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ABORT PROBLEMS OF THE LUNAR LANDING MISSION

1

2

G. Bartos and A. B. Greenberg Aerospace Corporation, El Segundo, Calif.

ABSTRACT

An investigation has been made of the abort problems associ- ated with the manned lunar landing mission. The abort maneu- vers and propulsion requirements for returning the crew cap- sule to Earth are examined for various phases of the mission, including the Earth-moon transfer, lunar landing, and lunar launch. Particular attention is given to the lunar landing phase for which two types of maneuvers are considered: l) descending to the lunar surface on a steep flight path at the terminus of a lunar Impact trajectory, and 2) landing from a low altitude lunar orbit along a grazing trajectory. The re- sults of the investigation indicate that most of the antici- pated abort maneuvers can be accomplished with the lunar take- off stage. Only those abort maneuvers required during ascent from the lunar surface are found to require the inclusion of propulsion capabilities in excess of those needed to accom- plish the nominal mission. It is also shown that the abort propulsion requirements during the landing phase of the mis- sion can be significantly reduced by initiating the landing from a low altitude lunar orbit.

INTRODUCTION

In recent years considerable attention has been focused on the flight mechanics of Earth-moon ballistic trajectories which result either in lunar impact or circumnavigation (l-4).3 These studies generally have been concerned with defining the magnitudes and accuracies of propulsion requirements needed to achieve such trajectories and have provided a basis for de- signing rocket vehicles suitable for launching unmanned instrument packages to the moon. More recently, increased

Presented at the ARS Lunar Missions Meeting, Cleveland, Ohio, July 1 7 - 1 9 , 1962.

•^Staff Engineer, Performance Analysis Department.

2Head, Performance Analysis Department.

^Numbers in parentheses indicate References at end of paper.

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G. BARTOS AND A. B. GREENBERG

interest has been directed toward the manned lunar landing mission. The previous flight mechanics studies are applic- able to this mission also. However, rocket vehicles for this application must be designed with an awareness of the propul- sion requirements not only to complete the mission success- fully, but to abort the mission at any time in the flight plan as well.

Little information exists defining the vehicle design fea- tures needed to provide abort capabilities during lunar landing missions. The propulsion requirements for abort during the Earth-to-moon phase of the flight have been de- scribed in Ref. 5 for the special case of return from pre- selected "way stations" to prescribed recovery sites on the Earth. Further, the abort problems associated with the ini- tial powered-flight launch phases of the mission have been analyzed in Refs. 6 and 7 · It is the purpose of this paper to define the more general propulsion requirements for returning to Earth from any point in the Earth-to-moon transfer, and during the subsequent lunar landing and launch phases of the manned lunar landing mission.

A variety of flight profiles have been proposed for a manned lunar landing mission. Many of these require that the vehicle first be injected into a circular lunar orbit at a low alti- tude. Descent to the lunar surface is subsequently accom- plished by means of a shallow, grazing trajectory. Although this approach to the lunar landing can be expected to offer excellent opportunities to abort the mission during the land- ing maneuver, it should be recognized that it poses certain navigational problems due to the multiple propulsive maneuvers in the vicinity of the moon, the interrupted opportunities for tracking and communicating with the vehicle from the Earth, and the limited time during the landing maneuver that the landing site is in view of the spacecraft. An alternative method that has been proposed for accomplishing the lunar landing involves approaching the moon on an impact trajectory aimed at the intended landing site. Better tracking and com- munication and simpler navigational requirements are claimed for this approach, because of the continuous ability to observe the spacecraft from the time it leaves the vicinity of Earth until it reaches the lunar surface. However, the choice of landing site is limited by this approach to the side of the moon facing the Earth. Furthermore, the steep lunar approach trajectory for this flight profile suggests that greater pro- pulsion requirements will be needed to effect abort during the terminal phase of the landing. Both of the above types of landing trajectories are considered in this paper, i.e., land- ing from a low-altitude lunar orbit, hereinafter referred to

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as a "parking orbit landing," and landing at the terminus of an Earth-moon impact trajectory, hereinafter designated a "di- rect landing."

DESCRIPTION OF PROBLEM

A large number of variables affect the ultimate choice of flight profile for a lunar landing mission, including such factors as the Earth launch site, date of launch, flight time, launch propulsion, intended lunar landing site, etc. It is beyond the scope of this paper to examine the effects of all of these variables. Instead, a representative set of mission variables has been selected and an investigation made of typi- cal abort conditions which must be considered in planning a manned lunar landing. The results of the analyses then permit generalization to an extent that will be useful in preliminary mission studies.

Trajectory Characteristics

The flight profiles assumed for the studies reported herein are illustrated in Fig. 1 . The spacecraft is launched from an Earth orbit into either a circumlunar or a lunar impact tra- jectory. Orbital elements for these Earth-moon trajectories were established with the aid of a three-dimensional, n-body trajectory simulation programmed for an IBM 7090 digital com- puter. Trajectory calculations were based upon the geometry of the solar system on June 4, 1968.

The circumlunar trajectory is employed for the Earth-moon transfer when a parking orbit landing is to be performed. A

close approach to the moon is desirable for this type of land- ing. Consequently, the circumlunar trajectory developed for use in this study approaches the moon to within 1 8 . 5 naut.

miles at perselenum (i.e., the point of closest approach to the moon). A retrograde maneuver is performed at perselenum, thereby causing the spacecraft to enter a circular lunar orbit at the perselenum altitude. At some subsequent time, a second retrograde maneuver is performed that simultaneously reduces the selenocentric velocity of the spacecraft to zero and the flight altitude to 10,000 ft. The latter condition was in- cluded to represent the standoff height needed to assure clearance of the lunar terrain during the descent and to per- mit final lateral adjustments to the desired landing site.

A circumlunar Earth-moon trajectory also may be used for a direct lunar landing. In this case a propulsive maneuver is required as the vehicle approaches the moon to alter the flight path to that of an impact trajectory. It has been

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G . BARTOS AND A. B. GREENBERG

found, however, that the propulsion requirements for such a maneuver are relatively large except for landing sites chosen

on the leading edge of the moon. Consequently, in this study, the direct landing is accomplished at the terminus of an Earth-moon impact trajectory initially aimed at the intended landing site.

In the case of a direct landing, the choice of landing site will influence the characteristics of the impact trajectory during the final approach to the moon. For example, if the landing site is chosen at an edge of the lunar disk, the

spacecraft will approach the moon on a grazing trajectory. In such cases, the propulsion requirements for purposes of abort will be similar to those required for a parking orbit landing.

For the purposes of this study, however, it was considered de- sirable to investigate the abort problems for a direct landing having a relatively steep final approach trajectory. Conse- quently, a landing site near the center of the lunar disk has been chosen, located on the lunar equator at a longitude of approximately 20° west.

Regardless of the type of landing trajectory employed, it is assumed that the same landing site is chosen. Return to the earth is then accomplished by means of a powered ascent to burnout conditions suitable for returning to the Earth with appropriate re-entry conditions. This phase of the mission is also illustrated in Fig. 1.

More detailed trajectory information relative to these flight profiles is presented in Figs. 2 through 6. Fig. 2 illustrates the variations of geocentric velocity, flight path angle, altitude, and time along the earth-moon circumlunar and impact trajectories. Only one set of trajectory parameters is shown, since the two trajectories are practically identical un- til the vehicle approaches the vicinity of the moon. The in- jection conditions chosen for these trajectories are repre- sentative of those achievable with Saturn class vehicles launched from a low-altitude circular earth orbit. For the circumlunar trajectory the flight time from injection to per- selenum is 62.^3 hr., and from perselenum to earth re-entry is 61.9 hr. For the impact trajectory the flight time from in- jection to impact is 61.63 hr.

Fig. 3 presents similar information for the circumlunar and impact trajectories in selenocentric terms. It can be seen that the velocity altitude characteristics for the two approach trajectories are. virtually identical, and that a maximum ve- locity of approximately 88ΟΟ fps is achieved in both cases.

Significant differences are to be noted, however, in the

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flight path angles for the two-approach trajectories. At per- selenum of the circumlunar trajectory the velocity and alti- tude are 8710 fps and 18.5 naut. miles, respectively. A retrograde deceleration of 3260 fps is required to inject the vehicle into a circular orbit at this altitude.

Figs. 4-6 illustrate the salient trajectory parameters for the powered phases of the mission as calculated for this study. Fig. 4 corresponds to the case of a parking orbit landing whereas Fig. 5· pertains to a direct landing. Fig. 6 presents the trajectory parameters for a launch from the lunar

surface into a trajectory for returning to the earth with suitable re-entry conditions. The powered trajectories, pre- sented in Figs. 4 through 6, were calculated by means of a two-dimensional, point mass trajectory simulation programmed for an IBM 7090 computer. However, the burnout conditions re- quired for the earth return trajectory were established by means of the η-body program described previously. The propul-

sion parameters employed in these calculations were chosen on the basis of considerations discussed in Vehicle Character- istics. The trajectory calculations were based on the use of gravity turns since preliminary studies indicated that only minor performance gains could be realized by utilizing opti- mum steering techniques. The figures present the local tra- jectory parameters as well as the "ideal" velocity V j _ , i.e., the velocity increment achievable by a given rocket in the absence of all external forces. Comparison of the actual and ideal velocities for these descent and launch trajectories in- dicates that the trajectory losses for maneuvers performed in the vicinity of the moon are quite small. Furthermore, it should be noted that with the propulsion parameters chosen for this study the ideal velocity required for the direct landing is approximately 96ΟΟ fps, whereas 9170 fps are required for the lunar capture and descent maneuvers performed in the park- ing orbit landing.

Vehicle Characteristics

At the time the mission vehicle is launched into the Earth- moon trajectory, it is assumed to include two propulsive

stages, one for accomplishing the lunar landing and one for performing the launch maneuver. In order to minimize the weight of the vehicle at that time it is desirable to utilize these stages to the greatest possible extent for meeting abort propulsion requirements as well. For the purposes of this study, it is assumed that both the lunar landing and launch stages employ hydrogen and oxygen as propellants. The landing stage utilizes a pump-fed propulsion system whereas the launch stage is pressure fed. A specific impulse of 420 sec. is

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G . BARTOS AND A. B. GREENBERG

representative of the performance achievable with such propul- sion systems.

Initial studies were made of a number of vehicle designs, each having different thrust/weight ratios in the lunar land- ing and launch stages. The purpose of this preliminary analy- sis was to establish appropriate values for the thrust/weight ratios of these stages. Typical results obtained from the in- vestigation for the case of a direct lunar landing are illus- trated in Fig. 7 · The figure presents the vehicle weight at the time of escape from the Earth as a function of the thrust/

weight ratios of the lunar landing and launch stages. It is clear from the figure that the choice of thrust/weight ratios does not have a strong effect on the total vehicle weight and that the optimum thrust/weight ratios for both stages are slightly less than unity.h

If the lunar launch stage is also to be used for abort pur- poses during a direct landing maneuver, it can be shown that the thrust/weight ratio of the launch stage should exceed that of the landing stage by a factor approximately equal to the mass ratio r, of the landing stage. Thus

(F/W). * [ r ( F/ w ) ]n

v 1 Jlaunch 1 N / Jlanding

This condition arises from the fact that on a direct landing the abort propulsion system must not only provide sufficient impulse to return the vehicle to earth, but must do so suffi- ciently fast to prevent the vehicle from impacting the lunar surface. To satisfy the latter requirement, the abort propul- sion system must have a thrust/weight ratio equal to or greater than the largest instantaneous value experienced by the landing stage. The largest instantaneous thrust/weight ratio occurs at the end of the landing phase and is a factor r greater than that at the initiation of retrothrust.

For the propulsion systems assumed in this study, the mass ratio of the landing stage is approximately two. Thus, ac- cording to the preceding criterion, the thrust/weight ratio of the launch stage should exceed that of the landing stage by a factor of two. The locus of thrust/weight ratios satisfying this criterion also is illustrated in Fig. 7 · It can be seen that the thrust/weight ratios of the stages can be selected to

satisfy abort requirements with only a small weight penalty to the system. Based on these results, values of thrust/weight ratios of 0. 5 1 and 1. 0 , respectively, were chosen in this k Throughout this paper, thrust/weight ratios are expressed in

terms of earth g!s .

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study for the landing and launch stages employed for a direct lunar landing.

A similar analysis vas made for the case of a parking orbit landing. In this case, however, the optimum thrust/weight ratio for the landing stage is governed primarily by the park- ing orbit altitude, as illustrated in Fig. 8. It can be seen that low parking orbit altitudes require high thrust/weight ratios to decelerate the vehicle to zero velocity while de- scending to a lunar altitude of

10,000

ft. on a gravity turn trajectory. Two thrust/weight ratios are given in Fig. 8.

The smaller value corresponds to the first ignition of the landing stage, at which time the vehicle is injected into the lunar parking orbit, whereas the larger value occurs at the second ignition that initiates the descent to the lunar sur- face. Fig.

8

indicates that thrust/weight ratios of

0.282

and

0.359

are appropriate for the first and second ignitions, re- spectively, of the landing stage employed for a parking orbit landing from an altitude of l8.5 naut. miles. The results will be somewhat different for non-gravity turn trajectories which are more flexible in trajectory control.

Similarly, the propulsion requirements for abort with the launch stage during a parking orbit landing are considerably different than those required during a direct landing. Be- cause of the grazing character of the descent trajectory from a parking orbit, an abort can be accomplished with practically any thrust/weight ratio in the order of 1 lunar g or more.

Consequently, a thrust/weight ratio of unity, chosen from Fig.

7 to optimize the lunar launch operation, is the clear choice.

Table 1 summarizes the propulsion characteristics chosen in this study for the lunar landing and launch stages.

Table 1 Typical propulsion characteristics for lunar landing and launch stages.

Initial thrust/ Ideal velocity, weight ratio fps (Figs, k (Figs. 7 and 8) through 6) Direct descent landing

Landing stage O. 5 I

96oo

a

Launch stage

1.0 9500

Parking orbit landing

Landing stage (ist ig ^nition) Ο.282

3260

Landing stage (2nd ig ^nition)

0.359 59io

a

Launch stage

1.0 9500

aHovering and final touchdown requirements are not included.

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G . BARTOS A N D A . B. GREENBERG

A B O R T C U R I N G T H E E A R T H - M O O N T R A N S F E R

The earliest requirement for an abort during the lunar land- ing mission can occur while the vehicle is outbound on the Earth-moon transfer trajectory. At that time the vehicle will

include one or more propulsive stages which can be utilized to redirect the flight path such that an early return to earth is achieved. Frequently, the abort situation will dictate the fastest possible return to Earth, in which case all of the available abort propulsion would be used. Thus, the abort problem reduces to one of utilizing the available propulsion to alter the magnitude and direction of the vehicle velocity such that an early return to the Earth is accomplished with suitable re-entry conditions. The flight mechanics of this type of abort situation are illustrated in Fig. 9> which shows abort return trajectories resulting from the use of one of the available lunar stages.

Calculations were made of the return conditions which result from an abort during the Earth-moon trajectory, the results of which are presented in Figs. 10 and 1 1 . The calculations were based on the use of abort velocity increments of 10,000 and 20,000 fps. These increments correspond approximately to the use of one or both of the lunar landing and launch stages.

The free-flights portions of the abort trajectories were cal- culated by means of two-body Keplerian mechanics, whereas the powered abort maneuver was computed with the aid of a trajec- tory simulation program. In all cases the abort velocity in- crement was applied in such a manner as to result in a return perigee altitude of 135*000 ft. The latter value was chosen to assure acceptable re-entry conditions. The results of the calculations are presented in Figs. 10 and 1 1 and indicate the re-entry velocity, re-entry flight path angle, and total- flight time as functions of the altitude at which the abort is initiated. It can be seen that an abort of this type can re- sult in a relatively rapid return of the vehicle to the earth.

It also should be noted in Figs. 10 and 1 1 that the re-entry velocity increases with increasing altitude at the time of abort. This is because, at high altitudes, the abort velocity increment becomes large compared to the local trajectory ve- locity. Consequently, the abort maneuver not only redirects the flight path angle back toward the Earth, but increases the magnitude of the velocity as well. The data presented in Figs. 10 and 1 1 extend only up to that abort altitude at which the resulting re-entry velocity is parabolic. At higher alti- tudes either smaller velocity increments would have to be utilized, or additional thermal protection would be required for the re-entry vehicle. For this reason, abort with a

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20,000-fps velocity increment is limited to flight altitudes from injection to

45,000

naut. miles, whereas an abort with a velocity increment of

10,000

fps can be accomplished up to al- titudes of approximately

l40,000

naut. miles. Beyond that al- titude velocity increments less than

10,000

fps will provide parabolic return to Earth, as illustrated in Fig. 1 2 . However, it can be seen that at these altitudes the total flight time to return to Earth becomes quite large and, in terms of pro- pulsion requirements, it becomes equally attractive to return to the Earth on a circumlunar trajectory.

ABORT DURING A PARKING ORBIT LANDING

The parking orbit landing involves two propulsive maneuvers.

The first maneuver occurs at perselenum of the circumlunar trajectory and injects the vehicle into a lunar parking orbit.

The second maneuver accomplishes the final descent to the lunar surface.

The propulsion requirement for an abort during the injection maneuver is essentially equal to the retrograde velocity in-

crement imparted to the vehicle prior to the abort. Thus, the maximum propulsion requirement occurs at the end of the injec- tion maneuver and is equal to 32ÔO fps. It should be noted that throughout this maneuver the velocity of the vehicle is orbital or greater, and the flight path angle is approximately horizontal. Consequently, an abort during the lunar injection maneuver can be accomplished with relatively modest thrust/

weight ratios and with the thrust applied nearly tangential to the flight path.

During the second propulsive maneuver (i.e., the descent to the lunar surface) the velocity of the vehicle is less than orbital, and the flight path becomes progressively steeper.

Consequently, an abort during this maneuver requires the ap- plication of thrust of suitable magnitude and orientation to perform a "pull-up" before the vehicle impacts the lunar sur- face. The flight mechanics of this abort situation are illus- trated in Fig. 1 3 . The pull-up need not result in a circular lunar orbit. An elliptic orbit would.be equally satisfactory provided that the perselenum is sufficiently high to assure clearance of the lunar terrain. The propulsion requirements for either case would be quite similar since the grazing na- ture of the descent trajectory would always result in an orbit of small eccentricity.

Calculations have been made of the propulsion requirements for an abort during the descent to the lunar surface. The calculations were based on the descent trajectory illustrated

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G . BARTOS AND A. B. GREENBERG

in Fig. k- and the use of the lunar launch stage for performing the abort. The propulsion requirements were computed by means of a number of powered flight trajectory simulations in which the vehicle was flown from points on the descent trajectory into low-altitude, circular lunar orbits. A subsequent pro- pulsive maneuver was then calculated which would return the vehicle to the Earth on a relatively slow transfer trajectory

(approximately 3-l/2 days). Two cases were considered in these trajectory simulations: (l) returning the vehicle to the original lunar parking orbit at an altitude of 18.5 naut.

miles with subsequent lunar escape, and (2) placing the vehi- cle into a lunar parking orbit the altitude of which is chosen to minimize the sum of the propulsive maneuvers required for

injection into the orbit and return to the Earth. The results of these calculations are presented in Fig. ik in terms of the ideal velocity increment required for both the pull-up into orbit and the subsequent lunar escape. It can be seen that the velocity required for abort into a parking orbit of vari- able altitude is considerably less than that required for abort back to the original parking orbit. In either case, however, the propulsive capability of the lunar launch stage, as given in Table 1, is adequate for accomplishing the abort maneuvers·

It is interesting to note in Fig. lk the optimum variation of the lunar orbit altitude following an abort. For an abort early in the descent trajectory, where the local velocity is high and the flight path is virtually horizontal, the loss in altitude during the abort maneuver is very small. As the time of abort increases, the changes of flight path angle and ve- locity result in a rapid lowering of the optimum orbit alti- tude after abort. In fact, during the latter portion of the descent trajectory the optimum orbit altitude after abort must be constrained to assure clearance of the lunar terrain. The

data in Fig. ik are based on a minimum orbit altitude of 6 naut. miles after an abort.

ABORT DURING A DIRECT LANDING

Only one propulsive maneuver is performed during a direct lunar landing. At an appropriate time prior to lunar impact, retrothrust is applied to simultaneously reduce the velocity of the' vehicle to zero and the altitude to 10,000 ft. An abort during this type of landing requires that the vehicle perform a pull-up to prevent impacting the lunar surface.

Furthermore, since the vehicle is on an impact trajectory from the time of'Earth departure, an abort prior to initiating retrothrust also will require a propulsive maneuver. In either event an abort initiated in the vicinity of the moon

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generally will result in the trajectory being deflected around the moon, as illustrated in Fig. 1 5 .

It should be noted that, prior to the start of retrothrust, the vehicle approaches the moon with hyperbolic velocities.

An efficient abort initiated during this period of time gener- ally will result in a hyperbolic abort trajectory around the moon. Conversely, an efficient abort maneuver initiated late

in the retrothrust phase, when the vehicle velocities are small, will place the vehicle in an elliptical orbit around the moon. In both cases a second propulsive maneuver then will be required to return the vehicle to the earth. This large variation in possible abort trajectories is further com- plicated by the fact that the orientations of the lines of ap- sides for the abort trajectories also vary with the time of abort. Two examples of this effect are illustrated in Fig.15- An abort hyperbola, entered before initiating retrothrust, will have a perselenum considerably beyond the intended land-

ing site, whereas an abort ellipse entered shortly before the final touchdown will have a perselenum close to the intended landing site.

Propulsion requirements have been calculated for an abort during the direct landing trajectory illustrated in Fig. 5·

This trajectory is representative of the steep descent paths followed in landings of this type. Two-dimensional, powered flight trajectory simulations were computed with the aid of an IBM 709O to establish the propulsion requirements for the first propulsive abort maneuver (i.e., to deflect the trajec- tory so as to avoid impacting the moon). In these simulations

it was assumed that the lunar launch stage described in Vehi- cle Characteristics was used for performing the abort maneu- vers. A number of simple steering modes (such as thrusting at a constant angle with respect to the local horizontal) were used for these simulations to find suitable propulsive maneu- vers that would deflect the trajectory around the moon. The resulting simulations also identified the orbital elements of the resulting abort trajectories.

The second propulsive maneuver, that transfers the vehicle from the abort trajectory to a trajectory suitable for return- ing to earth, was evaluated by simple two-body, sphere-of- influence calculations. In all cases the return trajectory was calculated to have a hyperbolic asymptote and velocity relative to the moon suitable for initiating a 3-l/2 day re- turn to the earth. Transfer to the return trajectory from an abort ellipse was assumed to occur at that point on the el- lipse at which the required velocity increment could be added tangentially. For those cases in which the abort trajectory

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G. BARTOS AND A. B. GREENBERG

after the first propulsive maneuver was near parabolic or hy- perbolic, the transfer to the desired return trajectory was assumed to occur at large distances from the moon.

The second propulsive maneuver was evaluated for each suit- able first propulsive maneuver found in the powered flight simulations. In this manner it was possible to identify the combination of maneuvers that resulted in the smallest overall propulsion requirement for an abort. This procedure was re- peated at each of a number of positions along the direct land- ing trajectory. The results of these calculations are pre- sented in Fig. l 6 . It can be seen that the propulsion re- quirements increase as the vehicle approaches the moon, de- crease sharply after the initiation of retrothrust, and remain essentially constant during the final powered phase of the landing. The initial increase of the propulsion requirements is due to three factors: (l) the velocity of the vehicle in- creases during the coasting approach to the moon, (2) the tra- jectory turning required to miss the moon increases, and (3) the abort trajectories after the first propulsive abort maneu- ver are generally hyperbolic with asymptotes unfavorably ori- ented relative to the asymptote of the Earth return trajec- tory. These three factors adversely affect the propulsion re- quirements for both the first and second propulsive maneuvers, as can be seen from Fig. l 6 . The abort propulsion require- ments decrease after the start of retrothrust due to a rapid transition of the abort trajectories from poorly oriented hy- perbolae and ellipses of high eccentricity to ellipses of mod- erate eccentricity and more favorable orientation. This ef- fect can be seen in Fig. l6 by the decrease of the propulsion requirement for the second propulsive maneuver immediately after the start of retrothrust. The propulsion requirements for abort during the final powered phase of the landing remain essentially constant due to the compensating effects of lower vehicle velocities and larger trajectory turning angles asso- ciated with aborts at that time.

The data presented in Fig. l6 indicate that, with the thrust/weight ratios assumed in this study for the lunar land- ing and launch stages, an abort is possible at all times dur- ing a direct lunar landing. However, the ideal velocity re- quired for abort briefly exceeds that available from the lunar launch stage used in this study.

Fig. l6 also illustrates the abort propulsion requirements for thrust/weight ratios less than unity in the launch stage.

In these cases it. is found that abort cannot be accomplished from all points during the retrothrust phase. This is because without adequate thrust acceleration, the downward motion of

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the vehicle cannot he stopped in time to prevent the vehicle from impacting on the moon. In fact, an abort with low

thrust/weight ratios from within a few miles of the lunar sur- face is only possible because the nominal trajectory was

shaped to reach zero velocity at an altitude of 10,000 ft. In the cases where abort is possible with low thrust/weight ra- tios, the vehicle actually approaches the lunar surface to within 10,000 ft. It is interesting to note that the data presented for abort with low thrust/weight ratios confirms the required relationship between thrust/weight ratios of the landing and launch stages postulated in Vehicle Characteris- tics.

Fig. 16 also indicates the propulsion requirements for a di- rect (rather than circumlunar) return to Earth initiated dur- ing the final coasting approach to the moon. The data indi- cate that such a maneuver is possible but requires signifi- cantly more abort velocity than that needed for a circumlunar return to Earth.

ABORT DURING THE LUNAR LAUNCH

For the landing site selected in this study, return to Earth is accomplished by means of a single-burn launch trajectory which terminates in a 2-l/2 day moon-Earth transfer orbit.

Earth return via a low lunar parking orbit would permit the use of a somewhat more efficient launch trajectory, but it was felt that the resulting moderate performance gain would be offset by the complication of requiring a second burning peri- od. The characteristics of the direct lunar launch trajectory are illustrated in Fig. 6.

An abort during the powered ascent will require a propulsive maneuver approximately equal to the ideal velocity still to be gained at the time of the abort. Some reduction of this re- quirement is possible by using a minimum-energy return trajec- tory involving longer flight time; however, only modest sav- ings can be obtained in this manner. The abort propulsion re- quirements for such a min imum -energy return to Earth are il- lustrated in Fig. 1 7 . These propulsion requirements are based on the use of an abort propulsion system having a thrust/

weight ratio of unity and a specific impulse of k-20 sec. The effect of employing a min imum-energy Earth return trajectory is evident by the fact that there are no propulsion require- ments for abort during the last 7 seconds of the launch tra- jectory.

Fig. 17 indicates that the propulsion requirements for abort to Earth during the lunar launch trajectory are large.

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G . BARTOS AND Α. Β. GREENBERG

Further, at this point in the mission the vehicle contains no significant propulsion capability beyond that required for the launch itself, and any attempt to incorporate such capabili- ties in the vehicle will result in a severe weight penalty to the system. Consequently, it appears to be preferable to de- sign the launch stage for high reliability, thereby reducing the probability of an abort during the lunar launch trajec- tory, rather than to provide a propulsive abort capability in the vehicle. (in attempting to achieve high reliability in the launch stage, it should be borne in mind that the stage should have restart capabilities to permit its use for aborts prior to the lunar launch. Consequently, the launch stage should not employ solid propellants.)

The preceding discussion applies to early lunar landing mis- sions for which it is essential that the crew be returned to earth in the event of an abort during the lunar launch. In later missions, however, it may be possible to recover space crews either from lunar orbits or from arbitrary locations on the surface of the moon. It is interesting to examine the ex- tent to which such additional rescue capabilities will relieve the abort problem during lunar launch. It will be noted that Fig. 17 also presents the propulsion requirements for aborts either to the lunar surface or to lunar orbits, and it is seen that such alternate abort modes greatly reduce the propulsion requirements during the early portion of the launch. Thus, if all modes of abort are available to the vehicle an abort pro- pulsion capability of only 3500 fps would be required to sat-

isfy all abort situations.

CONCLUSIONS

This study has examined the propulsion requirements for aborting a lunar landing mission at any time from Earth escape to Earth return. Although the methods of calculation employed in the studies included various approximations, and the chosen geometry of Earth, moon, and landing site may not correspond to any specific mission, it is believed that the results of the study indicate the general characteristics of such abort problems. The following general conclusions may be drawn from the results of this study.

1) The lunar landing and launch stages are suitable for ac- complishing many of the required abort maneuvers during a lu- nar landing mission. These stages can be designed to permit such secondary usage with small weight penalties to the over- all system.

2 ) The lunar landing and/or launch stages offer attractive

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propulsion characteristics for aborting the mission during the Earth-moon transfer.

3) Abort is possible at all times during the lunar landing, regardless of whether the landing is accomplished from a lunar parking orbit or at the terminus of a lunar impact trajectory.

In the case of a parking orbit landing, the lunar launch stage is adequate for accomplishing the abort. However, for a di- rect landing, the ideal velocity requirement for abort briefly exceeds that available from the lunar launch stage used in this study.

4) Although abort is possible during either parking orbit or direct landings, the relative simplicity of the abort ma- neuvers for the parking orbit landing make it preferable to the direct landing.

5) An abort during the lunar launch requires the use of a stage not otherwise needed for the mission. Furthermore, the propulsion requirements for such an abort are so large that to include such a stage in the vehicle would impose a prohibitive weight penalty on the system. Consequently, high reliability

in the lunar launch stage appears to be a preferable design approach to that of providing a separate propulsive stage.

It should be recalled that this paper has dealt only with the case of a mission abort with subsequent return of the ve- hicle to Earth. Although such conditions are appropriate for early lunar missions, future lunar operations may permit the recovery of space crews who abort from their intended missions either to a lunar orbit or to the lunar surface. If these flight options are considered in abort studies, one can expect to find a significant reduction in the propulsion requirements for abort.

ACKNOWLEDGMENTS

The authors wish to express their appreciation to Mr. J.

Michaels, who furnished the nominal circumlunar trajectory em- ployed in this study; to Messrs. D. Groves and D. Wallis for their support in computing the necessary powered flight simu- lations; and to Miss B. Wardwell for computational assistance during the course of the study.

REFERENCES

1 Buchheim, R.W., "Lunar flight trajectories," The Rand Corporation Rept. P-1268 (January 1958).

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G . BARTOS A N D A. B. GREENBERG

2 Weber, R.J., Pauson, W.M., and Bur ley, R.R., "Lunar tra- jectories," National Aeronautics and Space Administration, Rept. TN D-866 (August 1 9 6 l ) .

3 Lieske, H.A., "Lunar trajectory studies," The Rand Corpo- ration, Rept. P-1293.

k Mickelwait, A.B., and Booton, R.C., "Analytical and nu- merical studies of three-dimensional trajectories to the moon," Inst. Aerospace Sei. Paper no. 59-90 (June 1959)·

5 Kelly, T.J., and Adornato, R.J., "Determination of abort way-stations on a nominal circumlunar trajectory," ARS J. 32, 887-893 (1962).

6 Gervais, R.L., and Johnson, M.C., "Abort during manned ascent into space," Inst. Aerospace Sei. preprint 62-36.

7 Slye, R.E., "Velocity requirements for abort from the boost trajectory of a manned lunar mission," National Aero- nautics and Space Administration Rept. TN D-IO38 (July 1 9 6 1 ) .

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TRANSFER TO IMPACT OR CIRCUMLUNAR TRAJECTORY7 PARKING ^^"^^^^ ^^T~T<C /-PARKING ORBIT . / / ^-^X /LANDING ,oV^ ' «S DIRECT LANDING

/^P ^n M

FREE FL,GHT / WXm POWERED FLIGHT ^-CAPTURE Fig. 1 Typical trajectories for a lunar landing mission

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G . BARTOS AND A. B. GREENBERG

F L I G H T T I M E FROM E A R T H D E P A R T U R E , H R 0 0.25 0.5 I 2 3 4 6 10 3 0 6 2 . 4 3

— I l l j' 111! l " [ [ 11' i

0 I ' I I I I I I L _ U I 1 I—LJ 1 1 L_UJ

I 02 I 03 I 04 I 05 I 0(

GEOCENTRIC A L T I T U D E h, NAUT Ml

Fig. 2 Characteristics of Earth-moon ballistic trajectories (geocentric coordinates)

F L I G H T T I M E FROM E A R T H D E P A R T U R E , H R (CIRCUMLUNAR T R A J E C T O R Y )

62.43 62.3 62.0 61.0 6 0 0

S E L E N O C E N T R I C A L T I T U D E , NAUT Ml

Fig. 3 Characteristics of Earth-moon ballistic trajectories (selenocentric coordinates)

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CO

- 9 0 r ï 9 r 180 ι 1 1 1 1

g G R A V I T Y T U R N

- 8 0 - - 8 - 160 P A R K I N G O R B I T A L T I T U D E ! 18.5 N A U T Ml 1 ....

>2 I N I T I A L T H R U S T / W E I G H T ! 0 . 3 5 9 I

- 7 0 - t 7 - 140 S P E C I F I C I M P U L S E ! 4 2 0 SEC I 0 ο P O W E R E D F L I G H T R A N G E ! 186.5 N A U T Ml /l Q - 6 0 - üi 6 - t ! 2 0 P O W E R E D F L I G H T T I M E ! 418 SEC J j à - 5 0 - 2 5 - § 100

< 5 uj ^ ^ v ^ \ χ / ! κ-

ι - 4 0 - ? 4 - û 80 X . s

/ f

4 3 —

η - 3 0 - ^ 3 - J 6 0 > ζ Γ " Ν y «

ï - 2 0 - § 2 - 4 0 ^ ^ X \ " 1

- 1 0 - J I - 2 0 ^

—I

0L υ 0L 01 ^ 1 -I 1 I 1 1 1— _ k J —

0 0 0 1 0 0 2 0 0 3 0 0 4 0 0 T I M E F R O M I N I T I A T I O N O F R E T R O T H R U S T , S E C

Fig. k Powered flight trajectory for lunar landing from a low parking orbit

1 11

1—, 1

1 . L , _ I

1 , 1

ç ι

G R A V I T Y T U R N I co m I G N I T I O N A L T I T U D E : 2 8 7 . 2 N A U T Ml I

t u I N I T I A L T H R U S T / W E I G H T : 0.51 I I l

Ο S P E C I F I C I M P U L S E : 4 2 0 SEC A - 7 0 r - I 8 0 0 r - Ο 9 POWERED F L I G H T R A N G E : 81.3 NAUT Ml ]ZA

ν 1 POWERED F L I G H T T I M E : 4 1 8 SEC | / |

- 7 2 - 1 6 0 0 - X- 8 \ ' Η

ο O l - 7 4 - 1 4 0 0 - Η 7 " N ^ j | i

UJ > \ \ / X £D|

£ - 7 6 - LZ 1 2 0 0 - < 6 \ y \ J

î § s \ Xs ^ / \ !

g - 7 8 - - . 1 0 0 0 - § 5 \ — N r S 1 \A

< -C < \ V / \ I

Χ UJ \ > C \ |

5 - 8 0 - § 8 0 0 - > 4 X - / — ^ ^ i l

°" — κ χ / I

g - 8 2 - < 6 0 0 - 0 3 - ^ S ~

_i uj Χ X h >v u- > / X Xs^

- 8 4 - 4 0 0 - J 2

- 8 6 - 2 0 0 - S I S X ^ j

- 8 8 * - oL 0^——I ' 1 1 1 ' ' ^

0 1 0 0 2 0 0 3 0 0 4 0 0 T I M E FROM I N I T I A T I O N OF R E T R O T H R U S T , SEC

Fig. 5 Powered flight trajectory for a direct lunar landing

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G. BARTOS A N D Α. Β. GREENBERG

Fig. 6 Powered ascent trajectory from the lunar surface for return to Earth

Fig. Τ Effects of stage thrust/weight ratios on mission performance

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_ 40, r 1 1 ι ! ι — I \ GRAVITY T U R N DESCENT

\ \ SPECIFIC IMPULSE: 4 2 0 SEC

< \ \ ' 1 r— 1 ' ζ 30 -V Λ.

ÜJ \ \ Q \ \

ZD \ \

_] 20 — \ - — \ - 1 1 1

^ \ y—AT START OF DESCENT

£ Ν. / — A T INITIATION OF

Ο |o / LUNAR CAPTURE _

Ú " "

2

o l I I I I I 1 0.2 0.4 0.6 0.8

T H R U S T / W E I G H T RATIO OF LANDING STAGE

Fig. 8 Variation of landing stage thrust/weight ratio with orbit altitude for a parking orbit landing

R E - E N T R Y A L T I T U D E : 3 0 0 , 0 0 0 F T I N I T I A L T H R U S T / W E I G H T : 1.0 S P E C I F I C I M P U L S E : 4 2 0 S E C

I D E A L V E L O C I T Y E X P E N D E D : 1 0 , 0 0 0 F P S

^ - A B O R T T R A J E C T O R I E S ^ _ _ _ _ _ —

^ Z Z ' - ~ ~ ^ - - C I R C U M L U N A R h = 8 4 , 3 1 0 N A U T M l T R A J E C T O R Y — \ v = 6 0 3 0 F P S

A E A R T H ^ \ h = 6 1 , 3 8 4 N A U T M l

V ) ι \ ^ - ^ ν = 7 4 2 0 F P S

— T = T H R h = 3 1 , 6 1 8 N A U T M l / h= 1 8 , 2 4 8 N A U T Ml ν = 1 0 , 6 7 0 F P S / vs 1 4 , 0 4 0 F P S \ /

A B O R T C O N D I T I O N S

Fig. 9 Trajectory characteristics for abort during Earth-moon transfer with one lunar stage

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G . BARTOS A N D Α. Β. GREENBERG

ABORT TIME A F T E R EARTH DEPARTURE, HR

0.1 I 10 100

i._I '_Li Jl L±"

IO3 IO4 IO5

ABORT A L T I T U D E , NAUT Ml

Fig. 10 Abort capabilities during Earth-moon transfer using the lunar landing or launch stage (velocity increment

= 10,000 fps)

ABORT TIME A F T E R EARTH D E P A R T U R E , H R

0.1 I 10

»5 ABORT ALTITUDE,NAUT Ml

Fig. 1 1 Abort capabilities during Earth-moon transfer using both lunar landing and launch stages (velocity

increment = 20,000 fps)

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100 120 140 160 180 ABORT A L T I T U D E , 1000 NAUT Ml

Fig. 12 Abort velocity requirement and flight time for para- bolic return from the Earth-moon transfer trajectory

Fig. 13 Typical flight profile for abort during a parking orbit landing

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G. BARTOS AND A. B. GREENBERG

0 100 2 0 0 3 0 0 4 0 0 5 0 0 ABORT TIME A F T E R INITIATION OF RETROTHRUST FOR DESCENT, SEC

Fig. ih Velocity requirements for abort during a parking orbit landing

Fig. 15 Typical trajectory characteristics for abort during a direct landing

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TIME FROM S T A R T OF R E T R O T H R U S T , S E C .

4 0 0 3 0 0 2 0 0 1 0 0 0

1 4 , 1 1 1 h • — J J 1 1

f — R E T R O T H R U S T P H A S E - 4 - t C O A S T P H A S E -

í) ι

Ι

I \ ι

g- 2 _J I \y~ D I R E C T | 1 2 —I ë V " R E T U R N

g Z O N E O F NO A B O R T J w \ launlhx

, o χ "

t s [ I γ ΐ ° °

S I I \ - — V E L O C I T Y I N C R E M E N T

< Λ \ F O R P U L L - U P AND g 6 _ , / > > ^ R E T U R N T O I" A R T H

S I V E L O C I T Y I N C R E M E N T j A . . « ι F O R I N I T I A L P U L L - U P I \

< c W I T H F / W « I . O I \

9 j L A N D I N G S T A G E F / W 0 . 5 I

0 I — L 1—i__d 1 1 — ι _ _ û 1 1— l_ J 1 1—ι ι Γ Τ - 1 LjJ I 10 1 0 0 1 0 0 0 1 0 , 0 0 0 1 0 0 , 0 0 0

A L T I T U D E A T S T A R T O F A B O R T , N A U T Ml

Fig. l6 Propulsion requirements for abort during a direct landing

A B O R T A L T I T U D E , N A U T Ml

1 2 5 10 20 3 0 4 0 50 6 0 7 0 80 9 0 102

10 j -J 1L 1 1 1—Η 11— ' j —1 1

A B O R T I N T O 3 1/2 D A Y , . / — M O O N - E A R T H T R A J E C T O R Y |

v> / Á Η

u. 8 X > — ο j

* . _ \ ×â>

ai I

O 6

çô

Ν . S c\

Ji?

i '

H 4 _ A B O R T I N T O ^ < N ^ X X , ! ο L U N A R O R B I T ^ n X k P ° Χ ι 1 1 1

2 I / X \ \ J A B O R T F / W * 1.0

UJ I c / X. \ ^ V 1 . ,_ . 1

9 2

-JX?

~ i

^ 1 I

° 0 50 100 150 2 0 0 2 5 0 A B O R T T I M E A F T E R L U N A R L A U N C H , S E C

Fig. 1 7 Velocity requirements for abort during a lunar launch

Ábra

Fig. 2 Characteristics of Earth-moon ballistic trajectories  (geocentric coordinates)
Fig. k Powered flight trajectory for lunar landing from a low  parking orbit  1 1 1  1—, 1  1
Fig. 6 Powered ascent trajectory from the lunar surface for  return to Earth
Fig. 8 Variation of landing stage thrust/weight ratio with  orbit altitude for a parking orbit landing
+5

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