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fcfM) REPORT OTWUi
COPT
BB HOT REMOVE
ational aeronautics and space administration
MSC INTERNAL NOTE NO. 68-FM-67
March 8, 1968
LOGIC AND EQUATIONS FOR THE
REAL-TIME COMPUTATION OF THE
LM LAUNCH TARGETING
AND DISPLAY
By Jerome W. Kahanek,
Orbital Mission Analysis Branch
MISSION PLANNING AND ANALYSIS DIVISION
I)
A* W
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
UNITED STATES GOVERNMENT
Memorandum
to : See list below
from : FM/Mission Planning and Analysis Division
b
subject: Transmittal of detailed programming requirements
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MPAD REPORT CGfJTROL
COPY
DO KOI REMOVE
TE . 13 MAP 1368
68-FM61-79
The enclosed MSC Internal Note No. 68 -FM -67 presents detailed require¬
ments for the real-time computer program to be employed in support of
the Apollo missions beginning with the G Mission (CSM 107/IM-6).
Edgar C. Lineberry, Chief
Orbital Mission Analysis Branch
and Analysis Division
The Flight Software Branch concurs with the above recommendation.
Enclosure
Addressees:
IBM/J. Bednarcyk ( 5 )
H. Norman
R. Sogard
FS5/J. Stokes (3)
L. Dungan
FC/C. Charlesworth
FM/J. Mayer
H. W. Tindall, Jr.
C. R. Hubs
M. V. Jenkins
R. P. Paxten
Branch Chiefs
FM6/R. Regelbrugge
FM5/R. Ernull
cc:
See attached list
Buy U.S. Savings Bonds Regularly on the Payroll Savings Plan
4
1 3 m;irt is68
See list below
FM/Mission Planning and Analysis Division
68-FM61-79
Transmittal of detailed programming requirements
The enclosed MSC Internal Note No. 68-FM-67 presents detailed require¬
ments for the real-time computer program to be employed in support of
the Apollo missions beginning with the 0 Mission (CSM 107/IM-6).
. . ,
■ c. lAnobovyif
Edgar C. Lineberry, Chief
Orbital Mission Analysis Branch
Original ci,,..»a by
J, P, Mayer
John P. Mayer
Chief, Mission Planning
and Analysis Division
The Flight Software Branch concurs with the above recommendation.
Enclosure
Addressees:
IEM/J. Bednarcyk (5)
H. Norman
R. Sogard
FS5/J. Stokes (3)
L. Dungan
FC/C. Charlesworth
FM/J. Mayer
H. W. Tindall, Jr.
C. R. Huss
M. V. Jenkins
R. P. Parten
Branch Chiefss
concurre^/r, Regelbrugge
FM5/R
CE CODE k>
CC!
DATE ►
James C. Stokes, Jr., Chief
Flight Software Branch
OFFICIAlJj^ C
:OPY
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Belleomm/V. Mummert
IBM Library
TRW Library (4)
TRW/D. P. Johnson (3)
TRW/B. J. Gordon (7)
EM6/R. L. Phelts (2)
CF/W. J. North
EG/D. C. Cheatham
EG/R. G. Chilton
EG/R. A. Gardiner
KA/R. F. Thompson
KM/W. B. Evans
PA/G. M. Lew
PD/A. Cohen
PD/O. E. Maynard
PD7/R. V. Battey
PD8/J. P. Loftus, Jr.
FA/C. C. Kraft, Jr.
FA/S. A. Sjoberg
FA/R. G. Rose
FA/C. C. Critzos
FC/J. D. Hodge (5)
FL/J. B. HammacU (2)
IMI2/R. Ritz
FM12/E. B. Patterson (25)
FM13/M. A. Goodwin
Author
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MSC INTERNAL NOTE NO. 68-FM-67
PROJECT APOLLO
LOGIC AND EQUATIONS FOR THE REAL-TIME COMPUTATION
OF THE LM LAUNCH TARGETING AND DISPLAY
By Jerome W. Kahanek
Orbital Mission Analysis Branch
March 8, 1968
MISSION PLANNING AND ANALYSIS DIVISION
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
Approve
Orbital Mission Analysis Branch
MissiVn Planning and Analysis Division
LOGIC AND EQUATIONS FOR THE REAL-TIME COMPUTATION
OF THE LM LAUNCH TARGETING AND DISPLAY
By Jerome W. Kahanek
SUMMARY AND INTRODUCTION
This internal note presents the logic and equations for the lunar
module (LM) launch targeting processor (LLTP). The LM launch targeting
display will he a part of the lunar rendezvous plan table (LRPT) and
will be used by the flight controllers to verify the LM onboard targeting
computations.
LM LAUNCH TARGETING PROCESSOR
The LLTP computes the following targeting parameters.
i the same as those that will be used on the LRPT.
wedge ■)
AZ p
The wedge angle existing between the CSM orbit
plane and the plane resulting from inserting the
LM parallel to the CSM plane (assuming no yaw
steering), deg.
Cross-range distance from the launch site to the
CSM orbital plane that will normally steered be
out during the ascent maneuver, n. mi.
Wedge angle remaining between LM and CSM orbital
planes at LM insertion, deg. This value is
nominally zero unless input Y g is less than parallel
launch wedge angle.
Desired insertion cross-range distance measured from
the CSM orbital plane, n. mi.
Launch azimuth for plane parallel launch, deg
(measured clockwise from north).
2
’’LS ’ LS
GMTLO
The following quantities are the inputs necessary to compute the
targeting parameters.
CSM state vector and time
LM selenographic latitude and longitude on the lunar
surface, deg
Desired or actual Greenwich mean time of lift-off.
Y Wedge angle to he taken out hy yaw steering during
s IM ascent, if the input value of Y g < the parallel
launch wedge then the wedge angle at insertion
will he greater than zero.
t LM nominal powered flight time, sec
PF
p LM nominal powered flight arc, deg
*FA
COMPUTATION OF WEDGE ANGLE, CROSS-RANGE DISTANCE, AND PARALLEL AZIMUTH
The LM launch targeting processor uses subroutine ENSERT to generate
a LM insertion vector. Wedge angles are computed from the selenographic
orbital elements of the CSM and LM at insertion, using the following
equation:
= tan -1 [ci
„ cos :
i i sin ]
’ (hj.-hjy)]
where i - inclination of target orbit (CSM)
i^ - inclination of LM orbit
h g - ascending node of target orbit
h^ - ascending node of LM orbit
Cross-range distance is the distance from the launch site or insertion
point to a perpendicular intersection of the CSM orbit. It is measur^
by finding the angle between the LM vector and the projection of the IM
vector in the plane of the CSM orbit. This projection is found by creating
3
a coordinate system referenced to the CSM orbital plane and the 114
position by:
where
The parallel
AZp = tan -1
launch azimuth is computed from the following equation.
T cos i c cos 4> TR + sin ig sin 4>* sin <1> LS j
i - selenographic inclination of the target
C orbit (CSM)
$ _ selenographic latitude of launch site
- angular distance measured along the equator
between the launch site and the target
descending node at lift-off time.
4
The launch azimuth is computed and displayed for ground information
only since the LM onboard system does not use or display an azimuth.
The LLTP (see flow chart l) uses subroutines LATLON and ENSERT
(ref. l) and LSAEG (ref. 2) in its computations. LATLON computes an
inertial landing site vector and ENSERT computes the LM insertion vector.
LSAEG is used for vehicle ephemeris prediction.
SYMBOLS FOR LLTP FLOW CHART
Input Constants
3.141592.••
moon rotation rate
Input Variables
semimajor axis of CSM orbit
eccentricity of CSM orbit
inclination of CSM orbit
argument of pericynthion of CSM orbit
selenocentric node of CSM orbit
mean anomaly of CSM orbit
time of CSM orbital elements
lift-off time
LM insertion velocity, fps
LM insertion radius, ft
LM flight-path angle at insertion, deg
LM nominal powered flight time, sec
LM nominal powered flight arc, deg
yaw steering capability, deg
radius of the landing site, ft
6
6
wo
AR
6 w
selenographic latitude of the landing site, deg
selenographic longitude of the landing site, deg
Output Variables
wedge angle for zero yaw steering, deg
cross-range distance at lift-off, ft
wedge angle with yaw steering, deg
cross-range distance at insertion, ft
parallel launch azimuth, deg
7
LL TP F LOW CHART
f 6 Ti\K-rj
Co^fuTE fWG-ULh K
rAOtf * 't'To M of c-sAl
| J .* 6
Flov chart
Flow chart 1.- LLTP logic - continued.
9
13 6
1.- LLTP logic - continued.
10
l._ LLTP logic - continued.
11
|f-f 6
Flov chart 1,- LLTP logic - continued.
12
((> 6
Flow
LLTP logic - concluded.
13
REFERENCES
1. Sullivan, W. A.: Logic and Equations for the Computations of Lunar
Module Launch Window and Recommended Lift-Off Time. MSC Internal
Note 68-FM-5, January 5, 1968.
2. Ingram, D. S.; and Nickerson, K. G.: Generalized Lunar Satellite
Analytic Ephemeris Generator (GLSAEG). TRW Report 3842-H003-R0-000,
June 15, 1966.