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A LGUIDANCE AND NAVIGATION
Approved: . -,:_ ",' , /L. Date: .'_ __ _1
JOHN M. DAHLEN, DIRECTOR, SYSTEM ENGINEERINGAPOLLO GUIDANCE AND NAVIGATION PROGRAM
Approved: __.'1_-_\ _ _.,-_.. Date: '' ]",1" ,/
RICHARDH. BATTIN,DIRECTOR,MISSIONDEVEL.APOLLOGUIDANCEANDNAV,GATIONPROGRA_
Approved:' _,//'/"f'/__C'L_ D.at e ..,_, CuL¢ 7
DAVIDG: .OAG.-_,_ECTOR$7APOLLOGUmANCE"ANDNArrATION PROCRAM
Approved: ,; _La_.'Z: . _, , "(,._,_ .__DEPUTJ_IRECTOR_, Date: ,'/-_" ,, _,RALPH R. RABAN.
INSTRUM ENTATION LA BORA TORY
R-527 (Rev. 2) *.'_.:.,'-.,
GUIDANCE SYSTEM OPERATIONS PLAN _ _lec__:-' :z* yea_a_FOR UNMANNED LM EARTH ORBITAL MISSIONSUSING
PROGRAM SUNBURST
SECTION 7 G&N ERROR ANALYSES
DECEMBER 1967
| __ $ 5 _ . . tit '_..'-'.=," . ."_T'C__0TI_ _ I_ K ..... r _*:_- ,,,'-' •
pIOHiSII_-D 6¥ LAW. "_k
CAMBRIDGE
INSTRUMENTATION
,,, ,,.,,.¢.u,..,,, L A B O R AT O R Y
)
ACKNOW LEDGEM ENT
This report was prepared under DSR Project 55 23850, sponsored by the Manned
Spacecraft Center of the National Aeronautics and Space Administration through
Contract NAS 9-4065 with the Instrumentation Laboratory, Massachusetts Institute
of Technology, Cambridge, Mass.
This document, ontains informati affecting the
national defens, the Unite, within the
meaning of the Esp Title 18, U.S.C.o
Sections 793 and e transmission or the
revelation of manner to an
unauthorized person is d by law.
_o
• 4b
The publication of thi§._eport does not constitute approval by the National• 1 ' ,, . ,
Aeronautics and _pace Administration of the findings or the conclusions contained
therein. It is published only for the exchange and stimulation of ideas.
if
R-527(Rev.II)
GUIDANCE ANDNAVIGATIONSYSTEMOPERATIONSPLAN
MISSIONAS-204/LM - 1G&NERRORANALYSIS
(u)
ABSTRACT
The purpose of this document is to present a performance summary of
the Guidance and Navigation System in LM-1 and to compare this performance
with the requirements of Mission 204/LM-1. The calculated G&N errors
are based upon system performance as of November 26, 1967. More recent
data through December 1967 is included. This includes both IMU S/N 11 and
S_6. (The updated performance uncertainties derived using data up to this
time period, are shown for certain parameters. Other parameters could not
be derived because of system history and the lack of a large enough data
sample). The system performance of all the major components are shown.
The chapter contains an alignment summary of the G&N System. The one
sigma standard deviation for the accelerometer and gyro performance para-
meters are calculated. These uncertainties are utilized to calculate the
error in position and velocity. As a comparison, the Block II Performance
Specifications in the Master End Item (MEI) are also utilized to calculate
the mission position and velocity uncertainties. Utilizing those uncertainties
from the Block II Specifications show that updating before DPS 1 burn does
not reduce the perigee uncertainty in coast after APS 2 burn; in fact, it is
less with no update. With an update before the second APS burn, the perigee
uncertainty is slightly less than with no update.
December 1967
°..iii
7.0 G&N ERROR ANALYSIS
The Guidance System Operations Plan is published as seven separate
volumes (sections) as listed below:
Section 1 Pre-Launch
Section 2 Data Links
Section 3 Digital Auto Pilots
Section 4 Operational Modes
Section 5 Guidance Equations
Section 6 Control Data
Section 7 Error Analyses
This volume, Section 7 of the Guidance System Operations Plan, G&N Error
Analyses for Unmanned LM Earth Orbital Mission using Program SUNBURST was
based on the LM-1 missions.
The content
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
of this volume is arranged:
Introduction
Important Results of Error Study
Effectiveness of Navigational Update
Navigational Update Uncertainties
IMU Errors and Uncertainties
Accelerometer Error Coefficients
Gyro Drift Coefficients and S.M. Drift RateEquations
Stable Member Axes and Component OrientationRelative to S.M. Axes
Orientation of Stable Member Axes
Stable Member Pre-Launch Alignment Uncer°ta_nties
Effect of Stable Member Orientation on FlightUnc ertaintie s
PIPA Saturation Effects
Trajectory Data for Error Studies
Error Computation Procedures
Error Table Definitions
Page 7-77 Hardware Data
7-0
7.1 IntroductionThe results of anerror study of the effectsof IMU componenterrors on LM
guidanceandnavigationfor the LM-1 mission are givenhere. Three navigationalor state vector updateswere considered. Thesewere:
a) No on-board (R, V) navigationalupdatethroughoutthe flight.b) Navigational updatejust before DPSIburn.c) Navigational updatejust before APS2burn.
The error studiesinclude the effectsof tracking uncertainties on the statevector updates. Updatingdid not apply to the alignmentof the IMU StableMember,sincethis is not realigned during the LM-1 flight.
The orientation of the StableMember, relative to inertial axes, assumedforthe error studies is obtained(seeFig. 7_l) by rotating:
40 deg.aboutXi, then-30 deg.aboutZSM
This sameorientation wasassumedfor the previous error study(Rev. 1 - Jan. 1967).This was chosento prevent the middle gimbal anglemagnitudefrom exceeding50degreesduring the mission.
The present error study is basedona mission plan providing for two DPSandtwo APSburns. The previous error studyhad assumedshort 3rd and4th APSburns.Thesehavenowbeenomitted from the mission plan.
This error studywas carried out for two different sets of IMU uncertainties.Theseare:
a) Block II IMU uncertainties (seeTable 7.5)b) IMU uncertainties basedon mostrecent systemtest measurementsand
compensationvalues(seeTable 7.5a)
Both sets as listed in the tables are onesigmauncertainties.
7.2 Important Resultsof Error StudyOneimportant purposefor the error studywas to determine the actual perigee
altitudes for the coastsfollowing the DPSand APSburns assumingG&Nguidanceof the burns with adversethree-sigma andone-sigma IMU uncertainties. Tables 7. 1and 7.2 summarizethe datafor Block II IMU uncertainties. Tables 7. la and 7.2asummarize the datafor most recently measuredIMU uncertainties. The dataforcoast following SIVBcutoff are, for the normal mission, indication uncertainties,since the LM G&Nonly monitors the launchto earth orbit trajectory. However, seesection 7.3a for the contingencycasewhereSIVBthrust fails. Thefollowing com-ments canbe made.
7-1
XSt£
Horizontal planeat launchinstant
XSC(OGA)
TX I (along local vertical
at launch instant)
ZSM
"\\_ ZS_VI_ YSM (I_A)
YI
AXI shown positive
AZSIVl shown negative
XI" YI" ZI
Xc*_VI_ YSM, ZSM
XSC' YSC' ZSC
Launch Inertial Axes
IMU Stable Member Axes
Spacecraft Axes
NOTES: Orientation angles for Stable Member are AXI, AZSM
To align SM to the desired orientation, the SM axes are
initially set colinear with launch inertial axes. The SM
is then rotated about X I through the angle, AXI. Then it
is rotated about ZSM through the angle, AZSM.
For the error study AXI = 40 ° and AZSM -30 °
were assumed. AlsoAZ = 72 ° was assumed to be the
launch azimuth.
Fig. 7.1 Coordinate axes for 206 Launch Configuration
7-2
(This Page is UNCLASSIFIED)
IA XSM IA
Ifm___.OA
PRA
Z ,IA IA
OA
OA ZSM
IA _/2_RA _AIA
Seconds of Arc
_x _y
BDX 1 meru
BDY 1 meru
BDZ 1 meru
A DSRAX 1 meru
ADSRAZ 1 meru
ADIAX 1 meru
ADIAY 1 meru
ASF/SFX 10 3 PPM
ASF/SFY 103 PPM
ASF/SFZ 103 PPM
7XZ 1 sec
7Xy 1 sec
7yz 1 sec
?YX I sec
7Z X 1 sec
7Zy 1 sec
ABX 1 cm/sec 2
ABY 1 cm/sec 2
ABZ i cm/sec 2
_XZ 1 sec
ayz 1 sec
aZX 1 sec
98
143
-100.7
49.1
-53• 8
85.1
-71.6
17.3
-91.7
80
.25
36
12
52
33
- 09
43 7
75 7
-63 8
- 12
- 32
15
-56
-82
62
-28
31
-49
+41
-I0.
53
-46.
- 18
- 21
- 07
34
19
O5
-25. 7
-44. 7
-207
•06
.19
.49
9
6
2
4
1
3
3
2
a = PIPA IA Misalignment
_' = IRIG IA Misalignment
7-3
-.i
-.06
0
-.05
0
.09
-.03
.02
• 04
0
-0
-0
-0
-0
0
0
105
182
0
-.25
-.75
0
wl _ w m_ -in
(This Pageis UNCLASSIFIED )
With three-sigma Block II IMU uncertainties, dangerously low perigee altitudes
(less than 65 n. miles) occur only after the 2rid APS burn and only for the naviga-
tional update before DPS1 burn case. Here the perigee altitude is 36 n. miles.
With no update the perigee altitude for the coast following the 2nd APS burn is
75 n. miles, while with update before this burn the perigee altitude is 76 n. miles.
With one-sigma Block II IMU uncertainties no dangerously low perigee altitudes
occur. The lowest perigee altitudes all occur after the 2nd APS burn and is lowest
(100 n. miles) for the update before DPS1 burn case. The prime contributors to
altitude uncertainties at this perigee are the Y and Z gyro bias drift uncertainties
as Table 7.32 shows. For the no update and the update before APS2 burn cases the
ADIAX and ADIAY drift uncertainties are also important contributors to lowering of
perigee altitude as Table 7.29 and Table 7.37 show. In all cases the accelerometer
uncertainties have a secondary effect on altitude uncertainties.
Tables 7.8, 7. 9, and 7.10 give detailed summary data, with Block II IMU un-
certainties, respectively, on uncertainties with no update, with update before DPS1
burn, and with update before APS2 burn.
At the end of this section will be found computer printed error tables. Tables 7.17
through 7. 37 are with Block II IMU uncertainties. Tables 7. 38 through 7.51 are
with most recently measured IMU uncertainties.
7.3 Effectiveness of Navigational Update
Table 7.1 and Table 7.2 using Block II IMU uncertainties, show that updating
before the DPS1 burn produces lower perigee altitudes than no updating for the
coasts following the DPS2/APS1 burns and the APS2 burn. Further, these tables
also show that updating before the APS2 burn produces perigee altitudes roughly
the same as those obtained for the no update case.
7-4
Table 7.1
Altitude Uncertainties and Perigee Altitude due to 3a
IMU Uncertainties for LM-1 Mission
(AXI = 40 °, AYIP = 0 °, AZSM = -30 ° )
with Block II IMU uncertainties
Mission
Event
Launch
SIVB Cutoff
DPS 1
Cutoff
APS 1
Cutoff
At Perigeein
FollowingCoast
APS2
C uto ff
At Perigeein
FollowingCoast
Update ?
None
None
None
Bef. DPS 1
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
Bef. APS2
None
Bef. DPSI
Bef. APS2
Nominal
PerigeeAltitude
for FollowingCoast
n. miles
88.7
117.6
168.4
168.4
127. 7
127. 7
Altitude
with
Adverse
3(y
Altitude
Uncert.
n. miles
87.2
105, 9
117.6
154.3
158.9
151.0
118.3
158.4
156.6
165.8
l
3a
Altitude
Uncertainties
at Event
Time
n. mile s
0
2.1
13.1
8.5
25.9
60.7
11.3
13.2
3.9
Altitude Uncertainties
n. miles
Max. In
FollowingCoast
0
15.1
15.8
0.6
29.1
62.1
29.1
62.1
54.0
103.2
56.2
74.6
36.2
76.4
53.2
I00.2
54.0
54.0
103.2
56.2
Min. In
FollowingCoast
0
0.3
0.3
_-_0
10.8
0.5
10.8
0.5
10.8
1.7
0.1
10.8
1.7
0. I
7-5
0
The principal reasons why updating fails to reduce altitude uncertainties
more are:
1) Large drift angles due to gyro bias drift since launch generates velocity
uncertainties during the APS2/APS1 and the APS2 burns considerably greater
than those generated during the earth launch to orbit trajectory.
2) Initial Stable Member azimuth misaIignments due primarily to the gyro
acceleration sensitive drift undertainties, ADIAY and ADIAX, cause large
altitude uncertainties after the DPS2/APS1 and APS2 burns. This is due to
the fact that the thrust direction for these burns is approximately normal to
the orbital plane. The initial azimuth misalignment causes the accelerome-
ters to sense incorrectly accelerations in the orbital plane thus contributing
to velocity uncertainties in the altitude-range plane.
More detailed comments on the effect of updating on altitude uncertainties
follow. The principal contributors to the altitude uncertainties at perigee in coasts
following APS1 and APS2 cutoffs are for all cases: NBDZ, NBDY, ADIAY and ADIAX
with NBDZ as the prime contributor. (These are respectively the Z and Y gyro bias
drift, and the Y and X gyro input axis accelerationsensitive drift uncertainties.) In
general the in-flight effect of the NBDZ and NBDY terms is considerably greater
than the initial misalignment effect. However, for the ADIAY and ADIAX terms the
initial azimuth misalignment effect is at least an order of magnitude greater than
the inflight effect.
Table 7.3 gives position and velocity uncertainties due to NBDZ for all update
cases. The drift angle due to NBDZ of 2 meru is 0.09 milliradian (mr.) at SIV_
cutoff, while it is about 2.5 mr. for the DPS2/APS! burns, and 3.3 mr. for the AP_2
burn. The velocity uncertainty in the altitude-range plane was 2. 1 ft/sec, at SIVB
cutoff. However, the velocity uncertainty increase due to the DPS2/APS1 burns was
16. 6 ft/sec., and the increase due to the APS2 burn was 19 ft/sec, in the same
plane. The effectively large Stable Member mi_alignment due to driftduring these
burns accounts for the large increase in velocity uncertainty during these burns in
the altitude-range plane and for the large increase in altitude uncertainty at perigee
in the following coasts. For the update before DPS1 burn case the velocity uncertainties
generated during the APS2 burn are added effectively to those generated in the DPS2/
APS1 burns with the result that the altitude uncertainty gets large at perigee after the
APS2 burn. However, for the no update case, the velocity uncertainties generated
during the DPS2/APS1 burns tend to cancel the uncertainties existing at burn ignition
with the result that altitude uncertainties at following perigees are not as large as
for the first update case.
_r
7-6
Table 7. la
Altitude Uncertainties and Perigee Altitude due to 3_
IMU Uncertainties for LM-1 Mission
(AXI = 40 ° , AYIP = 0 °, AZSM = -30 ° )
with most recently measured IMU uncertainties
Mission
Event
Launch
SIVB Cutoff
DPS1
Cutoff
APSI
Cutoff
At Perigeein
FollowingCoast
APS2
Cutoff
At Perigeein
FollowingCoast
Update ?
None
None
None
Def. DPSI
None
Def. DPS 1
None
Def. DPSI
None
Def. DPS1
Def. APS2
None
Def. DPSI
Def. APS2
Nominal
PerigeeAltitude
for followingCoast
n. miles
88.7
117.6
168.4
168.4
127.7
127.7
Altitude
with
Adverse
3u
Altitude
Uncert.
n. miles
0
88.2
109.4
109.3
159.5
162.2
159.7
129.0
162.8
160.3
167.5
3(_
Altitude
Uncertainties
at Event
Time
n. miles
0
0.5
8.2
0.1
9.4
6.7
9.0
44.3
8.1
10.6
3.4
Altitude Uncertainties
n. miles
Max. In
Follow ingCoa st
0
11.3
11.6
0.6
31.0
58.3
31.0
58. 0
I
58.0
101.7
59.2
75.1
36.7
74.0
53.1
93.6
54. 3
58.0
101.7
59.2
Min. In
FollowingCoast
0
0.15
1.2
0.02
7.3
0.2
7.7
1.6
0.03
7.7
1.6
0.03
7-7
%
Table 7. 2
Altitude Uncertainties and Perigee Altitudes due to I_
IMU Uncertainties for LM-I Mission
(AXI = 40 ° , AYIP = 0 °, AZSM = -30 °)
with Block II IMU Uncertainties
Mi s sion
Event
Launch
SIVB Cutoff
DPS1
Cutoff
APS1
Cutoff
At Perigee
in
Following
Coast
APS2
Cutoff
At Perigee
in
Following
Coast
Update ?
None
None
N one
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
Bef. APS2
None
Bef. DPSI
Bef. APS2
Nominal
PerigeeAltitude
for FollowingCoast
n. mile s
88.7
117.6
168.4
168.4
127.7
127.7
Altitude
with
Adverse
Alt it ude
Unce ft.
n. miles
87.7
112.1
115.9
163.0
164.5
162.9
153.2
165.9
165.3
168.4
108.8
99.8
110.7
ICY
Altitude
Unc ert aintie s
at Event
Time
n. miles
0
0.4
3.7
4.4
2.9
4.3
16.7
3.8
4.2
1.3
17.4
30.0
16.6
Altitude Uncertainties
n. miles
Max. In
F ollowingCoast
0
5.0
5.3
0.2
9.7
20.7
9.7
20.7
18.0
34.4
18.7
18.0
34.4
18.7
Min. In
FollowingCoast
0
0.1
0. i
--,0
3.6
0.2
3.6
0.6
O. 02
3.6
0.6
O. 02
7-8
x m_upn P_l_LI imAIIC Ira, .... _ _T__ ____._
m,
Table 7.2a
Altitude Uncertainties and Perigee Altitude due to 1_
IMU Uncertainties for LM-1 Mission
(AXI = 40 ° , AYIP = 0°, AZSM = -30 ° )
with most recently measured IMU Uncertainties
Mission
Event
La un ch
SIVB Cutoff
DPS1
Cutoff
APS1
Cutoff
At Perigeein
FollowingCoast
APS2
Cutoff
At Perigeein
FollowingCoast
Update ?
None
None
None
Def. DPSl
None
Def. DPS1
None
Def. DPS1
None
Def. DPSI
Def. APS2
None
Def. DPS 1Def. APS2
Nominal
PerigeeAltitude
for FollowingCoast
n. miles
88.7
117.6
168.4
168.4
127.7
127.7
Altitudewith
Adversela
AltitudeUncert.
n. miles
88.5
114.9
114.9
165.8
166.7
165.8
158.6
168.2
167.3
169.7
110. 599.1
110.2
1(7
AltitudeUncertainties
at EventTime
n. miles
0.17
2.7
0.03
3.1
2.2
3.1
14.8
2.7
3.5
1.1
17.731.218.1
Altitude Uncertainties
n. miles
Max. in
FollowingCoast
3.8
3.9
0.05
10.3
19.4
10.3
19.4
19.3
33.9
19.7
19.333.919.7
Min. in
Follow ingCoast
0.05
0.4
0.01
2.4
0.1
2.6
0.5
0.01
2.60.50.01
7-9
n dpumnl_:nnpnnm_, .... • I
Table 7. 3
Uncertainties Due to NBDZ = 2 meru
{Combined effects of uncertainties caused by initial S.M. mis-
alignment due to NBDZ and in-flight effect are given here}
Event
La unc h
SIVB Cutoff
DPS1
Cutoff
DPS2
Ignition
pAPS1
Cutoff
At Perigee
in Follow-
ing Coast
APS2
Ignition
APS2
Cutoff
At Perigee
In Follow-
ing Coast
Update ?
None
None
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPS1
Bef. APS2
None
Bef. DPSI
Bef. APS2
None
Bef. DPS1
Bef. APS2
l_'osition
Uncertainties - n. milesL ,-
Alt. Track Range
0 0 0
0.04 1.19 0.05
0.84
0.03
0.86
0. 18"
0.85
5.05
0.89
0.04
0
0.92
0.33*
0.03*
10. 66*
17.18
10.58
1.76
0.21
1.83
0.38
0.48
0.17
0
- 5.42
- 9.43
0.07
3.83
9. 79
- 0.08
II. 51
0
- 8.81
- 2.56
- 30.67
- 40.03
0
- 28.24
- 37.30
O. 59
- 60.28
- 78.31
- 26.81
Velocity
Uncertainties- ft/sec
Alt.0 Track0 i Range0
1.76 28.02 1.14
0.06
0.28
4.03
9.71
4.55
29.24
- 5.54
- 3.71
0
8.12
19.53
3.13
- 18.18
- 2.06
- 5.08
26.69
0.25
19.85
2.53
19,54
-1, 12
J
23.20
2.87
0
35.24
22. 77
2.18
- 44.53
- 5.46
- 2.18
5.22
0.14
13.73
13.48
13.62
-20.61
11.71
12.99
0
25.16
28.72
18.75
-51.86
-81.91
-55.52
*Initial misalignment and in-flight effects tend to cancel here.
7-10
Table 7.4
Uncertainties Dueto Initial StableMemberAzimuth MisalignmentAboutXI of 50Seconds
Event
Launch
SIVBCutoff
DPS1Cutoff
DPS2
Ignition
APS1Cutoff
At PerigeeIn Follow-ing CoastAPS2
Ignition
APS2
Cutoff
At Perigee
In Follow-
Coast
Update ?
N one
None
None
Bef. DPS1
None
Bef. DPS1
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
Bef. APS2
None
Bef. DPSI
Bef. APS2
None
Bef. DPSI
Bef. APS2
0
- 30
- 750
0
Position
Uncertainties - feet
824
- 695
3, 076
-4,720
-1,978
Alt. Track
0
-1,471
4,344
0.3
1,190 -2,137
0 16
-1,609
- 72
802 -1,691
-3,582 - 137
1,241 - 18
91 - 72
0 0
573 - 26
-1,046 4,376
- 292 - 18
I, 023
-4,508
21
Range
0
- 79
15,680
0
14, 490
0
13,372
- 143
13,341
4, 803
7, 52 9
18, 173
0
6, 905
1 7, 496
67
5, 42 4
41,871
11,387
Ve loc ity
Uncertainties ft/sec
Alt.
0.65
0
0.08
0
-0.94
-1.32
0
-2.17
-4.30
-1.66
1.75
3.90
1.79
Track Range
0 0
-5.66 -0.30
3.07 0. 97
0.03 0
-5.37 -1.19
-0.03 0
-3.92 -0.53
-0.15 -0.30
-3.88 -0. 50
0.06 3.03
-4.34 -0.88
-0.1 7 -0.79
0 0
-4.39 0.28
-I. 47 -0.18
-0.09 -0.34
4.27 -2.69
0.16 i 4.20
0.09 i 1.65k
7-11
_* -.._b_,_,i,.,i'll_l I1_,11II,.,ilP=,..-un-. • mnmr
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o_-_N
"C_.g
% I1)
g
{_11_ "I¥_)I.LITYN) }10}1}1_ :K_rlIlllY 3301}1_d
7-13
_A& n IPmil IP_, P &.J mr it _ .i. _
L,_ ...... . a I el 'lUll-
The ADIAY and ADIAX terms are important contributors almost entirely through
their effect on initial Stable Member misalignments. Table 7.11 with Block II un-
certainties shows that the azimuth alignment uncertainty is 3. 3 mr. (690 secs) for
both these terms, and that they are the dominant contributors. The effect of the
azimuth misalignments on altitude uncertainty may be explained with recourse to
Table 7.4, which gives uncertainties due to an initial Stable Member misalignment
about azimuth of 50 secs. For the update before DPS1 burn case this table shows
that, while track uncertainties dominate for the DPS1 burn, the dominant uncertain-
ties for the DPS2/APS1 burns are in the altitude-range plane. The reason for this
phenomenon is as follows: The thrust direction for the DPS2/APS1 burns and for
the APS2 burn are approximately normal to the orbital plane. (For the DPS1 burn
the thrust is in the orbital plane. ) This is shown in Table 7.16 which gives data on
the AV components (integral of thrust acceleration) in and perpendicular to the
orbital plane. With the thrust normal to the orbital plane the azimuth misalignment
of the Stable Member causes the accelerometers to sense or pickup accelerations
in the orbital plane contributing to velocity and position uncertainties in the altitude-
range plane. For the no-update case the uncertainties generated in the DPS2/APS1
and APS2 tend to cancel partially the uncertainties existing prior to the DPS2 burn
as Table 7.4 indicates.
Figure 7. 3 shows the effect of initial Stable Member azimuth error on perigee
altitude error for the coast following the APS2 burn for the no update and the two up-
date conditons. These curves show that for a given azimuth error the perigee error
is greater with update before DPS1 burn than with no update.
Figure 7.4 shows the effect of Stable Member drift angle due to the three gyro
bias drift terms on perigee altitude error for the coast following the APS2 burn for
the no update and the two update cases. The Block II bias drift rate uncertainty is
2 meru or 0.03 deg. per hour. At APS2 cutoff the accumulated drift angle about each
S.M. axis is 3.3 mr. or 0.2 deg. Figure 7.4 shows that the Y and Z gyro drift terms
have a much greater affect on perigee error than the X gyro. It also shows that the
perigee error is greater with update before DPS1 burn than with no update for all gyro
drift terms.
7.3a Errors in Perigee Following SIVB Cutoff
For the contingency where the Saturn SIVB stage fails to perform correctly,
it is planned that the LM-1 will be able to perform the orbit insertion maneuver.
Here IMU uncertainties will directly affect uncertainties in perigee for coast follow-
ing LM-1 orbit insertion cutoff. Table 7.14 gives data on perigee uncertainties
due to Block II uncertainties. This table also gives the IMU error values required
to produce a 1 n. mile perigee altitude error.
7-14
7.3b Errors in Perigee for Premature Cutoff of APS2 Burn
During the APS2 burn the instantaneous perigee (the perigee associated
with the free-fall coast if cutoff occurred at that instant} declines to the
critically low figure of 54 n. miles before rising again to the value of 128 n. miles
at normal cutoff. It is important to knc,w how large altitude uncertainties would
be at perigee if premature cutoff took place at the point where instantaneous
perigee is lowest. This occurs at 2?0 secs after ignition and ,157 secs
before normal cutoff. Tabley 7. 14a gives data on perigee uncertainty with
Block II IMU uncertainties for the critical premature cutoff time for the no
update and the two update cases.
7.4 Navigational Update Uncertainties
Navigational or state vector updates of the CSM computer's data on spacecraft
position and velocity have been proposed prior to the first DPS burn and also prior to
the second APS burn. These updates would be made on the basis of observations
made by the radar tracking stations of the Manned Space Flight Network (MSFN).
Uncertainties in the tracking data exist because of the presence of radar noise, bias,
uncertainties in station location and in the knowledge of earth gravitational constant.
The covariance matrices (one sigma) for the tracking uncertainties existing prior to
the above burns were obtained from "Error Analysis of MSFN Tracking Data for
AS-206A" by P.T. Pixley and D.H. Fessenden (MSC Internal Note No. 66-FM-60,
June 22, 1966, MSC, Houston, Texas).
The one sigma position and velocity uncertainties, derived from the diagonal
terms of the covariance matrices, are glen in the following table relative to local
vertical axes at burn ignition. The propagated tracking update uncertainties are
given near the bottom of all relevant error tables.
Burn
DPS1
APS2 iPosition ncerttlVelocity ncertAlt. I Track Range Alt. Track
181 t 155 1,840, 2.18 0.31
5471411 2,102 I 2.15 0.40
Update Uncertainties at Burn Ignition
(ft/sec)I
Range I
0.88 I
0.49 J
7-15
7.5 IMU Errors and Uncertainties
IMU errors can classed into two groups. These are: (1) those errors that
the LGC (lunar module guidance computer) can provide compensation for, and
(2) those errors for which there is no compensation.
IMU errors are compensated as follows. The average error for the particu-
lar IMU component is first determined on the basis of system tests extending over
many months. The negative of the computed average error is then stored in the
LGC shortly before earth launch. Pre-launch and in-flight compensation is then
effected by means of stored programs in the LGC. The rms IMU component un-
certainties are then the unpredictable deviations of the actual instantaneous error
from the assumed average error.
Table 7.5 lists the Block II one-sigma IMU error uncertainties that were
assumed for the error studies in this chapter. These are the same as those given
on p. 3-25 of MEI No. 2015000, Part I, which lists Block II specifications for the
Apollo Command Module.
Table 7.5a lists the one-sigma IMU error uncertainties computed on the
basis of the most recent system test measurements.
The following IMU errors are errors that the guidance computer is equipped
to compensate for:
1) Accelerometer bias error
2) Accelerometer scale factor error
3) Gyro bias drift
4) Gyro input axis accel, sens. drift
5) Gyro spin ref. axis accel, sens. drift
These are defined and discussed in some detail in subsections 7.6 and 7.7.
The computer does not provide compensation for the following IMU errors:
1) Stable Member initial misalignment_ (those that are uncorrelated with
gyro drift)
2) Accelerometer input axis misalignments
3) Accelerometer acceleration-squared indication uncertainties
4) Gyro output axis acceleration sensitive drift
5) Gyro acceleration-squared sensitive drift
6) Gyro input axis misalignments
The subject of Stable Member initial misalignments will be covered in Section
7.10. It should be noted that those sources of initial S.M. alignment errors directly
due to gyro bias drift, to acceleration sensitive drift, and to accelerometer bias will,
of course, be compensated for.
Accelerometer input axis misalignments will be covered in the next subsection.
7-16
Table 7.5
Block II One-Sigma IMU Error Uncertainties
Error
Accelerometer Errors
Bias Error ACB Yes
S.F. Error SFE Yes
Accel. Sqd. Ind. Error NC No
Input Axis Misalignment a No
G.yro Errors
Bias Drift NBD Yes
IA Accel. Sens. Drift ADIA Yes
SRA Accel. Sens. Drift ADSRA Yes
OA Accel. Sens. Drift ADOA No
IA Misalign. about SPA "YSRA No
IA Misalign. about OA 7OA No
Stable Member Alignment Errors
Prelaunch Azimuth .... No
Vertical .... No
Free-Fall All Axes .... No
RMS Uncertainty(after compen-
Error Compen- sation whenSymbol sated ? applicable)
ErrorUnits
0.20 am/sea 2
11 6 ppm
10 U g/g2
20 seas.
2 meru
8 meru/g
5 meru/g
1" meru/g
50 $ seas.
50 _ secs.
50"* seas.
5** sees.
20 secs.
IAsted value for ADOA is not a Block II uncertainty.value used for the error studies.
It represents a reasonable
The error values listed for S.M. prelaunch azimuth and vertical alignments are notthose listed in MEI No. 2015000. They represent present estimates for these mis-alignments.
NOTE: 2 meru = 0.03 deg/hour
0.2 cm/sec 2 = 0. 00656 ft/sec 2 = 2.04 (10 -4 ) g
50 seas = 0.242 mi_iradian = 0.242 (10 -3 ) radian
7-17
Table 7.5a
Most Recently Computed One-Sigma IMU Error Uncertainties
Error
Accelerometer Errors
Bias Error
Scale Factor Error
Accel. Sqd. Ind. Error
Input Axis Misalignment
Input Axis Misalignment
Gyro Errors
Bias Drift
IA Accel. Sens. Drift
SRA Accel. Sens. Drift*
OA Accel. Sens. Drift
Input Axis Misalignment
Input Axis Misalignment
Stable Member Alignm. Errors
Prelaunch Azimuth
Prelaunch Vertical
ComputedError 1_
Symbol Uncertainties
Input Axes
ACB
SFE
NC
BD
A DIA
A DSRA
ADOA
7
7
X Y Z
0.08 0.06 0. i0
92 45 76
02 0.2 0.2
About Y About Z About X
3.0
About Z
-6.3
m9. 5
About X
--4.5
Input Axes
X Y
1.3 2.3
5.1 6.0
2.2 2.7
1 1
About Y About Z
20.0
About Y
Z
2.4
5.8
1.2
1
About X
-19.2 +19.4 -115
About Z About X About Y
-50.4
Error
Units
2cm/sec
PPM
. /g2
sees
secs
meru
meru/g
meru/g
meru/g
secs
-128.0 +87 secs
Launch Inertial Axes
XI YI ZI
50 ........ secs
.... 5 5 secs
*Denotes that listed uncertainty value is based on present estimates and not on system
test measurements.
**Prelaunch azimuth alignment uncertainty of 50 secs is based on rss estimate related
to specifications, since gyro IA misalignment data was incomplete at time of table
preparation.
NOTE: Computed uncertainty data for accelerometers were based on compilation period,
June 27 - Nov. 26, 1967. Uncertainty data for gyros were based on compilation
period, June 14 - Nov. 26, 1967.
7-18
CO: tam'm--P::=:==
Both aceelerometer acceleration-squared indication and uncertainty and gyro
acceleration-squared sensitive drift are difficult and time-consuming to measure.
For this reason and because their effects on trajectory uncertainties are secondary,
they are not compensated for. The effects of vibrations operating through these un-
certainties and through rectification effects may well have a greater effect than that
produced by burn thrust or reentry drag accelerations. However, no attempt was
made to study vibration effects in this chapter.
Gyro output axis acceleration sensitive drift (ADOA) is a relatively difficult
error to measure. The value of 1 meru/g for ADOA is a reasonable estimate for this
uncertainty.
Gyro input axis misalignments affect trajectory uncertainties only in their
effect on Stable Member azimuth misalignment prior to earth launch alignment when
gyro compassing is used for azimuth alignment. They are the prime contributors to
the pre-launch azimuth alignment uncertainty (uncorrelated) of 50 secs.
Since none of the above IMU errors are compensated for, uncertainties are the
same as errors for this group.
7.6 Accelerometer Error Coefficients
Accelerometer bias (ACB) is defined as the indicated acceleration of the
accelerometer with zero input acceleration. Bias is positive when the indicated accel-
eration is positive. This bias is due to torques about the output axis of the PIPA.
Accelerometer scale factor error (SFE) is defined as the deviation in the actual
PIPA scale factor from the nominal scale factor divided by the nominal scale factor.
The scale factor itself is conventionally defined as a given number of cm/sec 2 per
pulse/sec, delivered to the computer. The scale factor error is positive when the
mesaured scale factor (in cm/sec 2 per pulse/sec or cm/sec per pulse) is greater
than the nominal. However, it should be carefully noted that when scale factor error
is thought of as the deviation of indicated acceleration from the input acceleration
divided by the input acceleration (where ideal scale factor would then be unity), the
above definition of positive scale factor error corresponds to an indicated accelera-
tion less than the input acceleration.
Aeeelerometer input axis misalignments are not compensated for. A positive
misalignment is a positive rotation of the input axis about the appropriate S.M. axis.
There are two misalignments associated with each accelerometer. The misalignment
of the Z accelerometer input axis about YSM is nominally zero by definition. (See
definition of Stable Member axes in Section 7.8) However, for earth prelaunch align-
ment of the Stable Member the alignment of the accelerometer, whose input axis is
in the horizontal plane, is considered to be perfect relative to the horizontal plane.
This, of course, assumes a zero bias accelerometer.
7-19
f •
For the LM-1 earth launch Stable Member orientation (AXI = 40 °, AYIP = 0 °,
AZSM = -30 ° ) this means that, since ZIA is ideally horizontal (see Fig. 7.1), the
misalignments of ZIA about XSM and about YSM are both zero. The Block II rms
alignment uncertainty for each aceelerometer input axis is 20 seconds. Since the
misalignment of ZIA about YSM is zero, the misalignment of XIA about YSM must
be 28.3 secs. (That is, 28.3 secs. is the rss of the nominal misalignments of 20
secs. of ZIA and XIA about YSM.) Likewise, the misalignment of YIA about XSM
must be 28.3 secs, since misalignment of ZIA about XSM is zero. The misalign-
merits of XIA and of YIA about ZSM are computed on the basis of the following
equations:
Mlm. XIA about ZSM = 28.3 cos 2 (AZSM)
Mlm. YIA about ZSM = 28.3 sin 2 (AZSM)
where 28.3 is the rss of the nominal XIA and YIA misalignments about ZSM. Note
that if AZSM is zero (YIA horizontal), the first misalignment is 28.3 secs. and the
second is zero.
7.7 Gyro Drift Coefficients and S.M. Drift Rate Equations
Definitions for the gyro drift coefficients, NBD, ADIA, ADSRA, and ADOA
are given here. It is assumed in the following that the gyro is servo-controlled to
maintain the error signal at null.
NBD The normal excitation bias drift. It is non-acceleration sensi-
tive. NBD is positive when the S.M. drift rate is about the
positive gyro input axis (IA). A positive NBD is due to a nega-
tive torque about the output axis. The term BD is used to
designate gyro bias drift due to mechanical torques present prior
to gyro electrical excitation.
ADIA The acceleration sensitive drift rate due to gyro case
acceleration of one gravity along the input axis. It is positive
when the S.M. drift rate is about the positive gyro input axis
in response to a positive acceleration along the positive gyro
input axis. It will cause a negative torque about the output
axis. Internally this term is caused by a displacement of the
center of gravity with respect to the center of buoyancy of the
float along the positive SRA.
ADSRA The acceleration sensitive drift rate due to a gyro case accel-
eration of one gravity along the spin reference axis. It is
positive when the S. M. drift rate is about the positive gyro
input axis in response to a positive acceleration along the
7-20
positive gyro SRA. It will cause a negativetorque abouttheoutputaxis. Internally this term is causedby a displacementof the center of gravity with respect to the center of buoyancyof the float alongtheminus 1A.
AI_A The acceleration sensitivedrift rate dueto a gyro caseaccel-eration of one gravity along the outputaxis. It is positivewhenthe S.M. drift rate is aboutthe positive gyro input axisin responseto a positive acceleration alongthe positive gyroOA. TheADOAdrift coefficient is generally small relativeto the other drift coefficients. There is no computer compen-sation for the ADOAterms.
The following table gives the drift rates, WXSM, WysM, WZSM abouttheStableMember axes, XSM, YSM, ZSM, respectively, dueto the various gyro driftcoefficients. Figure 7.4 in the next sectionshowsthe orientation of the Block IIgyro axes relative to the StableMemberaxes. (Block I gyro axeshavethe sameorientation with the oneexceptionthat the Z gyro IA is along+ZsM.) The accel-eration components,AXSM, Ays M, AZSM, are positive with reference to S.M.axes. It is of interest to note that the correspondingdrift rate equationsforBlock I IMUs havethe samesigns with theexceptionthat NBDZcarries aplussign.
Drift Rate Gyro Drift Coefficientsabout
S.M. Axes NBD ADIA ADSRA ADOA
WXSM = NBDX +ADIAX(AxsM) -ADSRAX(AysM) +AIX)AX(AzsM)
Wys M = NBDY +ADIAY(AysM) -ADSRAY(AzsM) +ADOAY(AxsM)
WZS M = -NBDZ +ADIAZ(Azs M) +ADSRAZ(Ays M) +ADOAZ(Azs M)
I <
7.8 Stable Member Axes and Component Orientation Relative to S.M. Axes
IMU Stable Member axes are defined by the following equations:
YSM = unit (IGA)
ZSM = unit (component of ZIA in plane normal to YSM)
XSM = unit (YSM x ZSM)
In words YSM is identical with the direction of the IMU Inner Gimbal axis.
ZSM is defined by that component of the Z PIPA input axis which lies in the plane per-
pendicular to YSM.
7-21
The orientation of the three S.M. gyros (size - 25 IRIGs) for the Block II IMU
system are shown in Figure 7.4 relative to the positive Stable Member axes, XSM,
YSM, ZSM.
OAy XSM
SRA y _gyro
IAy
IAX
_.____ S RA X
OA X
X gyro
Z gyro
axe s.
Block IIIMU Gyro Axes Relative to S.M. Axes
Figure 7.4
The following table gives the orientation of gyro axes relative to Stable Member
Gyro
X
Y
IA
Along
XSM
SRA
Along
-YSM
OA
Along
ZSM
YSM -ZSM XSM
Z -ZSM -YSM XSM
The input axes of the X, Y, Z accelerometers (PIPAs) lie respectively along the
positive XSM, YSM, ZSM axes
7.9 Orientation of Stable Member Axes
The orientation fo the IMU Stable Member axes (XSM, YSM, ZSM) relative to
launch inertial axes are shown in Fig. 7.1. The launch inertial axes, X I and ZI,
define the initial reference trajectory plane as well as the initial pitch plane. The
axis, Z I, is in the horizontal plane at launch instant and oriented to the nominal
launch azimuth of 72 ° from north.
7-22
The orientation of the StableMemberrelative to launch inertial axesis mostconvenientlydescribedby the Euler rotation angles, AXI, AYIP, andAZSM. (See
Fig. 7.1) To reach the desired orientationthe S.M. is first rotatedaboutXI throughthe angle, AXI. ThenaboutYI (prime) throughthe angle,AYII:', andfinally aboutZSMthroughthe angle, AZSM. For the presenterror studythe StableMemberorien-tationangles assumedwere:
AXI = 40 ° , AYIP = 0°0 AZSM = -30 °
The corresponding IMU gimbal angles at launch were:
Aig = 0°, Amg = 30 ° , Aog = 140 °
7.10 Stable Member Pre-Launch Alignment Unce rtainties
The principal contributors to Stable Member pre-launch alignment uncertain-
ties are:
1) Effects of gyro IA alignment uncertainty on S.M. azimuth alignment.
(Called S.M. misalignment (uncorrelated) in error tables. )
2) Effects of gyro drift rate uncertainties on azimuth alignment of the Stable
Member. (Gyrocompassing to align the S.M. about azimuth is assumed.)
3) Effects of accelerometer bias and scale factor uncertainties on vertical
erection of the Stable Member.
The ways in which IMU component uncertainties contribute to pre-launch align-
ment uncertainty are described by the alignment error equations given in Table 7.6.
They are grouped under: 1) gyrocompassing errors, and 2) vertical erection errors.
The symbol, 4, is used to denote the Stable Member misalignment about the inertial
vector indicated by the subscript. For example, _XI is the S.M. misalignment about
X I. Note that misalignment about azimuth = -_XI" Second order terms are omitted
in these equations. These assume that AYIP = 0 and that Block II IMUs are used.
Table 7.11 gives data on initial azimuth alignment uncertainties due to gyro
drift uncertainties.for several different Stable Member orientations. The data were
computed, of course, from the equations of Table 7.6. Table 7.11 shows how
markedly the azimuth misalignment increases as AZSM goes from zero to -30 degrees
due to the effect of the gyro acceleration sensitive drift terms.
7.11 Effect of Stable Member Orientation on Flight Uncertainties
Table 7.12 for position and velocity uncertainties at SIVB cutoff shows how
the track uncertainty is more than doubled as AZSM goes from zero to -30 degrees
due to the effect on azimuth misalignment.
7-23
Table 7.6
Initial Stable Member Alignment Errors
G_yro-Compas sing Errors
X gyro drift effects
_Xl = NBDX sin (AZSM) cos (AZ - AXI)/Wh
+ADIAX(g) sin (AZSM) cos (AZSM) cos (AZ - AXI)/Wh
+ADSRAX (g) sin 2 (AZSM) cos (AZ - AXI)/Wh
Y gyro drift effects
_XI = NBDY cos (AZSM) cos (AZ - AXI)/Wh
-ADIAY (g) sin (AZSM) cos (AZSM) cos (AZ - AXI)/Wh
+ ADOAY (g) cos 2 (AZSM) cos (AZ - AXI)Wh
Z gyro drift effects
_XI = -NBDZ sin (AZ - AXI)/Wh
-ADSRAZ (g) sin (AZSM) sin (AZ - AXI)/Wh
-ADOAZ (g) cos (AZSM) sin (AZ - AXI)/Wh
Vertical Erection Errors
_YI = -ACBZ/g (cos (AXI) + sin (AZSM) sin (AXD)
-ACBY/g cos (AZSM) sin (AXI)
-(SFEY + SFEX) (sin (AZSM) cos (AZSM) sin (AXI))
_ZI = -ACBZ/g (sin (AX[) - sin (AZSM)cos (AXI))
+ACBY/g cos (AZSM) cos (AXI)
-(SFEY- SFEX) (sin (AZSM) cos (AZSM) cos (AXI))
where Wh = WIE cos (Lat) (earth's rate horizontal component)
AZ = azimuth angle of Z[ from north
g = acceleration due to gravity
NOTE: Aximuth alignment errors due to vertical gyro drift rate effect are not
included in above equations.
7-24
'I_ • --- ---- --. I • ilrll_- --
Table 7. 13 gives summary data on S.M. drifts and misalignments for various
event times throughout the LM-1 flight.
7.12 PIPA Saturation Effects
Because of the possibility that one of the IMU accelerometers (PIPAs) might
saturate during the earth launch trajectory, a special study was made of this problem.
For the S.M. orientation of AXI = 40 ° and AZSM = -30 ° the maximum accelera-
tion sensed during earth boost was 3.06 g's by the Y PIPA. This is sensed shortly
before S1B cutoff. Since the PIPA does not saturate unless the input acceleration
exceeds 3.3 g's, it is clear that under nominal conditions there will be no PIPA
saturation. However, with non-nominal conditions or with other Stable Member orien-
tation, the peak acceleration input could well exceed the PIPA saturation level. This
is indicated by the fact that the maximum vector acceleration reached during boost is
4.2 g's.
Although the Y PIPA will not saturate with the above S.M. orientation, a study
was made with the assumption that the Y PIPA had actually saturated at 2.82 g's.
This was 85% of its nominal saturation level (3.3 g's) and 92% of the peak acceleration
(3.06 g's) sensed by the Y PIPA. With this saturation level the AV lost by the Y
PIPA was 15.1 ft/sec.
Table 7.15 gives the indication uncertainties at SIVB cutoff and subsequent
events due to this particular AV loss. Comparison of these uncertainties with the
position and velocity uncertainties due to one-sigma IMU uncertainties given in Table
7.7 shows that a AV loss exceeding 15 ft/sec cannot be tolerated. Table 7.15 was
prepared for an earlier revision of this chapterp hence the slight discrepancies in
trajectory event times.
7.13 Trajectory Data for Error Studies
Error studies were made on the basis of trajectory data furnished in Volumes
I and II of "Apollo Mission AS-206 Spacecraft Operational Trajectory" prepared for
MSC-Houston by TRW Systems, (Vol. I date was Feb. 1967, Vol. II date was April
1967.)
Table 7.16 summarizes the trajectory data significant from the error study
point of view. Delta V (AV) is the integral of thrust acceleration.
7.14 Error Computation Procedure
The position, velocity and other uncertainties given in the error tables were
computed as follows. Approximate error equations describing the effect of IMU
component errors on acceleration indication error were incorporated in a computer
program. These equations included the effect of the position error on the computa-
tion of gravity. Through two successive integrations, errors in indicated trajectory
7-25
position and velocity could be obtained. The assumptions underlying the use of tbese
equations were (I) the errors were small relative to the parameters being measured,
and (2) the IMU component errors were statistically independent of each other.
Computation of the above errors required as inputs to the main computation
program two sets of vectors, one for spacecraft acceleration and the other for its
position. These were generated in a separate program where a nominal trajectory
was simulated. At significant events, such as powered trajectory cutoff, detailed
error printouts were made.
Perigee altitudes were computed as follows. For different points in coast
following burn cutoff the rss of the altitude uncertainties due to IMU uncertainties
propagated to that point in orbit was subtracted from the nominal orbit altitude to
obtain the altitude with adverse rss uncertainties. The point in orbit where this alti-
tude was at minimum was termed the altitude of closest approach or the perigee
altitude with i_ uncertainties. A spherical earth was assumed. The same proce-
dure was followed with 3_ uncertainties.
7.1 5 Error Table Definitions
Definitions of Local Vertical Axes - Most of the error tables give position and
velocity uncertainties relative to actual local vertical axes at nominal event time.
(Indicated local vertical axes are used at SIVB cutoff and in following coast.) Note
that actual local vertical axes are displaced from nominal local axes by the angle sub-
tended by the range error. (In previous reports the uncertainty tables were given
relative to nominal local vertical axes. For large range uncertainty the altitude rate
uncertainty also becomes large when expressed relative to nominal local axes.)
Altitude Outward along R at event time
Track Along V × R
Range Along Altitude × Track
Symbols for IMU Uncertainties
Accelerometer Bias Uncertainty
ACBX X accelerometer bias, etc.
CM/S. SQ. centimeters/see 2
Aeeelerometer Scale Factor Uncertainty
SFUX X aecelerometer scale factor uncertainty, etc.
PPM parts per million
Accelerometer Acceleration-Squared Indication Uncertainty
NCXX X accelerometer accel, squared indic,uncert., etc.
MG/GSQ micro-gs/g squared
7-26
Gyro Bias DriftNBDXINITNBDXFLGTNBDXCOMBMERU
Effect on initial S.M. misalignmentEffect of X gyrodrift during burnTotal or combinedeffects of K gyro bias driftMilli-earth rate unit = 0.015deg/hour
Gyro Acceleration SensitiveDriftADX-Terms RSSof uncertaintiesdueto X gyro's ADIAX, ADSRAX,
andADOAXdrift uncertainties. Uncertainty values for
ADIAX and ADSRAX are given in position and velocity
uncertainty tables. (See Section 7.6 for gyro drift rate
definitions. )
MERU/G Milli-earth rate unit/g = 0. 015 deg/hour/g
Gyro Acceleration Squared Sensitive Drift
ADIXX X gyro accelerationsquared sensitive drift due to
acceleration along its input axis
ADSYY Y gyro accelerationsquared sensitive drift due to accel-
eration along its spin reference axis
ADIZZ Z gyro acceleration-squared sensitive drift due to accel-
eration along its input axis
MERU/GSQ Milli-earth rate unit/g 2 = 0.01 5 deg/hour/g 2
7-27
Table 7. 7LM-1 Mission Uncertainty Summarywith Block II IMU Uncertainties
Event
Launch
SIVBCutoff
DPS1
Cutoff
DPS2
Ignition
APS1
Cutoff
At Perigee
in FollowingCoast
APS2
Ignition
APS2
Cutoff
At Perigee
in Following
Coast
Update ?
None
None
None
Bef. DPS1
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPSI
None
Bef. DPS1
Bef. APS2
None
Bef. DPS1
Bef. APS2
None
Bef. DPSI
Bef. APS2
i
RSS Position
Uncertaintyn. miles
Track Range
0
0.4
69.2
0.3
64.2
0.6
57.6
2.1
57.4
20.1
64.3
96.1
0.3
59.0
91.5
0.9
123.8
23.8 213.9
0.2 66.0
Alt.
0
10
18
2
38
56
38
60
29
32
2
82
117
47
RSS Velocity
Un certainty
ft/sec
Aft.
0 0
0.4 5.6
3.7 16.6
0.03 0.03
5.6 8.2
0.6 0. i
4.4 7.0
2.9 0.6
4.3 7.3
16.7 1.0
6.0 5.4
1.1 0.5
0.1 0.1
3.8 12.9
4.2 23. O
1.3 O.2
17.4 i0. 1
30.0
16.6
85
106
52
Track Range
0 0
132 9
72 29
1 1
125 I 33
1 3
99 27
7 21
98 27
3 82
104 32
8 26
0 1
123 31
51 35
5 26
136 93
12 173
5 88
7-28
o,
}
Event
Launch
Table 7.8
LM-1 Flight Uncertainties With No Navigation Update
with Block I! IMU Uncertainties
Time
From
Launch
secs
Altitude RSS Position
above earth Uncertainties
with ad- n._ milesverse rss --I
uncertain- AI_. i_a_ Rangeties
n. miles I,|
0 --- 0 0 0 0 0 0
RSS Velocity]
Uncertainties:
ft/sec
Alt. Track Range
SIVB Cutoff 591 87.7 0.4 5.6 0.4 10 132 9
At perigee
DPS1 ignit.
DPS1 cutoff
591 87.7 0.4 5.6 0.4 10 132 9
14,394 112.6 3.8 16.1: 68.8 14 77 31
14,440 112.1 3.7 16.6 69.2 18 72 29
DPS2 ignit.
DPS2 cutoff
16,606 164.0 5.6 8,2 64.2 9 125 33
17,334 163.0 4.4 7.1 57.6 38 99 28
APS1 cutoff
At perigee
APS2 ignit.
APS2 cutoff
At perigee
17,340 163.0 4.4 7.0 57.6 38 99 27
17,361 162.9 4.3 7.3 57.4 38 98 27
22,412 163.8 6.0 5.4 64.3 29 104 32
22,843 165.9 3.8:12.9! 59.0 82 123 31
25,774 108.8 17.4 10.1123.8 85 136 93
Other RSS
Uncertainties*
(u) V (U)7 (U) rNCft/sec ideg. deg.
i i ,.
0 0 0
9.0 0.02 0.31
9.0 0.02 0.31
:31. 1 0.03 0. 31
:29. 3 0.04 0.31
33.2 0.02 0.31
27.6 0.08 0.25
27. 5 0.09 0.25
26. q 0.09 0.25
32.0 0.07 0.25
31.5 0. 19 0. 35
93. 1 0. 19 0.35
_(U)V - uncertainty in inertial velocity magnitude
(U)7 - uncertainty in inertial flight path angle
(U)INC - uncertainty in orbit inclination
7-29
_ . P
Event
Table 7.9
LM-1 Flight Uncertainties With Navigation Update
Just Before DPSI Ignition with Block II IMU Uncertainties
Altitudeabove earth RSS Position RSS Velocity
Time with ad- Uncertainties I Uncertaintiesfrom verse rss n. miles ft/secLaunch uncertain-
secs. tiesn. miles Alt. TrackRange Alt. rracl Knge
Other RSSUncertainties_, -"
(U)V (U)_ (U)_NC
Launch
SIVB cutoff 591 (See Table 7.8)
At perigee 591
DPSI ignit.
DPS1 zutoff
DPS2 ignit.
DPS2 cutoff
14,394 116.4 0.031 0.03 0.30 2.2 0.3
14,440 115.9 0.03 0.03 0.31 2.2 1.0
16,606 168.9 0.56 0.08 0.64 1.2 0.8
17,334 164.6 2.84 0.591 2.09 54.9 6.6
0.9 0.9 .005 .001
0.9 0.9 .005 .001
2.8 2.8 .003 .002
20.6 20.6 .13 .017
APS1 cutoff
At perigee
APS2 ignit.
APS2 cutoff
At perigee
17,340 164.5 2.89 0.60 2.10 55.5 6.7
18,586 153.2 16.67 1.0120.13 59.7] 3.5
22,412 168.7 1.05 0.48 96.07 31.9 7.6
22,843 165.3 4.2222.9691.48 116.7_.5
25,774 99.8 29.9523.7721& 9 105.611.7
20.6 20.6 .13 .017
82.4 82.4 .14 .017
25.6 25.6 .07 .019
35.0 35.0 .25 .381
173.11172.9 .24 .381
(U)V
(u)_
(U)rNC
- uncertainty in inertial velocity magnitude
- uncertainty in inertial flight path angle
- uncertainty in orbit inclination
7-30
Event
Launch
SIVB cutoff
At perigee
DPS 1 ignit.
DPS1 cutoff
DPS2 ignit
DPS2 cutoff
!APS1 cutoff
!At perigee
APS2 ignit.
APS2 cutoff
At perigee
TimefromLaunch
seas.
0
591
591
14, 394
14, 440
16,606
17, 334
17, 340
17, 361
22,412
22,843
25,588
Table 7.10
LM-I Flight Uncertainties With Navigation UpdateJust Before APS2 Ignition with Block IIIMU Uncertainties
Altitude
above earth RSS Velocitywith ad- Uncertainties
verse rss ft/secuncertainties
n. miles Alt. Tra Rnge
RSS PositionUn ce rtaintie s
n. miles
Alt. rrad_ Rang_
Other RSSUncertainties*
(u)v (u)_ DINC
(See Table 7.8)
169.7 0.09 0.07 0.35 2.1 0.4 0.5 0.5 .001 .001
168.4 1.31 0.22 0.9146.5 5.0 25.825.8 .ii .012
110.7 16.6 0.25!66.0 51.9 5.088.388.3 .12 .012
(u)v
(u)_
(U)INC
uncertainty in inertial velocity magnitude
uncertainty in inertial flight path angle
uncertainty in orbit inclination
7-31
Table 7.11
Initial Azimuth Alignment Uncertainties Due to Gyro DriftRate Uncertainties For Different Stable Member Orientations
Error
Source
NBDX
NBDY
NBDZ
ADIAX
ADSRAX
A DOAX
A DIAY
ADSRAY
A DOAY
ADIAZ
ADSRAZ
ADOAZ
One SigmaUncert.
Value
2 meru
2 meru
2 meru
8 meru/g
5 meru/g
1 meru/g
8 meru/g
5 meru/g
1 meru/g
8 meru/g
5 meru/g
1 meru/g
{
RSS
S. M. AnglesAXI =
AYIP=
AZSM =
Alighment Uncertainty about Azimuth -millirad.
0 0
0 -90
0 0
0.146 2. 162
0.702 0.702
-2. 162 0.146
0. 583 0
0 0
0 -i. 081
0 0
0 1.756
O. 351 0
0 -0. 583
0 0
-i. 081 0
2. 623 3. 137
4O
0
0
0.146
1.928
-1.205
0. 583
0
0
0
0
0.964
0
0
-0.602
2.623
0
0
-30
-0.351
0.608
-2.162
-1.217
0. 439
0
1. 217
0
0. 263
0
2. 702
-0. 936
4.077
40o-30 °
-0.964
1.669
-1.205
-3.339
1.205
0
3.339
0
0. 723
0
1.506
-0.522
5.660
NOTE: I. The assumed drift rate uncertainties are Block If.
2. These alignment uncertainties do not include the vertical gyrodrift rate effect.
7-32
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7-33
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7 -34
Table 7.14
Perigee Errors in Coast Following Earth Orbit
Insertion with Active (Contingency Case) LM-1 Guidance
ResultingAssumed Perigee
IMU Error Value ErrorError (Block II) (feet)
MLMXI 50 secs 35
MLMYI 5 secs -107
MLMZI 5 secs -3
MXAY** 28.3 secs -470
MXAZ 21.2 secs 469
MYAX 28.3 secs 487
MYAZ 7.1 secs -61
ACBX 0.2 cm/sec 2 602
ACBY 0.2 cm/sec 2 1,353
ACBZ 0.2 cm/sec 2 1,033
SFEX 116 PPM -99
SFEY 116 PPM -640
SFEZ 116 PPM -139
NBDX 2 meru -58
NBDY 2 meru 174
MBDZ 2 meru -262
ADIAX 8 meru/g -180
ADIAY 8 meru/g 207
ADIAZ 8 meru/g 332
ADSRAX 5 meru/g 8
ADSRAY 5 meru/g 212
ADSRAZ 5 meru/g 516
IMU Errorthat results in a
1 n. mile Perigee Error
large
284 secs
large
366 secs
274 secs
353 secs
706 secs
2.0 cm/sec 2
O. 9 cm/sec 2
1.2 cm/sec 2
7, 130 PPM
1, 100 PPM
5, 060 PPM
208 meru
70 meru
46 meru
270 meru/g
235 meru/g
147 meru/g
3, 900 meru/g
143 meru/g
39 meru/g
_'MLMXI denotes S.M. misalignment about XI, etc.
**MXAY denotes X accelerom. IA misalignment about YSM.
Given errors are for combined initial MLM and in-flight effects.
7-35
_m
__ ....... ImImI | I_
Table 14a
Instantaneous Perigee Uncertainties for Premature APS2 BurnCutoff with 1 _ Block II IMU Uncertainties for No Update, andfor Updates before DPS1 Burn and before APS2 Burn.
Time fromAPS2 Burn
Ignitionsecs
-3.5
0
3O
60
90
120
150
180
210
24O
270
300
330
360
390
420
427.2
NominalInstantaneousPerigeeAltituden. miles
168 8
168 7
158 4
138 5
118 7
100 3
84 4
71 3
61 5
55 5
53 8
57 2
66 5
82 8
107, 7
120.0
127.7
Attitude Uncertainty atInstantaneous Nominal Perigee in n. miles
With
No Update
3.9
6.7
7.8
8.5
9.1
9.8
10 6
116
12 1
12 9
13 7
14 6
15.4
16.3
17.0
17.1
With Update BeforeDPS1 Burn Ign.
4.1
157
17 0
17 7
18 5
19 4
2O 4
21 4
22 4
23 4
24 3
25 0
25 4
25 2
22 0
18 5
With Update BeforeAPS2 Burn Ign.
0
1.1
2.3
3.5
4.6
5.8
7.0
8.2
9.4
10.6
11.9
13.1
14.2
15.2
15.0
13.6
Note: Altitude uncertainties are computed for nominal perigee location in orbit.Computations are approximate in that the effect of altitude uncertainties on perigeelocation were not considered as they were in Tables 7.1 and 7.2.
7-36
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7-37
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7-38
Error Tables with Block II IMU Uncertainties
Table 7. 17
Table 7. 18
Table 7.19
Table 7.20
Table 7.21
Table 7.22
Table 7.23
Table 7.24
Table 7.25
Table 7. 26
Table 7.27
Table 7.28
Table 7.29
Table 7. 30
Table 7.31
Table 7.32
Table 7.33
Table 7.34
Table 7. 35
Table 7. 36
Table 7. 37
SIVB Cutoff Indication Uncertainties
SIVB Cutoff Indication Uncertainties (AD Terms)
IMU S.M. Misalignments and Drift Angles at SIVB Cutoff
Flight Uncertainties at APS1 Cutoff-No Update
Flight Uncertainties at
Flight Uncertainties at
Flight Uncertainties at(AD Terms)
Flight Uncertainties atBefore DPS1 Burn
Flight Uncertainties atBefore DPS1 Burn (AD
Flight Uncertainties at
Flight Uncertainties at
Flight Uncertainties at
Flight Uncertainties atTerms)
Flight Uncertainties at
Flight Uncertainties at(AD Terms)
Flight Uncertainties atBefore DPS1 Burn
Flight Uncertainties at
APS1 Cutoff-No Update (AD Terms)
APS1 Cutoff with Update Before DPS1 Burn
APS1 Cutoff with Update Before DPS1 Burn
Perigee After APS1 Cutoff with Update
Perigee After APS1 Cutoff with UpdateTerms)
APS2 Cutoff-No Update
APS2 Cutoff-No Update (AD Terms)
Perigee After APS2 Cutoff-No Update
Perigee After APS2 Cutoff-No Update (AD
APS2 Cutoff with Update Before DPS1 Burn
APS2 Cutoff With Update Before DPS1 Burn
Perigee After APS2 Cutoff With Update
Perigee After APS2 Cutoff With UpdateBefore DPS1 Burn (AD Terms)
Flight Unce rtainties at APS2 Cutoff with Update Before APS2 Burn
Flight Uncertainties at APS2 Cutoff With Update Before APS2 Burn(AD Terms)
Flight Uncertainties atBefore APS2 Burn
Flight Uncertainties atBefore APS2 Burn (AD
Perigee After APS2 Cutoff With Update
Perigee After APS2 Cutoff With UpdateTerms)
7-39
Error Tables With Latest Measured IMU Uncertainties
Table 7.38
Table 7.39a
Table 7.39b
Table 7.40
Table 7.41
Table 7.42
Table 7.43
Table 7.44
Table 7.45
Table 7.46
Table 7.47
Table 7.48
Table 7.49
Table 7.50
Table 7.51
SIVB Cutoff Indication Uncertainties
IMU S.M. Misalignments and Drift Angles at SIVB Cutoff
IMU S. M. Misalignments and Drift Angles at SIVB Cutoff
Flight Uncertainties at APS1 Cutoff - No Update
Flight Uncertainties at APS1 Cutoff With Update Before DPS1 Burn
Flight Uncertainties at Perigee after APS1 Cutoff with UpdateBefore DPS1 Burn
Flight Uncertainties at APS2 Cutoff - No Update
Flight Uncertainties at Perigee After APS2 Cutoff - No Update
Flight Uncertainties at Perigee After APS2 Cutoff - No Update(AD Terms)
Flight Uncertainties at APS2 Cutoff with Update Before DPS1 Burn
Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore DPS1 Burn
Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore DPS1 Burn (AD Terms)
Flight Uncertainties at APS2 Cutoff with Update Before APS2 Burn
Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore APS2 Burn
Flight Uncertainties at Perigee After APS2 Cutoff with UpdateBefore APS2 Burn (AD Terms)
7-40
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LAUNCH VERTICALI
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Fig. 7-6 Apollo 5 LM Orbit and Burn Sequence
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DEFINITION OF POSITIVE SENSE
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IRIG ORIENTATION
Block II G&N
DF_II_I/_!QN Ota PO._ITI_E ,SENSE
IRIGi INP U_]-AX_S _I I]_ LIGNM_ENtTSwith respect to
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Fig. 7-9
7-83
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Angle in Sec
Term IMU 6
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IMU 11
-28
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J.A., n n.l hp, L LTi Al .......*_,,%_i _ u .......
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X
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IRIGs
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IRIGs
X
Y
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7 -85
A n --m
Dictionary of Terms
ACC
ACD
ADOA
AV ACC
AV RT
Blank
BIA
BCSW
CRQ
CDN
CVR
DGI
I_S
G&N
GP
HBS
I&A
IG CDU PROBLEM
KSC
LBS
LNO
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NBS
OOS
PRE ACC
RESIS CHG
RET
s/cSCK
SF, SFA
SPO
SPR
SVM
VIB
WCM
5PT
Acceptance of Data
After Cooldown
Acceleration Sensitive Drift Due to Acceleration along the OA
Average of Acceptance Data
Average of Retest Data
12 Day Storage
Bia_ Adjusted
Binary Current Switch
Component Re qualification
Post Cooldown
Component Verification
Degaussed IRIG
Degaussed
Guidance & Navigation System Measurement
Gaussed PIPAs
Hi Buss Voltage
Inspection and Acceptance
Inner Gimbal CDU Problem
Kennedy Space Ccntcr
Lo Buss Voltage
I_op Not Open
North American Aviation
Nominal Buss Voltage
Out of Spec
Pre Acceptance Data
Resistor Changed
Rete st
Spacecraft
ISS Check
Scale,Factor, Scale Factor Adjusted
ISS Post Vibration
ISS Pre Vibration
ISS Post Visual/Mechanical Inspection
After Vibration
Recheck After Welding Calibration Module
5 Point Test
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STANDARDDEVIATION(I_) OF THE IRIGANDPIPAPARAMETERUNCERTAINTIESUSEDFOR
MISSIONPERFORMANCESUMMARY(Corrected for ADOA)
IMU S/N 6
PARAMETER
IMU Axis PIPAsDataCompilationPeriodAccelerometer Bias (era/see2)
Scale Factor (ASF/SF ppm)
X Y Z
(6/26-i 1/26/67) (6/26- 11/26/67) (6/26-11/26/67)
+.08 +.06 +.10
(2/3/67-11/26/67)
92 45 76
IMU Axis IRIGs
Data Compilation Period
Bias Drift (MERU)
ADSRA (MERU/g)
ADIA (MERU/g)
X Y Z
(6/14-11/26/67) (6/14-11/26/67) (6/12-11/26/67)
1.3 2.3 2.4
2.2 2.7 1.2
5.1 6.0 5.8
Data is based uponperformance in,the IMU. Point-to-point stability in operation
is much better than the above data. The error computation for Mission 204 uses the
above data.
Accelerometer data taken prior to degaussing following incorrect procedures
has been excluded.
Current (11/26/67) Inertial Compensation Parameters are corrected for ADOA
and tablutated:
PARAMETER
X
Accelerometer Bias (cm/sec 2) +. 21
Scale Factor (ASF/SF ppm) -237
Bias Drift (MERU) -4.9
ADSRA (MERU/g) +5.7
ADIA (MERU/g} -35.6
Gyro data is the average of all KSC data.
degauss at KSC.
7-124
IMU AXIS
y Z
.10 +.08
-229 -444
-4. 7 -3.8
+0. 5 -1.0
-20.0 -1.6
PIP data the averages after last
2 _W i_ w
CORRECTIONS FOR THE ADOA DRIFT TERM
A drift term proportional to the acceleration along the output axis {ADOA}
is evident in the Apollo Gyro.
Due to the mechanization of G&N and spacecraft tests a factor times this
term is included in the NBD, ADSRA, and ADIA measurements. Table 7-52 gives
the drift values measured for each test configuration.
The Gyro data tabulation shown on pages 7-87, 88, 90, 92 and 93 include
the ADOA errors in each test configuration Table 7-52 shows. The Gyro curves
on pages 7-89, 91, and 94 and the standard deviation calculated for page 7-124
have been corrected for these ADOA errors.
A tabulation for the ADOA releases are given on page 7-127.
7 -125
Table 7-52
ERROR IN GYRO DRIFT TEST DUE TO ADOA TERM
FOR VARIOUS TEST CONFIGURATIONS
Drift TermMea sure d
NBD
ADSRA
ISS Test G&N Test Spacecraft
NBD X NBD x + ADOA X NBD X + ADOA X
NBDy NBDy + ADOAy NBDy + ADOAy
NBD Z NBD Z - ADOA Z NBD Z - ADOA Z
ADSRAx ADSRA X - ADOA X ADSRA X + 0. 414 ADOA x
ADSRAy ADSRAy - ADOAy ADSRAy - ADOAy
ADSRAz ADSRA Z - ADOA Z ADSRA Z - 2. 414 ADOA Z
ADIA ADIA x ADIA x + ADOA x ADIA x + ADOA X
ADIAy ADIAy + ADOAy ADIAy + 2 ADOAx- 0. 414 ADOAy
ADIA Z ADIA Z _ ADOA Z ADIA Z + ADOA Z
7-126
j
Table 7-53
The ADOA data included in the G&N NBD measurements are tabulated below:
ADOA
IMU S/N 6
, 12113166 1/17/67 2/5/67 3/11/67 AverageX
0.89 I. 52 1.31 0.46 I. 0
Y7/17/67 7/31/67
I. 57 0.89 1.23
Z12/28/66 1/17/67 2/5/67 3/ii/67
2.24 0.93 0.73 i. 24 1.28
_'7A97 had ADOA of 1.60 meru on 12/13/66 for calculation of correction toS/C ADIA on 1/17/67.
7-127
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:ii
);1
.,,:;!T
iil
0
7-131
Internal
R. Battin
G. Cherry (2)
E. Copps
W. Cooper
J. Dahlen
J. Dunbar
G. Edmonds
P. Felleman
J. Fleming
E. Gardner
L. Gediman
R. Gilbert
K. Greene
F. Grant
J. Hand
P. Heinemann
Letter of transmittal only
R-527 SUNBURST
Section 7
D. Hoag
M. Johnston
* J. Kingston
A. Klumpp
W. Kupfer (2)
A. Laats
L. Larson
R. Larson (3)
J. Lawrence
D. Lic k.ly
H. Little
R. Lones
F. Martin
G. Mayo
R. McKern
J. S. Miller
J. E. Miller (25)
R. Morth
J. Nevins
P. Philliou
R. Ragan
N. Sears
J. Shillingford
G. Stubbs
M. Sullivan
J. Suthe rland
W. Tempelman
R. Tinkham
J. Vittek
R. White
W. Widnall (3)
R. Weatherbee
Apollo Library (2)
MIT/IL Library (6)
Rev. 2 -12/67
MIT Instrumentation Laboratoryc/o North American Aviation, Inc.Space and Information Division12214 Lakewood BouIevardDowney, California 90241Attn: Mr. Thomas A. Hemker
MIT Instrumentation LaboratoryG&N Systems Laboratoryc/o Grumman Aircraft Engineering Corp.
LM Project - Plant 25Bethpage, Long Island, New YorkAttn: (TOD)
MIT Instrumentation LaboratoryP.O. Box 21025Kennedy Space Center, Florida 32815Attn: (TOD)
MIT Instrumentation LaboratoryCode EG/MIT Building 1 6NASA Manned Spacecraft CenterHouston, Texas 77058Attn: (TOD)
John F. Kennedy Space CenterNASA MSC HWBldg. M7 - 409FloridaAttn: Frank Hughes
Mr. A. Metzger (NASA/RASPO at MIT/IL)
AC Electronics DivisionGeneral Motors CorporationMilwaukee, WisconsinAttn: Mr. J. Stridde, Dept. 32-21Attn: Mr. Reino K arell
(13)(2)
Kollsman Instrument Corp.575 Underhill Boulevard
Syosset, Long IslandAttn: Mr. F. McCoy
Raytheon CompanyBoston Post RoadSudbury, Massachusetts 01 776Attn: Mr. C. Bradshaw
NASA/RASPO /NAA
KSC
National Aeronautics and Space AdministrationResident Apollo Spacecraft Program OfficeNorth American Aviation, Inc.Space & Information Systems Division12214 Lakewood BoulevardDowney, California
National Aeronautics and Space AdministrationJohn F. Kennedy Space CenterJ. F. Kennedy Space Center, Florida 32899Attn: Technical Document Control Office
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(10)
(1)
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(3)
HDQ NASA Headquarters600 Independence Ave. SWWashington, D.C. 20546Attn: MAP-2 (4)Attn: Mission Director, Code MA (1)Attn: Robert Aller, Code MAO (1)
(6)
AMES: National Aeronautics and Space AdministrationAmes Research CenterMoffett Field, CaliforniaAttn: Library
(2)
LEWIS: National Aeronautics and Space AdministrationLewis Research CenterCleveland, OhioAttn: Library
(2)
FRC: National Aeronautics and Space AdministrationFlight Research CenterEdwards AFB, CaliforniaAttn: Research Library
(1)
LRC: National Aeronautics and Space AdministrationLangley Research CenterLangley AFB, VirginiaAttn: Mr. A. T. Mattson
(2)
GSFC: National Aeronautics and Space AdministrationGoddard Space Flight CenterGreenbelt, MarylandAttn: Mr. Paul Pashby, Code 554
(2)
ERC: National Aeronautics and Space AdministrationElectronics Research Center575 Technology SquareCambridge, MassachusettsAttn: Mr. R. Hayes/Mr. A. Colella
(1)
GAEC: Grumman Aircraft Engineering CorporationBethpage, Long Island, New YorkAttn: Mr. C. Brown (10)
Mr. R. Adarnato (3)Mr. B. Sidor (1)Mr. H. Sherman (3)Mr. E. Stern (1R)Mr. R. Fleisig (I)Mr. G. Smith (I)Mr. R. Pratt (4)
(23 + 1R)
NAA North American Aviation, Inc.Space & Information Systems Division12214 Lakewood Boulevard
Downey, California 90241Attn: Apollo Data Requirements
Dept. 096-340Building 3, CA 99
(1 + IR)
\
NASA/RASPO/National Aeronautics and Space Administration
GAEC Resident Apollo Spacecraft Program Officer
Grumman Aircraft Engineering Corporation
Bethpage, Long Island, New York
NASA/ RA SPO/ACED
National Aeronautics and Space Administration
Resident Apollo Spacccraft Program Officer
Department 32-31AC Electronics Division of General Motors
Milwaukee, Wisconsin 53201
Attn: Mr. W. Swingle
WSMR: National Aeronautics and Space AdministrationPost Office Drawer MM
Las Cruces, New Mexico
Attn: RH4 Documentation
MSFC: National Aeronautics and Space Administration
George C. Marshall Space Flight CenterHuntsville, Alabama
Attn: J. Mack R-ASTR- 5 (1)
H. Ledford R-AERO-P (2)
L. McNair R-AERO-P (1)
T. Telfer R-AERO-DA (2)
E. Deaton R-AERO-DA (1)
J. Cremin R-AERO-DAP (i)
L. Stone R-AERO-F (1)
C. Hagood R-AERO-F (I)
O. Hardage R-AERO-FM (I)F. Moore R-ASTR-N (1)
S. Seltzer R-ASTR-NG (5)
H. Hosenthien R-ASTR-F (i)
A. McNair I-MO-R (l)
D. Germany I-I/IB-E (1)R. Barraza I-V-E (I)
W. Chubb R-ASTR/NG (I)
J. McCullough I-VE/T (1)
MSC:
BELLCOM M:
National Aeronautics and Space Administration
Manned Spacecraft Center
Apollo Document Control Group (PA 2)
Houston, Texas 77058
Attn: A. Alber, FS5 (letter of transmittal only)
(Above includes information copy for PD-6;letter PP7-66-775)
Bellcomm, Inc.11 00 17th Street N. W.
Washington, D.C. 20036
Attn: Info. Analysis Section
LINK : Link Div. of GPI
Hillcrest
Bingham, New YorkAttn: Mr. Fred Martikan
TRW: TRW Systems
1 Space ParkRedondo Beach, California
Attn: Mr. R. A. Evans, Bldg. 2Room 2044
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I00 +2R)
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(3)
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