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MSC INTERNAL NOTE NO. 68-FM-74

PROJECT APOLLO

LM POWERED ASCENT TRAJECTORY FORTHE APOLLO LUNAR LANDING MISSION

By Joe D. Payne, William C. Lamey, and Burl G. KirklandLunar Landing Branch

March 20, 1968

MISSION PLANNING AND ANALYSIS DIVISION

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

MANNED SPACECRAFT CENTER

HOUSTON, TEXAS

Approved: /,_'-_ ';L_:: /.."_-_--I_loyd V/)_ennett, ChiefLunar Landing Branch

Approved: _ _ -,John I_}I Mayer, ChiefMissio'_ Planning and Analysis Division

T

tlb

FIGURES

Figure

I

3

6

Time histories of IM trajectory parameters during

powered ascent

(a) IM altitude ....................

(b) LM altitude rate ..................

(c) IM central angle traveled ............

(d) IM velocity ....................

(e) IM flight-path angle ................(f) LM thrust angle (pitch) ..............

IM altitude rate versus altitude during powered

ascent ..... • • ..... • • • " ........

LM flight-path angle versus inertial velocity during

powered ascent ........... • ........

Time histories of relative IM-CSM parameters during

powered ascent

(a) IM-CSM range ....................

(b) IM-CSM range rate .................

(c) IM-CSM phase angle .................(d) IM-CSM angle from local vertical ..........

(e) IM rendezvous radar elevation angle ........

(f) X relative range (CSM referenced) .........

(g) Z relative range (CSM referenced) .........

Z relative range versus X relative range during

powered ascent (CSM referenced) ...........

LM-CSM range rate versus range during powered ascent. •

l_ge

56

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V

LM POWERED ASCENT TRAJECTORY FOR THE

APOLLO LUNAR LANDING MISSION

By Joe D. Payne, William C. Lamey, and Bur! G. Kirkland

SUMMARY

This document presents the LM powered ascent trajectory for the lunar

landing mission. The LM ascent utilizes a two-phase guided trajectory toachieve an orbit characterized by a periapsis altitude of 60 000 ft and

an apoapsis altitude of 30 n. mi. The total characteristic velocity ex-

pended during the ascent to nominal orbit insertion is 6012 fps. The nom-

inal ascent trajectory duration is 412.7 seconds.

INTRODUCTION

The last official publication containing the nominal lunar ascent tra-

Jectory was the "AS-50hA Preliminary Spacecraft Reference Trajectory"

(ref. 1), published July l, 1966. Since that time, there have been updates

in LMweights and engine performance data (ref. 2), and refinements to and

better definition of the onboard ascent guidance equations (refs. 3 and 4).

An unscheduled document (ref. 5), whose purpose was to describe the

data format planned for use in reference trajectory documentation, was

published February 16, 1968. It should be emphasized, however, that this

reference was not intended to be an official trajectory document and,

hence, did not reflect recent data and guidance equation changes.

The purposes of this report are to present the revised LM powered

ascent trajectory incorporating the latest available data along with the

latest guidance equations and to serve as an interim ascent trajectory

reference until the scheduled reference trajectory document is published.

Data describing the trajectory is defined in the tex_ and is presented in

tabular and graphical form.

i

DEFINITION OF THE LM POWERED ASCENT TRAJECTORY

Operational Phases

The LM powered ascent trajectory assumes an in-plane launch into a

60 000-ft (9.88-n. mi.) by 30-n. mi. orbit about the moon. The ascent

consists of two operational phases, a vertical rise phase (approximately

10-seconds duration) and a near-optimum guidance phase. The purpose of

the vertical rise phase is to obtain sufficient altitude for terrain

clearance prior to pitch over to the ascent guidance attitude. This phase

terminates on the first computing interval after achieving avertical ascent

rate of 50 fps. The near-optimum guidance phase is designed to insert the

LM into the desired nominal lunar orbit, which allows for completio_of

LM-CSM rendezvous in about 3 hours. Rendezvous maneuvers are performed

using the LM reaction control system (RCS). The LM-CSM phase angle at

insertion is 15.91 ° in this simulation.

Guidance and Targeting

The primary guidance and navigation control system (PGNCS) is used

to guide the LM into a preselected orbit. The ascent guidance uses a

fixed-thrust linear guidance concept (refs. 3 and 4) to control the powered

ascent to specific insertion conditions. The desired orbital conditionsat insertion are an altitude of 60 000 ft above the lunar launch site and

an inertial velocity magnitude of 5510 fps. The PGNCS guidance has posi-

tion control in the lateral and radial directions until the time to go

(T ) becomes less than l0 seconds. After T reaches l0 seconds, positiongo go

control is eliminated, but velocity control is maintained. When Tgo

reaches 4 seconds, the PGNCS initializes a_special timer to command engine

shutdown.

The time-to-go equation, included in the ascent guidance, contains

a parameter which is referred to as the Tg ° constant (KT). A change in

the value of this constant is reflected by a change in the shape of the

altitude and altitude-rate profiles and a change in the Characteristic

velocity required to achieve nominal insertion conditions, After consider-

able study (refs. 6 and 7), it was determined that KT should be assigned

a value of 0.5. The official source for guidance constants (ref. 4) now

reflects this value for KT; and is, therefore, used here.

POWEREDASCENTSIMULATIONDATA

t

Weight and Performance Data

The weight and performance data used to generate this trajectory were

obtained from reference 2. Table I gives a brief summary of these data.

The thrust used in simulating the ascent burn is the effective thrust

considering +X axis RCS thrusting for center-of-gravity control. The RCS

interconnect is used during ascent for center-of-gravity control; thus,

an average ascent burn specific impulse (Isp) is used. The ascent AV

budget of 6060 fps, which is now under configuration control, is a result

of a study documented in reference 8. This AV budget is confirmed by

reference 2 and was adhered to in designing of this trajectory•

TraJ ectory Data

The conditions achieved after a nominal ascent to insertion are listed

in table II. Time histories of trajectory parameters defining the LM

ascent are presented in figure 1. It should be noted that the oscillations

in the LM thrust angle [fig. l(f)] reflect the attitude damping by the

ascent guidance. The digital autopilot (DAP) was not included in this

simulation. Since the DAB affects attitude response, its inclusion in

the simulation would change the attitude damping characteristics. This

area will be explored further when hybrid simulation capabilities are

completed. Figure 2 shows the altitude rate with respect to altitude.

Figure 3 shows the inertial flight-path angle as a function of inertial

velocity• Time histories of the relative LM-CSM parameters are given in

figure 4. The X and Z relative range plots [figs. 4(f) and (g)] are ref-

erenced to a curvilinear coordinate system whose origin is at the CSM.

The fact that the X relative range is negative and the Z relative range

is positive means that the LM is behind and below the CSM. Figure 5 pre-sents Z relative range as a function of X relative range. Figure 6 shows

the LM-CSM range rate versus range.

CONCLUDING REMARKS

The LM powered ascent trajectory for the lunar landing mission has

been redesigned as a result of recent changes in LM weights and performance

data. These data changes also necessitated a reduction in the CSM lunar

parking orbit altitude from 80 to 60 n. mi. As far as the LM powered ascentis concerned, this altitude change affected only the time sequencing of the

LM-CSM rendezvous; and, is reflected in the relative motion plots. This

trajectory should be used in engineering simulations as the nominal LM

ascent trajectory for the Apollo lunar landing mission until it is super-

sededby the reference trajectory document.

TABLE I.- LM POWERED ASCENT WEIGHT AND PERFORMANCE DATA

Tots1 weight st lunar llft-off, lb ............

APS propellant (for AV = 6060 fpe), lb . . . . . . . . , .

APS and RCS effective thrust, lb .............

APS and RCS 8versge Isp , sec ...............

lO 729.0

4 962.0

3 627.0

303.4

TABLE II.- IM POWEKED ASCENT INSERTION CONDITIONS

Burn time, sec . . . . . . . . . . . . . . . . . . . . . . .

Burn src, deg .........................

Thrust sngle (pitch), deg ..................

Insertion phase 8ngle, deg .................

Insertion velocity, fps ...................

Insertion 81tltude, ft ...................

Delta V, fps ..... , ..................

Propellant used, lb .....................

Insertion weight, lb ....................

412.686

9.47

-5.44

15.91

5510.0

6O ooo.o

6011.74

4933.44

5795.56

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Time from lunar lift-off, rain

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Figure 1.- Time histories of LM trajectory parameters during powered ascent.

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22

REFERENCES

.

.

,

,

.

,

,

.

Mission Analysis Branch: AS-504A Preliminary Spacecraft Reference

Trajectory (U). MSC IN 66-FM-70, July l, 1966. Confidential.

Low, George M.: Apollo Spacecraft Weight and Mission Performance

Definition. December 12, 1967.

Payne, Joe D.: Comparison of LM PGNCS and AGS Orbit Insertion Guidance

Logic and Procedures. MSC IN 68-FM-73, March 22, 1968.

MIT instrumentation Laboratory: Guidance System Operations Plan for

Manned LM Lunar Landing Missions Using Program Luminary. Section 5

R-567. January 1968.

Lunar Mission Analysis Branch and Lunar Landing Branch: Preflight

Data for a Lunar Landing Mission. MSC IN 68-FM-41, February 16, 1968.

Lamey, William C.: Effects of Varying the Time-to-Go Equation for the

LMAscent. MSC IN 67-FM-133, September 22, 1967.

Payne, Joe D.: Specification of the Time-to-Go Constant for Lunar

Ascent. MSC Memo 67-FM91-8, November 27, 1967.

Bennett, Floyd V.: Revised LM Descent and Ascent AV Budgets for the

Lunar Landing Mission. MSC IN 67-FM-203, December 27, 1967.