guddance and navigation - ibiblio analysis...errors that would result from gyro performance...
TRANSCRIPT
.. 4 I DECLASSIFI
GUDDANCE AND NAVIGATION
Approved: a. * Date: ;/+q Mil ton B. Trageser, Mrector Apollo Guidance & Navigation Program
Approved ate:- ector
(Unclassified Title) E- 1473
ANALYSIS OF LEM MISS ION INERT I AL UNCERTAINTIES
by John M. Dahlen
Malcolm W. Johnston December 1963
I I I N ST R l J M E N TAT I 0 N
LAElORATORV CAMBRIDGE 39, MASSACHUSETTS
COPY# 7 OF W C O P I E S THIS DOCUMENT CONTAINS 7& PAGES
1 -
e ”
1
ACKNOWLEDGMENT
Helpful cooperation throughout this study was obtained f rom F. Grant, R. Brown, and R. Goss, all of the M . I . T . Instru- mentation Labor at o r y .
This report was prepared under DSR Project 55-191, spon-
sored by the Manned Spacecraft Center of the National Aero- nautics and Space Administration through Contract NAS 9- 153 .
This document the national defe States within the meaning of th Laws, Ti t le 18,
U. S. C . , Sections 793 e t ransmission or the revelation of nner to an unauthorized pe
The publication of this report does not constitute approval by the National Aeronautics and Space Administration of the
findings or the conclusions contained therein.
for the exchange and stimulation of ideas.
It is published only
2
c
E-1473
ANALYSIS OF LEM MISSION INERTIAL UNCERTAINTIES
ABSTRA.CT
The major sources contributing to LEM position and velocity uncertainties at perilune, hover, and burn-out are in- dividually investigated. ponent uncertainty through these phases a lso se rves as a common
basis upon which the following alternate inertial schemes a r e compared:
The format utilized to t r ace each com-
1. Gimballed v s gimballess iner t ia l measurement unit,
2 . Crude vs precision gyros,
3. Inertial realignment between injection and perilune vs no realignment.
by John M. Dahlen Malcolm W. Johnston
December 1963
3
TABLEOFCONTENTS Page
I LISTOFSYMBOLS. , , , , . . . . . , . . . . . . . 7
I1 INTRODUCTION , . , , . . , e . , : . , , . . 9
111 DISCUSSION , . , . , I . e . . . , . . , . . . - . 13 Orbital Navigation Uncertainties . , . . . . . . 1 3
LEM Inertial Uncertainties . o , a . . I . . . . 1 3
Illustrative Example . , . , . . . . . . . 13
IV CONCLUSIONS. , . . . I , . a , , . . . . + , . . 1 7
V REFERENCES. , . . , . I . , . . . . . , . 1 9
VI APPENDICES , . , . . , , . . , ._ - . . . . . . . 2 7
A. Analysis I GIMU - Precis ion Gyros -
B, Analysis I1 IMU - Precis ion Gyros -
C. Analysis I11 GIMU - Precis ion Gyros -
D. Analysis IV IMU - Precis ion Gyros -
Realignment . . . . e . . 2 7
Realignment . , . . . . 41
No Realignment. . , . . . . 43
No Realignment. , . . .) , 53 E Analysis V GIMU - Crude Gyros -
Realignment . . I . I 55 F. Analysis VI GIMU - Crude Gyros -
G.
No Realignment. . . , . . , 61
Description of Descent and Ascent Trajectory P a r a m e t e r s . . . . , . . a . e . _I . , . * * 67
5
I LIST OF SYMBOLS
IMU
GIMU
BDX, BDY, BDZ
ACBX, ACBY, ACBZ
SFEX, SFEY, SFEZ
MLM
In j
P e r
Hov
Gimballed inertial measurement unit
Gimballes s inertial measurement unit
Range , t rack, altitude uncertainty
Range ra te , t rack rate, altitude ra te uncertainty
Bias drift about x, y, z axes
A.ccelerometer bias along the x, y,
z axes
Accelerometer scale factor uncer- tainty along the x, y , z axes
Misalignment
Inject ion
P e r ilun e
Hover
7
t
.
ANALYSIS O F LEM MISSION INERTIAL UNCERTAINTIES
I1 INTRODUCTION
The major sources contributing to position and velocity
uncertainties during a LEM mission are investigated.
A format is presented (in the appendix) that t races the effects of each uncertainty source from injection of the LEM into its descent orbit through perilune and hover to burn-out.
The format s e rves three purposes:
1. It reveals the important sources of inertial un-
certainties and when they occur, It indicates the effects of "initial condition" o r orbital navigation uncertainties,
It se rves as a common basis for the analysis and comparison of several alternate inertial guidance schemes.
2.
3 .
Three comparisons were made:
1. 2. "Crude" vs "precision'' gyros,
3 .
Gimballed vs gimballess inertial measurement unit,
Realignment of IMU and GIMU between injection and perilune vs no realignment.
Table I summarizes the resul ts obtained when one assumes that each component uncertainty, though unknown, is constant over the entire mission profile.
resul ts if one assumes that each component uncertainty changes in random fashion from one phase to the next within the mission profile.
Table I1 shows the
A detailed analysis of each component contribution
9
f o r both tables is included in Appendices A-F. qualitatively the effects of guidance uncertainties on fuel r e - quirements. tainties f o r a normal ascent f rom the lunar surface.
Table I11 indicates
Table TV summar izes the resultant cut-off uncer-
Figure 1 il lustrates the phases of the LEM mission a s well a s indicating the coordinate systems utilized.
The body of this report w i l l be res t r ic ted to a brief discussion of the selected uncertainty sources followed by an
illustrative example of the analysis, tracing the effects of a
single uncertain.ty source through a l l mission phases.
The analyses involve L E M inertial uncertainties and
initial condition uncertainties only. external sensing during landing is considered. terminal guidance has the principal effect of nulling terminal velocity and altitude e r r o r s ) ,
No scheme employing
(External
F o r Tables I and 11, an abort f rom hover was used instead of a normal launch because the abort case appeared to be most cri t ical with respect to subsequent rendezvous maneuver
fuel requirements,
The position and velocity uncertainties listed in Tables
I and I1 a r e "Root-Sum-Square" values.
range uncertainty is the square root of the sum of the variances':' in range uncertainty due to each uncertainty source.
F o r example, the RSS
If the
::' The variance of a random variable, X, is the average value of the square of the difference between X and i t s average value, 'z- That is :
- 2 Variance (X) = (X - X)
The standard deviation o r ''one s igma variation" of X is the square root of the variance, That is:
'Vvariance (x) = STD. DEV. (x) = O ( X )
10
sources a r e independent (a valid assumption) the RSS range uncertainty is also the square root of the variance of the total range uncertainty. safely be called RMS o r 1 Q uncertainties.
The resul ts in Tables I and I1 may therefore
Certain qualifications regarding the analysis should be
pointed out. F i r s t , regarding accuracy of the GIMUs, two bias drift r a t e s were assumed to correspond to 1 1 crude" and "precision"
gyros. For "precision" gyros, 10 meru drift was used t o see the result that would occur i f gyro performance were not degraded in
the "strap-down'' environment. Fo r ' 'crude'' gyros, 66 . 7 meru (1 .0 degree/hour) drift was used t o gain feel for the t ra jectory e r r o r s that would result f rom gyro performance degradation.
While the best engineering judgment of the Apollo Staff anticipates a ser ious performance degradation in the ear ly application of the
gyro in the "strap-down" environment, there is no sound technical basis for assuming that such degradation can be t reated a s a factor of seven increase in bias drift. This treatment is simply the most
appropriate method in view of the lack of information and t ime needed for a more valid performance comparison.
Secondly, a s wil l be seen, gross t ra jectory e r r o r s associated
with 1 . 0 degree/hour gyro drift can be greatly decreased by re- alignment fifteen minutes before perilune.
that such a re-alignment , while possible, would ra ther ser iously
interfere with an otherwise order ly and comfortable sequence of
astronaut activities in preparation for the s ta r t of the powered descent. vehicle and about five minutes of t ime .
It should be understood
The re-alignment would require re-orientation of the
11
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C
I11 DISCUSSION
c \
..
This study concerns the uncertainties in position and
velocity existing at various phases of the LEM mission as a
result of orbital navigation schemes and LEM inertial instru-
mentation
analyzed (Appendices A-F) will clarify the following discussion.
Orbital Navigation Uncertainties
Reference to a summary sheet of one of the schemes
This category consists of those position and velocity un-
certainties that exist p r ior to LEM injection. the sum of all CM system uncertainties up to this point in the mission.
orbital navigation scheme - Model I - Std (Reference 1).
appearance on the summary sheet is desirable in order that LEM inertial uncertainties be kept in perspective. orbital navigation uncertainties would tend to overwhelm the LEM inertial uncertainties thus diminishing the importance of the la t ter .
They represent
The particular numbers used correspond to an M. I. T. Their
La rge r
LEM - Inertial Uncertainties
The f i r s t uncertainty source l isted under this category,
alignment, means the misalignment of the accelerometer
package which resul ts f rom s t a r tracking uncertainties, angle
read-out uncertainties, etc. Gyro bias dr i f t , accelerometer
bias, and acceierometer scale factor uncertainty constitute the most important inertial uncertainties for the LEM mission .-
though many more exist . (Reference 2 )
Illustrative Example
The example chosen to illustrate the use of appendices utilizes a GIMU with "precision" gyros and a realignment
1 3 k.
between injection and perilune. constant drift of 10 meru (0. 15 degrees/hour) of the y gyro will be t raced to burn-out,
In particular, the effect of the
(Appendix A, analysis I, BDY, page 34 )
The left hand column of this analysis sheet divides the mission into separate phases of instrument utilization, case four phases are delineated. separately, o r independently, s o that we can calculate the final uncertainties when the component uncertainty is assumed to vary from one phase to thc next.
In this
We consider each phase
Within each phase individual uncertainty sources are
listed. (It should be remembered that these a r e , in turn, a result of the single uncertainty source represented by the
particular analysis sheet, BDY in this ca se ) . The following
example may clarify the shorthand notation utilized throughout
the analyses: y Per mlm reads , "the misalignment about the y axis at perilune. 'I T o the right of each l isted source is seen its effects a t perilune, hover, and burn-out. Each of these phases
is described in more detail below.
1. Drift Between Alignment and Injection
Fifteen minutes of drift occuring between initial alignment and injection causes a misalignment about the y axis a t injection of 0.0375' (See F ig 1). Application of 373 feet/second
(essentially radial injection velocity) resul ts in a range ra te uncertainty of 0 24 feet/second at injection because of this thrust vector misalignment.
The perilune effects of this injection velocity uncertainty were obtained through free fall e r r o r propagation equations. (Reference 3 )
The perilune position and velocity uncertainties just
obtained a r e propagated to hover and burn-out by means of a
14
GIMU guidance e r r o r sub-routine'! into which is fed knowledge I I
of the descent and ascent trajectory parameters . this routine (developed by F. Grant - M, I. T. Instrumentation Laboratory) a r e used to determine all effects occurring during, o r being propagated through, any powered phase. (Description of the descent and ascent t ra jector ies used in the e r r o r sub-
routine are included as Appendix G).
The resu l t s of
2. Drift Between Realignment and Perilune
The misalignment at injection has been wiped out by the realignment performed 15 minutes before perilune.
Fifteen minutes of drift occurring between realignment
and perilune causes a misalignment about the y axis at perilune
of @. 0375'.
of this misalignment on position and velocity a t hover and
propagates these uncertainties at hover to burn-out.
The GIMU e r r o r sub-routine determines the effects
In addition, the misalignment at perilune t ransforms to
a like misalignment at hover, the effects of which are propagated to burn-out. (In this case the body and target axes coincide. A more complicated transformation is required if they don't. An x o r z misalignment at perilune resul ts in both an x and a
z misalignment at hover.
3 . Drift During Descent
During the s ix minutes of powered descent the continuous
gyro drift ra te causes position and velocity uncertainties at hover which are, in turn, propagated to burn-out.
In additinn, a misaligfiment at hover, due to the integrated
effect of gyro drift during descent, must a l so be propagated to
burn-out.
drift effects is necessary for the x and z gyros). (Again, a more complicated computation of integrated
4. Drift During Ascent
Finally, the continuous bias drift acting during the ascent
15
w i l l result in uncertainties at burn-out. Again, these a r e
obtained from the e r r o r sub-routine.
There a r e two different ways of handling the columns of uncertainty figures corresponding to perilune, hover, and burn-
out appearing on each analysis sheet. Remember that the ent i re sheet concerns a single instrument uncertainty. argued that the value of the instrument uncertainty is not the same during all phases of instrument utilization, i. e . , the drift during the injection is not the same as the drift during powered ascent, etc. Within each phase, however, it has been assumed that each component uncertainty can be assumed constant.
a s sumes that the instrument uncertainty shifts randomly from one phase to the next, it i s necessary to RSS the position and velocity uncertainties found for each phase.
It could be
If one
An alternate approach would be to consider that the un-
certainty, though unknown, is constant throughout the mission, in which case we arithmetically add the position and velocity uncertainties found f o r each phase,
Both procedures a r e followed on the analysis sheets, ' the la t ter technique is represented on Table I, the fo rmer on Table 11, The actual uncertainties wi l l , most likely, l ie somewhere between these two extremes.
1 6
IV CONCLUSION
The following remarks pr imari ly concern information appearing in summary form on Table I and 11,
Comparisons of analyses I and I1 o r 111 and IV indicate
the effects of a gimballed vs a gimballess inertial measurement
unit. Both systems yield essentially the same resul ts at perilune and hover while the gimballess system gives bet ter
resul ts at burn-out. This is a result of the fact that the body-
mounted gyros and accelerometers are flipped (as the vehicle is reoriented) a t hover so that the sense of their uncertainties
during ascent tends to cancel the uncertainties built up during
descent. This cancellation is much less pronounced i f the un- certainties are assumed to be variable (Table 11).
The effects of crude (1. Oo/hr o r 6 6 . 7 meru) v s precision 0 (0 . 15 / h r o r 10 meru ) gyros a r e found by comparing analysis
I and V o r I11 and VI. than a factor of s ix , all other effects contributing to the total uncertainty figures remain the same. Therefore, the effects of
gyro degradation a r e somewhat subdued. Nonetheless , reference to Table I indicates how significant such degradation is to hover and burn-out conditions, especially in t e r m s of C E P and burn- out velocity uncertainties.
Though the gyro bias drifts differ by more
The effects of realignment vs no realignment between injection and perilune can be seen by comparing analyses I and
111, o r I1 and IV, o r V and VI, In the f i r s t two comparisons,
where precision gyros a r e used, it is seen that the effects
pr imari ly involve la rger hover uncertainties. are employed and the system is not realigned p r io r to perilune,
If crude gyros
1 7
a poor scheme (V) becomes even worse (VI) in position and
velocity uncertainties at both hover and burn-out.
The principal differences between Tables I and I1 concern altitude and altitude ra te uncertainties. cancelled to a large extent because of the sequence of axes rotations i f one can assume constant uncertainties (Table I). The t e r m s a r e significant because they effect landing al t imeter
acquisition altitude and abort t ra jectory lofting. It is therefore important, to find a real is t ic method of analysis with respect to these te rms . inertial guidance uncertainties involve increased fuel consumption.
Table I11 attempts to point out the principal accuracy/fuel relationship without attempting to assign numerical values. The resul ts shown on Table IV suggest that a minimum time between alignment and launch is most cr i t ical , especially in a sys tem
utilizing crude gyros.
These a r e nicely
It is also important to point out that increased
Further discussion of the many ramifications of these resul ts wi l l not be attempted here.
18
V REFERENCES
* ..
1. Monthly Technical P r o g r e s s Report; P ro jec t Apollo Guidance and Navigation Program, M. I. T. Instrumentation Laboratory Report , E - 1306, Per iod
from January 11, 1963 to February 11, 1963.
2. IMU Error Data For Apollo Tra jec tor ies , F rede r i c D. Grant, M. I. T. Instrumentation Laboratory Report , E - 1 2 1 2 , September, 1962.
3. Summary of Error Propagation in an Inertial System,
Janusz Sciegienny, M. I. T. Instrumentation Laboratory Report ,E - 1388, August, 1963
19
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TABLE 111
Effects of Guidance Uncertainties
on Fuel Requirements
Guidance E r r o r ~~~
1. -Perilune Altitude
2 . Altitude late in powered descent
3, Range and t rack late in powered
descent
4, Velocity at cut-
off (Burn-out)
Effect on Fuel
Causes upward bias on nominal perilune altitude, thereby increasing landing fuel,
Defines time and altitude when al t imeter
data is required for safe guidance. Increased altitude e r r o r causes increased altimeter range requirement and ea r l i e r
acquisition which may in turn requi re earlier vehicle pitch-up with resultant landing fuel penalty.
Defines amount of terminal maneuvering
required to land on pre-determined target .
Defines amount of midcourse maneuvering required to place LEM on collision course with CSM.
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6. INJECTION MANEUVER (373 FEET/SECOND ESSENTIALLY
C. REALIGNMENT BETWEEN INJECTION AND PERILUNE
0. PERILUNE ( 5 0 K FEET)
E.
F. BURN-OUT (50K FEET)
ALIGNMENT PRIOR TO INJECTION (80 N.M. CIRCULAR ORBIT)
RADIALLY INWARD)
~~~~~ ~ ~~
HOVER (LESS THAN 1000 FEET) ~~
~~
Figure 1
25
4
VI APPENDICES
A. Analysis I GIMU - Precis ion Gyros - Realignment
The following represents a detailed outline of a n uncertainty analysis of a LEM abort f rom hover. utilized has the following character is t ics :
The system
1. 2. Precis ion gyros, 3.
Gimballess inertial measurement unit (GIMU),
Realignment between injection and perilune.
The f i r s t two pages summarize the subsequent analysis. The f i r s t summary represents the case where it has been
assumed that the instrument uncertainties a r e constant through- out the LEM mission. The second summary represents a case where instrument uncertainties a r e assumed to vary randomly throughout the LEM mission.
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0 0 - In - m l- O ) N m N O 0 0 . . 0 0 0 , 3 3 i 0
I OI
0
C
C
C
T
0
0
m 3 N W
3 0
0 0
i 4
c
.
- c
C C
C
C
C
c C
C
- C
P p.
C
C
C
I: r- c
3
-
3
3
3
3
3
3
- -
! I
n- -7-
0
to
0
" I
0 ,
o <
In o < @a
o c
-4+
0
m 0
d
3
3
n L U
3
3
>
3
3
n 3
.1
3
- p: -
c
C
C
C
C
C
C
0
0
0
0
-
4 r +2
Q 1
B
.- .r( C
N
v) t-
0
0
m
d h
0 0 0 v) 0 0 - 4
m N N 0 0 0
I- m m
d d d
4 ?~
0
N
0 0.
3 3 *
0
0 U
c
3
9
u I
- ? I
3
n ?
a U I
3
c Tc
I r
-
- I -
h m
i-
%
- 3 3
d
D
N 0
0
Lo m
0
ID
- m 0
0
0
r(
0
9
10 N
0
4 -
I
- r- r(
0 I
0
c- Lo
0 0
r- 3
C
Q:
7 - 3
3
0
0
0
0
- 0
0
C
0
C
C
-
r
- * N 0
0
t- 0
0 I
ID -r
0
(1 m
- N 3
3
0
(0 Lo
d
0 m
0
P
- c- 0
0
0
-r 0
0
- n -0
;
3
P
?
3
3
D -I
- 3
3
4
3
n
?
0 M
0
(0 m
- r- 0
0
0
-r 0
9
m m
C
lo
m m m m
0 0
I
c
.
B. Analysis I1 IMU - Precis ion Gyros - Realignment
The system analyzed i s identical to that utilized in Anal- ys i s I except that a gimballed inertial measurement unit (IMU) replaces the GIMU. The IMU analysis did not lend itself to the
detailed breakdown of Analysis I. Therefore, only a single sum- mary is included, representing the case where instrument un- certainties are assumed to be constant throughout the L E M mis- sion. Comparison of this data with that of Analysis I, Summary
A, indicates the effects of a gimballed vs a gimballess system.
41
T
d
= ? 0
3 0
m r(
d 0
W o m m
o r
C
0 :
o c < O F
.' ,
1
C. Analysis I11 GIMU - Precision Gyros - No Realignment
The system is identical to that utilized in Analysis I except that there is no realignment between injection and perilune. In addition, analyses f o r the following uncertainty sources are
identical to Analysis I. They wil l not be repeated.
ACBX ACBY ACBZ
SFEX SFEY SFEZ
43
r 0
0
r { In
r(
o m N I
LI
! 0
P-
o:
(0
0 8 0 " .
> o o
-Y N
3 0 . 0 a
cc 0 0 -
m rl m o c
r 0 0 :
N
I
.
3
n * 0
c- m. 3
0
0
m
m m m
0
0
cc m
0 3
0
0
t- N t- 3
0
- 0
0
0
0
0 m N
a
- 0
m (D
0
0
0
3
t- t.
0
0
m 9 3
0
0
3 - s
- C
C
C
C
C
- L
- 0
m 4 N
0
0
m m e 3
0
0
3
4
0
C
LI:
(1: -?
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
- C
C
C
C
c
<
3
3
01
0
0
0
0
0
0
0
0
0
- 0
0
0
C
C
C
0 0
7 ' -
0 0 m.7
(3
3 N m t - - 0 0
t - N o m i n =
-- o r m ,
N C
o c
t - u M Lr
c c
c1
(3 c :
Oi CSI - $:
i-
I
51 o c s 1
Oi I
C>' - - c o c
d s :
m i in
& ! i
Y 0
m N a2
r? 0 1-
9
rn rn
3
n 4
4
3
3
N ,-I
N
0
3.5
E 8 E E & i >
x x W N W N N N 0 0
0 0
o c
. .
a
D D
3
2
3
.I
P I
3
- 3
n 2 4
3
0
3 ?..
3
0
-
0
C
C
C
C
C
- -
j i
-
- C
C
a C C
P c
C
T c(
- C
C
C
'i
C
P C
C
Y E - -
- E - €
c- ln
d
0
0 m 0 I
d r)
U d
3
D * In I -- D 3
v I
3
4 n 5
.- n 4
0
m m m I
-- ,-I 10
d
0
m
d * I
(0
rn m
0
,-I
.r(
C
3
C
- - " C
C
C
C
< C c
C
0 0 m u m a N O o c
+I d d c
c
t
r
S !
9, Om ", N t - r
4 0 c d m r . . o o c Y c3
P
i . - 0
1- W
0 I
0
0
4 N N
0
+I-
O
c r-
0
0 > 3
3
3
I-
0
N W
r(
I
0
0
LD
L- m m
0
-4c
0
, I > m
c; . <
0
5
3 3 %
3
3
- 3
3
3
3
3
3
- !x --
c o o
s I- m u c o r n . . c 4 -
c o o
l c o c
I m m
u m m
I
t - m a m m
_ - c
7
I : o <
C
C
C
0
- 0
0
0
I
a c 3 e
C
J .. C r
C
j j E 2 E
2 E E
.I e
4
N
w
rn cd > h 0
4
0.L: c N X N 0 0
1 0 * 0, N - r - r w - 0 0
0 0 0
0, r 0 m
0
4
Analysis I V
The system analyzed is identical to that utilized in Anal- ysis I1 except that there i s no realignment between injection and perilune.
m a r y A, again indicates the effect of a gimballed vs a gimballess system.
IMU - Precision Gyros - No Realignment - ---- . D.
Comparison of this data with that of Analysis 111, Sum-
53
R W
N d:
0
m ? m
0 c- o!
0
r r 0 - R 0 C
C
0
*
r
d c
$ 3 . I
3
m 0
0
W m
0
m m
-- m 3
0 I
0
m
2
m 9 9
ln 09 r-
-8
l- c'!
ln 0 0 -F
m 0 t- *
m 0 N N
3
@? N 3
O i
@I 0 m
I
- 3 m d
0
cj
0 I
3
0 n m
C
CI: * 1 ..-
C P
O / O
E. Analysis V GIMU - Crude Gyros - Realignment
The system analyzed is identical to that utilized in Anal-
ys i s I except that crude gyros replace the precision gyros.
addition, analyses fo r the following uncertainty sources are identical to Analysis I.
In
They will not be repeated.
Align X Align Y Align Z ACBX
ACBY ACBZ
SFEX SFEY
SFEZ
55
0 0
0 0
0 0
0 0
0 0
o c
o c
o c
o c
_c
I
I 4 c
o c
i o c
G C
o c
J
.
- 0 m 3
W m
0
co W
d
m m m
t- m m
c- m * -- * m
3
m m
0
0 m d
,- 3 u
(0 t- Lo
m r- e 3
m
a
3
0 3
a 4
0 t-
m
3 0
l-
t- N
m N 4
m m m m
3 * 1 0 * _- m (D
W N
m m
v) N
m m m
* m * W
N
s L? v
L1
N m
-- m c -r
0
rn W
N
UY m
- Lo r- e
t- N
3
VI
P- o q o o - m n m " O S ' : d 0 In
m 0 ~ 0 0
- O K 0 0
3
* 6 ;
Lo
* o m 0 0
m o o l o c
N
M * c I :
N O :
0 0 : :
W
0 : o c 0
0
t- O N O C
- I N r - o r - c - * m
W
m 0 - 0 c
3
o a o c d
o o o c
m 0 - o c
6
u m
o m o c
m o o m c
3
N o e o c ,-
J * - N t-
o)
e 0
t-
t- (D
W N 3
0 Lo m m
m W
t- * -- m W
(0 N
* Lo
In N
m 0
m
m m v W
m W
-r *
In
N m 3
-- M u 4
m LO
d
?I 0
m c L3
m
t- * 03
m m In
3
m o m o c m o m -
d & d
C
N
o ~ o o o c
W t - m N . O N m O C
N d d
m m N , o g : o c
0
-r o m o o o c
m a - N O % - C ? O C w m -
m c u t - rn lr:
O O C d d o
o o o o o c
m m v 0 y o -
. o c d c o
{ o $ g o c
N
N o o o o o c
* o o % ~ o c e -
r - 0
@. (0
4 I
0
0
a a a I
C
-
J 3
I
>
>
51 I
3
-4
3
3 U
3
3
3
L'
C
- C
C
C
C
C
C
-
-
3
3
3
r n
I
C - 3
9 -I
n I
3
3
. 0 n
L
C
- C
C
C
C
C
C
-
I
-
3 3 ' " g d s : E E
E E 4
;5" x x c
0 0 0 0 0 - Y
N - m m
d d d
b
.
Ll 0 c 0 0 -r
9 " c
* Q m
7
C 0 9
l-
O C
C o c
r I
c(
0 ::
o c
C
0::
-- r
P
o a
o c
C o a
I
U
0:: r
o c
r 0 :
--
& E
ci d
7 m 2 1
"
0 1
t- N. :
0 1 W ,
t- m l
o <
0 L n <
$ ? ; I
- 4 k
t-
W '4
0
m 9 3 I
0 r-
-r m
0
0 N
W N I -- 0
5
0
0 '4 3 I
0 W -Y m
0
In
0 W
t- N
0
-F t-
m
0 W m m
0
m m 0
--
3 : k 2 E E
a c x s 0 0 0 0
z s N . N 0 0
I 0
W N.
0
m In
In I
o In m m
0
* * I "
- 0 : N I
0
t-
N 9:
0 N
m m I
0
-F
t- I m
- 0
0
0
0
0
0
- -
Y M
5
2 P
m U .-I c
5 .3
-
- (0
N c9
0
0 '4 3 I
0 (0 In r( I
0
m " " +I--
m
u; "
0
0
0 'f:
m m 4
,-I I
0
0
I
m 3
-- 0
0
0
0
0
o o c o c
l r t - O * n O O C
0 3
0 0 o c
0 O G c
c I- E - 0 :: c .-
o o o c
c o o
m lP
0 0 0
0 0 0
0 0 0
a O O Z
3
0 0 0
0
0
0
0
m N
t- 3
C
a t . *z 2
3 n 3
3
3
0 0 1"
c
0
0
0 0
m N
0
0
0
t- m m
0
-
0
0
0
0,
0
0 -
c r
: u c
a E i L a
-
0
0
m 0 W
-3
0
m 4
cn
0
0
m m 3
3
0
__
-- A
3 0
3 0
C c c o c -
0 0
-- *E- .:
0
0
0
0 -
0
0
c
0
C
C
-
- *i -
0 1 i
0
0
0
0
C
C
-
- 2: -
0
0
0
0
0
0 -
C
C
C
C
C
C -
r
L > w o a < . N X
o o c 0 0 '
Lo In , N 3 I
o m '
d o c
Analysis VI
The system analyzed is identical to that utilized in Anal- In
GIMU - Crude Gyros - No Realignment .-.-.----- F.
ys i s I11 except that crude gyros replace the precision gyros . addition, analyses f o r the following uncertainty sources a re identical to Analysis 111. They will not be repeated.
Align X Align Y Align Z ACBX ACBY ACBZ SFEX SFEY S F E Z
6 1
- 3
m In
0
0
0
c 3
0 3
C
- C
a L(
c
C
C
C P U
C
C
C
C
<
- W
3 7 m P-
o N o
t- N
m o m
9
m o * W
c
m 2 0 N
0
m a ?
-_ 0
* 0 4
0 0
0 W
O 3
0
O % m
0 0
m o * N
4 -- -
X
Q U ~m a 4
q 0 0 d
3
-
3
c + U
3
- - U P U
C
C
C
C
C
C
C C
C
3
3
J
3
3
3
3
-
3
3
.-
e
C
C
-
I
3
3
3
-
3
C
3
C
C
C
-
C
C
C
C
<
C
-
N W Lr, VI
e 3
u i *I
3
3
3 W n n
3
-
- - C I
<
t- N
0
0
0
t- d'
0
-4
0
0
C
C
C
C
-
C
C
C
C
C
I In w V
3 0 UJ
* I-
a
z a ir w V z 3
E ! * a, 5 2
C G E E L >
E E 4
x x
0 0 O N I
l o r n r - m
0 0 I
. . , 0 0 ci -
- C
C
C
C a
C 0: m I
0
0 In
* N
- P-
0 I
9
0
0
0 *.
m m N I
3 E
0 0 0 m
2
- C
r d:
0
0
9 d I
0 W m N
0
- m 9 0 4
0
P-
N I N.
0 W m t-
0
0 In N
T -4+
t-
(0 '9
0
m 01 4
0 t- m
0
0 N [D
U I __ 3 d:
3
3 9 * I
3 D
# 1
3
- C
C
C
C
C
C
-
I
1
1
c
C < C
C c
C
C
a
I
,
, I
c
r
C C
2
I
>
>
;
: ! j
I r P
C
C
P C C
a T
P
I r
C
C a r
-
I
E 2 h 00 .+ rn Q
t! Y
[ - e
3 0
--yr
3 0
- =. 0
I
3 0
3 0
c
R o
3 0
4 c
0
m ro d
0
0
* m (0 3
0
0
0
0
0
m N t- rl
0
-- 1 -_ 1
C
($ c
3 I
C
3
L- e n
C
- C
0. U
C
C
C
d 0.
U r
C
- I -
3
3
3
3
3
3
- 3
3
3
3
3
3
- 2 -
C
C
C
C
C
C
- C
C
C
C
C
C
- ,P -
3 1
c E t 0 C
. .- c 0:
h f U
+
E -2 ._ .A
N
0 0 0 L o
2
Description of Descent & Ascent Trajectory P a r a m e t e r s
The descent w a s initiated at a perilune altitude of 50, 000
-I--
G.
feet with the thrust vector oriented to 4O below the local hori- zontal.
maintained fo r 344 seconds at which point the hover condition w a s defined.
and the Isp at 305 seconds. 0 . 4.
A constant pitch rate of 0.1138 degrees/second was
The thrust level w a s maintained at 10, 000 pounds
The initial t h rus t /mass ra t io w a s
The ascent w a s assumed to initiate a t the hover point
(except f o r the normal ascent case, Table IV, when it initiated
from the lunar surface. ) The initial thrust vector angle w a s 158. 91' CW from the inertial horizontal (approx. 32O CCW f r o m
the local horizontal). A constant pitch rate of 0.1241 degrees / -
second was maintained f o r 343 seconds to cut-off. The thrust w a s maintained a t 4000 pounds and the Isp was again assumed
to be 305 seconds. The initial t h rus t /mass w a s again 0 . 4.
c
.
E-1473
DISTRIBUTIGN LIST
Internal
R. Alonso
J. Arnow (Lincoln)
R. Battin W. Bean
E. Berk
P. Bowditch
A. Boyce
R . Boyd P. Bryant
R . Byers G. Cher ry
E. Copps
s. COPPS (MITIACSP) W. Crocker G, Cushman J. Dahlen
E. Duggan J. Dunbar
K. Dunipace (MITIAMR)
R. Euvrard P. Fel leman S. Fe l ix (MITIS &, ID)
J. Flanders
J, Fleming
L. Gediman
F; Grant P. Philliou
Eldon Hall
I> Halzel
D. Hanley W. Heintz
E. Hickey
D. Hoag A. Hopkins
F, Houston M. Johnston
B. Katz A, Koso
M. K r a m e r
W. Kupfer
A. Laats D. Ladd A. LaPointe
J. Lawrence (MIT/GAEC) T. Lawton D. Lickly
R. Magee Go Mayo
J. McNeil R , McKern
R. Mudgett James Miller
John Miller
J. Suomala
J. Nevins G. Nielson
J. Nugent E. Glsson
C. P a r k e r
W. Pa t te rson
J. Po t t e r
K. Samuelian P. Sarmanian
R. Scholten J. Sciegienny N, Sears D. Shansky
T. Shuck W. Stameris E. Smith W. Tanner R. The r r i en W. Toth
M. Trageser R. Weatherbee R. White
L. Wilk
R . Woodbury W. Wrigley D. Yankovich
J, Shillingford
Apollo Library ( 2 )
MIT/ IL Library (6 )
69
Exte rnal
(ref. APCAN; 2 July 1963)
P. Ebersole (NASA/MSC)
W. Rhine (NASA/ RASPO)
S. Gregorek (NAA S &. ID/MIT) T. Hueurmann (GAEC/MIT) AC Sparkp lug Kollsman
Raythe on WESCO Capt: W. Delaney (Afsc/ MIT)
NAA RASPO: National Aeronautics and Space Administration Resident Apollo Spacecraft Pro jec t Officer North American, Inc. Space and Information Systems Division 12214 Lakewood Boulevard Dow ne y , C a1 i f o r nia
CAPE:
HDQ:
A.ME S:
LEWIS:
FRC:
JPL:
LRC :
National Aeronautics and Space A.dministration Kennedy Space Center Cape Kennedy, Flor ida Attn: M r , B. P. Brown NASA He adqua rte r s 1520 H Street Washington, D. C , Attn: Mr . G. M. Low, MD(P) National Aeronautics and Space Administration Ames Research Center Moffett Field, California Attn: Mr . Matthews National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio
National Aeronautics and Space Administration Flight Research Center Edwards AFB, California
National Aeronautics and Space Administration J e t Propuls ion Laboratory Pasadena, California Attn: M r . H, R . Lawrence
National Aeronautics and Space Administration Langley Research Center Langley AFB, Virginia A-ttn: M r . A. T. Mattson
( 3 )
70
GSFC:
MSFC :
GAEC:
NAR.:
National Aeronautics and Space Administration (2 ) Goddard Space Flight Center Greenbelt, Maryland
George C. Marshall Space Flight Center Huntsville, Alabama Attn: Dr . Kuettner
Rethpage, Long Island New York Attn: Mr . A. Whitaker
National Aeronautics and Space Administration (2 )
Grumman Aircraf t Engineering Corporation (1)
North American Aviation, Inc. Space and Information Systems Division 12214 Lakewood Boulevard Dow ne y , C a1 if ornia Attn: Mr. R. Be r ry
GAEC RASPO: National Aeronautics and Space Administration (1) Resident Apollo Spacecraft P ro jec t Officer Grumman Aircraf t Engineering Corporation Bethpage, Long Island, New York Attn: Mr. Jack Small
Pos t Office Drawer D White Sands M i s s i l e Range White Sands, New Mexico
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MSC: National Aeronautics and Space Administration (45 1
71