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

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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

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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 Conditions

Translunar 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

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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

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ILLUSTRATIONS

FIGURE

3-1

3-2

3-3

3-4

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3-7

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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

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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 Conditions

Translunar 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

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4-10

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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.

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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

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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 guidance

reference 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.

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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.

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1-4

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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

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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 were

transformed 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.

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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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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

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Translunar Injection

CSM Separation

ACTUAL

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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)

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(li_f/ft 2 )

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Range Time, sec

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VALUE

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TABLE 3-1V. STAGE

D5-15560-8

SEPARATION CONDITIONS

PARAMETER S-lC/S-IiSEPARATIONCOMMAND

Range Time, sec

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Surface Range,(n

Space-Fixed

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164.3

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2,754.3(9,036.4)

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deg

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deg N

19.383

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3-28

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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 post

injection 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

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Carnarvon

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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<T e. The begin time (Tb) and the end time (T e)for the polynomial segments are expressed in seconds.

** The acceleration components are expressed in the launchvehicle platform-accelerometer system (PACSSI2).

4-7

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

D5-15560-8

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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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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.

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B-66

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APPENDIX C

TIME HISTORY OF TRAJECTORY PARAMETERS - ENGLISH UNITS

The postflight trajectory, from guidance reference release

to CSM separation, is tabulated in English units in

Tables C-I through C-VII.

Table C-I gives the earth-fixed launch site position,

velocity, and acceleration components for the ascent phase

of flight.

Table C-II gives the launch vehicle navigation position,

velocity, and acceleration components for the ascent phase

of flight.

Table C-III gives the geographic polar coordinates for the

ascent phase of flight.

Table C-IV gives the geographic polar coordinates for the

parking orbit phase of flight.

Table C-V gives the earth-fixed launch site position,

velocity, and acceleration components for the second burn

phase of flight.

Table C-VI gives the launch vehicle navigation position,

velocity, and acceleration components for the second burn

phase of flight.

Table C-VII gives the geographic polar coordinates for the

second burn phase of flight.

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