Apollo Experience Report Evolution of the Rendezvous-Maneuver Plan for Lunar-Landing Missions

8/8/2019 Apollo Experience Report Evolution of the Rendezvous-Maneuver Plan for Lunar-Landing Missions

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N A S A T E C H N I C A L N O T E NASA TN D-7388

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APOLLO EXPERIENCE REPORT -EVOLUTION OF THE RENDEZVOUS-MANEUVERPLAN FOR LUN AR-LA ND ING MISSIONSby Jumes D. Alexunder und Robert We BeckerLyndon B, Johnson Spuce Centerf foas ton, Texus 77058

NA TIO NAL AERONAUTICS AN D SPACE ADMINIS TRATION WASHIN GTON, D. C. A U G U ST 1 9 7 3


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1. Report No. 2. Government Accession No,NASA TN D-7388 3. Recipient's Catalog No.4. Title and SubtitleAPOLLOEXPERIENCEREPORTEVOLUTIONOFTHERENDEZVOUS-MANEUVERPLANFOR THE LUNAR-LANDING MISSIONS7. Author(s)James D. Alexander and Robert W. Becker, JSC9. Performing Organization Name and AddressLyndon B. Johnson Space CenterHouston, Texas 77058

12. Sponsoring Agency Nam e and AddressNational Aeronautics and Space AdministrationWashington, D.C. 20546

15. Supplementary NotesThe JSC Director waived the use of the International System of Units (SI) f o r this Apollo ExperienceReport becaus e, in his judgment, the use of SI units would impair the usefulness of the repor t orresult in excessive cost.

16. Abstract

5. Report DateAugust 19736. Performing Organizatlon Code

8. Performing Organization Report No .JSC S-334

10. Work Unit No.924- 2-20- 0- 72-11. Contract or Grant No.

13. Type of Report and Period CoveredTechnical Note14. Sponsoring Agency Code

The evolution of the nominal rende zvous -maneuver plan for the lunar landing missions is presentedalong with a summary of the significant development s for the lunar module abo rt and re sc ue plan.A gene ral discuss ion of the rendezvous dispe rsion analy sis that wa s conducted in supp ort of boththe nominal and contingency rendezvous planning is included. Emphasis is placed on the technicaldevelopments fro m the ear ly 1960's through the Apollo 15 mission (July to August 1971), but perti-nent organizational factors al so ar e discussed briefly. Recommendations fo r rendezvous planningfo r future programs relative t o Apollo experience also a r e included.

19. Security Classif. (o f this report)None

17. Key Words (Suggested by Au thor( s) )' Lunar Orbita l Rendezvous* Rendezvous Traje ctor ies * Interception' Ascent TrajectoriesTrajectory Analysis

'Space Rendezvous' Abort Trajectories

$3.00one

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18. Distribution Statement

*For sa le by the Nat iona l Techn ica l In fo rmat ion Serv ice , Spr ing f ie ld , V i rg in ia 22151


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CONTENTS

Section PageSUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1NOMINAL RENDEZVOUS-MANEUVER-PLAN EVOLUTION . . . . . . . . . . . . 2

Launch Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Base Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Maneuver Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Terminal Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2

DEVELOPMENT OF LM ABORT AND RESCUE PLAN . . . . . . . . . . . . . . 14EVOLUTION OF APOLLO RENDEZVOUS DISPERSION PROGRAMREQUIREMENTS. DEVELOPMENT. AND ANALYSIS . . . . . . . . . . . . . 16

Rendezvous-Dispersion-Analysis Pr og ra m Requirements . . . . . . . . . . . 16Rendezvous-Dispersion-Analysis Pr og ra m Development 16Perfo rmance of Rendezvous Dispersion Analysis . . . . . . . . . . . . . . . . 18

SIGNIFICANT DEVELOPMENTAL CONTRIBUTIONS . . . . . . . . . . . . . . . 19Organizational Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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Contributions From Flight Experience . . . . . . . . . . . . . . . . . . . . . 20CONCLUDING REMARKS AND GENERAL RECOMMENDATIONS FORRENDEZVOUS PLANNING FOR FUTURE PROGRAMS . . . . . . . . . . . . . 20

Nominal Launch Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Base Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Maneuver Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Terminal Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Dispers ion Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

24eneral Development and Organizational Considerations . . . . . . . . . . . .iii


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FIGURES

Figure Page1 Representative direct-ascent technique . . . . . . . . . . . . . . . . 62 Representat ive phasing-orbit CSI/CDH coelliptic sequence 11echnique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 Representative shor t rendezvous technique 12. . . . . . . . . . . . .

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APOLLO EXPERIENCE REPORTEVOLUTION OF THE RENDEZVOUS-MANEUVER PLAN

FO R L U N A R - L A N D I N G M I S S I O N SB y J a m e s D. A l e x a n d e r a n d R o b e rt W. Be cke rL y n d o n B . J o h n s o n S pa ce C e n t e r

S UM M A RYIn the nominal rendezvous planning for lunar landing mi ions, the ge era1 pro-gre ss ion was fr om the direct -ascent technique, through the multiple-impulse phasing-orb it technique (coelliptic sequence), to the shor t rendezvous technique.The majo r objective throughout the rendezvous-plan evolution was a standardter minal approach that was executable by us e of the reaction control system, that wascontrollable manually, and that was relatively insensitive to powered-ascent dispers ion.Such a terminal approach was characteris tic of both the coelliptic sequence and thesh or t rendezvous techniques.The most significant fa ct or in the simplification and standardization of the orig-inally complex lunar module abort and rescue plan was the incorporation of variableinsertion targeting for aborts fr om powered descent. Other significant developmentsthat improved onboard capability and increased confidence and safety were the imple-mentation of the coelliptic- sequence logic and the very- high-f requency ranging in thecommand module.The development of the disper sion and trajectory analysi s capability significantlyinfluenced the development of both the nominal and contingency rendezvous planning.Planning discipl ines significantly influenced were propellant budgets, miss ion rules ,cr ew procedures, traj ectory constra ints, maneuver sequence, and ground and onboardpr og ra m verification. A significant organizational factor was the eventual assignment

to the rendezvoys spec iali sts of the responsibilities fo r the rendezvous dispersion pro-gr am development and f o r the rendezvous dispersion analysis .

INTRODUCTIONThe purpose of this report is to record significant developments in the evolutionof the rendezvous-maneuver plan for the Apollo lunar landing miss ions and to offer somegene ral recommendations for rendezvous planning for fut ure programs. The development


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of the rendezvous plan involved direct ion, coordination, analyses, and inputs fro mdisciplines and flight experience over severa l years. Moreover, it involved not onlythe nominal rendezvous situation but al so the contingency rendezvous situations. Thedisciplines included the crew and onboard sys tems , navigation planning, ground sup-port, dispersion analysis, consumable analysis, and mission rules. Important flightexperiences contributing to Apollo lunarrendezvous operation planning included theGemini rendezvous missions and the developmental Apollo rendezvous missions.

In t h i s report, emphasis is placed on the significant technical developments thatevolved i n the rendezvous-maneuver plan. Other significant developments, includingorganizational factors , also are identified.

NOMINAL RENDEZVOUS-MANEUVER-PLAN EVOLUTIONThe nominal rendezvous-maneuver plan for the lunar-landing missions progressedthrough the following basic techniques.1. Direct ascent2. Phasing (or parking) orbit, which ultimately evolved into the four-impulsecoelliptic sequence3. Short rendezvous

These techniques will be discussed fully later, but an ear ly understanding of their dif-ferences and similaritie s wi l l clarify the evolution of the nominal rendezvous plan.Originally considered in the ear ly 1960's, the di rec t ascent theoretically placed

the lunar module (LM), at powered-ascent cut-off (insertion), on a trajectory thatwould inte rcept the command and ser vice module (CSM). This technique had the fol-lowing major disadvantages.1. The incremental velocity ( AV) requirements during the final approach werebeyond the capability o f reaction control systems.2. The final approach (direction and relative velocity) varied as a function of thelift-off time within the normal launch window. Fur the rmore , powered-ascent disper-sions significantly increased the complexity of crew procedure s and techniques duringfinal approach.3. Because an intercept trajectory w a s targeted at insertion, the insertion tar-gets varied with lift-off time . Therefore, th e launch window was undesirably sensitiveto unsafe perigee occur rences .The first two major disadvantages of the direct-ascent technique we re overcomeby the incorporation of two nominal i ntermedia te maneuvers be fore the final intercepttr an sf er s (the terminal phase). The inte rmed iate maneuver not only regulated theascent so tha t the final approach involved relat ively low, manually controllable r a t eswithin the reaction control sy stem (RCS) capabi lity, but al so provided a capability to

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economi'cally abs orb (before termina l phase) powered-ascent dispers ion and, there-fore, afforded a high probabil ity of maintaining the standa rd approach. The new tech-nique was the four-impulse coelliptic sequence for which planning began in late 1964.The coelliptic sequence als o eventually involved standard inse rtion targeting; there-fore , the unsafe perigee sensitivity, related to insertion targeting, was eliminated.The sho rt rendezvous technique was developed beginning in la te 1969, following

flown. This new technique was a compromise between the first two techniques. Theshort rendezvous technique involved neither a direct-ascent nor a phasing-orbit coel-liptic sequence but incorporated important characteristics of both. It afforded the fastrendezvous time that was characte rist ic of the direct ascent yet retained the high prob-ability of achieving the standard terminal approach that w a s characteristic of thephasing-orbit coelliptic sequence. Although the inse rtion orb it w a s not a n intercepttrajec tory, an intercept tra jec tory was established by us e of the first in-orbit nominalmaneuver (about one- third revolution) aft er insertion. A nominally zero tweak maneu-ver scheduled a few minutes after inse rtion and used in combination with the intercept -tran sfe r maneuver served as a two-impulse (Lambert) dispers ion-absorption capability.Therefore, compared with the coelliptic sequence (which essentially involved Hohmanndispers ions could be absorbed conveniently and economically fo r the s hor t rendezvous.For l arg er dispersions o r for certain system failures, a "bailout" (abort) to the co-elliptic sequence was available to allow the standard final inte rcept conditions. Be-cause of thi s r esour ce and because of the confidence derived f ro m the Apollo ll and12 missions, the short rendezvous was incorporated as the primary rendezvous tech-nique beginning with the Apollo 14 mission.

the first lunar-landing mission in which the four-impulse coelliptic sequence was

t ransfers as the means of dispers ion absorption) only relatively sma ll powered-ascent

The third basic technique has been referred to by th ree different names: early,short, and direct. Although the te rm lldir ec tllbecame the most official name, in thisreport, the technique is referred to as the short rendezvous to avoid confusion betweenthe t e rms "direct-ascent rendezvous" and "direct rendezvous. '' Furthermore, thete rm designating the number of impulses fo r a particular rendezvous sequence (forexample, four-impulse coelliptic sequence) includes the nominal maneuvers aft er LMinsertion. The terminal phase (intercept transfe r initiation and braking) fo r thisimpulse-numbering method is assumed to have only two impulses.

The t e r m "concentric sequence" was used in the ear ly nominal planning becausethe ta rg et or bi t was always essentially circular. However, when the abor t and rescueplanning introduced relatively elliptical target orbits, the te rm "coelliptic sequence"was adopted to emphasize that the constant differential height condition could also beessentially established fo r elliptical orbits.Rendezvous planning f o r cer tain earth-orbit programs , such as Gemini andSkylab, had used a maneuver-line logic for which the number of maneuvers (or im-pulses) and th e number of revolutions were of prime consideration. By us e of th islogic, the maneuv ers and the revolutions could be trea ted as variables. However, asthe nominal rendezvous plan fo r the lunar-landing mis sions evolved, thes e par am et er swe re not treated as variables, mainly because of lim its on time and the concern forsafe perilune . The maneuver-line logic could involve nonhorizontal maneuvers, which,in some cases, would lower perigee significantly. Although planning for lunar rendez-vous definitely was affected by previous earth-orbit rendezvous planning, a new type of

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rendezvous planning was required. However, it might be of i nt er est to note how thenumber of impulses n and the number of revolutions m var ied during the evolutionof the nominal rendezvous. To indicate precisely its variation, the variable m, nor-mally expressed as an integer, is expressed in fractions. Hence, f or the di re ct ascent,n equaled 1, and m varied between 1/3 and 2,/3. During the evolution of the phasing-orb it coelliptic sequence, n increased fr om 2 to 3 and, finally, to 4, and m increasedfr om approximately 1-1/3 to 1-2/3. Then, f or the sho rt rendezvous technique, nequaled 2 and m equaled approximately 2/3. Other pri me planning fac tor s fo r lunarrendezvous included certain charact eri sti cs of the terminal phase and the placing ofmaneuvers re lative to the line of apsides.

Generally, t h e major areas of nominal rendezvous development were launch win-dow, base orbits, maneuver sequence, and terminal phase. Each of these areas isdiscussed separa tely . In lunar-mission planning, the maneuver sequence and the ter-minal phase wer e the dominant considerations; in fact, developments in the se two a r easessentially controlled the decisions fo r the launch window and base orbits. Fo r thi sreason, the maneuver sequence and the terminal phase a r e trea ted in gre at er detail inthe following sections.

L a u n c h W i n d owThe initial philosophy was that a nominal launch window of 4 to 5 minutes shouldexist. In othe r words, the nominal rendezvous sequence and time line should be appli-cable within this window. A l l direct-ascent technique planning and planning for thefirst par t of the phasing-orbit technique wer e influenced by thi s requirement. However,cert ain proposed changes in the base o rb it s and in the maneuver sequence (described inthe two following sec tions) would have reduced such a nominal launch window to l e s sthan 1 minute. It w as then decided that no realistic situations would require a nominallaunch window of more than a few seconds. If the LM could not lift off so that the nom-

inal sequence time line could be applied, eit her a CSM one-revolution delay or a con-tingency time line could be applied. In effect, the revi sed philosophy that was usedduring the remaining rendezvoustechnique development meant that no specific nominallaunch window existed.A significant fac tor in launch-window analy sis was the development of the "rec-ommended lift-off time" computer program. The progra m eventually could determinethe optimum lift-off time as a function of des ir ed pa ra me te rs for either the four-impulse coelliptic sequence o r the two-impulse shor t rendezvous.

B a se O r b i t sThe CSM lunar parking orbit. - The choice of altitude f o r the CSM lunar parkingorbit involved both nominal capabilities (initially including launch-window cons idera-tions) and powered-descent-abort phasing and ranging considerations. A nearlycircular orbit w as chosen because of its rendezvous advantages, mainly monitoring-

and-backup- technique simplification. The initia l rendezvous planning was based onthe assumption of a CSM parking-orbit altitude of 80 nautical mi le s ci rc ul ar . Directlybecause of limited LM RCS propellant and indi rect ly because of limited ascen t propul-sion system (APS) propellant, the CSM parking-orbit altitude was decreas ed to

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60 nautical miles circ ular . Lowering this altitude decr eased the nominal launch-window capability and was a fac tor i n the elimination of the 4- to 5-minute nominallaunch window. The 60-nautical-mile orbit was incorporated into the planning afterthe basic four-impulse coellip tic sequence was developed, and it was thereaft er main-tained as the nominal altitude.The LM insertion orbit. - Throughout the development of the nominal rendezvousplan, the LM insertion-orbi t r equirement alternated severa l tim es between a variableorbit and a constant orbit. A variable-insertion orbit is defined as one f o r which theinsertion target s are directly dependent on the CSM condit ions (position, velocity, andso forth). A constant-insertion orbit is defined as one fo r which the insertion tar get sremain essentially constant within certain limi ts reg ar dl es s of the CSM condition. Forthe direct- ascent technique, the insertion orbit var ied within the nominal launch win-dow and had whatever dimensions were required to establish, at insertion, an intercepttrajectory with the CSM in the 80-nautical-mile orbit. The A P S was thought capable ofobtaining any such requ ired orbi t; the only constraint was maintaining a safe perilune.For the original phasing-orbit technique, a low constant-insert ion orbit of ap-proximately 1 0 nautical mil es circular was considered. For the original coellipticplan, the insertion apolune varied as a function of lift-off time within the nominal launchwindow. The objective of this variation was to control final tran sf er initiation time.During thi s period of development, dispersion analyses showed that the targeted apo-lune of the inser tion orb it (about one-half revolution after inse rtion) should be no lowerthan 30 nautical mi les to ensure a safe orbit. The insertion altitude at perilune of60 000 feet (approximately 9.8 nautical miles) w a s influenced by APS AV considera-tions. The decision was made to incorporate a constant-insertion orbit when the basic

four-impulse coelliptic sequence was developed. The approximately 10- by 30-nautical-mile orbit was incorporated at th is point and remained nominal throughout most of thedevelopment of the coelliptic-sequence plan. Near the end of the development of thecoellip tic-sequence plan, the apolune altitude was increased to approximately 45 nau-tical miles, mainly to decr ease the relative range at insertion. The final change tothe coellip tic- sequence plan involved inserting the LM with a constant radial-velocitycomponent to shift apolune approximately 5 minutes ne arer the insertion point. Theapolune altitude remained at approximately 45 nautical miles , but the perilune altitudedecr eased to approximately 9.2 nautical miles.

The insert ion orb it fo r the short rendezvous technique was basically the same asf o r the final coelliptic sequence, but the apolune altitude varied f rom approximately45 to 50 nautical mi les as a function of the mission plan. The constant radial compo-nent at insertion was maintained, and the orbit was targeted to obtain a desired differ-ential height (Ah) at a specified time after insertion. Therefore, the final type of LMinsertion o rb it could be considered a nearly constant orbit.

Maneuver SequenceThe development of maneuver sequence has been introduced previously but isdiscussed i n detail here.Direct-ascent technique. - The original concept fo r the ascent-to-rendezvoustechnique wa s the direct-ascent concept. The analysis for the direct- ascent technique

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began in the early 1960's, before hardware charact eris tics and real isti c dispersionmagnitudes wer e well defined. An inert ial sketch and maneuver-sequence data thata r e representative of the direct- ascent technique ar e shown in figu re 1. The basiccha rac teris tics of this technique wer e as follows.1. A variable powered ascent (that

is, variable insertion targets) as a functionof the lift-off time within the nominal launchwindow, so that the LM would be insertedon a trajector y intercepting the CSMCSMat80n mi

2. A variable transfer angle(insertion- to-intercept) that varied fr omapproximately 120" to 300" as a functionof lift-off time, with AV optimization beingthe main objective3. Variable-time and variable -

relative-position midcourse correctionsthat were to include any plane change

IThe obvious advantage of the di rec t-ascent technique was the relatively shor tduration fr om lift-off to rendezvous com-

Time from pletion. However, as a result of experi-maneuver system problems were identified in the ear ly de-velopment of the Apollo rendezvous tech-nique (early 1964) by the flight crew and

the variable t ran sfe r angle and the cffectof predicted dispersions, the final approachvari ed considerably. This variable finalapproach involved complex crew-monitoring,more, because most of the rendezvousactivities occur red on the fa r side of themoon, almost no ground support was available. However, during the la te r phases ofdevelopment, the requir ement fo r ground support of the ter minal phase was eliminated,pr imar ily because of the development of excellent onboard guidance and navigationsystems. Also involved was an undesirab le sensitivity to unsafe perilune and cor-plexascent monitoring techniques because of the va riable (lift-offtime dependent) inser tiontargets. A technique was needed that would af fo rd a standard final approach, groundsupport of the primary maneuvers (based on assumptions at that time), and constant

insertion orbit condition. The direct-ascent technique lacked these characte rist ics,s o planning turned to some type of phasing- o r parking-drbit technique.

Nominal ence in the Gemini Program, two majorInsertion

Terminal braking R C S 80180 flight-control personnel. Because of bothalntercept trajectory targeted at insertionbApproximate operational braking total

Figure 1.- Representative direct-ascenttechnique. backup, and braking techniques. F'urther-

Multiple-impulse phasing-orbit technique. - The multiple-impulse phasing-orbittechnique progressed through several develoPmental phases. Each phase increased theacceptability of the technique f o r the requir ed applic&ions.

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Origina l phasing-orbit technique: Fo r the original phasing-orbit technique, t heLM w a s to be inser ted into a standard insertion orbit at an 8- to 10-nautical-mile alti-tude with an apolune alti tude of 1 0 o 20 nautical mile s, regardl ess of the lift-off timewithin the nominal launch window. The standard insert ion would both alleviate the un-safe perilune problem and simplify t h e crew monitoring techniques, as compared withthe variab le powered ascent of the direct-ascent technique. Then, at a selected phaseangle (or LM-to-CSM elevation angle), a direct inte rcept was to be initiated with astandard tr ans fe r angle of approximately 160" . This maneuver w a s referred to aster minal phase insert ion (TPI). The tim e of TPI would va ry as a function of the lift-offtime, but the nominal launch window would be bounded so that the conditions fo r T PIwould occur on the near s ide of the moon. The new advantages of the phasing-orbittechnique were a standard final approach from a re la tiv e standpoint (not lighting), in-cr ea sed ground-support capability for the terminal phase, and the opportunity to makea plane change at a common node before the terminal phase.A t thi s stage of development (early 1965), the following fact s became evident.1. Standard lighting for the t erminal phase w a s important. Because the TPItime could vary considerably as a function of lift-off time within the nominal launchwindow fo r thi s technique, the lighting for the terminal phase could likewise vary.2. Standard, relat ively slow ra te s before TP I would be advantageous to track ingand monitoring activi ties. This condition could be effected by a constant differential-height maneuver preceding TPI.3. To avoid visual l oss of the tar get vehicle, the final braking would have to beperformed by the RCS instead of by a major engine. The relative velocity and burn dura -tions for wha t w a s then an approximately 70-nautical-mile Ah at TPI were larger thanthe RCS could accommodate operationally.Therefore, it w a s agreed that a technique should be developed that could affordstandard lighting fo r the termina l phase, that would involve a coelliptic- orbit condition

befo re TPI, and that would provide acceptable braking rates for either the LM RCS o rthe service module (SM) RCS.Origina l (three-impulse) coelliptic sequence: For the origina l three- impulsecoelliptic-sequence technique, the apolune of the insert ion orbit var ied as a function oflift-off ti me within the nominal launch window. One-half revolution af te r insertion, acoelliptic maneuver wa s performed that essentially established a coelliptic or constantAh. The variation in the insertion orbi t and, therefore, the variation in the Ah at the

coelliptic maneuver theoretically would cause the desired conditions for TPI to occur ata fixed ti me r egar dl es s of lift-off tim e within the nominal launch window. The launchwindow w a s limited s o that it began when the resulting coelliptic Ah was 15 nauticalmi le s and ended when the coellip tic Ah increased to 50 nautical miles. The 50-nautical-mil e Ah coincided with an insert ion apolune of 30 nautical mi les (the CSM being at80 nautical miles), which had been designated as the lowest safe insertion orbit forwhich to target. The braking associated with a 50-nautical-mile Ah w a s then consideredacceptable for the RCS systems .

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owever, deta iled disper sion analyses (late 1965 to mid-1966) showed that in-sertion dispersions could result in larg e s lips in the TPI time for the three-impulsecoelliptic technique. No means existed for absorbing insertion dispersions before theter minal phase. Also, the var iable insert ion orbit was thought to involve complexmonitoring techniques. Therefore, a technique was needed fo r which predictable in-sert ion dispersions could be absorbed before the terminal phase and fo r which a stand-a r d or very nearly standard inse rtion orbi t was applicable. An additional maneuverwas needed that could be performed f rom a standard insertion orbi t and that, in com-bination with the coelliptic maneuver, could adjust for di sper sions. In an attempt toprovide the additional necessary techniques and maneuvers, the coelliptic- sequenceinitiat ion (CSI)/constant- differential- height (CDH) coelliptic sequence was developed.

Original (four-impulse) CSI/CDH coelliptic sequence: The original CSI/CDH co-elliptic sequence included the following characteristics.1. A standard insert ion orb it of 30 by 10 nautical miles (insertion at perigee)2. The CSI maneuver at 30 minutes af ter insertion3 . The CDH (coell iptic) maneuver at the resulting apolune afte r CSI4 . The TPI approximately over the landing site5. The termina l-phase CSM tra ve l angle of 140"The CSI AV direction was constrained to the horizontal to ensure no lowering ofthe perilune for a posigrade maneuver. The Ah at CDH vari ed f ro m approximately15 to 50 nautical mile s and the difference i n time (A t ) , between CSI and CDH, variedfrom approximately 51 to 28 minutes fo r the variation in lift-off time within the nom-inal launch window. By adjusting the catchup ra te (that is , by varying the upcoming

coellipt ic Ah), the CSI allowed not only for the nominal launch window but a ls o fo r theabsorption of insert ion dispers ions . Performing the CDH at the apolune afforded opti-mum AV usage. Because the CSM orb it wa s nearly c ircu lar, the CDH was always anear- horizontal maneuver.The new advantages of the CSI/CDH coel lipt ic sequence were the following.1. Better control of the T PI time slippage (as the CSI maneuver made this situa-tion le ss sensitive to insertion dispersion)2. Use of backup cha rt s to der ive solu tions because of the generally more s tand-ard ranges and rates3 . Decrease in complexity because of the s tand ard conditions around insertionAt this stage of development (early 1967), the rendezvous profile became es-sentially standard in relation to the landing site (or lighting). For the original three-impul se coelliptic sequence, the TPI had been scheduled at a fixed longitude (forexample, 30' E ) re ga rd le ss of the landing-site longitude. The emphas is on groundtracking assistance was changed fro m post-TPI to Pre-TP I as it was rea lized that the

pre-TPI assistance would be of the most value. Detailed analy sis concerning the

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termina l phase showed that the most favorable TPI lighting (TPI at 20 minutes beforedarkness) and the most favorable terminal-phase CSM tr av el angle (130" were notbeing used; therefore these optimum values were incorporated . An explanation of thechanges is included lat er in the report.A s the hardware char acteri stics became more clea rly defined and as the planningbecame m or e operationally or iented (early 1968), the RCS (that of the LM and, fo r there sc ue sequence, that of the SM) wa s found to contain insufficient accele rat ion capabilityto perfo rm rendezvous fo r the la rg er differential heights associated with the nominallaunch window. Furthermore, a significantly higher apolune insertion orbit was notadvisable because of a diminishing APS propellant margin . Also, fo r certain disper-sions, the rendezvous- ra da r range limit (400 nautical mi les) would be exceeded duringthe early pa rt of the rendezvous. The solution for these problems was a lower CSMparking orbit; therefore, the planned parking orbit w a s decreased f rom 80 to 60 nauti-cal miles . The lowering of the CSM orbit yielded smaller relative ranges and de-cre as ed the nominal LM RCS requirement. In addition, it decrea sed the requirementsfo r the descent propulsion sys tem fo r the landing phase and for the APS fr om an LM

abort standpoint. The associated elimination of the requirement for the nominal(4- to 5-minute) launch window essentially bounded the acceptable coelliptic Ah to lessthan approximately 25 nautical mi les (allowing predic table dispersions) and, therefore ,alleviated the RCS problems of both the LM and SM. Because the Ah variat ion w a ssmall, the CSI-to-TPI time line became more standardized. Otherwise, the time lineand maneuver logic remained essentially unchanged.However, as the NASA Lyndon B. Johnson Space Center (JSC), formerly theManned Spacecraft Center (MSC), began to develop the detailed procedures for the ren-dezvous t ime line (mid-1 968), the insertion- to-CSI and CSI-to-CDH time differences we refound to be too short. A plane-change capability somewhere between insert ion and TPIw a s al so necessa ry to avoid possible la rg e out-of-plane maneuvers during the terminal

phase.Extended CSI/CDH coelliptic sequence: The extended four-impulse CSI/CDH co-elliptic sequence mainly involved inc re as es in the A t between maneuvers and a forcednew nominal lighting requi rement for TPI. This extended sequence resulted in thefollowing changes.1. The insertion-to-CSI A t w a s increased to 50 minutes.2. The A t between CSI and CDH nominally resul ted in an incr ease to approxi-mately 50 minutes.3. The initiation of a nominally ze ro plane change was scheduled for a separateplane-change maneuver (PC) at 90" (approximately 29 minutes) before CDH, and theplane change was to be completed i n conjunction with CDH.4. The T PI lighting was necessa rily delayed (to the midpoint of darkness) becauseCDH now was scheduled only a f ew minutes before the previous TPI time. Although thisnew TPI lighting was not totally optimum, it was considered to be a reasonable trade-off f or th e extended time line.

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The longer insertion-to-CSI A t afforded a more accu rate CSI because platformalinement and additional tracking then could be performed before CSI. The platformalinement was originally scheduled after CSI. The pre- termina l-phase plane-changecapability could result in a nearly coplanar terminal phase even when out-of-planedispersions existed at insertion.

Further dispersion analyses in la te 1968 disclosed that the A t between CSI andCDH could decrease sharply for certain dispersions when CDH w a s performed at thefirst apsis af ter CSI, which had been the maneuver logic to thi s time. Furth ermor e,a plane-change completion at CDH could result in a AV vector that was primari ly outof plane, and such a maneuver would be especially costly as compared with combiningeither the initiation or completion of the plane change with a sizable in-plane maneuver.To standardize the time line between CSI and CDH re ga rd le ss of dispers ions , theoption to perform CDH one-half per iod a f te r CSI (instead of at the first apsis after CSI)was incorporated into the planning. Then, to avoid a relatively lar ge radial AV at CDH,CSI was scheduled at t h e apolune of the 30- by 10-nautical-mile insert ion orbi t (55 min-ut es after insertion). The plane change was initiated in conjunction with CSI and com-

pleted at PC, because this procedure was mo re economical than the PC/CDH planechange. When a sizable plane change was required, the CSI AV normally was signifi-cantly la rg er than that for CDH.A s the crew began rendezvous simulations, the relat ive range at the beginning ofthe desired very-high-frequency (VHF)-ranging t racking period before CSI was foundto be outside the VHF-ranging limi t. In addition, the nominal 33-minute A t betweenCDH and TPI w a s approximately 5 minutes sho rt er than desirable, considering possibleea rl y slippage caused by predictable navigation and maneuver dispersions. Termina l-phas e initiation was performed when the nominal elevation angle occurred, inst ead ofprecisely at the pre-lift-off nominal time, and the tim e of occurrenc e of the nominalelevation angle could vary f rom the nominal TP I time because of dispersions.Final CSI/CDH coelliptic sequence: After two additional signif icant changes, thedevelopment of the four-impulse CSI/CDH coellip tic sequence, as flown fo r Apollo 11and 12 , the first tw o lunar-landing missions, and as planned for Apollo 13, was com-plete . Insertion into the 45-nautical-mile apolune orbit corrected the VHF-tracking-range problem by decreasing the relat ive range at lift-off and did not in cr ea se thepredictable d ispers ion situation. Nominally, then, CSI was performed at the desiredcoelliptic Ah of 1 5 nautical miles , and CDH was a very small maneuver (theoreticallyzero if the CSM orbit were perfectly ci rc ul ar and no previous dispersions existed).To increase the A t between CDH and TPI by approximately 5 minutes without nom-inally delaying TPI, an upward radial component of approximately 30 fp s was ta rgeted

for insertion. The A t between insertion and apolune (and therefore CSI) was therebydecreased by approximately 5 minutes, as CSI was retained at apolune. Because theCSI-to-CDH A t was essentially fixed, the 5 minutes we re added to the CDH-to-TPI A t .

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The CDH-to-TPI A t was not adjusted sim-ply by delaying TPI because.a t that timeit was thought that a 5- to 6-minute delayin the nominal TPI ighting combined witha delay caused by predictable dispersionswuuld resul t in unacceptable final-approachlighting. An inerti al sketch and maneuver-sequence data representing the final CSI/CDH coelliptic-sequence technique areshown in figure 2. The final nominal CSI/CDH coelliptic sequence afforded a highprobability of achieving a standard termi-nal phase, fr om the standpoints of relativemotion and lighting considerations, regard-less of the occurrence of predictable dis-persions. However, the most undesirablefactor of the CSI/CDH coelliptical sequencewas the relatively long duration from inser-tion to intercept. The nearly perfect pow-ered ascents and rendezvous of Apollo 11

/- CSM at60 n. mi.circular

Nominalrendezvousmaneuver

Insertioncs ICD HTPITerminal braking

4514545145

RCS 611456016Ll

Iand 12 significantly increased the-confi- ahom LM lift-off.dence in the hardware and sys tem s perform-ance. Therefor e, ser ious consideration bApproximate operational braking total.was given to designing a technique thatwould significantly shorten the rendezvouswhile maintaining the s tandard (relativelylow- ate) terminal phase.

figure 2. - Representative Phasing-orbitCSI/CDH coelliptic sequence technique.Short rendezvous technique. - The two-impulse sho rt rendezvous technique w as

initially proposed and basically designed by the Apollo 15 crewmen, who began exper-imenting with it during simulations before Apollo 14. The technique was adopted forApollo 14mainly because it removed one revolution of approximately 2 hours durationfr om the rendezvous and, therefore, from the rendezvous day, which had lengthened(using the coelliptic sequence) to 23-1/2 hours. Although the Apollo 15 rendezvous daywas not quite as long and the final activi ties were not quite as demanding, the shortrendezvous w a s incorporated because of it s successful application on Apollo 14.

The s ho rt rendezvous technique involved a precisely timed insertion into the orbitfor which the nominal TPI off set conditions would resu lt at t h e des ired lighting position.The insertion-orbit apolune altitude was between 45 and 50 nautical miles, and the A tbetween insertion and TPI was between 38 and 45 minutes. These par ame ter s were afunction of the lunar s tay time and the exact CSM orbit for the particular mission. A sdiscussed previously, the nominal TPI lighting wa s delayed several minutes to allowsufficient time between insertion and TPI. Furthermore , because the LM orbit beforeTPI vas not coelliptic with the CSM orbit, the TPI maneuver was not a line-of-sight

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maneuver and w a s la rge enough to be per-formed accurately by the APS. BecauseTPI was no longer a line-of-sight maneuver,it was performed at the pre-lift-off nom-inal (fixed) time re ga rd le ss of predictabledispers ions. The major portion of thepredictable insertion di spersions could beabsorbed by an RCS tweak maneuver,used in combination with TPI, performed2 to 3 minutes after inse rtion. Shouldunexpectedly la rg e dispersions o r sys-te ms failures during the powered ascentrender the short rendezvous unsafe, abailout to a coelliptic sequence rendez-vous would be initiated at approximately5 minutes after insertion. In fact, amajor factor i n the adoption of the s hor trendezvous was the convenient bailoutcapability to the flight- tested coellipt icsequence. Should cer tain nonnominalsituations occur before LM lift-off, thecoelliptic-sequence rendezvous thenwould be flown from lift-off. An iner-tial sketch and maneuver- sequence datarepresenting the short rendezvous tech-nique a r e shown in figure 3.

InsertionTP ITerminal braking

//\

\

a 7 - APS 461943 b45 R C S a1a45

73 APS 61145

Y\TerminalI raking/'Insertion\ /-1\

...... i

Figure 3. - Representative sh ortrendemous technique.Terminal P hase

Early in rendezvous development, the major objective became a standard finalapproach that, regar dless of predictable dispersions, would be within the capability ofthe RCS and could be controlled manually with reasonably standard techniques and pro-cedures. Some of the terminal -phase considerations and require ments changed as thebasic rendezvous technique changed, but the ultimate objective, the standard final ap-proach, remained throughout.Standard approach. - The angular geometry and ine rti al line-of-sight rates forstandard approach were designed to be constant o r standard reg ard les s of dispersions.The Ah requirements at TPI or the AV requirements could change but were expectednot to vary more than 20 to 30 percent f ro m the nominal values. The maintenance of

standard angular geometry and nearly zer o inerti al line-of-sight rates allowed thefinal velocity match to be achieved by manually controlled braking maneuvers directedalong the line of sight to the targe t vehicle. The braking maneuvers were based onrange/range-rate gates and gradually decreased the relative velocity to zero. Fo r thenominal f i n a l approach, the LM cr os se d approximately 4 nautical mi le s below the CSMand then advanced approximately 1 / 2 nautical mile i n fro nt of the CSM as it matchedthe altitude of the CSM.

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Central trav el angle. - The target vehicle cent ral trav el angle Cp was selected asa trade-off between the in-plane AV situation and the possib le out-of-plane AV situation.The AV-optimum Cp for a totally in-plane situation would be nearly 180". However,when an out-of-plane angle existed, a nearly 180" Cp became very expensive. The re -fo re , to ens ure avoidance of a significant out-of-plane penalty, the Cp had to be at least30" to 40" le ss than 180'. However, if the @ was shortened to le ss than approximately120', the in-plane AV penalty again became large, and the terminal-phase time linewas impacted seriously. The initial compromise fo r Cp was 140". However, when theinertia l line-of-sight ra te during the final approach w a s found to be nea re r z er o and,therefore, easier to control for a @ of 130", the 130" @ w a s incorporated. This@ has been flown for all Apollo rendezvous to date, including the coelliptic sequenceand sho rt rendezvous.

Differential height at TPI. - To avoid visual lo ss of the ta rge t vehicle, the RCSsystem would be required t o perform the braking. Therefore, the nominal Ah at TPIw as selected so that, for predictab le dispersion, braking would rema in within the RCScapability and would not become extremely difficult as a manual operation. This nomi-nal A h value was s et at 15 nautical mile s, and the dispers ion range on the A h was ap-proximately *7 nautical miles .25 nautical miles, the braking would be hard to control with the RCS, especially that ofthe SM. If the Ah became less than 7 o r 8 nautical miles, the sensitivity to dispersionsinvolving low closing rates increas ed rapidly.

If the A h became greater than approximately 22 to

The TP I maneuver direction and timing. - Ear ly in rendezvous development, it wasdecided to incorporate the Gemini-initiated line-of-sight thrusting TPI (that is, the di-rect ion of the AV vector wa s approximately along the line of sight to the targ et vehicle).Th is type of TPI, when applied from the coelliptic-orbit situation, w a s not only nearlyoptimum f ro m a AV standpoint and afforded the desired angular geometry dis cussed pre-viously, but it al so afforded a manual backup technique. If no computer solution wa savailable, a AV proportional to the estimated Ah applied in the direction of the ta rgetvehicle wouId effecta near-in terc ept trajectory. When the sho rt rendezvous techniquewas incorporated fo r Apollo 14, the line-of-sight TP I was one of the trade-offs fo r thequicker rendezvous. Because TP I now was performed with the LM in th e elliptical in-sertion orbit, the TPI AV vector was not along the line of sigh t, but, because of a rela-tively lar ge radia lly down AV component, the AV vector direction was below the forwardhorizontal. Moreover , because of the increased magnitude of the TP I burn (70 to 90 fps),the decision was made to us e the APS for execution of the burn. Previously, fo r thecoellip tic-sequence plan, no nominal plan existed fo r relighting the APS because thelargest maneuver, which was CSI, was only 40 o 50 fps.

For the coellipt ic sequence, TPI was actually executed when the nominal angula rgeometry (elevation angle to the targ et vehicle) occurred and not neces sarily at the pre-cise pre-lift-off nominal TPI time. Because of smal l e r ro r s in navigation or small dis-pers ions in the intermedi ate phasing maneuvers, the occurrence of the nominal elevationangle could slip seve ral minutes either early or late from the nominal TP I time. Byexecuting TP I at the nominal elevation angle (nearly line-of-sight burn), the nominalangular geometry re sult ed throughout the termina l phase. However, when the switchto the sh or t rendezvous technique was made and the line-of-sight TPI was discontinued

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anyway, TPI a lway s was performed at the pre-lift-off nominal TP I time. This fixed-time TPI increased the sensitivity t o dispersions of the final approach, but the approachlimi ts fo r an acceptable final approach were broadened significantly.Lighting. - Initially, the lighting requirements fo r the terminal phase mainly in-volved TPI because the final braking occurred in darkness. The TP I was scheduled at

approximately 20 minutes before darkness, a position which optimized pre - and post-TPI tracking. Braking in darkness was no problem because of the LM tracking light andtwo ranging devices, the rendezvous ra da r on the LM and the VHF ranging on the CSM.Therefore, a triple failure would have had to occur before the braking in darkness wouldnot be feasible.However, when the extended coelliptic sequence was incorporated, the nominalTPI lighting was necessar ily delayed. The second choice fo r TPI lighting was at or nearthe midpoint of darkness, again because of tracking considerat ions . In addition, thelighting f o r braking (now in sunlight) became a factor because, if the TP I slipped lat erthan approximately 1 2 minutes, the LM crewmen would be forced to look dir ectlyinto the sun during par t of the fina l braking. The TPI o r terminai-phase lighting became

a compromise between acceptable tracking around TPI and avoidance of sun interferenceduring braking.When the short rendezvous was incorporated, the T PI lighting w as delayed approx-imately 7 minutes to allow a more acceptable At between inser tion and TPI. This delayw as not cr itical to the braking lighting because of the assoc iated fixed-time TPI.Midcourse corrections. - Terminal-phase nominally ze ro midcourse corre ctionswe re scheduled at approximately one-third and two-thirds of the way fr om TPI tobraking. If a maneuver was required to cor re ct the trajecto ry, the initial interceptposition and time we re targeted normally. If a major dispersion had caused the pre-dicted brakilig maneuvers to become unacceptably la rge, one of the midcourse maneu-

ver s would be used to dela) the intercept and thus de cre ase the braking AV. Thisdelaying technique was referred to as TP12.

DEVELOPMENT OF L M ABORT AND RESCUE PLANFrom the beginning of the development of the abort and re sc ue plan, the pr im ar yemphasis w a s on the powered descent and the period immediately af ter landing. Thesewe re considered the most probable phases in which an abort could occur. Considerableplanning also was devoted to fa il ur es associ ated with the LM-active Hohmann descent,

to cases of no-powered-descent initiation, and to correct-phasing LM asce nt s beforeo r af ter the nominal lift-off revolution. Ear ly program contingency planning al so in-cluded LM lift-offs for any time (without co rr ec t phasing) and in time-c rit ical situa-tions; however, because realistic single-failure ca se s we re not identified f or thesesituations, operational planning was limited.The oi-iginal abort and rescue maneuver zequences, beginning in 1964, were ex-tremely complex because of the limited onbaard capabilities. Fo r example, f o r an abor toccurring any time during powered descent, the LM was tar geted fo r a constant inser-tion orbit. Theref ore, seve ra l abor t reg ions existed, and the rendezvous technique

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varied fop each. For ear ly aborts , the LM final approach to the CSM w a s from above;for a la te r region, one-and-a-half revolutions were requi red between CSI and CDH in-below the CSM. Because of the complexity in the abo rt plan, the rescue plan w a s alsocomplex. The CSM did not have the CSI/CDH logic on board, and the command modulepilot had to depend ei the r on the ground o r on the mir ro r- image technique (that is, themethod by which the CSM applies the LM-computed maneuver essentially in the oppositedirection). The pri mar y rescue technique fo r bad-phasing situations w a s the six-impulse technique, whereby the CSM transfer red to a 20-nautical-mile cir cul ar orbitby means of the first two maneuvers , and then adjusted the phasing, became coelliptic,and executed the terminal phase (theoret ically, with two impulses) by means of the lastfour maneuvers.

stead of the normal one-half revolution; and, fo r late abor ts, the LM approached from

In ear ly 1968, analyses fo r the incorporation of several powered-descent-abortinsertion orbi ts (to vary as a function of abor t time reg ions) were begun. This workevolved by late 1968 into the variable-targeting concept. According to this technique,the corr ect insertion orbit, that would result in an LM approach from a coelliptic Ah of15 nautical mil es below the CSM, could be targeted f or all abor t times during the first10 minutes of powered descent. For an abort after 10 minutes, a constant 30-nautical-mile apolune insertion orbit w a s targeted; however, an in-orbit phasing maneuver (de-rived by the use of onboard programs in conjunction with onboard cha rt s) permitted thestandard LM approach from below (although one additional revolution w a s required).dezvous) replaced this phasing region for abor ts occurring after 10 minutes. Thevariable -targeting concept originally w a s thought not to be feasible because of the soft-ments, the technique was deemed feasible, and implementation began in ear ly 1969.

For Apollo 12, a second variable-target ing region (by means of a two-revolution ren-

ware requirements involved; however, after a detailed analysis of the pre cis e requ ire-

The variable targeting led to simplification and standardization of the abo rt andrescu e plan. The same basic technique now applied to almost a ll LM-active cas es .Therefore , the rescue techniques were standardized; for example, fo r a CSM-activete rminal phase , the CSM would always approach the LM from above.By t h i s time, the CSI/CDH logic had been placed on board the CSM, and an inde-pendent onboard rendezvous solution fo r the coelliptic sequence could be determined in

the CSM. This technique great ly improved the CSM support of any rendezvous sequenceusing CSI/CDH logic. Spacecraft independence w as emphasized because of the uncer-tainty in the lunar potential; therefore, nearly all rescue plans involved no mor e thanone exte rnal (ground) maneuver. When correct phasing existed initially, no externalmaneuver w a s requi red. The addition of VHF-ranging capability to the CSM c-nsuredfu rt he r independence and confidence. A s indicated previously, the VHF- ranging addi-tion al so affected the nominal development.

The original rescue AV budgeting philosophy, which remained unchanged throughApollo 13, was to allow re scue within the normal LM (ascent stage) lifetime for all fea-sible re scue situations. However, to allocate a greater AV budget for nominal objec-tives, the resc ue AV budget for Apollo 14 and subsequent missions had to be lowered,so that re sc ue f or ce rta in possible situations required powering down the LM to a min-imum life-support condition. However, the rescue situations that would requir e suchminimum power conditions were extremely improbable.

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Beginning with Apollo 13, the abort and rescue plan changed somewhat because ofthe change to the nominal plan (landing one revolution l ater rela tive to the main LM /CSM separation). However, the or de r of the occurrence of the regions (one-revolutiono r two-revolution rendezvous) was the only significant change. The bas ic techniqueswere the same. The final plan was not simple; but, compared with the plan approxi-mately a year before Apollo 11, the final plan was considerably simp ler and al so morestandard.

EVOLUTION OF APOLLO RENDEZVOUS DIS PE RS ION PRO GRAMREQU IREMENTS, DEVELOPMENT, AND ANALY S ISR e n d e z vo u s -D i s pe r s io n - A n a l y s i s P r o g r a m R e q u i r e m e n t s

F r om the beginning of the Apollo Program, dispe rsion analyses were essent ia l fo rall phases of each Apollo mission, particula rly for the rendezvous phase. The disper-sion analysis was required to aid in defining the nominal propellant budget, in establish-ing mission rule s and crew procedures, in defining constraints, in selecting themaneuver sequence that would give the highest overall probability of success, and inverifying general ground and onboard progr ams .

To develop a dispersion-analysis prog ram, careful consideration must be givento establishing the detailed program requirements fo r the overall dispersion-analysiseffort fo r any mission phase. These requirements come fro m many a re as and req uir ea reasonable amount of coordination. For the Apollo Program, most of thes e require-ments came fr om the support of mission-rules development, crew-procedures develop-ment, onboard-chart development, simulations, and propeliant budgeting.The rendezvous-dispersion-analysis progr am r equi rements fo r the Apollo Pro -

gr am were not outlined in the detail required f or an efficient progr am development ef-fort. This was partially because of a lack of knowledge of program objectives andpart ially because of the manner in which the responsibility for thi s effort w a s assigned.Thes e two problems resulted in significant tim e and manpower los se s.

Re n d e zvo u s -D i sp e r s i o n -An a l ys i s P r o g r a m D e v e l o p m e n tIn developing the rendezvous-dispersion-analysis program and in performing theanalysis itself, numerous problems had to be resolved. One of the first important tasksin developing a program of thi s t pe is to establish, in the ear ly development stages,

is selected should be responsible fo r the detailed miss ion planning and the trajector yanalysis for the particular mission phase because the dispersion analysis coincideswith the mission planning and the trajectory analysis work and requires similar skills.

the responsible organization for rhe detailed dispe rsion analysis. The organization that

In the Apollo Program, the responsibi lity was not initially ass igned to the organ-ization responsible for the detailed mission planning but instead was assigned to theorganization responsib le for developing the onboard guidance. The latter organizationpossessed little understanding of the detailed rendezvous techniques and associa teddispersion problems. A significant amount of manpower and ti me was lost in the

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attempt to complete the required program development in an operationally timely man-ner . When the responsib ility was reass igned to the organization doing the detailedmission planning and traj ectory analysis , the situation improved, manpower expendi-tu re s decreased, and, most important, the analysis was completed in a timely manner.Tlie main reason for th is improvement was that, to perform a detailed dispersionanalysis on a mission phase, a knowledge of the detailed mission-planning aspects andthe trajector y analysis of the phase was more essential than a detailed knowledge ofthe guidance and control mathematics and systems.

Official data tr an sf er between organizations should be re st ri ct ed mainly to thetype of data that does not change with every minor miss ion change o r procedureschange. This type of data should be generated internally in the program, if possible,and detailed verificat ion checks should be made on these data, as required, with theorganization o r organizations responsible fo r the data. In this way, miss ion and pro-cedure changes receive a timely response . Otherwise, interfaces tend to delay thecompletion of the analysi s.Caref ul consideration should be given to the construction of models in the pro-

gram. Complicated modeling should be used only when necessa ry, especia lly whensimple models, which usually a r e acceptable from an operational standpoint, wi l l suf-fice. This modeling problem usually can be resolved by consulting the groups or or-ganizations that have the technical skill i n these areas. Consideration also should begiven to the operational accuracy requirements of t h e data; fo r example, eight-digitaccuracy is needless when two- o r four-digit accuracy is acceptable.Pr og ra m inputs must be kept simple and logical, s o that the engineer running theprogram can make expedient changes to the program input without the assistance of aprog ra mer. Apollo experience also was indicative that covariance matrices are highlyeffective for those a re as in which minor mission o r procedure changes do not changethe basic dispersion. Covariance mat ric es ar e especially useful in the trans fer fro m

one mission phase to another.The actual p rog ram should be developed by personnel who a r e knowledgeable inthe particular mission phase that is to be considered. The basi c progr am should beflexible, and the us e of engineering simulations of both the onboard targeting and thenavigation and ground targeting programs should be detailed. This pro cess saves con-siderable program-development and verification time because the accuracy with whichthe onboard and ground pr og rams have been simulated is always a concern. If short-cuts are taken, some important area can be missed, and the correcti on of the oversightcan be ti me consuming. Apollo experience also proved that solving probl ems by known"brute force" methods, even if they involve significant additional machine time, isbe tt er than attempting to use untried sophisticated methods. When a tight schedule isinvolved, untried techniques are especia lly inappropriate because development of thesetechniques generally involves the expenditure of much money and engineering time, andthe techniques still have to be veri fied by a detailed simulation. Detailed documentationon the prog ram should be kept current. The program a l so should be programed in aprograming language that can be easily understood and changed by eithe r p ro gram er so r engineers.

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To perform the Apollo dispers ion analysi s, programs were developed that includedengineering simulations of spec ific spacecraft , Real Time Computer Complex (RTCC)rendezvous targeting and navigation programs, and various sy st em s models. Thesemodels included the engine guidance systems, spacecraft accele rometers , spacecraftplatform, rendezvous radar, sextant, and VHF tracking. A ll major er ro r sourcesassocia ted with each model in te rms of dr ift, bias, and noise were included. From thestart of Apollo 7 o Apollo 11, four different program development effo rts were under-taken fo r various reasons, which resulted in the existence of two operational rendezvous-dispersion-analysis programs by Apollo 9. One program, the lunar ascent andrendezvous program, which w a s being developed by a support contractor, was droppedbefore Apollo 7, and the in-house program developed to replace it became the prim eoperational program. The other operational program, a general Apollo dispersion-analysis program, wa s developed on the same support contract and actually underwenttwo different development stages , each of which was considered as a different programdevelopment. Parts of the general Apollo dispersion-ana lysis pr ogram we re droppedafter Apollo 7, but some pa rt s of that program-development effort wer e used to developthe remaining contrac tor operational program. The two operational pr og rams werenecessa ry to cross-check the data obtained fr om each program. This pr oces s provedhighly beneficial in verifying the operational data and improved the overall probabilityof mission success .

By the Apollo 11 mission, the nominal rendezvous dispersion analysis w a s per-formed similarly in both the in-house and contractor programs. However, the pr imein-house program wa s more ve rsatile and could perform dispersion analysis on anyrendezvous profile that the onboard o r RTCC sy st em s could fly. The contracto r pro-gr am basically was designed around the nominal mission prof ile and was developed byan independent source . Therefore, the er r o r model in the contractor's program wasnot identical to the error model in the in-house program.The dispers ion-analysis program development evolved fr om the mission planning

for each rendezvous mission, with the contractor progr am following the nominal devel-opment, and the in-house program following both the nominal mission planning and theLM abort and rescue planning. The in-house dispersion-analysis program ultimatelyacquired capabilities that were necessary to keep pace with and support the mission-planning effort. Therefore, the in-house pr ogram became the prime tool for dispersionanalysis.

P e r f o r m a n c e of R e n d e z v o us D i s p e r s i o n A n a l y s i sIn performing the dispersion analys is on each development mission preceding thelunar landing mission, different er r o r so ur ce s and inputs had to be considered for each

mission. Obviously, Apollo 11had the most complex se t of e r r o r sou rce s and inputs.On Apollo 7, only one maneuver so ur ce (RTCC maneuver solution) up to TPJ and twomaneuver sources (RTCC maneuver solution and command module computer maneuver

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solution) fo r TPI were used. A s many as four computer-maneuver so ur ce s (RTCC,command module computer , LM guidance computer, and LM auxiliary guidance s y s -tem) fo r specific maneuvers were used on Apollo 11.Initially, the RTCC, with the aid of ground tracking fro m the NASA Manned SpacFlight Network (MSFN), was considered to have the most relialjle maneuver solution,

especially for the earth-orbit missions. Therefore, it was used as the standard withwhich to compare the other solutions and was executed if the other solution or solutionsdid not compare within a given tolerance. However, fo r the lunar-orbit missions , theMSFN could not tr ack the spacecraft and determine their orbi ts fo r the rendezvous com-putation as well as it had been able to tra ck them in ea rth orbit. Thus, the spacecraftonboard navigation and maneuver computation became the p ri me sour ce f or therendezvous-maneuver solutions. With the change in the RTCC accuracy of themaneuver-solution sources w a s a high degree of confidence in the onboard sy st em s thathad been obtained during the earth-orbita l development flights. Therefore, therendezvous-maneuver solutions went from basically RTCC control on Apollo 7 to space-craf t onboard control on Apollo 11and subsequent flights. During the rendezvous devel-opment phase, the dispersion analysis also was used to assist in establishing theonboard navigation schedules and to establish and verify onboard procedures, crew timelines, and mission rules.

Apollo Pr og ra m experience has emphasized the need throughout mission planningfo r dispersion-analysis information. Therefore, an effort to provide dispersion-ana lys is information and support from the conception stage of the miss ion to the actual.flight must be made. The level of detail wi l l vary throughout miss ion planning, withthe most detailed and complex work being done on the operational trajec tory . Thiswork must be sta rted ear ly in the mission-planning stage so that timely inputs to theplanning effort are possible and trajectory and procedure changes are minimized.

SI G NI F IC AN T DEVELOPMENTAL CONTR IBUTIONSOrgan izat onal Contributions

The development of acceptable rendezvous techniques was the resul t of direct ion,coordination, analyses, and inputs f r om seve ral areas. Most of the tra jectory designand analys is was perfo rmed by mission-planning specia list s at the Manned SpacecraftCenter . During the planning of the Gemini rendezvous missions, seve ra l of the astro-nauts becztme actively involved in the rendezvous planning, and thei r ideas contributedsignificantly t o the initial development of the coelliptic sequence. A s the Gemini Pro -gr am near ed completion, sever al specialists familiar with Gemini procedures becameinvolved in Apollo design work and made valuable contributions.

The orig inal officia l centerwide interface involving the rendezvous developmentwas accomplished by the Flight Operations Panel. This panel was responsible for thecoordination of the const raints and requirements involved in the Apollo mission planning.La te r, the development of the detailed techniques was coordinated through the data-priority meetings.

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Some of the most important inputs during the year before Apollo 11 came fromareas directly involved with the crew procedures, training, and simulations. Many in-dividuals fr om the flight-crew, flight-control, and guidance and control areas contrib-uted significantly to the design of the Apollo rendezvous techniques.As the first unar-landing mission approached, an increasing number of peoplebegan working on the planning effort, and the hardware and software constra ints and

capabilities were defined concre tely. As a result, the rendezvous planning becamemore detailed and prec ise . Although se ve ra l minor changes wer e made to the tech-niques, no major changes to the nominal or contingency rendezvous plans occurredduring the l as t 6 months before Apollo 11. Furthermore, the only subsequent majorchange to the basic techniques w a s the change to the quicker short rendezvous techniquefo r the Apollo 14 and 1 5 nominal plans.Organizational fa ct or s and developments for the dispersion-analysis developmenthave been discussed previously. The most significant organizational development inthis a rea was the decision to give the responsibility and control of the rendezvous dis-persion analysis to the rendezvous specialists.

C o n t r i b u t i o n s f r o m F l i g h t E xp er ie n ceAs the Gemini rendezvous flights were flown, considerable information was intro-duced into the Apollo rendezvous planning, especially in rela tion t o the te rm in al phase.The actual flight rehe ar sa ls of the coelliptic sequence during Apollo 9 and 10 contrib-uted valuable data. Although a coelliptic rendezvous had been flown in the Gemini Pro-gram, the LM hardware and software wer e tes ted in actual flight fo r the first time onApollo 9 . The LM was positioned away from (above and behind) the CSM so that, be-ginning at CDH, the re lat ive motion and various r ela tive rates were essentially thoseplanned f o r the lunar-landing-mission rendezvous.The Apollo 10 rendezvous, a portion of the first LM performance in lunar orbit,actually included a relative-motion profile tha t was an almost exact model of the lunar-landing- mission rendezvous beginning at inse rtion. Although the LM w a s considerablyheavier during the Apollo 10 rendezvous than during the lunar-landing mission andtherefore the burn durations and handling quali ties wer e different, the information andconfidence gained were extremely valuable. The experience gained on Apollo 10 e-garding flight-control interface and the development of the LM abor t and re sc ue plan

considerably simplified the corresponding Apollo 11 situations. Other valuable informa-tion came fr om the operation of the LM and CSM navigational sys te ms in the uncertainlunar potential.

CONCLUDING REMARKS AND GENERAL RECOMMENDATIONSFO R RENDEZVOUS P LA NN ING FOR FUTURE PRO GRA MS

For the Apollo lunar-landing missions, the change of the nominal rendezvousplan from the direct-ascent rendezvous technique to a four-impulse phasing-orbit (co-elliptic sequence) technique was necessary to ensure a standard, manually executabletermina l approach. After the fi r s t two lunar landing miss ions, the change to .the two-impulse short rendezvous technique oc cu rr ed because of the significantly inc rea sed20


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confidence in the sys te ms and procedures resulting from actua l lunar flight experienceand because of the availability for a fallback to the familiar coelliptic sequence for con-tingency situations.Some of the most important factor s affecting the total rendezvous-plan evolution

.were the implementation of the variable targeting fo r powered-descent ab or ts in thelunar module descent program, the implementation of the coelliptic-rendezvous maneu-ve r sequence in both the lunar module backup guidance system and the command andse rv ice module pri ma ry guidance system, and the implementation of the very-high-frequency ranging on board the command module.Several problems had t o be corrected t o assu re a successful rendezvous disper-sion and tra jec tory analysis, These problems included the lack of precisely defined re-quirements fo r the overall analysis, the lack of proper interfaces with other respons ibleorganizations, the lack of computer-program flexibility and documentation, and the ini-tial assignment of the dispersion-analysis responsibility t o an organization not posse s-sing rendezvous skill.The following recommendat ions are divided into the main a r ea s of considerationdiscussed in the body of the repor t. Most of the recommendations should apply to ren-dezvous in almos t any situation, wherea s a few of the recommendations would applyonly for rendezvous conditions s im il ar to those in lunar orbit.

Nominal Launch WindowThe recommendations that apply to a nominal launch window relative to a surfacevehicle and an orbiting target vehicle are as follows.1. If the target vehicle has the capability of performing a plane change and aphase change to make its orbi t nearly coplanar with the surface vehicle when the opti-mum lift-off phasing exists, a launch window of only a few seconds is adequate fornominal considerations. Changes in lift-off revolution can also be handled by the plane/phase change capability.2. A planar situation should be planned that wi l l allow a revolution-late lift-offwithout a n additional target-vehicle plane change and with a minimal plahe change forthe ascending surface vehicle.

Base OrbitsThe recommendations that apply to the design of base orbits are as follows.1. The target-vehicle parking orbit should be based on both nominal and abo rt

situat ions, considering ranging and incremental-velocity capabilities of both the targetvehicle and the surface vehicle.2. If not prohibited by other considerations, a ci rcu la r target orbit should be

applied because of the simplification in rendezvous software and procedures .

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Maneuver S eq ue nceManeuver sequence in general. - The recommendations that apply to the maneuversequence in general (that is , nominal o r abort and rescue) a r e as follows.1. Dispersion-absorption and phasing capabilit ies should exist that will allow a

standard terminal phase, especially if the final approach is to be manually controlled.These capabilities may be as simple as a two-impulse tweak sequence if the initial sit-uation is nearly nominal; however, if la rg e dispersions o r nonnominal phasing initially.exists, the capabilities should involve sever al maneuvers at approximately half-revolution increments to avoid excessive propellant usage. The coelliptic-sequencerendezvous should be a prime candidate fo r this latter situation.2. There should be adequate time between maneuvers to allow fo r r equi red tr ack-ing, alinements, and maneuver preparation.3. The difference in tim e between a given pair of maneuvers should be as con-stant as prac tical to allow standardization of procedures.4. When elliptical orbits are involved, maneuver s should be near the line ofapsides to optimize incremental-velocity usage.5. The initial in-orbit maneuvers for the ascending surfa ce vehicle should be de-signed not to lower the insertion-orbit perigee.6. The sequence should be designed so that as much of the maneuver sequenceas possible is within vehicle-to-vehicle tracking capability.Nominal ascent-rendezvous-maneuver sequence . - The recommendations that

apply specifically to the nominal ascent- rendezvous-maneuver sequence are as follows.1. A sequence that is as short as practic al but allows a reasonable dispersion-absorption capability and a nearly standar d ter min al phase should be applied, especiallyif the incremental-velocity situation is tight and the final approach is to be manuallycontrolled.2. The nominal sequence should allow for a convenient switch to a contingencysequence if large dispersions o r certain failures occur.3. The nominal sequence should be designed to allow backup ground support whenpractical.Abort and rescue maneuver sequences. - The recommendations tha t apply specif-ically t o the abort and rescue planning are as follows.1. The plan should involve as much standardization as possible, and the sequencesshould be as similar as possible to the nominal.2. From a relative standpoint, the te rm inal phase should be nearly identical tothe nominal (for example, the ascending vehicle always approaching fr om below).

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3. . Onboard independence should be stre ssed by designing the sequences to makefull us e of onboard software (with minimum us e of ground-derived maneuvers).4. The sequences al so should be designed to af ford us e of relatively uncompli-cated backup charts.5. Software that involves insertion into the cor re ct phasing orbit f or an abortback to orbit anywhere dur ing the powered descent should be implemented because itaffords simplification and standardization.

Terminal PhaseThe recommendations that apply specifically t o a terminal phase that is man-ually control led and executed with a sm al l reaction control syst em type of propulsionare as follows.1. The approach should be standard from En angular-geometry stzindpoint, andthe various rates should not vary signif icantly from those of the nominal case. Theserates should be lar ge enough to allow crew determination of and reaction to the closingsituation but not s o large as to make the braking maneuvers extremely difficult usingthe relatively s ma ll propulsion system.2. The th ru st er or ientation should allow continuous visual contact between vehi-cl es during the f i n a l approach.3. Although pr ec is e lighting is not critical, the final approach should be designedso that the cr ewmen of the vehicle approaching from below a r e not requi red to lookwithin approximately 30" of the sun while maintaining visual contact with the othervehicle.4. The terminal phase should be nearly coplanar to allow the simplest final brak-ing procedures. This situation should be afforded by designing an in-orbit plane-changecapability before the te rminal phase.5. The terminal-phase-initiation maneuver with the incremental-velocity di rec-tion along the li ne of sight to the target vehicle should receive p rime consideration i f .a coelliptic phase is applied, because it allows standard angular geometry throughoutthe terminal phase and affor dsa convenient manual backup technique for the initiationmaneuver.6. The type of braking, in which the main maneuvering is along the line of sightto the ta rg et vehicle while the inertia l line-of-sight rate is maintained near ze ro shouldreceive pr im e consideration fo r a manually controlled final approach.

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D i s p e rs i o n A n a I s iThe recommendations rela tive t o the development of the dispers ion analys is andthe associated computer program are as follows.1. Dispersion analysis should be involved in the planning as ear ly as possible.2. Detailed requirements f or the dispersion-analysis prog ram and overall analy-

sis should be determined ear ly. .3. Proper interfaces with other responsible organizations should exist.4. Computer-program flexibility and adequate documentation should exist.5. Responsibility for and control of the rendezvous dispersion analysis should beassigned to the mission planning rendezvous experts.

Gene r a I D ve I p rnen a n d 0 gan z a ti na I Con s i e r a ti n sSome recommendations generally rela ting to the development of the maneuverplan and organizational considerations a r e as follows.1. Required inter faces with all disciplines and cooperating organizations shouldoccur as early and as often as practica l. Such in ter fac es definitely should involve, inaddition to the in ter faces with the other mission planning areas, such areas as flightcontrol , flight software, flight crew, f light-crew support, guidance and control , andother areas representing the hardware and science disciplines, The project officesand various panels should organize and cent rali ze these inter faces, but informalworking-level interfaces should be permitted.2. Onboard independence should be stressed in software and hardware design.3. Ground-based backup for all maneuvers and procedu res is desirable butshould not necessarily be a dominant factor if adequate onboard autonomy exis ts.4. Mission simulat ions in the control cent er involving the crew, flight control-l er s, and support personnel should simulate the various mission phases and involve asmany of the potential contingency si tua tions as possible within reasonable manpowerrequirements.5. Actual flight re he ar sa ls testing the hardware and software should be per-formed i f practical.

Lyndon B. Johnson Space CenterNational Aeronautics and Space AdministrationHouston, Texas, April 25 , 1973924-22-20- 0- 2

Documents

Apollo Experience Report Evolution of the Rendezvous-Maneuver Plan for Lunar-Landing Missions