apollo experience report development of guidance targeting techniques for the command module and...

8/8/2019 Apollo Experience Report Development of Guidance Targeting Techniques for the Command Module and Launch Ve

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N A S A T E C H N I C A L N O T E

APOLLO EXPERIENCE REPORT -DEVELOPMENT OF G U ID A N C E T A R G E T IN GTECHNIQUES FOR THE COMMAND MODULEAND LAUNCH VEHICLE

Houston, Texas 77058 N A T I O N A L A E R O N A U T IC S A N D S PA CE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. J U N E 1972


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- -

TECH LIBRARY KAFB, NM

- . . .1 1. Report No. -_ I 2. Government Accession No.I- -NASA TN D-6848 . . I4. Title and SubtitleAPOLLOEXPEFUENCEREPORT DEVELOPMENT OF GUIDANCE TARGETING TECHNIQUES FOR THE COMMAND MODULE AND LAUNCH VEHICLE

- - _7. Author(s)Je ro me D. Yencharis, Robert F. Wiley, Robert S. Davis,Quentin A. Holmes, and Kenneth T. Zeiler, MSC- _ _9. Perform ing Organizatio n Name and Address

Manned Spacecraft CenterHouston, Texas 77058

Washington, D. C. 20546

I ...I 3. Recipient's Catalog No .5. Re p o r t DateJune 19726. Performing O rganization Code

8. Performing Organization Report No.MSC S-308

10 . Work Unit No.924-22-20-00- 7211. Contract or Grant No.i - .-13. Type of Report and Period Covered

Technical Note~ ~ ~14. Sponsoring Agency Code

. . - I ..15. Supplementary NotesThe MSC Dire ctor waived the use of 'the Int ernat ion al Syst em of Units (SI)forthis Apollo Experience Report, because, in hi s judgment, us e of SI Units would impa ir the usefulnest

- - _ _ _ ~ ~ - _ .~The development of the guidance target ing techniques f o r the Apollo command module and launchvehicle is disc ussed for four types of maneuvers: (1)translunar injection, (2 ) translunar mid-course, (3 ) lunar orbit insertion, and (4) retur n to earth. The development of real-time targeting programs f or these maneuvers and the targeting procedures represented are discussed. Thisdocument is intended to convey historicall y the development of t he targe ting techniques req uir edto meet the defined tar get obje ctives and to illus tra te the solutions to problems encountered during that development.

-. - .. . . .17. Key Words (Suggested by Authoris)) 18. Distribution Statement* Apollo Maneuver Targeting Apollo SoftwareGuidance Targeting ' Burn Maneuvers'Vector Offset Techniques'Real-Time Computer ProgramIterative Procedures

~ -~1 19. Security Classif. (o f this report) 20. Security Classif. (of this page) 21 . No . of Pages 22. Price~ None I None ~ 37 $3.00L- . . . .

*For rk by th.NmtioculT.chniwl Infornutions.rViw,Spriwiold, Virginia 22161


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Section RETURN TO EARTH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Current Program Configuration . . . . . . . . . . . . . . . . . . . . . . . . . Early Program Development . . . . . . . . . . . . . . . . . . . . . . . . . . Initial Formulation of Abort Procedures . . . . . . . . . . . . . . . . . . . . Basic Program Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . The RTE Program in the Apollo 8 Mission . . . . . . . . . . . . . . . . . . . The RTE Program after the Apollo 8 Mission . . . . . . . . . . . . . . . . . Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ONBOARD SOFTWARE CONSIDERATIONS . . . . . . . . . . . . . . . . . . . . Onboard Midcourse Targeting . . . . . . . . . . . . . . . . . . . . . . . . . . Onboard Return-to-Earth Targeting . . . . . . . . . . . . . . . . . . . . . .

CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Page242425262729292929293031

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ACRONYMS ASTATDLPATPBAPCDHCMCCSMEFCUAFCUAIGMLO1LOPCMITMPTMSCMSFCNFRPTPRTCCRTERTEDs-IVS-IVBTCUA

Abort-Scan TableApollo Tra jecto ry Decision Logic Prototypealterna te tar get poiqtbes t adaptive pathconstant delta heightcommand module compute rcommand and service moduleextreme fuel-critical, unspecified ar e afuel-critical, unspecified areaIter ative Guidance Mode lunar-orbit insertion lunar-o rbit plane change Massachusetts Institute of Technology Maneuver Planning Table Manned Spacecraft Center Marshall Space Flight Center nonfree re turn primary target point real-time computer complex return to ea rth Return-to-Earth Digital Saturn IV Saturn IVB time-critical, unspecified area

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I I 1111111111111111111

TEI transearth injectionTEMC transearth midcourseTLI translunar injectionTLMC translunar midcourseTO Trade-off

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APOLLO EXPERIENCE REPORTDEVELOPMENT OF GU I DANCE TARGETING TECHNIQUES

FOR THE COM MA ND MODULE AND L AUN CH VEHICLEB y J e r o m e D . Ye n c h a r i s , Ro b e r t F. W i l e y , Ro b e r t S. Davis , Q u e n t i n A . H o lm e s , a n d K e n n e t h T. Z e i l e r M a n n e d S p a c ec ra ft C e n t e r

S U M M A R YTo develop guidance targeting techniques for the Apollo command module andlaunch vehicle, it w a s necessary to cons ider the onboard-guidance capability; the mission objectives, mission rules , and hardware constraints; the vehicle performancecapabilities, traje ctory ch ara cte ris tic s, and crew time line; the current optimizationand targeting techniques; the effect each maneuver would have upon subsequent maneuve rs ; and the vulnerability of each maneuver to varying initial conditions. However, inaccordance with the Apollo Pro gr am time line, these concepts and techniques werebeing developed in parallel with the development of targeting techniques. Consequently,the targeting development had to proceed in distinct phases, and each phase w a s dependent upon advances made in the previous phase.The development of the targeting procedures and associat ed real-tim e computerprograms for four types of maneuvers is discussed. Each targeting program, with theexception of the Translunar- Injection Targeting-Update P rogram, has been used successfully to targ et maneuvers for each Apollo lunar mission. Although capable of fulfilling the program objectives, the Translunar-Injection Targeting-Update Progr am hasnot been needed during any Apollo lunar mission through 1969.

I N T R O D U C T I O NT a r g e t i n g P r o c e s s

A series of 22 joint meet ings among NASA Manned Spacecraft Center (MSC) andprim e contractor personnel w a s held in 1965 and 1966 to investigate the operationaltargeting procedures fo r the Apollo lunar missions. During these meetings, the bas icconcepts and framework w er e formed for the development of guidance targetingtechniques.


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The following definitions, which were derived during these meetings, are givento clarify the terminology used in this report.1. Targeting is the pr oc ess followed to obtain guidance pa ra me ter s fo r specificmaneuvers throughout a mission.2. Target objectives are the exact requirements for a particu lar mission phase,which may be a single maneuver (e.g., tra nslu nar injection (TLI)) o r a series of maneuvers (e.g. , tra nslu nar midcou rse (TLMC) maneuvers).3. Target p ar ame ter s approximate the tar get objectives within an acceptabledegree of accuracy.4. Guidance pa ra me ter s rep resent the tar get p ara mete rs in the guidancemechanization.

A s an example, th is terminology is considered in context with the TLI targetingprocedure.1. Targ et objective- A translunar trajecto ry that has a specified altitude andmoon-referenced latitude at the c losest approach to the moon2. Target paramet ers-Quantities that define the hypersurface, an analyt icformulation that represents all possible translu nar tra ject ori es which satisfy the targ etobjectives3. Guidance parameters- The elements and orientation of the de sir ed ellipticaltrajectory at TLI cut-offThe adequacy of a targeting procedure can be expres sed in te rm s of a penaltyfunction, that is, the penalty imposed on subsequent mission pha ses if the given targe ting procedure is followed and the given target par ame te rs and guidance par ame ters a r eused. For TLI, th is penalty function could be the midcourse velocity change AV required to retur n the traj ecto ry to the given targe t objectives fo r TLI.

Development of Targeting Techniques for the Apollo MissionsThe development of the targeting procedures is discuss ed fo r four types of maneuve rs perf ormed during the Apollo lunar missions: (1)TLI, (2) TLMC maneuvers,(3) lunar- orbit in sert ion (LOI), and (4) re tu rn to ea rt h (RTE), which includes not only

abo rts fr om the nominal mission but also the nominal tr an sea rth injection (TEI) maneuver and the tr anse ar th midcourse (TEMC) maneuvers. The development of targetingprocedu res fo r the TLMC, LOI, and RTE maneuvers w a s the responsib ility of MSCpersonnel. Because of the nature of the Apollo Program, the TLI targeting procedurew a s developed jointly by MSC and NASA Marsha ll Space Flight Center (MSFC) pe rson nel. Development of the ta rget par am ete rs and of the associa ted guidance equationswas accomplished at MSFC. The real-t ime TLI targeti ng procedure and computer pro grams for the TLI targeting update were developed at MSC. Of these TLI developments,the real-time procedure and targeting-update computer programs are discussed in thisreport.

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For each of the four maneuvers considered, a computer program was developedfor use in real time to determine the guidance parameters for the maneuver. The histor ica l development of these programs and of the rela ted target ing procedures is discussed. To develop each program, it w a s necessary to consider the onboard-guidancecapability, the mission objectives, the mission rules, the hardware constraints, thevehicle performance capabilities, the trajectory char act eri sti cs (principally geometryand energy), and the crew time line. Furth er development considerations wer e thecurren t optimization and targe ting techniques (state-of-the-art knowledge), the effecteach maneuver would have on subsequent maneuvers, and the vulnerabi lity of each maneuver to varying initial conditions. Because of the schedule imposed on the ApolloPro gram, the efforts in many of these areas were conducted simultaneously with thetarge ting development effort. Therefore , the pr og re ss of the targeting- technique development w a s directly related (1)to the developments occurring in other phases of theApollo Prog ram (e. g. , the definition of guidance capability, hardware development,etc. ), (2) to the development of analytical tools, and (3 ) to the definition of t arget objectives for each maneuver.TRANSL UNAR- INJECTION TARGETING UPDATE

The TLI Targeting-Update Program w a s completed during the summ er of 1968and w a s first put into a real-time system fo r the Apollo 1 2 mission. The circumstancesthat would lead to the decision to update the targeting of the launch vehicle for the TLImaneuver had remained in doubt up to that time.The development of the TLI Pro gr am was concurrent with the definition of guidance equations; the development of the mission profile; and the development of hardware, software, and the associated constraints. The TLI Progr am also dependedheavily upon the Generalized Forward Itera tor. Some inefficiencies occurred in T UProgram development; however, like many other developments in the Apollo Program,the TLI Program began with inexperienced personnel who faced a restrictive time lineand the realization that this effort w a s also highly interdependent on other developmentsin the Apollo Program.

Pre- 1967 Deve IopmentInte rface between guidance equation development and targeting techniques. - Fromthe outset of the Apollo P rog ra m until 1965, the launch vehicle guidance and target ingfunctions were not well defined. However, within a few years after the Apollo Programbegan, som e detailed pre limina ry logic and equations fo r the command module computer (CMC) had been developed at the Massachusetts Inst itu te of Technology (MIT).Included among the progr ams available fo r the CMC was a set of guidance equations fo r TLI backup; that is, this giidance was to be used if the launch vehicle couldnot perfo rm the steer ing fo r the TLI burn. Cross-product steering, which was the typeof guidance for the CMC, used as target parameters a desired semimajor axis a andth re e position components of a target vector ?T.

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I I1 I1 Ill1lll11llIIIII

When the CMC equations became available, a significant effort w a s directedtoward understanding, analyzing, and evaluating the equations and developing ground-based logic to support the targeting problem. Two approaches were taken to developthe targeting logic.1. To iterate on the components of 3T and on a to achieve an optimum TLImaneuver that would place the spacecraft on a fre e-r etur n trajectory that had nominalperilune conditions2. To iterate on ignition time and to vary the outbound tr ajec tory in an attemptto fit the problem to the guidance capability

For the second approach, the TLI AV w a s not optimized within the cycle, but the overall effect of varying the set of the par am eter s on injection AV and midcourse AV wasconsidered.Studies were conducted fo r nominal and dispersed case s. A significant emphasis

w a s placed on a study of disperse d cases . However, the dispers ions used (for eart h-orbit insertion) were fo r an open-loop Saturn IV (S-IV) guidance scheme and we regr eat er than the dispersion cha ract eri stic s of the closed-loop scheme used on the S-IVBfor the lunar flights. The re su lt s of the study indicated a need for targeting update.However, in late 1965, dispersion c har acte rist ics became available for the S-IVB, andthe study w a s per formed again. This time, no targeting update w a s required in the 30case.The main drawback of these initial studies was that only coplanar translunar injections we re considered. Insufficient information w a s available about the targetingphilosophy and the launch window design based on that philosophy.Launch-vehicle guidance for TLI. - In the summer of 1965, an effort w a s begun toinvestigate the TLI guidance and targeting routines on board the launch vehicle. The following items were considered.1. What would be involved in the TLI targeting update?2. What were allowable 3a deviations at earth-o rbit insertion before the updatehad to be made?3 . Did any targeting-update capability exist in the launch vehicle; and, if so, what

were the details?In late 1965, an initial set of guidance equations w a s obtained. Within seve ra lmonths, the equations were programed into a computer simulation at MSC, The targeting routine for TLI (the hyper surface eventually developed at MSFC) was preliminaryand w a s not completely understood by MSC personnel for some time.

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Initial development of the prototype rea l-time program. - Meanwhile, a prototypereal -tim e p rog ram wa s under development by cont ractor personnel who used the analysis and development at MSC of the in-house ver sion of the program. The TLI updateproblem in this prototype progr am was tr eated as an extension of the trans lunar mid-cou rse problem. Like the midcourse, TLI w a s investigated by using a mission designprogram, a ver sion of the Generalized Forward Iterato r. The complicated logic fo rTLI update had two options: (1) to design TLI and accomplish a full-mission optimization o r (2) to design TLI to inje ct the spacecr aft into a free-r eturn trajectory that hadnominal perilune conditions. The logic had to have the capability to cons ide r a changeof the designated lunar landing site in rea l time. Finite burns and the requir ed analyticcalibration for the finite bur ns w er e taken into account. By June 1966, the prototypeprogram was composed of the following nece ssa ry modules.

1. The integration package2. The TLI guidance equations (launch vehicle and CMC)3. The LO1 guidance equations4. The translunar midcourse correction package5. The first-guess logic6. The forward iter ator7. The TLI burn calibration8. The Jacobi calibration9. The LO1 burn calibration

10. The CSM lunar-orb it plane change (LOPC) bur n calibra tion11. The TEI burn calibrati onThe fir st-g uess package w a s designed only to place the tr aje ctory of the spacecraf t in moon re fe ren ce and on the co rr ec t side of the moon. The launch vehicle TLIguidance equations, the Ite ra tive Guidance Mode (IGM), had been programed, as hadall the burn calibrations. However, the TLI burn calib ration had the capability fo rnominal cases only, and the other calibrations w e r e to be nullified when CMC cleanupbegan and the spacecr aft guidance laws changed fo r several of the burns.Deletion of spacec ra ft TLI guidance. - Among the first changes that were made tothe CMC guidance equations 6 ea rly 1966 was the deletion of the TLI (~ ! ~ , a )teering.

A guidance inter fac e still exis ted between the spacecra ft and the launch vehicle; and, bymid-1966, an extensive eff ort was being conducted by MIT personnel to implement theTLI equations (IGM) into the CMC. Late r i n 1966, fur the r deletions we re made on CMCprogra ms, and the IGM equations were among the first to be eliminated.In summary, by the end of 1966 no change had occurr ed in the T U pdate problemin the r eal-tim e prototype program. Full-mission optimization in e arth parking or bit

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was being considered. Because of a complicated setup of the iter ato r, many logica lpaths had to be followed in the progr am. The problem was sensiti ve and was heavilydependent on a combination of good first gue sses and proper setup of the ite rator.Much of the work that had been completed was inapplicable to the problem. Time hadbeen spent at MIT and at MSC in the development and evaluation of the TLI e,, a) back-up guidance equations, which we re now usele ss. An extensive effort had been put fo rward at MIT to enter the IGM equations into the CMC, and digital and analog studie swe re well underway when the decision was made to t ake the IGM out of the CMC.

P r o g r a m D e v e l o p m e n t D u r i n g L ate 19 66 a n d 1 9 67In 1966 and 1967, extens ive development of the TLI targeting technique and of thereal- time computer complex (RTCC) TLI Targeting-Update Pr og ra m was accomplished.In late 1966, when no CMC pr og ra m was availab le to back up TLI (although Lambert'starget ing in conjunction with c ross-p roduct stee ring was being evaluated for t his purpose at the time), in te re st increa sed concerning the capability to update the TLI tar ge tson board the launch vehicle. The initial RTCC requir ements for the TLI planning p roc

essor were to be due in the summer of 1967; the refore , it w as necessa ry to determineas quickly as possible what capabiliti es it should contain. In April 1967, the onboardtargeting -update capability w a s defined. Two target ing-update options were defined:(1) the hypersurface quantities were updated o r (2 ) only the time of r es ta rt preparationand the des ir ed cutoff ellipse wer e specified. During MSC-MSFC discussions, it w a sdecided that the first capability w a s not required; therefore, the decision w a s made tosuppor t only the second targeting-update option,Initial RTCC requi rement s. - In the sum me r of 1967, the first RTCC requirem ents

wer e submitted to the cont rac to r fo r the TLI planning process or. Although the significant decision not to allow a change of the desi red lunar landing site in real time simplified the program , it remained somewhat cumbersome. A decision also was made toput into the RTCC TLI Targeting-Update P ro gr am the capability to update the CMC withLambert's targeting for T U .In the ini tial definition of the TLI Targeting-Update Prog ram , fou r options wereavailable fo r rea l-ti me planning consideration.1. Solve onboard targeting (hypersurface).2. Optimize the full mission i n ear th parking orbit.3. Maximize apogee altitude for the amount of S-IVB AV available.4. Execute TLI to place the spacecraf t in a traj ecto ry with a specified apogeealtitude.Option 1was indicative of what would happen if no targeting update w a s made.Option 2 optimized the ser vi ce module fuel re se rv es for the full mission. Option 3 w a smade available fo r a nonnominal si tua tion in which the S-IVB did not have adequate A Vto pe rform the nominal TLI maneuver. Energy was maximized (in t er ms of apogeealtitude), and a tra ns fe r maneuver possibly could be made from that tra ject ory to continue the nominal mission or t o execute an altern ate lunar mission. Option 4 wa s made

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available fo r alternate earth -orb it missions and, more specifically, for the nominalearth-or bit lunar-landing- simulation mission (E-type miss ion) that w a s planned at thetime.A l l four options could be viewed fo r e ithe r a first o r a second TLI opportunity.For each option, one pa ss to generate the spacecraft targeting for TLI (Lambert's targeting) wa s made through the IGM equat ions after the last iteration. A s a measure of

merit, a midcourse correctio n w as computed fo r options 1 and 2; the midcourse wastargeted back to the nominal nodal conditions.The first set of requ ire men ts was rathe r complex. The IGM guidance equationshad to be added to the prog ram. The full-mission-optimization logic was complex andrequ ired extensive supportive analys is that would include ana lysis of the calibration-burn models. In 1967, the onboard (CMC) guidance equations we re being changed constantly, because the requ irem ents for onboard computer space w e r e somewhat gr ea te rthan the space available; thus, constant updates of the calibration-burn models wer erequired . The one calibrat ion on which work pro gressed steadily and by which goodresu lts were produced w a s tha t fo r an S-IVB-guided TLI. The major pa rt of the workconnected with th is calibration was completed in 1967.Significant simpli fica tion in RTCC requ irements . - The results of a study cond u c t e d m t a 9 m . i n d i c i c e d that the full -mission optimization was not necessa ry tothe TLI planning program. Thus, the second option in the progr am could be simplified .The study showed that nothing was saved by optimizing the miss ion while in ea rth orbitand that, by targe ting to the nominal perilune alt itude and latitude and fo r free return,no AV penalty would be inc urr ed. A decision als o w a s made to drop the TLI guidanceprogram fr om the spacecraft computer.These developments res ul ted in updated requ irem ents f or the TLI planning program . Full-mission optimization w a s eliminated as option 2; the new procedure w a sto ta rget TLI to the nominal perilune conditions (altitude and latitude) and fo r free re

turn. The procedure for generating spacecraft tar get s (Lambert 's targeting)w a s removed from the program.In summary, the program w a s at a relatively sound level in the winter of 1967and 1968. Although the first set of programing re qui reme nts had been complicated,simplification of the second se t had been made possible by the deletion of the full-mission optimization. The only inefficiency that occurr ed during this period resul tedfr om changes to the guidance requirement s in the CMC. However, at the end of thisperiod, it appeared that onboard and ground-based logic w a s becoming stabilized .

Development of Current ProgramsFurt her simplifications of the r eal-time program. - A t the beginning of 1968, eventhough the TLI update problem was relatively simple, fur the r simplifications we remade. The IGM guidance equations we re removed fr om the program. The retention ofthes e equations was no longer neces sary because of the deletion of the spac ecraf t TLIprogram.

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Option 2 continued to be the cause of most of the problems. The fir st- guess package that had been developed fo r option 2 was empi rica l, and physical conditions couldexist in which the f irs t- guess logic would provide inaccura te first guesses to the iterator. The emp iric al simulation of the TLI burn used in all four options w as hamperedbecause the simulation was reli able only for t he variat ions that had been considered fo rthe para mete rs which it generated; the simulation did not have the capacity for verylar ge plane changes that could occur in the iteration proce ss. Eventually, workaroundprocedures were developed fo r all known possible sour ce s of e rr or ; and, in the summ erof 1968, a revised set of pro gra m requirem ents was sent to the contractor.

Impact of the Apollo 8 mis sion on pr og ra m development. - In the f a l l of 1968, objectives for the Apollo-8 mission were announced. Because the RTCC would have tosupport a lunar mission within 4 months, it w a s decided to make the ground-based sys tem in the RTCC as simple as possible and yet give it the capability to support the m ission satisfacto rily. Accordingly, the TLI Targeting-Update Pr og ram w a s not added tothe system.From the f a l l of 1968 to the' su mm er of 1969, the TLI Targeting-Update Pro gramwas dormant. The progra m w as not a par t of the RTCC sys tem fo r the Apollo 8, 10,

and 11 mis sions. During the winter of 1968, a decision was made to eliminate the TLITargeting-Update Program . In the sum mer of 1969, t hi s decisionw a s reversed, andthe progr am was put into the RTCC sys tem fo r the Apollo 1 2 mission.Pro gr am on the RTCC system f or the Apollo 12 mission. - In mid-1968, se ve ra ldiscussions were held with MSFC-personnel regarding the process or. Personnel atMSC assumed that MSFC personnel would ve rify the RTCC capability to update thelaunch vehicle and to per for m a sati sfac tory TLI, based on the targeting update. Per sonnel at MSFC reques ted that defin ite guidelines be established in rega rd to when thisupdate capability would be used. In subsequent dis cus sions between personnel of thetwo centers, a conflict existed about establishing these guidelines; therefore, the verification effort w a s not begun.Meanwhile, an outline of the requirements had been made at MSC for the targeting-update capability. It w a s general ly agr eed among MSC personne l that re targeting w a srequire d to ensur e efficiency and to provide the br oade st capability. The circumstancesthat were conside red by MSC to wa rr an t considerat ion of a real -tim e targeting updatewere as follows.1. Provision for a real- tim e targeting-update capability in the presenc e of launchvehicle malfunctions or launch vehicle onboard-programing logic (or both) that wouldpermi t the achievement of e ar th or bi t but with insufficient S-IVB propellant to achievenominal TU-guided cut-off2. Provision fo r a rea l-time targeting capability in the presence of launch vehicle malfunctions or launch vehicle onboard programing logic (o r both) that would per mit the achievement of an e ar th parking orbit which would f a l l outside the capabil ity ofonboard targeting to compute a correct target or any target at all

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3. Provision for a rapid (1 to 2 days) prelaunch targeting capability to accommodate last-minute changes to the mission o r to the launch dates and to accommodatelaunch windows in excess of 3 or 4 days4. Provision f or the operational capability to accommodate real -tim e launch vehicle or spacecraft problems that could necessita te an injection attempt on the thir d

opportunity5. Provision for general operational real-time capability to accommodate anyunknown o r undefined launch vehicle or spac ecra ft problem that would prohibit the us eof the normally computed launch vehicle TLI targe tThe progr am f or the Apollo 1 2 mission had been changed little since the sum merof 1968. A targeting-update command load w a s generated during the Systems Integration Test and sent to the S-IVB. A verification was received that the command loadw a s accepted and ignition would be commanded at the corr ect time. The processor w a savailable in real time fo r the Apollo 1 2 mission but w a s never cal led up, because thepredicted TLI maneuver seemed reasonable.Development of improved first-guess logic. - Because of the high perilune altitudes achieved when the hybrid trajectory profile was used, the first -gu ess package inoption 2 yielded poor first guesses. Although this package w a s improved somewhat forthe Apollo 12 mission, it w a s decided to develop a new analytic first-guess packagethat would be relatively insensitive to the trajec tory prof ile flown. A task w a s assignedto one of the cont rac tor s fo r the development of the logic under the superv ision of MSCpersonnel.However, during the init ial planning for the Apollo 13 mission, a decision w a smade to us e a constant time of ar ri va l at the moon as one of the tar get objectives fo rTLI. Because of this decision, the prob lems with the empirical firs t-guess packagedisappeared. If thi s philosophy is maintained fo r the remainder of the Apollo missions,it is probable that the empir ical firs t-gu ess package will work wel l .In sum mar y, because of the time and eff or t that would be involved to incorporatethe version from the contracto r's task into the RTCC system, it w a s decided to keep theexisflng TLI program in the RTCC and not to implement the contractor-developed logicfor either the Apollo 14 o r the Apollo 15 mission. In fact, i f the same philosophy ofconstant time of ar ri va l is used for the remainder of the Apollo Spacecraft Pro gram,the logic developed by the contractor personnel will probably not be needed for re al -time use.

T R A N S L U N A R MI D C O U R S EEarly in the Apollo Progr am, lunar traje ctor ies were found to be extremely sensitive to dispersions at TLI. Because of this sensitivity, it w a s improbable, from anoperational viewpoint, that TLI would be per formed accurately enough to achieve a trajectory which would permit a des irable LO1 without the need to execute a TLMC maneuver. The RTCC midcourse- correction proc essor w as designed to determine flight

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maneuver s during translunar coast. Although an estimate of the probable deviations(30) in TLI was derived from stati stical studies, the RTCC proce sso r had to be capableof computing an acceptable traje ctory and targ et pa ra me te rs fr om any possible cut-offvector at TLI.

I n i t i a l R e q u ir e m e nt sIt w a s real ized that the TLMC maneuver would affect the time line of the enti remission and that complete optimization would entail recomputation of all major maneuve r s to determine the best adaptive path (BAP) modes. If a sever e dispersion at TLIprecluded a nominal luna r mission, the midcourse pr oc es so r would be used to computealternate mission plans with better fuel re se rv es and to compute precision fre e-r etu rntraj ecto ries (flyby modes) for us e i f a lunar-or bit mission was no longer desirable.Optimization of the midcourse maneuver w a s of primary importance becausespacecraft A V budgets were limited. Speed of computation was essential because themidcourse A V usually increased with delay time, and the evaluation of several alter

native maneuvers might be required. Patched conic traj ecto ries were used becausemany tra jec tor ies had to be computed to determine an optimum. It w a s assumed that,with a judiciously chosen value fo r the sphere of influence of the moon, the end conditions that were optimum fo r patched conic traj ector ies als o would be optimum for aprecision trajectory. The BAP modes of the midcourse proc essor wer e to be exercisedonly during the period fr om 5 to 20 hours after TLI.Because of lead-time considerations, the existing mission-design program w a sused as the basic vehicle fo r the midcourse pro ces sor . However, the Generalized Forward Iterator w as a general program with far more capability than the midcourse phaserequired. A much more specialized and regimented program w a s required fo r the real-time environment, and for this reason, a form al midcourse philosophy w a s needed.The initial real-t ime midcourse program design philosophy was a product of thecombined effo rts of MSC and thr ee con trac tor s. The personnel in these groups specifiedand developed a set of mission profil es that the midcour se pro ces sor would compute.These profiles o r options represen ted all the possible trajecto ry sequences that wereconsidered feasible in mid-1967.

C o m p u t a t i o n a l O p ti o n s of t h e M i d c o u r s e P r oc e ss o rDetailed logic w as developed for seven options in the midcourse processor duringthe initial program development.Option 1-nodal targeting. - For option 1 @, Y, Z , and T targeting), a trajectoryw a s computed f ro m point A to-point B. Option 1 w a s the simplest and, therefore, mostfoolproof of all options. A t the midcourse position, the maneuver w a s computed to determine a traj ecto ry that would bring the spacecra ft to the nominal location @, Y, Z ) ofLO1 at the nominal tim e T. This option w a s applicable to any mission scheme, if a setof targe t pa ra me te rs was known. The resulting trajecto ry was a fr ee r eturn only if thenodal targets were associated with a fre e-r etu rn trajector y, based upon the position ofthe spacecraft at maneuver time.

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- -

Option 2- fixed lunar parking orbit, free return. - Because Apollo Program.planningwas committed to free -ret urn trajecto ries, the midcourse pro cess or had tohave the capability fo r computing a free -ret urn trajector y that would intercept the nominal lunar parking orbit. This specification resulted in option 2, the fixed-orbit, free-re tu rn BAP. While retaining the nominal luna r-orbit orientation, th is optionreoptimized a complete fr ee- ret ur n mission profil e that included LOI, an LOPC toenable the command and se rv ic e module (CSM) to pa ss over the lunar landing site asecond time, and TEI maneuvers.

Option 3--free lunar parking orbit, free return. - Concern over dwindling fuelres erv es because of cs ti nu ed weight growth-of the spac ecraft re sulted in the inclusionof option 3, the fr ee -o rb it , f re e- re tu rn BAP. Because of the launch-window-designphilosophy, a single lunar-landing- site approach azimuth, usable over a 3-month period,was to be selecte d on the bas is of positive fuel re ser ve s. Therefore, on a specificlaunch day and with a TLI dispersion, the nominal azimuth was not nec ess ari ly optimum.To provide fo r this contingency, option 3 was devised by retaining the fr ee- ret ur n aspect of option 2 but freeing the azimuth at the lunar landing site. Full optimization determined a new approach azimuth that r esul ted in slightly less propellant being usedthan in the solution computed by option 2.

Options 4 and 5--nonfree return . - Options 4 and 5 represented a logical exten- _ _ _sion o F ~ edeas that produced o p t i o g . If TLI dispersions were great enough to makea fre e-re turn mission too costly in ter ms of AV, a nonfree re tu rn (NFR) possiblywould perm it continuation of the mission. Relaxation of the fr ee- ret urn traj ect or iesw a s not considered for the first lunar flights, However, the lunar module descent engine could be used, within limit s, as a backup (descent propulsion syst em a bor t) to return the spacecraft safely to ear th . Because of this safety margin , limited NFRtraj ecto ries became an actual alternative in real- time.Option 4 (fixed-orbit NFR BAP) w a s designed to provide the midcourse p roces sor

with any capability that might be r equ ired f o r the us e of NFR tr aj ec to ri es while retain ing the nominal approach azimuth to the lunar landing si te. Because transl unar flighttime w a s not uniquely dete rmined on an NFR tra jectory , a polynomial 6 (AT) w a s developed to predict the optimum translun ar t ri p time during the first 20 hours of trans-lunar coast (based upon the position and energy of the sp ace craft and the cur re ntearth- moon geometry).Option 5, the free-azim uth ve rsion of option 4, had s o much latitude that i t wouldnot reliably optimize to completion. Moreover, i f a zero AV LOPC maneuver was encountered, a nonoptimum solution would often be returned. To overcome this difficulty,the us er of option 5 was allowed t o specify by input (manual -entry device) whether to

allow a range of approach azimuths or to compute a di sc re te ,, nonnominal azimuth. Byusing a se ri es of di sc re te az imuth solutions in conjunction with a midcourse Trade-off(TO) Display, the dependence of end-of-mission fuel res er ve s upon the approach azimuth could be determined. Option 5 w a s included in the prog ram specifications but w a srecommended for us e in rea l-time analysis rathe r than for mission support.

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-~flybys.ptions 6 and 7- lunar ~ _ _- Options 6 and 7 (lunar flybys) completed theo r i g i n m f mission profi les. The intent was to provide computat ional support foralte rna te missions in the event of a badly disperse d TLI. It was in this aspect thatquestions ar os e concerning the prevailing assumptions and specifications fo r optimization. Option 6 w a s supposed to be an optimized lunar flyby passing through the nominalperilune latitude and altitude, whe reas option 7 w a s to retain the constraint on perilunelatitude, and the user w a s to specify perilune alt itude by manual input. The prevailingassumptions and constrai nts were not unreasonable for lar ge midcourse maneuvers(a AV of approximately 1500 ft ls ec ) executed earl y in translunar coast. Tar gets thatw e r e determined by conic optimization yielded midcourse maneuver s on integrated trajec to rie s that wer e nonoptimum by approximately 35 ft/sec; fo r extensive midcour semaneuvers, this er r o r could be considered acceptable. However, fo r small midcoursemaneuvers such as those that occ urr ed during the Apollo 8 mission, the differences between conic and integra ted tr aje ctori es caused the sma ll dispersion to be overwhelmedand thus invalidated this enti re approach. In mid-1967, it w a s known that, i f dispersions occurred, a perilune altitude other than nominal could result in a less expensiveluna r flyby. Ther efore, option 7 w a s creat ed in the hope that repeated u se of the optionmight perm it the us er to dete rmine empi rically an optimum lunar flyby during re al time.

A d a p t i n g to the R e a l - T i m e E n v i r o n m e n tThe complexity of the var ious mission pro fil es and the re al- tim e require ment ofspeed and reliability we re considered indications of the need fo r program automation.The idea of "wiring the man out" to reduce human e r r o r wa s a significant fact or i n theconstruction of the program sup erv iso r logic. Each option was to be executed as automatically as possible fr om s tore d data. However,. the forwar d iter ato r needed initialvalues, or first guesses, to begin solving problems. These values were crit ical andvarie d significantly with different launch days and even with di fferen t launch azimuthsand TLI opportunities. The conflict of varying init ial values and stor ed data w a s solvedpr ima ril y by contr acto r personnel with the concept of the Data Table.The Data Table w a s designed to st or e the independent var iabl es in such a way thatthe following conditions existed.1. The nominal values could be loaded preflight.2. The nominal values could be updated by midcourse computations.3. A l l values could be manually overridden.The Pr eflight Data Table w a s used in progra m testing. Because a table w a s re

quired for each possible time of launch, 10 distinct Data Table s existed for each launchday. Preflight Data Tables were generated for launch azimuths of 72", 81", go", 99".,and 108" fo r both first and second TLI oppor tunities. When a specific launch azimuthw a s selected, the appropriate Data Table w a s constructed by interpolation. This DataTable w a s called Data Table 1.

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The midcourse processo r, therefore, start ed each mission with an interpolatedtable. When a BAP was computed, the process or would crea te an updated table fro mthe associated values of the independent variables. The midcourse pro ces sor couldstore (in the midcourse TO Display) as many as six computed miss ion prof iles. EachBAP that w a s displayed had the implicit capability to produce an updated table. Such atable could be created and displayed by requesting Data Table 2. Thi s second table wasexperimental i n that a cert ain amount of miss ion planning w a s allowed to continue without affecting the rest of the midcourse system. Any succeeding midcourse computationcould use either the first or the second table fo r initial values. The second table, basedupon preci sion propagation, was usually preferable, because the first table held onlyconic data.

When a computed midcourse BAP maneuver w a s actually executed (or transferredto the Mission-Plan Table), the independent var iab les assoc iated with the maneuverwere loaded into Data Table 3. A l l succeeding midcourse computations used DataTable 3, unless othe rwise specified. Independent variables associate d with the nextexecuted BAP maneuvers were loaded into the fourth and fifth tables . If still anothermaneuver w a s executed, the table from that BAP went into the fifth table. The old datain the fifth table went into the fourth table, and the fourth into the third; and the olddata in the third table were deleted. By this procedure , the execution of any number ofBAP maneuvers w a s allowed, and an adequate maneuver his tory w a s retained.

L i m i t a t i o n s of C o n i c O p t i m i z a t i o nAnother difficult problem in the midcourse pr ocessor stemmed fro m the relationship between conic- and integrated-trajectory propagation. For computational speed,a conic-trajectory computer w a s used for all of the options dur ing optimization. Whenoptimization w a s complete, an integrated trajecto ry w a s computed that satisfied thesame end conditions at the moon. The midcourse maneuvers obtained with the conic

and precision trajectories were considerably different. To dec rea se the number ofiterations required to converge precision tr ajectories, a polynomial 6 (AV) w a s developed for application to the conic value for the scalar velocity at midcourse. Contractorpersonnel later suggested that computations begin with the desi red end conditions at themoon and converge to the midcourse position with precision propagation to overcomet h i s same difficulty. When this scheme w a s incorporated into the program, the resultswere even bette r; thus, the 6 (AV) polynomial w a s discarded.Because the midcourse maneuver that w a s predicted during optimization w a s considerably different fro m the maneuver derived by using precision t rajectories , thesolutions w e r e not fully optimized. Near the end of 1967, personnel of one of the contr ac to rs r eal ized the inadequacy of the specifications fo r optimizing lunar flybys, but

the problem could not be solved at tha t time because of insufficient understanding offlybys.

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I I Ill11111m11111

A p o l l o 8 M i s s i o n- L u n a r Flybys a n d t h eV e c t o r O f f s e t T e c h n i q u e s

Considerable effort and time wer e expended to improve the conic progr am by reducing the progr am e rr or . Work was completed on lunar- sphere- siz e studies, Jacobicalibra tions, and hybrid patched conic tr aje ctor ies . When the Apollo 8 mission wasscheduled as a CSM solo lunar mission, optimum lunar flybys we re r equ ire d to be computed from near-nominal tra ject ori es at any time during translu nar coast. Th is newrequirement w a s met by the vector offset method that w a s developed at MSC during theactivity which preceded the Apollo 8 mission.

By us e of the standard conic- and integrated-propagation routines, the superviso rlogic w a s structu red to m easure the difference in midcourse maneuvers between comparabl e conic and precision trajectories. This difference w a s applied as a velocitybias, or offset, to th e premid course s tat e during conic optimization. Thus, the integrated midcourse maneuver could be optimized while a conic trajectory computer w a sbeing used.Application of the vecto r offset to the flyby optimization opened up a new field oflunar trajectories as possible solutions to the problem. These traj ecto rie s led to abet ter understanding of the problem and resu lted in a complete rev ision of the origina lflyby specifications. New flyby options, 8 , 9a, and 9b, p rovided a variety of flybycapabili tie s. By use of option 9a, a flyby w a s possible that used the tr ue minimum AVto ret urn to ea rth within a range of inclinations of r etur n and perilune altitudes. Whenoption 9b was employed, the optimum lunar flyby for a specified inclination and rangeof perilune al tit udes w a s achieved. By us e of the computational support provided byoption 9a, the fr ee -r etur n landing point could be moved from any place on ear th intodeep water, for an additional AV of less than 50 ft /se c. The use of option 8 resultedin a lunar flyby to a specified inclination of fr ee- re tu rn and perilune altitude. Although

option 8 did not involve optimization, the vector offset w a s used to compute accu ratefirst gue sses for the integrated maneuver. Because of a lack of l ead time, the new flybyoptions we re not incorporated into the Apollo 8 RTCC midcourse pro cess or, but theseoptions we re made available in the Real-T ime Auxiliary Computing Facility and wereexe rci sed throughout transl una r coast during the Apollo 8 mission. A l l modes of themidcourse processo r were requir ed to function throughout tran slun ar coast.

V e c t o r O f f s e t A p p l i e d to NFR O p t i o n sIn early 1968, the NFR options, as specified, were found to be nonoptimum forsmall midcour se maneuvers because of the ubiquitous difference between patched conic

and pre cision propagation. Application of a velocity bia s at the m idco urse point couldnot completely elimina te' the problem, because , unlike the case of fr ee- re tu rn traj ector ies, tra nslu nar flight time on an NFR traje cto ry was not uniquely determined by th enodal position. The applica tion of a velocity offset at both ends of the tr anslunar trajec tor y during conic optimization and the use of flight time to te rmin ate each traj ecto rycompri sed the solution. A consequence of the solution w a s coupled optimization of boththe midcourse and the LO1 maneuvers into a close approximation of the actual maneuve rs . The princ ipal values of NFR tr aje ctor ies were recognized to be the fuel savingsand translunar-tr ip- time flexibility when these tr aje cto ri es were used in conjunctionwith the hybrid mission profile.1 4

1 1 . 1 1 1 1 1 1 1 . 1 1 , I 111 111111 I I 1 I 11111 I III II I I


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Apollo 10 a n d 11M i s s i o n s- V e c t o r O f fs e t I n c o r p o r a t e di n t o f r e e - R e t u r n B A P O p t io n sThe decision to use the sam e lunar orbit orientation on the Apollo 1 0 flight as onthe Apollo 11 flight was made too late to reta rge t TLI. The RTCC midcourse process orwould be used to compute midcourse maneuvers during translunar coast in or der to per

mit an LO1 into the desi red lunar orbit. The mismatch between the nominal translunartra jectory and the lunar-orbit orientation showed that, as originally specified, the free-re tur n BAP options would yield nonoptimum an swer s in the region approximately20 earth rad ii fr om the moon. Two alternatives were available: (1)change of theweighting scheme to place more importance on the plane change at LO1 (a form of symptomatic treatment) o r (2) incorpora tion of the vector offset technique. The latter wasselected and resulted in the progr am that w a s also used fo r the first manned lunarlanding.E n s u r i n g R T C C R e l i a b i l i t y

The mos t difficult and prolonged task of all w a s the effort to make the progra mcompletely reliable. For the real-time situation, a program w a s required that wouldnot fail. The RTCC midcourse w a s requir ed to optimize the small est of maneuversand still retain the capability to cor rec t dispersions for which corrective maneuvers ofsev eral thousands of f eet pe r second were needed.Because of the nature of i ter ati ve techniques that involved sev eral independentvariables, the Generalized Forwa rd Iterator re quired an exhaustive study to determinethe most rel iabl e independent-variable step si ze s and weighting schemes. Fine tuningof these par ame ter s fo r a specific launch date or maneuver time could cause dis astr ousresults in cas es for which a different geometry w a s encountered. In addition to studiesthat were conducted to determine the proper step size s and weighting schemes, cr iti caltrajectory routines such as Patch and LOPC that usually worked well w e r e reconstructedto eliminate all known problems. A t times, this reengineering entailed yet anotherweight and step-size study.In summary, the RTCC midcourse processor gradually evolved over a period ofyears as a res ult of constantly changing requirements. Key ideas and programing suppor t were contributed by personnel from var ious organizations. Many major developments were actively pursued, only to be abandoned or to remain unused after being fullydeveloped. Appreciation of the problem and of the behavior of the it er ator r esu lted inspecifications involving a sequence of ste ps that led to a final optimization computationins tead of a single all-out optimization. The resu ltan t program w a s more complex butafforded grea ter reliability. Perhaps the greatest pr ogr ess was in human understanding of the problem and of the ite ra to r used to solve it.

LUNA R-ORB I T INSERT IONWork on the real-time LO1 Targeting Pr og ra m proceeded in four phases. Thefirst phase (pre-1967) involved learning about the available guidance equations and theinherent capabilities of the equations. The second phase (spring 1967) was the first

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attempt at a targeting program . The problem of developing a real-time targeting procedure was assumed to have been solved by a n itera tive technique in which the burn wa ssimulated by integration through the guidance equations; therefore, it was assumed thatthe pro gram had only to be built. This attempt w a s unsuccessful because the LO1 problem was m ore complex than was originally conceived. In the thir d phase (1967 to 1968),the problem, after clos er examination, was bett er understood, and a design philosophyand program design were developed that should have been workable. An iterative technique and integration through the guidance equations were used. However, before th ispro gram was built, the fourth phase was begun, in which operational simplificationswere made to the LO1 burn. The mos t importan t simplification permi tted the LO1 burnto be simulated by an impulse; therefore, the program actually used for the Apollolunar missions w a s drast ica lly changed. The philosophy that w a s developed in the th irdphase of the program remained the same, but the method of implementing the pr og ramwas changed.

Pre-1967 DevelopmentInterface with guidance-equation development. - In 1964, MIT personnel developeda steering lay(CrFss-product steering) for the spacecraft, which required values for avelocity-to-be-gained vector. For the various CSM maneuvers, seve ral computer progr am s were used t o compute the values of this vector. A circularization guidance thatwas to be used f or LO1 was designed to provide a circular orbit at burnout, which occu rr ed whenever the spacecraf t position and velocity in the burn had an osculating eccentricity of zero . Also, with this guidance law, the space craf t would pass through agiven iner tial position. During the early work on the LO1 targeting problem, the intention was to gain knowledge of the capabil ities of c ircul ari zat ion guidance. This workwas als o necessary f or the mission-planning traj ecto ry scans; no effort w a s directedtoward the specific study of the LO1 targeting procedu res. Because circularizationguidance could result only in a circular orbit at burnout, no other profiles were studied.Objectives of ini tial stud ies. - The initial studies were completed through in-houseefforts an d task s perform ed by pr ime contractors. The objectives of these studies wer etwofold. One objective w a s to determine which guidance variables controlled each trajectory parameter. Because no closed- form analytical simulation of the burn w a s found,an iterative approach WXS used to determine guidance var iabl e values (e. g., ignitiontime) to obtain specified orbits after the burn. The necessi ty of ite rat ing w a s eliminatedonly when the LO1 burn became so rest rict ed by operational constraints that the burncould be simulated by an impulse. The second objective was to develop empi rica l equations to compute various guidance variables and to develop polynomial simulations ofthe LO1 burn. These developments were primar ily fo r us e in the mission-planning sca nwork to avoid the lengthy computer-run times a ssoc iate d with it erat ion through the guid

ance equations.Results and observations. - Several usable ideas were obtained from evaluation ofthe observations. A good understanding of c irc ula riz ati on guidance and some under- .standing of cross-produc t ste er ing were acquired. Empi rica l equations fo r guidancevar iab les and polynomial bu rn s imulations were developed, and the major LO1 traj ecto ryproblem s that would have to be processed in the real -tim e targeting-update programwe re observed. However, no detailed knowledge exis ted concerning the LO1 trajectoryproblems (e. g. , the eff ect of trajecto ry dispersions on the node of tw o orbits that are

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nearly coplanar); only guidance capabilities we r e known. The iter ative technique w a ssolidified as the solution to the LO1 targeting problem, jus t as it had been for themidcourse -correction problem.Several observations can be made about this earl y effort. Possible real-timetargeting problem s had appeared but were ignored. The LO1 was not regarded as aserious problem because the RTE and midcourse problems were s o complex comparedwith LO1 that LO1 was deemed relatively unimportant. Nevertheless, it was a mistakenot to have had at least one person working full time on the LO1 problem. A tendencydeveloped to take the approach of "do it like the midcourse" o r "the iteration can solvethe problem" and to ignore the problem s that had occurred. If this mistaken approachhad continued, a workable LO1 targeting program probably could not have been developedin the available time without a la rge effort being expended; however, the delay caused bythe spacecraft fire in January 1967 provided additional time for work on the problem.Consequently, real -time capabil ities and mission-planning freedom wer e not hampered.The probable rea son for the se mistake s w a s tha t the scope of the ea rly work w a stoo limited. The analy sis of the guidance equations w a s necessary, but the developmentof the LO1 targeting procedures should have been studied independently of the spec ificguidance problems. Prof ile changes, guidance changes, and traj ecto ry problems shouldhave been considered to gain an understanding of the re al-t ime targeting problem so thatthe necessary engineering trade-offs could be made and a real-tim e targeting progra mdeveloped.

f i r s t LO 1 T a r g e t i n g P r o g r a mConsiderations. - The development of the real- tim e LO1 Targeting Progr am w a sbegun in January 1967. A prototype set of RTCC computer prog rams fo r Apollo miss ionplanning had been under development during 1964 and 1965. The prototype RTCC logiccontained an LO1 Targeting Pr ogram that w a s an ite ration on ignition time and could not

have handled dispersions . Litt le difficulty w a s expected in developing the program, because it w a s assumed that only proper initialization of the iter ator w a s needed; that is ,the problem w a s assumed to be solved already . However, sev eral events that influencedthe program were occurring at thi s time. Some operational conside rations were beingadvanced, mainly the problem of onboard burn monitoring, the solution of which la te rled to the elliptical lunar orb it after LO1 and to the fixed-attitude LO1 burn.Impact of initia l operational considerations. - For the E-type mission, a simulatedLO1 burn into an elliptical orbit w as performed. Because circula rization guidance couldnot be used for this maneuver and because the guidances that could be used had beeneliminated from the onboard computer to gain computer storage, a rendezvous guidance(Lamber t's guidance) was evaluated fo r this maneuver. In this guidance, the velocity

to-be-gained vector w a s determined from Lam bert's problem (given a time of flight anda targ et vector). It was decided to include additional guidance in the LO1 Targeting Progr am to handle elliptical orbits after LOI. The development of the prog ram logic wouldnot be delayed fo r thi s guidance; however, the guidance logic would be added later i f itcould not be included in the initial program specifications. Externa l AV guidance(eventually used for all CSM burns) was available but w a s not considered because of theconcern that th is guidance might be too sensitive to disper sions.

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A s the LO1 Targeting Pro gra m developed, problems began to arise more frequently. The assumption that the problem was already solved inhibited complete examination of the problem, determination of the real nature of the problem (in more specif icte rms than the generality, "target LOI"}, and determination of the neces sar y engineering trade-offs. As a result, this first targeting program was inferior. Many logicpaths existed, each with an individual ite rat or setup. The run time was estimated to belong; and, because the simulations were available, an attempt w a s made to use thepolynomial burn simulations developed in earlier work. Thi s approach made the progr am highly inflexible, because the polynomials were tied to a specific profile and vehicle performance. Because of the problem with the progr am run time, considerationw a s given to expanding the polynomials so that they would have the capability to handleelliptical lunar o rbits.

Another aspect of the problem was that per sonnel working on the prog ram w e r einexperienced in th is type of work. A plan of attack and the dir ections the progra m development should take had not been established. However, th is first attempt at a progra m resulted in valuable experience in real-time-progr am design.In the first attempt at the development of an LO1 program, approaches to theproblem were broadened. A bett er understanding of the ite ra to r and of cross-productsteer ing (independent of the velocity- to-be-gained vector computation)w a s deemed necessary. A critical realization was that situations occur when all the desi red end conditions cannot be attained (i. e., a physically insoluble problem) because the approachhyperbola is fixed. Therefore, one o r mor e end conditions must be relaxed. However,the best maneuver that could be targeted would be as close as possible to the relaxedend conditions. It w a s als o real ized that, with the natu re of cross- product stee ring andvehicle-performance capabilities, a maximum allowable A V for LO1 would have to bespecified as an external input to the program. These observations were the res ult of acloser view of the problem than had been taken in the earlier work. However, by ea rly1967, a workable program was still a long way fr om completion.

Second LO1 T a r g e t i n g P r o g r a mNeed for inc reased flexibility. - A s the tim e fo r manned lunar flights approached,operational considerations wer e becoming more and more important. Fo r this reasonand because of the dissa tisfaction with the first efforts at developing a program, a decision w a s made to take a fre sh look at the LO1 problem.Many per turbations occ urr ed in the development of the LO1 Targeting Program,which w a s originally designed to support a nominal 80-nautical-mile circular lunarparking orbit. The circ ular izat ion logic w a s deleted from the onboard software. In

addition, concern over degraded lunar module per form ance because of increased lunarmodule weight and the LO1 monitoring problem resul ted in r econsideration of elliptica llunar parking orb its ra the r than circula r orbi ts, of lower altitude orbits, and of fixed-attitude stee ring rather than Lambert' s steering.. Because of these uncertain ties, adecision was made to redevelop this program to provide more flexibility.Design philosophy. - Reconsiderat ion of the development of an LO1 Targeting Pro gr am resulted in the development of a good design philosophy and the necessary technical understanding to implement it. The design philosophy tha t wa s developed by late

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1967 w a s ca rri ed over to the final program and primari ly was responsible for the quickprogram development (approximately 1 month). This philosophy cons isted of th re eparts.The first pa rt of the design philosophy was car ri ed over fro m the ear ly progra mdevelopment efforts and included the idea of relaxing end conditions. Initially, trade -

of fs had been made between obtaining the desi red landing si te and obtaining the d esi redorb it shape. In this second effort, the following priorit y w a s set: the desired orbitshape w a s to be obtained within the maximum allowable LO1 AV constra ints, and thenthe desi red landing site was to be obtained i f the orb it shape had been obtained. Thereason was that the orbital geometry sometime s made passage over the landing siteeither impossible or obviously unreasonable, even with reasonably sm all dispersions inthe lunar approach hyperbola, whereas only unreasonably lar ge dispersions of the approach hyperbola would prevent achievement of the orbi t shape. During the first efforts,either the landing-site latitude or the mis s distance at the landing site had been used asthe it er ato r's dependent variable to obtain a traj ecto ry that would have been as close tothe landing site as possible, within landing-site azimuth constra ints. In the second effort, because it was realized that what w a s desired was an orbit plane (or planes, if arange of azimuths at the landing site was acceptable) that passed over the landing site,the landing-site variabl es such as azimuth (or a range of azimuths), latitude, and longitude could therefore be replaced by a single variable, a wedge angle. Thus, it w a s neces sa ry only that this wedge angle at the landing sit e be driven as near as possible tozer o during the iterations, because the itera tor could optimize in only one variabl e(i.e. , drive the variable as near as possible to a desi red result). Therefore, the concept of the wedge angle w a s one of the most criti cal rea lizations, fo r the landing si tecould now be attained by optimizing on only one variable (wedge angle). Optimization onthe orbit shape w a s accomplished by fixing apolune altitude and optimizing perilune altitude (for elliptical orbits) o r by optimizing circular altitude (for circular orbits).

The second par t of the design philosophy involved the elimination of e r r o r s thatresu lted from making the lunar-orbit shape more important than the landing site . Thesolution was to provide the flight controller with more information than that required toevaluate only the planned maneuver. Therefore, the flight controller would have thecapability to obtain a more acceptable maneuver o r to make trade-offs. Fo r example,the flight controller w a s provided with information about the int erse ction between theapproach hyperbola and the two planes that passed over the landing site with the specified two extreme azimuths.

The thir d part of the design philosophy w a s to make the program general by specifying as many degrees of freedom as possible to be left as inputs (e. g., the apolune andperilune altitudes after LOI). This philosophy allowed the flight con tro ller t o us e available information to compute other maneuvers i f desired; this approach w a s also requiredbecause of unc erta int ies in the lunar-orbit profil e and in the guidance.

The second and third par ts of the philosophy can be sum mari zed by the statementthat the program w a s designed to support automatically the known LO1 options, butenough additional information was computed and displayed, and enough inputs were provided, to handle the unexpected. It was hoped that the p rogram would then be stab le andrelatively immune to perturbations o r that at least the pro gram would handle changes inthe lunar-orbit profile procedura lly until the program could be modified to handle thesenew prof iles automatically.19


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I I I I 1 I lI~111111111111III

Engineering trade-offs. - To develop the design philosophy, a complete understanding of th e trajec tor y and operational aspe cts of th e problem w a s needed. With th isunderstanding, the nec ess ary engineering trade-offs could be made in orde r to implement the philosophy. The following charact er ist ics of the program we r e considered.1. Ite ration through the guidance equations could be used.2. The lunar-orb it plane and shape could be redefined by input.3. Lambert's targeting and external AV guidance could be used.4. Orbit shape could have prior ity over the landing site.5. No trade-off could be made between LO1 AV and any in-orbit AV.6. Often, the AV remaining could not be optimized.7. No in-orb it maneuve rs could be used to a ttain targeting objectives.

In addition, polynomial burn simulations wer e to be used; however, because of the inflexibility of the polynomials, it w a s decided later not t o use them.Work w a s being completed to provide the neces sar y background for building theprogram . Lamb ert' s guidance was thoroughly evaluated to determine which vari able scontrolled each trajectory param eter and which var iabl es should be used in the iteration. Because the end conditions were somet imes unattainable, an investigation of theoptimization mode of the it er ator w a s attempted. The impor tan t problem of lengthycomputer run time w a s investiga ted by trying methods of fu rt he r integration through theguidance (e. g., la rg er s tep size s). A computer progr am w a s to be built to allow eval

uation of some of the ideas. However, development of the prog ra m was slowed by thecontrac tor personnel 's lack of experience with the it er ator and lack of understandingof the engineering, and by the lack of de tailed direction and programing specif icat ionsby MSC. By the time thi s computer progra m was available, the final real-time programwas al ready in us e (with an impulsive burn simulation and no iter ations); consequently,the contra ctor's work w a s never used.In summary, a workable computer pr ogra m evolved as a re su lt of the followingfour developments.1. The operational inputs were obtained.2. A good understanding of the problem w a s achieved.3. A new approach i n thinking was taken.4. A design philosophy consistent with the first two developments w a s adopted.Most of the ea rly work was not useful. Empirical equations, burn polynomials,and circulariza tion-gu idance knowledge eventually were discarded. However, theknowledge of cross-product ste eri ng and of LO1 tr aje cto ry prob lems w a s useful. Thesecond LO1 Targeting Pr og ra m was never advanced to the engineering stage; that is,

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-~ ... . .. . . ...... .. . . ,. ,

the computer prog ram was never built so that the theory could be tested. Much timewould have been requir ed to develop a real -tim e computer progra m based on the theory.However, it was thought that a good ba si s had been estab lished and that the second LO1Targeting Pro gr am had the capability to handle all LO1 targeting changes that werelikely to arise. This approach would not have been desi rable if the problem were mor econstra ined, but, because of the nature of the guidance, the approach w a s required.Final Program

Operational inputs and simplifications. - A t th is point, a major operational input_ _-was obtained. To make the -onboard atti tude monitoring easier, a fixed-attitude maneuver w a s selected fo r LOI. The per formanc e penaltie s of a fixed-attitude bu rn over avariable-attitude burn were negligible. Also, the decision w a s made to us e an ellipticalorbit after LO1 to ease the overburn-monitoring problem. Because of these constra int s,some major simplifi cations could be made.In one of the stud ies conducted during the second effort at developing a program,a very important discovery w a s that a fixed-attitude burn resulted i n a postmaneuver

orbit of which the alti tude at the node between the premaneuver and postmaneuver p laneswas equal to the premaneuver orbi t altitude at that point. Alte ration of the burn AV o rattitudes (or both) would not achieve a different result. This situationw a s unforeseen,and considerable time was spent in an effort to understand the problem. The discoveryw a s important because, when a fixed-attitude burn w a s selected for monitoring reasons,it w a s no longer nec ess ary to ite ra te through the guidance equations. Because the LO1burn could be simulated by an impulse, the lengthy computer run time and the possibleunreliability associate d with an ite rati ve solution to the LO1 targeting problem wereeliminated. The only iteration nec essa ry would be to determine the guidance paramet er s needed to burn into the impulsively defined orb it, and this procedure would be noproblem because of the work that had been done previously fo r many differen t hyperbolasand lunar-orbit geometries.It might have been possible that approaching the problem initially from a generalviewpoint, that is , concentrating on guidance and traj ecto ries in gener al r ath er than ona par ticu lar guidance (c ircular ization) , would have shown that a fixed-attitude burn resulted in no nodal altitude difference. If the desirabili ty of the fixed-attitude bur n hadbeen revealed, it is probable that, ea rl y in the progra m, the fixed-attitude LO1 burncould have been adopted and considerable work avoided. To justify the fixed-attitudeburn, the operationa l simplifications would have had to have been reached at an ear l ierdate.Use of the fixed-attitude bur n eliminated the capability of targeting out plannednodal-altitude dif ferences . However, because of the elliptical lunar orbit, th is capabil

ity could still be achieved when the nodal al titude incre ase d from the planned value as ares ul t of dispe rsions, because the ellipse line of a psi des could be rot ated until the nodalaltitudes matched.The second LO1 program (which was based on us e of the ite ra to r) w a s not the bestfor particular constraints, but it would be acceptab le for a wide range of cons tra ints.Because of t hese new operational constr ain ts, dra sti c changes were made in the LO1Targeting Prog ram . The philosophy remained the same; the changes made we re in themethod of implementation.

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Construction of the ta rge ting prog ram. - Relaxation of the end conditions wasmaintained because physica lly insoluble probl em s could occur. However, instead ofcomputing only one solution (maneuver) that could att ain the orb it shape within a givenAV and then could obtain the landing site, 10 solutions were computed with vari ous endconditions relaxed (perilune altitude, desir ed azimuth, wedge angle, etc. ). These10 solutions improved the prog ram beca use s ev er al maneuve rs were now available, andthe flight con troller could se lec t the best m aneuver, to the extent that the best could bedetermined by the mission conditions at that time. It was poss ible to compute the10 solutions because of the computational speed that resulted fr om the impulsive burnsimulation.

Relaxation of the r equirem ent fo r passin g directly over the landing sit e was stillaccomplished by the wedge-angle concept. Minimizing this wedge angle within a AVconstra int was the means of coming as close as possible to the landing site. It w a spossible to compute the wedge angle at the landing site from the LO1 impulsive pointbecaus e solutions with a rang e of azimuths over the landing si te have angular momentum vectors that very nearly lie in a single plane. Af t e r LOI, the angula r momentumvec tors of the planes that would pas s over the landing si te could be ass umed to li e in theplane formed by the angu lar momentum vector s of the o rbi ts (propagated back to LOI)associa ted with the two extr eme azimuths over the landing site. With the us e of thisconcept, the computation of the various LO1 solutions was straigh tforwar d and simple.

The 10 solutions fulfilled the re qui rements of the second par t of the philosophy,providing the flight con trol ler with information to make trade-offs and to use the inputsintelligently. Most of the deg rees of freedom to the problem were s pecified as inputs.Targeting program use. - The de sire for a circular orbit at the time of the constant delta height (CDH) maneuver during rendezvous on the Apollo 11 and 1 2 missionsillus tra ted how we l l th is philosophy had worked. No automatically computed solutionexisted to establi sh a second maneuver to obtain a circular orbit at some f uture pointaf te r LOI, but a luna r-orbit perilune altitude could be determined that would allowLOI-2 to re su lt i n an orb it which would be perturbed so that it w a s circular at CDH.Determination of the luna r-orb it pe rilune altitude requ ired knowledge of the nodal al titude and of the t ru e anomaly on the hyperbola (which were computed by the p rogra m anddisplayed) and availability of the ta rg et perilune altitude as a prog ram input. Therefore, in re al time, the co rre ct target perilune altitude would be determined fro mpreflight-computed graphs aft er one run with the nominal perilune altitude. Thus, anew prog ram requirement could be fulfilled by preflight work and rea l-t ime evaluation,without a change in the real-time program.Summary and observations. - Pr og ra m deficiencies did develop, however. Notall degr ees of freedom w ere specified as inputs, and one particul arly se rio us omissionwas the control of one of the two possible ways the line of a ps ides of the post-LO1ellipse could rotate. Some awkward procedu res wer e used in the attempts to overcomethis prog ram deficiency. The omission s resulted in progra m changes. Some of the"do it like the midcourse" philosophy still existed, espec ially regarding the computation of the AV remain ing af te r TEI. Some difficulty res ulted fr om the fa ilu re to viewthi s portion of the prog ram as mor e than a computation that had to be performed andthen added to the display data af te r computing the impulsive solutions. Also, some ofthe proc edur es that were perform ed "like the midcourse" could have been accomplished

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by a bet ter method. Fo r example, the lunar orb it w a s propagated by using conic trajec tor ies with nodal regres sion, primar ily because the sa me method was used fo r themidcourse program.After seve ral missions, it was found that th e problem had been oversupplied withsolutions fo r a range of approach azimuths to the landing site, because it became appar

ent that ground personnel were very reluc tant to use an approach path other than the onef o r which the flight cr ew had tra ined and for which the l unar- orbit propagation had beenverified. Although it wa s des irable , the computation of AV remaining after TEI wasdetermined to be unnecessary . However, because of the situat ion at the time the progr am was designed (i.e., that landing-site azimuth could easily change in real time),justif ication fo r excluding the range-of -azimuth capability would have been difficult.When the landing-site azimuth changed, the AV remaining after TEI could also changesignificantly; thus, justif ication fo r excluding the AV remaining after TEI would havebeen difficult also .The maneuver targets were computed by the Maneuver Planning Table (MPT),which ite rat ed on guidance pa ra me te rs to give a burn that attained the impulsively de

fined lunar orbit. Originally, the guidance param eter s were to be computed in the LO1Targe ting Pr og ra m to eliminate the MPT interf ace. Thi s type of computation w a s notused because the program could be put into the RTCC more quickly with the MPT interface. No problems aro se as a res ult of this interface; theref ore, the co rr ec t decisionw a s not to compute the guidance pa ra me te rs in the LO1 Targe ting Progr am. However,some inputs to the MPT were base d on knowledge of the LO1 geometry. To ensu re thatth er e would be no trouble in the computation of guidance par am et er s in the MPT, a se tof controllable va riab les w a s defined in the iter ation for guidance para meters .No inputs wer e available fr om the Lunar Orbi ter Pro gra m. An attempt was madeto determine the Lunar Or bit er proc edu res for LO1 in the fall of 1967 , but this studywas unsuccessful.Although it w a s a mistake to delay the start of the pr og ram development fo r solong (until early 1967), the delay probably resu lted in the development of a much betterprogram. Had a prog ram been working before the decision w a s made to us e the fixed-attitude burn, it would have been difficult (although not impossib le) to change the program. Consequently, the program-development delay probably result ed in a betterreal-time tool.Three major observations can be based on this experience.1. Operational inputs ar e important because operational simplifications mayresult in dra stic changes to the targeting program.2. Pr og ra m generality and flexibility are necessary because program requirements and operational con stra int s can change.3. A thorough understanding of the problem is requir ed fo r the development of adesign philosophy consistent with the tra jec tor y pr oblem s and the des ire d functions ofthe pro gra m and for an app roach to the problem with an outlook that is not dependentupon previous methods fo r the solution of other r ela ted difficulties.

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RETU RN TO EARTHThe RTE Abort Pr og ram was a real -tim e support pr oc ess or through which maneuver s could be computed to place a spacecraft on a traj ecto ry that would retu rn the spacecraft to the earth. These maneuvers might have been determined fo r any state vector

contained in cislunar space. Although the pr og ram name implied that abort or nonnominal maneuvers we re generated, the program also could compute the nominally plannedTEI and TEMC maneuvers.

C ur re n t Program C o n f igurat ionThe RTE Abo r t Pro gr am presen ted solutions on one of thr ee real -tim e output displays: an analog display (the TO Display) and two tabular displays called the Abort-ScanTable (AST) and the Return-to-Ear th Digital (RTED) Display. The disp lays differed in(1)the amount of information given fo r each solution, (2) the number of solutions pr esented, and (3 ) the precision of the solutions presented.Trade-off Display and solutions. - The TO Display provided solutions that werechar acte rize d by impulsi vema neuvers , by conic (analytic) o r patched conic c oast s frommaneuver to entry, and by a curve-f it entr y s imulation which would produce the landingpoint. This display pres ente d a continuum of solu tions fo r a range of maneuver andlanding tim es on the premane uver trajectory . Only the solutions that would retu rn thespacecraft to a specified landing sit e were produced by the TO Display. Two types oflanding sites w e r e available. The primary tar get point (P TP )site w a s a specific latitude-longitude point on the su rfa ce of the earth. The alt erna te ta rg et point (ATP) site was apredominantly north-south line on the s ur fac e of the ea rth defined by as many as fivelatitude-longitude points. Fo r both solution types, the TO Display pres ente d the maneuver A V (for dif ferent landing tim es) plotted as a function of maneuver time. In addition, mi ss distance to the PT P was given fo r the PT P mode, whereas latitude of landingwas given fo r the ATP mode. Based upon the avai labi lity of solutions within the const ra in ts and maneuver times , the TO Display might contain a single solution or as manyas 240 basic solutions.Abort-Scan Table Display and solutions. - The AST displayed up to seven disc re tesolutions that we re char acte rize d by impulsive maneuvers, by precision-integratedcoast to entry, and by curve-fit entry simulation. Fo r each solution, 1 7 parameters,including those on the TO Display, were tabulated. Eight solution modes were availablein the AST. At a specified maneuver time, the AST could produce ATP and P TP solutions that corresponded to the so lutions of the TO Display. A fuel-critical, unspecified-

area (FCUA) mode at a disc ret e maneuver tim e was available. A time-critical,unspeci fied-area (TCUA) mode and a specialized FCUA mode called the extr eme fuel-critical , unspecified-area (EFCUA) mode wer e available fo r ear th reference. Formoon ref erence, the th re e di scr ete modes (ATP, PTP , and FCUA) als o had a search-mode counterpart. Fo r the sear ch modes, the solution was the maneuver within theconstraints that requi red the lowest maneuver AV over a range of maneuver tim es.Return-to-Earth Digital_ ~ Display and solutions. - The last display, the RTED, contained only two solutions. These solutions we re the most prec ise in that they were totally integrated from the finite thrus t maneuver to the guided atmospheric entry. More

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information describing each solution was als o displayed; 55 paramete rs were listed.The RTED Display generated a solution either fr om one of the solutions cur rent ly sto redin the AST Display o r f rom a solution defined manually by the flight controller . TheRTED Display solutions wer e available fo r tran sfer to other processo rs, and a spacecra ft targ et load could be generat ed for either solution.Cha ract eris tics of display usage. - Two gene ral cha rac ter ist ics of the RTE Displays, in th e x r- ocf r om the TO Display to the AST Display and then to the RTEDDisplay, were that (1) fewer solutions were presented and (2) more precision for eachsolution became avai lable at each ensuing display. Therefo re, the TO Display had thegre ates t capability to compare or tr ade off solutions, and the RTED Display had theleast capability. The TO Display provided the u se r with the capability to dete rmin e andcompare the behavior of solutions over a wide range of maneuver tim es. Computationtim es were reasonable because the solutions we re not integrated. However, the solutions were sufficiently ac cur ate for selecting the possible candidates for the real -timesituation. Then, the prime-candida te solutions selected by the flight con trol ler we rerecomputed with mor e preci sio n in the AST. Fr om the candidate solutions, the onesolution that w a s most app ropriat e was generated i n the RTED Display and became

available fo r incorporation into the planned trajecto ry.E a r l y P r o g r a m D e v e lo p m e n t

Apollo Trajectory Decision Logic Prototype Program. - During 1964 and 1965, aprototype real -tim e-tr aj ectory planning and evaluation program , known as the ApolloTrajectory Decision Logic Prototype (ATDLP) Program, w a s developed. Various module s of the ATDLP Pro gra m comprised the abort-maneuver logic for a lunar-landingtype mission. The definition of thi s abort-p rogram logic occurre d at a series ofmeet ings between MSC and contrac tor per'sonnel. The specificat ion of th is logic orig inated at these meetings as well as fr om existing MSC and prime-c ontracto r programlogic and analysis.

The ABORT Program. - Concurrently with the ATDLP Program, a program knownas ABORT w a x z n g developed to s erve as a real-tim e-progr am candidate and as ageneral abort-maneuver-analysis tool. The solution modes fo r the abo rt-p roc esso rpa rt of the ATDLP Progr am generally para llel ed those of the ABORT Prog ram. TheABORT Program contained both ear th- and moon-centered conic- solution logic as wellas precision-integrated-coast ogic and finite-burn- solution logic. The solution characteristics of each mode in the ABORT Pr og ra m were determined from conic propagations by scanning over the key traj ecto ry para mete rs. Therefo re, optimum solutionswe re conic optimums and not neces sari ly precision optimums.The MINMAX Program. - A third program, called MINMAX, which had the capability of solving abort problem s and contributed logic to the ATDLP Pro gram , was underdevelopment. The MINMAX Pr og ram solved trajectory-planning pro blems by an optimi

apollo experience report development of guidance targeting techniques for the command module and...

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