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NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MSC INTERNAL NOTE NO. 70-FM-23
March 23, 1970
RTCC REQUIREMENTS FOR
APOLLO 14 (H-3) MISSION:
EARTH-CENTERED RETURN-TO-EARTH
CONIC SUBPROCESSOR
Lunar Mission Analysis Branch
MISSION PLANNING AND ANALYSIS DIVISION
»
MANNED SPACECRAFT CENTER
houston.texas
MSC INTERNAL NOTE NO. 70-FM-23
MSC-Ol567
PROJECT APOLLO
RTCC REQUIREMENTS FOR APOLLO 14 (H-3) MISSION-
EARTH-CENTERED RETURN-TO-EARTH CONIC SUBPROCESSOR
By D. R. Davis and T. P. Garrison
TRW Systems Group
March 23, 1970
MISSION PLANNING AND ANALYSIS DIVISION
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
MSC Task Monitor: R. S. Davis
Approved:
Approved:
CONTENTS
Section Page
1.0 SUMMARY AND INTRODUCTION . 1
2.0 ABBREVIATIONS . 1
3.0 EARTH-CENTERED SUBPROCESSOR MODES . 2
3.1 Time Critical Unspecified Area. 2
3.2 Fuel Critical Unspecified Area. 4
3.3 Primary Target Point Mode . 5
3.3.1 PTP tradeoff. 5
3.3.2 PTP discrete. 8
3.4 Alternate Target Point Mode . 9
3.4.1 ATP tradeoff. 9
3.4.2 ATP discrete. 11
APPENDIX A - DEFINITION OF SYMBOLS USED
IN FLOW CHARTS. 1 3
APPENDIX B - LOGIC FLOW OF THE EARTH-
CENTERED RETURN-TO-EARTH CONIC SUBPROCESSOR .... 21
SUBROUTINE DVMINQ . . . .. .... 22
SUBROUTINE FCUA. 26
SUBROUTINE INITAL. 30
SUBOURTINE MAIN. 34
SUBROUTINE MSDS. 36
SUBROUTINE PRTIAL . 40
SUBROUTINE RENTRY . 42
SUBROUTINE RUBR. 44
SUBROUTINE SCAN. 47
iii
Section Page
SUBROUTINE TCOMP . 50
SUBROUTINE TMIN. 54
SUBROUTINE VACOMP . 58
SUBROUTINE VARMIN . 60
SUBROUTINE VELCOM . 62
SUBROUTINE VUP2. 64
REFERENCES. 68
RTCC REQUIREMENTS FOR APOLLO l4 (H-3) MISSION:
EARTH-CENTERED RETURN-TO-EARTH CONIC SUBPROCESSOR
By D. R. Davis and T. P. Garrison
TRW Systems
1.0 SUMMARY AND INTRODUCTION
This documentation of the earth-centered return-to-earth conic
subprocessor completes the logic specification, corrects errors found in
reference 1, and incorporates several changes that have been made since
the previous documentation. New subroutines added are the analytic calib¬
ration subroutine and the entry simulation subroutine. This document
completely defines the earth-centered conic subprocessor with the excep¬
tion of the state vector advance subroutine. Some of the control logic
has been restructured to correspond more closely with the current RTCC
formulation or to present a more logical flow sequence. Modifications
to the program which eliminate the polynomial'curve fits in subroutine
ETAARF are included in this document and are indicated by bars in the
margin of the affected pages. Symbol definitions are, presented in
appendix A for the logic defined in appendix B, which is the specification
for the earth-centered return-to-earth conic subprocessor for Apollo l4
and subsequent missions and supersedes that defined in reference 1.
Detailed logic of the moon-centered return-to-earth conic subpro¬
cessor is presented in reference 2. The supervisory and precision
computation logic which completes the RTCC requirements for the return-
to-earth processor (RTEAP) for Apollo l4 and subsequent missions is
presented in reference 3.
2.0 ABBREVIATIONS
ATP alternate target point
DV change in velocity
DVM maximum allowable DV
EFCUA
2
extreme fuel critical unspecified area
FCUA fuel critical unspecified area
MD miss distance to a PTP
MDM maximum allowable miss distance to a PTP
MSI moon's sphere of influence
PTP primary target point, that is, a point on the
earth's surface
RTCC Real-Time Computer Complex
RTEAP Return-to-Earth Abort Processor
TCUA time critical unspecified area
3.0 EARTH-CENTERED SUBPROCESSOR MODES
The following subsections describe the manner in which solutions
are generated in this subprocessor, the input required to operate the
different modes, and the output parameters for each mode. In addition
to the required input, each subprocessor mode is initialized with a
premaneuver state vector(s) X(j), where J is the total number of
state vectors, and a reference epoch time from the abort processor's
supervisory logic.
3.1 Time Critical Unspecified Area
The TCUA mode generates the trajectories that return to a specified,
reentry target line with the smallest transit time without regard to
landing point. This solution will be characterized by either maximum
allowable DV at abort or by the maximum allowable reentry speed. The
solution plane coincides with the preabort plane of motion if the
preabort inclination is not greater than the maximum allowable inclina¬
tion; otherwise, the maneuver plane is rotated to the plane characterized
by maximum inclination (the rotation being through the smaller angle
because there are generally two planes that have a specified inclination
passing through the abort position).
The solution generated in this mode is user determined in the sense
that it is characterized by either maximum reentry speed or maximum DV
for the maneuver. The solution is generated in subroutine TMIN and the
inclination constraints are checked in subroutine INITAL.
The input quantities for the TCUA mode are the following.
DVM
Maximum DV to be used for the abort maneuver
T
Time at which the maneuver is to be computed
ICRNGG
Flag that defines the reentry mode which is to be simulated
I rmax
Maximum inclination computed at reentry
U rmax
Maximum reentry speed
RRBI
Constant reentry relative range (down range) which
will be substituted for the relative range value
obtained from the reentry curve fits
IMSFN
Flag that selects the reentry target line
The output quantities to the abort processor supervisory logic (ref. 3)
are as follows.
DV
Maneuver velocity vector increment (calibrated)
DVC
Conic DV magnitude (uncalibrated)
HR
Reentry radius vector
U
r
Reentry velocity vector
T
Time of reentry
X z and 6 i
s Longitude and geocentric latitude of landing site
n rz
9 cr
Down-range angle from reentry to landing
Cross-range angle from reentry to landing
T rz
NOSOLN
Time from reentry to landing
Error flag indicating whether a valid solution
was found in the conic program
NOSOLN
3.2 Fuel Critical Unspecified Area
The FCUA mode generates the minimum fuel maneuver required to return
to acceptable reentry conditions ignoring landing point constraints.
The earth reference logic first analytically determines the fuel critical
inplane solution that returns to the specified reentry target line. If
the preabort inclination is acceptable, the solution is determined in the
preabort plane. Otherwise, a plane change is made to the maximum
inclination plane that is selected in the same manner as the TCUA mode,
and the solution is found in this plane.
If sufficient DV is allowed for an abort, the return is computed
to the selected reentry target line. However, if the DVM constraint is
violated, the logic attempts to generate a trajectory using DVM to
minimize the deviation from the desired reentry target line. The program
uses flight-path angle at reentry as the independent variable to drive
DV to DVM. If this solution is available, it becomes the solution returned
by the FCUA mode and is called the extreme fuel critical unspecified
area (EFCUA) solution. If the DVM cannot be satisfied by varying the
reentry path angle between 90° and 110°., the logic returns no solution.
The input quantities for this option are identical to those given
for the TCUA mode.
The output quantities to the abort processor supervisory logic
(ref. 3) are as follows.
Maneuver velocity vector increment (uncalibrated)
Reentry radius vector
Reentry velocity vector
Time of reentry
Longitude and geocentric latitude of landing site
Down-range angle from reentry to landing
Cross-range angle from reentry to landing
Time from reentry to landing
Error flag that indicates whether a valid solution
was found in the conic program
5
3.3 Primary Target Point Mode
This mode generates, for the maneuver time considered, the DV and
trip time required to return to a specified PTP. Whenever the PTP is
accessible within the constraints, the minimum fuel solution for the
specified miss distance is generated.
3.3.1 PTP tradeoff .- Two formats are available for the PTP trade¬
off mode, namely the near-earth tradeoff and the remote-earth tradeoff.
The basic logic for generating solutions is identical; however, the
near-earth format will consider up to five different values for MDM,
while the remote-earth format is limited to the zero miss distance
solution. Each tradeoff display consists of all the solutions for up
to forty state vectors within the allowed range of maneuver times.
The logic presented is the current RTCC logic known as the fuel-
critical PTP logic. The initial presentation of the PTP mode (ref. U)
considered the reentry maneuver as a planar profile. Because this
approximation has proved invalid, the logic discussed here considers a
reentry profile which has a cross-range component and whose characteristics
are determined by the geocentric position as well as by the velocity
magnitude and direction at reentry. The PTP solution generation logic
is not an exact simulation, but this logic is the first iteration of a
procedure which can generate a more precise PTP solution. The
procedure is described here and is the same as that defined for the PTP
discrete mode, except that for the PTP discrete mode only a single
maneuver time and a single miss distance are considered.
The first computation is the determination of the minimum trip
time solution (subroutine TMIN). For this transit time, the azimuth
of a plane which contains the PTP is computed. This azimuth is test¬
ed against the pair of azimuths which were chosen as the most con¬
straining planes based on the inclination and DVM constraints. If the
azimuth or the plane which contains the site is acceptable, then the plane
through the desired landing site is chosen to be the maneuver plane;
otherwise, the constraint plane that has an azimuth closest to the azi¬
muth of the site plane is selected. Note that this choice of azimuth
minimizes the miss distance, where the miss distance may be defined
(as a function of azimuth) as the minimuni great circle distance between
the desired landing site and the actual impact point. The reentry point
is defined for the trajectory with the specified transit time and with
the defined azimuth. The reentry trajectory and the associated impact
point are computed for this reentry point. The coordinates of the PTP
are offset by the negative of the difference between the impact point
defined by this out-of-plane reentry profile and the one defined by the
corresponding planar reentry profile. (This offset is defined such that,
if the planar reentry trajectory passes through the offset landing point,
the out-of-plane reentry profile would pass through the PTPl) For this
new impact point, the miss distance is computed with the azimuth re-defined
for the offset reentry to minimize the miss distance. The miss distance
6
is computed in subroutine MSDS. Transit time is now increased by a
small amount, and the miss distance is recomputed by the above procedure.
The logic next goes to subroutine TCOMP which computes the next value of
transit time based on the present and past values of miss distance
and the desired direction of motion of the impact point. At this point,
the logic is attempting to minimize the miss distance; therefore, if the
present value of miss distance is smaller than the past value, TCOMP
continues to increase the transit time. This procedure continues until
the maximum allowable miss distance is achieved or until a min imum in the
MD is found. If a minimum is found, a flag is set based on the direction
of motion of the impact point. If motion of the impact point is
easterly, the miss distance should be maximized before the next minimum
is sought. If motion of the impact point is westerly, the transit time is
incremented by 2k hours and a new minimum immediately sought. When the
miss distance is equal to the maximum allowable miss distance (MDM), a
scan is performed by incrementing transit time. During this scan, the
azimuth is varied for each trip time to generate the set of trajectories
which miss by the specified miss distances. The miss distance is used in
each case to minimize the required plane change and therefore DV. This
procedure is repeated until the miss distance is larger than the maximum
distance allowed. When the maximum distance is exceeded, the search is
re-initiated to determine the next time interval of PTP accessibility
within the framework of problem constraints. The entire process is
repeated for each state vector.
The PTP tradeoff near-earth option produces a graph that presents
time at abort along the abcissa and two other parameters, DV required for
the abort and time at landing, along the ordinate. Both latter parameters
are given for several fixed values of miss distance.
The PTP remote-earth option of the tradeoff display is designed
to display abort solutions for those flight regions in which the DV
difference between miss distance contours is very small. The interval
between landing times of these solutions is approximately 2k hours. For
this option, the abort time is plotted along the abcissa, and the
required DV is plotted along the ordinate. Only the zero miss distance
contour is presented in this option. The multiple curves which will
appear on the display are identified by their time at landing, rather
than with a separate curve. For aborts outside the MSI, only solutions
which return directly to the earth (posigrade) are generated and
displayed.
All solutions are computed to the specified reentry target line and
include the selected reentry profile. All appropriate constraints are
considered.
The input quantities for both PTP modes
follows.
Earliest abort time to be considered
T
omax
DVM
X and 6
T zmin
T
zmax
Latest abort time to be considered
Maximum DV to be used for the abort maneuver
Longitude and geocentric latitude of the desired
PTP landing site
Minimum time at landing
Maximum time at landing
ICRNGG Flag that selects one of the reentry modes
Irmax Maximum inclination at reentry
U Maximum reentry speed
rmax J *
RRBI Constant reentry relative range (down range) which
will be substituted for the relative range
value obtained from the reentry curve fit
IMSFN Flag that selects the reentry target line.
The abort time range indicated (T - T . ) will be limited by
omax omm
the RTEAP logic to a maximum of either 2k hours on the trajectory of the
input state vector or the period associated with the initial abort state
vector, whichever is smaller.
The output of the PTP tradeoff option to the abort processor super¬
visory logic (ref. 3) is as follows.
DV Change in velocity at abort (calibrated)
as a function of
T
Time at which abort solution is generated
Time of landing
Miss distance to the PTP
NOSOLN Error flag that indicates whether a valid solution
was found for any state vector in the conic program
The output is displayed as .a set.of curves of constant miss distance
with the DV required at abort and time at landing given as a function of
abort time.
3.3.2 PTP discrete .- These computations are exactly those of the
PTP tradeoff mode, except that a single miss distance, a single approximate
landing time, and single time of maneuver are considered.
The following quantities are supplied to the PTP discrete option.
T q Time at which an abort solution will be generated
T . , T
zmin zmax
X and 6
z z
ICREGG
MDM
I
rmax
U
rmax
RRBI
Minimum and maximum landing times that bracket the
approximate landing time of the abort solution
Longitude and geocentric latitude of the desired
PTP landing site
Flag that selects the reentry mode
Maximum miss distance to a PTP
Maximum inclination measured at reentry
Maximum reentry speed
Constant reentry relative range (down range) which
will be substituted for the relative range
value obtained from the reentry curve fit
IMSFN Flag that selects the reentry target line
The output quantities to the abort processor supervisory logic (ref. 3)
are as follows.
DV Maneuver velocity vector increment (calibrated)
RR Reentry radius vector
Reentry velocity vector
9
T
r
Time of reentry
A and 6
z z
Longitude and geocentric latitude of landing site
Down-range angle from reentry to landing
Cross-range angle from reentry to landing
T
Time from reentry to landing
NOSOLN
Error flag that indicates whether a valid solution
was found in the conic program
3.4 Alternate Target Point Mode
The ATP generates solutions which return to lines defined on the
earth's surface by successive pairs of latitude and longitude. The
trajectories return in the plane of original motion if this plane satisfies
the inclination constraint. If the plane of preabort motion is not
acceptable, the return is computed in the plane with an acceptable
inclination which requires minimum fuel for plane change. This logic
operates in a manner quite similar to the PTP logic. The minimum trip
time solution is generated (subroutine TMIN), and the miss distance for
this trajectory is computed (subroutine MSDS). For the ATP mode, only
the zero miss distance solution is an acceptable solution. The miss
distance for the ATP is defined as the longitude difference between the
impact point and the ATP measured at the latitude of the impact point.
The logic then attempts to drive the miss distance to zero. If it succeeds
the solution is stored if no constraints are violated. After storing a
solution or finding a non-zero minimum, the logic increments transit
time to search for the next possible solution. If motion is easterly,
the miss distance must first be maximized prior to seeking the next minimum
If motion is westerly, the transit time is increased by 24 hours and a
new solution sought if the maximum trip time constraint is not violated.
The logic is limited to ATP definitions which have a variation in
latitude; that is, constant latitude ATP's are unacceptable.
3.4.1 ATP tradeoff .- The ATP procedure is applied sequentially to
each state vector within the allowed range of maneuver times. The two
formats for the tradeoff display are the same as that for PTP tradeoffs,
except that for the near-earth format only the zero miss distance is
computed and, in addition, the latitude of the landing point is displayed
as an ordinate. The ATP tradeoff input are as follows.
10
T omin
Earliest abort time to be considered
Tpmax
Latest abort time to be considered
DVM
Maximum DV to be used for the abort maneuver
X'(j)
6*(J)
j longitude-latitude pairs that define the ATP line
Maximum value for j; that is, the number of points
that defines the ATP line
T zmin
Minimum time at landing
T zmax
Maximum time at landing
ICRNGG
Flag that selects one of the reentry modes
I
rmax
Maximum inclination at reentry
U rmax
Maximum reentry speed
RRBI
Constant reentry relative range (down range) which
will be substituted for the relative range value
obtained from the reentry curve fit
IMSFN
Flag that selects the reentry target line
The abort time range indicated (T - T . ) will be limited by
omax omin
the RTEAP logic to a maximum of either 2b hours on the trajectory of the
input state vector or the period associated with the initial abort
state vector, whichever is smaller.
The output of the ATP tradeoff option to the abort processor super¬
visory logic (ref. 3) is as follows.
The conic program returns
DV change in velocity at abort (calibrated)
as a function of
Time at which abort solution is generated
11
T Time of landing
6 z Geocentric latitude of the landing site
NOSOLN Error flag that indicates whether a valid solution
was found for any of the state vectors in the
conic program
The ATP format gives DV required at abort, time of landing, and,
only in the near-earth option, latitude of landing as a function of abort
time, but only for the zero miss distance condition.
3.4.2 ATP discrete .- The ATP discrete mode generates the ATP solution
for a single maneuver time and a single approximate landing time. The
following quantities are entered as input to the ATP discrete option.
T Time at which an abort solution will be generated
T zmin’ T zmax and maximum landing times that bracket
the approximate landing time of the abort solution
i longitude-latitude pairs that define the ATP line
Maximum value for j, that is, the number of points that
defines the ATP line
Flag that selects the reentry mode
Maximum inclination measured at reentry
Maximum reentry speed
Constant reentry relative range (down range)
which will be substituted for the relative range
value obtained from the reentry curve fit
Flag that selects the reentry target line
The output quantities to the abort processor supervisory logic (ref. 3)
are as follows.
Mm
«'(j)
Maneuver velocity vector increment (calibrated)
12
RE
Reentry radius vector
U
r
Reentry speed vector
T r
Time of reentry
and 6^
Longitude and geocentric latitude of landing site
\z
6 cr
Down-range angle from reentry to landing
Cross-range angle from reentry to landing
T
rz
Time from reentry to landing
NOSOLN
Error flag that indicates whether a valid solution
was found in the conic program
APPENDIX A
DEFINITION OF SYMBOLS USED IN FLOW CHARTS
15
APPENDIX A
DEFINITION OF SYMBOLS USED IN FLOW CHARTS
A,B,C ,D,E
a
Coefficients of quartic equation giving normals to
locus of acceptable abort velocity from preabort
velocity
Semimajor axis
AFG
Flag used in subroutine MSDS in PTP mode. A non¬
zero value indicates that the preabort motion is
retrograde and that the return plane is to be
determined by computing the miss distance in two
different planes and selecting the one that yields
the smaller miss distance.
CE
Cosine of eccentric anomaly
CUT
Number of steps taken across the landing site
DDT
Fraction of the step size to be taken in trip time
DFDA
Conic partial derivative 3f/3a
DL
Longitude difference between successive ATP points
DT
Step size in trip time
DTDA
Conic partial derivative 3T/3a
DV, DVS
Maneuver velocity change
DVC
Conic DV magnitude (uncalibrated)
DVM
Maximum allowable DV
DVSP
Total DV for minimum DV solution previously found
DVSSP
Past value of DVSP
DVT, DVM, DVR
Tangential, normal, and radial components of the
DV vector
16
E
Eccentric anomaly
Eccentricity
ERR
Difference in transfer angle between impact point
and PTP
f
True anomaly
I
Inclination
J
m
Number of state vectors to be considered
k
Indicator that gives number of roots
L
Longitude on ATP measured at latitude of impact point
MD1
Miss distance which is first found to satisfy the
desired conditions
MDMM
Minimum possible miss distance for the present trip
time
NOSOLN
Number of ATP latitude, longitude pairs
Flag that indicates whether solution has been
found. If NOSOLN
= 0, TCUA or FCUA solution found
= 1, no solution found
= 2, PTP or ATP solution found
P ar
Function that the PTP mode attempts to drive to zero
to generate acceptable solutions
Q
Step size in trip time for scanning across the maximum
allowable miss distance contour
R a
Preabort position vector
RR
Reentry radius
R
Unit vector through impact point
SE
Sine of eccentric anomaly
SEEK
Indicates whether a zero miss distance is possible
IT
SF Sine of true anomaly
SOL Indicates whether a solution has teen found
SW Flag used in TMIN. SW = 0 initially, SW = 1 during
the iteration for the minimum time solution, and
SW - 0 if the upper bound on the iteration exceeds
T
max
SW2 Control flag used in the PTP, ATP, and FCUA modes.
For the PTP mode, flag..is used to generate PTP
solutions within a maximum miss contour.
When SW2 = 0, the logic is searching for the
maximum miss boundary; when SW2 = 1, the direction
for the optimizing scan is being determined;
and when SW2 = 2 the logic is performing the
optimizing scan across the maximum miss contour.
When SW2 is used in the ATP logic, it changes from
0 to 1 when the ATP line has been bracketed and a
linear partial is to be used to generate the
solution. For the FCUA mode, SW2 indicates the type
of computation being performed. When SW2
= 0, a solution is sought to the entry target line
= 1, a solution is sought with DV < DVM
= 2, a solution is sought with DV = DVM
SW6 Indicates whether the impact point moves easterly or
westerly with increasing trip time
= 0, indicates easterly motion
= 1, indicates westerly motion
SWT Indicates whether a time step based on longitude error
has been previously taken
@ 0, indicates no such step previously taken
= 1, otherwise
T Trip time
T^, Tg, T^ Limits on transit time for iteration
T Flight time from abort to reentry when the abort
P occurs at apogee on the post maneuver trajectory
TARSP
Transit time that corresponds to MD1
18
TEST
Indicates whether the possibility of a zero has been
detected in the function being minimized
TP
Past value of trip time
T max
Maximum allowable trip time
T .
mm
Minimum allowable trip time
T .
mt
Minimum possible trip time, computed in subroutine TM1N
U
Preabort velocity vector
U
r
Reentry speed
V
a
Preabort velocity vector
VT a , VR a> VR a
Tangential, normal, and radial components of the
postabort velocity vector
X, X(j)
Seven-dimension array that defines the preabort state
vector (i.e., position vector, velocity vector, and
time)
X, Y, Z
Unit vectors along geocentric Cartesian coordinate
axes
Rvv**
Values for nonradial component of speed
XK
Indicates whether the function is being minimized
or maximized
VVV T u
Values for radial component of speed
Right ascension of impact point
e a
Postabort flight-path angle
e o
Preabort flight-path angle
Reentry flight-path angle
19
Maximum change in azimuth with allowable miss
distance
Latitude of one ATP point
Geocentric latitude of the desired PTP
True anomaly
Difference in azimuth from preabort plane to
transfer plane
Difference in azimuth from preabort plane to plane
that contains the desired landing point
Longitude of one ATP point
Longitude of the desired PTP
Earth's gravitational parameter
Angle inplane from abort to impact point
Angle inplane from abort to desired landing point
Earth's rotational rate
21
APPENDIX B
LOGIC FLOW OF THE EARTH-CENTERED
RETURN-TO-EARTH CONIC SUBPROCESSOR
22
DVMINQ
Description
Page 1
APPENDIX B
LOGIC FLOW OF THE EARTH-CENTERED
RETURN-TO-EARTH CONIC SUBPROCESSOR
SUBROUTINE DVMINQ
Purpose
This subroutine, called'from FCUA, is used to establish the minimum
fuel required to obtain safe reentry conditions with specified initial
position, velocity, flight-path angle, reentry radius, and reentry flight-
path angle. The input flag, FLAG, is used to specify whether apogee
passage is desired on the postabort trajectory.
Input
FLAG Input flag
= 1, solution trajectory has a negative radial rate
= -1, solution trajectory has a positive radial rate
Q g Postabort direction of motion
=0, direct
= 1, retrograde
Q q Preabort direction of motion
=0, direct
= 1, retrograde
RR Radial distance at reentry
R q Radial distance at abort
U Preabort velocity
6 q Preabort flight-path angle
Path angle at reentry
DVMINQ
Description
Page 2
Output
DV Minimum change in velocity required at abort
QA Apogee passage flag
= 0, no apogee passage
-1, apogee passage
V a Postahort velocity magnitude
Postabort flight-path angle
25
DVMINQ
logic Flow
Page 1
26
FCUA
Description
Page 1
SUBROUTINE FCUA
Purpose
This subroutine computes the fuel critical unspecified area solution
which has a reentry.velocity and flight-path angle satisfying the re¬
entry target line conditions and with DV less than DVM. This solution
is generated through subroutine DVMINQ. DVMINQ generates the minimum DV
solutions for a given preabort state, reentry radius, and reentry flight-
path angle. The reentry speed for this solution is then computed, and
the flight-path angle corresponding to this reentry speed is generated
from the target line. If this reentry path angle is equal to the value
supplied to DVMINQ, the solution is accepted; otherwise, the most recent
value of path angle is supplied to DVMINQ, and the solution is repeated
until convergence is achieved. The input constraints are then checked.
If no solution is found that satisfies these constraints, the logic
attempts to find an extreme fuel-critical solution with a reentry flight-
path angle between 90° and 110° that satisfies the available fuel and
maximum velocity at reentry constraints.
DV allowed for abort (may include rotation to
acceptable inclination)
KR Reentry radius
R a > R a Position vector at abort and its magnitude
SW2 Control flag
= 0, when generating the normal FCUA solution that
satisfies the reentry target line
= 1 or 2, when generating the EFCUA solution,
depending on the state of the search
6 q Preabort flight-path angle
$ r Reentry flight-path angle
Earth's gravitational parameter
27
FCUA
Description
Page 2
Output
Change in velocity
Reentry speed
Reentry flight-path angle
Logic Flow
Page 1
30
INITAL
Description
Page 1
SUBROUTINE INITAL
Purpose
This routine initializes the program at the beginning of each
state vector.
DVM
Input
Maximum allowable change in velocity
I rmax
Maximum inclination of postabort orbit
RR
Reentry radius
R
P
Unit vector in direction of abort position vector
T o
Time of abort
T rz (avg)
Average time from reentry to landing
T zmax ° r STMX
Maximum time of landing
T zmin or STMN
Minimum time of landing
"o
Rreabort velocity vector
U rmax
Maximum allowable reentry velocity
X
Preabort position vector
6
Latitude of desired landing site
Ami
Output
Constraint that limits the inclination of the
postabort orbit north of the equator
Am2
Constraint that limits the inclination of the
postabort orbit south of the equator
31
t
DDT
DT
Q 0
VR
VT
||
“g
“go
INITAL
Description
Page 2
Azimuth of premaneuver velocity vector
Fraction of trip time increment to be taken
during the search for PTP and ATP solutions
Trip time increment used in searching for PTP
and ATP solutions
Semi-latus rectum for preabort orbit
Preabort motion direction flag
Unit vector in direction of premaneuver angular
momentum
Unit vector in preabort plane of motion which is
orthogonal to abort position vector
Trip time for which motion of the impact point
switches from easterly to westerly
Maximum allowable trip time
Minimum trip time
Magnitude of preabort velocity
Radial component of preabort velocity
Tangential component of preabort velocity
Magnitude of abort position
Right ascension at Greenwich at abort time
Right ascension of Greenwich at 0 h on day of abort
Preabort flight-path angle
Average down-range distance
Azimuth change to south inclination constraint
Azimuth change to north inclination constraint
Azimuth change to nearest inclination constraint
INITAL
Logic Flow
Page 1
INITAL
Logic Flow
33
3b
MAIN
Description
Page 1
SUBROUTINE MAIN
Purpose
This subroutine is the main control routine and the entry point
for the conic program. In the flow chart are shown the logic flow for
the overall program and the sequence in which subroutines are used to
generate solutions.
Input
See section 3 for the mode specified input and appendix A.
35
i
MAIN
Logic Flow
36
MSDS
Description
Page 1
SUBROUTINE MSDS
Purpose
This subroutine computes the miss distance (i.e., the distance
between the current impact point and the desired landing site) for the
ATP and the PTP modes. If an ATP solution is being generated, the impact
point may be computed immediately because the plane of the postmaneuver
conic is known. From the impact point, the miss distance is computed as
the longitude difference between the impact point and the desired landing
line, measured at the latitude of the impact point.
For PTP modes, the return plane must first be determined. The return
plane is chosen to be that which minimizes the miss distance from the
site without violating either the inclination or AV constraints. The
miss distance in this mode is the smallest distance between the impact
point and the desired landing site. To determine the return plane, the
subroutine first generates the azimuths of trajectory planes determined by
the inclination and AV constraints and retains the most constraining set
as limits on the azimuth of the postabort velocity vector. Next, the
azimuth of a plane passing through the desired landing site (at the
current transit time) is computed. If this azimuth is between the limiting
values, then the plane through the site is determined to be the postabort
plane of motion. Otherwise, the constraint plane nearest the plane passing
through the site is selected. When the return plane is known, the impact
point and corresponding miss distance may be determined. This subroutine
was formulated using logic from subroutines PHICOM, THZCOM, and the ATP
computations found in reference 1.
Input
A r
Preabort azimuth
z
DVM
Maximum allowable DV
DVR
Radial component of the AV vector
R
Unit vector in direction of abort point
Unit vector in direction of preabort angular
P
momentum
Unit vector in direction of (R. x r )
37
MSDS
Description
Page 2
g
5
6' (mm)
X' (mm)
X
Tangential component of the postabort velocity
vector
Tangential component of the preabort velocity
vector
Bight ascension of Greenvich at the abort time
Latitude of the desired landing site
mm latitude-longitude pairs defining the ATP line
Longitude of the desired landing site
Transfer angle from abort to reentry
Azimuth change to maximum inclination plane with
azimuth > 90°
Azimuth change to maximum inclination plane
with an azimuth < 90°
Output
MD Miss distance
6 Latitude of the impact point
$ Total transfer angle to the impact point
'f’z Total transfer angle from abort to desired landing
site
Longitude of the impact point
Azimuth change to desired landing site
38
MSDS
Logic Flow
39
PRTIAL
Description
Page 1
SUBROUTINE PRTIAL
Purpose
The purpose of this subroutine is to compute the partial derivative
3n
from the conic equations of motion. The partial is computed by
on on
using the chain rule to write y T ~ r - = - ~ ar
The derivatives may then be calculated from Kepler's equations, and the
polar equation of the orbit. Also from the fact that the perigee radius
is nearly constant along the target line (it varies from 3091 n. mi. to
3465 n. mi. as the entry speed varies from 25 000 fps to 38 000 fps),
the approximation that perigee radius is constant is made.
FLAG
- 1, preapogee on conic trajectory
= -1, postapogee on conic trajectory
RR
Reentry radius magnitude
R
Abort radius magnitude
U
Reentry speed
Output
Conic partial derivative Sn^/ST^
DNDT
0 -
-G>
42
RENTRY
Description
Page 1
SUBROUTINE RENTRY
Purpose
The function of this subroutine is to compute down-range distance,
cross-range distance, and time from reentry to landing when the state
vector at reentry is given.
ICRNGG
L/D
RRBI
Input
= 1, constant G reentry
= 2, G&N reentry
= 10, compute R0 only; RO is that portion of
the down-range distance that depends on reentry
speed only
= 1, use shallow reentry target line
= 2, use steep reentry target line
Lift over drag
Constant relative range (down range)
Unit vector in direction of abort point
Unit vector in direction of preabort angular
momentum
Unit vector in direction of (R, x r )
1 o
Reentry speed
Transfer angle from abort to reentry
Azimuth change
Output
Time from reentry to landing
Down-range angle
Cross-range angle.
•>6 r ) + <3(5, DBFN)«Vb + Q(6,
41 *
SUBROUTINE RUBR
This subroutine constructs a trajectory between
at abort and the radial distance at reentry when the
angle at the reentry altitude are given.
Input
QA Apogee passage flag
QE Postabort motion flag
RR Reentry radius magnitude
R & Radial distance at abort
U Preabort speed
U r Reentry speed
@ Q Preabort flight-path angle
6 r Reentry flight-path angle
Output
A Semimajor axis
DV Change in velocity required for
e Eccentricity
T Trip time from abort to reentry
V Postabort speed
RUBR
Description
Page 1
the radial distance
speed and path
inplane maneuver
Postabort flight-path angle
47
SCAM
Description
Page 1
SUBROUTINE SCAN
Purpose
This subroutine is used only for non-zero maximum miss cases in
the PTP mode. It determines the plane change permissable within the
maximum miss constraint which minimizes AV required, and it controls the
optimization scan across the maximum miss circle to produce the minimum
AV solution. At the completion of a scan, it re-initializes the
problem to begin the search for the next solution region. This sub¬
routine was formulated from part of the T = f(MD) logic found in
reference 1.
Input
DVS Saved value of DV
MD Miss distance
MDSP(KK) KK values of maximum allowable miss distance.
Up to five values may be run during a single
tradeoff case
SW6 East - west motion flag
T Trip time
<|> Total transfer angle to impact point
<f> Total transfer angle from abort to desired
landing site
Output
T Trip time
XK Indicates whether the function is being minimized
or maximized
SCAN
Logic Flow
48
Page 1
Tradeoff
50
TCOMP
Description
Page 1
SUBROUTINE TCOMP
Purpose
This subroutine computes the new transit time based on the miss
distance determined from the current transit time and the way that
the miss distance is changing. This computation is done for both the
ATP and PTP modes. This subroutine encompasses part of the ATP and
T = f(MD) logic found in reference 1.
DVMAX
MD
R
2
T
T
max
XK
fi'(l), <5'(mm)
Input
Maximum allowable DV
Miss distance
Maximum miss distance
Unit vector in direction of abort point
Unit vector in direction of preabort angular
momentum
Unit vector in direction of (R. x r )
1 P
Current value of trip time
Maximum allowable trip time
Minimum possible trip time
Indicates whether the function is being minimized
or maximized
Right ascension of desired landing site
Latitudes of end points on the ATP line
Total transfer angle to the impact point
TCOMP
Description
Page 2
Total transfer angle from abort to desired
landing site
Azimuth change between the preabort and postabort
planes
Azimuth change to desired landing site
Output
Trip time for next iteration
Indicates whether the function is being minimized
or maximized
52
TCOMP
Logic Flow
Page 1
I
5U
TMIN
Description
Page 1
SUBROUTINE TMIN
Purpose
This subroutine computes the minimum trip time solution which
returns to the reentry target line and satisfies the following
constraints: maximum fuel, maximum reentry velocity, maximum in¬
clination, and minimum landing time. The logic first generates the
solution that has the maximum allowable reentry speed; and, if this
trajectory satisfies all constraints, it is accepted and the subroutine
is exited. Otherwise, an attempt is made to generate a solution using
all the available DV to minimize the flight time. The procedure is
to iteratively drive DV to DVM using transit time as the independent
variable. The maximum entry speed solution is used as a lower bound
on trip time; an upper bound is generated from the minimum fuel
unspecified area solution. A new trip time is selected by averaging
the upper and lower hounds, and the DV is computed for this flight
time. If DV = DVM, the solution is accepted; otherwise, the upper.
or lower hound on transit time is reset with the current transit time
depending on whether DV is greater than DVM or less than DVM. The
iteration continues until an acceptable solution is generated or
until the upper and lower bounds become equal.
Input
DVM Maximum allowable DV at abort (with acceptable
inclination)
T Minimum allowable transit time
min
U Maximum allowable entry speed
rmax
6 Azimuth change necessary to satisfy inclination
constraint
Output
DV Change in velocity
FLAG Used to force a solution with a negative radial
rate from FCUA
55
TMIN
Description
Page 2
T Transit time
U Reentry speed
VT a Tangential component of postabort velocity
VT^ Radial component of postabort velocity
57
TMIN
Logic Flow
Page 1
VACOMP
Description
Page 1
SUBROUTINE VACOMP
Purpose
This subroutine computes the vector to the conic impact point,
the latitude and longitude of the impact point, the postabort velocity-
vector, and the time of landing. In the case of a PTP solution, if
a solution has been found within the maximum allowable miss distance,
this subroutine tries to minimize fuel consumption by increasing the
miss distance to the maximum allowable before it computes the impact
point.
Input
Unit vector in direction of abort point
Unit vector in direction of preabort angular
momentum
Unit vector in direction of (R, x R )
1 P
Radial component of postabort velocity
Tangential component of postabort velocity
Change in azimuth to minimize the miss distance
Change in azimuth to nearest acceptable plane
Maximum changes in azimuth from preabort
azimuth based on inclination constraints
Output
DV Change in velocity vector
T z Time of landing
v a Postabort velocity vector
a Right ascension of the impact point
6 Latitude of impact point
Longitude of impact point
VARMIN
Description
Page 1
SUBROUTINE VARMIN
Purpose
This subroutine determines the direction of the scan for the
required landing site by deciding whether the difference between the
past and present values of the miss distance is small enough to be
considered an extremum and if so, sets the time increment, direction,
and scan flag to the proper values.
Input
DDT Independent variable
MD Function to be minimized (miss distance)
MDP Past value of MD
XK Flag that indicates whether a minimization or
maximization is to be performed
DDT
MDP
SOL
XK a
Output
Independent variable
Present value of miss distance stored for the
next pass
Flag that indicates a zero or an extremum
Flag that indicates whether a minimization or
maximization is to be performed
If XK - -1, then a maximization is performed until an extremum
is reached; then XK is set to 1 and the minimization is continued.
6l
VARMIN
Logic Flow
62
VELCOM
Description
Page 1
SUBROUTINE VELCOM
Purpose
This subroutine is used to generate trajectories which return to the
reentry target line with a specified transit time.
Input
T Desired transit time
RR Radial distance at reentry
R & Abort radial distance
6 r Current value of the flight-path angle at reentry
6 rp Past value of the flight-path angle at reentry
Output
DT Time increment
p Semilatus rectum
Apogee passage flag
= 1, apogee passage
= 0, no apogee passage
Direction of motion flag at impact point
Reentry speed
Radial component of required velocity
Tangential component of required velocity
Flight-path angle at abort
Flight-path angle at reentry
Transfer angle from abort to reentry
n rz (ave) Down-range angle based on reentry speed only; that
is, geometry effects are neglected
Subroutine INTER, which is frequently used but not specified is a
general interpolation subroutine. In this program, it is used to determine
the reentry flight-path angle given the reentry speed and the data point
for the specified reentry target line. Subroutines INTER and AESR,
which are conic trajectory utility subroutines, are specified in
reference 2.
QA
sw6
u
VR a
VT
e a
e r
64
VUP2
Description
Page 1
SUBROUTINE VUP2
Purpose
This subroutine is used to calibrate the postabort velocity by
accounting for the lunar third-body effects.
Input
R & Position vector at abort
R__ Position of the moon with respect to the earth
moon c
T^ Trip time from abort to reentry
V Postabort velocity vector
3 r Reentry flight-path angle
Output
Postabort velocity calibrated to include the
lunar third-body effects
VUP2
Logic Flow
Page 2
66
67
VUP2
Logic Flow
Page 3
►
68
REFERENCES
1. Lee, W. R.: AS-503A Requirements for the RTCC: Return-to-Earth
Abort Conic Subprocessor, Revision 1. MSC IN 67-FM-56,
Dec. 12, 1967'.
2. Northcutt, F. M. : RTCC Requirements for Apollo lit (H-3) Mission:
Moon-Centered. Return-to-Earth Conic Subprocessor. MSC IN 70-FM-19,
Jan. 30, 1970.
3. Davis, R. S.: RTCC Requirements for Apollo 14 (H-3) Mission:
Return-to-Earth Processor Supervisory and Precision Computation
Logic. MSC IN to be published.
4. Berry, R. L.; and Lee, W. R.: AS-503A Requirements for the RTCC:
Return-to-Earth Abort Conic Subprocessor. MSC IN 66-FM-117,
Oct. 19, 1966.