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R-477
(Unclassified Title)
GUIDANCE AND NAVIGATION
SYSTEM OPERATIONS PLAN
APOLLO MISSION 202
January 1965
John M. Dahlen
Albrecht Kosmala
Daniel J. Liqkly
John T. Shillingford
Balraj Sokkappa
CAMBRIDGE
I NSTRU M E NTATI O N
LABORATORY39, MASSACHUSETTS
COPY# //__ OF _,°.3¢3 COPIES
THIS DOCUMENT CONTAINS I.,P_ PAGES
- +-""' " l - " 2_:I_'_2 '.7
r
ACKNOW LEDGMENT
This report was prepared under DSR Project 55-191,
sponsored by the Manned Spacecraft Center of the National
Aeronautics and Space Administration through Contract
NAS 9-153.
This documen_contains/ormation affecting
the national defe_ of_e United States within
the meaning of the_onage Laws, Title 18,
U. S. C., Sections 793_94, the transmission
or the revelation oflhich "_. a?y manner to an
unauthorized perso_ is prohi_d by law.
2
TABLE OF CONTENTS
Section
1
2
3
4
5
6
7
8
9
10
INTRODUCTION
G&N FLIGHT OPERATIONS SUMMARY
LOGIC AND TIMELINE FOR SPACE-
CRAFT AND MISSION CONTROL
GUIDANCE EQUATIONS
CONTROL DATA
G&N ERROR ANALYSIS
G&N CONFIGURATION
INSTRUMENTATION
G&N PERFORMANCE ANALYSIS
DISTRIBUTION
l° INTRODUCTION
i. 1 Purpose
This plan governs the operation of the Guidance and Navigation System and
defines its functional interface with the spacecraft and ground support systems on
Mission 202.
1.2 Authority
This plan constitutes a control document to govern the implementation of:
(1) Detailed G&N flight test objectives
(2) G&N interfaces with the spacecraft and launch vehicle
(3) Digital UPLINK to the Apollo Guidance Computer (AGC)
(4) AGC logic and timeline for spacecraft control
(5) Guidance and navigation equations _'"
(6) Digital DOWNLINK from the AGC
(7) G&N System configuration
Revisions to this plan which reflect changes in control items (1) through (7) require
approval of the NASA Configuration Control Board.
This plan also constitutes an information document to define:
(i) Trajectory uncertainties due to G&N component errors (Error Analysis)
(2) Trajectory deviations due to spacecraft performance variations and
launch vehicle cut-off dispersions (Performance Analysis)
(3) G&N instrumentation (PCM telemetry and on-board recording) exclusive
of AGC DOWNLINK
(4) External tracking data
Revisions to this plan which reflect changes in information items (1) through (4)
will not require approval of the NASA CCB.
1.3 Preliminary Data
Unapproved data are printed in red.
#To support these functions this document contains a Control Data section which
defines the reference trajectory, AGC memory data and applicable mission data
(mass, propulsion, aerodynamic and SCS data)
1-1
•" _,_T_.._._.._ _
2. G&N FLIGHT OPERATIONS SUMMARY
This section defines the mission plan as originated by NASA and summarizes the
manner in which the G&N system will operate to implement this plan as developed by
M[T in cooperalion with NASA and NAA/S&ID. This section is divided into three parts:
Par 2. 1 Test Objectives
Par 2.2 Spacecraft and Mission Control
Par 2.3 Mission Description
2. 1 Test Objectives
2. I. 1 Spacecraft Test Objectives which require proper operation of G&N
System:
i) Evaluate the thermal performance of the CM heat shieldablator
during a high heat load, long duration entry.
2) Demonstrate CM adequacy for manned entry from low earth orbit.
3) Determine nominal mode separation characteristics of the CSM
from the SIVB and the CM from the SM.
4) Demonstrate multiple SPS restart (after the second major burn,
two 3 second burns with i0 second intervals between burns are
required).
5) Determine performance of CSM systems: G&N, SCS, ECS (pressure
and temperature control), EPS, RCS and Telecommunications.
2. I. 2 Detailed G&N Test Objectives
i) Evaluate performance of the following integrated G&N/Spacecraft
modes of operation:
a. Boost Monitor
b. Thrust Vector Control
c. Orbit Attitude Control
d. Lift Vector Control
e. Unmanned Spacecraft Control
2) Determine accuracy of G&N system in computation of spacecraft
position and velocity during all mission phases.
2.2 Spacecraft & Mission Control
2.2.1 Spacecraft Control
Spacecraft Control is implemented by the Apollo Guidance Computer
(AGC) provided by MIT and the Mission Control Programmer (MCP) pro-
vided by NAA/S&ID. Basically, the MCP performs those non-guidance func-
tions that would otherwise be performed by the crew, while the AGC initiates
major modes which are dependent upon trajectory or guidance functions.
The function interface between the AGC and the MCP is complex and
its description is deferred until Section 3. The electrical interface is simple,
2-1
being relay contacts in the AGCDSKYwired to the MCP, and is describedin ICD MH01-01200-216. Thefollowing AGCoutputdiscrete signalsare
G&NATT. CONTR. MODESELECTG&NENTRYMODESELECTG&NAV MODESELECT+ X TRANSLATIONON/OFFCM/SM SEPARATIONCOMMANDFDAI ALIGNT/C ANTENNASWITCHG&NFAIL INDICATION
9) 0.05 g INDICATIONI0) GIMBAL MOTORPOWERON/OFFii) SPARE
2.2. 2 Mission ControlMission Control is provided by the Clear Lake Mission Control Cen-
ter (CLMCC)via the Digital CommandSystem(DCS),which has manydis-crete inputsto the spacecraft andanUPLINK to theAGC. The discretecommandsto the spacecraft andthe AGC UPLINK are described in Section3.
TheAGCUPLINKprovides the CLMCCwith the capability to enterthe AGC with any instruction or datawhich canbe enteredby the crew via theDSKYkeyboard. It is specifically plannedto use this link to provide the AGCwith several discrete commandsfor contingencies. This link will also beusedto updatethe orbit parameters in erasable memory with more accuratedata if it is available from ground tracking.2.2.3 GuidanceErrors
Theperformanceof the G&Nsystem for mission 202hasbeenestimatedassumingthat nonavigation datais inserted via the AGC UP-LINK.
provided:I)2)3)4)5)6)7)8)
Themost significant G&Nerror is that error in the critical pathangleat entry which is estimated to be 0. 165degreeona one sigma basis.Thenextmost significant error is manifestedin the CEPat splashwhich isestimatedto be 15.6 n.m.
A completebreakdownof G&Nerrors is given in Section8.
2.3 Mission DescriptionThepurposeof this section is to describe G&Nfunctions during eachmission
phase. Note that thesefunctions are describedin greater detail, sufficient todefineprogrammingrequirements, in Section3.
2-2• - , .Im
D
J
The reference trajectory is defined in Section S in sufficient detail to satisfy
MIT's requirements for development of guidance equations, spacecraft control
logic and determination of flight environment.
Section 9 presents those path and attitude characteristics resulting from
guidance control which are believed to have significant effects on other spacecraft
equipment and ground support systems.
The overall mission profile is illustrated in Fig. 5-i and Table 5-1 and
mi_:ht well be examined at this point.
2.3.1 Pre-gaunch
During this phase the IMU stable member is held at a fixed orientation
with respect to the earth. The X PIPA input axis is held to the local vertical
(up) by torquing the stable member about Y and Z in response to Y and Z PIPA
outputs. Azimuth orientation about the X axis is held by a gyro-compassing
loop such that the Z PIPA axis point downrange at an a_imuth of 105 degrees
East of True North. Initial azimuth is determined by tracking a ground target
with the G&N Sextant prior to closeout at -i i hours. Upon receipt of the
GUIDANCE RELEASE signal from the Saturn I.U. the stable member is
released to maintain a fixed orientation in inertial space for the remainder
of the mission. In this manner the Saturn and Apollo IMU stable members
retain a fixed relative orientation. Also at the time of GUIDANCE RELEASE
the G&N system_ starts its computation of position and velocity which corLtinucs
until first SPS burn cut-off.
2.3.2 SI Boost
The boost trajectory is described in Fig. 5- 2 . Upon receipt of the
LIFT OFF signal from the Saturn I.U. the AGC will command the CDUs to
the time history of gimbal angles associated with the nominal SI attitude
polynomials. The CDU outputs will then represent vehicle attitude errors
and will be displayed on the FDAI and telemetered to the ground. This SI
attitude monitor is a required element of the launch vehicle malfunction de-
tection scheme, and, in association with computed position and velocity,
constitute the Boost Monitor data provided by the G&N system during this
period.
2.3.3 Staging, Coast and SIVB Boost
The G&N system will not have the capability to control the SIVB.
During this period the G&N system will monitor IMU gimbal angles to detect
tumbling and will compute the free fall time to entry interface altitude
(300,000 ft.) from present position and velocity. These quantities are used
in the Abort Logic and, in association with computed position and velocity,
constitute the Boost Monitor data provided by the G&N system during this
period.
2-3
2. 3.4 Aborts from SIVBBoostAborts from the boostphaseare mechanizedin the sameway as
mannedflight aborts wheneverpossible. G&Ncontrol of CSMaborts fromSIVBboost is enabledby the MCP 2 secondsafter start of the MCPSIVB/CSMSeparationsequence. Uponreceipt of the SIVB/CSMSEPARATIONsignal from the spacecraft the AGC determinesa sequenceof eventsusingthe control logic givenin SectionS. Briefly, the sequenceof eventsisderived from three tests:
A. Has the AGCreceived the ABORT signal from the groundviathe UPLINK?
B. Dothe spacecraftbody rates exceedthe tumbling threshold?C. Doesthe free-fall time to entry interface altitude fall below
the abort Tf criterion of 160seconds?
For NOABORTandNO TUMBLING, the AGC commandsa normalseparationandSPSburn to the nominal First Burn aim point as describedmore fully below.
If the ABORT signal is received and there is NO TUMBLING, the
AGC commands an abort separation sequence followed by an SPS abort burn
to the downrange Atlantic Recovery Point. Landing area control capability
is illustrated on Fig. 5-1which shows a continuous recovery area and the
selected downrange Atlantic Recovery Point. This downrange point is the
splash point obtained if, after a nominaISIVB cut-off and separation sequence,
the SPS is fired for 7 seconds in the trajectory plane with the spacecraft
X axis 35 degrees above the visible horizon and the CM is oriented for full
up lift during the entry phase. The G&N system will control the thrust and
lift vectors to achieve this splash point with the constraints, (i) that the
spacecraft X axis be directed 35 degrees above the visible horizon during
thrusting and (2) that the entry point - splash point separation provide CM
lift sufficiently positive to reduce entry g's below a level acceptable for
human tolerance. A I0 g limit is incorporated in the entry program also to
minimize excessive g loads.
If the abort occurs too early in the boost phase or at an "unsafe"
flight path angle, the selected downrange Atlantic Recovery Point cannot be
reached because either (i) there is insufficient fuel in the SM tanks, or (2)
the booster cut-off conditions are such that the spacecraft would dip into the
atmosphere while thrusting. These two conditions are avoided by test C
which is mechanized as an interrupt. If the free-fall time falls below 160
seconds so that test C results in a NO answer, the AGC will command engine
shutdown and a CSM attitude maneuver to the CM/SM separation attitude.
2-4
When the free falltime to entry interface altitude falls below 75 seconds the
AGC will command CM/SM SEPARATION and CM orientation to the aero-
dynamic trim attitude. The liftvector will be up during the entry phase.
Note that "early" aborts result in splash points within the continuous recovery
area.
If TUMBLING is detected, the AGC will start the SPS 2.5 seconds after
separation. This will result in stabilization by the SCS rate loops, and SPS
cutoff by the AGC when it senses that spacecraft body rates have dropped
below the tumbling threshold. Following SPS shutdown the AGC will estimate
the maneuver time, TM, required to orient to the abort SPS burn attitude
(X axis 35 degrees above the visible horizon). If the free-fall time to entry
interface altitude is greater than T M + 160, the AGC will command the CSM
to the abort SPS burn attitude, command engine on at T M and guide to the
downrange Atlantic Recovery area. Again as in the non-tumbling abort case
the engine will be shutdown if free-fall time drops below 160 seconds. If
after tumbling arrest burn shutdown the free-fall time is less than T M + 160,
the AGC will command the CSM to the CM/SM SEPARATION attitude. Abort
area control is illustrated in Fig. 9-4.
2.3.5 CSM/SIVB Separation
There are two CSM/SIVB separation sequences, a normal sequence
and an abort sequence used if tumbling or the abort signal is present. In the
normal sequence the SPS is ignited by the AGC a fixed time delay of 12.7
seconds after it receives the CSM/SIVB SEPARATION signal. This time delay
permits the RCS ullage thrust to build up enough separation distance to prevent
the SPS from damaging the SIVB or upsetting its attitude. On the other hand
the time delay is not so long as to cause an unjustified ZXV penalty. After
separation the AGC computes the initial SPS thrust attitude and commands
the required attitude maneuver. If the spacecraft is not completely oriented
at the end of the fixed time delay, the SPS is started anyway and orientation
is completed during the first few seconds of the burn. Only when large rates
and/or large negative pitch attitude dispersions exist at SIVB cut-off will the
fixed time delay be too short to permit completion of spacecraft orientation
before SPS ignition.
In the abort separation sequence, the SPS is ignited by the AGC a time
delay of 2.5 seconds after it receives the CSM/SIVB SEPARATION signal.
This time delay is made as short as possible to minimize the probability of
CSM-SIVB re-contact or loss of IMU reference in the tumbling case and to get
the CSM away from the SIVB as quickly as possible in any abort case.
2-5
2.3.6 SPS First Burn
First burn thrust will be controlled by the G&N system to achieve the
reference trajectory major axis and eccentricity at cut-off. The trajectory
plane at cut-off will include the Pacific Recovery Point at nominal splash
time. The nominal attitude, flight path angle and altitude histories are
given by Fig. 9-1. Section 9 also contains tables which show the effects of
CSM performance variations and launch vehicle cutoff dispersions. The
steer law used in this maneuver is given in Section 4, where are found all
the CSM guidance equations for Mission 202. It will be noted that the
universal cross product steering law for Apollo is used whenever possible,
specifically, for this mission, in all cases except tumbling arrest and the
short third and fourth burns.
2. 3.7 Coast Phase, First Burn Cut-off to Second Burn Ignition
Following first burn cut-off the AGC will compute and command a
spacecraft attitude maneuver to align the X-axis to the local vertical, nose
down, and the Y-axis to a fixed angle of 0 degrees from the angular momentum
vector R * V. Simultaneously the AGC will establish the second burn
ignition point by a process of precision numerical integration.
When the inner gimbal angle reaches degrees the AGC will com-
mand FDAI ALIGN for i0 seconds thereby resetting the backup attitude
reference to correct for its accumulated drift error. The CSM attitude during
this interval will be within 1 degree of a pre-determined attitude with respect
to the IMU stable member.
After a time interval of 2006 secs. from first burn cut-off the vehicle
attitude in tracking the local vertical will come closest, in the nominal case,
to the second burn ignition attitude. At this time the local vertical mode will
be terminated and the AGC will command the vehicle to the second burn
ignition attitude, which it will hold inertially until ignition.
2.3.8 Second, Third and Fourth SPS Burns
Second burn ignition occurs after a fixed time delay of 3041 seconds
from first burn cut-off. The AGC will command + X TRANSLATION 30 seconds
before ignition to provide ullage. Thrust is controlled by the G&N system to
achieve the reference trajectory major axis and eccentricity at cut-off, and
a trajectory plane which includes the Pacific Recovery Point at nominal splash
time.
Second burn is terminated by the AGC six seconds before the required
velocity is attained. The spacecraft attitude at this time will be held until
fourth burn cutoff. During second burn the G&N attitude error signal will
develop a bias proportional to the e.g. shift from the engine gimbal trim
position set in prior to second burn ignition. After second burn cutoff the
2-6
CDUs will be moved off from their position at cutoff by a stored estimate of
this bias in order to minimize the attitude transient after engine shutdown.
The AGC will start and shutdown the SPS on a time basis so that the
last two burns are each of 3 seconds duration and so that the two short coast
periods are each of i0 seconds duration. The AGC will control the + X TRANS-
LATION signal so that the RCS will provide ullage thrust as well as attitude
control during the i0 second coast periods. Note that the SCS disables
+X translation during SPS firing.
The nominal attitude, flightpath angle and altitude histories are
given by Fig. 9-2. Figure 9-3 shows the slant range, azimuth and elevation
to the CSM from the Carnarvon tracking station. Tables in Section 9 show the
effects of CSM performance variations and launch vehicle cut off dispersions.
2.3.9 Pre-Entry Sequence
The fourth burn cutoff attitude is held until the free-fall time to entry
interface altitude drops below the normal Tf criterion of 160 seconds, when
the G&N system will s_ar_ pitching the spacecraft up to the CM/SM separation
attitude (+ X axis up in the trajectory plane and tipped forward in the direetion
of motion 60 degrees above the velocity vector. When the free-fall time drops
below 75 seconds the AGC will command CM/SM SEPARATION. After a 5 second
time delay to allow for separation and stabilization, the G&N system will start
orienting the CM to the entry attitude. The CM will then be at the aerodynamic
trim angle of attack with roll angle for down lift.
2.3. I0 Entry
The velocity and critical flightpath angle at entry are directly controlled
by the G&N system during the second, third and fourth burns. The nominal
entry trajectory provided by the guidance equations is illustrated in Fig. 9-4.
The entry guidance equations, which are given in Section 4, are designed to
provide a trajectory which will satisfy heat shield test objectives while con-
trolling the roll angle so as to splash at the designated Pacific Recovery Point.
2-7
3. LOGIC AND TIMELINE FOR SPACECRAFT AND MISSION CONTROL
3.1 Interfaces, Ground Commands and Constraints
3. 1. 1 G&N Interface with Spacecraft
The following interfaces will be effective on Mission 202/AF 011/
AGE 017:
3. I. I. I AGC Outputs to MCP
This interface is documented in ICD No. MH01-01200-216
and provides the following signals:
(i) G&N ATTITUDE CONTROL MODE SELECT
(2) G&N ENTRY MODE SELECT
(3) G&N AV MODE SELECT
(4) +X TRANSLATION ON/OFF
There is a requirement for this command (over and
above the translation requirement) to provide for termination
of Direct Ullage mode.
At SIVB/CSM Separation the AGC must command "+X
TRANSLATION ON" to key the MCP to terminate the "SIVB/
CSM Separate" command to the MESC, which in turn deacti-
vates the MESC-controlled "DIRECT ULLAGE" command.
The MESC will not terminate direct ullage earlier than 3.5
sec after receipt of "SIVB/CSM Separate" nor continue it
longer than 12 _ec regardless of whether the SIVB/CSM
Separate command is terminated or not.
(5) CM/SM SEPARATION COMMAND
(6) FDAI ALIGN
This signal will be initiated and held for 10 seconds soon
after orientation to SPS second burn attitude when the IMU
gimbal angles are near prescribed values. This will result
in FDAI ALIGN when the spacecraft is within 1-1/2 degrees
of a prescribed inertial orientation.
(7) T/C ANTENNA SWITCH
The AGC has the capability to switch the T/C Antennas
although the requirements for this function have not yet been
defined and thus not incorpor porated in AGC programming.
(8) G&N FAIL INDICATION
This signal is generated by the AGC based upon its as-
sessment of certain functions with the G&N. The AGC gen-
erated G&N FAIL INDICATION will be an "OR" of the fol-
lowing normal Block i FAIL indices;
3-i
IMU FAIL - an "OR" of IG servo errorMG servo errorOGservo error3200 CPS loss
wheel supply loss
ACCEL FAIL - an "OR" of
x PIPA error
y PIPA error
z PIPA error
CDU FAIL - an "OR" of CDU 25. 6 KC supply
CDU Motor excit, loss
Inner CDU error
Middle CDU error
Outer CDU error
Each of these three FAIL signals (IMU, ACCEL, CDU)
are subject to AGC program processing as there are certain
phases of normal G&N operation where the FAIL parameters
will exceed FAIL thresholds, thus requiring AGC inhibition
of FAIL indication. The G{N FAIL circuitry will be scanned
for evidence of failure every _50 ms.
As is apparent from the FAIL parameters the G&N FAIL
INDICATION signal is basically a monitor of the inertial sub-
system and not of the AGC. Thus, confirmation of an AGC
failure must be made by the ground by examination of the
DIGITAL DOWNLINK.
The G&N FAIL INDICATION can also be sent to the MCP
via the Up Data Link (UDL) based upon ground assessment of
tracking or telemetry data. Upon receipt of G&N FAIL INDI-
CATION the MCP immediately disables all mode commands
from the AGC and commands the SCS system to SCS ATTITUDE
CONTROL MODE. The attitude reference becomes the BMAG's.
The SCS system is now no longer responsive to any G&N
originated attitude signals, attitude error signals, engine on-
off commands (disabled by removal of AV mode), or AGC
commands via the MCP.
The MCP can be reset once to retransfer S/C control to
G&N, however, this command must come from the ground.
(9) .05G INDICATION
G&N will sense . 05G with the PIPA's, give this indication
to the SCS (via the MCP) and the SCS system will inhibit pitch
and yaw attitude control on the assumption that these axes will
3-2
i[
b_ st_Liiizcdby aerodynamic forces. Should the G&N .05G
indication not be received by the MCP/SCS this attitude con-
trol would not be inhibited, and if sufficient pitch and yaw
attitude errors are generated, ,RCS fuel would be wasted
throughout entry. The G&N entry program will attempt to
null the pitch and yaw error signals during entry based on its
estimation of the pitch and yaw trim angles of attack. MIT
estimates that the resulting pitch and yaw attitude errors will
not exceed the deadbands in the SCSo Should this be incorrect
IICS fuel loss will occur. The G&N 0.05G indication is not
used within the re-entry program, however, so should this
function be backed up by a redundant CM sensor or by the UDL
signal, no AGC confusion should result.
(10) GIMBAL MOTOR POWER ON/OFF
The AGC must terminate SPS GIMBAL MOTOR POWER
in order to key the MCP to select the appropriate SPS motor
gimbal trim inputs. The MCP does this sequentially and
therefore the AGC must terminate this command only once
after 1st SPS burn, (to select trim position for 2nd burn) and
once after 2nd SPS burn (to select trim position for 3rd burn-
ing). The trim position for the 1st burn is selected by MCP
upon keying from the SIVB/CSM Separate Command. The 3rd
burn trim position is also satisfactory for the 4th burn.
(ii) SPARE
This is a relay identical to those used in (i) through (I0)
and is identically wired to the MIT/NAA interface.
3. I. I. i. 1 Detailed Interface Operation
Certain additional facts are pertinent to the use
and comprehension of the AGC/MCP interface:
(I) The AGC must not command more than one SCS mode
simultaneously. This requires termination of each mode
before commanding the next; 250 ms has been established
as sufficient time interval between termination and selec-
tion.
(2) The response of the SCS system to the commands and/or
indication signals of the AGC via the 141CP are subject to the
arming of these command/indications by the MCP. Pres-
ently the arming logic for the G&N/MCP interface is as
shown in Fig. 3-i.
MCP_28 VDC
G&N FAIL: G&N _[__
G&N FAIL: GROUND[_
SPS GIMBAL MOTOR POWERCONTROL ARM
FDAI ALIGN ARM
T/C ANTENNA SWITCH ARM
SIVB/CSM SEP START-
SATURN I. II
LET JETT: SATURNI. U. OR GROUND
ABORT: GROIIND
CM/SM SEP C___MND: G&____N_
CM/SM SEP CMND. GttOUNDq_]
G&N ENTRY MODE
G&N AV MODE
G&NATT. CONT. MODE
CM/SM SEP COMMAND
+X TRANS ON/OFF
• 05 G IND. ARM
MCP +28 VDC
G&N FAIL INHIBIT: GROUNDG&N FAIL IND. ARM
Fig. 3-1 Arming Logic for G&N/MCP Interface
3-4
ICD. NO.
MH01-01024-416
MH01-01025-416
MH01-01038-216
MH01-01028-216
MH01-01028-216
MH01-01036-200
MH01-01278-216
MH01-01280-216
(3) In all case the MCP initiates SIVB/CSM Separation. For
normal cases its action is keyed upon notification from
the Saturn I.U.. For aborts the ground must command
the MCP to start the separation.
3. I. I. 2 Additional Interfaces
Pertinent G&N electrical signal interfaces with other S/C
subsystems are described in detail in the ICD's below.
TITLE
Attitude Error Signals
Total Attitude Signals
Engine On Signal to SCS
Central Timing Equipment
Synch. Pulse
G&N DATA Transmission
to Operational PCM
Telemetry Equipment
ACE Uplink/Spacecraft
Digital Up-Data Link toAGC
Launch Vehicle to G&N Inter-
faces (Block I Series i00)
Vehicle Separation Signals
to AGC (Block I Series i00)
SIGNALS INCLUDED
Pitch Error (Body & Body Offset)
Yaw Error (Body)
Yaw Error (Body Offset)
Roll Error (Body)
Roll Error (Body Offset)
Error Sign_.l Reference
(all signals go from G&N to SCS)
SIN AIG
COS AIG
SIN AMG
COS AMG
SIN AOG
i-I g'_kzK_2S A g'_g-_
Attitude Signal Reference
(all signals go from G&N to SCS)
Engine ON/OFF
(AGC command to SCS system - notvia MCP)
AGC synch, pulse to PCM telemetry
system
G&N analog data and AGC serial
digital data (AGC Downlink) to PCM
(Includes flight recorder aata).
Coded data input to AGC from ground
1. Liftoff
2. Guidance Reference Release
1. CSM/SIVB Separate
3-5
3.1.2 GroundCommands3. i. 2. 1 Digital UPLINK to AGC
By meansof the AGC Uplink, the groundcaninsert dataorinstruct the AGCin the samemanner normally performed by the crewusingthe DSKYKeyboard. The AGCwill be programmedto acceptthefollowing Uplink inputs:
(i) ABORTINDICATION(required for abort logic as describedearlier)
(2) LIFT-OFF (backupto discrete input)(3) SIV-B/CSMSEPARATION(backupto discrete input)(4) G&NATTITUDE CONTROLMODESELECT(5) G&NAV MODESELFCT(6) G&NENTRY MODESELECT(7) +X TRANSLATIONON/OFF(8) GIMBALMOTORPOWERON/OFF
(inputs (4) - (8)will causethe AGCto issue thesecom-mandsto the MCP)
(9) Position andVelocity data (provides groundcapabilityto updatenavigationdatain the AGC).
Operationalprocedures governingthe use of theseUplinkinputs mustbe developedto ensureproper operationwithin program con-straint s.
All information receivedby the AGCfrom the Uplink is in theform of keyboardcharacters. Eachcharacter transmitted to the AGCistriply redundant. Thus, if C is the 5 bit character code, then the 16bitmessagehasthe form:
ICCCwhere-Cdenotesthe bit-by bit complementof C. To these 16bits ofinformation the groundaddsa 3bit code specifyingwhich system aboardthe spacecraft is to be the final recipient of the dataand a 3 bit codeindicatingwhich spacecraft should receive the information. The 22 totalbits are sub-bit encoded(replacing eachbit with a 5bit codefor trans-mission. ) The rate of transmission is 1 K bits/sec, allowing for slightlyover 9 keyboardcharacters per sec. If the messageis receivedandsuccessfullydecoded,the receiver onboardwill sendback an 8 bit"messageacceptedpulse" to the groundandshift the original 16bits tothe AGC(ICCC).
3-6
3. i° 2. _ Discrete Real Time Commands to MCP
The following list details the real-time commands planned
for support of the Apollo 202 Mission. This list is restricted to com-
mands for the Command/Service Module Systems and is exclusive of
commands to the SIVB and AGC Uplink commands:
i. Abor_(Also Backup for SIV-B/CSM Separation Start)
2.
3o
4.
5.
6.
7.
8.
9.
i0.
ii
12
13
14.
15
16
17.
18.
19.
20.
21.
22-23
24-25
26-27
28-29
30-31
32-33
LET Jettison Start-Backup to onboard command fromS -IVB.
Thrust off- Turn off SPS engine; backup to onboard com-mand in case of malfunction.
Thrust On - Turns on SPS engine; backup to onboard com-mand in case of malfunction.
CM/SM Separation - Backup to onboard command fromthe G&N.
Lifting Entry - Necessary for no-roll entry in the SCSentry mode.
G&N Failure - Backup to G&N function.
G&N Failure Inhibit - Reset G&N failure.
Roll Rate Gyro Backup - Switches roll BMAG to rate mode
and uses this gyro for roll rate data.
Yaw Rate Gyro Backup - Switches yaw BMAG to rate
mode and uses this gyro for yaw data.
Pitch Rate Gyro Backup - Switches pitch BMAG to rate
mode and uses this gyro for pitch rate data.
Roll A and C Channel Disable - Disables the automatic
A and C RCS roll channels.
Roll B and D Channel Disable - Disables the automatic
B and D RCS roll channels.
Pitch Channel Disable - Disables the automatic pitchRCS channels.
Yaw Channel Disable - Disables the automatic yaw RCSchannels.
-Direct rotation + pitch
-Direct rotation - pitch
-Direct rotation + yaw
-Direct rotation - yaw
-Direct rotation + roll
-Direct rotation - roll
SM _uad A Propellant Off/On.
SM Quad B Propellant Off/On.
SM Quad C Propellant Off/On.
SM Quad D Propellant Off/On.
CM System A Propellant Off/On.
CM System B Propellant Off/On.
3-7
34,
35-37
38
39-40
41
42 -45
Direct Ullage (Also sets SCS AV mode)
Fuel Cell Purge (cell #1 - cell #3)
FDAI align
T/C Antenna Switch (-Z, +Z)
UDL/S-Band Comm. Switch
Cryogenic Heater Fan Switch (02#1, 02#2 H2#1, H2#2)
Commands 12-21 will be used to control S/C attitude in cases
where the G&N is not operable.
Of these commands only six are intimately concerned with
G&N operation; abort, thrust off, thrust on, G&N Failure Inhibit,
G&N Fail, Direct Ullage.
Abort: As discussed above, this abort command may be accom-
panied by an abort command to the AGC via AGC Uplink.
Thrust
Off:
The ground may thus inhibit starting of or may stop the SPS
thrust. Should AGC-controlled firing be inhibited or shut-
down the AV monitor logic would after i0 seconds exit from
thrust vector control and hold attitude until the free-fall
interrupt occurs.
Thrust
On:
AGC Engine On logic presently includes a monitor of AV to
ensure engine ignition. This monitor continues for i0 sec
after sensing no thrust during which time the ground might
start the SPS engine. If suitable AV has not been sensed
after i0 seconds the AGC would exit from thrust vector con-
trol and hold attitude until the free-fall interrupt occurs.
Should the ground successfully start the engine within i0 sec
the AGC will guide the burn normally. It must be assumed
however that as the AGC Engine On command did not work
correctly, AGC Engine Off will not either. The ground must
therefore command a timely "Thrust Off" compatible with
the AGC TVC calculations.
G&N
Failure:
This command is a ground backup for the G&N originated
command. As all control of the vehicle by G&N is thereby
inhibited, the resulting confusion of the AGC (it has no know-
ledge of the ground command) is interesting but irrelevant.
Direct
Ullage:
A backup command for ground use during a ground controlled
burn in the SCS AV mode. Its use during G&N controlled
flight would inhibit G&N attitude control with the possibility
of the G&N being unaware of the control loss.
G&N
Failure
Inhibit:
This command overrides the G&N FAIL signal.
3-8
3.2
3.1.3 BackupControl SystemsConstraintson G&NOperation3. I. 3. 1 BackupAttitude ReferenceSystem
The backupattitude reference system is _,heSCSBMAGsinconjunctionwith AGCU. G&Ncontrol of the CSMorientation is alwaysdonewith considerationfor the maintenanceandaccuracy of this sys-time. As the SCSsystemis presently designed,the BMAG's operateas free gyros in the C_N AV MODE; in other modes they are caged
through the AGCU.
As the mechanical stops of the BMAG's are at ±17 ° it is
apparent that during boost (MONITOR MODE) and attitude maneuvers
(G&N ATTITUDE CONTROL OR ENTRY MODES) both involving angular
changes of over 17 ° the BMAG's must be caged. In the G&N AV mode
however, attitude changes over 17 ° might occur.
The rate limits of the backup attitude reference system in the
caged mode are 5°/sec in Pitch and Yaw and 20°/sec in Roll. To pre-
clude controlling the S/C at rates beyond which the backup attitude
reference system can maintain its reference, the G&N will limit its
command rate to the CSM.
3. I. 3.2 Backup Entry Control
During the pre-entry coast the G&N system must orient
the CM for aerodynamic trim and lift vector down. Then, in the event
of G&N FAIL INDICATION, the MCP/SCS will hold this attitude until it
senses a prescribed "g" level at which time it will command a continuous
roll angular velocity.
Normal and Abort Mission Logic
The following pages describe the timeline and logic for AGC control of the
spacecraft.
3.2.1
3.2.2
Normal Sequence of Events
AGC Program Logic
3-9
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3-17
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3-23
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3-26
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-20
3-27
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3-28
3.2.2 AGC Program Logic, Mission 202
The following diagrams illustrate the AGC logic for Mission 202.
Each group of logical decisions and/or computations enclosed within a
dotted line represents a routine. Routines marked * are performed at
a specified time under AGC waitlist control. Such routines cannot be
interrupted by an other AGC activity and will run to completion.
The terminology used is defined as follows:
Call - Cause a specified routine (an AGC "waitlist task") to be
started at a specific time. Waitlist tasks are designated *
(a task called once at a specified time) or ** (a task
which, once called, continues until terminated)
Go To - Branch to another part of the program without return
Do - Branch to a routine with a return to the next operation in
sequence.
Set - A permanent change of state of a flag or register valid until
being reset.
T - Present time.
Store - Store indicated quantity in erasable for future reference.
3 -29
PRE LA U 1,0C H
T
i"1I/v_, _,_rN,,L- _._N_- I
i
I [ca_._. _,N,_^. Mo-roR Pa.0_ 0N_r II iI ('.-ALL _"D_l_.."Ir.. ALI_N ON I
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TE_N_NA'rE FiNE ALIGNj MO(:__.. I
IN _&,.N S'YSTE/_ Ii
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3-30
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I_-ro_,._Co_o.)-dl SET ABOI?..T FI-AG
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I_ OPER.A-FF-_SPA_E RELAyTO _ov_oE_ I
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3-31
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_EL_YS (_sas SYs-rE_A L_ /
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3-32
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3-33
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3-34
4. GUIDANCE EQUATIONS FOR CSM
4.1 Powered Flight Guidance Scheme
The guidance scheme for Mission 202 is the same as that planned for
all Apollo CSM powered flights. It is based on the possibility of an analyti-
cal description of a required velocity (v r) which is defined as the velocity
required at the present position r, in order to achieve the stated objective of
a particular powered flight maneuver.
If v is the present velocity, then the velocity to be gained (Vg) is givenby
V -- V--g --r
Differentiation of both sides yields
where
- vu
--v g-a T--r
= b a T
(i)
(2)
(3)
(4)
b = v - gur
and g is the gravitational acceleration.
The steering command is developed by formulating a desired thrust
acceleration (aTD) as that which satisfies the equation
aTD* v = cb * v--g -- --g
where c is a constant scalar.
(5)
(6)
Indicates vector cross product
4-1
aTHencea measureof the error betweena_TD
is givenby
©
V * m
c IVgl
and the actual acceleration
(7)
where
e
m = cb - a T (8)
It can be verified that ¢0 is also the axis about which the thrust vector should-- e
be rotated to null the error. Hence co is used as the steering command.--C
Once a required velocity v r is defined satisfactorily, the procedure for
the generation of the steering command _--c is the same for all phases of
towered flight. The equations for the required velocity for the various
hases are described in the succeeding pages. Descriptions of the initial
alignment procedure, ignition and cutoff logic and implementation in AGC
are also included.
4.2 Nominal Mission
4.2.1 Required Velocity
The required velocity for the first and second burns of the
nominal mission is defined as that velocity which will put the vehicle
in an elliptical trajectory of predefined parameters (semi major axis
a, and eccentricity e). The values used are
First Burn Second Burn
a 2.22806 X 107 2.82776 x 107
e 0. 102415 0. 252865
These numbers correspond to the trajectory described in Section 5.
The value of c inEq. (6) is 1.
The required velocity can be written as
v = i + iH v H--r --r v rad(9)
4-2
where
.vrad: 2 1,I] (i0)
(11)
and
p = a (I - e 2)
r
i ---r
Irl
= * i )i H UNIT (i N --,
(12)
(13)
(14)
The positive sign is used in Eq. (i0) for the radial velocity during first
burn and the negative sign is used during second burn.
4.2.2 Yaw Steering
Plane control during the nominal mission is achieved by spec-
ifying the normal (i N) to the required plane appearing in Eq. (14). The
required trajectory plane is defined to be the plane containing the pres-
ent position vector (r_) and the landing site vector (rLs; 14.9N, 165.6E)
at the nominal time (5090 sec) of landing and is given by
i N _ UNIT (r * rLS) Sign [(r * [LS ) -iw] (15)
where i is the earth's polar unit vector. At cutoff the vehicle veloc---W
ity will be equal to v r, thereby ensuring the trajectory plane to be i N
according to Eqs. (9) and (14).
During the third and fourth burns, no computations are made
for v . The desired thrust direction is held fixed at the direction--r
computed at the end of the second burn.
4.2.3 Engine Ignition
In the nominal mission the engine is always ignited after a
fixed interval of time from a previous event. The first burn is
4-3
initiated 12.7 seconds after receipt of SIV-B/CSM separation signal,
the second burn 3041 seconds after first burn cutoff, the third
burn i0 seconds after second burn cutoff and the fourth burn
i0 seconds after third burn cutoff.
4.2.4 Engine Cutoff
During all the burns a time to cutoff (T g) is continuously be-
ing estimated from the equation
Tg = [Vg/[aTI
The accuracy of Tgincreases as Tg-*0, because aSlVg [ -*0,Ibis-0.
For the first burn, when T falls, for the first time, belowg
the computational repetitive interval of At, the clock is set to turn off
the engine T seconds later. The second burn is turned off the mo-g
ment T falls below 6 seconds for the first time.g
In the third and fourth burns the engine is turned off 3 seconds
after ignition.
4.3 Aborts During Boost
The guidance equations for aborts during boost have been designed to
meet the following constraints that have been imposed on the spacecraft atti-
tude.
The visual horizon is to be kept on a hairline on the forward window
during the entire powered flight and this line should be independent of the
time at which abort is initiated.
The window geometry indicates that this requires the thrust direction
to be between 4 ° and 36 ° to the line of sight to the visual horizon. Within
this limitation, the larger the angle, the greater is the interval of time be-
fore nominal SIV-B cutoff during which the capability exists to reach a par-
ticular recovery area in the event of an abort. Hence a thrust angle of 35 °
to the line of sight to the horizon is used. (See Fig. 4.1 ).
4.3.1 Required Velocity
The definition of a required velocity, in the usual sense, con-
sistent with the direction of thrust pre-speeifled as above, is not pos-
sible.
(16)
Hence, a pseudo required velocity is defined for aborts, which,
4-4
i_._ _I-
I0-_- 0_- I ,-- oz" I N
....._ _-_%._....
Z _0 -N _
0'T
"r
zoN
0
,.J
@
I
/ I
/
0
0
.r-I
!
. r-q
4-5
when incorporated into the general steering scheme, will satisfy not
only the constraint on the thrust direction but also permit recovery
from a specified landing area.
Let r be the entry position (300,000 ft) eorresponding to a--e
free fall from the present position. Then we can write
and
sin @f
r e cot 7 + r cot 7 e
r - re
2x
x2+ 1
2x -i
cos 8f = 2x +1
(17)
(18)
(19)
(20)
where
cot 7
v.i-- --r
v-i H
cot 7 e = r/p [e 2 -(r_e--e- 1) 2]1/2
(2i)
(22)
' * iI H' = ip --r
(23)
i = UNIT (r * v)--p
(24)
Of is the free-fall central angle to the entry point,
r is the radius at 300,000 ft altitude,e
7 e is the flight path angle w. r.t. the local vertical at entry
is the present flight path angle (w. r.t. vertical)
The entry-point is given by
r = r (i r cos ef+i H, sin Of)--e e(25)
4-6
Now, let r T be the desired entry point (target vector). The error d
can be written as
d°IrT re l (26)
The target vector is the inertial position of 14, 3926°N latitude
and 313 ° longitude at 975 seconds from lift-off. This choice corre-
sponds to minimum plane change for aborts at 617.4 seconds from the
nominal boost trajectory.
The rate of change of this error is computed by differencing
r as--e
(27)
Ire - r I /Atn --en-1
(28)
where the subscript n denotes the nth computational repetition
Observing that d/d is a measure of the time to cutoff (Tg) and
that Tg according to Eq. (16) iSIvg I / IaT lin the general scheme, the
magnitude of v is defined as--g
or
Izgl= d I TId
Izgl-- __-ald L_v[
(29)
(30)
where Avis the velocity increment measured with the aceelerometers
in the interval At.
Now consider Eq. (6). Set c = 0; then
_ = 0aTD * Vg
(31)
If the direction of v is chosen as the desired and known direction of--g
a T , the specified constraint on the spacecraft attitude will be satisfied.
4-7
Figure 4-I shows the geometry of the spacecraft window.
The angle ¢ between the thrust and r is given by
RvhI (32)
where e is the specified angle (35 °) to the horizon and Rvh
to the visual horizon.
From Eq. (32) and Eq. (30) we can define v as,--g
d JA___vJ
Vg-- _-d (-cos fi r + sin_ ill,)
is the radius
(33)
4.3.2 Yaw and Roll Steering
The development of Eq. (33) is based oni r andiH, which are
both in the present trajectory plane according to Eq. (23). However,
normally, a plane change will be required to reach the same landing
site from different points of aborts on the boost trajectory.
Let the plane containing the present position r and the target
vector (See Section 4.3. l) [T be defined by
IN= UNIT (r * r T) Sign [(r_ * rT).lw] (34)
The velocity increment along_ip (normal to v_) to null the error
between i andi N is given by (See Fig. 4-2).--p
Av N '= [vi (ip * i N ). i(35)
The acceleration along ip required to accomplish the plane
change is given by
aN = i--p
Av N
T + 6g
(36)
where 6 is a small scalar (5 seconds). In order to prevent large yaw
rate commands, a limit of 5 ft/sec 2 is imposed on I aN - aN n 1 I"n -
4-8
as
Equation (33) can be now modified, to include yaw steering,
v = iT I vl--g Ad(37)
where
i T =[UNIT - i_r cos_b + UNIT (ill,a T +an)sin _] (38)
and aT is the magnitude of the thrust acceleration.
The required velocity is given by
V = V + V--r -- --g
(39)
where v is given by Eq. (37). With the required velocity so computed--g
and with e = 0, the same steering (Eq. 6) as for the nominal mission
is used.
The rate command resulting from the required velocity v has--ronly pitch and yaw components. However, the vehicle must be rolled
such that the pitch axis is in the horizontal plane (See Fig. 4-1) This
is achieved by generating a roll command (_R) from
_R =-(-JR ipitch) iroll (39a)
The negative sign is the result of the desired orientation in which the
spacecraft z - axis is pointed up.
The roll rate command is added to the rate command genera-
ted from Eq. (7). Note that the roll rate computed according to Eq. (39a)
must not be commanded unless the spacecraft z-axis is within 90° of
local vertieal.
4.3.3 Engine Ignition
In the ease of a non-tumbling abort the engine is ignited 2.5
sees after receipt of the SIV-B/CSM separation signal.
Iftumbling has been detected by the time the separation signal
is received, the engine is ignited 2.5 sees later and is shut down when
tumbling has been arrested. Ifthe capability of landing area control
4-9
-'r
HORIZONTALPLANE
_.___ i4IN
- ,_.p
_ _iT
ff
Fig. 4-2 Computation of a n andi t
4-10
|exists, the engine is re-ignited after a time interval calculated to be
sufficient to orient to the desired initial thrust direction.
4.3.4 Engine Cutoff
When T falls below At, the clock is set to turn off the engineg
T seconds later under normal area control. However, the engine willg
be turned off if any one of the following violations has occurred before
T < At.g
a) Free-fall time to 300,000ft is below 160seconds
b) --eris beyondr T. That is,
r. r e < r. r r(40)
I
ft should be pointed out that the estimate of T is very poor ing
the early part of the burn for long burns. Hence its value at ignition
cannot be used in back-up systems.
4.4 AGC Computations
Since the information about the thrust acceleration comes from the ac-
celerometers in the form of velocity increments (Av), the computations in
the AGC are in terms of increments of velocity rather than instantaneous
acceleration. The repetetive guidance computations are shown in the form
of a block diagram in Fig. 4-3. The computational blocks are common to all
powered flight maneuvers except the computation of v described in the pre---r
ceeding sections.
4.4.1 Average g Equations
The vector position and velocity are updated in each computa-
tional cycle with a set of equations based on the average gravitational
acceleration written as
gn- %itr n
n
(46)
g •+
g+ --n-_ --n At + Av (47)
v n= v n-i2
4-11
>I
U
31
z,,, 0
_I "_
ouJ
IOl [:
O
©_9_DC9
°_
_9
©
h_
c9o
!
.r-i
4-12
and
(r = + At + At + --
--n rn-1 Vn-1 gn-1 2 2
where the subscript n denotes the nth computational repetition.
4.4.2 Steering Command
The vector bwas defined in Eq. (5) as
b = v -g
(48)
(5)
In the AGC (as shown in Fig. 4-3), the increment (b At) is
computed as
bAt _ Av - gAt
Then the steering command in Eq. (7) can be written as
(49)
where
v * Am-g
A0 - At
--c Iv_llZXm I(50)
A0 = co ZXt (51)--e --c
Am = c b At - A___v (52)
4. 4. 3 Orbital Integration Equations
Position and velocity during the free-fall phases of the mission
are calculated by a direct numerical integration of the equations of
motion. Since the disturbing accelerations are small the technique of
differential acceleration due to Encke is mechanized in the AGC, as
described in MIT Report R-467, The Compleat Sunrise.
4.5 Initial Thrust Alignment
Before the engine is ignited for any particular maneuver, the vehicle
should be oriented so that on ignition the thrust is in the desired direction at
that point. Since the time of ignition is known beforehand, the position and
velocity at ignition can be computed prior to the arrival of the vehicle at that
4-13
point. By integrating over At seconds from that point, the vectors v and--g
bat can be computed as shown in Fig. 4-3.
The desired thrust direction can be now calculated (prior to arrival at
the ignition point) as
i T = UNIT (cb + (q - i • cb) i- --g -- --g
where
i = UNIT (Vg)--g
q = (aT 2 - (cb) 2 + (_.ig • cb_)2) 1/2
(53)
(54)
(55)
and a T is an estimate of the magnitude of the thrust acceleration.
Once_i T is computed from Eq. (53), the vehicle is oriented prior to
arrival at the ignition point such that the thrust axis is alongi T.
4. 6 Entry Mode
Included in this section is a set of flow charts that describe the logic
and equations that control the entry vehicle. Figure 4.4 shows the overall
picture of the sequence of operations during entry. Each block in Figure 4.4
is described in detail in subsequent charts. Table 4-1 defines symbols which
represent computed variables stored in erasable memory. The value and
definition of constants is given in Section 5.
Every pass through the entry equations, which is now anticipated to be
once every 2 seconds, is begun with the section called navigation. (See
Figure 4.5). This integrates to determine the vehicles new position and
velocity vector. This sub-routine is used by other phases than entry and
will probably be operated during all of flight 202.
Next, the targeting is done. This updates the desired landing site
position vector and computes some quantities based on the vehicles position
and velocity and the position of the landing site. (See Figure 4.6).
The next sequence of calculations is dependent upon the phase of the
entry trajectory that is currently being flown. First is the initial roll angle
computation. (See Figure 4.7). This merely adjusts the initial roll angle
(180 ° for flight 202 is now planned) and tests when to start the next phase.
4 -14
Fig. 4-4 Re-Entry Steering
4-15
@
vEs_
-Icr= u_ rr (_.'), _z
I:_ E_AD & CLE/_I_,,,P|P/_$
5_VE VEL. INC_:_M_.NT
AT _a_ 2
_. - _-_ ZX-T -_-_
_j_I_.T _ _IkV IG/kT I O_
Li
1TE/x,,', + ,c_-r- _ + ix-t- _ J
T 2 I
I
Fig. 4-5 Re-Entry Steering - Navigation
i
4-16
I v:_,_,w,_ _v_ IvsQ: vZ/v s_,--F _ _ IROOT: _. Wa_T (_a} .I
LE(:_-- (,VSG-_-I') _S,
DC)LD = D
D = ABVAL (._') /AT
[RELVELSW: 1 It
t
I LATAIx3G = UI_ IT ( __.T _) • _ N
I'T._rA: co_ -_ (,U_,T(_-T_-U_,T(_./)t
t
Fig. 4-6 Re-Entry Steering - Targetting
4-17
N'E_ NO 1
YEs I e,aO
I T_.C)LL C.-- C_ IC:)
I._=° I!
o',-+v _.o,..,',-,-..o,_N_:_
I_°_°_°II_:_ II GO -TO _40_r-_S -T I
Fig. 4-7 Re-Entry Steering- Initial Roll
4-18
The next phase maintains a constant drag trajectory while testing to
see if it is time to go into the up-control phase. The testing is presented
in Figures 4.8 and 4.9. The eonstant drag equations are given in Figure 4. i0.
The other phases (up-control, ballistic and final) are listed in Figure 4. ii,
4.12 and 4.13. The final phase is aeeornplished by a stored reference
trajectory. Its eharaeteristies as well as the steering gains are stored as
shown in Figure 4. 14o The routine that prevents excessive acceleration
build-up (G limiter) is given in Figure 4.15. And finally, the section that
does the lateral logic calculations and computes the commanded roll angle
is shown in Figure 4. 16.
4-19
S _4UI,4"I'INC) _'b,l_
lax-aa lT
(1_ DO -- C'9 NEG'_
k) o Y_S_
J
ALP = 2_C)
VL = V.%
_:EPLE_. _.AP,_G.F-- CALCt_ L_-r'l_l_
SlIJ_ = S'l_ (I_.D_TL/VL.) z
I
iS VL--VLlV_I_'-J k3E.C3 _"_--_0Y_# .
tI_,SV-Ep : V-EPLE_ RANGE I
_, _.{7 V_ / _J_..I
I AsP 3 : q5 ((_6-r_PCrTL), GI%I_N_ CO_.R._X_
_ i_ Tt-4ETI_/_--A5 P SJE_. _l
Fig. 4-8 Re-Entry Steering - Huntest
4-20
ILv=,,_,T.<_o.__oo-,_/V,,,_,-_Ii
)
I,,,=w+ v _o_. i v_ =vl+ ,ooo Iv,_.v,.+vco,_l lGo To _O_'re..ST_i
'q "4l v_ = v, -vco_/=_l
FACT z: _,'--_(_P-,)/Ao_,EL.IE::C.'T¢ot_-... --- _-)¢::_C-O)_"T'_.OL..
Go To UPc_.OK.)TI:_::_.
Fig. 4-9 Re-Entry Steering = End Huntest
4-21
i
i
Fig. 4-I0 Re-Entry Steering- CONSTD
4-22
Go "TO _'J_-_WES'-_ I
Fig. 4-1 1 Re-Entry Steering - UP CONTRL
4-23
-T N -If VX
EGsw = I I P,'_H " _ k_1
SELECTo_x= P_EDIC_r
Y_,w = 0
Fig. 4- 12 Re-Entry Steering - Ballistic
4-24
(DOLD- D)
(DOLD* _') /e.
PI_EDAN C-:-:-bL= _TO_O (V') ¢ F2 (V)(DADVt - DAI::)VR.(V)_
+_-_ (v)(D-D_E_-_(V))
L/D = LO D + 4- (T,ETNN,, -- pIP_,._= DAI',aGL) _y (. V)
Fig. 4-13 Re-Entry Steering- Predict 3
4-25
p_o
p_
n4
(D
_Z0 e4 O0 C'Q _ D-- O_ ,-_ ¢Q c'q co LO _
(J
I" I" I 16 I" n° l" I _', , , , _, _
A
•"4 I I I I
_J
0cO
¢)
c_
,--Ic_
.r-I
1--II
.,-I
4-26
IS GN_,A>(.-_:::_ PO_:_
yES_
IGc>"to3,oI
-,(aH_ _,,,,_,xl,,) _" I
I_,-,_R.,-v_.QI
_)lO(D
IL/D--O.Z (R DOTC_- - R_Z:_C:_-")ID -
I_°_°_,°I,
Fig. 4-15 Re-Entry Steering - GLIMITER
4-27
NO
Fig. 4- 16 Re-Entry Steering - Lateral Logic
4-28
TABLE 4-i
VAR_BLES FOR RE-ENTRY CONTROL
q, T_
!'7
\/
O
I
OT_"
!,T _
mT
'!_,! f
_,L._
A gK FD
Eqr_l
^ SD! 'P
r_
m_
D_FF
F2
r4CT!
F._r T2
v 2or'Ll__
I.^TANC
LF©
Lrhr
LV
OP,_T
Prh_TR_F
OrJL t..r"
r_D_TL
T
Tl-lc T A
TM_'- TN M
\/cOpo
V
Vt
VL
VP='F
VBAPS
V£1")
!aT
Y
HUNT[Nh
HIMD
qFLV_!_ gW
_GSVl
V-"L _r T TY V_CTC 'r
or_c T T T _,_ V_:qTpO
\l_CTqP F#.CT A T TNTTTA L T^_..r-_T
Mt_O_AI_ T _ DT c ^n, lh II z
T ,_._r: _"T VCr- TOo
IJ_uIT k'C)'_,;AI. TC TP,_.JF('TrhPY PLY, _r
T_IITIAI _ePC, F:©o L.:DC_'T_t_
r'n,',_qT FOP UPC*_'Tr_[
_rPLrP _AN_F"
FT_.'AL PH, ASF PANG c
GAM_4A ('©OPFCTTPL'
Om_DICTEF _AN rq_ = _SKEP+ACD]+ASPLJP+,_SP3
TqTAt. ECCCl =re#Tit')K,
cml,,TOrH I.. _'r'. cr_4CT mm,_C
_CFEP_.'C c D DP,_G/DV (_Tn!aL p_^SF)
RFFSRF_ CE [;RAG
r-qCCNTq lqI TY
r)_ANG. F/C DPh, G (FINAL PP'AS_)
,m_ f, _ r- P / _A O r_ T "_c, (F ! N_ L PH ,_.qc)..
r_*,_CT _0 ° tJDC©_.ITRL
r_!qT FC.o LIDr_'T_I.
I,! C I: Im t_,l I ID (- f",_, T _ I
I_'PTCATO9 Fr'm '_r'[! c','TT(-U (])
I ATFPAI_ _,':tN,'-_
-_XCFSS C,F. qvFr_ C.m,:V =lV_r__l )re
l_/r_ C_OPCTT _ FP_I-" i:r_-r_,'TOl._
h _r t.Mr- m / r,V
OP_I'-TF;-; Pa,_Ii_V (FTNaL pH_SF)
A!..T [ Tr'_F D':TF
D-'zI:_:D'-z'_,.I,r'P ,2..lh (q _("D ..D'- _1_ T q I..
_XTT P'b0T F__P 'D(-C'*'Tr:'i
RAK, G,F TO _r, (FT_.'AL a_-,'.S;l
T f Mr
V_.LOCITy CO_PFCT'[,O_,I _'__o UI:_r"('MTOL.
Vr[.r_q T Ty H ' _/u ! Tt !F_":
INITTt. L VFL:_,C]TY #fhq IIp,[,,'!Tfl_
taXi T VrL_CTTy F,_ _iP,",'t, tT'_".
RF-FFr_m_,CF VTL'D, CTTY FC': ',JPCr'_,T_i.
2 2
Vl_ /\/c,& T
2 ?
N_F_MALI qpr_ V_'-i_C'CTT Y _'::'t_AO::i "_ = 'v' ',,'Ct, T
#'A PTH _ t_T _ X TTM"
c,!,.dTTC# TO C, FLFCT C(_K,!CT I_ L_Vr--I. r',
SWITCH TO ITFR!_'TF tN {-;I_NT[ CT r
_L VFLOC!TY F'v,'!Tq'-' 0
qW ] ] :-H :!
4 -29
5. MISSION AND VEHICLE DATA
5.1 Scope
Section 5 is a summary of all Flight 202 mission and vehicle data that have
an impact on AGC programming. Data have been collected under the following
headings:
Section 5.2 Mission Data. Establishes the outlines of the mission in terms
of trajectories, profiles etc. Includes performance figures for Saturn boost phase
inasmuch as they affect conditions pertaining at take-over of control by G&N system.
Section 5.3 Memory Data. Contains all mission- and vehicle-dependent data
that are, in one form or another, written directly into the memory of the AGC. In
a wired-memory computer such as the AGC, the very limited erasable section is
intended primarily for storage 6f computational variables. An attempt has been
made to consign those mission parameters that do not change during flight to the
fixed section of the memory. Some exceptions have had to be made in the case of
the Saturn boost polynomials and SPS aim-point criteria, since these will not be
available until shortly before the flight.
Section 5.4 Vehicle Data. Contains information that will mainly affect simula-
tions and rope verification and will not, with only one or two exceptions, appear
directly in the AGC program.
Section 5.5 Physical Constants. These definitions will be used in AGC programs
and verification work.
Numerical data are presented in the most convenient and widely accepted units.
The AGC is, however, programmed in the metric set of kilogram, meter, and
centisecond (10 -2 sec). Conversion to other sets of units is done by use of the factors
defined in Section 5.5.2.
Points on the surface of the earth are defined in terms of geodetic latitude and
longitude referred to the Fischer ellipsoid of 1960, and geocentric radius.
5-1
5.2 Mission Data
5.2.1 Mission Trajectories
Referencetrajectory(Saturnboost, SPS1,coast, SPS2)Referenceentry trajectory(Pre-05g to touch-down)Nominal mission profileMajor eventsduring nominal missionNominal Saturnboostprofile
inot available
not available 1
see Fig. 5.1
see Table 5.1
see Fig. 5.2
Note I. No officialtrajectories issued. All dependent data in this report are derived
from MSC SA-202 optimum trajectory dated September 1964, and an undated
entry reference trajectory communicated on ii November 1964.
5-2
Z z z
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5-5
TABLE 5-I. MAJOR EVENTS, MISSION 202
_-VENT
Lift- off
SIB c/o
SIVB Ign
LES Jett
iSIVB c/(
SPS Ign.
SPS c/o
Apogee
Ullage
SPS Ign.
SPS c/o
SPS Ign.
SPS c/o
SPS Ign.
SPS c/O
Entry
End of
Entry
t , V i
(sec) ( fps_
0
145.5
151
161
617.4
628.4""
882.0
12528.
3893.4
3923.4
4014.
4024.
7,022
6,953!
7,037
121,848
21,834
I
.25,632
122,713!
!24 837I
124,923
i127,739
27,647I
4o27 27,751
037 j27,789 039. £'L27,878
i319.6 28,690
5087.6 1,791
AZi
(deg)
o 9o. ooi
24.02 i02.43i
I22.80 102.49
21.01 102.66
2. 635_112.05
2. 395}112.31i
5.77 Ll17.70
-0.006105.89
-5.80
-5.82
-7. 67
-7.53
-7.56
-7.44
-7.46
-3.51
64.61
63.99
62.18
ALT. N. GEOD.
LAT.
0 28.53
175,508 28.23
190,757 28.21
216,802 28.17
544,569! 23.43
554,8931 23.20
918,95_ 16.46
3,606,[email protected]
1,620,50Q-19.95
1_43, 64fl-19. 24t
1243,964 -16.26!
1218,301 -16.15
1,207,390 -16.05
1,171,147 -15.72
1,161,917 -15.60
397,603- 5.16
49,613 14.9
E. LONG:WEIGHT
1
279.42 1,322 530
279.98! 434,058
280.06 320,240
280.21 306,928
294.61 83,099
295.18 45,701
309.35 27,956
29.56 27,956
109.25 27,942
110.95 27,942
116.48 21,589
116.63 21,589
116.82 21,379
117.43 21,379
117.59 21,200
134.85
165.6
End of Entry for No SPS AV1469.4
End of Entry for No SPS &V 24977.
9.25 320.6
4.7 148.4
Data from this time on is from MIT 202 performance simulations
Fourth Burn cutoff due to propellant depletion in this simulation
5-6
5.2.2 Nominal SIVBSeparationAttitude Conditions
X-axis in planeof maneuver, forward of localvertical by
(Y-axis alongmomentumvector R* V
Z-axis abovelocal horizontal)
Roll rate
Pitch rate
Yaw rate
67.20°
0°/sec
0°/sec
0°/sec
5-7
5.2.3 3a Dispersions from Nominal at SIVB Separation
X-axis attitude dispersion 2°
Y-axis attitude dispersion 2°
Z-axis attitude dispersion 2°
Roll rate residual 0.2°/sec
Pitch rate residual O. 2°/sec
Yaw rate residual O. 2°/sec
5-8
5.2.4 SIVBEngine-off Transient
Decaytime 100%-10%
Decaytime 10%-0%
Tail-off impulse 100%-10%
Tail-off impulse 10%-0%
not available
not available
not available
not available
Q
5-9
5.3 Memory Data
5. 3. 1 Prelaunch
Launch position: Latitude
Longitude
Radius
Inertial reference plane (IMU) azimuth
Memory
Type
F
F
F
F
Value
28.53253 ° N
279.41701°E
6,373,305.2meters
105.0000 ° E of N
O
5-10
5.3.2 Saturn Boost
Roll polynomial coefficient (s)
Pitch polynomial coefficient(s )
Heading polynomial coefficient(s )
Interval: Lift-off-SI attitude monitor
terminate
Interval: Lift-off-LET jetison
assumed complete
Memory
Type
E
E
E
F
F
Value
not available
not available
not available
150 sec
171 sec
5-11
5.3.3 Attitude Maneuvers
MemoryType
Value
Limit: commanded S/C angular
rate:
Roll (CSM) F 7.2°/sec
Roll (CM only) F 15°/sec
Pitch, Yaw (CSM, CM) F 4°/sec
Interval between attitude updates (CSM)F 1 sec
(CM only) F 0.5 sec
Interval for stabilization after
maneuver
(CSM) F 6 sec
(CM) F 3 sec
5-12
5.3.4 TVC (Normal mission)
Memory
Type
CSM c.g. displacement in X-Y plane:
(SPS 1 ) F
CSM c.g. displacement in X-Y plane:
(SPS 2) F
CSM c.g. displacement in X-Y plane:
(SPS 3) F
CSM c.g. displacement in X-Z plane:
(SPS I) F
CSM c.g. displacement in X-Z plane:
(SPS 2) F
CSM c.g. displacement in X-Z plane:
(SPS 3) F
Mass loss rate of SPS engine F
Initial mass of CSM + propellants F
Tailoff impulse (mean) of SPS engine F
Minimum AV criterion for thrust monitor F
Interval for thrust monitor F
Interval between steering updates F
Steer law gain F
Steer law velocity bias F
Steer law coefficient (C) F
Interval: freeze CDUs to engine-off command F
Value
6.60 ° 1
3.35 ° 1
0.30 ° 1
2.25 ° I
0.60 ° 1
-0.70 ° 1
2. I75 slug/sec
1,428 slugs
8,400 lb-sec
1 ft/s/s
10 sec
1 sec
0.25
160 ft/sec
1.0
1.8 sec
Interval: SIVB/CSM Sep. - SPS 1 ignition F 12.7 sec
Interval: SPS 1 cut-off - SPS 2 ignition E 3041 sec
Interval: SPS 2, 3 cut-off - SPS 3, 4 ignition F I0 sec
Note 1: Figures derived from data in Section 5.4.1 using weight data in Table 5-1.
5-13
Interval: SPS 3, 4 ignition - SPS 3, 4 cut-off
Interval: + X translation - SPS 2 ignition
Interval: between SCS mode change eommands
Interval: Gimbal mot. power ON - Enginestart F
SPS 1 aim-point criteria
Semi-major axis E
Eccentricity E
SPS 2 aim-point criteria:
Semi-major axis E
Eccentricity E
Interval: Lift-off - touch down. (Nominal
mission) E
Memory
Type
F
F
F
Value
3 sec
30 sec
0.25 sec
2 sec
2.22806x107ff
0.102415
2.82776x107ft
0.252865
5090 see
5-14
5. 3.5 Entry (Normal mission)
CSM attitude for SM/CM Separation:
X-axis above velocity vector by
(Y-axis along monentum vector (R * V),
Z-axis above velocity vector)
CM Pacific pre-entry attitude:
X-axis below velocity vector by
(Y-axis along momentum vector (R * V),
Z-axis below velocity rectory. A lift-
vector down attitude )
Trim angle of attack
Interval: SM/CM Sop. - start maneuver
Pacific recovery point: Latitude
Longitude
Constant on ALP
Initial shaping roll
Constant drag gain (on drag)
Constant drag gain (on RDOT)
Lead velocity for up control start
Minimum constant drag
Minimum D for lift up
Minimum drag to start Kepler
Minimum drag to end Kepler
G-limit
Minimum drag for lift up if down
Up control gain, optimized
Up control gain, optimized
Lateral switch gain
Time of flight calculation gain
5-15
Symbol
C1
C10
C16
C17
C18
C19
C20
DMIN
DMIN2
GMAX
KA
KB3
KB4
KLAT
KTETA
Memory
Type
F
F
F
F
E
E
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
Value
60 °
160 °
20 °
5 sec
14. 000°N
165. 600°E
1.25
0
0.01
0. 0002
5o0 ft/s
35 ft/s/s
200 ft/s/s
6 ft/s/s
6. 5 ft/s/s
lOg
O. 2g
O. 0034
"3. 4
O. OO75
1, 500
Max L/D
LAD cos (15°)
Up control L/D
Final phase L/D
Final phase range
Final phase dR/dV
Final phase initialvelocity
Final phase dR/dRDOT
Final phase initialRDOT
Minimum drag for up control
Minimum RDOT to close loop
Minimum VL
Normalization factor, acceleration
Atmosphere Scale Height
Normalization factor, velocity
Nominal earth's radius (entry only)
MemorySymbol Type
LAD F
L/DCMINR F
LEWD F
LOD F
Q2 F
Q3 F
Q4 F
Q5 F
Q6 F
Q7 F
VRCONTRL F
VLMIN F
GS F
HS F
VSA T F
RE F
Value
0.3
O. 2895
0. i
0.18
641 n.m.
O. 07 n. m/ft/s
23,500 ft/s
O. 3 n. m/ft/s
820 ft/s
6 ftls/s
700 ft/s
18,000 ft/s
32.2 ft/s/s
28,500 ft
25, 766. 197ft/sec
21,202, 909ft
5-16
5.3.6 TVC (Abort)
Criterion for tumbling detection
Symbol
Memory
Type Value
F not
available
Interval: SIVB/CSM Sep. - SPS ignition
(tumbling and abort) F 2.5 sec
Interval: Time-to-go bias
Interval: between steering updates
Thrust attitude:
X-axis above visual horizon by
(Y-axis normal to local vertical,
Z-axis above local horizontal)
Limit: commanded change in yaw accelera-tion
Abort alm-point: Latitude
l__ngitude
Interval: Lift-off - abort aim-point
(Abort from nominal mission (See Section 4.0))
Mean geo-centric radius of visual horizon Rvh
F 5 sec
F 2 sec
F 35 °
F
E
E
E
F
5ft/s/s
14.3926°N
313.0000°E
975 sec
not
available
5-17
5.3.7 Entry (Abort)
CM Atlantic pre-entry attitude:
X-axis above velocity vector by
(Y-axis along neg. momentum vector (V'R)
Z-axis above velocity vector
A lift-vector up attitude)
Atlantic recovery point: Latitude
Longitude
MemoryType
F
E
E
Value
160 °
not avail-
ablenot avail-able
5-18
5.3.8Free-fall time (Tf) monitor
Entry interface altitude
Abort Tf criterion (A) to start orientation
to CM/SM Separation Attitude
Normal Tf criterion (N) to start orientation
to CM/SM Separation Attitude
Interval: rain Tf to start CM/SM
Separation
Interval: between Tf updates
Memory
Type
F
F
F
F
F
Value
300, 000 ft
160 sec
160 see
75 sec
1 sec
5-19
5.4 Vehicle Data
5.4.1 CSM Data
Weight empty
Weight of initial fuel load
Variation
Variation
Variation
Variation
Variation
Variation
Variation
Variation
Variation
of principal inertia with mass
of principal inertia with mass
of principal inertia with mass
of product of inertia with mass
of product of inertia with mass
of product of inertia with mass
of C.G. X-location 2 with mass
2of C. G. Y-location with mass
of C.G. Z-location 2 with mass
MS 21, 200 lbs
ML 24, 500 lbs
IXX Defined in Fig. 5.4
IYY Defined in Fig. 5.5
IZZ Defined in Fig. 5.6
IXY Defined in Fig. 5.7
IYZ Defined in Fig. 5.8
IZX Defined in Fig. 5.9
CGX Defined in Figs.5.10, 5.11
CGY Defined in Figs.5.12, 5.13
CGZ Defined in Figs.5.14, 5. 15
MF 14.3 slugs
MO 44.6 slugs
RF 958 ins. (ApolloRef. )
RO 966 ins. (ApolloRef. )
WF 4.07 1 rad/sec
ZF .005
WO 3.82 i rad/sec
ZO .005
LT 7.1 feet
LE 833 ins. (ApolloRef. )See Fig. 5-3
Fuel equivalent slosh mass
Oxidizer equivalent slosh mass
Fuel mass C.G. X-location
Oxidizer mass C.G. X-location
Fuel mass natural frequency
Fuel mass damping ratio
Oxidizer mass natural frequency
Oxidizer mass damping ratio
RCS thruster moment arm
Engine hinge point location
Spacecraft Launch Configuration
NOTE: 1. Data corresponds to initial thrust acceleration of 20.9 ft/sec 2
(W2aT 2and the relation )t = (W a T) initial is assumed.
2. Angles given as positive rotations of ¢ngine hinge'point to c. gJ
line about positive CSM Y and Z axes.
5-20
x L - 406.5
X o - 1490.0
LAUNCH
ESCAPE
SYSTEM
COMMANDMODULE
X a = 1gO0.0 ----
Xc=0
SERVICEMODULE
l ZL
133.5"
TO HEAT SHIELD
STRUC1 URE
162.0'
i
SPACECRAFT
DIMENS IONAL
DIAGRAM
XL=G
X c = 83. S
X o = I083,5
154.0' DIAMETEr,'
X a = 833.2 ENGINE GIMBAL PLANE
SPACECRAFT
LEM ADAPTER
X a = .502.0- --
Z o
_SD_ Stabilizing _'embers
Fig. 5-3 CSM Launch Configuration
5-21
44000
40000
36000
Z
2
Z
70
_ 32OO0
28000
....................... i ......
• , .... ° .... ° ....... "_
_l:_:.,............. i.......... ,................
12000 14000 16000 18000 20000 22000
IXX ROLL MOMENT OF INERTIA (SLUG FEET SQUARED)
Fig. 5-4 IXX Moment of Inertia against CSM Weight
5 -22
44000
40000
3,5000
2
Z
320000
28000
24000
36 000 40000 44000 48000 52000 56000
IYY PITCH MOMENT OF INERTIA (SLUG-FEET SQUARED)
60000
Fig. 5-5 IYY Moment of Inertia against CSM Weight
5 -23
Ir,_lFJ.l_ : _ -.
¢'1
Z
oa.
z
o
44oo0¸ _ L I ......._- __._44I •
• I _
36000" i .foI• . , . ..., 1 I .
...... t
_--t _ /,• [ L '
ooo i...... t !:- _/4
z,ooo l ....... _ '
36 000 40000 440 O0 48000 52000 $ 6000 60000
I .....
. [ . .
IZZ YAW MOMENT OF INERTIA(SLUG FEET SQUARED)
Fig. 5-6 IZZ Moment of Inertia against CSM Weight
5 -24
44000 - .
40000
36000
z 32000
0
z
0
28000
24000
J _ ....
t ii!iliilit ........... i iii
, , _ ,
; , - ; '
44000
4200O
40000
51000
-4000 - 3000 -2000 - 1000 0
_XY PRODUCT OF INERTIA ( SLUG FEET SQUARED)
Fig. 5-7 IXY Product of Inertia against CSM Weight
5 -25
44000
40000
3_000
32000
28000
24000
1
I
-400 0 40o BCC 12oo 16o0
IYZ PRODUCT O_ i/',_RTiAISLUG-FEET _f_UAREDi
2000
Fig. 5-8 IYZ Product of Inertia against CSM Weight
5 -26
44000
40000
3O000
ZD
28000
I
" i .....
400
Fig. 5-9 IXZ Product of Inertia against CSM Weight
5 -27
-- CO:t!FZ:;_IT:,kL -
44000
40000
3_000
32000
28000
24000
94,4 948 952 956 960 964 968 972 976
X. CENTER OF GRAVITY - APOLLO S/C STATIONS
Fig. 5-10 C.g. X-Axis Coordinate against CSM Weight
5 -28
CO ..... !" : '"-" " '-
v1..--.
Z
0
z
o
1,1.1
44000
40000
36000
32000
28000
24000
I "'1';I'1;I '1 ;II I I L, 1 Ill! I i _ t t ; ; ; I 1 ] ! .....
.....I....I[.....i I....I .....!.....I I........./,
t .....[...................t......I....r....I.-::!_i,.........!'I!t! ..........l/l,_...,_....I!.....I_":,,_::::_:,:: : i .... :;t _ t_..._":::: : ......... "t
iiiit_[ii_itii itii tii i[iii;I_tiiii_tii:_tiii_{iiiiitii_itii
i ....:.... ::::! ........ _r::::":::r:"::) :l::}:I:i::t::=:I::
..... t ..... t .... t .... 1- .... t ' . • _÷ .... ,t ..... _...... _...
...... : ........... , I TTF , FT, -: _" '
..... : t : i [ ] ! i[_ } I , i [
.............. _' " ±-" _-'_ r I ! l t i T I ] I ' I ; ; ; ! i IIl ! _--i--i---;" : ' '
. .- i . • : :: : : i . ! . . . i : ! ,, ; ;.. _ .... , ] . . . , . .
. °
2 3 4 5 6
SPS TRUE GIMBAL ANGLE FROM THE X AXIS, DEGREES
Fig. 5-ii SPS True Gimbal Angle from X-Axis against CSM Weight.
5 -29
z
oa.
z
I
o
44000
40000
36000
3 2000
28000
...... I ....
.... ....
t
i
I
2_0C_
_. 6 8 10 12
CENTER O_: GRAVITY- _NCHES
Fig. 5-12 C.g. Y-Axis Coordinate against CSM Weight
5 -30
44000
40000
36000
a
Z
o
z
32000O
uJ
i - -
28000 i
1
24000
.... t .....
10 20 3.0 40 5.0 60
SPS ENGINE GIMBAL ANGLE IN X-Y PLANE, DEGREES
Fig. 5-13 SPS Gimbal Angle in X-Y Plane against CSM Weight.
5-31
I
m
44000
J ....
40000
3000O
Z
0
Z
_ 32000
0
28000
24000
-40 -3.0 -20 -I.0 0 1.0
Z CENTER OF GRAVITY- iNCHES
2.0
Fig. 5-14 C.g. Z-Axis Coordinate against CSM Weight
5 -32
44(
Z
o 32000
Z
0
28(
240
o .
' !1!! I!!!l!i!!l!!!/!!!t!!!l!!!t!!!i!!!t!!!t!!!l!!!l!!!,!-!!l!!!'f
:: :::: ....................... ' ...... ri ......t-t- r-:-::.._i_...t.::t:::l!:I I!_:]!:_t!:!t!_]_.! _!_-_.:_y_................ _ ................ Ii ..... : ......... & ...... ,•..1...... t'-' 1'-'1'"t....t,"'!....t'"t ...... 1_'.,...... t......•-..-...I......i ............:....... ....,7......i -I.i!iilii i iliiiliiiliiil iliiiliiiEiiiliiiliiilHiiliiiliiilii
•.. ........................... ._,.!._.: .... ,./,,... .... ,,.,_.. .........A '
2iiti212ilii21:i21ii21ili i1222_Z,22;_ii211ilil?iil_iti2it?]/
- • • ! .... • . .
............ • ...:-. :..._....J ...r..,..: ...,:..,....-... ....
...... i " It ..... .;I ..... I' I .... I .... 1 I"'1 .... I ............• . . ,... *...a.-. _.- .f... t...t.., t...i.., v...v...i...i...| ....
• .I...I...I... _.,...I...1...1...1...I...i..-.I .... 1...1 ..........
• il;,".,;_'/_i .... ; ;";' ;; '; .... ;; "; ....... 1"
i --._,_" ................. :. :'.l..:l::.i_..l..:i.:,i:.:i ............................ '''I''" I'''I '''I''.I...I...I .... ; • i • .
-0.4 0 0.4 0.8 1.2 1.6 2.0 2.4
SPS ENGINE GIMBAL ANGLE IN X-Z PLANE, DEGREES
Fig. 5-15 SPS Gimbal Angle in X-Z Plane against CSM Weight.
5 -33
5.4.2 SPS Engine Data
Item
Mass
Inertia (IY = IZ = IR)
Hinge to c.g. radius
Vacuum thrust
Specific impulse
Maximum start and shutdown transients
Mean thrust-off impulse
Displacement, thrust vector from engine
gimbal axes intersection
Misalignment, thrust vector from engine
mount plane normal
Symbol
ME
IR
LE
TF
ISP
Value
20 slugs
213 slug ft 2
8.0 inches
2. 19 x 104 Ibs
(+ I% after 30 sec)
+10%(-1% after 750sec)
318.7 sec (3avalue
after 750 sec)
See Fig. 5.16
8,400 Ib-sec
<0. 125 inches
<0.5 deg.
t
5-34
i __m
I I I I 1 I I 1 I o0 0 0 0 0 00 oO ,.0 _ c'_
ISA_HI (]31V_ %
O_
o°t-IO_
0"o
o_
"o
GI
o
oelb.O
'elI
.r-I
5-35
5.4. 3 TVC Autopilot Data
TVC Autopilot Data
Configurat ion
Attitude error gain
Attitude rate gain
Rate command limit
Symbol Pitch (Y) Yaw (Z) Units
Defined in Fig. 5. 17
KA I. 00 rad/rad
KR 0. 500 rad/rad/sec
L 0. 140 rad
(effectively 16°/see)
Art. rate filter lead time constant _-I
Art. rate filter lag time constant T 2
Forward filter gain KE
Commanded position breakpoint LMP(1)
Commanded position limit LMP(2)
Clutch servo amplifier gain KS
Clutch servo amp. lead time const. T 3
Clutch servo amp. lagtime const. I"4
Clutch servo current limit LMI
Clutch gain KC
Actuator moment arm RA
Clutch lead time constant T 5
Clutch lag time constant T 6
Total actuator load inertia JT
Actuator load time constant 77
A ctuator load natural freqUency WB
Actuator load damping ratio
Engine rate limit LMR
Engine position limit (pitch) LMY
Engine position limit (yaw) LMZ
Position feedback gain KD
Position pickoff frequency WD
Rate feedback gain KG
Rate pickoff frequency WC
5 -36
1.00
0. 125 sec
0. 042 sec
1.50
0. 105 rads(6 °)
0. 227 rads(13 °)
20.0 Amps/rad
0. 025 sec
0.029
0.600
3,530
0.022
0.029
281
0.150
104
0.104
0.300
±0.105
1.05
287
0. 154
81.7
0. 137
+0.218
-0.078
1.00
63.0 46.2
0.090
48,1 40.0
sec
Amps
s/amplb
feet
see
sec
slug-ft 2
tad/see
rad/see
rad/sec
rad(i6 °)
.,+12 50_
raat_4. _o /
rads/ft/sec
rads/_
rads/sec
_-+ ], +_ ,
_1 "'_
r
"il++Ii
I
Z
_0
00
<_Z *
oo
Ni,I
I'+v
I--
_,o I
t:_
@e..-i
©.,-I
04_
!
5 -37
0
Z
<
0
_T0 i
0 0
.E"au o
o
vi ii II I
p..
d
d _
d
_ 0 0 I 0
0J
.d
0 0 0
o _ ,.g
_ t:_
t'-.-o
I I, , c; o"I
<
V
0 0
o _
I i, , o" d
I
<
b-0
,4 c; dI
<
i 0i
t_
c_I
<
<
@
b_
• ¢_ o9
,-_ 0 0 =
0 _:
@
0c;
j_
0 ,_
.0G_
_r.)
N_
I:_ r./'/
._ oO
0 _
0 . _b_ 0
••,-I r/_
_t ._.-I r---I r---t
g s ss_ % N% N N
5-38
r- ----
_w<(
1U.I
I
o I
"1L
I-- I.J
_- kJ --
LU US
uJ 0_J
¢10
I
IL
III
F'I
I--
I,-- t'v
II oII
_1_1
ly
U.I
C3 _D 0
%
-1
-- i
I!
W
1!
°1
! i
-- !II UJ
--I
III
Z
_- 0
c_
c_
cio
o
o
<m
-?
.,-4
5 -39
5.4.5
Item
RCS Reaction Jet Data
Configuration
Nominal vacuum thrust
Specific impulse (steady)
Minimum impulse
Thrust rise lag
Thrust rise time constant
Thrust decay lag
Thrust decay time constant
Duration, minimum impulse
electrical signal
Units
Ibs
secs
ib-sec
millisec
millisec
millisec
millisec
millisec
Value
SM
(see Fig. 5. 19)
I00+ 5
300 + 5
0.5+0.1
<12. 5
2. 0 (exp)
<6. O
2. 0 (exp)
18.0±4.0
CM
(see Fig. 5.20)
91+3
270 + 4
2.0+0.3
<13. 0
2.0 (linear)
<4.0
5. 0 (linear)
18.0±4.0
5-40
_e v ..... %rklTl A I
TENSION TIE &
UMBILICAL (3 PLACES)
RCS ENGINE
( 4 PLACES )I
SEXTANT I -- 50"
S EXTANT TT = 70"
SEXTANT 111"=60*
SEXTANT 1_7 =50*
SEXTANT _ =70"
SEXTANT _7T =60*
12o45 ,
÷Z
I
RCS l
ENGINE 7.1El
ct.MEAN
RADIUS
T_r
EQUIPMENT BAY
Trr
(empties
first )
DIZER TANK
( empties
first)
)Xl D I ZE
Irr
(emptie
÷Y
FUEL
( emlotie
EQUIPMENT BAY
I
15'
Fig. 5-19 (1) CSM Reaction Jet Positions
5 -41
Fig. 5-19 (2) CSM Reaction Jet Positions
5 -42
F
ji!
<
O
br_
__T_ _
_z /=o- •; _, /,_
,,'" t..,_-o------
-Qo
>
0
z
02
E
\fq
\
_ Z
.zC_
.o <
Z
_ u_
) i , I t i i z • _
w
"' "_ : oO . ; z
, _;z z :_o ._ z
r_
0
-r'4
o
o
c_
r..)
o
I
5 -43
5.4.6 CM Data
Control Weight
Principal inertia (IXX)
Principal inertia (IYY)
Principal inertia (IZZ)
Product of inertias (IXY)
Product of inertias (IYZ)
Product of inertias (IXZ)
CG X-location
CG Y-location
CG Z-location
Aerodynamlc
Aerodynamlc
Aerodynamlc
Variation of coefficients with
Mach number
reference area
reference diameter
coefficients
11,000 lbs
5065.0 slug-ft 2
4491.3 slug-ft 2
3973.5 slug-ft 2
-1.7 slug-ft 2
-43.5 slug-ft 2
-291.8 slug-ft 2
43.4 inches ] from CM
0.5 inches / origin =5.3 inches S/C sta. 1000
129.4 square feet
154.0 inches
see: Table (5.2), Fig. (5. 21)
see: Fig. (5.22)
5-44
Table 5. 2
Aerodynamic Coefficients Against Angle of Attack
for the Command Module with Protuberances
_,deg.
140.465
145.465
150.465
155.465
160.465
165.465
170.465
175.465
C M
0. 03282
0. O2686
0. O1851
0. 00779
-0. 00268
-0. 01411
-0. 02601
-0. 03708
C N
0. 13187 -0
0. 10490 -i
0. 07990 -I
0. 06223 -i
0. 05562 -I
0. 04354 -1
0. 01772 -1
-0. 00144 -i
C A C L
99218 0.52987
10571 0.54042
20796 0.52595
29105 0.47950
36511 0.40405
42967 0.31666
47186 0.22634
50081 0.12010
%
0.84915
0.97033
1 09038
1 20032
1 30513
1 39484
1 45446
1 49600
L/D
0.62400
0.55695
0.48236
0.39947
0.30958
0.22702
0.15562
0.08082
NOTES: i.
2.
Above Table for Math I0.0
Coefficients for Moment Center at
X = 1043.1 inchesC.g.
Y = O. 0 inchesc.g.
Z = 5.4 inchese.g.
5-45
000
_b,,I
"i,
0
.r'4
©
E
q_
I
.r--_
5 -46
200
150
Qtrim
100
5O
0 I I2 4
MACH
I I6 8
NUMBER
I10
0.4
0.3
L/D trim0.2-
0.1-
0 I I I I2 4 6 8
MACH NUMBER
I10
o.sI-
0.6 L
C L trim / _
0.4 /0.2
0
2.0
1.5
CD trim1.0
0.5
I I I I t o2 4 6 8 10
MACH NUMBER
NOTE" COEFFICIENTS FOR MOMENT
Xc.g. = I043.1 ins
Yc.g. :0.0 ins
Zc.g. : 5.4 ins
I I I I 12 4 6 8 !0
MACH NUMBER
CENTER AT
Fig. 5-22 Experimental Trim Values for Block I CM with ExternalProtruberances
5 -47
5.5 Physical constants
5. 5. 1 Geophysical constants
Earth's gravitation constant
Gravity potential harmonic coeff.
Earth's mean equatorial radius
Earth's sidereal rate
Reference ellipsoid
Symbol
MUE
J
H
D
RE
WIE
Value
3. 986 032 233 x 1014
meters3/sec 2
1.62345x 10 -3
-5-0. 575 x i0
0.7875 x 10 -5
6. 378 165 x 106 meters
-57. 292 106 35x i0
radians/sec
Fischer, 1960
5 -48
5.5.2 Conversion Factors
International feet to meters
Pounds to newtons
Slugs to kilograms
Nautical miles to kilometers
Statute miles to kilometers
Slugs to pounds (g)
Multiply by
0.304 8
4. 448 221 530
14. 593 902 680
1. 852
1. 609 344 000
32. 174 048 000 ft/s/s
5 -49
6. G&N ERROR ANA LYSIS
This section provides the results of G&N Error Analysis. Table G-1 summarizes
the one-sigma total error at each major event time and breaks these down into the con-
tributions of IMU errors accumulated during each powered phase. Tables 6-2 through
6-16 break down each line of Table 6-1 into the contributions of each IMU sensor error
term.
On the basis of these data the following key errors are estimated:
Entry 3' i (one sigma)
Entry V i (one sigma)
CEP at Pacific Recovery Point:
, 0. 165 degree
18.0 feet per second
15.6 nautical miles
The following comments expla_," the terminology, method of analysis and the basic
assumptions used.Xsm _ SM_ STABLE
l) The IMU Stable Member axes are aligned prior J MEMBER/
to launch relative to local vertical axes as in- |]
dicated in sketch. XSM is up along local verti- [
cal at instant of launch, while ZSM is along _/_/_ll _ _ Zsmlocal horizontal pointed down-range at an _l',._'kocol _-.,.'_--Earth
Verticalazimuth of 105 degrees. V__i
1
2) The data in the error tables are given relative to local vertical axes (altitude,
track, range) at the particular event designated.
ol _nly ,he stgnlllcan_ error figures have been listed in the error tables.
4) No realignment of the Stable Member was assumed.
5) Accexerometer bias errors affect indication errors in two ways. First, they
affect the initial pre-launch alignment of the Stable Member. Second, they
affect the in-flight computation of position and velocity. The two effects are
summed in the tables, since the accelerometer bias error prior to launch is
assumed to be correlated with the bias error during flight.
6) Accelerometer inputs to the AGC are not used during the free-fall phases of
the trajectory.
7) "Initial S.M. Alignment Errors" includes only the uncorrelated alignment
errors. They do not include the alignment errors due to accelerometer bias
errors. The azimuth alignment error (about XSM) is affected principally by
by Z gyro drift effect on the gyro-compassing loop. Since there are other con-
tributing factors to azimuth misalignment, this alignment error has been
°=s .... ,_+,,_._ °+_+_=+_,._11y independent of Z ..... A_¢¢+
6-1
8) The position and velocity errors given in the tables for the various IIV[U
sensor error terms are indication errors. No steering error was assumed.
The indication errors in position and velocity were computed separately for
each sensor error term using an array of error equations and the input position
and acceleration trajectory data. These equations take into account the effect
of the platform error on the gravity vector computation. For each trajectory
run the position and velocity errors due to each platform error are computed
simultaneously and printed in a summary table for all trajectory events of
interest.
6-2
u nun N "
All .... . w
TABLE 6-1
Time
fromEvent
start
(mlns)
SIVB
Cutoff 10.3
SPS 1 st
Burn 14.7
Cutoff
Coast
Apogee 42.2
Coast i_na
End (SPS2nd Burn 65.4
Ignition)
SPS
2nd Burn
Cutoff67.0
EntryStart
72.0
EntryEnd
(at altitude
of 50, 000ft)
202 TRAJECTORY ERRORS
Position Error (n. miles)Type of Error
A It. Track Range
Velocity Error (ft/sec)
Alt. Tra ck Range
i) Total Indication Error 0.34 3.07 0.17 9.2 72.1 4.2
I) Total Indication Error 0.75 6. 35 0.53 13. 5 79. 5 7.72) Effect of IMU Errors
during SPS ist Burn 0.06 0.34 0.05 3.3 17.7 2. 3
i) Total Indication Error 2.68 ii. 14 5.84 33.8 46.2 12.22) Effect of IMU Errors
during SPS Ist Burn 0.74 2.72 i. 16 7.3 3.6 3.1
i) Total Indication Error 3.84 5.35 ii. 36 70. 3 73.5 16. 12) Effect of IMU Errors
during SPS ist Burn i. 46 0.08 2.99 20.0 17.1 6.2
i) Total Indication Error
2) Effect of IMU Errors
during SPS ist & 2ndBurns
3) Effect of !MU errors
during SPS 2nd Burn
1) Total Indication Error
2) Effect of IMU Errors
during SPS 1st & 2ndBurns
3) Effect of IMU Errors
during SPS 2nd Burn
3.78 6.51 11.80 73.2 74.1 17.7
I. 46 0.39 3.20
0.02 0.05 0.01
3.17 9.70 13.20
i. 24 I. 43 3.93
0.20 0.34 0.04
4.76 12.06 14.43
20.7 22.1 7. 7
3.1 6.1 1.6
82. 5 53. 5 18.0
24. 3 19.8 7. 5
3.9 5.6 0.6
116.0 38.7 28.61) Total Indication Error
2) Effect of IMU Errors
during SPS 1st & 2nd
Burns & Entry 2.253) Effect of IMU Error
during SPS 2nd Burn
& Entry 1.074) Effect of IMU Errors
during Entry only 1.70
3.60 4.92 56.1 50.3 ii. 9
1.64 0.62 36.8 49.0 9.7
1.66 0.31 45. 3 48.9 7.80
6-3
g, i,
m_
Ore
UO
Error
Position
A
T _-----_- R
/
(E)Xio
(F)YIo
(F)ZIo
RMS
Frror
0 ft
0 ft
0 ft
I
0
Velocity
Initial
S.M.
Alignment
l'rrors
Ace, 1. IA
Nonorthog-
onality
Bias
Error
Scale
Factor
Error
A eccl. Sq.Sensitive
Indication
]:] rror
Bias
Drift
Acceler-
ation
Sensitiw"
Drift
Acceler-
ation
SquaredSensitive
Drift
(I___) VXI o -4
(l')VyI o
0 it/see
0 it/see
{I')Vz[ 0 it/sec
A(SM)X I 3_ 6 mr
A(SM)Y I 0.04 mr
A(SM)ZI 0.07 mr
XtoY 0.1 mr
X to Z 0. 1 mr
0.1 mrYtoZ
Direct effect
ACBX Fff on Init Mira
Combined Fff
Direct effect
ACBY Fff on Init Mira
Combined Fff
Direct effect
ACBZ Fff on Init Mlm
Combined Fff
SFEX
SFEY
SFF, Z
0.2 cm/sec 2
0.2 cm/sec 2
0.2 cm/sec 2
87 PPM
87 PPM
87 PPM
i0 ,g/g2NCXX
NCYY 10_g/g2
NCZZ I0 ug/g2
BDX Direct effect 3.6 meru
BDY Direc( effect 3.6 rnPru
BDZ Direct effect 3.6 meru
A DIAX
A DSRAY
A DIA Z
15 meru/g
I0.5 meru /g
_)X
A2 D(SRA)(SRA)Y
2
,A A(tA)(IA) z
15 meru /g
1 meru/g 2
1 meru/g 2
1 meru/g 2
Root Sum Square Error (in ft and ft/se_')
Root Sum Square Error (in n. mi. and it/see)
Final Position Error
in Local Axes
(in feeG
Alt. ]Track Rangel
; II
Final Velocity Error
in Local Axes
(in it/see)
Alt. Track Range
0 0 0 0 0 0
-18,580 -71.61
153 - 283 0.75
I 403 0.89
-0.73
557 157 2.34 -0.61
-I,316 369 -4.65 1.18
,- i.194[
1,1731
359 ___ i-__, 142_
779 1,441
-1,138 29'_
573 15S
_____; R__
134 !
l95
-1.24
-'_ 83
07
__ -I. 62
0 lI
_30 1_ -C. 5_
28 -0.24
- 3.69
2.60
- 1.09
-3.52
3.73
0.21
0.38
0
-1.65
0.05
C 0
2i 68 -0.09 -0.27
333 - i.97
281 302 1.86 -1.29
213 0.74
- 1,594 F7.71692 642 -4.95 3. 19
608 2.47
....... ...........
94 ____-- - 88 __ 0.85__ ........... -0.42
58 O. 23
l2 t 069 18,667 1 t 028 9.20 72. 12 4. 16
0.34 3.07 0.17 9.2 72.1 I 4.2
Table 6-2 Total Indication Errors at SIVB Cutoff
6-4
_ _r-,c-,sdkjl_11k_ i_ iba ,s-._ _A a
i .
IL-,%,,_'. _ • . i,.F I.. I .i j w# _L
8_.
¢
0
P]z'ror
P_,sitior,
V,'locit V
Initial
S. lVl.
A!_gnment|"r'rors
A(','cl. IA
No rio rt ho R -
,reality
Bias
Error
Scale
Factor
I':r rot
Acrel. Sq.
Sensitive
IndJ cation
F rror
Bias
Drift
Acceler-
ation
Sensitive
Dr] ft
A ccelel'.-
ation
Squared
Sensitive
Drift
A
jf
( E)X Io
(F)YIo
(F)ZIo
V)VxI o
(l")Vyl o
(F')VzI o
A(SM)XI
A(SM)YI
A(SM)ZI
XtoY
XtoZ
YtoZ
Direct effect
ACBX Eff on Init Mlm
Combined Fff
Direct effect
ACBY Fff on Init Mlm
Combined Vff
Direct effect
ACBZ Elf on Init Mlm
Combined Fff
SFEX
SFEY
SFEZ
NCXX
NCYY
NCZZ
BDX Direct effect
BDY Direct effect
BDZ Direct effect
A DIAX
ADSRAY
A DIA Z
A 2 D_IA)(IA)X2
A D(SRA)(SRA) Y
2
A A(EA )([A) z
RMS
Error
O ft
0 ft
0 ft
0 ft/sec
0 ft/sec
0 ft/see
3.6 mr
0.04 mr
O, 07 mr
0.1 mr
0.1 mr
0; I mr
0.2 cm/sec 2
0.2 cm/sec 2
0.2 cm/sec 2
87 PPM
87 PPM
87 PPM
10 ug/g 2
10 ug/g 2
10 ug/g2
3. R meru
3.6 meru
3.6 meru
15 meru/g
10.5 meru /g
15 meru /g
I meru/g 2
1 meru/g 2
1 meru/g 2
Rcot Sum Square Error (in ft and ft/spr)
Root Sum Square Error (in n. mi, and ft/sec)
Final Position Error
in Local Axes
(in feet)
Alt. Track Range
O 0 0
Final Velocity Error
in Local Axes
(in ft/sec)
Alt. Track ]Range
r
o o o
-38,364 -78.85
240 558 0.83 -0.92
622 0.75
1,160 671 3.12 -!.47
-2,598 1,491 -6.97 3.2.t
- 2,307
1.812
495
-1,412
-1,224
-2_636
962
0
,- 4.72
2 20
- 2,52
-1,893 -3.61 -3.19
2,844 -4.22 4.67
951 -7.83 0.88
539 -2.07 0.82
0
h_;:4 L 762 -!.44 -I,54
152 84 -0.31 0. I]
0 0
89 120 -0.22 -0.22
938 -2.73
685 894 2.55 -2.26
41 0.77
- 3,81_ -9.27
-1,842 2,174 -6.92 5.96
I 1,294 2.71
, 363 -0.82245 290 0.91 -0,78
122 0.25
4,506 38,600 3,224 13.50 79.54 7.66
0.75 6.35 0.53 13.5 79.5 7.7
Table 6-3 Total Indication Errors at SPS 1st Burn Cutoff
6-5
M
O
O
<
Error
Position
Velocity
Initial
S.M.
AlignmentFFF_FS
Aecel. IA
Nonorihog -
onality
Bias
Error
Scale
Factor
Frror
A ccel. Sq.Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
A
L_,/
(E)Xio
(F)YIo
(F)ZIo
(F)VxI o
(E)VyI o
(F)VzI o
A(SM)XI
A(SM)YI
A(SM)ZI
XtoY
iX to Z
YtoZ
)irec_ effect
ACBX Eff on Init Mlm
Combined Eff
_Direct effect
ACBY Fff on Init Mlm
Combined Fff
Direct effect
ACBZ Fff on Init Mira
Combined Fff
SFEX
SFEY
SFEZ
NCXX
NCYY
NCZZ
BDX
BDY
BDZ
RMS
Frror
0 ft
Oft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
3.6mr
O. 04 mr
O. 07 mr
0.1 mr
O.I mr
0.1 mr
0.2 cm/sec 2
0.2 cm/see 2
O, 2 cm/sec 2
87 PPM
87 PPM
87 PPM
10 _g/g2
I0 _g/g2
10 _g/g2
Direct effect 3.6 meru
Direct effect 3.6 meru
Direct effect 3.6 meru
ADIAX 15 meru/g
ADSRAY 10.5 meru /g
ADIAZ 15 meru /g
A 2 D(IA )(IA)X
A2 D(SRA)(SRA)Y
2
A A (IA)(IA) z
Root Sum Square Error (in ft and ft/ser)
Root Sum Square Error (in n. ml. and ft/sec)
Final Position Error
in Local Axes
(in feet)
Final Velocity Error
in Local Axes
(in ft/sec)
Alt. Track Range Alt. Track Range
0 0 0 0 0 0
-2,041 -17, 46
17 - 15 -0. 15 -0. 13
0.05
49 - 31 0,42 0.27
-180 115 -1.44 0.90
-116
89
-205
- 7
- 27
0
-210
IR
-191
-176 -9.93
79 -0.78
- 97 71
4 -6.06
0
- 41 -0.24
0 0
2 3 -0.02
107
82 - 73 0.77
17
290
1-237 210 -2.16
71
1 meru/g 2 23
1 meru/g 2 31 - 28 0.28
1 meru/g 2 7
376 2,074 276 3.25
O. 06 O. 34 O. 05 3.3
I. 64
0.15
1.49
-1.37
0.67
-0.70
0.03
0
-0.35
6
0
-0.02
-0.98
-0.66
0.14
-2.51
1.84
0.58
-0.20
-0.24
O. 05
17.74 2.32
17.7 2.3
Table 6-4 Effect of IMU Errors during SPS i st Burnat SPS i st Burn Cutoff
6-6
--_=_f%kl CIIt_CIklTI A L ,
e_
©cg
oL)<
2
!_]rror
Position
Velocity
Imtial
S.M.
AlignmentFrrors
Aecel. IA
Nonortho g -
onality
Bias
Error
Scale
Factor
Error
Accel. Sq,Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
A
---..- R
TJff
E)XIo
(F)YIo
(F)ZIo
(I")VxI o
(F)Vyi o
(F)VzI o
RMS
A(SM)ZI
Error
0 ft
O ft
0 ft
0 ft/sec
O ft/sec
O ft/sec
A(SM)XI 3.6 mr
A(SM)YI 0.04 mr
0.07 mr
X to Y 0.1 mr
X to Z 0.1 mr
0.1mrYtoZ
Direct effect
ACBX Eff on Init Mlm
Combined Eff
Direct effect
ACBY Fff on Init Mira
Combinpd Fff
]i)irect effect
ACBZ_f_ o,1 Init Mlm
I Comb;n_- Fff
SFEX
SFEY
SFFZ
0.2 em/sec 2
0.2 cm/sec 2
0.2 cm/sec 2
87 PPM
87 PPM
87 PPM
in _, g/gZ
I0 /j g/g2
NCXX
NCYY
NCZZ 10 ug/g 2
BDX Direct effect 3.6 meru
B DY Direct effect 3.6 meru
BDZ Direct effect 3.6 meru
ADIAX 15 meru/g
ADSRAY 10.5 meru /g
ADIAZ
Final Position Wrror
in Local Axes
(in feet)
Aft. Track Range
Final Velocity Error
in Local Axes
(in ft/sec)
Alt. [Track [Range
0 0 0 0 0 0
32,300 72.86
- 2,715 3,804 - 4.62 2.01
573 - 0.67
58 -10,813 9.70
57 24,562 -22.12
1,945
- 1_669
276
4.36
- i.95
2.41
-25,226 71,29_ -75.49
_843 ..... --I 9, 39! _ 23_ 57 ....
-ll,3a3 51,3_Y -51.92 I
-' .........- _._a_.,............ 2_!"_3::'_c!2:VK....I 0
.... I i26a 1,aa._ - ,.,,_ :
- 1,508 4,29( - 4.54
714 2.57
- 5,996 4,75{ - 7.23
- 354 - 0.71
3,080 8.64
15,515 -I0, 67( 17.30
15meru /g - 1,085 - 2.51
1 meru/g 2 300 9.76iA2DIIA)(IA)X
A 2DISRA)(SRA )Y
A 2A(IA)(IA)Z
1 meru/g 2 - 2,010 1,361 - 2.23
] I. 26!i
- 2.70
l14.70
10.27
4.43
0.07
1 meru/g 2
Root Sum Square Error (in ft and ft/seri
Root Sum Square Error (in n. mi. and ft/sec)
_ _ ¥_r
I
[ 5.93
0.05
I O. 88
1.62
- 102 - O. 23
23,320 32,485 69,050 70.32 73.51 16.06
3.84 5.35 11.36 70.3 73.5 ] 16.1
I
I
Table 6-5 Total Indication Errors at Coast End
(SPS 2nd Burn Ignition)
6-7
M 0
M
<
0
Error
Position
Velocity
Initial
S.M.
Alignment_rrors
Accel. IA
Nonorthog-
onality
Bias
Error
Scale
Factor
Error
Accel. Sq.Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
A
_---.--.----._ BTJ
ff
(E)XIo
i(E)Yio
(F)ZIo
(F)VxI o
i(E)Vyi o
(F)VzI o
RMS
l_rror
A(SM)ZI
oft
Oft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
A(SM)XI 3.6 mr
A(SM)YI 0.04 mr
0.07 mr
XtoY 0. i mr
Xto Z 0.1 mr
0.1 mrYtoZ
Direct effect
ACBX Eff on Init Mlm
Combined Fff
:irect effect
ACBY Fff on Init Mlm
Combined Fff
Direct effect
ACBZ Fff on Init Mlm
Combined Fff
SFEX
SFEY
SFEZ
NCXX
NCYY
NCZZ
BDX Direct effect
BDY Direct -effect
BDZ Direct effect
ADIAX
0.2 cm/sec 2
0.2 cm/sec 2
0.2 cm/sec 2
87 PPM
87 PPM
87 PPM
10 ,g/g2
I0 _g/g2
10 .g/g2
3.6 meru
3.6 meru
3.6 meru
15 meru/g
ADSRAY 10.5 meru /g
ADIAZ 15 meru /g
A 2 D(IA)(IA)X
A2D(sRA)(SRA)Y
2
A A (IA)(IA) z
1 meru/g 2
1 meru/g 2
1 meru/g 2
Root Sum Square Error (in ft and ft/see)
Root Sum Square Error (in n. mi. and ft/sec)
m 6_4 Awv ¥¢#"
Final Position Error Final Velocity Error
in Local Axes in Local Axes
(in feet) (in ft/sec)
Alt. Track Range Alt. Track Range
0 0 0 0 0 0
432 377 - 0.58 0.33
2 - 0.05
478 16.83
763 132 - 0.58 0.63
2,515 278 1.78 -2.09
64 I. 58
% - 0.14
58 i. 44
-7,204 18,366 -19.86 4.43
2,204 - 1,922 2.98 -1.68
-5,000 16,444 -16. 88 2.75
97 - 1i 0.07 -0,08
0 0
-1,841 4,679 - 5.06 1.13
1 C 0 0
- 129
0 0
328 - 0.36 0.08
20 0.94
-2,191 1,932 - 2.98 1.67
4 - 0.14
66 2.42
6, 142 - 5,39_ 8.34 -4.67
- 19 - 0.56
5 0.19
789 690 - 1.07 0.60
2 - 0.05
8,893 492 18, 180 19.96 17. i0 6.24
I. 46 O. 08 2.99 20.0 17. 1 6.2
Table 6-6 Effect of IMU Errors during SPS I st Burn at Coast End
(SPS 2nd Burn Ignition)
6-8
-"$: ".-I........ L '
*°ir
"D L.
CC
©
C_
f
!i
i
2
t<rror
°csition
Velocity
Initial
S. IVl.
Aligmnent
l"rrors
A cc,'l. IA
Nonorthog -
onality
Bias
Error
Scale
Factor
Error
A ccel. Sq.
Sensitive
Indication
Error
_! ias
Dr'ft
Acc _qer-
ation
Sensitive
Dri?tAcceier-
atlonSquared
SensitiveDrift
A
( K)Xio
J(F)YIo
(F)ZIo
(F)VxI o
(F)Vyi o
(F)Vz[ o
A(SM)XI
A(SM)YI
A(SM)ZI
R his
Frror
0 ft
O ft
0 ft
0 ft/sec
8 ft/sec
0 f_/sec
3.6 mr
0.04 mr
0.07 mr
X to Y 0. 1 mr
X to Z 0.1 mr
Y to Z 0. I mr
',
Direct effect !
iACBX Fff on [nit Mlm
Combined Nff
Direct effect
ACBY __iVff on Init Mlm
Combined Fff
IDirect effect
ACBZ Fff on Init Mlm
Combined Fff
SFEX
SFEY i
+SFEZ I
NCXX [
NCYY
INCZZ
BDX Direct effect
BDY Direct effect
BDZ Direct effect
0.2 cm/sec 2
0.2 cm/sec 2
0.2 era/sec 2
87 PPM
87 PPM
87 PFM
1O_g/g 2
1O ug/g 2
iO ug/g 2 ]3.6 meru
3.6 meru
3.6 meru
ADIAX 15 meru/g
ADSRAY 10.5 mere2 /gI
ADIAZ
!A2D ........
(SRA){SflA)Y
I 2]A A (IA)(IA) Z
15 meru /g
1 meru/g 2
! meru/g2
I meru/g 2
Root Sum Square Error (in ft and ftlser)
Root Sum Square Error (in n. ml. and ft/sec)
Final Position Error
in Local Axes
Alt.
- 2,720
- 323
574
-24,424
13,866
-10,558
- I, 268
- 9 fl55
260
(in feet)
Track
i-39,336
- 626
2 322
t- 1,824
4981
i, 022
- i. 460
- 6)019
304
3,926
15,864] -i3, 70_
1
]- i, 222
373
.... j
22,982 39,576 71, 72_
3.78 i 6.51 11.30
Final Velocity Error
in Local Axes
(in ft/sec)
Range Alt., ] Track I Range
' ii 1
o o o I o
II
!73.40
4,30_ - 4.96 2. i2
1- 0.43!
-10,662 9.92 1.40
iI24,23[ -21.87 I ° 3.52
1-----
3.47
- 1.241
2.23 i
75, 515 -79.58 I i5.03
-21,97] 25.28 I -i0.79
I53, 54( -54.30 4.24
I0,506 -I0.34 - O. 15
O 0
3n ._6_ -32. 23 5. 75
0 i,725 - I. 74 0.030
4,541 - 4.80 0.87
J .......
3.88
5,964 - 5.58 6.31
1.87
8.98
18.29 -13. 86
- 0.271-
O. 78
- % --.
- 2.35 1.80
- 0.03
73. 17 74. II 17.70
73.2 74. I 17.7
Table 6-7 Total ..................... at ...... Burn _ULOliII l_li C _:t. t lO i I _ , pc.r',L'L'OL'_ _D L_ ,D /.II(l
6-9
C n" ........ TIC,'
x o
>.O
Error
Position
Velocity
Initial
S.M.
Alignment|-'trots
Accel. IA
Nonorthog -
onality
Bias
Error
Scale
Factor
Error
A ceel. Sq.Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
[loot Sum Square
Root Sum Square
A
t
jf
(E)XIo
(F)YIo
(F)ZIo(V)VxI o
RMS
Frror
0 ft
0 ft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
A(SM)X I 3.6 mr
A(SM)Y [ v. 04 mr
O. 07 mrA(SM)ZI
X to Y 0. I mr
XtoZ 0.1mr
Y to Z 0. I mr
Direct effect
ACBX Fff on Init Mira
Combined Fff
Direct effect
ACBY Fff on Init M1m
iCombined Fff
)irect effect
ACBZ Eff on Init Mlm
Combined Fff
SFEX
SFEY
SFEZ
NCXX
NCYY
NCZZ
BDX Direct eff, ct
BDY Direct effect
BDZ Direct effect
A DIA X
ADIAZ
2O. 2 cm/sec
Final Position Error
in Local Axes
(in feet)
Alt. t Track
0 0
-2,318
440
I
Final Velocity Error
in Local Axes
(in ft/sec)
Range A1t. Track Range
0 0 0 0
21.56
46] - 0.55 0.40
0.12
796 279 - 0.59 0.60
2,670 794 2.69 -2.59
185 0.93
0.2 cm/sec 2 ..3 O. 35
188 128
-__7__0.22 19, aI_ -2n 76 4 _5
0.2 cm/sec 2 2,245 I - 2,35_ 2.82 -2.03
-4,777 ] 17,26_ -17.94 2.92
87 PPM 110 [ 3_ 0.26 -0.20
87 PPM 0 0
87 PPM -1,802 4,988 - 5.45 1.03
10 pg/g2 2 - 1 0_ 02 -0.01
ug/g2_ 0 010
ug/g 2 - 126 350 - 0.37 0.0810
3.6 meru 175 I 2.35
3.6 meru -2,136 2,407 - 0.75 3.09
3.6 meru 97 2.39
15 meru/g 332 3.17
ADSRAY 10.5 meru (g__ 6,_2_49 ........ - .6f59__ __7. 81 .... -5.71
15 m_,ru /g 24 1.55
2 2 .....
A D_ ......... 1__mer_u/g _ -t 26 O. 25
SRA, ....lZo u/ : i........ 84:-100 0732 1 meru/g 2 2 0. 14
A A (IA)(IA) z
IJ 8_,870 2,3_9 19,472 ...........20.66 22.14 7.73Error (in ft and ft/_rl #-Error (in n. mi. anti ft/sec) _1.46 0.39 ; 3.20 20.7 22. 1 7.7
Table 6-8 Effect of IMU Errors during SPS 1st and 2nd Burnat SPS 2nd Burn Cutoff
6-10
Effect of IMU Errors during SP5 2nd }lurn at SI'5 2nd }{urn Cutoff
[d
r.1
OO
<
Error
Position
Velocity
Initial
S.M.
Alignment
l.'rrors
Aecel. IA
Nonorthog -
onality
Bias
Error
St
ff
i(E)Xlo
r(F)Ylo
(F)ZIo
(F)VxI o
(F_)VyI o
(F)VzI o
A(SM)XI
A(SM)YI
A(SM)ZI
XtoY
XtoZ
YtoZ
Direct effect
ACBXIEff on Init Mlm
Combined Fff
i.Direct effect
ACBY Fff on Init Mlm
Combined Fff
Direct effect
ACBZ Eff on Init Mlm
Combined Fff
Scale
Factor
Error
A ccel. Sq.
Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
Squared
Sensitive
Drift
RMS
Frror
Final Position Error
in Local Axes
0 ft
O ft
0 ft
0 ft/sec
0 ft/sec
O ft/sec
3.6mr
0.04 mr
0.07 mr
0.1 mr
0.1 mr
0.1 mr
O. 2 cm/see 2
5 F" K X
SFEY
SFEZ
NCXX
NCYY
NCZZ
BDX Direct effect
BDY Direct effect
BDZ Direct effect
A DIA X
A DSRAY
A DIA Z
2 2
2
A A(EA)(LA) Z I m_'ru/_ 2
Root Sum Square Error ,in ......ft .... ,ft/ ..... I liO- _- 73
"ootSum quareError,inn.mt..... 10.05100,
Final Velocity El for
in Local Axes
(in feet) (in ft/sec)
Alt. Track [ Range Alt. Track Range
I
0 0 0 0 0 0
227 4.88
5 2 0.10 0.05
8 0.17
5 - 3 0.11 -0.07
25 - 17 0.53 -0.35
30 -O 63
0.2 cm/sec 2 23 0.49
7 -0.14
17 25 0.35 0.53
0.2 cm/sec 2 23 12 -0.51 -0.26
6 13 -0.16 0.27
87 PPM 8 5 0. 18 -0. 12
87 PPM0 0
87 PPM 3 5 -0.07 -0. 10
9
10pg/g_ 1 0 0.02 -0.01
10 ug/g 2 0 0
I0 pg/g2 0 0 0 0
3.6 meru 65 1.42
3.6 meru 118 60 2,58 1.33
3.6 meru 115 2.52
15 meru/g 35 0.77
10.5 meru /g 70 35 -1.51 -0.77
15 meru /g 97 2.10
1 meru/g 2 3 .............. 0.06 .....
4 0.19 0.10
0.19
3.06 6.11 1.61
3.1 6.1 1.6
Table 6-9 Effect of IMU Errors during SPS 2nd Burn at SPS2rid Burn Cutoff
6-11
X O
ee
O
Id
_9_9<
Error
Position
Velocity
InitialS.M.
AlignmentFFFOFS
A'ccel. IA
Nonorthog -
onality
Bias
Error
Scale
Factor
Error
Accel, Sq,
Sensitive
Indication
Error
Bias
Drift
A cceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
A
f
(E)XIo
I(F)YIo
(F)VxI o
(F)VyI o
(F)VzI o
A(SM)XI
A(SM)YI
IA(sM)ZI
XtoY
YtoZ
Direct effect
ACBX Eff on Init Mlm
Combined Eff
Direct effect
ACBY Fff on Init Mira
Combined Fff
Direct effect
ACBZ Eff on Init Mlm
Combined Fff
SFEX
!!
i
Xto Z
0.1 mr
87 PPM
SFEY 87 PPM
SFEZ 87 PPM
NCXX
NCYY 10 ug/g2
NCZZ I0 ug/g 2
BDX Direct effect 3.6 meru
BDY Direct effect 3.6 meru
BDZ Dii'ect effect 3.6 meru
iA DIAX 15 meru/g
ADSRAY 10.5 meru /g
A DIA Z
_X
A 2 D(SRA)(SRA)Y
2
A A (IA)(IA) z
RMS
Error
0 ft
9 ft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
3.6 mr
0.04 mr
0.07 mr
0.1 mr
0.1mr
0.2 cm/sec 2
O. 2 cm/sec 2
0.2 cm/sec 2
10 _g/g2
15 meru /g
1 meru/g 2
i meru/g 2
I meru/g 2
Root Sum Square Error .(in ft and ft/s_'_'_
Root Sum Square Error (in n. mi. and ft/sec)
Final Position Error Final Velocity Error
in Local Axes in Local Axes
(in feet) (in ft/aec)
Alt. Track Range Alt. Track Range
0 0 0 0 0 0
58,534 52.86
2,400 5,968 - 6.26 2. 17
- 714 - 0.15
- 1,351 - 9,853 9.84 1.80
3,063 22, 286 -21.93 - 4.62
-18, 174
12,230
- 5, 944
348
- 7,444
117
- 1,092
i- 4,917
15,079
3,201 2.31
- 0.43- 2.079
Ij122 1.88
2,102
262
6,33O
- 1,227
88,387 -91.67
-30, 427 31.94
57, 956-59.73
10,7451-11. 12
35,501 -37.25
1,803 - 1.89
5,304 - 5.53
9,94f - 7.84
-24, 114 25.69
14.40
-11.06
3.34
- 0.37
0
5.63
0.01
0
0.84
3.23
5.61
1.87
6.83
-14.57
0.25
...... 2781....- 1,955!
117
19,231 58,944
3.17 9.70
0.58
3,104 - 3.31
0.02
1.89
!
80,193 82.52 [ 53.48 18.03
13.20 82.5 I 53.5 18.0
Table 6-i0 Total Indication Errors at Entry Start
6-12
• a __
E i
F:r 1"oI"
Position
A
Imp.. R
//
(E)XIo
Ii
RMS
! Vrror
0 ft
(F)YIo 0 ft
(F)Zlo 0 ft
m_
r_
[4
O
J
UU<
?
Velocity
Initial
S.M.
Alignmentl' rrors
Accel. IA
Nonbrthog-
onality
Bias
Error
Scale
Factor
Hrror
A ccel. Sq.Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-ation
Squared
Sensitive
Drift
(V)VxI o ') f,/sec
(F)Vy[ ° 0 ft/sec
V)VzI o
A(SM)XI
A(SM)YI
A(SM)ZI
XtoY
0 ft/sec
3.6 mr
O. 04 mr
0.07 mr
0. I mr
X to Z 0.1 mr
0.1 mrYtoZ
Direct effect
ACRX Fffon Init Mira
Combined Fff
Direct effect
ACBY Vff on Init Mlm
Combined Fff
Direct effect
ACBZ_on Init Mlm
C_m-ffi.--__KSFEX
SFEY
SFFZ
I .......t_lL, AA
NCYY
,3.2 cm/sec 2
0.2 cm/sec 2
0.2 cm/sec 2
67 PPM
87 PPM
87 PPM
,n _1_2_u_g/g
10 ug/g 2
10 /._g/g_NCZZ
BDX Direct effect 3.6 meru
BDY Direct effect 3.6 meru
BDZ I Direct effect 3.6 meru
i
_DIAX i5 meru/g
_DSRAY 10.5 meru /g
DIAZ
_A)X
2
D(SRA)(SRA) Y
2
A(IA)(IA) Z
15 meru /g
1 meru/g 2
1 meru/g 2
i meru/g 2
Root Sum Square Error (in ft and ft/soc}
Root Sum Squ "e Error (in n. mi. and ft/sec)
Table 6- i i
Final P()sition Frror
ie l,ocal Axi:s
(in feet)
Air. [Track Range
l l
t !0 t7 ! 0
8,514
4OO
37 I
827
Final Velocity Frror
in Local Axes
(in ft/see}
Alt. Track _('
I
i
II
0 C e
it
19.27
746 _ 0._5 0,40
0.11
793 - 1.01 0.69
2,971 I- 2,778 3.94
448 O. 80
...... I07 0.33
555 I. 13
-5,334 23,528 -24.05
2,037 - 3,816 3.82
-3,297 19_712 -20.23
l154 - 16C 0.28
0 _ __.... ----.-r T[ ....
98 42{
855 [ __ 2. 13
-1,179 3,867 1.12
793 2.20
1,243 2.83
5,633 -10, 67{ 10.56
477 !. 44
97 0.22
..................... J ____
725 1,35{ - 1.36
42 ........ 0.. 13- "
I-
7,513 8,715 23,88( 24.25 19.81
1.24 1.43 3.93 24.3 19.8
-3. 15
4.73
-2.05
2.68
-0.27
1.07
-0.02 i
0.08
2.14
-5.70
0.73
7.53
7.5
Effect of IMU Errors during SPS 1st and 2nd Burns
at Entry Start
6 -13
o
._
i
w •[. I
0 '
_J
0L)<
o0
Error
Position
V,.!oeity
Initial
S.M.
Aligrm_ent
l"rrors
A eccl. IA
Norlorthog "
onality
A
f
(E)XIo
(F)YIo
(I')Zio
(I')Vxi o
I(V)VyI o
.C )vzi o
__5sM_J_x!...................
A(SM)YI
A(SM)ZI
XtoY
iX to Z
L
Y to Z
I JDirect effect
ACBX Eff on Init Mlm
Combined Fff
Direct effectBias
ACBY T'ff on Init MlmError
Combined Vff
)irect effe(t
',CBZ l"ff on Init Mira
Combined I f[
Scale _,FEX
RMS
Error
0 ft
0 ft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
3.6mr
0. 04 mr
0.07 mr
O. lmr
0.1mr
0. I mr
O. 2 cm/see 2
0, 2 era/see 2
F'.nal Position Frror
in Local Axes
(in fertl (in
All. I Track Range
1ItI
0 ] G 0
Ii
ii
11,648 [
40 3
57
I i29 i- 39
),34 ] .... ]-180
- 214
196
- '_8189 118 0.59
0.2 cm/see 2 205 - 13 -0.66
16 105
87 Fi'/q 44 - 80
Final Velocity Error
in Local Axes
ft/sec)
Aft. ]Track iRange
II
i o o
!I
II
i4.49
0.13 I 0.010.16
o.o_ I I-0.11
1 l--0.44 ]
i
q 0 _ 5O
I_"-_- d----
, 0,31
I I-0.03
' i-0.07 i 0.28
0. 14 'I -0. 17
EaCIOF
Error
A ccel. Sq.
Srnsitive
Intlicatioll
Error
_ I"EY
S["V Z
NCXX
NCYY
Direct effect
NCZZ
:_DX :3.6 meru
2 1 0.01
Bias
Drift
Acceler-
ation
Sensihve
Drift
Acceler-
atlon
Squared
Sensitive
Drift
BDY Direct effect 3.6 meru
BDZ Direct effect 3.6 meru
%DIAX 15 meru/g
A DSRAY I0.5
ADIAZ 15
A2I)_ ............ 1
A2 DISRA)(SRA)Y 1
2 1A A(IA)IlA) Z
Root Sum Square Error (in ft and ft/serl
Root Sum Square Error (in n. mi. and ft/sec)
_z4r_ 4_,v v_r
Table 6-12 Effect of IMU Errors during SPS 2nd Burn
at Re-entry Start
(; -14
m
.6_kca [.,.1
r. ¢jo[.-
re
o
Error
Position
Velocity
Initial
S. M.
AlignmentFrrors
Accel.. IA
Nonorthog -
onality
Bias
Error
Scale
Factor
Error
Accel. Sq.Sensitive
Indication
Error
A
T./_--R
f
(E)Xlo
(F)YIo
(F)ZIo
(F)VxI o
(F)VyI o
(F)VzI o
A(SM)XI
A(SM)YI
A(SM)ZI
XtoY
[t M S
t'rror
0 ft
0 ft
0 ft
0 ft/sec
0 ft/sec
0 ft/sec
Final Position Frror
in L(*:a} Axes
(t,_ f*.,.t)
3.6 mr
Alt.
0.04 mr - 3. 317
0.07 mr
0. i mr
X to Z 0.1 mr
0.1 mrYtoZ
Direct effect
ACBX Eff on Init Mlm
Combined Fff
Direct effecti
ACBY[Fff on init Mlm
Combined Fir
Direct effect
ACBZ Eff on Init Mlm
Combined Fff
SEEX
SFEY
SFEZ
0.2 cm/sec 2
903
1,757
1_631
9.2 cm/sec 2 - 2,778
- lm147
ITrack Range
!t 0 0
72,198
8,430
953
- 6.514
NCXX
NCYY
NCZZ
Final Velocity Error
in Local Axes
(in ft lsec)
Aft. [ Trac_ [Range
tii
II
0 0 ] 01
l
II
....
1.86 t
- 11.06 ] - 1.21
- 1.13 l
.39
12,345 - i7.64 -15.0C
- 6.11
- 3.30
- 9.41
.m
...... q
----M
-25.28
6.18
-19.10
-23,933 100_229 -111.25
0.2 cm/sec 2 16,909 -42,983 56.39
- 7_023 57,246 - 54.86
- 1,298 10,112 - 11.47] - 1.82 d
m
87 PPM
87 PPM 0 0
67 PPM -11,211 40,671 - 49.221 - 9.58
10ug,/g _ 220 1,570 - 2.18 ___28 ]___._t
lO ug/g 2 o
1Opg/g 2 - 1,599 6,039 - 7.05 -- _.47
BDX Direct effect 3.6 meru a qnv *n no
Bias BDY Direct effect 3.6 meru -_'" __ ""'_- .... -J o_Drlft -12 a 100 1_4 6,,_ -.,#. V._$ - ,. o,
..... BDZ Direct effect 3.6 meru 8_270 ........ | 2_00 ........-- ---- --............ 4 :_..o ........
Acceler- ADIAX 15 meru/g 8,174 -1-t- 2. B_
1
atlon A R 0 ....................DS AY I .5 meru /g 22,045,]- -41,88t) 85. t9 ] I 2.:6
Sensitive ........... _--........... j_ .... ] -- ]Drift ADIAZ 15 inert _ - 5 670 -1_ _ i................. .... I---"- ...... ....[-- t _!eel 2 / 2 / ]
Ac. er- A 13.......... 1 meru _ I 8_" / ..... Iati,m _IP)JIIPLIA ' t ' r i..r_ ,
Squared A2D(SHA}(S_.IA)y 1 morll/g z _ 2,8D61 . 5,40n 8.8i[ [ 0. Sa ]
S,-nsi,ive TK ......................... :-_ -_-_ -- I --- _ .... ] , .... 1
,Or', S ..... Square Error _ft an(_ ,t]._o._' I 2">'23_2_7,6951 ]!6.0::_73
_oot s.... S.,,s_r e_,'o_ ,'inn._. a.d ft/_._) [ .. v,; I ,_.06 I ,,* 43 II 116 0 t 38.7 I ... I
Table 6-13 Total Indication Error_ nt F:ntry Pnd (at _a non ÷'+ 51+)
(;-15
>1 o
©,w
(9O
oO
EFFoF
I'_,:,itiun
Vvlocity
[nitialS. M.
A 11gnmcntI l'l'OI'S
4' <'_+I. IA
(_<,tlc3t't hog -
_m:Jlity
_las
Error
Scale
Factor
Error
Accel. Sq.
Sensitive
Indication
Error
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
-A
................ _. ,- ,
(i.)N ( ° u +t
............. ""(i,)Z[o 0 ft
(}.)Vx[ ° U lt/_ec
(1.,IVy[ ° 0 n ,' sec
+(i)Vz[ ° 0 ft / _,ec
RMS
I rror
A(SM)X I :_. 6 mr
A(SM)Y[ O.U_ mr
AISIM)Z[ I). !17 n,r
X to Y 0, 1 nlr.i
X to Z 19, [ nlF
Y to Z O. I mr
IJirect ct [e<-t
ACB_ I'J[,n lnit Mint 0.2 cm/sec 2
('ond]hlr!(I l'ff
IIirect c fl"_'t:l
ACI3Y Iff on hut Min, 0.2 cn_/scc 2
Cornbined Fff
Direct effect
ACBZ P:ff on Init Mira 0.2 cm/sec 2
Combined Fff
SFEX 87 PPM
SFEY 87 PPM
SFEZ 87 PPM
NCXX 10 ug/g 2
NCYY 10 ug/g 2
NCZZ 10 ug/g 2
BDX Direct effect 3.6 meru
BDY Direct effect 3.6 meru
BDZ Direct effect 3.6 meru
ADIAX 15 meru/g
ADSRAY 10.5 meru /g
ADIAZ 15 meru /g
A2 D(IA)(IA)X i meru/g 2
A2D(sRA)ISRA)Y
2
A A(IA)(IA) Z
Final Position Error Final Velocity Error
in Local Axes in Local Axes
(in feet) (in ft/sec)
Aft. Track Range Alt. Track Range
0 0 0 0 0 0
20,284 31.15
720 1,195 - 2.54 - 0.26
3:]6 - I. 72
- 1,148 1,781 - 2.58 - 0.62
3,777 - 8,881 a.05 - 5.38
- I, 003
,980
,- 1_9,2_8 :_ ......
3, fi 73
- 1,093
262
- 2,300 7,140
12 ,- 154
4
- 122
- 7,370
- -i. 30
- 5.00
3.30
- 6,092 i2.9_ 1.31
21,025 -11.5_ - _i.80
74 0,76 2.03
51 - 0.07
-9.43 ,- 1.37
- 0.08 - 0.67
- 0.02
493 - 0.47 - 0.12
2. 8441 I0.67
4+180 -39.52 - 7.59
- 5,740 -31.32
2,510 - 0.23
10,148 -16,954 35.33 32.58
- 3,870 -19.11
323 1.34
1 meru/g 2 - 1,352 2,169 - 4.94 - 0.57
1 meru/g 2
Root Sum Square Error (in ft and ft/se¢')
Root Sum Square Error (in n. ml. and ft/sec)
391 - 2.08
13,665 21,867 29,873 56.08 50.27 11.91
2.25 3.60 4.92 56.1 50.3 11.9
Table 6-14 Effect of IMU Errors during SPS ist and 2nd Burnsand Entry End (Alt. of 50,000 ft)
6-16
--_I_I plhpL, l"_ai • I
_- _ _ _ _- "--21F_- -" J----
Error
FinM Position l<rror
hi Local A×es
(in f,,et)
Alt, 'Iraek Hange
_ effect
AC]RX _ 0.2 era/see 2
m L IC_mbtned Ff_f _! IDirect _ffect
._ ]ACBY]Fff on Init Mlm 0 2 cm/sec*
,at,o, 1--
INCXX ! l0 /2 _,/gAccel, Sq, _ ...... {
Sensitive tNCY Y ] 10 tag/E 2
Indication _-_ ........ --4 ...... } - -
_ Err°r :? Zz __g 10ug/g
Bias [BDY ] Direct effectA_ - 3.6 meru _
,)rift .4BDZZJ_ Direct effectT-[ .3.6 _m_eeru _
atton ]ADSRAY __. 10. 5 meru /1_,Sensitive _ ..................... _i....
Drift ADIAZ I 15 mPru /g
T_Aceeler- ItIA)X / 1 meru/g
ation ) , 2 _'-"_ ....... _-........... 5-Squared [A_D(sRAIISRAIY n 1 meru/g _
Sensittw' kT_- _z'_'" ='-L_=-"" " _ ................. _.--
Drift [A_A(IA)(__ . ____I.A)Z ......... ___ .... lm. 17_re_a/L_
Root Sum Square I,:rror (in ft and ft/seel
Root Sum Square Error (in n. mi. anti ft/sec) --.
}S'inal VPloclty Frror
in l.ucM Axes
fin ft/see)
0 0
Table 6-15 Effect of IMU Errors during SPS 2nd Burn and Entryat Entry End (50,000 ft alt)
6-17
___L-__,.__,__:_ :"- _" _ __ . "a''"2_- -
o
ML-
0
M,4MUU<
o>,cD
_rror
Position
Velocity
InitialS.M.
AlignmentFrrors
A ccel.. [A
Nonorthog -
onality
Bias
Error
Scale
Factor
Error
Accel. Sq.
Sensitive
IndicationError
Bias
Drift
Acceler-
ation
Sensitive
Drift
Acceler-
ation
SquaredSensitive
Drift
A
I_/
(E)XIo
{E)Yio
{F)ZIo
(F)VxI o
_-R
RMS
Error
0 ft
0 ft
0 ft
0 ft/sec
(F)Vyi ° 0 ft/sec
(F)VzI ° 0 ft/sec
A(SM)X I 3.6 mr
A{SM)Y I 0.04 mr
A(SM)Z I 0.07 mr
XtoY 0.1mr
Xto Z 0.1 mr
Y to Z 0. I mr
Direct effect
ACBX Eff on Init Mlm 0.2 cm/sec 2
Combined Eff
Direct effect
ACBY Fff on Init Mlm 9.2 cm/sec 2
Combined Fff
)irect effect
ACBZ Eff on Init Mlm 0.2 cm/sec 2
Combined Fff
SFEX 87 PPM
SFEY 87 PPM
SFEZ 67 PPM
NCXX 10 _g/g2
NCYY 10 ug/g 2
NCZZ 1O _g/g2
BDX Direct effect 3.6 meru
BDY Direct effect 3.6 meru
BDZ Direct effect 3.6 meru
ADIAX 15 meru/g
ADSRAY 10.5 meru /g
ADIAZ 15 meru /g
:_IA)X 1 meru/g 2
A2D(sR A)(SRA)Y 1 meru/g 2
2 1 meru/g 2A A (IA)(IA) Z
Root Sum Square Error (in ft and ft/ser)
Root Sum Square Error (in n. ml0 and ft/sec)
,lu¢¢ 4av ¥#J-
Final Position Error
in Local Axes
(in feet)
Alt. ITrack Range
Final Velocity Error
in Local Axes
(in ft/see)
Alt. Track [Range _
0 O 0 0 0 0
2,493
284
- 433
11 - 1,25
i0 - 69 - 0. ii
- 212 - 1,795 - 0.63
- 1,797
- 1.261
- 3.058
2.201 31E 6.57
1_446 5[ 6.39
3,647 373 12.96
69 53[ 0.31
51
55 7 - 0.67
18 - 132 - 0.09
- 4
13 2 0. Ii
928
- 8,757 254 -39.66
- 7,662
I0(
4,107 201 17.34
- 5,103
120
572 1{ - 2.63
500
10,359 10,069 1,942 45.30
1.70 1.66 0.31 45.3
28.14
-0,, 16
-1.75 1
._-- -0p78
I -4.31
- 4.33
- 5, 09
- 9, 42
-0.77
0.83
0.06
2.15
- 0.07
0.09
-0.66
- 0.02
-0.01
i0_25
-5.50
-31.84
- 0.68
1.84
-19.49
1.30
-0.39
- 2.11
48.88 7.80
48.9 7.80
Table 6 - 1 6 Effect of IMU Errors during Entry only at Entry End(50,000 ft Aft)
6 -18
7...C"'"" -- ),:" 'A"
7. G&N CONFIGURA TION
System 017 will be the G&N system for Mission 202. It is a Block I series 50
system with one modification; the wiring of the 11 spare relays in the main DSKY to
the MCP to provide the AGC/MCP signal interface (refer ICD #MH01-01200-216)
described in Section 3.
Without giving a detailed analysis of each G&N Block configuration, a brief descrip-
tion of each and the reason for its evolution is useful in understanding G&N's capabilities
for Mission 202.
Block I is the original G&N design. It is composed of IMU, AGC, PSA, CDU's
(mechanical), Harnesses, and OPTICS (sextant and telescope). As the G&N flight
requirements became more clearly defined it was apparaent that Block I would need
modification to qualify for flight.
Block I, series i00 therefore evolved. It is the Block I system modified generally
as follows:
(a) IMU - Vibration dampers added; moisture insulation added.
(b) AGC - Cooling inierface modified; humidity proofing added.
(c) PSA - Cooling interface modified; humidity proofing added.
(d) CDU's - Minor electrical and mechanical changes.
(e) Harnesses - All wiring changed to teflon; connectors humidity proofed.
(f) OPTICS - Addition of automatic star tracker, photometer and minor servo
modifications.
When the full design and production schedule impact of the series i00 modifications
become clear the Block I series 50 configuration was originated, being a limited i00
series modification qualified for flight and available on an early schedule.
Block I series 50 is basically the Block I series i00 system less the automatic star
tracker and the photometer.
7-I
8. INSTRUMENTA TION
8. 1 G&N Instrumentation
The inflight information from G&N is available in three distinct forms: PCM
telemetry of the AGC DIGITAL DOWNLINK, (PCMD); PCM telemetry of low band-
width G&N measurements, (PCM +, PCM, PCME); and on-board recording of high
band-width G&N measurements (TR).
The PCM telemetry of the AGC DIGITAL DOWNLINK has been clearly defined
at the MIT/NAA interface as 50 words of 40 bits each per second. The particular
format of this DOWNLINK is AGC program variable and can remain under MiT's
control without having interface repercussion (see 8. i. i).
The PCM telemetry of the low band-width measurement and the on-board
recording of the high band-width measurements have been defined by NASA in "NASA
Program Apollo Working Paper 1141, Apollo SC Measurement Requirements, Apollo
MissionA-202, Spacecraft 001" dated November ii,1964 (see 8.1.2).
8. i. 1 AGC Digital Downlink
The AGC digital downlink consists of 50 words/sec on the high rate
and i0 words/sec on the low rate. Each "word" contains 40 bits (a 16 bit
register transmitted twice and an 8 bit "word order code"). Since the high
rate will be used exclusively for flight 202 all further discussion will use the
50 words/sec rate.
The digital downlink format is controlled by an AGC program which
loads the next word to be transmitted into register OUT4. The program has
an established priority (see Fig. 8-1). This program is entered on an inter-
rupt caused by an "endpulse" from the telemetry system. Relay words have
the highest priority and will be sent down on the next telemetry word. These
relay words contain the state of all latching DSKY relays and therefore indi-
cate displays (display word) and mode status of the G&N and MCP/SCS. Relay
words for flight 202 are listed below.
The maximum rate for relay words is 1 word/120 msec. If a relay
command has occurred, a relay word is loaded into OUT4 and the AGC returns
to whatever program it was in before the interrupt. In a similar way, if no
relay word is used, the AGC checks to see if an "input character word" has
been received (manual keyboard entry, mark, or uplink). The maximum rate
of input character words could occur due to uplink words; this rate is 1 key-
board character/ll0 msee (see section 3.1.2. I). If no relay or input word is
indicated, the AGC checks to see if an IDword is required (there is an ID word
for every block of 4 data words). If no relay, input, or ID word is senLthe AGC
will load OUT4 with the next data word to be sent. A list of the data words
While it is theoretically possible to get almost 18 relay and input character
words/sec leaving only 32 words/sec for both ID and data words, it is estimated
that the AGC will average at least 32 data words/sec and 8 ID words/sec.
8 -1
TELEMETER
RELAY
WOR D
( MODE S &
DISPLAYS )
i
EXIT
TELEMETER t
INPUT
CHARACTER
WORD
EXIT
TELEMETER LID
WOR D ,F
EXIT
YES
YES
YES
PULSE
I D \.
I TELEMETERDATA
WORD
EXIT
Fig. 8-i AGC Downlink Transmission Logic
8-2
RELAY WORDS
A. Display Words
Item
Vg x Vgy Vg z
Tff
WX
B.
i•
2o
3o
Remark
three components of velocity-to-be-galned duringpowered flight
free-fall time to 300, 000 ft when calculated
W Wy z
Spacecraft Body Rates when calculated
Other Relay Commands
Item Remark
G/N ATT CONTROL SELECT
G/N AV MODE SELECT
G/N ENTRY MODE SELECT
CM/SM SEP COMMAND
+X TRANSLATION ON/OFF
G/N FAIL INDICATION• 05 G INDICATION
GIMBAL MOTOR POWER ON/OFFFDA I A LIGN
T/C ANTENNA SWITCH
MCP/SCS Modes
ZERO ENCODE
COA RSE A LIGN
LOCK CDU
FINE ALIGN
RE-ENTRY
ATT CONTR
ZERO OPT. CDUVs
G&N Modes
CDU ZERO LIGHT
CDU FAIL LIGHT
PIPA FAIL LIGHT
IMU FAIL LIGHT
OR OFALLALARMS
COND LAMP TEST
FAILURE & WARNING LIGHTS
8-3
DA TA WORDS
This list is comprised of three groups: Group I is transmitted throughout
the flight; group II is transmitted only in non-powered flight; and group III is
transmitted only in powered flight.
Point Measured Remarks
Group I
Time I AGC Timing Register
Time II
IN0
IN2
IN3
AGC Timing Register
Contains keyboard characters, mark, block uplink,inhibit upsinc
Four lowest order time bits, CDU, PIPA, and IMUFail and Parity Alarm, Lift Off, Guid Release,SIVB Separate,
Zero CDU encoders, lock CDU, fine align, re-entry,OPT modes 2 & 3, star present, zero OPT, Coarsealign, A TT SW and TRN SW, Sextant On, OR OFC1-C33
OUT1
Position & Velocity
Engine on; block end pulse; ID word; RUPT trap reset;T/M, program, and program check fail alarms, keyrelease, and computer activity
Six double precision words (12 words in all)
Group II
3 actual CDU counters Used to monitor platform alignment
Group III
PIPA Contents of the three PIP accumulation registers
CDU's (actual anddesired)
6 AGC registers which give actual and desired CDUangles
8.1.2 G&N PCM Telemetry (exclusive of DIGITAL DOWNLINK) and On-Board Recording for Mission #202
OPERA TIONA L
CG0001 V Computer Digital Data PCMD
CGll01 V -28 VDC Supply PCM+
CGlll0 V 2.5 VDC TM Bias PCM+
CG1503 X IMU +28 VDC Operate PCME
CG1513 X IMU +28 VDC Standby PCME
CG1523 X AGC +28 VDC PCME
50 s/sI
1
I0
i0
i0
(See 8.1.1)
8-4
CG1533
CG2110
CG2112
CG2113
CG2117
CG2140
CG2142
CG2143
CG2147
CG2167
CG2170
CG2172
CG2173
CG2177
CG2206
CG2236
CG2264
CG2266
CG2300
CG2301
CG2302
CG2303
CG3102
CG3112
CG3200
CG3209
CG3220
CG3229
OPERA TIONA L (Cont'd)
X OPTX +28 VDC PCME
V IGA Torque Motor Input PCM
V IGA IX Res Output, sine,
inphase PCM
V IGA IX Res Output, cos,
inphase PCM
V IGA Servo Error, inphase PCM
V MGA Torque Motor Input PCM
V MGA IX Resolver Output,
sine inphase PCM
V MGA IX Resolver Output,
cos, inphase PCM
V MGA Servo Error in Phase PCM
V OGA Servo Error in Phase PCM
V OGA Torque Motor Input PCM
V OGA IX Resolver Output,
sine inphase PCM
V OGA IX Resolver Output,
cos, inphase PCM
V OGA Servo Error, in Phase PCM
V IGA CDU IX Res Error,
in phase PCM
V MGA CDU IX Res Error,
in phase PCM
V OGA CDU 16X Res Error, PCM+
in phase
V OGA CDU IX Res Error, PCM
in phase
T PIPA Temp. PCM+
T IRIG Temp. PCM+
C IMU Heater Current PCM+
C IMU Blower Current PCM+
V SXT Trun Motor Drive
in phase PCM
V SXT Shaft Motor Drive,
in phase PCM
V Trun CDU Motor Drive
in phase PCM
V OPTX Direct Trunnion
Contlr, in phase PCM
V Shaft CDU Motor Drive
in phase PCM
V OPTX Direct Shaft Contlr
in phase PCM
10
10
10
10
100
10
10
10
100
1
10
lO
10
100
1
1
10
1
1
1
1
1
10
10
10
10
10
10
8-5
8.2
OPERA TIONA L (Cont'd)
CG4300 T AGC Temp. PCM I0
CG5000 X PIPA FAIL PCME i0
CG5001 X IMU FAIL PCME i0
CG5002 X CDU FAIL PCME i0
CG5003 X Gimbal Lock Warning PCME I0
CG5005 X Error Detect PCME i0
CG5006 X IMU Temp. Light PCME i0
CG5007 X Zero Encoder Light PCME I0
CG5008 X IMU Delay Light PCME i0
CG5020 X AGC Alarm #I (Program) PCME i0
CG5021 X AGCAlarm #2 (AGC Activity) PCME i0
CG5022 X AGC Alarm #3 (T/M) PCME i0
CG5023 X AGC Alarm #4 (PROG CHK
FAIL) PCME I0
CG5024 X AGC Alarm #5 (Scalar FAIL) PCME I0
CG5025 X AGC Alarm #6 (Parity FAIL) PCME i0
CG5026 X AGC Alarm #7 (Counter FAIL) PCME i0
CG5027 X AGC Alarm #8 (Key Release) PCME I0
CG5028 X AGC Alarm #9 (RUPT Lock) PCME I0
CG5029 X AGC Alarm #i0 (TC Trap) PCME i0
CG5030 X Computer Power Fail Light PCME i0
CG6000 P IMU Pressure PCM 1
FLIGHT QUA LIFICA TION
CG2010 V XPIPASG. Output, inphase TR 2000 eps.
CG2030 V Y PIPA SG. Output, inphase TR 2000 cps.
CG2050 V Z PIPA SG. Output, inphase TR 2000 cps.
CG6001 D NAV Base Roll Vibration TR 2000 eps.
CG6002 D NAV Base Pitch Vibration TR 2000 cps.
CG6003 D NAV Base Yaw Vibration TR 2000 cps.
External Data Requirements
G&N requirements for external data fall into three categories:
8.2. 1 Navigation Data via the Uplink
No requirement for this data is made at this time.
8.2.2 Radar Tracking Data for Post Flight Analysis
Tracking data requirements to a degree of accuracy and completeness
which would permit the most comprehensive determination of G&N flight per-
formance, are given in Table 8-1. Subsequent revisions of this plan will
reflect more realistic requirements.
8-6
8.2.3 Radar Tracking Data for Real-Time Monitor of G&N
This requirement is given by Table 8-2, which is derived from the
total indication error expected in the position and velocity data telmetered
to the ground via the AGC DOWNLINK.
8-7
TA BLE 8-1
EXTERNA L TRA CKING DA TA REQUIREM ENTS
TO SUPPORT POST FLIGHT ANA LYSIS OF G&N
Three orthogonal components of position and velocity are required in IMU
coordinates at one second intervals during each powered phase. The re-
quired accuracies are given in this table in local vertical coordinates.
Phase
one sigma
Position Error (ft)
one sigma
Velocity Error (fps)
Alt. Track Range Aft. Track Range
S-IB Boost 200 1900 i00 0.9 7.2 0.4
ist SPS Burn 40 210 30 0. 3 i. 8 0.2
2nd, 3rd, 4th SPS Burns I0 30 i0 0.3 0.6 0.2
Entry 1100 1000 200 4.6 4.9 0.8
8-8
TABLE 8-2
EXTERNAL TRACKINGDATA REQUIREMENTSTO PROVIDEREAL-TIME MONITOROF G&N
Three orthogonalcomponentsof position andvelocity are required in IMUcoordinatesat one secondintervals during eachpoweredphase. The re-quired accuraciesare givenin this table in local vertical coordinates.
onesigmaPosition Error (ft)
one sigmaVelocity Error (fps)
Aft. Track Rang_ Alt. Track Range
S-IB Boost 200 1900 I00 0.9 7.2 0.4
ist SPSBurn 400 3900 300 i. 4 8.0 0.8
2nd, 3rd, 4thSPSBurns 2300 4000 7200 7.3 7.4 1.8
Entry 2900 7300 8800 ii. 6 3.9 2.9
8-9
b
9. G&N Performance Analysis
This section presents brief summaries of the performance of those phases of Ii_.
202 mission that are under G&N control. The data (in Fi;_s. 9-i, 9-2, 0-3, 9-i, ?-7,,
and 9-6) has been derived from point mass studies using the Saturn Boost phas_ _ o_ the
trajectory referenced in Section 5.
The data in the Tables 9-I through 9-8 present performance data derived by
perturbing the nominal mission with the dispersions listed on the following page.
The affects of these dispersions are demonstrated in the tables as follows:
Table 9-1 Time, latitude, longitude, altitude, velocity, flight path angle and
range (central angle from SIVB eut-off point) at the start of the firstSPS burn.
Table 9-2 Same as Table 9-1 at the end of the first SPS burn, plus fuel remain-
ing and burn time.
Table 9-3 Time latitude, longitude, altitude, velocity flight path angle, R, A,and E from Carnarvon at the start of the second SPS burn.
Table 9-4 Same as Table 9-3 at the end of the second SPS burn.
Table 9-5 Same as Table 9-8 at the final cut off.
Table 9-6 Time latitude, longitude, altitude, velocity flight path angle at entry
after fourth burn or fuel depletion.
Table 9-7 Velocity and flight path angle at entry without the two short burns.
Table 9-8 Same as Table 9-6 after the first burn only.
The radar at Carnarvon was taken to be at 24. 867S latitude and liB. 63E longitude
at a radius of 20, 913,669 feet.
The latitude and longitude at entry in Table 9-7 above will be practically the same
as Table 9-6 above.
Fig. 9-6 shows the track during the nominal second SPS burn and the two short
burns. The ignition point and final cut off points of extrem_ cases are also shown. It
should be observed that
a) The maximum westerly dispersion at ignition is about 0.5 ° longitude.
b) The dispersion in track (213036) cannot be rectified by modification of
the second ignition logic.
Any downrange dispersion at SIVB cut-off will move the entire trajectory downrange
by the amount of dispersion.
D
9-1
Mac Run
210066
210067
210068
210069
210070
210071
210072
210073
210074
210075
210076
210077
210078
210890
210891
211683
213036
List of Dispersions
617.
617.
617.
617.
617.
617.
617.
617.
617.
617.
617.
617.
617.
60O
4 see
4 sec
4 sec
4 sec
4 sec
4 sec
4 sec
4 sec
4 sec
4 sec
4 sec,
Dispersions
+ 200']sec inertial velocity
+ 40']sec inertial velocity
-40'/see inertial velocity
+ 3000 ft altitude
- 3000 ft altitude
+ 0.5 ° flight path angle
- 0. 5 ° flight path angle
+ 3 sec Isp
-3 sec Isp
+ 660 Ibs thrust
-660 ibs thrust
4 sec, + 500 ibs weight
4 sec, - 500 Ibs weight
sec, + 30, 000 ft. altitude
-2 ° flight path angle
-3 sec Isp
- 660 ibs thrust
+ 500 Ibs weight
600 sec, negative of above
617.4 see, nominal
617.4 sec, +i ° azimuth
-i. 63 southern latitude
NOTE: i. Nominal I was increased by 3 seconds over the Novembersp
figure.
2o AI] cases have an ii second coast between SIVB time indi-
cated and SPS 1 ignition.
3. Altitude is in feet
Velocity is in ft/sec
All ang]es are in de_rees
Time is in seconds" _ot_l time is measured from lift-off
Range [_1om Carnarvon is slant range in n.m.
Radius of earth used in 20, 925,738 feet.
The coast time used is 3041 seconds
Precision integration was used during coast
9-2
I
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'_ co _I4 c,o o_ (:_ ',_0 00 0 0
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_ 1.0 _ u'3 LO LO L('b
O,I ,--_ ,.--,
LO LO LO
CO _ 0') 0 0 0 0 0
_0 _ _ _ CO _ _ ",/3
6 c_ (5 6 c_ _5 c_ c_
t_- L'.- 0 0
C.O c..o _0
• ° ° °0 ¢) ¢_ 0
C0
,-.lo,1 ¢',,Io,.I o,I _ o,1
c',l _ 00 D--
• ° o ,
,-l
0 0 0 0 0 0 0 00,1 ¢'_ o,] O,1 0_ o,1 0,1 o,1
0,] 0_ 0,1 ¢_ _ 0,] o,1
o3 CO 0 COI/3 LO 0,1 tO
• ° ° °
0,1 0,1 0,1 0,1
0
0,1 0,1 0,1 0,] 0,1 _ 0,1 0,1 ,_
• . ° o
¢.0 ¢.0 _0 ¢.0
C..O _ CO _ ['-.. L"- L'-'- L"- 'L"W" Cb (_) CO 0'_0 C' 0 0 0 0 ¢_, 0 0 C) CO CO _C) 0¢_' ¢) 0 ¢) C, 0 ¢_' 0 +" (_' ¢) C) _ O'3
9-9
!
0
0
uJ
°_
0t_
[
ct_ _ oO _ _ _ CO _ L_- CO _ O_ 0"_ CO CO _ 0
0 0 0 0 0 0 0 0 0 0 0 0 0 _ 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 _ _ _ 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _
9 -10
0
I
0
c_
_ O_ _ CXI C_ CXI C_ 0,1 CXl 0,1 O_ _ 0,1 0,1 _'_ CXl
I I I I I I I I I I l I I I I I I
I I I I I I I I I I I I I I I
_0
0
0
_ _ _ 0 _ _ _ _ _ _ _ _ _ _ _ 0
0 0 0 0 0 0 0 0 0 0 0 0 0 oo oo co 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 _ co
9-11
I
,.Q
cO _ _ c_- 0 oo q_ ,--4 Go _1_ _ b.- _ _ b '= _ _'_o'_ _ 0 _ C-- _ _ _ _ _ _ L_- L_- _ _ _ CO
_ ¢0 _._ _ _ _ _ _ L_- CO _ _ _ _ CO
c_ _ C_- C-.= _ _ _ L_- L_- _ _ _0 _ _0 _ _
I I I I I I I I I I I I I I I I I
L_- _ b- L_- _ _ L_= _'- L_" _ _ I_- _ i.(3 rE) _ _.
O _'_ _ 0 _ _ _ _ L_" _ _ _ 0_ _ _q_ O3
3_0 o_ _ _ _0 _o L_ ,_ ¢_I 0 _0 L_- ¢_ 00 0_ L_ O0
CO L_- _ "_ b" _ 0 _ ¢_ O_ _ b- LO ¢_ "_ _0
0 0 ¢_ _ 0 0 _ O 0
00 O_I
_0 L'_ _0 _ 0 _'_ C_I ¢0 _ _ _0 E_- O0 0 ,'_ _0_0 _0 _0 ¢.0 L_" L_" _ L" E" _ _ L_" L"- O_ ¢_ O0 O_
0 O 0 O 0 0 _ 0 ¢_ _ 0 _ O 0 _ _ ¢0
9-12
0
0
r,.)t_
LO 0 _ CO O_ _ C_ _ _._ ,._ O_ _ _ CO
0 0"_ _ O_ 0 _ QO CO L_" _ 0'_ _ CO
CO 0 _ CO _ _ 0 _ C_ CO 0'_ CO _
I I I I I I I I I I I I I I
oO _ C'_ L_ ,--_ _.- _ _ _ CO O0 _ CO0 _ _ CO _ _ _ _ _ _ ,-_ _ 0 _"
CO CO CO CO 0'_ _ CO CO O0 _ CO _ CO
L_- _ _ _- 12"- _ _ L_. 12"- _ _ _ _ L_-
_ _ _ _ _ '_ CO _ LO _ _ L_- '_
o=
VVVVVTVT VVV VVV
O0 _- _ "_ L_. _ _ ,-_ _0 O_ _ _ h_ _0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
o o0 _- _- _- oo ._ _o _ _ o _ _- _-
_ _ _ _ _ _ _ _ L_- L_- [_- 12.- CO,0 0 0 0 0 0 0 0 0 0 0 0 0 _._;I
0 0 0 0 0 0 0 0 0 0 0 0 0 ,--_
9 -13
O
o_
O'_ O O O O O _ O O O O ¢Xl O'_ L_ 00 O O
I I I I I i I l I I I I I I I I I
>CO L_ ¢N1 O L"- _ L_ _ O'_ _ Ca CO CO O _ L_
O O_ O'_ 00 CO O'_ O_ O'_ 00 C_ O'_ O_ O _ _ COb- ¢.,.C; _ e,.C. _ ¢..O e..C; ¢_ ¢4D _ e_ e,O t"- _ ¢_ _ ¢D
CO CO CO CO CO CO CO CO O0 CO CO CO O0 _ b" CO CO
C',1 ¢"xl ¢N1 _ C_1 C',1 C'd C_1 ¢",1 ¢X1 C',1 _ _ C_1 _ C'd ¢N1
00 O_ C_ _ _ _ _0 _ ¢._ _ _ O O'_ _ O O0
"_ _ _ _ L_ _ _ _ _ L_ L_ L_ L_ _ C'_ L_
I I I I I I I I I I I I I I I I I
I
o
'-o
o=
> O O _ co O_ '_ O O'_ O'_ _ ¢'_ _-_ _'_ _ co Ot _. b- _ ¢_ ¢.O ¢._ _ _ _ C.C) cad ¢._ _ _ _ ¢._
CO CO CO CO oO CO CO CO CO CO O0 o0 CO _._ L-_ cO 00
__O_ ______O_OO_OO_
b_ t'-- C_ O O_ _ _ _ O C_ _ O'_ O CO oo _'_ O O
o "_ 4 _ ,_ ,_ ,# _ ,_ _ ,_ _ _ ,_ _ ,_ _ _
"_ _ _ O _ _ _ _ O _ O COT_ C-,1 C_
I I I I I I I I I I I I I I I I I
C',3 CN1 CN1 CN1 O ¢'_ _ C-,.1 _ _ ON1 _ CO erj _
O O O O O O O O O O O O O CO oo _ O
O O O O O O O O O O O O O O O _ ¢'_
9-14
Table 9-7
Entry Conditions(400,000ft) After SecondBurn(noshort burns)
MacRun V 7
210O66210067210068210069210070210071210072210073210074210075210076210077210078211683213036
28497 -3. 57-3. 57-3. 57-3. 57-3. 57-3. 57-3. 56-3. 57-3. 57
-3. 57
-3. 57
-3. 57
-3.56
-3. 57
-3. 57
28518
28514
28502
28501
28518
28515
28516
28516
28508
28520
28506
28526
28501
28514
9-15
cO m 01 _ 0
O_ 0
_ O_
N
I I I I I I I I I ! I I I I I
> 0",1 C_ 0,1 0,,1 0,.1 _ 04 _ 0,1 0.,1 C',,1 _ Ol _'1
C_ _'_ @,1 C'4 @,1 _ C'_ C_1 _ 0'.1 0,1 _ 0',1
0"_ L"- _t _ C'_ CO CO CO L_ _,0 CO I_ _ 0"_ LO 0
o ,.6 _6 ;H _6 _ _ _ _ u3 _ _ _ _6 _ _
I I I I I I I I I I I I I I I
_.D _ _ C.O _ _ _ _ _ _ _ _ _ CO CO tO O O O O O O _ O O O O O _,O OiO O O O O O O O O O O O O _ c'_
O
O
O
O
OOO
c_O
.o
O
O)
9-16
R-477
DISTRIBUTION LIST
Internal
R. Alonso
R. Arrufo
R. Baker
R. Battin (5)
P. Bowditch
D. Bowler
R. Boyd
E. Copps
R. Crisp
J. Dahlen (5)
E. Duggan
K. Dunipace (MIT/AMR)
J. B. Feldman
S. Felix (MIT/S&ID)
J. Flanders
J. Fleming
G. Fujimoto
F. Grant
Eldon Hall
Edward Hall
E. Hickey
D. Hoag
A. Hopkins
F. Houston
L. B. Johnson
M. Johnston
A. Kosmala (3)
A. Koso
M. Kramer
A. Laats
L. Larson
J. Lawrence (MIT/GAEC)
T. J. Lawton (2)
T. M:. Lawton (MIT/MSC)
D. Lickly
H. Little
G. Mayo
J. McNeil
H. McOuat
R. Morth
James Miller (2}
John Miller
J. Nevins
J. Nugent
E. Olsson
J. Rhode
M. Richter
M. Sanders
M. Sapuppo
R. Scholten
E. Schwarm
J. Shillingford (3)
W. Shotwell (MIT/ACSP)
J. Sitomer
B. Sokappa
M. Sullivan
J. Suomala
R. Therrien
W. Toth
M. Trageser
R. Weatherbee
L. Wilk
R. Woodbury
W. Wrigley
Apollo Library (2)
MIT/IL Library (6)
External
(ref PPl-64; April 8, 1964)P. Ebersole (NASA/MSC)
W. Rhine (NASA/RASPO)
L. Holdridge (NAA SAID/MIT)T. Heueremann (GAEC/MIT)
AC Spark PlugKollsman
RaytheonMajor W. Delaney (AFSC/MIT)
NAA RASPO: National Aeronautics and Space AdministrationResident Apollo Spacecraft Program OfficeNorth American Aviation, Inc.Space and Information Systems Division12214 Lakewood BoulevardDowney, California
FO: National Aeronautics and Space Administration,Florida Operations, Box MSCocoa Beach, Florida 32931Attn: Mr. B. P. Brown
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AMES:
LEWIS:
FRC:
LRC :
National Aeronautics and Space AdministrationAmes Research CenterMoffett Field, CaliforniaAttn: Library
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Attn: Manned Flight Support Office Code 512
MSC
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MSFC:
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GAEC :
NAA :
GAEC RASPO:
ACSP RASPO:
WSMR:
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National Aeronautics and Space Administration
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Mr. L. Hogan (10)
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(20)
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