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D5-15560-8
APOLLO/SATURNV
POSTFLIGHTTRAJECTORY
AS-508
A
(NASA OR OR TMX OR AD NUMBER)
(CODE)
(CATEGORY)
JUNEi0, 1970
THE _I'D'LrJ'/VO COMPANY • AEROSPACE GROUP
SOUTHEAST DIVISION
DOCUMENT NO.D5-15560-8
TITLE APOLLO/SATURN V POSTFLIGHT TRAJECTORY - AS-508
MODEL NO.SATURN V
CONTRACT NO. NAS8-5608, EXHIBIT CC,
SCHEDULE II, PART IIA,TASK 8.1.6, LINE ITEM 42
TRACKING AND FLIGHT RECONSTRUCTION
JUNE i0, 1970
S. C. KRAUSSE, MANAGERSATURN ENGINEERING
ISSUE NO. ISSUED TO
THE _'l#l_l#'_ COMPANY SPACE DIVISION LAUNCH SYSTEMS BRANCH
ORIGINAL PAOE ISOF POOR QUALITY
D5-15560-8
REV.SYM
REVIS IONS
DESCRIPTION DATE APPROV_
ii
m'
D5-15560-8
ABSTRACT AND LIST OF KEY WORDS
This document presents the postflight trajectory for the
Apollo/Saturn V AS-508 flight. Included is an analysis of
the orbital and powered flight trajectories of the launch
vehicle and the free flight trajectories of the expended
S-IC and S-II stages. Trajectory dependent parameters are
provided in earth-fixed launch site, launch vehicle
navigation, and geographic polar coordinate systems. The
time history of the trajectory parameters for the launch
vehicle is presented from guidance reference release to
Command/Service Module (CSM) separation.
Tables of significant parameters at engine cutoff, stage
separation, parking orbit insertion, and translunar injection
are included in this document. Figures of such parameters
as altitude, surface and cross ranges, and magnitudes of
total velocity and acceleration as a function of range time
for the powered flight trajectories are presented.
The following is a list of key words for use in indexing
this document for data retrieval:
Apollo/Saturn V
AS-508
Postflight Trajectory
Powered Flight Trajectory
Orbital Trajectory
Spent Stage Trajectory
Apollo 13
iii
D5-15560-8
CONTENTS
PARAGRAPH
REVISIONSABSTRACTAND LIST OF KEY WORDSCONTENTSILLUSTRATIONSTABLESREFERENCESACKNOWLEDGEMENTSOURCEDATA PAGE
SECTION 1 - SUMMARYAND INTRODUCTION
SECTION 2 - COORDINATESYSTEMSAND LAUNCHPARAMETERS
SECTION 3 - POWEREDFLIGHT TRAJECTORYRECONSTRUCTION
3.13.1.13.1.23.1.33.23.2.13.2.23.33.3.13.3.2
POWEREDFLIGHT TRAJECTORYAscent PhaseSecond Burn PhaseTargeting ParametersDATA SOURCESAscent PhaseSecond Burn PhaseTRAJECTORYRECONSTRUCTIONAscent PhaseSecond Burn Phase
SECTION 4 - ORBITAL TRAJECTORYRECONSTRUCTION
4.14.24.2.14.2.24.34.3.14.3.24.4
ORBITAL TRAJECTORIESORBITAL DATA SOURCESOrbital Tracking DataOrbital Venting Acceleration DataTRAJECTORYRECONSTRUCTIONParking Orbit Insertion ConditionsTranslunar Injection Conditions
ORBITAL TRACKING ANALYSIS
SECTION 5 - TRAJECTORY ERROR ANALYSIS
5.1
5.1.1
5.1.2
5.1.3
5.1.4
ERROR ANALYSIS
Quantity of Tracking Data
Quality of Tracking Data
Consistency Between Tracking and Guidance
Velocity Data
Continuity Between Trajectory Segments
PAGE
ii
iii
iv
vi
vii
viii
ix
X
i-i
2-1
3-1
3-1
3-1
3-1
3-2
3-2
3-2
3-5
3-5
3-5
3-6
4-1
4-1
4-2
4-2
4-2
4-2
4-2
4-3
4-3
5-1
5-1
5-1
5-1
5-2
5-2
iv
D5-15560-8
CONTENTS (Continued)
PARAGRAPH
5.2 TRAJECTORY UNCERTAINTIES
SECTION 6 - SPENT STAGE TRAJECTORIES
6.1 S-IC SPENT STAGE TRAJECTORY
6.2 S-II SPENT STAGE TRAJECTORY
APPENDIX A - DEFINITIONS OF TRAJECTORY
SYMBOLS AND COORDINATE SYSTEMS
APPENDIX B - TIME HISTORY OF TRAJECTORY
PARAMETERS - METRIC UNITS
APPENDIX C - TIME HISTORY OF TRAJECTORY
PARAMETERS - ENGLISH UNITS
PAGE
5-3
6-1
6-1
6-1
A-I
B-I
C-I
v
w'
D5-15560-8
ILLUSTRATIONS
FIGURE
3-1
3-2
3-3
3-4
3-5
3-6
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
3-16
3-17
3-18
4-14-2
5-1
6-1
Ground Track and Tracking Stations -Ascent Phase
Altitude - Ascent Phase
Surface Range - Ascent Phase
Cross Range - Ascent Phase
Space-Fixed Velocity and Flight Path
Angle - Ascent Phase
Total Inertial Acceleration - Ascent Phase
Mach Number and Dynamic Pressure - S-ICPhase
Altitude - Second Burn Phase
Space-Fixed Velocity and Flight PathAngle - Second Burn Phase
Total Inertial Acceleration - Second Burn
Phase
Available Tracking Data - Ascent Phase
Antenna Locations and Center of Gravity
Azimuth Angle Tracking Deviations -Ascent Phase
Elevation Angle Tracking Deviations -Ascent Phase
Slant Range Tracking Deviations - Ascent
Phase
X Angle Tracking Deviations - Ascent Phase
Y Angle Tracking Deviations - Ascent Phase
Range Rate Tracking Deviations -Ascent Phase
Orbital Acceleration Due to VentingGround Track
Estimated Trajectory Uncertainty - AscentPhase
Ground Tracks for S-IC and S-II Spent
Stages
PAGE
3-7
3-8
3-9
3-10
3-11
3-12
3-13
3-14
3-15
3-16
3-17
3-18
3-19
3-20
3-21
3-22
3-23
3-24
4-4
4-5
5-4
6-2
vi
D5-15560-8
TABLES
TABLE PAGE
3-I3-II3-III3-IV3-V3-VI4-I
4-II4-III4-IV4-V4-VI
4-VII
5-I5-II
5-III6-I6-II
Times of Significant EventsSignificant Trajectory ParametersEngine Cutoff ConditionsStage Separation ConditionsTargeting ParametersAvailable Tracking Data - Ascent PhaseSummary of Orbital Tracking DataAvailableOrbital Venting Acceleration PolynomialsParking Orbit Insertion ConditionsTranslunar Injection Conditions
CSM Separation Conditions
Parking Orbit Tracking Utilization
Summary
Post TLI Tracking Utilization
Summary
Tracking Data Spread - Ascent Phase
Tracking Data Spread - Parking OrbitPhase
Tracking Data Spread - Post TLI Phase
S-IC Spent Stage Trajectory Parameters
S-II Spent Stage Trajectory Parameters
3-25
3-26
3-27
3-28
3-29
3-30
4-6
4-7
4-8
4-9
4-10
4-11
4-12
5-5
5-6
5-7
6-3
6-4
vii
D5-15560-8
REFERENCES
•
•
•
•
o
NASA Document SE 008-001-1, "Project Apollo
Coordinate System Standards," June, 1965.
NASA Document M-D E 8020.008B, "Natural Environment
and Physical Standards for the Apollo Program,"
April, 1965.
Boeing Document D5-15551(I)-8, "Saturn V AS-508 'H-2'
Mission Launch Vehicle Operational Flight Trajectory -
March Launch Month," December 8, 1969.
Boeing Contract Memorandum 5-9400-H-423, "Saturn V
AS-508 'H-2' Mission Launch Vehicle Operational
Flight Trajectory - April Launch Month,"
January 5, 1970.
Lockheed Document TM 54/30-150, "Manual for the GATE
Program," September, 1967.
viii
D5-15560-8
ACKNOWLEDGEMENT
The analyses presented in this document were conducted bythe following Operational Flight Analysis personnel:
OPERATIONALFLIGHT ANALYSIS
G. EngelsJ. GrahamF. HortinJ. Jaap
J. LiuR. McCurdyD. SkocovskyD. Wedell
FLIGHT SIMULATIONS
C. DorriesW. CaseR. SimmonsS. Strickland
Questions concerning the information presented in thisdocument should be directed to the technical supervisor:
G. T. Pinson, JC-80THE BOEING COMPANYHuntsville, Alabama
V. V. Moore, ChiefOperational Flight Analysis
ix
D5-15560-8
SOURCEDATA PAGE
The following listed government-furnished documentation wasused in the preparation of this document:
EXHIBIT FFLINE ITEM DATENUMBER GFD TITLE RECEIVED
R-AERO-P-#35cR-AERO-P-#17
R-AERO-P-#35bDRL-172F
3/11/704/3/70
OMPTFormatTracking and NetworkSpecificationsTransponder LocationsOperational TrajectoryCertified Data
I-MO-#4a Insertion Point and/or 4/12/70Orbital Elements
I-MO-#4c Six Seconds Raw Radar 4/12/70I-MO-#4f Meteorological Data (Final) 4/17/70I-MO-#6 IP Raw MP 4/13/70I-MO-#9 Pulse Radar Bermuda and 4/13/70
Merritt Island USBHawaii C-Band 4/21/70
I-MO-#17c Final Significant Time of 5/6/70Events
I-MO-#18a Preliminary Guidance 4/13/70Velocities
I-MO-#18c Orbital Venting Accelerations 4/23/70Data Cards
4/3/704/3/70
X
D5-15560-8
SECTION 1
SUMMARY AND INTRODUCTION
The Apollo/Saturn V AS-508 vehicle was launched from Launch
Complex 39, Pad A at the Kennedy Space Center on April ii, 1970,
at 2:13:00 P.M. Eastern Standard Time (Range Time Zero) at
an azimuth of 90 degrees east of north. Range time, which
is referenced to Range Time Zero, is used throughout this
document unless otherwise specified. Guidance reference
release (GRR) was established to have occurred at -16.961
seconds. First motion occurred at 0.3 second. At 12.6
seconds, a roll maneuver was initiated orienting the
vehicle to a flight azimuth of 72.043 degrees east of north.
This flight azimuth, dependent on the launch time, launch
day and month, is calculated using polynomial coefficients
taken from the guidance presettings in order to achieve
the desired translunar targeting parameters. The translunar
targeting parameters are functions of the moon position,
earth parking orbit inclination, earth-moon distance, andmoon travel rate.
The trajectory parameters were close to nominal through S-IC
stage burn and through the first portion of the S-II stage
burn until the early shutdown of the S-II center engine. The
premature S-II center engine cutoff (CECO) caused considerable
deviations from nominal for certain launch vehicle trajectory
parameters. These deviations were particularly evident at
S-II center and outboard engine cutoffs. However, the
S-IVB burn time was extended by the guidance unit so
that the vehicle achieved near nominal earth parking orbitinsertion conditions.
The vehicle was inserted into a parking orbit at 759.83 seconds
at an altitude of 191.6 km (103.5 n mi) and a total space-
fixed velocity of 7,792.5 m/s (25,565.9 ft/s). The vehicle
remained in orbit for approximately one and one-half
revolutions. The S-IVB stage was restarted during the second
revolution over Australia at 9,346.3 seconds.
At 9,707.15 seconds, the vehicle was injected onto a
circumlunar trajectory at an altitude of 337.9 km (182.5 n mi)
and a total space-fixed velocity of 10,832.1 m/s (35,538.4 ft/s).
At 11,198.9 seconds, the CSM separated from the launch vehicle
at an altitude of 6,997.9 km (3,778.6 n mi) and a total
space-fixed velocity of 7,628.9 m/s (25,029.2 ft/s).
The impact location of the expended S-IC stage was determined
to be 30.177 degrees north latitude and 74.065 degrees west
longitude at 546.9 seconds. The impact location of the
expended S-II stage was determined to be 31.320 degrees north
i-i
D5-15560-8
SECTION 1 (Continued)
latitude and 33.289 degrees west longitude at 1,258.1 seconds.
Section 2 of this document defines the coordinate systemsand launch parameters used for the postflight trajectoryanalysis.
The postflight mass point trajectory related parameters andanalytical procedures are presented in Sections 3 through 6.The trajectory is divided into five phases:
a. Ascent Phase
b. Orbital Phase
c. Second Burn Phase
d. Post TLI Phase
e. Free Flight Phase
The ascent phase, covering the portion of flight from guidancereference release to orbital insertion (759.83 seconds), is dis-
cussed in Section 3. This trajectory was established from track-
ing data provided by external C-band and S-band radars and tele-
metered onboard data obtained from the ST-124M inertial platform.
The second burn phase, also discussed in Section 3, covers the
portion of flight from 8,950 seconds to translunar injection
(9,707.15 seconds). This trajectory was established by
the integration of the telemetered guidance accelerometerdata and constrained to the state vectors obtained from the
orbital and post TLI trajectory phases.
The orbital phase, discussed in Section 4, covers the portion
of flight from orbital insertion to 8,950 seconds. The
orbital trajectory was established from data provided by the
_adars of the Manned Space Flight Network.
The post translunar injection (TLI) phase, discussed in
Section 4, covers the portion of flight from the translunar
injection to CSM separation (11,198.9 seconds). This
trajectory was established from data provided by the radars
of the Manned Space Flight Network.
The error analysis of the reconstructed trajectory is discussed
in Section 5. The criteria for error analysis are included
and trajectory uncertainty limits are assigned to the ascent,
parking orbit, second burn, and post TLI phases.
1-2
ORIGINAL PAGE !..¢
OF POOR QUALIT_
D5-15560-8
SECTION 1 (Continued)
The free flight phase, discussed in Section 6, covers the
trajectories of the expended S-IC and S-II stages. These
trajectories are based on initial conditions obtained from the
postflight trajectory at separation. The nominal separation
impulses for both stages were used in the simulation.
Appendix A provides a detailed definition of the symbols,
nomenclature, and coordinate systems used throughout thedocument.
Appendix B tabulates the time history of selected trajectory
parameters in metric units.
Appendix C tabulates the time history of selected trajectory
parameters in English units.
1-3
D5-15560-8
THIS PAGE INTENTIONALLY LEFT BLANK.
1-4
D5-15560-8
SECTION 2
COORDINATESYSTEMSAND LAUNCHPARAMETERS
The time history of Observed Mass Point Trajectory parametersin both metric and English units is tabulated in Appendices Band C, respectively. These tabulations are in earth-fixedlaunch site, launch vehicle navigation, and geographic polarcoordinate systems. These coordinate systems are defined inReference i, "Project Apollo Coordinate System Standards,"(PACSS) and are designated PACSSI0, PACSSI3, and PACSSI,respectively. The trajectory symbols and terminology usedin this document are defined in Appendix A.
The Fischer Ellipsoid of 1960 (Reference 2) is used as therepresentative model for the earth and its gravitationalfield. All latitude and longitude coordinates are definedwith respect to this ellipsoid.
The geographic coordinates for Launch Complex 39, Pad A,at the Kennedy Space Center are as follows:
Geodetic LatitudeLongitude
28.608422 degrees north80.604133 degrees west
The height of the center of gravity of the launch vehicleabove the reference ellipsoid is 59.6 m (195.5 ft).
The azimuth alignments are as follows:
Launch AzimuthFlight AzimuthST-124M Platform Azimuth
90.0 degrees east of north72.043 degrees east of north72.043 degrees east of north
2-1
D5-15560-8
THIS PAGE INTENTIONALLY LEFT BLANK.
2-2
D5-15560-8
SECTION 3
POWEREDFLIGHT TRAJECTORYRECONSTRUCTION
3.1 POWEREDFLIGHT TRAJECTORY
3.1.1 Ascent Phase
A comparison of actual and nominal times for significantflight events is presented in Table 3-I. The nominal timesfor these events are taken from References 3 and 4.
The tracking stations and the vehicle ground track for theascent phase are shown in Figure 3-1.
The actual altitude, surface range, and cross range are shownin Figures 3-2 through 3-4, respectively, for the entire ascenttrajectory. The magnitude of the total space-fixed velocityvector and the associated flight path angle are shown inFigure 3-5. The magnitude of the total inertial accelerationvector is shown in Figure 3-6. Mach number and dynamicpressure are shown during the S-IC phase of the ascenttrajectory in Figure 3-7.
Pertinent trajectory parameters, such as altitude, velocity,and acceleration, are given at significant event times inTable 3-II.
Engine cutoff and stage separation conditions are given inTables 3-III and 3-IV, respectively.
The ascent trajectory, from guidance reference release toparking orbit insertion, is tabulated in Tables B-I throughB-III in metric units, and in Tables C-I through C-III inEnglish units. These tables present the trajectory in theearth-fixed launch site (PACSSI0), launch vehicle navigation(PACSSI3), and geographic polar (PACSSI) coordinate systems.The definitions pertaining to the trajectory symbols and thecoordinate systems are given in Appendix A.
3.1.2 Second Burn Phase
A comparison of actual and nominal times for significantflight events pertaining to the second burn phase is includedin Table 3-I.
The actual altitude is shown in Figure 3-8. The magnitude ofthe total space-fixed velocity vector and the associated flightpath angle are shown in Figure 3-9. The magnitude of the total
3-1
D5-15560-8
3.1.2 (Continued)
inertial acceleration vector is shown in Figure 3-10. Themaximum total inertial acceleration and earth-fixed velocityare shown in Table 3-II.
The second burn trajectory, from the time of S-IVB restartpreparations to CSM separation, is tabulated in Tables B-Vthrough B-VII in metric units, and in Tables C-V throughC-VII in English units. These tables present the trajectoryin the earth-fixed launch site (PACSSI0), launch vehiclenavigation (PACSSI3), and geographic polar (PACSSI) coordinatesystems. The definitions pertaining to the trajectory symbolsand the coordinate systems are given in Appendix A.
3.1.3 Targeting Parameters
The actual and nominal targeting parameters are given in
Table 3-V. These nominal parameters are taken from References 3
and 4 as terminal conditions for the powered flight phases. The
actual parameters achieved were close to nominal.
3.2 DATA SOURCES
3.2.1 Ascent Phase
Tracking data and telemetered guidance velocity data were
received during the period from first motion through orbital
insertion. The time periods for which tracking system cover-
age was available are shown in Figure 3-11 and itemized in
Table 3-VI. The geographic locations of the tracking stations
and the ground track for the ascent trajectory are shown in
Figure 3-1. The antenna locations for the tracking system and
the actual and nominal vehicle center of gravity time history
are shown in Figure 3-12.
C-Band and USB tracking data were available from
the stations located at Patrick Air Force Base, Merritt Island,
Grand Turk Island, and Bermuda Island. The C-Band tracking
data were provided as measured parameters in azimuth angle,
elevation angle, and slant range. These measurements are
defined in Reference 1 and designated as PACSS3a. The USB
tracking data were provided as measured parameters in X angle,
Y angle, and range rate. These measurements are defined
in Reference 1 and designated as PACSS3c.
Comparisons between these data and the ascent trajectory were
calculated in PACSS3a and PACSS3c. The position components
of the ascent trajectory in PACSSI0 were corrected for the
differences between the center of gravity (nominal) and the
3-2
D5-15560-8
3.2.1 (Continued)
transponder location. The corrected position components weretransformed into the measured parameters of PACSS3a and
PACSS3c. Differences or deviations (tracking data minus
corresponding parameters derived from the ascent trajectory)
were calculated, smoothed, and plotted as functions of time,
and are shown in Figures 3-13 through 3-15 for C-Band, and in
Figures 3-16 through 3-18 for USB data.
3.2.1.1 C-Band Tracking Data
Patrick (0.18) radar provided tracking data from 27 to 527
seconds. The azimuth angle measurements were of good quality
except in the time interval of 27 to 130 seconds, where the
measurements were noisy. The Patrick azimuth angles deviated
considerably from the trajectory up to 200 seconds. They
converged to the trajectory thereafter with a maximum
deviation of 0.005 degree. The elevation angle measurements
were noisy during the early portion (27 to 90 seconds) and
the latter portion (440 to 527 seconds) of tracking. These
measurements also deviated considerably from the trajectory
up to about 80 seconds and agreed favorably with the
trajectory within the time interval from 80 to 527 seconds
with a maximum deviation of 0.028 degree. The slant range
measurements were of good quality throughout the tracking
period with a maximum deviation of 85 m (279 ft) from the
trajectory. The slant range measurements had a discontinuity
at about 175 seconds, indicating a switch from beacon to
skin tracking.
Grand Turk (7.18) radar supplied data from 227 to 586 seconds.
The azimuth and elevation angle measurements had a character-
istic deviation in the time interval of 450 to 500 seconds.
The azimuth angle measurements were noisy between 350 and
586 seconds. The elevation angle measurements were noisy
throughout the tracking period. Outside the time interval
for the characteristic deviation, the azimuth and elevation
angle measurements had the maximum deviations of 0.041 and
0.049 degree respectively. The slant range measurements were
of good quality throughout the tracking period with a
maximum deviation of 40 m (131 ft).
Merritt Island (19.18) radar furnished data from 16 to 527
seconds. The azimuth and elevation angle measurements were
erratic in the interval from 16 to 190 seconds. The azimuth
angle measurements reached a maximum deviation of 0.048
degree and decreased rapidly after 80 seconds with a maximum
deviation of 0.005 degree after 210 seconds. The elevation
angle measurements deviated a maximum of 0.043 degree from
the trajectory at 90 seconds and decreased rapidly thereafter
with a maximum deviation of 0.005 degree after 200 seconds.
3-3
D5-15560-8
3.2.1.1 (Continued)
The slant range measurements were of good quality throughoutthe tracking period with a maximum deviation of 50 m(164 ft).
Bermuda (67.16) radar provided data from 273 to 759 seconds.The elevation angle measurements were noisy from 273 to370 seconds. The elevation angle measurements agreedfavorably with the trajectory with a maximum deviation of0.040 degree. The azimuth angle measurements were in goodagreement with the trajectory with a maximum deviation of0.015 degree. The slant range measurements were of goodquality throughout the tracking period with a maximum deviationof 85 m (279 ft).
Bermuda (67.18) radar provided data from 272 to 759 seconds.The azimuth angle measurements were in good agreement withthe trajectory, except in the time interval of 530 to 600seconds where a characteristic deviation occurred, with amaximum deviation of 0.021 degree. The elevation anglemeasurements were noisy during the early portion (272 to350 seconds) and the latter portion (680 to 759 seconds) oftracking. The elevation angle measurements agreed favorablywith the trajectory with a maximum deviation of 0.020 degree.The slant range measurements were of good quality throughoutthe tracking period with a maximum deviation of I00 m (328 ft).
3.2.1.2 USB Tracking Data
Merritt Island radar furnished data from 26 to 359 seconds.The X and Y angle measurements were erratic in the timeintervals of 26 to 41 seconds, 196 to 214 seconds, and 326 to332 seconds. The X angle measurements oscillated considerablyto about 220 seconds, and agreed favorably thereafter with amaximum deviation of 0.029 degree. The Y angle measurementsdeviated considerably from the trajectory up to about 180seconds, but agreed with the trajectory thereafter with amaximum deviation of 0.004 degree. The range rate measure-ments were erratic in the time intervals of 128 to 140 seconds,164 to 168 seconds, 196 to 201 seconds, and 326 to 332 seconds.The range rate measurements excluding the erratic time intervals,
' ,
agreed with the trajectory wlth a maximum deviation of 0.4 m/sec
(1.3 ft/sec).
Bermuda radar supplied data from 283 to 759 seconds. The
X angle measurements were noisy in the time intervalsof 283 to 410 seconds, and 700 to 759 seconds. The
X angle measurements agreed favorably with the trajectoryin the time interval of 283 to 700 seconds with a maximum
3-4
D5-15560-8
3.2.1.2 (Continued)
deviation of 0.020 degree. The Y angle measurements wereof good quality and agreed favorably with the trajectorywith a maximum deviation of 0.020 degree. The rangerate measurements exhibited a characteristic closestapproach phenomenon from 535 to 585 seconds, but wereconsistent with the trajectory outside this interval.
3.2.2 Second Burn Phase
Telemetered guidance velocity data during the S-IVB secondburn period were used as generating parameters inreconstructing the second burn trajectory. Notracking data were available during the S-IVB secondburn period.
3.3 TRAJECTORYRECONSTRUCTION
3.3.1 Ascent Phase
The ascent trajectory from guidance reference release toorbital insertion was established by a composite solutionof available tracking data and telemetered onboard guidancevelocity data.
Before the data were used in the trajectory solution, oneor more of the following processing steps were performed:
a. Inspecting for format and parity errors
b. Time editing
c. Data editing and filtering
d. Refraction correction
e. Reformatting
f. Coordinate transformation
The position components of the tracking point of the vehicle
in PACSSI0 were established by merging the launch phase and
ascent phase trajectory segments.
The launch phase (from first motion to 20 seconds) was
established by integrating the telemetered guidance acceler-
ometer data and constraining it to the early portion of the
ascent phase trajectory. The ascent phase (from 20 seconds
to orbital insertion at 759.83 seconds) was based on a
3-5
D5-15560-8
3.3.1 (Continued)
composite fit of external tracking data and telemetered onboard
guidance velocity data and was constrained to the insertion
vector obtained from the orbital analysis as described in
Section 4. The reconstructed trajectory is referenced to
the vehicle _enter of gravity.
In the above analysis, a computer program (GATE), which uses
a guidance error model, was utilized. The telemetered guidance
velocity data were used as the generating parameter, and
error coefficients were estimated to best fit the tracking
observations. The Kalman recursive method was used for the
estimation. Reference 5 gives a theoretical discussion of
the GATE program.
The position components, in PACSSI0, were filtered anddifferentiated to obtain vehicle velocity and acceleration
components. Since numerical differentiators tend to distort
the data through the transient areas (engine cutoffs), the
guidance velocity data were integrated and used to fill in
these areas.
The trajectory data in PACSSI0 were then transformed to
several coordinate systems. Various trajectory parameters
were also calculated and are presented in Appendices B and C.
In calculating the Mach number and dynamic pressure, measured
meteorological data were used.
3.3.2 Second Burn Phase
The second burn trajectory was established by combining an
orbital trajectory segment and a powered flight trajectory
segment.
The orbital trajectory segment covers the portion of flight
from the beginning of S-IVB restart preparations (8,768.1
seconds) to 8,950 seconds. This trajectory segment was
obtained from the orbital solution as described in Section 4.
The powered flight trajectory segment covers the time span
from 8,950 seconds to translunar injection (9,707.15 seconds).
This trajectory segment was established by integrating the
telemetered guidance velocities, which were used as
generating parameters, and was constrained to the translunar
injection vector (obtained from the post TLI trajectory ofSection 4). The GATE program was utilized for the solution.
The position components, in PACSSI0, were filtered,
differentiated, shaped, and transformed in the same manner
as described in Paragraph 3.3.1.
3-6
D5-15560-8
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D5-15560-8
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RANGE TIME - SECONDS
FIGURE 3-12. ANTENNA LOCATIONS AND CENTER OF GRAVITY
3-18
D5-15560-8
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TABLE 3-I.
D5-15560-8
TIMES OF SIGNIFICANT EVENTS
RANGE TIME, SECONDS
EVENT
Guidance Reference Release
First Motion
Start of Time Base 1
Mach 1
Maximum Dynamic Pressure
S-IC Center Engine Cutoff
S-IC Outboard Engine Cutoff
S-IC/S-II Separation Command
S-II Center Engine Cutoff
S-II Outboard Engine Cutoff
S-II/S-IVB Separation Command
S-IVB Ist Guidance Cutoff
Parking Orbit Insertion
Begin S-IVB Restart Prepara-rations
S-IVB Engine Reignition(STDV Open)
S-lVB 2nd Guidance Cutoff
Translunar Injection
CSM Separation
ACTUAL
-16.961
0.3
0.6
68.4
81.3
135.18
163.60
164.3
330.64
592.64
593.5
749.83
759.83
8,768.1
9,346.3
9,697.15
9,707.15
II ,198.9
NOMINAL
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85.3
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164.00
164.7
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558.11
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715.76
8,749.9
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44.07
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13.56
38.9
3-25
D5-15560-8
TABLE 3-11. SIGNIFICANT TRAJECTORY PARAMETERS
EVENT
Flr._t Motion
Mach 1
Maximum Dynamic Pressure
Maximum Total Inertial
Acceleration: S-IC
S-ll
S-IVB 1st Burn
S-IVB |nd Burn
Maximum Eirth-Ftxed
Velocity: S-IC
S-11
S-IVB 1st Burn
S-IVB Znd Burn
PARAMFTER
Range Time, sec
Total Inertial Acceleration, m/} 2
(ft/s g )
(g)
Ranqe Time, sec
Altitude, km
(n mI)
Range Time, sec
Dynamic Pressure, N/cm ?
(li_f/ft 2 )
Altitude, km
(n ml)
Range Time, sac
Acceleration, m/s 2
(ft/si)
(g)
Range Time, sac
Acceleration I m/s 2ft/s 2 )
(g)
Range Time, sec
Acceleration, m/s 2
(ft/s 2 )
(g)
Range Time, sac
Acceleratlon t m/s 2
(ft/s 2 )
(g)
Range Time, sac
Velocity, m/s
(ft/$)
Range Time, sac
Valocltyt m/s
(ft/$)
Range Time, sac
Velocity, m/s(ftls)
Range Time, sac
Veloctty t m/s(ftli)
VALUE
0.3
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68.4
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12.5
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163.70
37,60
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537.00
16.25
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6.66
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593.50
6,492.7
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3-26
D5-15560-8
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3-27
TABLE 3-1V. STAGE
D5-15560-8
SEPARATION CONDITIONS
PARAMETER S-lC/S-IiSEPARATIONCOMMAND
Range Time, sec
Altitude, km(n mi)
Surface Range,(n
Space-Fixed
kmmi)
m/sVelocit it/s)
164.3
68.0(36.7)
96.0(51.8)
2,754.3(9,036.4)
Flight Path Angle,
Heading Angle, deg
Cross Range, km(n mi)
deg
Cross Range Velocity, m/s(ft/s)
Geodetic Latitude,
Longitude, deg E
deg N
19.383
75.693
1.0(O.5)
23.6(77.4)
28.864
-79.666
S-II/S-IVBSEPARATIONCOMMAND
593.5
189.2(102.2)
1,791.8(967.5)
6,895.9(22,624.3)
0.650
83.380
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3-28
D5-15560-8
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3-30
D5-15560-8
SECTION 4
ORBITAL TRAJECTORY RECONSTRUCTION
4.1 ORBITAL TRAJECTORIES
The S-IVB/LM/CSM was inserted into a near circular parking
orbit at 759.83 seconds. While in parking orbit, vehicle
subsystem checkout was carried out from the Mission
Control Center at Houston. During the second
revolution over Australia, the S-IVB stage was restarted and
the vehicle was placed onto a translunar trajectory.
The parking orbit insertion conditions were close to nominal.
The space-fixed velocity at insertion was 0.5 m/s (1.7 ft/s)
less than nominal, and the flight path angle was 0.005 degree
greater than nominal. The eccentricity was 0.0001 greater
than nominal. The apogee was 0.5 km (0.3 n mi) greater than
nominal, and the perigee was 1.2 km (0.6 n mi) less than
nominal.
The translunar injection (TLI) conditions were also close to
nominal. The eccentricity was equal to nominal, the inclin-
ation was 0.016 degree less than nominal, and the node was
0.034 degree lower than nominal. The space-fixed velocity
was 3.7 m/s (12.2 ft/s) greater than nominal, the altitude
was 4.5 km (2.4 n mi) less than nominal, and C 3 was 9 m2/s2(97 ft2/s 2) less than nominal.
The parking orbit trajectory spans the interval from insertion
to 8,950 seconds. The post TLI trajectory covers the period
from translunar injection (9,707.15 seconds) to CSM
separation (11,198.9 seconds). These two orbital trajectories
were established by the integration of the orbital model
equations using the insertion/injection vector as the initial
conditions.
The insertion/injection conditions, as determined by the
Orbital Correction Program (OCP), were obtained by a
differential correction procedure which adjusted the estimated
insertion/injection conditions to fit the tracking data in
accordance with the weights assigned to the data. After all
available tracking data were analyzed, the stations and
passes providing the better quality data were used in the
determination of the insertion/injection conditions.
4-1
D5-15560-8
4.2 ORBITAL DATA SOURCES
4.2.1 Orbital Tracking Data
Orbital tracking was conducted by the NASA Manned SpaceFlight Network (MSFN). A summary of the orbital trackingdata is given in Table 4-I. The C-band and Unified S-bandtracking data were mutually consistent and both agreedfavorably with the reconstructed trajeatory.
4.2.2 Orbital Venting Acceleration Data
During the orbit, no major thrusting occurred; however, theorbit was continuously perturbed by low-level LH2 ventingthrust. To accurately model the orbit of the vehicle, thisperturbation was taken into account. The venting model wasderived from telemetered guidance velocity data from theST-124M guidance platform. The guidance velocity data werefitted in segments by polynomials in time. These polynomialswere analytically differentiated to model the accelerationcomponents measured by the guidance platform. Table 4-IIlists the acceleration polynomials derived by this method.Figure 4-1 reflects the best estimate of the total ventingacceleration (RSS of components) after atmospheric effectsand biases have been removed.
4.3 TRAJECTORYRECONSTRUCTION
4.3.1 Parking Orbit Insertion Conditions
The Orbital Correction Program (OCP) was used to solve forthe parking orbit insertion conditions utilizing the trackingdata and the above-mentioned vent model. The insertionconditions are given in Table 4-III. The parking orbitsolution was based on a composite fit of the two Bermudastations at insertion, pass one of Canary Island S-band, passone of Carnarvon, pass two of MILA, and pass two of Carnarvon.This combination of trackers is geometrically spaced toinsure adequate coverage of the parking orbit. The Bermudadata at insertion were also used in the trajectory reconstructionof the ascent phase. The use of Bermuda data in the ascentphase solution and also in the orbital phase solution aids inassuring the continuity of the trajectory. The orbitalsolution, with the exception of the FPS-16M Bermuda radar,is based on the higher quality FPQ-6 or TPQ-18 radars. Theground track from parking orbit insertion to CSM separationis given in Figure 4-2. The parking orbit trajectory inPACSSI is given in Tables B-IV and C-IV.
4-2
D5-15560-8
4.3.2 Translunar Injection Conditions
The translunar injection (TLI) conditions were determined bythe Orbital Correction Program (OCP) utilizing the postinjection tracking data. The post TLI trajectory is based
on a composite fit of Hawaii, MILA, Bermuda C-band data and
Hawaii, MILA, Corpus Christi Unified S-band data. The
Goldstone Wing Site data were utilized to verify the integrity
of this trajectory segment. The TLI conditions are given in
Table 4-IV. The post TLI trajectory is included in Tables B-V
through B-VII in metric units and Tables C-V through C-VII
in English units. The CSM separation conditions are givenin Table 4-V.
4.4 ORBITAL TRACKING ANALYSIS
The stations used to obtain the parking orbit insertion
conditions and translunar injection conditions are given by
Tables 4-VI and 4-VII, respectively. These two tables also
include the number of data points and the Root-Mean-Square
(RMS) errors of the residuals for each data type. These RMS
errors represent the difference between the actualobservations and the calculated observations based on the
orbital ephemeris defined by the initial conditions. The
RMS residual errors include high frequency errors (assumed
Gaussian), systematic errors due to instrumentation biases,
mathematical model error, and errors in the correction for
atmospheric refraction.
The maximum RMS error of the residuals for the parking orbit
was 21 m (69 ft) in slant range, 0.036 degree in elevation
angle, and 0.018 degree in azimuth angle for the C-band
trackers and 0.8 m/s (2.6 ft/s) in range rate, 0.035 degree
in X-angle, and 0.014 degree in Y-angle for the UnifiedS-band tracker. The maximum RMS error of the residuals for
the post TLI trajectory was 5 m (16 ft) in slant range,
0.039 degree in elevation angle, and 0.018 degree in azimuth
angle for the C-band trackers and 0.3 m/s (i.0 ft/s) in range
rate, 0.012 degree in X-angle and 0.008 degree in Y-angle for
the Unified S-band trackers. The magnitudes of these RMS
errors are reasonable and indicate the validity of the
parking orbit and post TLI trajectory.
4-3
D5-15560-8
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D5-15560-8
TABLE 4-I. SUMMARY OF ORBITAL TRACKING DATA AVAILABLE
m
STATION TYPE OF RADARS
Bermuda
Bermuda
Vanguard Ship
FPS-16M
FPQ-6
FPS-16M
REV 1
X
I
X
Canary Island
Carnarvon
Guaymas
Merritt Island
Hawaii
Goldstone*
Hawaii
Merritt Island
Corpus Christi
X
X X
REV 2 POST TLI
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FPS-16M
USB-85'
USB-30'
USB-30'
USB-30'
X
* Jet Propulsion Laboratory Wing Site measuring hour angle,declination, and range rate (PACSS3b).
4-6
D5-15560-8
TABLE 4-11. ORBITAL VENTING ACCELERATION POLYNOMIALS*
T b 759
T e 9,281-6
CO -0.74495042 x I0-9
C 1 -0.93528923 x I0-11
C 2 0.12408145 x I0
C 3 -0.37716176 x 10 -15-19
C4 0.42706252 x I0
C 5 -0.16021814 x 10 -23°°
Y
T b 759
T e 9,281-7
CO -0.58670000 x I0
C 1 0
C2 0
C3 0
C4 0
C 5 0
T b 759 952
T e 952 9,281
CO 0.37549244 x 10 -5 0.11845452 x 10 -5
CI -0.11401015 x 10 -7 -0.21655062 x 10 -8-12
C2 0 0.72556226 x I0
C3 0 -0.93970400 x 10 -17-19
C4 0 -0.18107583 x 10
C5 0 0.14722653 x 10 -23
t 2 C3 t3 4+C 5* Polynomials are of the form a=Co+Clt+C 2 + +C4t t 5
where a is the acceleration component:(km/s 2) and t = T-T b
where Tb_T
D5-15560-8
TABLE 4-111. PARKING ORBIT INSERTION CONDITIONS
PARAMETER
Range Time, sec
Altitude, km(n mi)
Space-Fixed Velocity, m/s(ft/s)
Flight Path Angle, deg
Heading Angle, deg
Inclination, deg
Descending Node, deg
Eccentricity
Apogee*, km(n mi)
Perigee*, km(n mi)
Period, min
Geodetic Latitude, deg N
Longitude, deg E
VALUE
759.83
191.6
(103,5)
7,792.5(25,565.9)
0.005
90.148
32.525
123.084
0.0001
185.7
(I00.3)
183.9
(99.3)
88.19
32.694
-50.490
*Based on a spherical earth of radius 6,378.165 km(3,443.934 n mi)
4-8
D5-15560-8
TABLE 4-1V. TRANSLUNARINJECTION CONDITIONS
PARAMETER
Range Time, sec
Altitude, km(n mi)
Space-Fixed Velocity, m/s(ft/s)
Flight Path Angle, deg
Heading Angle, deg
Inclination, deg
Descending Node, deg
Eccentricity
, m2/s 2C3" (ft2/s2)
Geodetic Latitude, deg N
Longitude, deg E
VALUE
9,707.15
337 o9(182.5)
10,832.1(35,538.4)
7.635
59.318
31.817
122.997
0.9772
-1,376,274(-14,814,090)
-8.919
167.207
*Twice the specific energy of orbit
2 2uC3 = V
R
where V = Inertial Velocity= Gravitational Constant
R = Radius from center of earth
4-9
TABLE 4-V.
D5-1 5560-8
CSM SEPARATIONCONDITIONS
=.,
PARAMETER VALUE
Range Time, sec
Altitude, km(n mi)
Space-Fixed Velocity, m/s(ft/s)
11,198.9
6,997.9(3,778.6)
7,628.9(25,029.2)
Flight Path Angle, deg
Heading Angle, deg
Geodetic Latitude, deg N
Longitude, deg E
45.030
72.315
26.952
-129o677
4-10
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4-12
D5-15560-8
SECTION 5
TRAJECTORY ERROR ANALYSIS
5.1 ERROR ANALYSIS
The confidence level or uncertainty that is assigned to a
reconstructed trajectory depends on the degree of fulfillment
of the following criteria:
a. Quantity of Tracking Data
b. Quality of Tracking Data
c. Consistency between Tracking and Guidance Velocity Data
d. Continuity between Trajectory Segments
These criteria vary from flight to flight. Therefore, a
rigorous statistical error analysis of the reconstructed
trajectory is difficult to obtain. The following paragraphs
summarize the results for this flight, and lead to the
position and velocity uncertainties for the reconstructed
trajectory.
5.1.1 Quantity of Tracking Data
The available tracking data for the ascent phase are
given in Figure 3-11 and Table 3-VI. The tracking coverages
for the parking orbit and post TLI phases are given inTable 4-I.
The tracking stations for the ascent and post TLI phases
provided extensive redundant coverage. The available tracking
data during parking orbit provided adequate coverage. No
tracking data were available for the second burn phase.
5.1.2 Quality of Tracking Data
The C-band and S-band tracking data were of good quality.
Comparisons of the C-band data in measured parameters
(PACSS3a) with the ascent trajectory are shown in Figures 3-13
through 3-15. Comparisons of the S-band data in measured
parameters (PACSS3c) with the ascent trajectory are shown in
Figures 3-16 through 3-18. These plots indicate that the
tracking data from the different stations were mutually
consistent and the data deviations were of acceptable
magnitude. The tracking data obtained during the parking
orbit and post TLI phases were of good quality. The RMS
errors of residuals for each data type are given in Tables 4-VI
and 4-VII, respectively.
5-1
D5-15560-8
5.1.2 (Continued)
The tracking data were transformed into the earth-fixedlaunch site coordinate system (PACSSI0) and differenced withthe reconstructed trajectory to provide a more directindication of the spread of the tracking data. The trackingdata spreads for the ascent, parking orbit, and post TLIphases are given in Tables 5-I through 5-III, respectively.
5.1.3 Consistency Between Tracking and Guidance VelocityData
The consistency between tracking and guidance velocity datacan be obtained by examining the guidance velocity error plotsduring powered flight trajectory segments. These error plotsgive the differences between the guidance velocities from theST-124M platform and those derived from the reconstructedtrajectory.
The guidance velocity error plots for the ascent phase hadreasonable shapes and magnitudes. The maximum error amountedto 1.6 m/s (5.2 ft/s) in the X-direction, 3.7 m/s (12.1 ft/s)in the Y-direction, and 0.5 m/s (1.6 ft/s) in the Z-direction,referenced to launch vehicle platform-accelerometer coordinatesystem (PACSSI2).
The guidance velocity error plots for the second burn phasealso had reasonable shapes and magnitudes. The maximum erroramounted to I.i m/s (3.6 ft/s) in the X-direction, 1.2 m/s(3.9 ft/s) in the Y-direction, and 7.0 m/s (23.0 ft/s) in theZ-direction, referenced to PACSSI2.
5.1.4 Continuity Between Trajectory Segments
The continuity between trajectory segments can be obtained byexamining the insertion and injection parameters determinedby the orbital and powered flight solutions before thetrajectory segments were merged together.
Comparisons of the state vector differences at parking orbitinsertion obtained independently by the powered flight andorbital analyses yielded good agreement. The position andvelocity components of the solutions had a spread of i0 m(33 ft) and 0.2 m/s (0.7 ft/s) in the downrange direction,340 m (1,115 ft) and 1.4 m/s (4.6 ft/s) in the verticaldirection, and 120 m (394 ft) and 0.8 m/s (2.6 ft/s) in thecrossrange direction, referenced to the earth-fixed launchsite coordinate system (PACSSI0).
Comparisons of the TLI vectors determined independently fromthe powered flight and orbital analyses also yielded good
5-2
D5-15560-8
5.1.4 (Continued)
agreement. The TLI vector from the powered flight analysiswas obtained by propagating forward the state vector at 8,950seconds (from parking orbit analysis) to 9,707.15 seconds,using the telemetered guidance velocity data as the generatingparameter. The TLI vector from the orbital analysis was deter-mined separately by fitting the post TLI tracking data. Theposition and velocity components of the two solutions hadrespectively a difference of 580 m (1,903 ft) and 4.7 m/s (15.4(15.4 ft/s) in the X-direction, 140 m (459 ft) and 2.0 m/s(6.6 ft/s) in the Y-direction, and 480 m (1,575 ft) and5.0 m/s (16.4 ft/s) in the Z-direction, referenced to theearth-fixed launch site coordinate system (PACSSI0).
A dispersion analysis was performed for the TLI trajectoryby selecting various tracking data combinations. The TLIvectors had a spread in position and velocity componentsin PACSSI0:
a. 310 m (1,017 ft) - 0.2 m/s (0.7 ft/s)
b. 1,210 m (3,970 ft) - 2.8 m/s (9.2 ft/s)
c. 520 m (1,706 ft) - 0.9 m/s (3.0 ft/s)
As an additional validity check on the post TLI trajectory,the translunar injection conditions were propagated forwardto lunar impact with all planned velocity incrementsaccounted for. The resultant lunar impact point is inreasonable agreement with the actual lunar impact as deter-mined by the MSFC Lunar Impact Team from deep space trackingdata.
5.2 TRAJECTORYUNCERTAINTIES
Based on the information of Paragraph 5.1 and a priori know-ledge, the trajectory uncertainties were estimated.
The uncertainties for the ascent phase are shown in Figure 5-1.At S-IC OECO, the uncertainties in position and velocitycomponents in PACSSI0 are ±70 m (±230 ft) and ±0.4 m/s(_1.3 ft/s), respectively. At S-II OECO, the uncertainties inposition and velocity components in PACSSI0 are ±360 m(±1,181 ft) and _0.7 m/s (±2.3 ft/s), respectively. Atinsertion and throughout the parking orbit, the uncertaintiesin position and velocity components in PACSSI0 are ±500 m(±1,640 ft) and ±i.0 m/s (±3.3 ft/s), respectively. The
trajectory uncertainties increased to ±750 m (±2,461 ft)
in position components and ±1.5 m/s (±4.9 ft/s) in velocity
components at TLI and throughout the post TLI trajectory.
5-3
D5-15560-8
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5-8
D5-15560-8
SECTION 6
SPENT STAGE TRAJECTORIES
6.1 S-IC SPENT STAGE TRAJECTORY
Postflight predictions of earth surface impact parameters for
the spent S-IC stage were computed using a mass point
trajectory simulation computer program. S-IC postflight
burnout position and velocity data were combined with nominal
main propulsion system decay performance and nominal retro-
rocket performance to initialize the simulation program.
Three separate theoretical trajectories were computed for the
spent S-IC stage. These three trajectories represent the
following booster atmospheric entry conditions:
a. Zero degree angle-of-attack entry
b. Ninety degree angle-of-attack entry
c. Tumbling entry
The tumbling booster case is considered to define actual case
impact conditions although no tracking coverage was availablefor confirmation.
Results of the three computed S-IC spent stage trajectories
are summarized in Table 6-I. The ground track is shown in
Figure 6-1.
6.2 S-II SPENT STAGE TRAJECTORY
Three separate theoretical trajectories, corresponding to the
zero-degree, ninety-degree, and tumbling-case trajectories
computed for the S-IC stage, were computed for the spent S-II
stage.
The computed results, assuming a tumbling stage, were
considered to define stage impact conditions since no tracking
coverage of the spent S-II stage was available.
Results of the three computed S-II spent stage trajectories
are summarized in Table 6-II. The ground track is shown in
Figure 6-1.
6-1
D5-15560-8
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6-2
D5-15560-8
TABLE 6-I. S-IC SPENT STAGE TRAJECTORY PARAMETERS
Impact:
EVENT PARAMETER VALUE
Tumbling Case
Impact: 0 ° Angle-of-Attack
Impact: 90 ° Angle-of-Attack
Apex: Tumbling Case
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Altitude, km(n mi)
Surface Range, km(n mi)
546.9
30.177
-74.065
658.0(355.3)
506.6
30.195
-73.973
667.1(360.2)
581.1
30.164
-74.127
651.9(352.0)
271.7
116.9(63.1)
325.9(176.0)
6-3
TABLE 6-11. S-II SPENT
D5-15560-8
STAGE TRAJECTORY PARAMETERS
Impact:
Impact:
Impact:
Apex:
EVENT
Tumbling Case
PARAMETER
Range Time, sec
Latitude, deg N
Longitude, deg
Surface Range,
E
km
VALUE
1,258.l
31.320
-33.289
4,542.3
0 ° Angle-of-Attack
90 ° Angle-of-Attack
Tumbling Case
(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Latitude, deg N
Longitude, deg E
Surface Range, km(n mi)
Range Time, sec
Altitude, km(n mi)
Surface Range, km(n mi)
(2,452.6)
1,224.0
31.280
-33.034
4,567.0(2,466.0)
1,297.6
31.361
-33.550
4,517.1(2,439.0)
632.2
190.7(]03.0)
2,035.0(I,098.8)
6-4
D5-15560-8
APPENDIX A
DEFINITIONS OF TRAJECTORY SYMBOLS AND COORDINATE SYSTEMS
SYMBOL DEFINITION
XE, YE, ZE
DXE, DYE, DZE
DDXE, DDYE, DDZE
Position, velocity, and acceleration
components of vehicle center of gravityin Earth-Fixed Launch Site Coordinate
System. The origin of this system is
at the intersection of Fischer Ellipsoid
(1960) and the normal to it which passes
through the launch site. The X axis
coincides with the ellipsoid normal
passing through the site, positive upward.
The Z axis is parallel to the earth-
fixed flight azimuth, defined at guidance
reference release time, and is positive
down range. The Y axis completes a
right-handed system. This coordinate
system is identical to Standard
Coordinate System i0 of Project Apollo
Coordinate System Standards, abbreviatedas PACSSI0.
XS, YS, ZS
DXS, DYS, DZS
DDXS, DDYS, DDZS
Position, velocity, and acceleration
components of vehicle center of gravityin Launch Vehicle Navigation Coordinate
System. The origin of this system is atthe center of the earth. The X axis is
parallel to Fischer Ellipsoid normal
through the launch site, positive
upward. The Z axis is parallel to the
flight azimuth, positive downrange. The
Y axis completes a right-handed system.
The direction of the coordinate axes
remains fixed in space at guidancereference release. This coordinate
system is identical to Standard Coordinate
System 13 of Project Apollo Coordinate
System Standards, abbreviated as PACSSI3.
GC DIST
GC LAT
GD LAT
LONG
Position components of vehicle center of
gravity in Geographic Polar Coordinate
System. Position in this system is
defined by the geocentric distance
(GC DIST), geocentric latitude (GC LAT),
geodetic latitude (GD LAT), and longitude(LONG). Geocentric distance is the
distance from the geocenter to vehicle
center of gravity. Geocentric latitude
is the angle between the radius vector
A-I
D5-15560-8
APPENDIX A (Continued)
of the subvehicle point and theequatorial plane, positive north of theequatorial plane. Geodetic latitude isthe angle between the normal to theFischer Ellipsoid through the subvehiclepoint and the equatorial plane, positivenorth of the equatorial plane. Longitudeis the angle between the projection ofthe radius vector into the equatorialplane and the Greenwich meridian, positiveeast of the Greenwich meridian. Thiscoordinate system is identical toStandard Coordinate System 1 of ProjectApollo Coordinate System Standards,abbreviated as PACSSI.
EF VELVEL-AZVEL-EL
Earth-fixed velocity of vehicle center ofgravity in Geographic Polar CoordinateSystem. Velocity in this system is givenin terms of azimuth (VEL-AZ), elevation(VEL-EL), and magnitude of the velocityvector (EF VEL). Azimuth is the anglebetween the projection of the velocityvector into the local horizontal planeand the north direction in this plane,positive east of north. Elevation is theangle between the velocity vector and thelocal horizontal plane, positive above thehorizontal plane. This coordinate system isidentical to Standard Coordinate System 1of Project Apollo Coordinate SystemStandards, abbreviated as PACSSI.
SF VELFLT-PATHHEAD
Space-fixed velocity of vehicle center ofgravity in Geographic Polar CoordinateSystem. Velocity in this system is givenin terms of heading angle (HEAD), flightpath angle (FLT-PATH), and magnitude ofvelocity vector (SF VEL). Heading angleis the angle between the projection of thevelocity vector into the local horizontalplane and the north direction in thisplane, positive east of north. Flightpath angle is the angle between the velocityvector and the local horizontal plane,positive above the horizontal plane. Thiscoordinate system is identical toStandard Coordinate System 1 of ProjectApollo Coordinate System Standards,abbreviated as PACSSI.
A-2
D5-15560-8
APPENDIX A (Continued)
SYMBOL
ALTITUDE
RANGE
TIME
DEFINITION
Perpendicular distance from vehiclecenter of gravity to Fischer Ellipsoid,positive above Fischer Ellipsoid.
Surface range, measured along FischerEllipsoid from the launch site to thesubvehicle point.
Range time, referenced to nearestinteger second before IU umbilicaldisconnect.
A-3
D5-15560-8
THIS PAGE INTENTIONALLY LEFT BLANK.
A-4
D5-15560-8
APPENDIX B
TIME HISTORY OF TRAJECTORYPARAMETERS- METRIC UNITS
The postflight trajectory, from guidance reference releaseto CSM separation, is tabulated in metric units inTables B-I through B-VII.
Table B-I gives the earth-fixed launch site position,velocity, and acceleration components for the ascent phaseof flight.
Table B-II gives the launch vehicle navigation position,velocity, and acceleration components for the ascent phaseof flight.
Table B-III gives the geographic polar coordinates for theascent phase of flight.
Table B-IV gives the geographic polar coordinates for theparking orbit phase of flight.
Table B-V gives the earth-fixed launch site position,velocity, and acceleration components for the second burnphase of flight.
Table B-VI gives the launch vehicle navigation position,velocity, and acceleration components for the second burnphase of flight.
Table B-VII gives the geographic polar coordinates for thesecond burn phase of flight.
B-I
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