Propulsion System 

Abort Sensor Assembly 

Bermuda (tracking station) 

Coupling Data Unit 

Crew Optical Alignment Sight 

Comnand Module 

Comnand Module Computer 

Digital Auto Pilot 

Data Entry and Display Assembly 

Descent Propulsion System 

Display and Keyboard 

Earth Prelaunch Calibration 

Flight Director Attitude Indicator 

Glmbal Drive Actuator 

Goldstone (tracking station) 

Ground Elapsed Time (Range Time) 

Guidance and Navigation 

Guidance System Operational Plan 

Houston Optratlons Predictor/ Estimator 

Inflight Calibration 

Inertlal Measurement Unit 

Inertlal Rate Integrating Gyro 

Jet Propulsion Laboratory 



x1 



j 

! 

i 



1 "- • . 






! 



^^ 



4*^( 



•^J 




^f**hmW^y^^ 



^%.x 



V 



Nomenclature (Continued) 



tji ', 

'^K- 



■ \ 



>r" , 




LGC 

LM 

LOS 

LOX 

MCC 

MERU 

MIC 

MSC 

NASA 

NAT 

Omega P* error 

Omega U* error 

Omega V*error 

P error 

PGNCS 

PIC 

PIPA 

PPM 

PTC 

RCS 

REFSMMAT 

RHC 

RSS 

RTCC 

S/C 

SFE(X. Y, 2) 

SM 

SODB 

SPS 

SIVBIU 



LM Guidance Computer 

Lunar Module 

Line-of-sight 

Liquid Oxygen 

Midcourse Correction 

Milli-Earth Rotational Units 

Minimum Impulse Control (mode) 

Manned Spacecraft Center 

National Aeronautics and Space Administration 

NASA Apollo Trajectory 

Rate error about P axis 

Rate error about U* axis 

Rate error about V* axis 

Yaw axis error 

Primary Guidance, Navigation and Control 
System 

Pre-Installation Calibration 

Pulsed, Integrating Pendulous Accelerometer 

Parts per Million 

Passive Thermal Control 

Reaction Control System 

Reference to Stable Member Matrix 

Rotational Hand Controller 

Root of the Sum of *he Squares 

Real Time Cortrol Center 

Spacecraft 

Scale Factor (Channels X, Y, Z) 

Service Module 

System Operational Data Book 

Service Propulsion System 

Saturn IVB Instri^nentatlon Unit 



^ 1 












xli 



Nomenclature (Continued) 






TEI 
THC 
TLI 
TTCA 
U error 
U' error 

V error 

V error 
VG 

VO (X. Y, Z) 
a„ 



2 

P, U, V axis 



QUAD I 



Trans-Earth Insertion 

Trans lational Hand Controller 

Trans-Lunar Injection 

Thrust and Translation Controller 

Computed Errors 

Computed Errors 

Computed Errors 

Computed Errors 

Velocity Gained 

Velocity Offset (X, Y, Z) 

Measured gravity vector in IMU coor- 
dinates (x) 

Measured gravity vector in IMU coor- 
dinates (y) 

Measured gravity vector in IMU coor- 
dinates (z) 

Micro-gravities 

DAP control axis oriented relative to 
LM body axes as shown below: 




FCHI«AtO 

DIRECTION 

FOVAN 
OCCUPANT 
OF THC LM 



^ 



xiii 



^ 



^ ;•' -''v.r.. i-^' 



V 



1.0 INTRODUCTION 



This n^wrt presents the oonclusicHis of the analyses of the inflight 
perfonnance of the Apollo 13 mission Qoidance, Navigation and OMitrol 
equipment cnboard the CSM-109 and l/i-7 spacecrafts* This analysis is 
supplanent 1 to the i^Uo 13 Mission Report (Referenoe 1) . 












^ 






1-1 



SJ* 









^.. 



^ 



2.0 SUmARY 

CM IHU 

Analysis of the ascent and TLI bum errors indicated an X-gyro con- 
stant drift which was outside of the la specification (2 meru). The 
derived values were 3,14 meru for ascent and 2.35 meru for TLI. There 
is evidence that this apparent instrument error actually resulted from 
an inappropriate gyro drift compensation load. PIPA bias values were 

reasonably stable during the time the IMU was turned on, but the Z PIPA 

2 
bias value shifted approximately 1.64 cm/sec across the long power down 

period and required a CMC compensation update prior to entry. 

After the SM LOX tank incident occurred, the IMU power supply under- 
went degradation. Concurrently, the PIPA's registered a Ir level 
acceleration which was first interpreted as venting. Howeve. , doppler 
radar failed to confirm venting of the necessary magnitude. It is now 
believed that the degradation in power supply voltage induced a corres- 
ponding transient in PIPA performance. 

CM OPTICAL NAVIGATION 

Processing of translunar P23 (star-horizon) data indicates that the 
actual horizon altitude was about 18 kilometers. However, the apparent 
altitude (due to small sighting errors) was about 10 kilometers. 

LM IMU 

IMU performance was good. PIPA bias values were quite stable about 
their prelaunch values. No direct measurement of gyro drift was obtained, 
but there is good evidence that total (RSS) misalignment of the IMU at 
the time of the TEI buiTi-after 20.5 hours of gyro drift - was of the 
order of 0.5 to 0.6 degrees. The lo value from LM IMU drift alone 
(ignoring Initialization errors) Is 1.1 degrees, indicating excellent 
gyro performance. 







.Jd 



2-1 



\ ^- 



I 



«3». 






LM DIGITAL AUTOPILOT 

During the mission, the LM DAP was called upon to control both LM/CSM 
and LM/CM spacecraft configurations in auto maneuver and attitude hold modes. 
Performance was satisfactory in all cases although in some instances 
violations of deadband limits did occur. 

The roll 6DA was observed to drive approximately -1,3 degrees from 
its initial position at the start of the TEI burn, stimulating conjecture 
that the engine gimbal trim function might have been abnormal. Detailed 
analysis indicated that this position change was necessary to relieve com- 
pliance and correct for initial mistrim. Performance is now believed to 
have been nominal. 

Difficulty was encountered when attempting to maneuver the space- 
craft into the PTC attitu.-*® following the TEI burn. Downlink data were 
not available for the maneuver, so that investigation was necessarily 
restricted. One explanation was found by a theoretical examination of cross 
couplings resulting from various control modes. It was determined that 
the use of rotational commands would have resulted in significant cross 
coupling (due to jet impingement forces) and drastic alterations in the 
intended commands. Although purely translational commands were planned for 
this maneuver, it is hypothesized that some rotational commands were inter- 
mingled and were the source of the problem. 

Another possible explanation is that the difficulty arose from the 
necessity of determining hand controller conmands purely by interpreting 
gimbal angle displays on the DSKY. This was necessary because the FDAI was 
powered down. 

LM ABORT GUIDANCE SYSTEM 

The AGS was used for spacecraft control in two burns, MCC 3 and 
MCC 4. In both cases* performance was satisfactory. 




2-2 






««% 



^> 












AGS gyro and accelerometer errors were estimated from free flight 
data and from AGS/P6NCS velocity comparisons obtained during the TEI 
burn. Instrument static errors showed excellent stability. The TEI 
burn afforded the only opportunity for observing acceleration sensitive 
errors. Instrument dynamic performance during that burn was within the 
2a limits determined from the ASA023 error model. This is excellent per- 
formance, particularly in view of the fact thai: the ASA023 dropped 

o 

23 degrees F below its specified minimum temperature (60 F) during the 

24 hour period in which it was shut down prior to the TEI burn. 

LM OPTICAL ALIGNMENT CHECKS 

Prior to the TEI burn the L6C was used to aim the AOT line-of-sight 

in the LGC calculated sun direction. This was done to assess IMU align- 
ment errors and resulted in an estimated misalignment of 0.5 degrees. 
By its nature, the check could not resolve errors about the line-of-sight. 
However, the line-of-sight direction was such that misalignments about 
it had negligible impact on significant state vector errors induced by 
the IMU during the TEI burn. As conducted, the check determined only 
the .nagnitude of the misalignment in one plane - that plane in which 
h isalignments were of greatest consequence. The direction of these 
errors was not determined, and therefore the appropriate corrective IMU 
torques could not be calculated. The IMU misalignment generated a burn 
error of approximately 5-3 feet/second in the TEI burn. Unfortunately, much 
of this error was in the direction most critical to entry flight path angle; 
the resultant (potential) error in the post-TEI trajectory entry flight 
path angle was in excess of -4 degrees. The allowable error in flight path 
angle is 0.5 degrees. Two midcourse corrections were subsequently required 
to correct this error. 



^C^ 






\:4- 



».-""■ "^v ->'i««-' 



2-3 



I 

it 



«m 



^> 



a- 









An alignment of the LM IMU was performed using the sun and moon 
as optical targets in oreraration for the MCC 4 burn. A star anqle d-:f- 
ference of -1.1? degrees was computed by the LGC and displayed on the 
DSKY, indicating a very large astronaut sighting error. It was sub- 
sequently determined that the actual sighting error was only about ,08 
degree. The remainder of the apparent sighting error arose from in- 
accurate LGC ephemeris data for the moon and sun, and from the LGC 
software. 



— '*•* 



2-4 



3.0 CM SYSTEMS 



>V 



^T '/ 




•^ ^ - ^'^^' 






3.1 CM INERTIAL MEASUREMENT UNIT 

3.1J Velocity Comparisons During Ascent and TLI 

The Apollo 13 CM IMU performance analysis was based on comparisons 
of Apollo (denoted G&N) and Saturn (denoted S-IVB) measured velocities. 
Analysis centered around the "sensed" velocities - those resulting 
from integration of that portion of the vehicles acceleration which can 
be sensed by the accelerometers. Sensed velocities exclude the influence 
of the gravitational field. In addition to the sensed velocity com- 
parison, a cross check of ascent phase results was obtained by analyzing 
"totaV velocity differences. Total velocity is the actual vehicle 
velocity in inertial space. It is obtained by integrating both sensed 
acceleration (due to engine thrusting) and gravitational acceleration. 
The cross check was performed because telemetry data dropouts caused 
minor discrepancies in the GN sensed velocity estimates. Sensed and 
total velocity differences are presented below for the end of the ascent 
phase (t = 752 seconds, CMC clock time) and for TLI cutoff (t = 9704.48) 



Time 


Type of 
Comparison 


Comparison 


aX 
(ft/sec) 


aY 
(ft/sec) 


aZ 
(ft/sec) 


752.0 sec 


Sensed 


G&N - S-IVBIU 


-6.75 


87.04 


- 3.82 


752.0 sec 


Total 


G&N - S-IVBIU 


-5.41 


75.51 


1.02 


9704.48 sec 


Sensed 


G&N - SIVBIU 


-20.50 


- 2.50 


2.03 



lU represents the edited Saturn telemetry data. 



3-1 



«att^ 



- -. _:;^ 



4 



The ascent and TLI uncompensated sensed velocity differences (G&N - 
S-IVBIU) appear in Figures 3-1 through 3-6. Those IMU errors solved for 
in this analysis are defined in Table 3.1. IMU error sets derived to 
fit the ascent and TLI velocity differences are presented in Table 3.2. 
Close agreement was obtained between the results of the sensed and total 
velocity analyses, so that inclusion of the results for the total was 
unnecessary. Compensated sensed velocity differences (G&N - S-IVBIU, where 
the G&N data has been compensated with the derived IMU errors) are pre- 
sented in Figures 3-7 through 3-12. 

3.1.2 Ascent and TLI Error Determination 

The Apollo 13 G&C system accuracy analysis was based upon the deter- 
mination of a common set of errors which resulted in small residuals for 
both the boost to orbit phase and the translunar insertion phase. The 
analysis is accomplished with the aid of a Kalman Filter which solves 
for a "best" set of IMU errors for minimizing the velocity differences 
in a least squares sense. Several constraints were imposed on the 
errors used. The bias values for accelerometers (Table 3,3) and gyros 
were force j to be in close agreement with inflight determined values 
and the other error terms were chosen to agree favorably with preflight 
calibration histories. Due to various physical factors such as actual 
parameter shifts during the boost phase and degradation of the reference 
data between the two flight phases (2.4 hours of drift between ascent 
and TLI) it was again recognized that all of the above conditions could 
not be fnet at all times. Based on engineering judgement, the approach 
pursued was to seek two sets of error sources with bounded variations 
(^ Ic). The error terms derived for the sensed analyses are presented 
in Table 3.2, and using these values, the G&N corrected trajectories 
fit the respective external measurement (S-IVBIU) trajectories. The maxi- 
mum deviation between the derived ascent and TLI error sources was 0.86o^, 



• ! 




3-2 



^ 






''"" ™--i^' 
>/,">". 



n 




The derived boost and TLI values for NBDX (X Gyro Constant Drift 
Rate) exceeded the la (2 meru) instrument stability criteria. The de- 
rived values were 3.14 meru (ascent) and 2.35 meru (TLI). These 
represent 1.57a and I.I80 values respectively for boost and TLI. Pre- 
flight data obtained at Cape Kennedy, from 3 July 1969 to 3 April 1970, 
revealed a pronounced negative trend which peaked out at -3.3 meru on 
6 January 1970. Overall NBDX Cape test results are somewhat erratic. 
Following the referenced negative peak, NBDX results varied considerably. 
For the subsequent four calibrations, the quantity began trending positive 
and the last calibration value on 3 April 1970 was 0,5 meru. The CM com- 
puter erasable memory compensation value for NBDX was -0.7 meru. If the 
term continued to trend positively, it is probable that an effective error 
on the order of 2-3 meru did exist during ascent and Til. Consequently, 
it is understandable that the derived values for NBDX did exceed the It 
instrument stability criteria. The apparently large shift in drift prob- 
ably reflects a compensation error rather than instrument degradation. 
All other error sources were within lo limits. 

3.1.3 Quick Look Evaluation 

It is worthwhile to point out that a technique has been developed 
for taking a gross "quick look" at IMU performance without recovering 
individual instrument errors. This was done for the Apollo 13 CM IMU 
by comparing actual ascent cut-off state errors with standard deviations 
of these errors. The standard deviations used for this comparison were 
obtained by integrating an ensemble of lo IMU instrument errors along 
the ascent trajectory. Resultant lo state errors formed trajectory 
bounds from which IMU performance could be gauged in the system sense; 
i.e., from which it could be determined whether or not overall IMU per- 
formance as a navigation instrument was within lo bounds. This gross 
**quick look" technique provided an additional confidence factor in the 
derived NBDX error source values discussed, inasmuch as it demonstrated 
that IMU performance was not within specifications during ascent. A 
comparison of actual with lo velocity errors Is presented as follows 
(at t « 752 seconds GET): 



3-3 






! * 



«««> 



1,7 : 

A Actual : 



X 
(Ft)* 

1434 
3555.8 



Y 
(Ft) 

27630 
32220.6 



Z 

3542 
1315 



AX 

(Ft/Sec) 

4.46 
-5.41 



AY 

(Ft/Sec) 

61.89 
75.51 



aZ 
(Ft/Sec ) 

9.88 
1.02 



* . 



^ V 



4 










*The position and velocity values are totals 
(u lits as noted). 



3.1.4 Impact of Power Supply Degradation on CM PIPA Behavior 

Immediately following the SM LOX tank incident at 55:54:53 GET, 
the CM downlink recorded PIPA pulses which resembled the effect of venting. 
However, efforts to reconcile these data with doppler radar measurements 
met with failure. Consequently it was theorized that the actual pheno- 
menon being observed might be a bias shift in the PIPA's due to power 
supply transients, rather than accelerations due to venting. To support 
this hypothesis, an effort was made to correlate power supply transients 
with observed PIPA data. 

Figure 3-13 is a plot of the 28VDC Main A, 120VDC PIPA supply and 
the 3.2 KC 28V power supplies at the time of the LO2 tank event at 55:54:53 
GET. The 120V PIPA supply and the 3-2 KC 28V supply began to degrade when 
the 28V0C Main A supply reached 26.3 volts. Figure 3.14 is a plot of the 
accumulated thrust velocity (V^j^. V^y, V^^) indicated by the PIPA's through 
the time of the voltage transient; superimposed on this is a plot of MSFN 
doDpler radar residuals for the same time period. The change in PIPA 
velocities can be directly correlated to the degraded voltage. The reason 
for the different PIPA responses (i.e.* XPIPA does not show response to the 
sharp voltage transient at 56:00 and 56:03 as do Y and Z) is unknown. 
Referring to the plot of the Bermuda/Golds tone tracking station doppler 
residuals through the period of Interest, no appreciable change Is noted 
between 55:57:56 and 56:03:10, the region of the 120V PIPA supply transient. 



r* ^' 



3.4 



«% 



V 




Shifts in the doppler residuals near 55:55:00 and 56:03:30 resemble velo- 
city changes indicated by the X PIPA which is pointed principally along 
the LOS to Earth. The trend shown by the X PIPA however, is not reflected 
in the doppler data, thus indicating that X PIPA velocity indication- were 
erroneous. 

Following the event, the CSM IMU was powered down (including instrument 

heaters) at 58:40 GET and remained down until 140:10 GET, At IMU power up, 

2 

a shift of 1.64 cm/sec was noted on the Z PIPA and as a result a biat* update 

was performed prior to entry. Table 3.3 is a summary or' the PIPA bias 
before and after the event. 

3.2 CM OPTICAL NAVIGATION 

Prior to the SM LOX tank incident, two batches of navigation sight- 
ings were conducted. The data obtained from these sightings is listed 
in Table 3.4. These data were analyzed for the purpose of estimating 
sextant trunnion bias and earth horizon bias. 

Two basic options were available for analysis of these data. In 
Option 1, only trunnion angle data Is processed. This option assumes 
that the astronaut was successful in locating the substellar "point" - 
i.e.. in placing his horizon line-of-slght on the line connecting the 
star with the earth's center. Option two utilizes gimbal and shaft 
angle data for the purpose of correcting erroneous determinations of 
the substellar point. In addition to these options, batch one was pro- 
cessed using: 

Method 1: Horizon altitude only estimation, and 

Method 2: Horizon altitude and trunnion bias estimation, 
with no a priori estimate of these parameters 
(i.e., with initial estimates weighted such that 
they had no effect on the soiution). 







3-5 






iPHI 



HH» 



^ 



s • • 



>^ 



The combination of methods one and two with options one and two 
yielded four cases. The output of these cases were used as the input 
(initialization values) for the processing of batch two. Table 3,6 
presents these combined results. Option 1 results from batch 1 were 
used onl> with option 1 runs for batch 2. Likewise, option 2 results 
from batch 1 were used only with option 2 runs for batch 2. 

The results indicate that the actual horizon altitude was about 18 
kilometers. However, due to small sighting errors the astronaut was 
actually sighting on an effective altitude of about 10 kilometers. 




^'^^••.^^ 



3-6 



«% 

























QA 























u 







C 






w 


u 

D 




w 


G 




w 


3 




4J 




1-4 


v: 




>* 


a 




>* 


*H 




>s 


u 




>» 


fa 


•H 




u 


c 




w 


a 




U 


3 




4J 




X 




•H 


•H 




•H 


« 




f4 







•H 


•o 


4 




> 






> 






> 






> 


0) 






*H 


00 




l-t 


oo 




•H 


00 




•H 


u 


V 


y) 


4J 


c 




4i 


c 




U 


c 




W 


fl) 


u 


u 


•rt 


o 




•H 







•H 







•M 


3 


c 





W) 


^ 




U) 


-^ 




tA 


«H 




to 


cr 


4> 


u 


C 


CO 




C 


(fl 




c: 


tfl 




6 


(0 


u 


u 


a> 






0) 






0) 






a> 




0) 


Ul 


tA 


e 






to 


g 




eft 


§ 




(0 





0) 





OJ 


•w 




<t> 


•^ 




4) 


•M 




Q) 


•H 


u 


u 


4J 


4-t 




u 


4-1 




4i 


iJ 




4J 


w 




> 


rt 


fl 




rt 


« 




rt 


tQ 




4 


fl) 


c 


o 


u 






Wi 






u 






h 


» 


a 




4J 


<-t 


• 


u 


#H 


• 


4J 


<M 


• 


u 


*H 


(0 




(M 


4) 


(A 


tM 


0) 


(A 


^*4 


V 


to 


(M 


4> 






•H 


U 


•H 


•H 


o 


•H 


•^ 


o 


•f^ 


•H 


u 


0) 




h 


u 


X 


W 


o 


X 


Iri 


o 


M 


U 


u 


X 




:a 


fl 


« 


O 


(0 


<0 


o 


(Q 


19 


Q 


m 


4i 






to 
c 
o 
u 



o -^ 
^ c 

-* 
O E 

ou ;) 



!S ^ S 

1-4 H^ »^ 

Q q o 

-< -E < 



(/) C/3 C/3 

3 3 5 





o 



u 

(0 



V 



o S 



> ^ 

-4 « 

w g 

•p4 g 

3 •• 1 

tt W w 

* i 3 



(A 



3 ? 



g 
-< 








*4 


s s s 


a 


Q a 


8.8 


^ ^ ^ 




S: is 


^i 









§ 



>. 


S 


» 


X 


>• 


N 


. i 


WJ 


(A 


Q 


a 


-a 


3 


9 


a 
< 


Z 


flQ 

z 


i 



3 il 

M 4) 



illl 



00 

c 



a 

3 
O 

g 



•art 
> 



(/) 



m 

u 

g 
u 



1 



H Ul 



3 <• 
O -^ 



•3 



(A 

u 

aO •** 

e u 

*- o 

-^ 

— 1* 






II 



5 - 



Table 3.1 INU ERROR SOURCES - ACRONYM DEFINITIONS 

3-7 



T'i- 





N. 









if 



2 z 

5 r: i 

^ <^ m 



\\\ 

t - 8 

III 



ft 

s ! 



ii ' 



e 

r*. 
d 

tt 

R 
« 
1 

! 

! 

i 

1 


• 

R 

R 
R 
1 
f 

! 

i 

K 

1 


it 
1 

1 


s 

o 

7 

*^ 

R 

R 
R 

! 
! 
3 

i 

i 


o 

d 

• 

V 

ft 

« 

! 

i 
i 

i 
i 

\ 


i 

d 

7 

• 

1 
1 



5 5 

I I 

g a ^ § i 8 o 

d d d d d 

J |s ;2 S :2 '^i = 

t. 8 a » « T - 

7 - 7 »^ 7 * - 

8 K R ft 5 S s 

* 7 *? T ? T 7 

:: ft » 3 9 3 & 
- « p • i, ^ i 

• *• ^ « X A A 

M i 5 S $ 8 

7 • 7 • - o ^ 

5 : : ; i 5 s 

! S I S c 8 « 

t t" 7 7 ; d '^ 

ilfltll 

ilHlif 



-3? 

So J^ 3 

3*0- 
^ 5 < c 



UJ (/> z 

ae u. < 



O 

rs >-* _j 
X -JUJ 



H 
O 



O 



* X M u 

ilii 



V ' ^ .' 




r--^ 



i 



^*''--^^^ 

l)*^^?^-' 



Table 3.3 CM IMU PIPA BIASES 



GET 


X Bias (cm/sec^) 


Y Bias (cm/sec^) 


2 1 
Z Bias (cm/sec ) 




10:10 


-0.20 


-0.21 




0.0 




12:25 


-0.20 


-0.20 




0.0 




13:05 


-0.19 


-0.21 




0.0 


, ■■ ..-^- 


14:35 


-0.20 


-0.20 




0.0 


■ ,. '•■, »" 


16:35 


-0.20 


-0.20 




0.0 


.»>«•-_ 


35:09 


-0.20 


-0.21 




0.01 




42:48 


-0.20 


-0.20 




0.0 


%:-% 


57:16 
141 :00 


-0.21 
-0.18 


-0.12 
-0.16 




-0.01 
-1.66 









'■tie: 



PT?1T.T^ING 



PAGE BLANK NOT fM» 



3-11 



c 



f 1*11 Pl^ . l » , < i 



^^'V^--* ^^ 



N 



^- 



I 



OCi 



c c c c c 

o o o o o 



fO TS 'O lO If) 

W I. u w s. 

X3 ^ ^ Xt J3 



lO (O <o <o (O 

o u u u o 



1^ p-^ f^ 

<\i CM (\J 

o o o 
o o o o o 



r'- f"^ ^" fQ W <0 *0 *© <0 

<OiO« 4J4->4-i 4-»-^4-i 

4->4^4-> UUU UUO 

oou ooo ooo 

o o o -~^ — — ' -^—w.-^ 

««--,-''—' #^ ^- ,— in in in 

ro ro CO CM OJ CNJ CJ cm cm 

CO on CO CM CM CM t— r— .— 



r>.r^co oovn^ r^^-io 

»— r** o ^ I— I— in^r.— 

CX} «:!• r- CM C7^ ^ cor-o 

r^ 00 o^ in^*^ oo»— 



fO <o <o fO 



u o u u 
oooo 



oo oo 

«3- ^ ^ ^ 



CM in 00 o 
CO CM r^ ^ 
or*^ ^a* CO 

O O^ O^ CT» 



00 00 00 ^ ^- ^ ^^^ 

CO CO CO CO CO CO CO CO CO 



in *o *o *o 



u o o u 

oooo 



CM CM CM CM 
^ ^ ^ ^ 



OOOO 

in r-- o 00 
00 o ^ r- 

CM CO CO CO 



i 



^T" CO CO CO 
CO CO CO CO 



in in tn in 

CM CM CM CM 



s 'f 



. i 



^v 









CO c. 
OO 



O O O O O 



cy^ o o 

I— CM 0\ 

m xr o 
r-o o 



^ m «a- 

CM f— CM 
O <T»0 

in ^" in 



in a^ CM 
CM CO IN* 
CM O O 

in CM ch 



<MO ^ 00 

CO o^ vo CO 
CJ* CO o ^ 

CT* CO CO *T 



^ :' 



CM 



a. 



>- e 
o a; 
c o 



oo oo o 
^ •a- ^ <r ^ 

CO CO CO CO CO 



r^ r** f^ 

CM CSJ CM 



1^ rs. f^ 
0% 0^ Ov 

CM CSJ CM 



CO ^^ t^ 
0\ Ch o> 
CM CM CM 



CM CM »— f— 

oooo 

CO CO CO CO 









O 00 lOi— 

o o coo 

CM ^ CO •— 



00 (X) 00 CM CM CM O O 0» •— «— CM CM r^ 00 9^ vo 

f^i^f^ ooo o>o^ro s£>U3v0^n ,_,_,»,_ 

CM CM CM I— r— ,— CM CM CM t— t~ #— i^ CM CM CM CM 



^f 


^' 






CO •* ^ in in 


ooo* 


ovoo 


^ vo r-v 


in oc 00 00 


CO *3- ^ ^ 


• 




'^ 


„— ^ 


r^ CO o o\ 00 


00 O CO 


CM C7\ m 


in Csi I— 


lo O r- ^ 


00 CO 0^ O^ 


CO 




s: 

CJ 


rsi c 


CM 00 in CO CM 


<T^ CM ^ 


r^ CM cy» 


r^ CO r— 


in 00 •a ^ 


-o o m in 


01 


or 

3^ 


ZZ 0) 
O Q 
(-J — ' 


in ^ ^ ^r ^r 


.— CM CM 


^ «»■ CO 


CM •— O 


c»> r^ r^ r*< 


r*- r**. ^n in 


CO 




O^ Ot 0\ 


00 00 00 


r-v r^ r*^ 


r^ r^ r^ r^ 


o^ o^ o\ oy 


^ 


—5 






in tn in 


in m in 


in in in 


m in in m 


in in in in 


<o 


-J 






C^ CO CO 


CO CO CO 


CO CO CO 


CO CO CO CO 


CO CO CO CO 



00 00 00 oc CO o r- po o o »— #— CO in r— »— CO ^ cr» 00 CO c^ 

oocT^Or- f— ^ ^ CM lo c CO m CM o OMn CO 00 in c c CO 

^^inr^ccoo cocMOi ino^#— »— r^^a- iocmc. co oioiooo 

ooooo cocmo cocmcm ooor^ oocooo 0000% 



r- r- f— O 
O^ O^ CJl o> 
CM CM CM CM 



X 


a; 




c 


00 CM inio lO 

00 00 ^ lO Q 

CO <y% ro^ o^ 
CM 00 \o m m 


CM CO r^ 

00 0%^ 

CM CM m 
00 in 


moof- 
r— men 


5325 
4885 
5874 


CM r— 00 m 

oommm 
CO ^ r^ 00 


oc in CO 00 
r*^ oc so 

00 f— 1— CM 

^ r^ Ot m 





r^ 10 vo ^ m 
a- ^ ^ ^ ^ 


00 00 00 
m in tn 


in mm 


OS OS 0> 

m m m 


CM CO CM CM 

ic m 10 10 


CM CM CM CM 

m m 10 10 




00 ^- lO CO ^ 

cj^ocMCOin 


^rocM 
CMf^ in 


CMr^ 
«a-Q0O 


r- CO CO 

CO m in 


CO CM «T CO 
#— 00 OCM 


CMO 00^ 
f— roa»vo 




r- 00 co^ a* 

<«■ CM CO ^ 

r^ F— CM CM CM 


OCTiO^ 
^ t— CM 

r- CM 


CM m CO 

00 00 OS 


0*. COr- 
^r CO ^ 

CM CO ^ 
CM CM CM 


r- m 

CC CMCO 

CM CO ro CO 


oc c^r- 00 
r* m CM m 

Oi O' »— •- 
CO ro ^ ^ 



r- 



•h\ 



m lO IC t£» ID 



vo m \c 



sC *D lO ^O 10 ID ID ID ID iD iD ^ ID ^ 



3-li! 



o 



O 



c c c 
ooo 



to n to 
s. w u 

^ ^ ^ 



to to m 

o u u 



^— ^" ^— (Q tl <0 



u u u 

ooo 




CM esi csj 

CM CSJ CSJ 



to to fO f^ r-" ^— 



u u u 
ooo 



CV! CM CM 

CM CM CM 



to to to 

•M •!-> 4-) 
U U U 

ooo 

mt nr <t 
^ ^ ^ 



to to to t— r— ^ 



U U U 

ooo 



CM CM CM 
CM CM CM 



to to to 

^ 4J +J 

u u u 
ooo 

r*^ rv f^ 

r^ f^ r^ 






"O 
0) 



c 



O 



r**r>.r^ corooo ioct^^ mcMO ooo cTt^f*^ mr^r^ 

^aCMCM ^^0> ^f— VO CMLOCX) VOiOLT) CT^mrO t^Kt iTi 

ooo 000000 000^ f^h^r^ r^r^vD CJ>o«— »X)vor^ 

ooo 000000 cMCMi— r^t^f^ coroco f^ooco a^a^<T^ 



1 I ( 



PO CO CO 

CM CM CM 



r^ r^ r^ ,»,»,. 
f*- ^ ^ CO CO ro 



in ir> LT) 
CO CO ro 



CO CO CO 






^i-V 






o o 
o^ — I 



CO 

to 



V) 



c 

•^ 

•^ 
CO 

CM 

C 

O f 
••" O '_ 

(o fO o a> 
C. CO o o 

-r- CJ* — 

> 
z 

c 

3 



ooo 



CO 

CM 

a. 



o 
c 






OI 



u 






Oh CT* O* 

in tn in 

PO CO CO 



coco^ 
mco o 
inco o 



oo o 

<^ CO CO 



I s 



00 en Ch 



m in 
coco 



in m in 

r-CM 



ot^io CMONr^ oor— Oh ohcmo mo»CM «a"^r^ 

1/)*— 00 oiOHin crio^ f^co^ cmocm t— mo 

OHO. vo ^r^in coiocM r^mm ^*CMr— ohcm<- 

00 I— CM oi f— CO r^ 00 o CO I— in r^ ^ cm go go *^ 





^ in in 

OH OH OH 
CM CM CM 


r^ 00 00 


CM CM CO 
CO CO CO 


CM CM f— 

m in ^ 


ooo 

CO CO CO 


OH o^ o< 
ooo 

CO CO CO 






lO vo vo 
in m in 
Oh O* oh 


O OH 

CO r^ 

CO 00 

ooo 


^ in ^ 
o in o 
^ €7H in 
CO co^ 


.6812 
.7361 
.8020 


^ r^ CM 
in CO in 

00^*— 

cmo u> 


cor^o 
r^ CO oi 
CM lO oc 
in CM C7H 


r^ r^ 00 

00 00 00 

CMCMi— 

^ ^ CO 

• • * 


o 

rsi 

a: 

o 

2 


Z 

o 

M 

1— 1 

O 

3: 
a: 



OH 

in 

CO 



ooo 00 

OlOH^ 

lOOO^ 

OHO f— 



CO CM CM cOT^\o in «n 00 

lOCOOH \pCOf* lOOi 

- - — ^esif^ — 



OH fs. CO 



OHO^ 



iS^ 



ip hN rs. 
ooo 

CO CO CO 



IP^ 00 

^ om 
CO CM in 

f-i-OH 



r*» rv r*^ ^ooogi opo^op 
CO CO c^ 



ss^ 



ro 



5SS 

CO CO CO 



SS5 

P**iO^ 



^^^ 


gs;£ 


CMOOro 


^ m CO 


♦ CJr- 


f^OOr- 



Oh r^ ir> 
m CO o 

S^S" CO 
OCvi 



CM^r*» 

CM^^ 



00 00 00 XOf^f^ 



COlO CO 
«CM 



O^CM 
CM CM CM 



fO*C0 
CO^ 



«mio 

CM CM CM 



m cMf^ 

<* CO 



00 o« f^ 

CM CM CO 



OH OCM 

^ ^ m 



^ m m 

CO CO CO 



Oh Oh O^ 

in in in 

CO CO CO 






0£ 



in f^ OH o •— CM 

lo 00 in a> f^ t^ 

00 00 ^ vn 00 CO 

CO f— O OH 00 00 



1^ ^ r^ lO ici lO 
OOO ooo 

CO CO CO CO CO CO 



00 in r^ 
OH OH 5: 

Cs. OH CO 

r^ c> 00 





^^^ 


m in m 
rococo 


m m in 
ro CO CO 


mm in 
<•> CO en 


CO CO CO 


i^i 


oomcM 
« • • 


s^^ 


r^cncM 

f-*OCM 


mc*»^ 

r^f^co 

• • • 


m CO CO 

OOfOO^ 

• • • 


oomi- 

iop->« 

• • • 


• • > 



HT 00 m 
m CO CO 



p-CMCO 




K^ 



CO CO CO CO CO CO CO CO CO CO CO fO CO CO CO m CO CO CO CO CO 



3-13 



«% 



V 



>v 






Table 3.5 


COMBINED RESULTS OF PROCESSING 
BATCHES 1 AND 2 OF P23 DATA 




Initialization 


Option 1 Results 


Option 2 Results 


Run 1 








Met|}od 2 


10.61 km 


10.13 




b 


0.00952 nirad -0.02236 




% 
p 


4.C8 km 


4.57 




0.07975 mrad 0.05386 




0.27406 


0.12275 




Run 2 








Method 2 








17.42 




17.55 


b 


-0.02827 




-0.03093 


p 


4.88 




4.57 


0.07975 




0.05386 


0.27406 




0.12276 



Run 3 
Metjiod 1 



Run 4 
Netitod 1 

b 



9.61 

-0.05236 
4.69 

10-5 

0.0 



17.04 
-0.05236 
4.69 
■5 



9.86 
-0.05236 
4.53 

10-5 
-0.00001 



10 
0.0 



17.35 
-0.05236 
4.53 

10-5 
-0.00001 



'-t " i*l t( 



where , 

h = tstiinate of altitude bias 

b = estimate of trunnion angle bias 

0. = standard deviation of estimate of altitude bias 
from covan'ance matrix 

aj^ = standard deviation of estimate of trunnion bias 
fro«n covariance matrix 

p = correlation coefficient of estimates of altitude and 
trunnion bias from covariance matrix 



3-14 



• I 



$ 









I 



«3% 






<t ' 






,1' 






_«^! 



:^'^ 



>^.:i>r?' - 







00 

t 

X 

< 



^ 



— ■ T ■ 1 I T T 



• IM If* IM 



••» •«• ik«l 



TIME(SEC) 



Figure 3-1 UNCOMPENSATED ASCENT VELOCITY 
COMPARISON (6&N • S-IVB) 




3-15 



V 



V' 



^^ 









o 
to 



< 



^ ' 






TIME(SEC) 



Figure 3-2 UNCOMPENSATED ASCENT VELOCITY 
COMPARISON (GftN - S-IVB) 



3-16 



V ■ 



V 



^v 
















M^MK 



4^ 



o 

UJ 

t 

< 

























































































































































































~ '*^*-" 








. ^_^ 

















• l» 



•M 4M 



TIME(SEC) 



Figure 3-3 UNCOMPENSATED ASCENT VELOCITY 
COMPARISON (6&N - S-IVB) 



3-17 



i 

i 

1 



^v 












o 

LU 

to 








































































































TIM 


1 = 


934( 


).48( 


















/" 


FART 


TLI 


) 
































































































































































1 


STOP 


TLI 


TU 


E - 


970- 


L48 


1 

3 



l« ••!< 



•tV% W^ 









TIME(SEC) 



Figure 3-4 UNCOMPENSATED TLI VELOCITY 
COMPARISON (G&N - S-IVB) 



K, 



3-18 









UJ 



J 

/ 



START TLI TIME = 9346.480 



» 



STOP TLI TIME = 9704.480' 



I I I 



••ft •••• 



TIME (SEC) 




Figure 3-5 UNCOMPENSATED TLI VELOCITY 
COMPARISON (G&N - S-IVB) 



3-19 



t< 



i 


. 


1* 








































































1^ 


































- 






































(f 






































































UI 
4/) 

t 

rsi 

< 


* 


i 


"ST 

/ 


\RT 


TLI 


TIME 


3 ( 


346 


480 
















i 

r 

30 






STO 


> TL 


[ TI 


M - 


97C 


4.41 


' V '; 

4^^^^ - '. 








































































i 





































































••T4 f«l« 






'^^;i;"'^- 



^^ifrfik-. 



TIME(SEC) 




Figure 3-6 UNCOMPENSATED TLI VELOCITY 
COMPARISON (G&N - S-IVB) 



h-- 



3-20 






««% 



"W*^'- 1 



in 

































































































































































































































1 




• i 


• M 


• « 


• M 


M t 


M •< 


• U 


»• 1 ••• 



TIME(SEC) 



Figure 3-7 COMPENSATED ASCENT VELOCITY 
COHPA.7IS0N (G&N - S-IVB) 






3-21 



) 



V 




UJ 






) 






TIME (SEC) 



Figure 3-8 COMPENSATED ASCENT VELOCITY 
COMPARISON (G«N - S-IVB) 



3-22 



h 



>. 









t 













































1 






















r 


























































- 




































































































» 1 












M « 


M • 


M « 


M *•«■ 



TIHE(SEC) 



Figurt 3-9 COMPENSATED ASCENT VELOCITY 
COMPARISON (6M • S-IVB) 



3-23 



>0' y%- 



i-..,..t.4-.*? 




V 



\ '} 







o 

Ul 



X 

< 











■ 


I 
































































































STA 


IT T 


LI T 


I ME 


» 9: 


346.480 






















\ 


















































STOf 


TL 


TI 


€ ■ 


97C 


4.4i 


i 








































































































* 
• • 


/t 


% 


!• 


«* 






!r— ^ 




rr— ' 




•* 


• 


#♦ 


»< 


»« 


•t« 



T!HE(SEC) 




Figure 3-10 COMPENSATED TLI VELOCITY 
COMPARISON (GIN - S-IVB) 



: 24 



r 



^.v 









"r-'^-ii^^^ 



^w^ 



y;#^*4.'.^^^;^^^'- 



o 

Ui 

t 





































































































st; 


RT • 


LI ■ 


IME 


» 9 


346. 


480 




















/ 












































STOf 


TL] 


Til 


IE = 


970 


4.4j 


1. 





















































































































W^ •!»* VM^ ••*• tW^ Mtl M*^ ••»* «^** 



TIME(SEC) 



Figure 3-11 COMPENSATED TLI VELOCITY 
COMPARISON (G&N - S-IVB) 



3-25 



^ 



t \ 

I 



'v! 




O 

CO 



5* 



I— 













































































































STAI 


^T T 


LI T 


IME 


= 92 


46.' 


80 




















1 


















































STC 


P TL 


I T 


ME 


■■ 97 


34J 


s 

80 
























































































































.... 









«»n •m *u^ 



t4t« «M« •«*« tflt< 



• »?* •m 



TIME(SEC) 



Figure 3-12 COMPENSATED TLI VELOCITY 
COMPARISON (G&N - S>IVB) 



3-26 



.->.■ 









»f 



\ 

] 



- '.fi J-X"->^*J^'''^^:;j:^'"''' M ,,^^,„,i,.j„^ 



♦ *if 






•r I 

N 



1 









\ 



--1 




g R R Pi « « « 

snoA 'MAttyNivw 



£ » 



S S § S i§ 



snoA 'Aliens WW XA«i 



«£ UJ 

a. »- 
s: o 



03S/li)"A'''»A 



T" 


' IT ±: . 5t 4^ - < 


4 5 


-< 1 c 


"I t 7 -"t:, 


-.Ci-f---^ 


— 1 1 


— \ — 

i 4 . .,,. J ^' 1 . 


ir< xnt " j - -4- 


i 1 1 
< 1 ' ... ] 1 ' — \ — 


~^~~. 1 ^S ^ ,Z| 1 1 1 


^^< n:" ^ ^^ ■ ^-^ 


— \ ^ ■ , 1 - 


-^ ■ ■"IT v-.^ -I- -^ r--^- 


__ — -^ — p^ ^^ 

! lO I _i_ .. .,.--. — >\ < *-^ 


i ; ! 1 ^ipv ^i -^ M 


r—— ' — T" > \ 1' ! ■ 


^ — r'^- ■ 1 ■ \r ^^i \ 


-^~< 1 ! 1/ ' 


"^-5-^r- ' 1 y^^ ■ \ 7 


1— i s-i — — 1 — ' — ' — ' — ' — jf^ — ! — —X— -- "■j ' "J" « 1 


"^'' , r ' 1 _\\. A 


— J S^^-gf ^ — ^— -/* "^ — ^ — T" '"■ ~' t \ \ , 


'i "^ y ! - V 


\ ' \ i/' \ • ,: i„ — ^ — — X— 1 1- ■ 


^ 1^ 1— ' ! ' — ■' . ■ ■' ' 1 


. ! '• • ' _, _^_ __^Ja:^i_^ 


TTT'IUZl^ _^ X 4 -W- 


-7— 1+1-: i ' i ji i ±: 4 4:41 


— --ph-i-f- ; 1 :^ 4 4 


"! ^ ^i""TT^ X^ r-1 VI- 


im:^ "A 1 1 , 1 -x^ S" 


"^ \ -^T -r-- H 


■^T" ^ 1 IT _^ n T 


TT " Ji 4^ 33- L 


~M~'~>^ 1 s i 


iriuE it ^- H 


-r 1 T, it ^ 



%^^ 






Ol UJ 
o < I 



g 
» 



3 

pa 
o 



i 




(M O Ul « « 

(J3S W) SIvnolSJa Hlld^OQ NJSrt 



r* m r\ 



(ril/ii) "A 



" I ' ^ ' iu. ' - ^ * --"!:"" 



~''"'"^:c^ 



^^^:' 




V 



4.0 LM SYSTEMS 



4.1 LM INERTIAL MEASUREMENT UNIT 

4.1.1 Transearth Injection Burn: Cut-Off Velocity Errors 

4.1.1.1 Velocity Errors 

Velocity errors generated by the IMU during the TEI burn were in- 
vestigated. To do this, "best" ignition and cut-off vectors were deter- 
mined from free flight data. Three such vectors were determined for the 
time of ignition; one was determined for the time of cut-off. These 
vectors are presented in Table 4.1. The ignition vectors were extra- 
polated to the time of cut-off using accelerometer data from the LGC 
downlink. These extrapolated vectors may be thought of as LGC "best 
guesses" as to the vehicle state at time of cut-off. They were differ- 
enced with the free flight cut-off vector (assumed correct) to obtain 
estimates of the IMU induced trajectory errors. Only the velocity 
components were calculated, and the results of these calculations are 
presented below for each ignition vector and each of three coordinate 
frames. The coordinate frames chosen were: BRCS (Basic Reference 
Coordinates); IMU, and; local. All reference frames were moon centered. 
The local frame is defined to agree with MIT*s convention, as follows: 

X: completes the right hand set 

Y: along the negative angular momentum vector (-R x V^) 

Z: along the negative of the radius vector (-R) 



aV 



aV 



(GYMX289 - NBEX343) (HAWX300 - NBEX343) 



ix^V 



aV 
("Best" - NBrX343) 

X^Y^ZX^Y^ZX^YZ^ 

BRCS (+3.85; +3.02; +2.i2)(+2.92; -1.21; +9.62) (+3.53; -0.14; +t.44) 

IMU (-3.77; -3.83; -1 .07)(-2.72; -2.92; -9.31) (-3.23; -3.53; -7.80) 

LOCAL (+5.46; +0-41; -0.56)(+5.10; +8.72; -0.72) (+5.70; +7.12; -0.66) 
Magnitude 5.48ft/sec 10.13 ft/sec 9.15 ft/sec 



4-1 




■:x't^"'»^' 






-; . ._4«i^' 



^?H 



«% 



V 



I 



1 
i 






The GYMX 289 and HAWX 300 ignition vectors yield similar velocity 
errors whereas errors for the "best" ignition vector differ from these 
mr*rkedly. The first two vectors were obtained by the RTCC in real time. 
aYMX 289 was the vector with which the TEI burn was targeted. However, 
both vectors contain only data obtained prior to perilune. The "best" 
vector was obtained at TRW by fitting data on both sides of perilune. 
It provided much more satisfactory range and doppler residuals after 
perilune and consequently has been chosen as the preferred vector for 
purposes of this report. The disagreement between the preferred vector 
a.id the other two vectors lie almost entirely in the out of plane 
("Y", in local coordinates) direction; this is the direction in which 
velocity is least accurately determined by ground based radar (and, 
therefore, the one in which the greatest uncertainties are experienced). 

4.1.1,2 Frror Sources 

The principal sources of velocity error are likely to have been 
IMU misalignments (l.7 deqrees/axis, due to lo- drifts alone) and dis- 
crepancies in the ignition and cut-off vectors obtained from free flight 
data. These free flight vector unc-^rtainties are not known explicitly. 
However, the ignition vector is credited with very good accuracy; on Lhe 
order of .1 ft/sec, out-of-plane» and less than .1 in the other two 
axes. The cut-off vector is suspected of greater errors, but these may 
well be less than one ft/sec (total). With that hypothesis. It was 
concluded that the majority of the error could be attributed to IMU 
misalignments. Since alignment errors are perpendicular to the velo- 
city gained, it was of interest to determine how much of the observed 
error satisfied that condition. This was done as follows: 

Vp (parallel to VG) = (V) • (unit VG) = -1.47 ft/sec 

Vp = Vp (unit VG) = [-1.27; +0.73; -0.16], In IMU 
coordinates 

V (normal to VG) = V - V^ » [-2.50; -4.56; -0.91], 



-n 



IMU coordinates 



V^ « 5.27 ft/sec 



4-2 






. l^Mf"' 



ML^lHUPI^lll^l 



^"X-^ 



'4k 



i 

.^.-'■1 

*.^"*».^> 






Most of the error was perpendicular to VG, tending to support the 
argument for IMU misalignments as the principal factor. The -1.45 ft/sec 
of error parallel to VG cannot be attributed to IMU misalignments and since 

other IMU contributions can reasonably be expected to have been much less 
than this, it seems probable that the free flight cut-off vector contained 
a -1.47 ft/sec error along VG (and an unknown, but presumaoly small com- 
ponent perpendicular to it), 

4.1.2 IMU Misalignments at Time of TEI Burn 

Three approaches were taken to determine the IMU alignment errors 
which existed at the time of the burn. These are described in the 
following paragraphs. 

4.1.2.1 Sun Check 

The crew sun check (discussed in Section 4.4.1) performed at 73:47 
GET provided information concerning IMU misalignments perpendicular to 
the line-of-sight. Unfortunately, there were Insufficient data to deter- 
mine the direction of those errors which were observed. However, it 
was determined that the magnitude of observable errors was approximately 
0.51 degrees. This provided a useful method of testing the validity 
of other estimates. 

4.1.2.2 Drift Check 

An effort was made to determine alignment errors from gyro drift 
data. These data included LM prelaunch and CM inflight measurements. 
Basically, it was assumed that LM IMU error at any given time was the sum 
of: 

CM IMU drift prior to the docked alignment, plus 

LM IMU drift subsequent to the docked alignment. 

The uncertainty In the estimate thus obtained was taken to be the RSS 

of CM and LM initialization errors. Uncertainties in the drift rates 

were Ignored. The point of this was to determine whether misalignments 

could have been reliably deduced from existing Instrument performance 

data and eliminated prior to the midcourse burn. Table 4.2 presents 

the results of these estimates. 

4-3 



•.\:i.^^nwj^^^ — ''^rr;™" •:^;,^gi": i ,-^' ■. ■-. -^^ 





:^^£" 



i 



From the table it can be determined that the magnitude of misalign- 
ment estimated from drift data is 0.60 degrees, with a la uncertainty 
due to initialization of +.28. Almost all of this would have been 
visible to the sun check. Thus, the magnitude of the predicted error 
agrees rather well with that observed in the sun check, and the dis- 
agreement lies well within the bounds of predicted uncertainty. 

4.1.2.3 Velocity Error Check 

Once the velocity error at TEI cut-off was determined, it was 
possible to determine in two steps a unique set of alignment errors which 
satisfied the constraint that the sum of the squares of the error angles 
was minimized. Step one consisted of determining that component of 
velocity error perpendicular to the velocity gained vector. This was 
done because IMU misalignments can be shown to produce only perpen- 
dicular errors. The procedure and results were described in Section 
4.1.1.2. The second step consisted of solving for a "minimum** set of 
error angles. The constraint equations are: 

Minimize 1*1= ! ^i^ , subject to 

(V6) X (i) = aV^, where 

the vector of error angles 
the velocity gained in the burn 
:.V.; that component of burn velocity error perpendicular 



to VG . 

The solution obtained from these constraints is: 
2 



i=(vG) 



{J^)^x (VG) 



Applying this relationship to the quantities generated In Section 4. 
yields: 

I = [-.062; -.035; +.344] degrees 
' t!= .351 degrees 




4-4 



^ 



It must be understood that, assuming a correct measure of aV , these are 

the errors which generated A\r (moreover, most of this would have been 

— n 

visible in the sun check). However, these errors do not necessarily 
reflect total IMU misalignment. Platform misalignments about VG would 
generate no velocity error. Consequently, that component of total IMU 
misalignment which was about VG cannot be determined by an analysis of 
aV . It is to be expected that total IMU misalignment magnitude would 
be no less than ,351 and would probably be greater. The discrepancy 
would arise from the irresolvable component about VG. 

A pattern of reasonably good agreement emerged from the above error 
estimates as evidenced in the summary below: 



Source of Estimate 

Sun Check 
Drift Check 
Velocity Check 



!x !x !x 



!z 



-0.26 +0.24 
-0.06 



-0.07 
-0.04 



+0,14 



+0.54 

+3.34 



+0.04 



0.51 

0.60 +0.28 
0.35 



Agreement between the three methods in the Z component, and in magni- 
tude, is fairly good. Also, agreement in magnitude and in the "X" and "Y" 
estimates lies within the lo uncertainty band. 

4.1.3 PIPA Bias and IRIG Drift 

LM PIPA biases were stable throughout the periods the LM IMU was 
activated. The LM IMU was turned on for the first time shortly after 
the CSM incident and remained powered up until after the TEI burn. Heater 
power was always maintained in the system. The system was activated 
for the second time at 134 hours GET in preparation for the MCC 4 maneu- 
ver. Samples of PIPA bias during the periods the system was activated 
indicated the following mean values and data variations. 



h>t 



wt'.n- 


V ■-*§>. 








. *^ vv/^Sfchl^''* 


■%^'^m^K'^^^^' 


^* 'I'^jHp'.',*'^ 


^m^^.\[.% 



i 



4-5 



> t«ia^ 












A' I 



Number of Sample* 

PIPA Samples Mean Value Standard Deviation 

X 19 1,494 cm/sec^ 0.014 cm/sec^ 
Y 19 -1.427 cm/sec^ 0.038 cm/sec^ 
Z 19 1.573 cm/sec^ 0.011 cm/sec^ 

♦Design Specification Uncertainty (1j) = 0.2 cm/sec^. 

Insufficient data were available to evaluate IMU IRIG drift on this 
mission. However, based on the small values of LM IMU misalignment at 
the time of the TEI burn determined from the error separation study in 
Section 4. 1.2. J, it can be deduced that the gyro drifts were small and 
easily within the 2c design uncertainty of 0.09 deg/hr. 

4.2 LM DIGITAL A'lTO^ILOT 

An analysis of the DAP '^ortrol functions during the Apollo 13 mission 
was performed to verify proper DAP performance. Th2 following items were 
considered: 

The MCC 2 DPS free return maneuver 

The TEI (pericynthion + 2 hour) DPS maneuver 

The maneuver to the LM PGNCS PTC attitude. 

The attitude hold capability of the LM DAP in the 
LM/CSM and LM/CM configuration. 

The automatic maneuver capability of the LM DAP in 
the LM/CSM configuration. 

The manual maneuver capability of the LM DAP in the 
LM/CSM and LM/CM configuration. 

4.2.1 MCC 2 DPS Free Return Maneuver Analysis 

A four jet. 8.01 second ullage was initiated prior to the MCC 2 - 
DPS burn at 61:29:36.06 GET. DPS ignition occurred at 61:29:42.84 GET. 
Prior to the OPS burn the U-V rotational jets (i.e.» X translation jets) 
were not manually inhibited as is usually the procedure. Manual throttle- 
up from 11.9% to 36.8% occurred at approximately 61:29:50 GET. Program 
sequencing prior to and during the bum was nominal. Manual throttle-up 

4-6 





«*b 



V 









-f-"^" "^ 



to 36.8% was nominal and required aV of approximately 38 ft/sec was 
achieved. The burn residuals were 0.2, 0, and 0.3 ft/sec for the X» 
Y, and Z components, respectively. No manual nulling of these residuals 
was necessary. Table 4.3 shows the magnitudes of the maximum estimated 
rates and the rate gyro signal maximum values during this burn. The 
low magnitudes indicate good burn performance and no discernible 
sloshing effects. Little or no slosh would be expected since the APS 
and SPS were fully loaded during the burn and the DPS was fully loaded 
at the start of the bum. Table 4,4 shows the magnitudes of the maximum 
attitude errors and rate errors obtained during this burn. Figures 4-1, 
4-2, and 4-3 show the phase plane plots for the P, U, and V axes, re- 
spectively, for the MCC 2 burn (Relationship between P, U, V and X, Y, Z 
axes is shown in nomenclature). These plots indicate nominal DAP perfor- 
mance. Table 4.5 shows the RCS fuel consumption required to maintain 
attitude control during this burn. The total RCS propellant (excluding 
ullage) required during MCC 2 was 12.90 lbs. Figures 4-4 and 4-5 show the 
pitch and roll GDA positions throughout this burn and indicate satisfactory 
GDA performance. During the manual throttle-up from 11.9% to 36.8%, the 
effects of a transient due to the compliance of the DPS gimbal system can 
be seen. This compliance effect results in the GDA*s driving in + pitch 
and a - roll direction. After relieving this compliance, the GDA movement 
is as expected in trying to track the e.g. 

4.2.2 TEI DPS Maneuver Analysis 

Prior to the TEI burn, jets 6 and 14 were used for a two jet, 11.1 
second ullage which began at 79:27:23.43 GET. DPS Ignition occurred 
at 79:27:38.30 GET. Prior to the burn, the U-V t-otational jets were 
manually Inhibited as required by the preburn checklist. A nominal 
manual throttle-up from 11.4% to 37.7% occurred at approximately 
79:27:45 GET. The automatic throttle-up to 93.9% occurred at approxi- 
mately 79:28:05 GET, The burn residuals were 1.0, 0.3, and ft/sec for 
the X, Y, and Z components, respectively. No manual nulling of these 
residuals was performed. Table 4.6 shows the magnitudes of the maximum 
estimated rates and the rate gyro signals maximum values during this burn. 



4-7 



^1^ .^^ 








^ . ^m£ 



■^«#"i 



^v 






ft ^ ' " " 



„. # ._ 



I 



The values indicate nominal performance and very smull slosh effects, 
as would be expt ,ed with the propellant loadings that were present, 
i.e., APS full and DPS and SPS nearly full. Table 4,7 presents the 
magnitude of the maximum attitude errors and rate error which occurred 
during this burn. Figures 4-6, 4-7, and 4-8 show the phase plane plots 
for the P, U, and V axes, respectively. The time period plotted begins 
10 seconds before ullage and extends 20 to 30 seconds beyond the start 
of autotnatic throttle-up. The plots indicate nominal DAP performance. 
The U and V axes plots indicate two large excursions beyond the dead- 
band. In each case, the first excursion is smaller and is associated 
with manual throttle-up. The second excursion is associated with auto- 
matic throttle-up. Tablr 4.5 presents the RCS fuel consumption required 
to maintain attitude control during the burn. The total RCS propellent 
(excluding ullage) was 4.90 lbs (all expended in P-axis contrcl). 
Figures 4-9 and 4-10 show the pitch and roll GOA positions from DPS 
ignition through the automatic throttle-up maneuver and indicate nominal 
GOA performance. Some concern was expressed about the fact that the roll 
GDA drove approximately -1.3 degrees from its Initial position at the 
start of the TEI burn. This appears to be nominal behavior caused by 
relieving compliance and perhaps correcting for some mistrim, The 
following facts are known. 

a) The preferred direction for compliance is in a "+ pitch" 
and a '*- roll" direction. 

b) Compliance appears to be highly non-linear and transient 
effects cannot always be observed. 

c) Previous simulations using the now-inoperative MSC bit- 
by-bit simulation have shown similar transient compli- 
ance effects on all tests. 

d) For the MCC 2 buni the pitch GDA drove +1.05 degrees 
during throttle-up from 11.9% to 36. 8t and the roll 
GDA drove -0.75 degree during throttle-up from 11.9% 
to 36.8'^. These effects were apparently due to the 
effects of compliance. 

e) At the end of the MCC 2 bum both the pitch and roll 
GDA's were driving in a positive direction in trying 
to track the e.g. 

4-3 



^;i 



^ 



f) For the TEI burn the pitch GDA drove +0.435 degree 
during throttle-up from 11.4% to 37.7% and the roll 
GDA drove -1.335 degrees during this throttle-up 
period. 

g) The root- sum- square GDA change due to compliance was 
approximately 1.29 degrees for the MCC 2 burn and 
1.402 degrees for the TEI burn. 

h) For the TEI burn the pitch GDA showed no noticpable 
change during throttle-up from 37.7% to 93.9%. The 
roll GDA drove -1.245 degrees during this throttle-up 
period. The root-sum-square GDA change of 1.245 degrees 
agrees closely with the previously discussed values of 
1.29 degrees and 1.402 degrees. 

Evaluation of the facts discussed above leads to the conclusion that the 
GDA behavior for both the MCC 2 burn and the TEI burn was nominal. 

4.2.3 Maneuver To PTC Attitude 

The <!ifficulties encountered in maneuvering to the PTC attitude 
subsequent to the TEI burn prompted an investigation of the torques 
associated with each LM reaction control jet and with the various 
rotational and translational firing policies available in the LGC. 
This investigation included the effects of impingement forces on the 
plume deflectors. 

At the time of the maneuver, the best estimate of LM and CSM 
weights were 25666.2 lbs and 62489,7 lbs, respectively, or a total 
weight of 88155.9 lbs. This value was referred to in the SODB 
(Reference 2) which defined the combined vehicle eg, location in the 
CSM body frame as follows: X^ « +1049.38 Inches; Y^ ^ +2.49 inches; 
and Z* « +3.59 Inches. These values were obtained by linear inter- 
polation of the values recorded in the SODB. These data were used to 
transfcnn the e.g. location into LM body axes. 




4-9 







J \ 



: • 1 



The SODB also defined the locations of the points at which the re- 
action control jet forces are applies-. The location of the impingement 
forces on the plume deflectors was defined by Reference 3. Based on the 
location of each of the sixteen reaction jets with respect to the e.g. and 
the thrust vector, the torque for each jet was calculated. Using the data 
from Reference 3, torques were calculated for the impingement forces result- 
ing frOni each of the downward firing thrusters. 

The GSOP (Reference 4) gives the let policies to be used in the 
various translation and U-V rotational maneuvers that can be performed. 
Tables 4.8 and 4.9 indicate the torques which result from the use of 
each of these policies. In addition, there are possible jet policies 
associated with Q and R axes rotations in the minimum impulse modo. 
These are not defined in the GSOP. However, the various policies have 
been determined and the torques resulting from each policy are defined 
in Table 4.10. 

The maneuvering problem reported by the astronauts primarily was 
a cross-coupling effect between the pitch (Y or Q) axis and the ro'l 
(Z or R) axis. No downlink data is available for the period of the 
maneuver. However, certain assumptions can be made. 

a) All jets were functioning; this implies that primary 
jet-policies were in effect at all times. 

b) The maneuver was conducted manually using either: 

1) Y-axis and Z-axis translation commands through 
the TTCA; or 

2) Three-axis (X, Y, and Z) rotational commands 
through the ACA. 

Examination of Table 4.8 reveals :hat Y-axis and Z-axIs translation com- 
mands produce only minor cross-coupling around the yaw axis. Pitch^roll 
cross-coupling is non-existent. Examination of X-axis rotational policies 
In Table 4.9 reveals that primary jet-policies, using cUher four jets 
or two, produce only X-axis rotations. Data for Y-axis and Z*ax1s rota- 
tions are shown in Table 4.10. The use of four jets for any rotational 
maneuver produces very minor cross-coupling. However, the GSOP states 
that pitch and roll maneuvers in the minimum impulse mode will be 



4-10 




I — 



,„%»*- 



• 






.m 



accomplished with two jets. Examination of the jet-policies which use 
two jets reveals cross-coupling torques that have the same magnitude as 
the primary torques. This occurs because each of these jet-policies 
employs one downward firing jC. The resulting impingement force acts 
equally about the Y-axis and the Z-axis using the long X-axis moment 
arm. The result is to reduce the primary torque by a factor of two 
and produce the large cross-coupling force - 

Although data for this time period is lacking, examination of data 
for a later period revealed that these rotational firings took place. 
Data indicated a +R (+Z) rotational command at ^37:22. 43. 616 and -0 (-v) 
rotational command at 137:23:01.616. Examination of jet firings data 
showed corresponding 60 millisecond firings of jets 5 and 10 at 137:22:50.434 
and of jets 10 and 13 at 137:23:01.234, Analysis has shown that jets 5 
and 10 produce a primary +R torque and jets 10 and 13 produce a primary -Q 
torquvr. Since two jet Y and Z axes torques occurred at these times, it 
is not unreasonable to infer that they also occurred during the maneuver 
to PTC attitude and that they produced not only the primary torque but a 
cross-coupling torque of equal magnitude as well. If the THC was used 
to perform maneuvers in the LM/CSM docked configuration, no unexpected 
problems should be encountered if the crew is familiar with this type 
of operation. However, use of the RHC or the MIC can produce results 
which would be very unexpected. 

It is recognized that the above analysis represents only one of a number 
of possible explanations of the control difficulties encountered. Another 
probable source of difficulty is the fact that the FDAI was powered down 
during the maneuver. Without that source of attitude infomation, it was 
necessary to monitor attitude by observing gimbal angles displayed on the 
DSKY. Because the spacecraft yaw axis was not coincident with that of 
the platform, either a pitch or a roll command would cause a change in both 
of the corresponding gimbal angle displays. That this was a factor is sup- 
ported by the fact that, after the vehicle's and platform's corresponding 
axes were brought into closer alignment, passive thermal control was estab- 
lished satisfactorily. 

4-11 



i<#.^,^>"' 




£ 



- Arf' 



^._ .,, ,.,^-^-...^. 



*v- 



<a% 



^s 






*^ 



4.2.4 DAP Control of the LM/CSM Configuration 

DAP attitude control was evaluated for periods of attitude hold, 
and for periods of automatic and manual maneuvers. The available data 
were for a 5 degree deadb^nd. Figures 4-11, 4-12 and 4-13 (P, U, and 
V axes, respectively) present both periods of auto maneuver and attitude 
hold. The auto maneuver period was 61:25:17 to 61:25:20 GET. The atti- 
tude hold period began at 61:25:21 GET and was plotted for approximately 
2 minutes. This period precedes the MCC 2 maneuver and nominal DAP 
performance is indicated. An auto maneuver prior to the TEI burn is 
presented in Figures 4-14, 4-15, 4-16 (P, U, and V axes, respectively). 
The maneuver began at 79:21:43 and was terminated 3 seconds later. 
Nominal DAP performance is indicated. A five minute period of attitude 
hold subsequent to this maneuver is plotted in Figures 4-17, 4-18, and 
4-19 (P, U, and V axes, respectively) The period covered is 79:22:00 
to 79:27:00. The U and V axes phase Dlanes are plotted for the entire 
time period. The P axis was functior-ing in a much faster duty cycle of 
which one complete cycle has been plotted. Manual maneuvers were per- 
formed in the minimum impulse mode where the desired CDU angles are 
set equal to the actual CDU angles. Since no attitude errors exist, 
it is not possible to generate a meaningful phase plane plot. However, 
it was determined that the rate errors did not exceed the deadband 
limits. 

4.2.5 DAP Control of the LM/CM Configuration 

DAP attitude control was evaluated for a time period that contained 
both attitude hold and a manual maneuver. The P, U, and V axes phase 
plane plots are presented in Figures 4-20, 4-21 and 4-22, respectively. 
The attitude hold period presented began at 140:49:12 GET and terminated 
at 140:51:25 GET at which time the manual maneuver began. Since the 
manual maneuver was performed In the minimum impulse mode, the attitude 
error remained approximately zero as shown by the three figures. 




1— .• 



4-^12 



■':X'^|t'.:' 



^i^T" 



uf: 



^^ 



V 



4.3 LM ABORT GUIDANCE SYSTEM 

Investigation of AGS performance was conducted with the objectives 



Determining the stability of AGS sensor static err-^rs 
(accelerometer bias; gyro static, or bias drift). 

Determining AGS sensor dynamic errors from comparisons 
of AGS and PGNCS measurements during the TEI burn. 

Comparing AGS and PGNCS measurements of velocity gained 
and vehicle attitude during midcourse burns. 



After the Service Module LOX tank incident, four burns were made to 
return the spacecraft to earth as quickly and safely as possible. The 
first and second burns were made under PGNCS control with the LM DPS; 
the AGS was powered up for the second burn and used in the "back-up" 
mode in case of PGNCS failure. The AGS was used to perform the last 
two burns, a DPS burn of 7.8 ft/sec and an RCS burn of 2.8 ft/sec. 

4.3.1 Burn Analysis 

TEI (AGS in Follow-Up) 

The second LM DPS burn was initiated at approximately 79:27:41 
following an X-axis RCS burn for ullage. This burn was performed with 
PGNCS control and the AGS in follow-up. Although the AGS was not tar- 
geted for the maneuver, its Indication of sensed velocity and attitude 
were available to confirm success of the burn. After AGS power-up, 
a Body Axis Align was performed. Throughout most of the burn, the astronauts 
monitored "X" sensed velocity in body coordinates on the DEDA and PGNCS sensed 
velocity on the DSKY. These velocities are plotted in Figure 4-23 and 
Indicate good agreement between the AGS and PGNCS. 

Following the burn, AGS power-down (including heaters off) began at 
approximatley 79:51:00, 



I 




4-13 



4**' 



:&I. 



,.<!■. . 



- i^ 



>^i 



MCC 3 (AGS Controlled ■ DPS) 

This burn, a small maneuver to increase the entry flight path 
angle, was performed under AGS control. Plots of sensed velocities 
are shown in Figure 4-24. Since the burn was insensitive to burn time 
cut-off errors and attitude errors, the primary burn rule was to avoid 
excessive rates (more than 10 leg/sec) about any axis. 

System power-up for the burn was initiated at approximately 
104:40:00. At approximately 104:58:20, the ASA temperature had risen 
above 115 degrees F and the AGS was activated. 

DPS burn time was voiced up as 15 sec although the astronauts were 
told to shut-down after 14 sec to avoid an overturn, which would require 
an RCS trim, impinging on the command module. 

Figures 4-25, 4-26, and 4-27 show the attitude rates and attitude 
errors. Rate and attitude error data indicate no appreciable disturb- 
ances since all three channels appeared to be in normal limit cycle 
operation. 

Because of the planned early shutdown, the maneuver was a slight 
underburn. An RCS trim burn was performed approximately one minute 
later, increasing the burn aV by 0.2 ft/sec to 7.8 ft/sec. Subsequently, 
the AGS was powered-down including heater power off. 

MCC 4 (AGS Controlled - RCS) 

PGNCS and AGS were powered-up at approximately 136 hours and the 
maneuver to burn attitude for this midcourse correction was with the 
PGNCS. 

In Figures 4-29, 4-30, and 4-31 comparisons between the AGS and 
PGNCS indicated attitude* are made for the period of manual maneuver- 
ing to acquire the appropriate spacecraft attitude for MCC 4. (An 
AGS to PGNCS align preceded the re-orientation.) Following acquisition of 
the burn attitude, Guidance/Control was switched to AGS. 






' LM 



4-14 




"."Z"^^-.-' 



^""^k:h 



.*K 



«* 



*^\ 

/•^l 






The burn was initiated at approximately 137:39:52 with the X-axis RCS, 
The DSKY was used tO observe the accumulated velocity. After about 23 
seconds, the RCS was turned off after achieving a aV of 2.7 ft/sec. A 
partial trim was effected 15 sec later, bringing the total aV to 2.8 ft/sec. 
This was short of the desired value of 3.1 ft/sec, but was indicated as 
acceptable by the ground. The aV's are shown in Figure 4-28. 

No attitude control problems were noted during the burn, with manual 
pitch and roll provided by the TTCA and AGS yaw control by the AGS at:itude 
hold mode as seen in Figure 4-32. 

4.3.2 Sensor Performance (ASA 023) 

4.3.2.1 Accel erometer Errors 

Free Flight Performance - Free flight accelerometer static bia^ data 
were obtained for two time periods, pre-TEI and post-MCC 4. Bias esti- 
mates obtained from these data appear in Table 4.11. Table 4.12 compares 
the shifts undergone by this parameter after prelaunch calibration with 
standard deviations of this shift. The AGS Capability Estimate one sigma 
values result from data samples taken from a number of AGS systems; as such, 
they are representative of general AGS perfonnance. The table reveals that 
static bias perfonnance was easily within la of AGS Capability Estimate. 
This is excellent performance in view of the fact that the ASA dropped 

o 

23 degrees F below the specified minimum (60 F) during the 24 hour period 
in which it was shutdown prior to the TEI burn. 

Powered Flight Performance - The TEI burn was the only one performed 
during Apollo Mission 13 of sufficient duration and thrust to permit 
estimation of AGS dynamic sensor performance. Figures 4-33, 4-34, and 4-35 
show the accumulated sensed velocity along the body axes. The aV magnitude 
was about 860 ft/sec. 

Accelerometer errors were found from AGS/PGNCS sensed velocity 
comparisons. The P6NCS velocities were compensated for known static 



\: % 


y .1 










i^S^' 


¥ 

'V*.. 



4-15 



*»9~ 



«J% 



I 

t 

I 

I 
f 






bias errors, interpolated to AGS times, transformed to body coordinates, 
and subtracted from the corresponding AGS velocities. The differences 
are shown i.. Figures 4-36, 4-37, and 4-38. Since PGNCS gimbal angles 
were used to transform the velocities, these differences reflect only 
accelerometer errors (plus noise due to AGS downlink and PGNCS gimbal angle 
quantizations). 

The estimates of dynamic and total accelerometer error are listed in 
Table 4.13. The total errors were derived with a digital computer pro- 
gram which determines a set of "best" AGS errors for the purpose of mini- 
mizing the AGS-PGNCS velocity residuals in a least squares sense. The 
dynamic errors were obtained by subtracting the static bias (measured over 
a 15 minute interval just before the burn) from the totals. Table 4.15 
presents ratios of the shifts (from prelaunch values) in these parameters 
to shi^^s predicted by the ASA 023 error model. The table shows that all 
of these errors were within the error model 2o limits. Plots of the velocity 
residuals, compensated for the recovered errors, are shown in Figures 4-39, 
4-40, and 4-4 u 
4.3.2.2 Gyro Erro rs 

Free Flight Performance - Free flight gyro static drift data were 
obtained during two time periods, pre-TEI and post-MCC 4 (the interval ' "om 
140:29 to 140:51 GET). Drift estimates obtained from these data appear n 
Table 4.11. X channel data were noisy and interpretation was correspondingly 
difficult. Thus it was necessary to specify a range of possible performance 
values. Instrument performance was within ^o AGS Capability Estimate 
tolerances, so that it may be said that the static drift performance was 
quite satisfactory. 

Powered Flight Performance - Gyro error was obtained from AGS/ PGNCS 
attitude differences obtained just before and during the bum. These 
differences are shown in Figure 4-42, 4-43» and 4*44. Because of 
relatively constant inertia! attitude and thrust level, the effects 
of dynamic drift, scale factor er^or, input axis misalignment, and mass 



4-16 



jn' 







..^f 




^. . .^te^ 






<5% 



unbalance cannot be separated. However, since the burn was perfonried 
in the "attitude hold" mode, the effect of a significant scale factor 
error or input axis misalignment would have been negligible. Because 
of the low thrust level (about 0.1 g), mass unbalance probably con- 
tributed very little error. Thus most of the error was attributed to 
gyro static and dynamic drift. The total errors were determined by 
measuring the slopes of the attitude differences during the burn. 
The dynamic error was obtained by subtracting the static values from 
the totals. The dynamic and total errors are presented in Table 4.14. 

Listed in Table 4.15 are ratioi of the shiftr in measured parameters 
to their lo values. None of the errors exceeded 2o with respect to ASA 023 
preUunch performance. 

4.4 LM OPTICAL ALIGNMENT CHECKS 

4.4.1 Sun Check for TEI Alignment 

Shortly after the service modul** LOX tank incident, the crew per- 
fonned a docked LM IMU alignment to the CM IMU. At 73:47 GET a check 
of this alignment was performed. At the time of the check, visibility 
through the optical instruments was extremely poor due to an agregation 
of debris surrounding the spacecraft. In addition it was desired that 
maneuvering be held to a minimum to conserve RCj propel 1 ant. Conse- 
quently the decision was made to limit the initial check to one celestial 
body. The sun was chosen because of the visibiV-y conditions. The 
check consisted of pointing the AOT line-of-sight toward the LGC calculated 
sun direction and then noting the approximate magnitude of the offset. 
The LGC was placed In P52 and routine R52 (Auto Optics Positioning) was 
used to establish *he LGC-estimated poiniing vector. The FDAl attitude 
error displays were used to hold this spacecraft attitude while the 
position of the sun in the field of view was determined. It was deter- 
mined on the ground that the solar disc would subtend approximately 
one-half of a degree in the AOT field of view. From that fact and the 
observed sun Image the crew determined an image (and therefore an IMU) 
misalignment of approximately one-half of a degree in an undetermined 
direction. Since this single target optical check could not resolve 
errors about the llne-of-sight, no estimate of possible misalignments in 
that direction was obtained. The mission rule established for this 



4-17 








,,.%«.iar*' 



>V ! 





'- ,. 


,^^ ^ 


♦ 






,' "*•' ' 









check was that any observed t-:ror of less than one degree was tolerable. 
No effort was made to correct the error observed, or to determine the 
error about the line-of-sight, prior to the TEI burn. 

In conducting a single target alignment check such as this it is import- 
ant to select a line-of-sight which reveals those alignment errors of con- 
sequence in subsequent powered flight phases. More explicitly, it 
should be chosen to measure all misalignments having a significant impact 
on trajectory parameters of importance to a safe re-entry. One very 
crucial parameter is entry flight path angle, and during the deep space 
phases of transearth flight this is governed largely by inplane velocity 
perpendicular to the earth centered radius vector. The sun was an ex- 
cellent choice of targets for detecting misalignments as they effected 
Apollo 13*s post-TEI entry corridor. This is demonstrated by the 
results presented below: 

Let . = entry flight path angle 

V = velocity error in the direction which effects flight path angle 

V = velocity gained in the TEI burn 

Unit (LOS)= the unit line-of-sight vector to the sun at the 
time of the sun check » 



Then 



^LOS" ^'^^ misalignment about the line-of-sight vector 



LOS 






(V X Unit 



LOS)| 



-.088 



This quantity Is unitless and serves to show that a one degree misalign- 
ment (for example) of the IMU about the line-of-sight vector would have 
produced only -•088 degrees of error in the entry angle of the post-TEI 
trajectory. Restated, entry flight path angle errors were extremely 
Insensitive to misalignments which the sun check could not resolve. 

Conversely, a was quite sensitive to those errors which cou'i be 
observed by the sun check, as Illustrated below: 



— -^'-15 



T' 



> 

i 



3a 

3* 



■10., where o. Is misalignment observed In 



the sun check. 



4-18 



t- 



I 






,o&; 



^J^i:^^^^^ 



- } 



Based on the above study, it is concluded that: 

^he choice of the sun as the target for this optical check 
was an excellent one, and; 

Compensative torquing of the IMU to eliminate the error ob- 
served in the sun check would have resulted in a much safer 
post-TEI trajectory. 

4.4.2 Sun/Moon Alignment Star Angle Difference 

During the time interval from 134:45 through 135:02 of ground elapsed 
time the Apollo 13 crew performed a P52 alignment of the LM IMU. The 
sun and moon (centers) were the optical targets. A star angle difference 
of -1.12 degrees was calculated by routine R54, indicating a very large 
astronaut sighting error. However, a postf light investigation shows 
the actual star angle difference to have been approximately 0.08 degree. 

The LGC has an algorithm and associateo ephemeris data stored within 
it for computing pointing vectors to various celestial bodies, including 
the sun and moon. For the star angle difference calculations, this al- 
gorithm is used and the scalar product of the resulting vectors is 
computed. The arc cosine of this quantity forms the LGC's best estimate 
of the angle between the sighting vectors. The LGC also computes the 
angle ^>etween the measured vectors, and these two angles are differenced 
to obtain an error (stored - measured) for presentation to the crew. 
After the above mentioned Apollo 13 sightings, the crew display showed 
an angular error of -1.12 degrees. In order to check this value, the 
two angles and their differences were recomputed independently as 
described below. 

Procedurally, the crew can make as many as five measurements of each 
vec*.>r. The I GO averages these measurements and transmits the two aver- 
age vectors on the downlink. These vectors (unitized) together with 
t\.} time interval In which they were taken, are presented below In 
platform coordinates (before realignment). 



<^^^ 




4-19 



<^ 



^^ 



■■\ 









I 

-i 



i 



,^4 



Sun 
(134:45 - 134:48) 

Moon 

(134:57 - 135:02) 



+.80/89816 



-.16146112 



.00424996 



-.02178924 



+.58930660 



•.98663840 



The angle subtended by these two vectors is 135.38 degrees. 

In order to determine the actual subtended angle at the time of 
mark, two sources of data were used. The first was the NASA Apollo 
Trajectory (NAT), from which a spacecraft state vector was obtained 
for an epoch immediately prior to the sightings. This vector and time 
were : 



Time 
X 
Y 
Z 
X 
Y 
Z 



17 April 1970, 09:50:00.00 GMT (134:37:00.00 GET) 

-.28228044E9 ft 

+.18416553E9 

+.83610975E8 

+.533054E4 ft/sec 

-.581689E4 

-.294957E4 



This vector and the TRW Houston Operations Predictor Estimator program 
were used to obtair spacecraft-centered sun and moon vectors from the 
most recent JPL ephemeris tape (JPL DE69D) at the start and stop times of 
each measurement interval. These vectors were then unitized and averaged. 
They are presented in Basic Reference Coordinates. 

Sun X Y Z 

(134:46.5) +.89145748 +.41570609 +.18025559 



Moon 
(134:59.0) 



.95321902 +.27595070 +.12338832 



The angle subtended by these vectors Is 135.46 degrees. Therefore, the 
actual difference in the angles Is seen to be 135.46 - 135.38 > .08 degree. 
Therefore, an LGC calculated angular discrepancy of -1.12 - (.08) « -1.20 
Is seen to exist and Is attributed to the LGC ephemeris data and software. 



4-20 







%.;L.^jma^ 






9..^\ 



>« 
S 



s s 



• Ml « 



s i 



1 



s 

I 



i § 



o 






CD ^^ 
00 



~i is' 









3 



8 



8 



8 



I 



S 9( 



8 . 

O 

i t 



^«. as I s 

oil m i I 

W ^» V *«* 




1 



4-21 



"""."rr^-"^ 



T-. 



riijr 






«s% 



Table 4.2 LM IMU PREDICTED MISALIGNMENTS (DEGREES) 



*^V 





X 
Axis 


Y 
Axis 


Z 
Axis 


CM IMU Drift 
(At a 10 hours) 

LM IMU Drift at Sun Check 
(At = 15 hours) 


-0.200 
-0.045 


-0.040 
-0.022 


-0.020 
+0.382 


Total Drift at Sun Check 

(At - 25 hours; t - 73:47 GET)) 


-0.245 


-0.062 


+0.402 


IMU Drift-Sun Check to TEI 
(At » 5.5 hours) 


-0.016 


-0.008 


+0.138 


Total Drift at TEI 

(At = 30.5 hours; t « 79:27) 


-0.261 


-0.070 


+0.540 






Uncertainty Due to CM IMU 
Initial Alignment (lo) 

Uncertainty Due to LM IMU 
Initial Docked Alignment (lo) 

ToUl Initialization 
Uncertainty (In) 



+0.011 +0.011 



+0.237 



+0.237 



+0.011 



+0.144 +0.038 



+0.144 +0.040 












r 



4.22 



CM 

IJJ 

I- 



4) 











u 




^MH^ 


a> 




OJ 


p- »n 


wt 00 r- 


-D 


r~ *^ 


VD 00 ^ 


3 


O CT 


^ o^ Ch 


••-> 


oe 0) 


CM o <r 


•r- 


-o 


a • • 


C 


>.^ 




a» 






S 










'^^ 






,„ 






#0 


^>M« 




c 


u 




o> 


JC 0) 




•r- 


u ut 


^ CO f^ 


00 


-M-v. 


\0 00 r- 




.1- CT 


o^ o^ o> 


Q 


O. 0) 


CM o ^ 


^ 


^ 


• • * 


>^ 






CD 






0) 
4-1 










s 






1 




^ ^ »— 




SS'-v 


\o vo "vr 


K 


>- a 


• • • 


£ 


5 














*^^ 


'u 




4) 


OC 0) 




-o 


uj a 


r^ p- o 




in CM $ 


•^ 


E^ 


o *- rf> 


e 


• • • 


w 
















m 






ae 


U 




1 




00 ^ {^ 


•o 


S;S 


• • • 


0) 






'M 






j 










4J 






U) 






Ui 


3< 




1 


o m CO 


"k 

1 


^ 


<M ^ CM 

o o — 

* • • 




^^^ 




01 




«^ 




4^ 




8^ 




!5 % 


1/1 




f 


^ ♦* ^ 


1 8 S 








^in! 




(/> C • lA 




fe r: -? 



s 
^£ 

CO 

UJ u> 

g: 

Is 



0) 






g 



s 






§ 






u 
o */> 

UJ 0) 



ex: o 

Ui 9 
Of 



i 



CM 

O 



CM VO 
VO CM 
O <^ 



in 



o f*> 
r** o 
o r^ 



CM 

CM 



CM VD 
CM CM 

O »- 



OC 0) 
UJ -o 



1-5 

Ui ^ 



^ CO 
rl O 






o ^ 



'I 



CM 



2 a 



fO 



I s 






5 e 

C • 

in 



E 

4-» 

I 



4.23 




Mffk' '■»« 



^ 



^i 



a ^ir^ M 



1/) 
O c 

t-. O 

O •— tfl 



o 

LU 



0^9 

Ui Q£ 

z 
zo 
00 






o< 



OCX 



in 






CO 

o c 
u^-^ o 

C ^ 01 

O r* 4/> 

> 0* 



CM Lf> 



o o 



o o 



o o 



»— -o 
o c 
u— * o 

C ^ 0^ 
Of—*/) 

ID O* 



4/) 

I— "O 

o c 
u^^ o 

•M (/t O 
C ^ 0) 
O ^- i/» 

=3 0> 



»— -o 

C^^ O 

4-» i/t U 

C ^ 01 

Of- iA 

a. Of 



r- as 

i— 00 

O CO 

10 vo 



GO ^ 
00 ^ 

in CO 



csj in 

vo 00 

r- CO 

o d 



o o 



o o 



-u wi u 

C ^ 0) 



5C 



a. 



3 



m 00 
vo ^ 

• • 



o o 



4-24 



CNI r>«. 





^ I: 



m: 
%^' 




CD 



I- 



«/) 



2 'oT 



o 

o 

CO 



X 



vO 



01 








r 












^.■-^ 


u 












<u 


0) 


^ 


r^ 


^ 


o 


r^ 


•o 


f— in 


^ 


^ 


^ 


r^ 


r— 


3 




a\ 


a> 


O^ 


00 


as 


•M 


o a> 


^ 


^ 


CSI 


o 


KO 


•^ 


QC 0) 


• 


• 


• 


• 


• 


C 


■o 








r^ 




O^ 














*0 


























^ 














<0 














c 


.«>— .^ 












o> 


o 














x: oi 


<■ 


^ 


^ 


^ 


^ 


IJi 


U t/) 


^ 


^0 


\a 


VO 


\o 




-•-» — 


as 


o\ 


as 


as 


as 


o 


•1- Ol 


CSJ 


CSJ 


CSJ 


CSJ 


CSJ 


w 


a. 0) 




• 


• 


• 


• 


>* 


-o 












o 














0) 














4-> 














Q£ 














g 


^i^ 












3 


u 












£ 


01 


^ 


r** 


r* 


r— 


^ 


•^ 


2 </) 


vo 


^ 


^ 


^ 


^ 


X 


<o ^ 


en 


<n 


o^ 


as 


a^ 


«0 


>- o» 


CM 


^ 


^ 


^ 


^ 


£ 


3 


• 
























^(■^ 


u 












a; 


QC 0) 


^M 


ro 


r^ 


00 


a* 


-o 


< i/> 


in 


r^ 


r** 


CO 


in 


3 




00 


00 


^ 


as 


in 


4-» 


UJ a> 


o 


ro 


^ 


r^ 


^ 


C 


i^ 




• 


" 


• 


' 


O) 


««»>' 












«0 














z 














^— ' 














0) 














•M 














«o 


^■^ 












C^ 


u 














or 0) 


itt 


lO 


r*^ 


^ 


CSJ 


>) 


< (/> 


m 


r«N. 


r«*» 


^ 


^ 




C9 "^^ 


§ 


CSJ 


in 


o 


^ 


s 


UJ Oi 


o 


o 


1— 


CSJ 


^3 


« 






* 


• 


•o 














01 






































" ' 


E 




























4-» 














1/) 


^»«« 












UJ 


O 














a. a» 


Ot 


^ 


F— 


s 


PN. 


B 


3-S 


CO 


fNi. 


r** 


as 


g 


^ 


o 


o 


r^ 


^ 


g| 


o 






^ 


CSJ 


K 


• 


• 


* 


• 


• 


£ 


















o. 


a. 










3 


3 










1 


W 1 


ex 


w a. 






01 


0) 0> 


3 


s? 




E 




♦*•— 


1 


01 


3 


^ 


«•- ♦* 


01 


«•- o> 


4/» 


m 


-M 


< <M 




<^ 


(0 




e 


o 


♦i 


4-» 


£ 


c 


iA U 


4i» 


lA "M 


£ Of 


jE 


?iS 


£ 


?S 




'e'** 




o 

Or- 


JS 


SiE 




DPS 
Throt 

Nanua 


10-se 
Nanua 

Auto 


23-Se 
Auto 




4-25 



F 



r Vvfl 






** 



00 

o 
a: 
oe: 



LU Of 
O ZD 

=3 CO 



< I- 

UJ uo 
X Q£ 

< O 

-J Q£ 
O UJ 



S2 






*T3 



a> 



or u 
UJ to 

UJ*— ' 



UJ (/} 

o "a 



a: 

QC (J 

oe 0) 

UJ t/) 

a. o> 

< qj 






o o» 



O CO VD CSJ <Ti 

#— c^J CSJ in CSJ 






^ o o rv 

O I— r- r- 



o 

CM 
CSJ 



o en 

Q£ OJ 






0) 



•* 00 ^ ro r— 

So CSJ in ro 

r- CO a> 00 

CSJ f— ^ •— 



o CO ^ as csi 

lO CSJ m CSJ r^ 

p- CO o *f *^ 

• • • * • 

r- CSJ CSJ ^ 



^ CO 

m at 

CO o 



O^ 00 



s *^ 



00 

00 

C7^ O 



E 0) 01 0) 3 0)3 

4-> ^-. 4-> 01 V 0» 

f* 4^ < 4^ ^ < p» 

C p O ^ 4-> 

O 4-» 10 01 « 01 

P 3 to 3 P U) O 

flU£<5O*0 3C03 



«;.. '-^^ 




4-26 




vtTF 



V 



Table 4.tt BODY TORQUES CREATED BY TRANSLATIONAL 
POLICIES DEFINED IN GSOP (Reference 4) 



> V 











' > 


ir 


^V-V 




<K 




■Kr 


* = 


K 


«h 




,Tt ' • 


*^oW^^ 


.i^-V'-j 



¥--- --*^*- 



Axis 


Jets 


Body Axis Torque 


(in-lb) 


(in-lb) 


(in-lb) 


+X (+P) 
4 jet 

2 jet,sys A . 
2 jet,sys B 


2,6,10,14 

2.10 

6,14 







-128.2 

- 64.1 

- 64.1 


+ 1559.2 
+ 779.6 
+ 779.6 


-X (-P) 
4 jet 

2 jet.sys A 
2 jet.sys B 


1,5,9,13 

5,13 

1.9 







-144 
+ 72 
+ 72 


- 1740 

- 870 

- 870 


+Y (+Q) 

2 jet, pri * 

1 jet, tack** 


12.16 

16,15/16,7 

12,3/12,11 


+ 72 
+ 36 
-36 ! 

1 







-23,874 
-11,937 
-11,937 


-Y (-Q) 
2 jet, pri 
1 jet, tack 


4,8 

8,7/8,15 

4,3/4,11 


-72 , 

- 36 

- 36 







+23,874 
+11,937 
+11,937 


+Z (+R) 
2 jet, pri 
1 jet, tack 


7,11 

7,8/7,16 

11,4/11.12 


-870 
-435 
-435 


+23.874 
+11.937 
+11,937 








*Pri ■ Primary Mode 
**Tack ■ Tacking Mode 



i 



4-27 



■^' 



Table 4.8 (Continued) 






>v 



' ;^^^. ':'"'- 

.v'^^- '**,^ 



Axis 


Jets 


Body Axis Torque 


(in-lb) 


(in-lb) 


(in-lb) 


-Z (-R) 
2 jet, pri * 
1 jet, tack 


3,15 

15,8/15.16 

3,4/3.12 


+870 
+435 
+435 


-23,874 
-11,937 
-11,937 







+U (=+Y, +Z) 
4 jet, pri 
2 jet, alf* 


7,11,12,16 

7,16 

11,12 


-798 
-399 
-399 


+23 ,874 
+11,937 
+11,937 


-23,874 
-11,937 

-11,93/ : 

1 


-U (=-Y, -Z) 
4 jet, pri 
2 jet, alt 


3,4,8,15 

8.15 

3.4 


+798 
+399 
+399 


-23,8/4 
-11.937 
-11,937 


+23,874 
+11,937 

+11,937 

1 


+V (=-Y, +Z) 
1 4 jet, pri 
2 jet, alt 


4,7.8.11 

7,8 

4,11 


-942 
-471 
-471 


+23,874 
+11,937 
+11,937 


1 

+23,874 
+11,937 
+TI.937 


-V {«+Y, -Z) 
4 jet, pri 
2 jet. alt 


3,12,15,16 

15,16 

3,12 


+942 
♦471 
+471 


-23,874 
-11,937 
-11,937 


-23,874 
-11,937 
-11,937 



*Pri 
»*Alt 



Primary Mode 
Alternate Mode 



r'-"::" 



4-28 



Table 4.9 BODY TORQUES CREATED BY ROTATIONAL 

POLICIES DEFINED IN GSOP (Reference 4) 









1 

1 



J 


Body Axis Torque 




Axis 


Jets 


^X 


Ty 


^Z 








(in-lb) 


(in-lb) 


(in-lb) 




+X(+P) 
4 jet 


4,7,12,15 


+26,440 










2 jet, pri * 


4,12 
7.15 


+13,220 
+13,2i:U 












2 jet, alt** 


4.7 
7,12 


+12,749 
+12,821 


+11,937 
+11,937 


+11,937 
-11,937 






12,15 


+13,691 


-11,937 


-11.937 






4.15 


+13,619 


-11,937 


+11.937 




-X{-P). 
4 jet 


3.8.11.16 


-26.440 










2 jet.prl 


3.11 
8.16 


-13,220 
-13,220 












2 jet,alt 


8.11 
11.16 


-13,691 
-13,619 


+11,937 
+11,937 


+11,937 
-11,937 






3.16 


-12,749 


-11,937 


-11,937 






3,8 


-12,821 


-11,937 


+11,937 




2 jet, pri 
1 jet, alt 


5.14 

14 

5 


+ 196.4 
+ 196.4 



+ 6,236.8 
- 409.2 
+ 6,646 


+ 6,187.9 
+ 12.9 
+ 6,175 




-U{- -Y.-Z) 
2 jet, pri 
1 jet, alt 


6.13 

6 

13 


- 196.4 

- 196. 




- 6,229.4 
^ + 344.6 

- 6,574 


- 6,278.3 
+ 766.7 

- 7,045 




* Pri • 


Primary Mode 




** Alt - 


Alternate Mode 











i*ii? 



:-J»*', 



4-29 



!Wr 



V 






>V' 







Table 4.9 (Continued) 



Axis 



+V(= -Y. +Z) 
2 jet, pri 
1 jet-alt 



-V(=+Y.-Z) 
2 jet. pri 
1 jet.alt 



I-- 



Oets 



1,10 

1 

10 



2,9 

9 

2 



Bocjy Axis Torque 



'X 
(in-lb) 



166.4 


166.4 



+ 166.4 


+ 166.4 



'Y 
(in-lb) 



'Z 
(in-lb) 



- 6,229.4 I * 6.187.9 

- 6,574 . + 6,175 

+ 344.6 1 + 12.9 



+ 6,236.8 
+ 6,646 
- 409.2 



- 6.278.3 

- 7,045 

+ 766.7 



.-i 






^' 



r- 



4-30 



,1 



<% 



V 



Table 4.10 BODY TORQUES CREATED BY POSSIBLE 
PITCH ROLL ROTATIONAL POLICIES 







Boc|y Axis Torque 


\ 


' , 




Axis 


Jets 


(in-lb) 


(in-lb) 


(in-lb) 




4 


+Y (+Q) 
4 jet 
2 jet 


2.5,9,14 

2,5 

9.14 


t362.8 
+166.4 
+196.4 


+12,473.6 
+ 6,236.8 
+ 6,236.8 


90.4 
+ 6,941.7 
- 7,032.1 


; 

i 


i 

\ 


-Y (.Q) 
4 jet 
2 jet 


1.6,10,13 

1.6 

10.13 


-362.8 
-196.4 
-166.4 


-12,458.8 

- 6,229.4 

- 6,229.4 


90.4 
+ 6,941.7 
- 7,032.1 




:' 


,1 


+z (+R) 
4 jet 
2 jet 


1.5.10.14 

1.14 

5,10 


+ 30.0 
+196.4 
-166.4 


+ 7.4 
- 6,983.2 
+ 6,990.6 


+12,375.8 
+ 6,187.9 
+ 6,187.9 








-Z (-R) 
4 Jet 
2 jet 


2.6.9,13 

2.13 

6,9 


- 30.0 
+166.4 
-196.4 


+ 7.4 
- 6,983.2 
+ 6,990.6 


•12.556.6 

- 6.278.3 

- 6.278.3 








— ^- -r 


-* • 












p ^' 



4-31 



.# 



''fit ' 



«5% 



TADLE 4.11 
Sensor Static Bias Errors 



'1 







PIC (3/17/70) 


TEI (4/14/70) 


MCC 4 
(4/15/70) 


Gyro Static 
Bias Errors 


X 
Y 

2 


0.067hr 
-0.307hr 
-0.477hr 


*(-0.11 to -0.19)7hr 
-0.34°/hr 
-0.527hr 


-0.127hr 
-0.2371ir 
-0.617hr 


Accel eronieter 
Static Bias 
Errors 


X 
Y 
Z 


60.0 uQ 

-31.0 ug 

47.0 '.g 


- 5.0 wg 

-59.0 ug 

57.0 ug 


-16.8 ug 

-55. 4 ug 

47.0 ug 



Reasonable range derived from noisy data 



i'-^-. 
'».'+•' 



-.aA,, ._,^ 



Acceler- 
Oineter 



TABLE 4.12 
Sensor Static Bias Stability 



Shift from PIC 
to TEI (30 days) 



Exoected 

Ic 



Shift from TEI 
to MCC 4 (1 day) 



Gyros X (-0.17 to -0.2b)*7hr 0.287hr 

Y - 0.047'hr 0.237hr 

Z - 0.057'hr 0.287hr 



•65.0 u9 

■28.0 ,g 

10.0 i.g 



Range determined fron noisy data. 



77 u9 
77 ug 
77 pg 



•11.8 u9 
■ 0.4 ,^g 
•10.0 ug 



exceeded 



(-0.01 to 0.07)*7r.r O.lZ'/r^r 

O.ir/hr 0.22'/^r 

- 0.097hr 0.2?'','hr 



30 „g 
30 j.g 
30 3 









IV: 



"i 
'^^* 



4*32 



1L-A1L^ 



#^|S{^_ 



TABLE 4.13 
Equivalent Accelerometer Bias Errors (pg) 



Accelerometer Bias 
and Nonlinearity 



ASA 023 
Inflight 
Estimate 
(TED 


ASA 023 

Pref light 

Estimate 

Mean 3o 


X -65 (1) 


135 


Y -28 0) 


125 


I 10 (1) 


147 



X-Scale Factor and 
Dynamic Errors 



X - 1 (2) 



22 









Y and Z Dynamic Errors, 
ASA Accelerometer Internal 
Misalignrnent and ASA w IMU 
Mounting Points Misalignnent 

Total (yg) 



Y 


- 4 


(2) 


- 3.3 


60 


Z 


-58 (2) 


-21.5 


59 


X 


-66 




C 


137 


Y 


-32 




- 3.3 


138 


Z 


-48 




-21.5 


158 



NOTES: 1. Inflight Estimate: Shift between freef light period and 

last compensation value. 



2. Inflight Estimate: 



Difference between measured total 
error and measured fixeo bias. 






:y> 



4-33 



«* 



V 






TABLE 4.14 
Equivalent Gyro Bias Errors (deg/hr) 



f 

f 



>4- 



i**' 










ASA 0?3 
Inflight 
Estimate 

(TED 




ASA 023 
Preflight 
Estimate 

Mean 3o 


Gyro Fixed Drift 


X 


(-.17 to -0.25)* 


(1) 





0.59 




Y 


-0.04 


(1) 





0.66 




Z 


-0.05 


(1) 





0.67 


X-Syro Dynamic 
Drift 

X-Gyro Spin Axis 
Mass Unbalance 


X 

x' 


(0.0 to O.OS) 
1 


(2) 


-0.14 



0.35 
0.07 


Y and Z Gyro Dynamic 
Drift 


Y 

Z 

X 


0.04 
-0.15 


(2) 
(2) 


-0.08 
-0.09 


0.34 
0.30 


Total (deg/hr) 


-0.17 


-0.14 


0.69 




Y 


0.0 




-0.08 


" 0.73 




Z 


-0.20 




-0.09 


0.73 



NOTES: 1- Inflight Estimate: Shift from last f reef light period and 

last compensaticn value. 

2. Inflight Estimate: Difference between measured total 

error and measured fixed bias. 

it 

Possible range derived from noisy data. 



4-34 





Ite . -r:.-i.^ 



V 






i 



TABLE 4.15 



Gyro Dynamic Error 

Total Gyro Powered Flight 
Error 

Accelerometer Dynamic Error 
(Yv^Z misalignment, 
X scale factor) 

Total Accel erometet" 
Powered Flight Error 



(1.17 to K83)** 
-.13 



-0-95 



-1.58 



1.18 -0.60 

0.33 -0.45 

-0,04 -1.86 

-0.62 -0.50 



* From ASA 023 Preflight Estimate. 

** Range Determined from Uoisy Data. Includes spin axis 
mass unbalance. 




i 



4-35 



■■ *W^. 




^^^ 



>v 



t * 



■ ■• ■ I i ■ rr I .... I ■ 

'J!l:iJi!Ji:l"^!!:l"::T:F':i=/t"" 




3L a 



(3J?/B3C) MWII3 4r)3WO 



^'1 



iiC^iw. 




o 



9t 

V) 

m 
c ^ 
w a. 

CSJ X 
O < 

k' => 

CNi 
I 

Of 

L. 



'S 









@ I 



a * 



■V » 



i:n/^]o) tOMJ niAito 



^.^& 



- 1 



'- . 1 11= II ■ • ■ ■■ '!■ ■ IBdileUr 



ll' IH I' U I HHl i ] n il I 

i- l .li:. ! " 'ii Ml 



■-!=:1:\r=t TilTi: ! 1" r"*| !. L "-I -^:i-^:t«..:^ 'i- f:"."""^;! 



B^M 






i'!Pii |M ii m'j ' 1 



i\tBEi i l.a g.iu. J j J- ii r |i|ii i 14 i — !r 






4"J.:ii:.T ' -." | 

\\ m ■ i I ■ 



■I— f- 
i L:;:--l_ 



t-i-l 1. 






-jrH- 



i^iii nj' ja 



~ ■■ . .;;,;• %'■ '.* _,: i:^i 



t^ ^ fi 4 K ^nQnK M3s 



^fcT— .1 



UIU^ 




■»M ■!■»«!« RI«i'n«THmifli;»l';:,;:!*::Mm!!UnSil!'9ilHaiaBlliill 



t* »* »' * 

OH/m) MM} i 



a. 



CM W 

o o 



9 
C7» 



pa 




u 


i 


c 


i >4r 


-< 


» 


A4 


1 


O 


1^.^ 


S 


r^ ■ • 


g 


1 


a 
tf 


1 >v 


A. 


IJT 




l'^& 



1 

t 



•r- 



^^ ; 



V 



I.... _ 
r 






.... 1 



I." 

. . ;... I.- 



— ;"T;' 

L_.-..l_Jj|-. 



+ 



.......1 .. 

j..... 



t-tTtX 



■■t 



tzTztn 






~f^. 



(-rr 



l~*a 



__4_l 






r_.„_4_j.^_^..j— ..;- i.-...f 



I : i;:r- 

L ... J - ; — I - 



til+ltttttJ ,— .: 






:|... 



rf- 



I- 



-J-^+-rt-^ 



■I I- ;■ 



■:■ I- 



J__i-.;-4- 



..J..^.. 



J L. 



: -|- 

I. ■ ■ q.. 



,. !....:.{.. 



...-..^...i.. 



r-f~ f- 



: r ■■ 1 ■ 



-♦ 1 I— r- 

J— i L 



+-i— I- 



.4-—+ 









: : i L— -i.— "i ; 



: ...I : ... 

1 I 



-M4 



.t^^-T--..' 




o») NOiiisod WO toird 



< 

C3 



c 
&* c 

3 O 

GO -r- 

tJ O 



S 





I^ 


s 


H 


■*■ CM 


^ 


^' « 




Sg 


H 




O 




:2; 


8 E 

i 


1 




m 


P 


tq 


o 


V 


<J 




Oi 



o 



^«^ 



,'^- 



*• 






r. 






. I 




{030) NOUlSOd VTO TK)W 






o 

Of 

E 

CD 



o 
in a. 



a; 



S { 

g 

2 I 

C5 f 



^ 
£ 




i 



^ 








msw^r^ 
















: ! ; i J I j|.= -f-r-^ 



[ "■! : 



d=-! :4ri-=H:::ty 



;^--»— =^ 



■ x~?.~ 



i:. :■., s 



— rrr-T 
-Hi. -4 + 



LliM 



-i-4-= 




■ ■■■: ■■ ...l+^.-yi 

: : i...::i 1::t"j... j 



■!■■■- 



1 ■■■ .1; 



-iT..h ;-tt±:: InHDiiii;™: 



le 



Ir:!"-' : .;■■'!" ! I ; ^ j . ^ 









FiF- 







^■^Tiii 



■ " lii:: ::. 



















a. o 0) 
° .^"^ 

O '/> 

CO '^^ 

"^ 4-> D_ 

^ *- :d 

^3 



g 



£ 



. 



K^^. 



4— 



r- 



(D3S/D3Q) aoaaa dV*)3HC 



J'V 




, 1 I U 

....... ...., —I I f \ 



I * 






03S/9») VOWS nv9»o 



O 0» "B 

-I" 

•r- +* •*- 

^ i5 

C O C 
^ »- S- « 
UJ ^-C »— 

H- ooi» a. 



I 



i 



fe^:- 



-i 



V 



• V" 



i 
.1 




—•••I- !-^ 



1 1 j r- 



•'••■4-:- i !■■•■ 



1 .:;-•■!■ !■ — T,"* '■■■■ I ■ — -■• 



s-Sf-i.iJ-.- 









m 



1^-f 



: >- .,..._L .-., 



y:... ....,,. i.-.^ 



L4-- 



- I 



! 
-H 



I I I 



uTT'-n 



;;p 



o w "* 

• ^ W 'F- 



4-> I O 

C O C 

1^ £- 1- « 

oc 



Hi 

i. 



t03S/O3O) HOtlbl AWIWO' 






^v 



• V ' 



.-ju— - 



< 4 




3 



O 

o o 

c c 

t- o 



UJ O 

h- a. 



<u 




J- 




3 


CO 


o» 


in 

1 



(93Q1 N0UISO4 VQ9 H^lld 




"tW) KOl.'lSMWS ITM ' 



o ^ ^ 
c c c> 



3 







t- 



l ■ 



r 



«r.^ 



*: 



'•1 



J 



— i k 



i 
1 




« • *j 



I " 

*P C -M 

t^ lO o. o 

3 t f- 

Of t. 'O a. 

4- > o 4; 
c ax c 

O « «Q 

O C Off— 

to -Ma* 
o o •»- v» 

X a v jc 



fe- 



>v 



ZCELL.y.-!_LLlI 






hi-i-rtit-^Vrt++-i I ti--; i -M^i-rf- 



- — 1 1-» "H ! .-.: " • 1 — ■>■■ - 

;-••■•-• ;--j---i •••;•: ;:. 



j. .:. 



XiLG^IXI-r!^ 



^"-•Krfrm-W 



.1..:. .IT 



r- r — ^■- 



.-■q- ■ 






...I 



... .. 

! 



.r 



■ I ■ 
■+ — 



: : ! ■ : • 

•-- ■■ i r 






.. :. .. ; .;. 



.if ■■ ; 

■■• — " r ■ 

i 
;. i ...... I .. . 

■i — * I- — — '■ ^ 



r ■* ' — ■ ' : ■" 

ifr:.::..L; ._..:. ..L.:_ 

i. ■ ■- ... : .... 


: , . M i./ , i 


1- 




: - • /•■' • :•• ! 






1 




^_-_^... ...... 


■ \ 
\ 


1 / . ; ■ = 




1 I ■ i ; 1 


1 : f ■ 




J. — r"*a^J- - 


i 1 


• 




t 






t 




.-"[''-•:';■"' i . .. 


j-;<G;"^|~ j 




-i~ 


KT" 


■^ 




'"*" 


■H 


ri i 1 


1 '" st^^jiW'^ "■ [■'" ! 






— T 


.. .^ i ■ I ■ 


^i^?:' '!^'j?lii;;""^ 




t 


V. 




--U 




.• 

>---#- 




.„ \fl • (M- 1^*0 "! ! 






S 


1 ! 


,1 -„^U'-j \ 








• - 





/' ■ 




' ^:. > * : 


-H-- 






,«« £ ' '^ j i 








^ 


f 


^ 


;-" ; ^il ,- 1 , 


—--- 




i 


i ' 










1 




_+. 




J ._, 




''■'■■■. '-*- '" ""t' ' ' '7 '" 




i 
— t— --— 




1 






i 


• 










*- 




/ 


ijT 




t 




i 




. , j. 


^ ; "It 




j 






j 


l=i 




' '; . 


i i 












J 










: 


f" 




i 


r 


i 


\ 




- ■; r ... • t := 


— 


^ 




! 


/ 




1 


! 


t 






















\ — 




L —. * . — 1 1 ( 








—r- 


— " 


[ 


-J-— 


-i.. 


1 J.J 


■ ■■ i 1 i 






1 . t . _. _ 


. ., ,; ., „.i _-.i.. -j 




'.' 




• ■ 


1 


1 H 


V- 


T^IlpJl- 
















f 


' 












■•• ii-" ~ it 








1 
















^: 




1 






....j j 




...J — 1 






1 






_(_., . ^ „ ., 


i 




-^» i _. 3 




1 




, .... 










i, , ,i,-.,i. ,. 


III • 1 'It iii 11 nil 11 1 






— 


,0- 








! 






• 1 












. ■ . ' i : : ; •: 


lifili-Sdltlt 






-J — 


: 




i 


. . . ■;:■■■ i 






r-^ 


t^ 








i-:.,..:..:r'"r:: •" 

3 3 j 


J 



(33^/ inn] nvDiMO 



•r- C 

■M C 
C o^ 
O *t Q- 

-*-J -D 0/ 
T) C W 
U <o « 
3 or 

O) &. a. 

H- > to 

C 3 *«- 

O 0) X 

O C< 

3:5=5 
on I 

O OTJ 

-^ +j ^ 

X 3 O 

-KX 



at 

3 



m 



r-- 



L 



^A' 



V 



^ ^ 



>'iii ' r I A *i 



Tt ^ 




O f 
4-> O 

<: o 

*^ 4-> a; 
**..- c 

(O 4-r « 

3 < a. 

•»- -o a> 
«♦- c wi 
c m « 
o £ 

X > »/» 

CO 3 -f- 

o a; K 



03S/91Q} MM] Ar:aHO 



^'^ 






V 



\ 



-h-:; - 



. + ... I. — 




■! ! !! 



rTT: — 



.-!... I 






^-iU. 



.... L : 



^-^ 



r: 1 ■ ■■:■ 



■■\ i 



+:: ^"i-T-rT-r 



-f-i-M »■■ 



-r-^i-TT" 



rW^ 



.Lf-i-L... 



H— j_ 



k-L. 



-I i 



■+-i-4-: I-: 



it: 



-HiH 



:dxj 









i r- 



.i..-4-. 



..:... J . 



+..-^i- 



-}-■ ^w-t■ :■■ 



ttii 



-J-J — i- 



■i 1". 



T?-:-l ■! 



Esxri^^ 



I ! I I — -f ■ ■ 




(^3^/*)3ai MOaaj ^voiwo 



3 




< 




at 




g;s 




'f JC 




-«-> a. 




TJ 




W tn 




3 *^ 




C7» X 




.^cC 




«♦- 




r c;- >J 




O J o 






0) Q- 




X > 




to 3 at 




o a; c 




\ C ^0 




X 'o^ 




^a: o- 




•tr 




*— 




^ 




a> 




1L 




3 




cn 


ro 




iD 



^i 



',,*s^, 






'1 



\. 



«^ 



} 

^ ' 




3 

o a; c 
^ z o. 



0) 

3 



I 



r 



Sv 



VV. 



OK/QX) MIIMI rmitt ' 



^v 



11 111. lliM. 1 ,U^ ..I.. .1 l. l l l.tU. I ' I 111 1 .,1.11 1 1. . f.L ! 

■ H-^- *"ri— M- f — r--- ■ *-"■■ h-^= 

i I ■ ' - i i— i— ! ! i ] • ' 






I ■ i 



r^ T - : 




nil.., .1. 1 ..,\ I — I — r"i — ! ' "} 111]! ' . 1 — r. 'Tii'l — T"" — j 



/ ■ ■.; ! ■ j ■ -t— j — ! '^—-i !-r-; 



i- 




m^ 



{:n/r)ic "'f*' ^i^jio 



c 

O 'D 

•<- -c 



52S 









r 



l':r:]i,liWS iifeHS 




■ 4-' 



L:l.;..!4- :-r:±d2±: 



4--;^ 



H-L 




3 I — 
C X c 

uj w a- 









I 



*•;*:-%- 
" v^- 



OK/t . rOk^] «A^ 



„„■ . j - .L— ■ ^--— "*- - i ■-■■ 







: ■ ■ ! I : I : ■: "J : I : 

.::j: l : 1 I j I l. :-i'^|-^-» 



■ i ■ ■ t 

: ! . 1 



I ■ ■ 

!— — ■ 

I 













: I 



! 1— 



f- ■■ t - 



;:|ill:lt~T-4~---^-l---' 



..j :. I j. .. .j . ■ -T- — : J 






I- i 



— i — ; — 



-i — +.-^.-4-^-: 



. i i 



-ri *-■ 



-♦ ■■■!"■ 



.. . I : . _.s ■ { 



4-r-»- 



, .J 

: ^ 



[•::1....; L:.i.-i :r.;-.._; :..'n"^ 



I i = 



.1... i:,, 

■4 -r— r-^— r- ■: 



i ■ 



.... .- .. • 



nr^ 



j.... i 



: I 



r-+-^ 



.:u_4. 




r : ! 



"■^ -i 



_J_L i — r 






illLLL-Ui rr 



8 ^, 



C tA 
O -^ 
-.- K 

S- 3> O 

^ O 01 
C X C 
O <Q 

(_> 01 *— 

i/^ +J Oi 
E ■*-> -c 



O) 



.*■.■ 






C 



-7 






R 



r!j j_, . 1 ■?!■■ — . 1 . 1 ■ ■ II I'l l 
I I. ' ' ■■ 1 a [■ ! 



=■ ! .1=4. 



II 



i " r::S::ir. 



l:;:i::i..ii^ kas 



T -:) ■■ j T - + '^ H ' I — r— [ -:•■ J7-fH 
J ! I U ' ' " 1 L_L : l1 



a::T.-rK: 








-I"^- 



i +.. 



i u— 






-+-+■ 



44 



■4_.. .1.. 



I : 

A — i- 



1 :....i 



I - ..#. . . 



H- 



r-iO-; 



> -: I -J 



■t -l-i- 

-+-r-*-H- 



ra: 






ri-rt 



■: ! ■ i 






..f 









M 



.... I-- 



■j--^-. ; ;- 



J-4- 



' ' I !- 



f - *- 



-h-r-T:- 



+ i-- 



£13;;. 



1-...^ . i _^ ....; j.,.^ ■ 



r-lr:: 



f.. 



-j-^H 






■4 1- 



+ ■ T- -r- 



I ' I- 




^[ 



■f+ 



■4-+- 



^ 



fhfAp 






-U-: 



n^- 



^4?^ 



■■i-^t I 



■i i 



■-■+ 



..: I 



J-^J 



rar 



■ • I 



:rr 



1^ 

1- 



-^^ 






}f^ 



: : !■ : JLii;:'. I ■ ■ I - i:i:i.;Jri!P': ! ! i : i .. i ii i 
g •= § « r^ 

. p 1 o 






O fO 

to ■«-» (U 
^ <£ O. 



£ 

3 



' .* * >. - 



>^f 



:^m^^ l,^^^\J:^^^:4^^^ 



-\r4-4^ 



T" ! ■■:■■ ■ 



i — ! 

-"--■-r ■ 
■■!■■ 



-I— ^-f- 



y--*-+-i" 



[y^n^-i^ i jiih i =-i-T--Kp^i H 



■■■■* ; . ! : 



■ T i T :■.' 1 ■'..■.:. : . = : 




c -a .- 

OCX 

*.- « <C 

m i. a. o 
t. Of I •— 
3 > -O Q. 

.— 0/0 0/ 

«*- c 3: c 
O Z OJ <— 

z: 'itf 4^ a> 

"^ C 4-> *0 
£ <0 4-> JC 

o 

CM 

f 



^ 



*■■ ■■ 



f3n/'33C) (JCdal 4V0WO 




^ 




^.-j--— — ' — r- r- --+~^ . ...-...- ..... . i 

u* % 4! : J . : ■ I 

s-rr ■ ■ i :-=1"-- • =••• • • • -i 

.. «i--j^.t : j-i i .. .: , rr 






t 7 



_i 1 . — I : I Jr* I ; ; 1 I : i 



i . ■■ i-i-.-^ 



— I— 
■i ■!■ ■=■+■ 

■rr 



i~ 



I- -■!--■? 



— -^r-: r 



m 



1 *T 



,=.L 



i ::.4.--..: 



■m 



rL 



■if:*- 



rart" 



i:±:— :r1- 



-h-..4 --I- 



^-^ — J. .. 



. 1. 



ii^ 



n 






Mi 



■—«-!""* I 



•"T .l-l-l^ Ti 



■jirm 



i I !■ 



i 



4-r4. 



TT 

ii-- I- JL 



03S/93a) VOIMS nwjHO ' 



*o -a 

c o 
fo X ■♦-' 
X o 
ox— 

C 3 
*•- -r- C 
ID 4->f— 

£. «£ a. 

3 
WO O) 

<*- (O ftj 

c x: 
o s- a. 

> irt 

o a; K 
> c< 

-I X => 



-iSf 



''SLM*#!lf>V' 



■tt^^^^^.W' 



^ 
#- 




jT- * "!/ ■: I i .: ! ; J {H : — "*r[r 

■■■"■;■■ T| 1 ,r .j. : ■ :. : 



4:-+«-|....-^.. H 
^ ^ ■- ^ J ■■>■■■ I d 



f— T3 




fO^ 




3 O 




C X -M 




«T3 O 




X aj — 




TJQ. 




C 3 




o +> a; 




•,- -^ c 




4J 4-> H» 




fd -M »- 




u«io. 




3 




Oi-a Qi 




•»- C (/» 




M- (0 fl 




C £ 




o t. a. 




O 0) 




> tA 




Z 3 — 




o a> K 




-^ c«t 




3: fo 




-IX > 




OsJ 




CM 




^ 




0^ 




J- 


cr\ 




r^ 



=1 

i 



-« 



}• 






(33S/5M) »«W1 ^W3W0 



s 



- 1 
-4 







Figure 4-23 AGS/PGNCS Sensed Velocity 
Comparison During TEI Burn 



4-81 




.*J i 



1- 




u> ^ c\* 






Figure ^ 24 AGS Sensed Velocity Along 
Body Axes During MfC-3 Burn 

4-82 



Ron Altitude Error - Deg 

\0 ST c^ 



i 




3aS/b»a - 9*»M U0« 



Figure 4-25 Roll Rate and Attitude Error 
During MCC-3 (AGS Controlled) 



4-83 



iP^y- 










Pitch Attitude Error - Deg 




tt±t^ 



• ; i iZlZ"- II-"':- -Jsir 

: |-v--v--:---l:-::r-rr-l":-;:-r~ 1 . .^ 

I ="" ! .7 1 ■ - ■: ■: :■ ■■■:■■■■■ ; ■■ ' 

L-Lii ■— -I — i—i — -^—r":. 



■f- 



. l- 



-I" 






l..Si ■■■■ ; I 1 ■' — 




;. _ i 



'- — : : I : 1 ! ni" ■■:■■ • J -L = i- ^ =-^- — ^'t ■■ ^ oo 



:: :i. 



..-—I 






I I 4nI Jl 










Fiaure 4-26 Pitch Rate and Attitude Error 
Figure ^^.^^ j^j._3 ^^gj controlled) 



4-84 



.*%-. 






r 



p^i^iEir^SS^H^^ 









1 


• ° .1 


•^ 


to 


^ 
^ 


i 

* 






.;; • ;J: ■- ■ ' 




"\M: "V: ,' 


^ i- 


JL'^. ■. 


00 








'■i:"v : ■ 


■!-:;;./ 


, 1.,,. i_- 






:' I : : ' 


"=!== 






t 


1 ' ' 

■ i... i , ,, 




■ 


--m 


\ ^ T/ 


■ • . -.1 ■ 


1 






U— kt» 


L.i \.^^ 


iji- ! 






1 • . 


— *-t^ — -pw^ 




. U •.*::^ ■ 




_o_l_. , 






r — \ — 1 — ^HH — r 
! ■ ; ■ 


— [r4-*^-*-f ' i 1 ! 




; . . t ' 


Mi 


; . ,. 1 


""" C) 




— i-!-^-~ 




-1-1- :■-!■■— 1 ! 


— i 


2 

i 




1 1 — 

1 




: . i -. __ 


"^ 1 




:• i i 




: j 








SU^ 


I ."II 








: ■; ■■■ 


...:;:.. ■.:: ■ : ; j .j 




i__: . _.-:„.! 


:-i:=f^--|- 


=■■ " i ■ i ■ i 


■pf : 










. .1. ., .... - 




• :.*: ' u : 


• 4«4*^ 




■,. 2 •£ ' 








:.| : : ' 


. » * . '.*'',' 


I- 1 


,!.,' -'-'" 


. 














'■•.l-g- 






* 






1 r. 


:: *i:: -i • ::• 


r'.v-'r'] : 


L_ "''"^^ 


'' '-' . •'•: '. : 


-I 5 ! 




- +-4-i-- 


; ■ 

: 1 


*'>-': 


-•j: — - 




:-| — |— -1 — h" 


-1 s 




: ■ 




. ; ... .... 




:;t— -i;r 


• 1 . :::i:-: 




■ •! I'iii" 


.- 8 




.. i:.:, i, . 




: . 


. 1 . 

:.. I. ■ i- 

■ 1 ". : 


4. jil .._^d 


.! ■. ■ i- 


-L.i^ 


t 


..■ 






" !■■: 


1 _ .; 




^ 


.. : 1 . 


; I .: ; . 


; 




i -- -. 

:.■.: 1 


• 


. 




1 ! • : 


T j. ■ |:: 


..;■ ■.; ■■ 


■. 1 1 


: ■ . :'. 






i. ■■ 




J^ . !:. 


■ ■ :' : i:i: " 




■ : ■ '■': :■■ i:: 


:::! 


-^At'. 


:i::, ' •:::i:::i :,: 


;!■■■ :;; ..:: :;:!. \ 




■ ■ \y\ ill; .1 




! . . " .' r 1 - 1 


^:::: 






I i 


■ "jH^ ■ ■ 


■■; :■:■ c 


■ ■ ■' '-"d 


i ' '.:■. 


.;: ce 
:::: *v, 


^ 


: : 1 


+r \—r — |— 

1 ! ' 


-.;-. .-.j;ii. 






lirir . '.i..- ■' 


• * 




!■■■ i 1 . 




::::t::::;=:a 


■■. ■■ ■■■■■ : :■ 




::;: « 


". ■ i 


T i — r^i^ 


t=3Si: .- 


' ■ " ; ; 1 ; ■ ; ■ j ■ ■, 


■ . : :■" .1.: : 


■■■ ■ ■ ::i 


:.". 




:; .i ...:;.:. ::•: ;. 


|— ... r*^ 


'"p^'ih-i 




: ■ ■::: :::' ' : 


.■ ■ : .:i 




lU; 




■:,:...::•:=¥; 


• tfflfc:;:: 


~ !::! :■:■ 


■ :'■'.] :i : :::. : ' 


■■ i ■.:' 


;::■ =:■ 


TT- 






4^ -^ 




'!*■ ■;'! r';r ■■ 




: : ■■ 


::. Vr. 




. : j. ■ ..; 


i ■ ■ .::: . 




.■ ! :::: r:: :: 




: ;:■: :t: 


T7T 




: ■ . 


! •.. i 


■"t"SI 


■■■.!"■ ■ 


uZMw 


. . .:. . : ■■:■ ::; 


!*nP * 


, ^_ ,^ 


. i 


i : 


1 !..:•=•::••.. 


:. : !: ■ rr 


i:ii.:):. tiv 


. . i 


liljas 






*^ 


rg 1 


9 


• 


1 




8 





Figure 4-27 Yaw Rate and Attitude Error 
During MCC-3 (AGS Controlled) 



'\ 



4-85 




^^gr 



-It 



CM O 



Figure 4-28 AGS Sensed Velocity Along 
Body Axes During HCC-4 Burn 



4-86 




I 

f 

J 



I 

-t 

J 




■{lUtfUtt •Tmbi 



I 






r.^... 



I 



Figure 4-29 Acquisition of Yaw 

Attitude for MCC-4 Burn 



4-87 



>v 



I .- 







Figure 4-30 Acquisition of Pitch 

Attitude for MCC-4 Bum 



4>88 



> 







v.^l 



Figure 4-31 Acquisition of Roll 

Attitude for NCC-4 Burn 



4-69 



S 



r- 


~T 


1— ;- 




tT 


1 


^ 


nf ;: 


•t .t 


tf* 




i , . 


1 


,;i, 


...... 

i,,.. . 


■ 


-A'-- 






ii 


#:- 




i 


'l-i'- 




"!} 


X^. 


4— H 

i ' 




s 




-4— i ^ 




-4— - 




i? 


4 


r 






■ 


... - 




-i 


V 












o — 

UJ 


-t- 




'T ' 


4— 


—,'. 


/ 





















N 


t 










.... 


- — 




^l 


7 










i 








1 


H 


s^ 




• - 


' 




^- 


- 


f 


^ 












V 


__- 




— 


— -t- 

1 


1 






. ., 


-:-- 


•i- 




\ 


\ 










m 




-A 


\^ 


/■ 








.4 








\ 




... 












\ 




^ — - 

/ 




o 

UJ 

% 

< 


.... 




-t"* 


: — 






N 










cj 




„_ 


-v.. 






-— 






• i 






,.,._ 


, 


\ 
























1 — 




/^ 




— - 




; 




"*; 






1 














i \ r \ 


-J 






R 








)> 


ir 








• 










"" 
















~~ 


4 


4 
















1 


...^,. -. J 












— -- 










1... 


i^ 


R 


















._^ 


--" 












^ — 








lil 




X — f 


















- 




\ 






ni 






-T — V 


— 


-- + -- 


-_. 




-- 








— i 


1 


\V 














-\ 








-- 










1 




, — . — ;. — —— 1 

1 


j 


















X 






















\ ■ 






















1 




























„i„„ 


- i — 


' * t 
i 


--: 










\ 








•w 




. 






\ 
























i 










.- - 




h 




\ 








— 


-• 


"": 


L- 












\ 






« 












\ 












i 














\ 














\ 




i 


\ 












- • 












•4 














It 




1 \ 












• • 












1 














lA 




I \ 











- 












1 


i_ 










- 


■" 






1 • 






- -- 












— 


IL 


-■ — 






1 » 




'! — 








.1 




■ 

















m 


iruM 


«tt- 


. J5 


i^ 


< • 














'^ 








- 






— 


Ik..— 








■*s — 








i« 




ji — 




'• 






<l 






t " 


' ' 


ifki 


Lfic 


IM- 


1 


hIm 
























'*. 


ai — 


■ 






J» — 








1 








■s ^. 




" 




It ; 


* 
. 1 .. 




f 


m 




T«- 


1 » 


D rsj 


(' 



Figure 4-32 Spacecraft Attitude During 

MCC-4 Burn (AGS Euler Angles) 



4-90 






•■ 




^fip ■— ^ 



^- 



UJ 



o 





















































1 

off . 














































1 


























































































































































"■ "1 




































































































































































Ignition 




















• 


I ' 





















79:27:15 28:05 28:55 29:45 30:35 31:25 32:15 



TIME GET {HR:MIN:SEC) 



FIGURE 4-33 ACCUMULATED X-AXIS SENSED VELOCITY 




4-91 



K-'^ 



^■\ 






O 

























1 
























off . 






























































































































































































































































































































































































ignition 




















t~ 





















I-'V ••; 



79:"27:15 28:05 ZsTsS 29745 30:35 31:25 32Tlb 



il^ 



^.^ 



TIME GET (HR:MIN:SEC) 






FIGURE 4-34 ACCUMULATED Y-AXIS SENSED VELOCITY 






4-92 



V 



- i 



sr>Vd^,i.r. 



5 

1 






o 





















































'cut-' 
off. 












































































































































































































































































y 
















» 1* 










-" 


















-[ 


























Ignition 


..'" 
























i._ 


-* 




















• in 



























79:27:15 28:05 28:55 29:45 30:35 31:25 32: 

TIME GET {HR:MIN:SEC) 

FIGURE 4-35 ACCUMULATED Z-AXIS SENSED VELOCITY 






f."^, ;. 



V^-'' 



4-93 



^v 



LU 



o 

LU 



Q 

>- 
I- 
»— I 

LU 

> 

X 



', I. 

II MMMMM ^^mmmm ^mhhh ^mhhh ii^MrtMi otmmpm* mm>^mmm mm«mi-m 



79:27:15 28:05 28:55 29:45 30:35 31:25 32:15 



^a^g^i'' 



TIME GET (HR:MIN:SEC) 



FIGURE 4.36 X AXIS VELOCITY DIFFERENCES 
(NO AGS COMPENSATION) 



4-94 



1. 1 *• •»» 
00 



Ui 



o 



^^ ^^^— ^ M^MMMMM M^Ma^rfM M^ma^M M^MNMBM ^MMMIMH I^HM^I^ ^aBB^MM H^^BHH 
MM ^-MM^ ,^^^^^ ^^^^ H^^HH ^^^^H MMH^MM lli^ II M ^MMawM Ml ■ 1^1 



:^ 



.^ 



79:27:15 28:05 28:55 29:45 30:35 31:25 32:15 



TIME GET (HR:NIN:SEC) 



■#■■;•■■ 




FIGURE 4-37 Y AXIS VELOCITY DIFFERENCES 
(NO AGS COMPENSATION) 



4-9S 



^ 



>> 




y W4«« 


























■it t»i» 


















































ULi 
CO 


















































UJ 

o 


















































UJ 

u, 
o 


















































>- 


























o 

o 


























Ui 

> 




























































































































































• «M 



























79:27:15 28:05 



28: S5 



29:45 



30:35 



TrT25 32715 



TIME GET (HR:MIN:SED) 



FIGURE 4-38 Z AXIS VELOCITY DIFFERENCES 
(NO AGS COMPENSATION) 



r 



4-96 



^mm 



o 

LU 



o 

I 



o 



79 :*27:15 28:05 28:55 29:45 30:35 31:25 32:1 5 



TIME GET (HR:MIN:SEC) 



FIGURE 4-39 X AXIS VELOCITY DIFFERENCES (COMPENSATED FOR 
AGS ACCELEROMETER ERRORS) 



4-97 




> V 



UJ 

t 






o 
o 



t •« 


















































• ■« 


















































t t« 














































































































































































































k *« 










L^ «^ 

















79:27:15 28:05 



23:55 29:45 30:35 31:25 



32:15 



TIME GET (HR:MIN:SEC) 



FIGURE 4-40 Y AXIS VELOCITY DIFFERENCES (COMPENSATED 
FOR AGS mCCELEROMETER ERRORS) 



4-98 



N 



O 

UJ 

t 

UJ 



jfcf 



• •! 




















































» •« 












































































• *! 








































































































































































































































•ft •• 



























79:27:15 28:05 28:55 .29:45 30:35 31:25 32:15 



TIME GET (HR:MIN:SEC) 




I 



FIGURE 4-41 Z AXIS VELOCITY DIFFERENCES (COMPENSATED 
FOR AGS ACCELEROfCTER ERRORS) 



4-99 



I 



^v 



»•• 
































































^ l»t 






















UJ 

oc 

UJ 

U- 

u- 

< 
—1 
3 
C7 'ft* 




*••. 


.": 


r^ 


A 


















X 




f 






A * 


- 


X 


















' 


. 


*M# 






















~4## 






















•M 























79:25:35 



26:25 



27:15 



28:55 



30:35 



32:15 



'ftTr-lifc; ' 



TIME GET (HR:NIN:SEC) 



FIGURE 4-42 AGS/PGNCS ANGULAR DRin - X BODY 



4-100 






¥-— ■ 



(A 






o 






79:25:35 



mr 



•19^ 



^^> > 



27:15 



28:55 



30:35 



32:15 



TIHC GET (HR:MIN:SEC) 



FIGURF 4-43 A6S/P6MCS MIGULAR.DRIFT - Y BODY 



4-101 







t--- 



>^ 



o 






































































IM 
-t 




























-^'. V . 






^ 






















/ 


*. 



























































































\ 



79:25:35 



26:25 



27:15 



28:55 



30:35 



32:15 



TIME GET (HR:MIN:SEC) 




FIGURE 4-44 A6S/PGNCS ANGULAR DRIFT Z BODY 



l^— 



4-102 



5.0 SEPARATION MANEUVERS 



*» 



•i 



jdkm 



Prior to re-entry there were two separation maneuvers to extricate 
the CM from the LM/CM/SM stack. 

5-1 SM SEPARATION FROM THE LM/CM 

Service module separation was performed by applying a positive X 
body velocity using the LM RCS thrusters, firing the separation latches, 
and then applying a retro aV using the LM RCS thrusters. The pre-planned 
maneuver called for 0.5 fps of positive aV„ followed by a negative 0.5 
fps aV„. LM IMU sensed aV at the time of separation indicated approximately 
0.7 fps was applied in the positive direction and a subsequent 1.9 fps was 
applied in the retro direction. Approximately one minute later the retro 
velocity was decreased by 0.3 fps leaving a net inertial velocity of 
approximately .9 fps applied to the LM/CM stack and 1.6 fps of relative 
velocity between the SM and the LM/CM stack. 

5.2 LM SEPARATION FROM THE CM 

LM separation from the CM was performed by leaving the CM/LM tunnel 
partially pressurized, firing the latches, and allowing the trapped gas to 
force the two vehicles apart. A similar type of separation occurred on 
Apollo 10 between CSM and LM at LM jettison. On Apollo 10, however, the 
tunnel pressure was approximately 80% higher than on Apollo 13. From the 
Apollo 10 data, LM separation velocity was determined and then considering 
the lower tunnel pressure, an impulse was calculated for Apollo 13, 
Applying the analytical impulse to CM and LM, an estimated W of 2.15 
fps and 0.86 fps was calculated for CM and LM, respectively. Actual experi- 
enced AV at separation was 1.88 fps and 0.65 fps for CM and LM, respectively, 
indicating good agreement with the estimated impulse. The sensed vectors 
at separation are derived below. 






. -* V * ' 



:^^ 






5-1 



c 



5.2.1 LM AV 



^'^ 



After bias correction, PI PA counts telemetered from the LGC indicate 
the forowing inertial thrust velocity changes during the 2 second interval 
141:30:00.16 to 141:30:02.16 GET bracketing the time of LM jettison. 

tH^ = -.294 ft/sec 

aV = .555 ft/stc 

aV^ = -.169 ft/sec 

TTie gimbal angles at the time of separation were: CDUX = -156.1707 deg; 
CDUY = -31.4429 deg; COUZ - 57.4145 deg yielding a direction cosine matrix 
which transforms from platform to body. 



aV, 



body 



-0.65 
-0.017 
-0.003 J 



ft/sec 



AGS telemetry data shows Vg^ « -.625 during the 1 second Interval 
141:29:59.85 GET confirming the LM IMU data. 

5.2.2 CM AV 

Since the CMC telemetry was in low-bit-rate (data available at 1/5 
the normal sample rate) during separation. It was necessary to compute 10 
second DELV's from the available state vector data. Gimbal angles near the 
center of the 10 second computations cycle were used to transform the Iner- 
tial accelerations into CM Body Coordinates. 

The CM showed evidence of some venting for about 40 seconds after the 
separation event. 



i:';»"aii 



5-2 



From the reconstructed thrust accelerations it appears that the CM 
experienced the following velocity change across the separation period: 



aV^ (body) = -1.54 ft/sec 
aV (body) = 0.42 ft/sec 



aV^ (body) 



0.99 ft/sec 



The CM DSKY display of thrust velocity in body coordinates (V16 N83) 
during the LM separation maneuver differed significantly from the derived 
values above due to the large Z PIPA bias error that existed. Application 
of this Z-PIPA bias error greatly reduces the discrepancy between the magni- 
tudes of the reconstructed and of the DSKY displayed aV (from 4.19 ft/sec 
to 1.98 ft/sec). The remaining 1.08 ft/sec discrepancy is unexplained. 



;^ 




1 



5-3 



f 



'> 



REFERENCES 

1. MSC Internal Note, "Apollo 13 Mission Report," 197&, 

2. NASA SNA-8-0.027, "CSM/LM Spacecraft Operational Data Book," Vol. 
Ill ( Mass Properties), Revision 2, 20 August 1969. 

3. P. Pantason, Grumman IOC No. LAV-500.853. "Effects of RCS Jet 
Thruster Plume Reflectors on LM Attitude Control Authority," 
17 March 1969. 

4. MIT/IL R-567, "Guidance System Operational Plan for Manned LM 
Earth Orbital and Lunar Missions Using Program Luminary IC 
(Rev 130)," Section 3 (Digital Autopilot), Revision 3, October 
1969. 




NASA — MSC 



5-4 




mmA:mm