Journey Into Space Research

Continuation of a Career at NASA

Langley Research Center

W. Hewitt Phillips

Monographs in Aerospace History

Number 40

July 2005

NASA/SP-2005-4540
Journey Into Space Research

Continuation of a Career at NASA

Langley Research Center

by

W. Hewitt Phillips

NASA History Office

Office of Policy and Plans

NASA Headquarters

Washington DC 20546

Monographs in Aerospace History

Number 40

July 2005
Cover photograph (L-05136): Little Joe rocket being launched from

Wallops Island. Several of these rockets were launched to study

separation of the escape capsule from the Mercury capsule.

The use of trademarks or names of manufacturers in this monograph is

for accurate reporting and does not constitute an official endorsement,

either expressed or implied, of such products or manufacturers by the

National Aeronautics and Space Administration.
L-63-3268

Phillips in 1963 at the age of 45. At this time, he was chief of the Space Mechanics Division.

Monographs in Aerospace History Number 40—Journey Into Space Research v

Table of Contents

List of Figures vii

CHAPTER 1 Introduction 1

CHAPTER 2 Blast Off Into Space 3

Education in New Fields of Research 4

Initial Space Research at the Flight Research Division 6

Initial Space Research at Langley 13

CHAPTER 3 Stability and Control of Space 

Vehicles 17

Rotating Vehicles in Free Space 18

Moments Acting on a Satellite 22

Gravitational and Centrifugal Moments 22

Magnetic Moments 24

Effect of Radiation Pressure 24

Effect of Aerodynamic Forces 25

CHAPTER 4 Rendezvous 29

Effect of Orbital Mechanics 30

Simulation Experiments 31

Implementation of Rendezvous in Apollo Program 32

CHAPTER 5 Space Simulation Studies 35

Lunar Landing Research Facility 36

Lunar Orbit and Landing Approach (LOLA) Simulator 45
vi Monographs in Aerospace History Number 40—Journey Into Space Research

Table of Contents

Docking Simulator 47

Aids for Extravehicular Maneuvering 48

CHAPTER 6 My Work With Johnson Space Center 51

Design of Shuttle Control System 51

Studies of Shuttle Control System 53

Problem With Pilot-Induced Oscillations 55

Flight Control Review Group 56

CHAPTER 7 Continuation of Research Following 

Decline of Space Program 59

Variable Sweep Wing Supersonic Transport 59

Differential Maneuvering Simulator (DMS) 61

Circulation Control 64

Control Configured Vehicles (CCV) 65

Propulsive Effects Due to Flight Through Turbulence 66

Decoupled Controls 67

Soaring Gliders 68

Complementary Filters 70

Turbulence Problems 71

CHAPTER 8 Some Nonaerodynamic Studies 75

Some Studies of Fireplaces 75

Control System for a Small Hydrofoil Boat 77

CHAPTER 9 Concluding Remarks 79

Appendix 83

References 87

Index 91

About the Author 95
Monographs in Aerospace History Number 40—Journey Into Space Research vii

List of Figures

FIGURE 2.1. List of topics covered in Henry A. 

Pearson’s lecture series. 5

FIGURE 2.2. Drawing of concept for entry vehicle 

studied by members of Flight Research 

Division. 8

FIGURE 2.3. Effect of entry angle on variations of 

deceleration, velocity, and flight-path 

angle, g, with altitude. Wing loading, 20 lb/

ft2; angle of attack, 90°. 10

FIGURE 2.4. Time histories showing effect of reduction 

of angle of attack on deceleration and 

other trajectory variables. Initial flight-path 

angle –0.5°, wing loading 20 lb/ft2. 10

FIGURE 2.5. Effect of entry angle, γo, on heat-transfer 

rates for entries at 90° angle of attack. 

Wing loading, 20 lb/ft2; entry altitude, 

350,000 ft. 11

FIGURE 2.6. Large model of entry vehicle being tested 

in Langley Spin Tunnel to study control at 

or near 90° angle of attack. 12
viii Monographs in Aerospace History Number 40—Journey Into Space Research

List of Figures

FIGURE 3.1. Illustration of motion of ellipsoid of inertia 

during free rotation of body in space. 

(Taken from ref. 2.1.) 19

FIGURE 3.2. Model used to illustrate stability of rotation 

of body in space. 21

FIGURE 3.3. Sketch of drag device proposed for 

causing an orbiting spacecraft to enter 

Earth’s atmosphere in case of failure of 

retro-rocket. Many small vanes could 

produce required drag. 26

FIGURE 5.1-1. Pilot model for LLRF being flown by NASA 

test pilot Jack Reeder. 39

FIGURE 5.1-2. Lunar Landing Research Vehicle showing 

original cab for pilot. 40

FIGURE 5.1-3. Lunar Landing Research Vehicle hovering 

with stand-up cab for pilot. 42

FIGURE 5.1-4. Lunar Landing Research Facility at NASA 

Langley Research Center, Hampton, 

Virginia. 42

FIGURE 5.1-5. Simulated craters on terrain in landing 

area of LLRF. Shadow of vehicle with 

lighting simulates low Sun angle. 43

FIGURE 5.1-6. Lunar Landing Research Facility in use at 

crash test facility. 44

FIGURE 5.3-1. Docking simulator. 48
Monographs in Aerospace History Number 40—Journey Into Space Research ix

FIGURE 6.1. Comparison of height response of several 

airplanes: F-104 and B-52—conventional 

aft tail, YF-12, B-58, and Shuttle—delta 

wing. Note that the Shuttle requires 2.15 s 

for the c.g. to return to its original altitude. 

57

FIGURE 7.1. Figure 7.1. Glider model of supersonic 

transport with variable-sweep wing and 

retractable canards. Length, 30 in., span 

(swept) 15 in., span (unswept) 26 in. 60

FIGURE 7.2-1. Pictorial view of Differential Maneuvering 

Simulator (DMS). The large spheres are 

projection screens, and they contain the 

pilots’ cockpits, projectors, and 

servomechanisms to move the projected 

displays. Each pilot sees a view of the 

opposing airplane. 62

FIGURE 7.2-2. More detailed sketch of Differential 

Maneuvering Simulator. 62

FIGURE 7.3-1. Use of Coanda effect to deflect airstream 

at trailing edge of wing. Illustration shows 

effect of oscillating cylinder that closes 

one side of the opening or the other. A 

slightly smaller rotating cylinder could 

alternately close and open gaps at a high 

frequency, producing a rapidly oscillating 

airflow. 64

FIGURE 7.4-1. Control-configured vehicle (CCV) chart. 

66

FIGURE 7.4-2. Damping and stability control chart. 66
x Monographs in Aerospace History Number 40—Journey Into Space Research

List of Figures

FIGURE 7.5. Heavily weighted glider (40-in. wingspan) 

gliding slowly (about 3 ft/s) underwater in 

large tank. Fluorescent dye is emitted 

from wing tips. When glider made 

complete circles, trails from previous circle 

were always well above glider. 69

FIGURE 7.6. Comparison of attenuation of lift due to 

spanwise averaging on an elliptical wing 

with that due to unsteady lift effects for 

wings of aspect ratios 3 and 6. 73
Monographs in Aerospace History Number 40—Journey Into Space Research 1

CHAPTER 1 Introduction

Space flight has long been a subject of

interest both to scientists and to the

general public. Science fiction became

popular with the works of Jules Verne,

whose fanciful stories of space exploits

inspired many later science fiction publications. These stories were usually not

based on valid science and technology

or they were ahead of the developments

that might have made them possible.

These works, however, served to stimulate thought on space flight for many

years. Some groups, such as the British

Interplanetary Society, made serious

studies of the requirements for space

flight. These efforts failed to lead to

practical developments because of lack

of financial support or interest from governmental organizations or from the

public. These early studies had little

effect on actual developments in the

space program because, with greater

support and larger numbers of investigators, the results were quickly rediscovered and not until later was it found

that some important results had been

worked out previously.

Studies of the possible military applications of space flight were started by military organizations in the United States

about 1950, but these studies were

classified secret. I, like the general public, was unaware of any activity in this

field until the nation was startled by the

Russian launching of Sputnik. The last

chapter of the preceding volume on the

history of my work at Langley (ref. 1.1)

describes how the nation was galvanized into action and started a national

space program. These developments

are described in more detail in the book

Spaceflight Revolution (ref. 1.2).

The advent of the space program was a

welcome event to many of the research

groups at Langley. One reason for this

attitude was that aeronautical research

had reached a plateau at this time.

Many of the research contributions of

Langley and other National Advisory

Committee for Aeronautics (NACA) centers had reached fruition in the design

and production of advanced airplanes.

These airplanes included jet bombers

and transports, and supersonic fighter

airplanes. Research and design work

on the supersonic transports, the

British Concorde and the Russian

TU144, had progressed to a point that

construction could proceed with some

assurance of success. No really revolutionary advances for atmospheric aircraft were envisioned at that time or

have occurred in the ensuing years.

Some of the wind-tunnel organizations,

however, expressed concern that their

work might be cut back or otherwise
2 Monographs in Aerospace History Number 40—Journey Into Space Research

Introduction

affected by the emphasis on space

research. 

In the case of my work and that of the

Flight Research Division, another event

occurred that required a change in

direction. A NACA Headquarters edict,

published in 1958, stated that no further

testing of high-speed airplanes would

be done at Langley. All future flight

research on such airplanes was to be

done at the Edwards Air Force Base in

California (now called the Dryden Flight

Research Center). The engineers in my

division therefore were available for

assignments in the field of space

research.
Monographs in Aerospace History Number 40—Journey Into Space Research 3

CHAPTER 2 Blast Off Into Space

With the start of the space program, a

rapid transition occurred in the types of

research performed at Langley. At

first, the emphasis was on educating

research personnel so that they could

become acquainted with the new disciplines and skills required in space

research. Second, there was a diverse

effort in space research, applying the

newly acquired knowledge to the solution of problems that were recognized

as being important in this field. Soon,

however, a national space program was

established, involving both unmanned

and manned satellites. Space flight centers were established to take the lead

in specific types of work, such as scientific satellites, interplanetary probes,

and manned space flight. The various

groups at Langley generally initiated

work that would contribute to a specific

phase of the national space program,

and general research programs were

phased out. In some cases, research

programs were stopped by management because they did not fit in the

national space program or because the

work being done had been assigned to

other centers.

The discussion that follows applies

mainly to the work being done under my

direction in the Guidance and Control

Branch of the Flight Research Division

(1959–1962), the Aerospace Mechanics

Division (1962–1963) and the Space

Mechanics Division (1963–1970). No

attempt has been made to present

the dates or time periods of different

research programs. Because over

40 years has passed since the start of

the national space program, however,

many readers today may be unfamiliar

with the progress of space flight and the

times at which certain goals were

accomplished. To assist the reader in

relating the work described to the

progress in space flight, an abbreviated

chronology of space launches and missions, both Russian and American, is

presented in appendix I. These data

were obtained from the TRW Space Log

(ref. 2.1). Much more detailed discussions of the various NASA space programs are available in the NASA

Historical Publications that have been

prepared to describe each major program. Some of these publications are

given in references 2.2, 2.3, and 2.4.

Others are given in the lists of reference

works included in these publications.
4 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

Education in New Fields of 

Research

The start of the space program was a

time of rapid transition for most aeronautical research organizations in the

country. The Russian feats of orbiting

Sputnik satellites had captured the interest of the general public, first from a

sense of wonder that space vehicles

actually existed and second from a

sense of fear that these vehicles, with

unknown capabilities, might signal the

start of an era in which the enemy would

have technical expertise exceeding our

own. The engineering community was

perhaps less alarmed but nevertheless

realized that a great deal of study and

research was necessary to become

familiar with the disciplines involved in

this relatively unknown field.

The effect on the administrators in

Washington, as is well known, was to

cause them to initiate the change of the

NACA, the National Advisory Committee for Aeronautics, from a small government organization reporting directly

to the president, to the NASA, the

National Aeronautics and Space Administration, a large government agency

reporting to Congress and involving

many new research centers and operational centers in addition to those in the

original NACA. This change, however,

did not immediately affect the research

programs at the Langley Research Center. The change in research emphasis at

this center came primarily from the

interest of the center personnel in new

fields of work involving flight in space

and the desire to learn as much as possible about a promising new area of

research.

In the Flight Research Division, I was

still assigned as Head of the Stability

and Control Branch. At this time,

Henry A. Pearson, Head of the Aircraft

Loads Branch, initiated a program in

which various engineers would look

up some subject involved in space

research and give a lecture on it to the

whole division. The notes on these

lectures were collected in a volume

(ref. 2.5), the table of contents of which

is given in figure 2.1. These notes were

widely distributed in the NASA centers

but were never published. A copy of this

volume is available in the Langley

Research Center Library. As stated in

the preface of the volume, the initial

demand for the notes was so great that,

“for the sake of expediency, this goal (of

rapid distribution) is best achieved by

making the material available in its

present unedited form instead of following the usual NACA editing procedure.”

Later, most of the engineers involved

had become involved in specific space

projects and therefore had no time for

the work of preparing the volume for

more formal publication. 

Similar studies and lectures were continued after the distribution of the volume. Among the subjects I studied were

the rotational motion of a free body in

space and later, the relative motion of

two bodies, a subject of importance in

connection with space rendezvous.

Many other research organizations, in

this period, were equally involved in an

intense educational effort to learn

everything possible about space flight.

These organizations included the aeronautical departments of engineering

colleges and government research

groups in the Army, Air Force, and Navy.

In studying these problems, it was

impressive to find how much famous

mathematicians centuries ago, who had

no idea of applying their theories to

space travel, had learned in studying

the motions of planetary bodies. These

brilliant men had studied these problems as pure academic exercises, without modern computing facilities and

without the incentive provided by experimental research with artificial satellites.
Education in New Fields of Research

Monographs in Aerospace History Number 40—Journey Into Space Research 5

In many cases, they originated mathematical techniques used in space

research, particularly the techniques

required for the calculation of satellite

orbits.

I was also impressed by the progress

made by astronomers. These scientists, who devoted their lives to abstract

studies to understand the nature of the

universe, soon realized that they had

knowledge of value in the space program. An example of this research,

which could be classed as an engineering study as well as a scientific effort, is

given in a brief note entitled Exploration

of Space from the University of Virginia,

published in the University of Virginia

News Letter in January 1959 (ref. 2.6).

This note points out that the exploration

of space there had been going on for

75 years, since the acquisition of a large

telescope in 1888. The main object of

these studies is the field known as

astronometrics, the study of the distances to and relative positions of the

stars and other heavenly bodies. The

University of Virginia at Charlottesville,

Virginia is one of the colleges closest to

Langley with an astronomy department,

and valuable contacts were established

there that later aided in the work on the

Apollo program. 

The subjects presented in these lectures included many disciplines that

had little relation to the aeronautical

work previously conducted by these

branches. For example, a lecture on

hypersonic flow was included because

such flow conditions would be involved

in the flight of rockets or space vehicles

while entering or leaving the atmosphere. Orbital mechanics was considered important because vehicles

operating in space would be subject

to the same laws that had been developed for planets and other heavenly

FIGURE 2.1. List of topics covered in Henry 

A. Pearson’s lecture 

series.

I

II

III

IV

V

VI

VII

VIII

IX

X

XI

XII

XIII

XIV

XV

XVI

XVII

W. B. Huston and J. P. Mayer

T. H. Skopinski

J. P. Mayer

A. P. Mayo

A. P. Mayo

J. J. Donegan

D. C. Cheatham

C. W. Mathews

H. A. Hamer

J. G. Thibodaux, Jr. and H. A. Hamer

W. B. Huston

W. S. Aiken, Jr.

E. M. Fields

C. R. Huss

W. J. OʼSullivan and J. L. Mitchell

P. A. Gainer and R. L. Schott

D. Adamson

W. A. McGowan

Elementary Orbital Mechanics

Satellite Time and Position With Respect to a 

Rotating Earth Surface

The Motion of a Space Vehicle Within the 

Earth-Moon System: The Restricted 

Three-Body Problem

Orbital Transfer

Reentry With Two Degrees of Freedom

Six Degree of Freedom Equations of Motion 

and Trajectory Equations of a Rigid Fin 

Stabilized Missile With Variable Mass

Inertial Space Navigation

Guidance and Control of Space Vehicles

Elements of Rocket Propulsion

Characteristics of Modern Rockets and 

Propellants

Aerodynamic Heating and Heat Transmission

Heat Protection

Properties of High Temperature Materials

The Solar System

Appendix on the Earthʼs Atmosphere

Communication and Tracking

Some Dynamical Aspects of the Special and 

General Theories of Relativity

Environmental Requirements
6 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

bodies. The theory of relativity was

considered important because it had

been involved previously in astronomical studies. This theory becomes important when the motion of the bodies

involved approaches the speed of light.

Such speeds were not contemplated in

the type of space operations required in

the early years of the space program.

Nevertheless, the desire to understand

the laws governing the universe made

relativity a subject of interest in the new

field of space flight. It was known that a

slight motion of the perihelion of the

planet Mercury had been detected

that was not explained by Newtonian

mechanics and was one of the examples presented by Einstein as a method

of verifying his theory of general relativity. Thus, relativity might have an effect

even on the motion of objects in the

solar system. In later space projects

involving precise measurements of time

or in the use of spacecraft for navigation

purposes, inclusion of relativistic effects

was found necessary to obtain the

degree of precision desired. 

Fortunately, an engineer with a knowledge of Einstein’s theories, working

in the Physical Research Division at

Langley, was available. He was David

Adamson, an Englishman who studied

physics at Durham University but was

employed at the Royal Aircraft Establishment (RAE) in England during WWII

in research on airplane handling qualities. After the war he came to work at

Langley. As a result of his experience in

engineering as well as in physics, his

lectures on the complex subject of relativity were presented to the engineers

with unusual clarity.

Item 3 in the list of topics in figure 2.1 is

a lecture by J. P. Mayer on the subject of

the three-body problem. This notable

problem concerns the motion of three

bodies in space, such as, for example,

the Sun, Moon, and Earth, under the

influence of their mutual gravitational

attraction. This problem has been studied by many famous mathematicians

over the centuries. Despite the amount

of effort expended in its solution, this

problem, in all its generality, has never

been completely solved. As often happens when brilliant mathematicians

work on a very difficult problem, however, the work led to advances in many

fields of mathematics. As an aside,

John P. Mayer later joined the Space

Task Group working on the Mercury

Project and was later in charge of all the

computing facilities at the Johnson

Space Center during the Gemini and

Apollo programs. Practically all the engineers in the Aircraft Loads Branch later

joined the Space Program, either in

the Space Task Group or at the new

Goddard Space Flight Center. In the

list of lecturers given in figure 2.l,

these engineers include Wilbur B.

Huston, John P. Mayer, Ted H. Skopinski, Alton P. Mayo, James J. Donegan,

and Carl R. Huss. Others on the list,

who worked in my branch, are Donald

C. Cheatham and Charles W. Mathews.

Mathews later moved to NASA Headquarters in Washington and became

head of the Gemini project, one of the

most successful space flight projects.

Cheatham worked at the Johnson

Space Flight Center and did important

work in the design of the Space Shuttle

control system.

Initial Space Research at 

the Flight Research Division

One of the main objectives of many

research organizations both in the

NACA and in the armed services was

to beat the Russians in a race to place

a man in space. The Air Force had

its MISS program (Man in Space Soonest). At Langley, the Pilotless Aircraft

Research Division (PARD) was in

charge of Robert R. Gilruth, formerly my
Initial Space Research at the Flight Research Division

Monographs in Aerospace History Number 40—Journey Into Space Research 7

boss in the Flight Research Division.

Members of PARD, who had developed

experience in handling rockets by using

them to propel test vehicles used in

aeronautical research, proposed placing

the astronaut in a capsule that could be

launched into space by the existing

Atlas Rocket and recovered by parachute with a splashdown in the ocean.

This imaginative program, largely the

concept of Maxime A. Faget, an engineer in PARD, later won the approval of

NASA and developed into the Mercury

Project. The Air Force Program, meanwhile, continued with several studies of

vehicles called the Robo, Brass Bell,

and Hywards. Finally these studies

were consolidated into the Dynasoar

project, also called the X-20. This program received considerable support and

reached an advanced state of engineering development, but was cancelled in

1963. The reasons for the cancellation

were that no well-defined military mission for the vehicle could be found, that

the cost was excessive, and that

by 1963 the NASA Gemini program

planned to accomplish many of the

objectives of the Dynasoar program.

During the early stages of the Mercury

program studies, there was much concern that the ocean splash-down would

be impractical and that the vehicle

should allow the astronaut to land

“like a gentleman,” with a conventional

airplane-type landing at an airport.

In considering this problem, I tried

to take advantage of the concept

developed by H. Julian Allen and A. J.

Eggers, Jr. of the NASA Ames

Research Center that a blunt-faced

object would be much more suitable for

entry into the atmosphere than a

pointed, rocket-like object (ref. 2.7). This

concept was based on the fact that such

an object would dissipate the tremendous energy of the vehicle entering the

atmosphere in the form of shock waves

that carried the energy away from the

vehicle, rather than in the form of heat

that would produce temperatures high

enough to melt or decompose most

materials. The same concept was

employed in the Mercury project by having the capsule enter the atmosphere

blunt end first, with a suitable heat

shield on the blunt end. 

In considering the application of this

concept to an airplane-like configuration, I visualized that the airplane could

enter the atmosphere at near 90° angle

of attack, then pitch down to normal

gliding attitude after the speed had

decreased sufficiently that heating

would not be a problem. A delta-wing

configuration seemed suitable for this

purpose, but controls had to be provided to control the attitude of the vehicle during entry and to pitch the airplane

down to normal attitudes for landing. A

sketch of the resulting vehicle is shown

in figure 2.2. To pitch the airplane down

after entry into the atmosphere, a set of

tail surfaces was provided that folded

into the shielded region behind the vehicle during entry, but unfolded for the

pitch-down maneuver and subsequent

glide. In addition, four hinged surfaces

were provided around the outline of the

vehicle, which, by suitable combination

of deflections, could provide pitch, yaw,

and roll control during entry. Such controls are now known as controllable

strakes and are now being used on the

nose of a fighter airplane to assist in

control at high angles of attack. The

advantage of these controls for an entry

vehicle was that they simply extended

the outline of the vehicle at angles of

attack near 90° and were not subject to

any more heating than the lower surface

of the vehicle, on which the heating was

reduced because of its large area.

Soon, considerable interest was generated in further studies of a vehicle of the

proposed type. I made a small model to

illustrate the concept. Many engineers

in my branch, with some assistance
8 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

from others in the Aircraft Loads Branch

and the Performance Branch, made

detailed studies of such aspects as

heating, structural loads, and stability

and control. The vehicle was sized to

weigh about 2000 pounds, the same as

the Mercury capsule, so that it could be

carried on the nose of the Atlas Rocket.

Preliminary calculations showed that a

vehicle capable of carrying a single

astronaut could be made within this

weight limitation.

The heating studies were made by

John A. Zalovcik of the Performance

Branch. He had previously gained considerable familiarity with this branch of

aerodynamics in his studies of airspeed

measurements and heating problems of

supersonic aircraft. 

Among the phases of flight studied were

the orbital phase, the atmospheric entry,

the transition from flight in the vacuum

of space to flight in the atmosphere, and

the control of the vehicle as the airspeed decreased from hypersonic

speed during the initial entry to supersonic speed and finally to low subsonic

speed for landing. Most of these operations were unfamiliar to aeronautical

engineers who had previously dealt

with conventional airplanes. Some of

the newly acquired knowledge of the

dynamics of orbital flight was applied in

this work.

FIGURE 2.2. Drawing of 

concept for entry vehicle studied by members of Flight 

Research Division.

(a) Reentry.

(b) Landing.
Initial Space Research at the Flight Research Division

Monographs in Aerospace History Number 40—Journey Into Space Research 9

The return from an orbit around the

Earth required firing a rocket to cause

the vehicle to change its orbit from a

near-circular path around the Earth to

an orbit that entered the atmosphere.

Though the initial thought based on airplane experience would be to fire a

rocket perpendicular to the flight path,

studies showed that a much smaller

rocket impulse would be required if the

rocket were fired along the path in a

direction to slow the vehicle down. Then

the force of gravity would take over to

bring the vehicle down into the atmosphere. This rocket was therefore called

a retro-rocket, a term now familiar in discussions of space flight operations. A

study was made of the effect of the

magnitude of the retro-rocket impulse

on the angle at which the vehicle

entered the atmosphere and the

distance traveled before entering the

atmosphere.

With too shallow an entry angle, the

vehicle would skip back out of the atmosphere, whereas with too steep an

entry, the vehicle would experience

excessive deceleration, resulting in

intolerable loads on the human pilot.

Tilting the vehicle from an attitude in

which the lower surface was perpendicular to the flight direction to one in which

the longitudinal axis of the vehicle

made a smaller angle with the flight

direction, provided a lift force to slow the

vehicle’s entry into the denser region of

the atmosphere and a desirable reduction in the deceleration of the vehicle. In

general, the entry angle needed to be

between –0.5° and –1°. Some of these

results are illustrated in figure 2.3. The

range of –0.5° to –1° appears small, but

the accuracy of the direction and magnitude of the retro-rocket burn was well

within the capability of existing rockets

and control systems. A fortunate effect

of the laws of orbital motion is that the

entry angle is very insensitive to the tilt

of the deorbit impulse. Variations of this

angle by as much ±10° from the flight

direction produced less than a 0.02°

change in the entry angle. In general, at

shallow entry angles, the entry angle

had little effect on the variation of deceleration, which reached a maximum

value of about 8 g for the conditions

considered. Tilting the vehicle longitudinal axis from the perpendicular position

by just 10° shortly after the start of

the buildup of deceleration reduced

the maximum value to the more desirable value of about 5 g, as shown in

figure 2.4.

The effects of variation in the entry

angle of the vehicle on the aerodynamic

heating were also investigated. Some of

these results are shown in figure 2.5.

The maximum heating rate remained

about the same for entry angles

between –1° and –0.25°, but this maximum occurred later in the entry at the

shallower angles.

At that time, some studies had been

made of the effects of different heat

shield materials for use on the research

airplanes such as the X-1; heat resistant alloys such as Rene 41, a nickelchromium alloy, withstood temperatures

up to 1600 °F. This material would allow

the use of a steeper entry with less total

heat input to the vehicle because the

high temperature surface would radiate

much heat. On the other hand, beryllium

has a high heat capacity, so that a reasonable thickness of the material would

absorb the heat of entry. These two

materials typified what were called radiative and heat sink type heat shields,

respectively. A combination of these

materials was at that time thought suitable to protect the vehicle from aerodynamic heating. At that time, ablative

materials, such as Teflon®, had shown

promise in tests in hypersonic wind tunnels, but the amount of data available

was not sufficient to allow consideration

of their use on a vehicle. Ablative materials decompose at high temperatures.
10 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

FIGURE 2.3. Effect of 

entry angle on variations of deceleration, 

velocity, and flightpath angle, γ, with altitude. Wing loading, 20 

lb/ft2; angle of attack, 

90°.

FIGURE 2.4. Time histories showing effect of 

reduction of angle of 

attack on deceleration 

and other trajectory 

variables. Initial flightpath angle –0.5°, wing 

loading 20 lb/ft2.

–0.25

–0.5

–1.0

–2.0

10

8

6

4

2

0

28

24

20

16

12

8

4

0

–16

–12

–8

–4

0

350 300 250 200

Altitude, ft

150 100 × 103

× 103

Deceleration,

g units

Velocity,

ft/sec

90 t > 0 s

90 t < 370 s

80 t > 370 s

4

2

0

4

6

8

10

10

0

20

30

100

0

200

300

400

Altitude,

ft

Velocity,

ft/s

Deceleration,

g units

Flight-path

angle, deg

Distance,

miles

2

0

–40

–60

–80

–100

–20

0

0 200 100 300 500 400

Time, s

600 700

× 103

× 103

× 103

{
Initial Space Research at the Flight Research Division

Monographs in Aerospace History Number 40—Journey Into Space Research 11

This process absorbs heat and the

outer layers turn to gaseous products

that carry the heat away from the vehicle. Later, many additional developments were made both in ablative and

radiative heat shields, as typified by the

heat shields on the Apollo capsule and

on the Shuttle Orbiter, respectively. 

The studies associated with the winged

entry vehicle were published as NASA

Technical Memorandum X-226 entitled

A Concept of a Manned Satellite Reentry Which Is Completed With a Glide

Landing by the Staff of Langley

Flight Research Division, compiled by

Donald C. Cheatham (ref. 2.8). This

memorandum was originally classified

confidential but has since been declassified. Also, a patent was issued in

my name entitled Variable Geometry

Winged Entry Vehicle. At that time, personnel at many of the wind tunnels at

Langley wished to contribute to the

space program, but not many designs

for entry vehicles had been proposed.

The results of the Flight Research

Division study, however, had been

discussed with personnel involved in

aerodynamic research. As a result,

independently of my efforts, branch

heads in a number of the wind tunnels

operating in different speed ranges had

models with folding wing tip panels constructed and ran tests.

A large model of the Flight Research

Division vehicle was built for tests in the

spin tunnel. A picture of the model being

tested is shown in figure 2.6. These

tests were intended to study the ability

of the four-hinged surfaces around the

border of the vehicle to provide stability

and control during descent at 90° angle

of attack. These tests showed that the

control was easily accomplished. Later,

an air jet was fitted to the rear of the

fuselage and the model was mounted in

a vertical position in the test section

of the NASA 30- by 60-Foot Tunnel to

FIGURE 2.5. Effect of 

entry angle, γo, on 

heat-transfer rates for 

entries at 90° angle of 

attack. Wing loading, 

20 lb/ft2; entry altitude, 

350,000 ft.

–2.0

–1.0

–0.5

–0.25

20

16

12

8

4

0

× 103

Heat-transfer rate,

q, Btu/sec-ft2

0 200 100 300 500 400

Time, s

600
12 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

study the use of the folding tail surfaces

to provide transition from 90° angle of

attack to a glide attitude. This maneuver

was again easily accomplished by gradually deploying the tail surfaces as the

tunnel speed was increased from zero

to the speed for horizontal flight. In fact,

the configuration showed promise as a

tail-sitter vertical takeoff and landing

(VTOL) airplane.

FIGURE 2.6. Large 

model of entry vehicle 

being tested in Langley Spin Tunnel to 

study control at or 

near 90° angle of 

attack. 
Initial Space Research at Langley

Monographs in Aerospace History Number 40—Journey Into Space Research 13

This configuration, or some variations of

it, for a time acquired the most complete

set of aerodynamic data of any winged

entry configuration, covering the entire

range of Mach numbers within the capabilities of the Langley wind-tunnel facilities. A Langley committee called the

Steering Committee for Manned Space

Flight served to communicate the

research results among the various

groups. Several of these wind-tunnel

studies were published as NASA Technical Memorandums (refs. 2.9–2.11).

These reports also contain long lists of

references containing additional tests

on these and other configurations made

during the same time period. By the

time these data were published, the

Space Task Group had been formed to

implement the Mercury project. This

group was relocated in Houston, Texas

to form the nucleus of the Johnson

Space Flight Center. Before the group

moved to Houston, however, they

requested a presentation of the results

of the Flight Research Division study to

compare the relative advantages of the

two approaches. The presentation had

little effect on the planning for the Mercury project, mainly because, with the

desire to put a man in space as soon as

possible, the Mercury development was

obviously simpler and involved less

development. In addition, Mercury

included the feature of an escape tower

that was considered essential for astronaut safety in case the Atlas rocket malfunctioned on the launch pad. 

The beneficial results of the Flight

Research Division study included educational background for many of the

engineers who later joined the Space

Task Group and early analysis of trajectory and heating problems that provided

results applicable to most types of entry

vehicles. In addition, the later development of the Shuttle Orbiter involved a

configuration somewhat similar to that

studied by the Flight Research Division.

As a result, the engineers who had

joined the space task group and later

worked at the Johnson Space Center

were able to apply this experience in the

design of the Shuttle Orbiter.

Initial Space Research at 

Langley

Just as the Flight Research Division

rapidly changed its emphasis from

research on airplanes to research on

space vehicles, all the other divisions at

Langley attempted to use their expertise

to investigate many problems of space

flight. This research was not confined to

studies of the initial brief orbital missions but included studies of unmanned

satellites and of manned orbiting space

stations intended for long durations in

space. Many problems confronting the

crew of a space station were immediately recognized. They included numerous biomedical problems, such as the

effects of zero gravity, protection from

the vacuum of space, protection from

ionizing radiation (already discovered by

Van Allen in his initial orbital experiments), and provision of food, water,

and oxygen over long periods. In connection with the vehicle itself, there

were problems of temperature control,

generation and storage of energy, protection from meteoroids, and effects of

the space environment on materials and

structures. It is remarkable that much

basic knowledge of many of these subjects was obtained in the first two years

of the Space program.

A brief discussion of some of the work

done at Langley on these space-related

problems is now presented. I was not

connected with these projects but

learned of them through participation

in committee meetings and visits to

see items of research equipment.

These comments are based on my recollections and may not be historically
14 Monographs in Aerospace History Number 40—Journey Into Space Research

Blast Off Into Space

accurate, but they reflect the opinions of

the research that I formed at that time. 

In the areas of biomedical research,

Dan Popma of the Instrument Research

Division (ref. 2.12) headed an extensive

program. He proposed ingenious ideas

for methods to purify the atmosphere of

a space station, to provide oxygen, and

to recycle wastewater and urine. Methods of testing these devices in groundbased facilities were suggested. He also

considered the medical effects of zero

gravity and studied centrifuges, rotating

space stations, and other ideas, many

of which were finally tested in space

many years later. This promising work

came to an abrupt halt when NASA

Headquarters ruled that all biomedical

research should be conducted in a new

facility at the Ames Research Center,

manned mainly by medical doctors. I

considered it a mistake to place this

work in the hands of doctors rather than

engineers. Dan Popma was an engineer, and his approach was much more

logical and could have produced the

required information for manned space

flight much more quickly than the program that actually evolved. The doctors,

who frequently lacked research experience and had no experimental data to

go on, feared that unknown effects in

space might cause a human being to

become disoriented or might even prove

fatal, and they therefore proposed that

difficult and inconclusive animal experiments should be performed before a

man was allowed to go into space. Test

pilots, on the other hand, had experienced, in high-altitude flight, many of

the problems that at least approached

those expected in space and did not see

any reason to delay placing a man in

orbit. The eventual program represented

a compromise of these views. After a

few manned space flights had been

made, the Ames group became involved

in other research, such as theories of

the origin of life. Such theories are an

important subject for scientific research,

but they have little bearing on the problems of manned space flight.

Other groups at Langley were concerned with methods of overcoming the

effects of zero gravity. An obvious concept was the use of a rotating space

station to allow the centripetal acceleration to simulate gravity. Paul Hill and

others in the PARD conceived an inflatable rotating toroidal space station, like

a large inner tube. This design would

allow the device to be folded compactly

for launching and then to be deployed in

space. A contract was given to the

Goodyear Corporation to build an engineering model of this concept. The

model was about 15 feet in diameter

and was set up to study inflation,

strength, puncture resistance, and leakage. When Charles Donlan, at that time

the Deputy Director of Langley, heard of

this work, he immediately ordered it

stopped because a large space station

was not at that time part of the NASA

space program. This and other experiences made it clear that the freedom to

pursue new ideas that had existed

under the NACA was curtailed under

NASA, and projects had to fit the overall

space program as established by NASA

Headquarters.

Several groups studied the problem of

durability of materials and electronic

equipment in the space environment.

An electron accelerator of the Van de

Graaf type was acquired for this

research. Later, a large laboratory,

called the Space Radiation Effects Lab

(SREL) was built in Newport News and

run in cooperation with the College of

William and Mary. A large cyclotron supplied the required radiation. This work

continued for many years, but after the

end of the Apollo Program, funds for this

project were discontinued. Later still, the

cyclotron was removed, but the building

was used as part of the Thomas

Jefferson Research Laboratory, which
Initial Space Research at Langley

Monographs in Aerospace History Number 40—Journey Into Space Research 15

contains a large, continuous beam electron accelerator for basic research in

nuclear physics. My rather surprising

involvement in tiding over the use of the

facility during the lull in funding between

the Apollo era and the development of

the electron accelerator is described in

a later chapter.

Engineers at Langley also foresaw the

need for studies of other aspects of the

space environment on many types of

materials. Some work could be conducted in vacuum tanks. An example of

this research is the study of friction of

moving parts in the vacuum of space.

Despite the desire to conduct much

research of this type, very little was

done because instead of first putting

up a space station and later proceeding with more complex missions, President Kennedy initiated the Apollo program, which required a relatively shortduration mission. As a result, the effects

of long exposure to space have been

studied extensively only in recent years

by using the Long Duration Exposure

Facility (LDEF) satellite launched and

recovered by the Space Shuttle.

A number of engineers at Langley

investigated space power systems.

About the time these studies were being

started, I learned about rechargeable

nickel-cadmium batteries for powering

the transmitters, receivers, and servos

of radio-controlled model airplanes. The

great advantage of these batteries is

that they can be charged and discharged many hundreds of times without deterioration. I contacted one of the

engineers working on the space systems and found that he had not yet

heard about these batteries. This experience shows that hobbyists are sometimes more alert to new developments

than professionals. Nickel-cadmium batteries, or NiCads as they are called,

have since been used extensively in

spacecraft power systems.

Another engineer who turned his attention to space power systems was Albert

E. Von Doenhoff, a former airfoil expert

who was mentioned in reference 1.1 for

his aircraft landing study. Assisted by

Roland Ohlson and Joseph M. Halissy,

he made an analysis of solar regenerative space power systems (ref. 2.13). In

this type of system, a solar collector

heats and vaporizes a working fluid,

which drives an engine similar to a

steam engine or steam turbine. The

working fluid is then condensed

for reuse by a radiator that radiates

heat to the blackness of space. The

steam engine, of course, may then drive

an electric generator. I thought that

Von Doenhoff’s analysis was excellent,

but in that same period, solar photovoltaic cells were developed to a usable

stage. These cells, together with NiCad

batteries to store the energy, have been

used since then on practically all space

missions. The weight and complication

of the regenerative power systems have

discouraged their use. Such systems

still might be candidates for power on

very large spacecraft or on planetary

bases.

Roland Ohlson, who formerly worked in

the NACA towing tank testing seaplanes

and flying boat hulls, complained to me

after his retirement that nothing he had

ever worked on was used anymore. I

suppose that many research engineers

must expect this outcome of their career

specialties in this time of rapid development of scientific and technical ideas.

Monographs in Aerospace History Number 40—Journey Into Space Research 17

CHAPTER 3 Stability and Control of 

Space Vehicles

This historical document is not intended

to present a theoretical discussion of

the problems encountered in designing

space vehicles. The conditions in space,

however, are so different from the familiar Earth-based environment that some

appreciation of the effect of these conditions on the dynamics and control of

space vehicles is required to understand the reasons for the research studies conducted in the course of the

space program. In flight in free space,

far removed from any influence of other

heavenly bodies, a vehicle experiences

no disturbances. This condition is not

attainable on Earth. In the solar system

and in particular in Earth orbit, some

very small disturbing influences exist.

These influences include effects of gravity, forces due to flight through rarified

gas, moments from magnetic fields, and

effects of solar radiation. Although these

effects are small, they are of great

importance because they provide the

only means of controlling a spacecraft

without the expenditure of fuel or

energy. This chapter is therefore

intended to give a discussion of these

problems with as little dependence as

possible on mathematical derivations.

Primary emphasis is placed on a physical appreciation of the phenomena

involved.

A term used in analyzing the rotational

motion of a body is the moment of inertia about some specified axis. The

moment of inertia resists rotational

acceleration of the body, just as its mass

resists linear acceleration. The moment

of inertia of a small element of mass in

the body is determined by multiplying

the mass of the element by the square

of the perpendicular distance from the

axis. The moment of inertia of the entire

body is determined by summing the

contributions of all the elements of

mass.

To allow calculation of the motion of the

body resulting from torques (also called

moments) applied about arbitrary axes,

the moments of inertia are first determined about three mutually perpendicular axes through the center of gravity of

the body. In all rigid bodies, these values of inertia serve to define an ellipsoid, called the ellipsoid of inertia, the

formula for which is given in the following text. The axes defining the maximum

and minimum values of inertia, together

with the third axis perpendicular to

these two, are called the principal axes

of inertia. These axes are of special

importance in determining the rotational

motion of bodies. 

The ellipsoid of inertia may be the same

for many different bodies that have the
18 Monographs in Aerospace History Number 40—Journey Into Space Research

Stability and Control of Space Vehicles

elements of mass distributed differently.

The angular motion of all these bodies

in response to a given applied torque

would be the same.

Rotating Vehicles in Free 

Space

One of the most obvious problems

encountered in studying the motion of

rigid bodies is the motion of an arbitrary

body when it is started with a rotating

motion. Students of elementary physics

learn that the translational motion of the

center of gravity of a body depends on

the external forces applied at this point

and that the rotational motion about the

center of gravity is independent of the

translational motion. The problem of the

rotational motion can therefore be studied independently of the forces acting at

the center of gravity of a body.

Although the rotation of a rigid body in

the absence of all external moments

would appear to be the first problem to

study in this field, the solution of this

problem is not well-known. In my graduate course at MIT, Introduction to Theoretical Mechanics, I do not recall this

problem being mentioned. There are

probably two reasons for this neglect.

First, for bodies rotating on the Earth,

there are always eternal moments

applied during the course of the motion.

A rather complex mounting system

would be required to reduce these

moments to very small values. Actual

freely rotating vehicles, such as baseballs, airplanes, boats, etc. have relatively large moments applied by the

surrounding air or liquid medium. Second, the solution to this problem of

motion with no external moments is very

complex, and little was to be gained by

teaching this solution when no practical

examples existed. 

Many problems of rotating bodies occur

when external moments are applied.

The equations for the solution of these

problems are known as Euler’s dynamical equations. These equations are

taught in standard courses in mechanics. I used these equations in the analysis of the effect of steady rolling on

stability of airplanes, a problem later

known by the name “roll coupling”

(ref. 1.1). 

In 1957, before the start of the space

program, I had some introduction to the

problem of rotation of rigid bodies without external moments. I became familiar

with a report by G. W. Braün, an engineer at the Wright Air Development

Center, on an analysis of the spinning of

airplanes (ref. 3.1). Braün assumed that

at high altitudes, the aerodynamic

forces on a spinning airplane would be

small compared to the inertial forces. As

a result, the equations with no external

moments appeared to be a good starting point for the studies of such spins.

With the advent of space flight, bodies

in space outside the Earth’s atmosphere

experience extremely small external

moments. The rotational motion of these

bodies in space is therefore a problem

of practical importance. I also looked up

further information in a book on classical mechanics by Goldstein (ref. 3.2), on

which the subsequent discussion is

based.

Although the mathematical details of

this problem are too complex to present

herein, a novel geometric solution of

this problem obtained in 1834 by Louis

Poinsot, a French mathematician, is

presented. To describe this solution, a

brief discussion of the method of specifying the applicable characteristics of a

rigid body is considered desirable.

For studying the rotational motion of a

rigid body, the detailed distribution of the

elements of mass in the body or the

shape of the body is not required. The
Rotating Vehicles in Free Space

Monographs in Aerospace History Number 40—Journey Into Space Research 19

body may be described by the moments

of inertia about three mutually perpendicular axes, with their origin at the center of gravity, called the principal axes of

inertia. These values of moments of

inertia, represented as vectors IX, IY,

and IZ along the three principal axes,

can be used to determine the axes of an

ellipsoid, called the ellipsoid of inertia.

The shape of the ellipsoid is determined

by the mathematical formula for an ellipsoid:

where a, b, and c represent the distances from the center of the ellipsoid to

its surface along the X, Y, and Z axes,

respectively. The ellipsoid of inertia is

defined by setting

, , and 

Vectors drawn from the origin to other

points on the ellipsoid may be used to

calculate the values of moments of inertia about any other axes through the

center of gravity by using similar formulas. Different bodies with different

detailed distribution of mass elements

may have the same ellipsoid of inertia.

For any given ellipsoid of inertia, a solution of Euler’s dynamical equations with

the external moments set equal to zero

allows the calculation of the motion following a disturbance in terms of elliptic

integrals. A closed-form solution is thus

available, but the calculations required

are quite lengthy. Poinsot gave a very

ingenious method of visualizing the

motion of a freely rotating body in

space. During the motion, in which the

body rotates about the center of gravity,

the ellipsoid of inertia rolls on a plane,

called the invariable plane. Poinsot

called the curve on the invariable plane

traced out by the point of contact of the

ellipsoid and the plane the herpolhode,

and the curve on the ellipsoid traced out

by the point of contact the polhode.

Thus, the brief explanation of the

motion, as quoted in Goldstein’s book

on Classical Mechanics (ref. 3.2) is “The

polhode rolls without slipping on the

herpolhode lying in the invariable plane.”

A sketch of this construction is shown in

figure 3.1.

The assumption that no external

moments act on the body implies that

FIGURE 3.1. Illustration 

of motion of ellipsoid 

of inertia during free 

rotation of body in 

space. (Taken from 

ref. 3.2.)

Ellipsoid of inertia

Polhode

Herpolhode

Invariable plane

Angular momentum vector

x

a

y

b

z

c

2

2

2

2

2

2 ++=1

a I x =1/ b I y =1/ c Iz =1/
20 Monographs in Aerospace History Number 40—Journey Into Space Research

Stability and Control of Space Vehicles

there are no damping moments. A

motion once started, therefore, will continue indefinitely. The only steady rotations occur when the body is rotating

about one of its principal axes, as seen

from the fact that the tip of the axis then

touches the invariable plane in just one

point. In general, the motions started in

any other manner would be highly oscillatory; that is, the principal axes would

oscillate through large angles with

respect to a fixed reference system.

Such oscillatory motions would be

very undesirable for most practical

applications. 

A question also arises as to the stability

of the motion when it is started about

one of the principal axes. The moments

of inertia may always be classified as

minimum, intermediate, and maximum.

If the body is rotating about the axes of

minimum or maximum moment of inertia, and is slightly disturbed, it will

acquire a small oscillation or wobble. If it

is rotating about the axis of intermediate

inertia, however, and is slightly disturbed, it will immediately swing through

a large angle and continue in a largeamplitude oscillation. The rotation about

the axis of intermediate inertia may

therefore be considered statically unstable and is unsuitable for a vehicle

intended to perform a steady rotation.

In the early days of the space program,

there was considerable discussion of

the design of rotating space stations

intended to provide a centrifugal force

on the bodies of the astronauts to simulate the gravitational force existing on

Earth. Once, in a meeting of one of

the research coordinating committees

chaired by Eugene Draley, an Assistant

Director of Langley at that time, a presentation was made for the design of

a rotating space station that rotated

about its axis of intermediate inertia. I

pointed out that the vehicle would be

unstable as a result of the considerations described previously. This fact

was not known to any other member of

the committee. The design of the vehicle

was stopped at this point for further

study. As a result, we avoided some

embarrassment to Langley that might

have occurred had the design been proposed to NASA Headquarters. 

A simple method of visualizing the tendency of a rotating body to rotate about

its axis of maximum inertia is to consider that each element of mass in the

body experiences a centrifugal force

tending to pull it into the plane of rotation. The body as a whole will then tend

to move to a condition in which its elements are as close as possible to the

plane of rotation. This tendency will

cause a pancake-shaped body, for

example, to approach a condition in

which the rotation is about an axis normal to the plane of the pancake. With no

source of damping, however, the body, if

started in an orientation displaced from

the plane of rotation, will overshoot this

orientation and continue to oscillate

back and forth about it. 

To illustrate these points further, I had

a model constructed, sketched in figure 3.2, in which a flat slab of aluminum

was pivoted on a universal joint and

could be rotated about a fixed axis by

turning a handle. The aluminum slab

represented the dynamic characteristics

of a rotating space station. If the rotation

were started with the plane of the slab

in the axis of rotation, a condition of

rotation about the intermediate axis of

inertia, the slab performed a largeamplitude oscillation. The oscillation

damped out fairly quickly because of air

resistance and bearing friction, and the

slab ended up with its plane normal to

the axis. In space, where the damping

forces are much less, such an oscillation would continue much longer. If the

rotation is started with the plane of the

slab perpendicular to the axis of rotation, corresponding to rotation about its
Rotating Vehicles in Free Space

Monographs in Aerospace History Number 40—Journey Into Space Research 21

axis of maximum inertia, the steady

rotation continues.

The theory discussed so far assumes a

rigid body. All space vehicles, in practice, have some flexibility, or some movable parts. When the body distorts, or

when parts move, some energy is dissipated by internal damping or friction.

This energy can come only from the

rotating body itself.

Newton’s laws state that the angular

momentum of a body will remain constant in the absence of external

moments. If energy is dissipated

through internal causes, however, the

nature of the motion must change. If

the rotating motion continues for a

long time, the motion will eventually

change to a rotation about the axis of

maximum inertia, because this motion,

for a given angular momentum, has the

least energy. Detailed consideration of

how damping forces act on various

parts of the body might be extremely

complicated, but the end result is

always the same. The body assumes a

steady rotation about the axis of maximum inertia. This condition results even

when the body starts rotating about its

axis of minimum inertia, a stable condition for a rigid body. So far as I know,

this result has been known to designers

of satellites launched by the United

States, and in some cases intentional

damping devices have been installed to

speed the settling down to a steady

rotation about the axis of maximum

FIGURE 3.2. Model used 

to illustrate stability of 

rotation of body in 

space.

(a) Rotation about axis 

of intermediate inertia. When rotation is 

started with the plate 

in this position, it 

immediately swings 

through the position 

shown in part (b) and 

continues to oscillate 

back and forth until 

the oscillation damps 

out.

(b) Rotation about axis 

of maximum inertia. 

When rotation is 

started with the plate 

in this position, it 

remains in this 

orientation during 

the rotation.
22 Monographs in Aerospace History Number 40—Journey Into Space Research

Stability and Control of Space Vehicles

inertia. Goldstein, in his book, Classical

Mechanics, however, states: “This fact

was learned the hard way by early

designers of spacecraft.” In other words,

there must have been some spinstabilized satellite that was launched

spinning about its axis of minimum inertia and was intended to continue spinning in this manner, but which, because

of internal energy dissipation, ended in

a flat spin about its axis of maximum

inertia.

Moments Acting on a 

Satellite

Moments acting on a satellite may come

from the following sources that are

inherent in the environment or motion of

the vehicle. These moments are in addition to those supplied intentionally by

mechanisms such as jets, gyroscopes,

or inertia wheels.

1. Gravitational fields in space

2. Centrifugal force on parts of the 

satellite

3. Magnetic fields in space

4. Radiation pressure

5. Aerodynamic forces 

In the early days of the Space program,

I presented a lecture on these moments

to members of the Flight Research Division as part of the Pearson lecture

series. Information on these topics was

obtained from then current technical

papers. Since then, textbooks and

reports that discuss these subjects in

greater depth have become available

(ref. 3.3). These texts, however, necessarily present derivations involving

rather complex mathematics. To avoid

the need for such derivations, I will confine this presentation to discussion of

the illustrative examples worked out in

my lecture.

For convenience, the moments are designated as rolling, yawing, and pitching

moments in a way analogous to the

usual definitions for aircraft. Thus, if a

satellite is in an orbit, a rolling moment

tends to rotate the satellite about a horizontal axis in the orbital plane, a yawing

moment about a vertical axis in the

orbital plane, and a pitching moment

about an axis normal to the orbital

plane.

Gravitational and Centrifugal 

Moments

Consider first the effects of gravity and

centrifugal force on the pitching

moments of a satellite in an orbit about

a planet. A dumbbell-shaped satellite is

used as an example. The dumbbell consists of two equal concentrated masses

connected by a weightless rod. This

configuration is used because it experiences the greatest gravitational and

centrifugal moments of any body of the

same total weight and size.

If such a body is aligned with the direction of flight and rotated to various

angles about an axis normal to the

orbital plane (a pitching motion), the

centrifugal forces due to the angular

velocity of orbital rotation may be shown

to be zero, but the gravitational forces

tend to hold the body in a vertical attitude. This effect is usually called the

gravity gradient effect; it results because

the lower mass of the dumbbell is

nearer to the center of the planet than

the upper mass. The gravitational attraction, which varies inversely as the

square of the distance from the center

of the planet, is therefore greater on the

lower mass. The moment tending to

align the dumbbell vertically is zero

when the dumbbell is horizontal or vertical and reaches a maximum at a pitch

angle of 45°.
Gravitational and Centrifugal Moments

Monographs in Aerospace History Number 40—Journey Into Space Research 23

The rolling moment on a dumbbellshaped body is discussed for the case

in which the body is aligned normal to

the orbital plane and is rotated to various angles about a horizontal axis in the

orbital plane. The analysis for the gravitational effects is identical to that for the

pitching moments, but in this case, the

centrifugal effects due to orbital angular

velocity also tend to align the dumbbell

with its long axis vertical. The magnitude of the rolling moment due to centrifugal forces is 1/3 that due to the

gravity gradient. As a result, the total

rolling moment is 4/3 that of the pitching

moment.

The yawing moment on a dumbbellshaped body is discussed for the case

in which the body is aligned with its long

axis horizontal and is rotated to various

angles about a vertical axis. In this

case, gravity gradient effects are zero,

but the centrifugal forces create a

moment tending to align the body with

the flight direction. The magnitude of

this effect is the same as for the rolling

moment, that is, 1/3 the magnitude of

the pitching moment. This effect is

caused by the tendency, discussed previously, of all elements of mass of a

rotating body to move into the plane of

rotation.

All pitching, rolling, and yawing

moments on a satellite do not really

depend on the fact that the satellite is in

orbit. A body on the surface of the

Earth, located on the equator and experiencing the Earth’s rotation, would feel

the moments from the same sources.

These moments are so small, however,

that only in the weightless condition of

space are they noticeable. On Earth, it

would be very difficult to mount the body

on a bearing supporting its weight that

would be sufficiently close to its center

of gravity or sufficiently frictionless to

avoid masking these effects.

To give an idea of the small magnitude

of these moments, the period of oscillation of the dumbbell about its equilibrium attitude in orbit may be calculated.

The period is given as a fraction of the

orbital period.

Pitch

Roll

Yaw 1.0

The orbital period of a satellite in a low

Earth orbit is about 90 minutes; therefore, the period in minutes for these

three cases is

Pitch 51.96

Roll 63.6

Yaw 90

The periods for any other satellite would

be longer than those of the dumbbellshaped body considered. 

Another comparison of the magnitude of

these effects may be made by comparing the periods of the motion with those

of a more familiar vehicle such as an airplane. For a typical light airplane, the

period of the lateral oscillation in the

cruise condition would be about 3 seconds. For a dumbbell-shaped satellite

with the same moment of inertia in yaw

as the light airplane, the period of the

lateral oscillation would be 90 minutes

or 5400 seconds. For a given moment of

inertia, the restoring moment in yaw varies inversely as the square of the

period. The restoring moment on the

body in orbit is therefore (3/5400)2 or

3.1 × 10–7 times as great. 

The very small magnitude of the

moments acting on a vehicle in space

1

3

1

2
24 Monographs in Aerospace History Number 40—Journey Into Space Research

Stability and Control of Space Vehicles

requires the development of new concepts for stability and control. Despite

the very small magnitude of moments

produced by gravity gradient effects,

such moments may be used as the

basis of a stabilization system for a satellite. Usually, such moments are used

to keep an elongated vehicle in a vertical orientation, to keep an antenna or

sensor pointed at the Earth. In addition

to the restoring moment provided by the

gravity gradient, damping devices must

be used to damp out oscillations about

the equilibrium attitude. Without the provision of damping, oscillations would

continue indefinitely.

Magnetic Moments

Magnetic moments may arise from the

interaction of the Earth’s magnetic field

with a permanent magnet or other magnetized material on a satellite, or from

eddy-current damping of a rotating satellite made of conducting material. The

interaction of the Earth’s field with a

magnet on a satellite in orbit is similar to

that of the Earth’s field on a compass

needle. This problem is discussed in

many available textbooks and is therefore not considered further herein.

If any conducting body is rotated in a

magnetic field, currents are induced in

the body. These currents generate magnetic flux that interacts with the original

magnetic flux to produce a torque. The

torque is always in a direction to oppose

the rotation. The energy required to

maintain the rotation is lost in the form

of heat generated by the ohmic resistance to the current in the body. 

The moments due to eddy-current

damping are quite important in many

satellite applications because of the

practice of spinning bodies to provide

attitude stabilization. An estimate of the

time for the original rotation to decay is

needed. This problem can be solved

analytically only for simple geometric

shapes, such as cylinders or spheres

(ref. 3.4). As an example, consider an

aluminum cylinder that is long compared to its radius spinning about its

long axis in a low Earth orbit. If the rotation is such as to cut the magnetic lines

of force at right angles, the rotation is

shown to damp to half its initial angular

velocity in about 3.1 days. To determine

the effect of the Earth’s field on an

actual spinning satellite, however,

experimental measurements are usually

required. The accuracy of these measurements may be increased and the

time for the test may be greatly reduced

by spinning the satellite in an artificial

magnetic field many times the strength

of the Earth’s field. If the actual satellite

is too large to test in this manner, a

scale model simulating the inertial and

electrical characteristics of the full-scale

device may be used.

Effect of Radiation Pressure

Frequently, persons unfamiliar with

space research do not realize that sunlight shining on a surface exerts a pressure. The magnitude of this pressure on

a black surface normal to the incident

radiation is

where W is the intensity of the incident

energy and c is the velocity of light. This

pressure may be approximately doubled

by the use of an aluminized surface to

reflect the radiation. At the Earth’s

radius, ergs/s cm2 and

 cm/s. Hence P for a reflecting surface is dyne/cm2.

A moment tending to point a satellite

towards the Sun may be obtained by

P Wc =

W = × 1 3 106 .

c = ×3 1010

0 866 10 4 . × −
Effect of Aerodynamic Forces

Monographs in Aerospace History Number 40—Journey Into Space Research 25

equipping the satellite with a fin of

reflecting material supported on a light

structure. The moment provided by such

a fin varies as the sine squared of the

angle between the sunlight and the fin.

The fin is therefore quite ineffective at

small angles of deviation. This problem

may be overcome by using a pair of fins

in the form of a V. The maximum effect

is obtained by setting each fin at an

angle of 45°.

The magnitude of the restoring moment

provided by such an arrangement may

be illustrated by the following example.

Consider a 20-inch-diameter satellite

equipped with a V-shaped pair of fins

each 1 m2. Assume the following characteristics:

The period of small oscillations about

the equilibrium position is 13.5 minutes.

The period is a much smaller fraction of

the orbital period than that obtained by

gravity gradient or centrifugal effects.

The effect of radiation pressure acting

on large, light “solar sails” has been

studied as a means of propulsion in

space. The acceleration produced by

this method is small, but because of the

lack of aerodynamic resistance in

space, large changes in velocity may be

obtained by allowing this force to act

over a long period of time.

Effect of Aerodynamic 

Forces

The forces and moments acting on an

object in the rarified atmosphere at

high altitudes above the Earth are governed by aerodynamic effects existing in

a flow condition called Newtonian flow.

The laws for aerodynamic forces in

Newtonian flow are equivalent to those

for radiation pressure. The density of the

atmosphere falls off continuously with

increasing altitude. A point of interest is

the altitude at which the impact pressure due to this rarified gas on a satellite traveling at orbital speed would be

equivalent to the radiation pressure. A

rough calculation indicates that this

condition exists at an altitude of about

420 miles. The satellite with V-shaped

fins discussed previously, flying at this

altitude in the shadow of the Earth

would have the same oscillation period

due to aerodynamic forces alone

(13.5 minutes) as that of the satellite

exposed to solar radiation in a complete vacuum. At lower altitudes, the

period due to aerodynamic forces

would decrease until at an altitude of

200 miles; the period would be about

48 seconds.

At an altitude of 420 miles, assuming a

nearly circular orbit, the loss in altitude

per orbit due to aerodynamic drag on

the fin-stabilized satellite would be only

0.0058 miles (30.6 feet) while at an altitude of 200 miles, the loss would be

1.47 miles. These figures illustrate that

aerodynamic forces can have a large

effect on the angular motions of a satellite while they are still small enough to

have a minor effect on the trajectory.

Another application of this effect is

the ability of aerodynamic forces to

align an entry vehicle in the correct

direction before aerodynamic heating

and deceleration become large. For

example, consider a vehicle weighing

4000 pounds and having directional stability equivalent to a fin area of 18 feet2

acting at a moment arm of 3 feet from

the center of gravity. If the vehicle enters

the atmosphere at a sideslip angle

of 90°, the aerodynamic forces at an

altitude of 350,000 feet will be sufficient

Moment of inertia in 

yaw

2 × 106 gm cm2

Distance from center 

of gravity to centroid 

of V

75 cm
26 Monographs in Aerospace History Number 40—Journey Into Space Research

Stability and Control of Space Vehicles

to produce an angular acceleration of

about 0.5° per second2. The vehicle

would pick up an angular velocity of

5° per second in 10 seconds and would

pass through zero sideslip in about

20 seconds. Other studies have shown

that the aerodynamic heating rate does

not start to build up, at least in a flat

entry (flight path angle less than –3° at

300,000 feet) until about 100 seconds

after this point. The deceleration does

not build up until a later time. For successful alignment of the vehicle, however, artificial damping would probably

have to be provided; otherwise, it would

oscillate back and forth through a large

amplitude with very little damping.

At the time the Mercury capsule was

under consideration, Mr. Robert Gilruth,

then Chief of PARD, expressed concern

that if the retro-rocket on the capsule

failed to fire, the capsule might be left in

orbit so long that the oxygen and other

supplies onboard the vehicle would be

exhausted. I proposed a device that

could be deployed to add a sufficiently

large amount of aerodynamic drag on

the vehicle to cause it to enter the atmosphere in a reasonable time. A sketch of

this device is shown in figure 3.3. My

thought was that an ordinary parachute

might fail to open because of the small

dynamic pressure. In the device proposed, a series of curved vanes would

be attached to thin cables wrapped

around a bobbin. The bobbin would be

expelled from the vehicle by a spring or

a small explosive charge. As it traveled

back, the vanes would unwind from the

bobbin, forming a train long enough to

add the required amount of drag. Gyroscopic effect would keep the bobbin

itself in a stable attitude, and it would fall

free at the end of the deployment. This

device would allow placement of the

train of drag vanes in a straight line

behind the vehicle without relying on the

very small aerodynamic drag to stretch

out the thin cables and vanes. I made a

small model of the device using a bobbin for sewing thread and vanes of

paper. The model illustrated the principle successfully. The idea was never

used, possibly because the attitude control rockets could serve as a backup to

the retro-rocket.

The methods mentioned previously for

applying moments to satellites are usually slow acting and limited to applications requiring small moments. For

FIGURE 3.3. Sketch of 

drag device proposed 

for causing an orbiting 

spacecraft to enter 

Earth’s atmosphere in 

case of failure of retrorocket. Many small 

vanes could produce 

required drag.

Part of spacecraft

Vanes

Bobbin

Side view

Top view
Effect of Aerodynamic Forces

Monographs in Aerospace History Number 40—Journey Into Space Research 27

applications requiring larger moments,

rockets or flywheels may be used. Both

of these techniques have a limited total

impulse. For example, the rocket can

be used until its fuel is used up, after

which it can no longer provide a

moment. The flywheel can be spun up

by a motor, producing a moment on the

satellite in the opposite direction. The

motor turns the flywheel faster and

faster until it reaches its limiting speed

or the flywheel fails due to excessive

centrifugal stresses. Alternatively, the

flywheel can be run at a constant speed

and mounted in gimbals like a gyroscope. A moment applied to an axis perpendicular to the axis of rotation will

then cause the gyro wheel to precess,

while the gimbal to which the moment is

applied will not move. As a result, an

opposite moment will be applied to the

satellite. The gyro wheel will precess

until its axis is in alignment with the axis

about which the moment is applied. At

this point, the gyroscope is said to be

saturated and will no longer resist the

applied moment.

A combination of a gyroscope and a

rocket may be used so that when the

gyro is approaching saturation, a

moment may be applied to the satellite

with a rocket to precess the gyro so that

it its gimbals rotate back to the original

orientation. In this way, the gyro may

continue to be used until the rocket fuel

is exhausted, or perhaps some other

slower acting source of torque may be

used to desaturate the gyro. The gyroscope method, in some cases, has an

advantage that its ability to hold the satellite in the desired orientation is practically unlimited except for effects of

structural flexibility.

Monographs in Aerospace History Number 40—Journey Into Space Research 29

CHAPTER 4 Rendezvous

Rendezvous of a spacecraft with a target vehicle means maneuvering the

spacecraft in such a way that it comes in

close to the target vehicle with small or

zero relative velocity. Docking, a maneuver that often follows rendezvous,

means that the spacecraft is attached to

the target vehicle to allow transfer of

equipment or personnel.

In this chapter, three aspects of my work

on rendezvous are discussed. From the

earliest days of the space program, the

importance of rendezvous in conducting

space operations was realized. If the

space program had been influenced primarily by scientific and technical thinking rather than by political considerations, a logical development would have

been to test some small manned satellites and then place a space station in

orbit. Such a space station would have

allowed much basic research on problems of space flight with application to

later missions to the Moon or planets.

Obviously, rendezvous of supply vessels with the space station would have

been necessary to conduct these operations. Many researchers in the space

program made studies to determine

how a spacecraft should be controlled in

a rendezvous maneuver. A brief review

will be given of the work that I did in this

field.

In an effort to overcome the perception

that the Russians were ahead of the

United States in space research, and,

by implication, in all scientific and technical developments, president John F.

Kennedy, on May 25, 1961, made his

bold commitment that the United States

should place a man on the Moon within

a decade. This extraordinarily difficult

task required new developments in

many fields. As it turned out, rendezvous was an important consideration in

two of the three mission plans that were

considered. The three mission plans

were direct ascent, Earth orbit rendezvous, and lunar orbit rendezvous. The

part played by engineers in my division

and by others at the Langley Research

Center in reaching the decision to use

the lunar orbit rendezvous technique is

described in this chapter.

The third subject discussed in this chapter is the development of the actual

guidance and navigation systems used

in the Apollo mission. Although the original Langley research was effective in

convincing officials of the space program that the lunar orbit rendezvous

mode was the correct technique to use,

later developments showed that the

original Langley concepts were oversimplified, and that much more sophisticated methods were used in the actual
30 Monographs in Aerospace History Number 40—Journey Into Space Research

Rendezvous

Apollo mission, both in the theoretical

developments and in the design of hardware.

Effect of Orbital Mechanics

In the early stages of the space program, I and many other researchers

made studies to determine how a

spacecraft should be controlled to perform a rendezvous maneuver. Because

of the relatively short time usually

allowed for such a maneuver, the

spacecraft is assumed to be maneuvered by use of jets or rockets that allow

control of rotation about three axes and

control of velocity along three axes.

If two vehicles are in the vacuum of

space and are sufficiently far from other

heavenly bodies that the effects of gravitational fields of these bodies are negligible, then rendezvous is a relatively

simple procedure. In a two-dimensional

analogy, it would be much like one

skater on ice maneuvering to catch up

with and move along with another

skater. Obviously there are many paths

that could be followed in such a maneuver. Other constraints would have to be

imposed to specify a definite maneuver,

such as the time for the maneuver, the

energy (or fuel) expended, or vehicle

direction and motion as limited by visual

or other constraints.

In maneuvers within the solar system,

the effects of gravitational fields of the

Sun and planets are always of some

importance. In most practical cases,

both vehicles are in orbit about the

same planet. If the two vehicles are at

the same altitude and speed, but displaced in different positions in a circular

orbit, they continue to move in the

same relative position because both

vehicles are subject to the same gravitational acceleration. Any attempt to perform a rendezvous, however, places

the vehicles in different orbits, requiring

the application of more complex variations of force to perform the desired

maneuver.

If the vehicles are in sufficient proximity

and are moving with small relative

velocity, differences in acceleration

caused by differences in gravitational or

centrifugal force are small. In this case,

the maneuver required to perform a rendezvous is only slightly different from

that required in space far from the influence of heavenly bodies. As the relative

velocity of or displacement between the

vehicles increases, the required maneuver becomes different. My initial studies

were concerned with calculation of the

paths required of the rendezvous vehicle at larger values of the displacement

and relative velocity.

Although the derivation of the equations

for the motion of the vehicle requires the

use of mathematics, in this presentation

an attempt is made to give only the

method involved. The equations for the

orbit of a body around a planet may be

set up considering the initial conditions

of the body and the acceleration due to

the gravitational field of the planet. Adding small increments to the variables in

these equations gives the equations of

a second vehicle that can be considered

the rendezvous vehicle. Subtracting the

first set of equations from the second

then gives the equations describing the

relative motion of the rendezvous vehicle and the orbiting vehicle. Readers

familiar with differential calculus will

realize that this procedure incorporates

the derivation of the methods of calculus. The procedure may be simplified

using the methods of calculus by simply

taking the differential of the original

equation.

The resulting equations are nonlinear

because the gravitational force varies

inversely as the square of the distance

from the center of the planet. In general,
Simulation Experiments

Monographs in Aerospace History Number 40—Journey Into Space Research 31

there is no closed-form solution of these

equations. A closed-form solution is one

that can be expressed in terms of

known functions, such as trigonometric

functions or other tabulated functions.

To obtain a closed-form solution, the

variables may be expanded in power

series and terms higher than the first

order may be neglected. If the relative

displacements and velocities of the

vehicles are sufficiently small, the

higher order terms will be very small

and the solution of the linearized equations will be reasonably accurate.

As explained in the book Journey in

Aeronautical Research (ref. 1.1), the linearized equations for the motion of an

airplane for small disturbances are

highly accurate because the aerodynamic forces and moments vary linearly

with the displacements and velocities

in the range used in normal flight. It

is natural, then, that I should try the

same method in the problem of rendezvous. Many other research groups

derived these linearized rendezvous

equations about the same time that I

did. A paper by W. H. Clohessy and

R. S.Wiltshire of the Martin Company,

containing these equations, was presented in June 1959 (ref. 4.1). As a

result, these equations were usually

referred to as the Clohessy-Wiltshire

equations, although these authors

acknowledge that an earlier paper containing these equations was brought to

their attention after the presentation of

the paper. My work was never published

because of the earlier appearance of

these other papers in the literature.

Simulation Experiments

A complete chapter devoted to simulation of space operations will be presented subsequently. At this point,

however, some early work on simulation

of rendezvous is introduced because it

was one of the first simulation studies

conducted, and because it had an

important bearing on subsequent developments in the space program.

The purpose of the simulation was to

investigate whether a spacecraft pilot

could rendezvous with a target vehicle

by observing the illuminated vehicle

against a star background. Simulation

equipment at that time (about 1959) did

not have the advantage of computergenerated displays and digital computer

solutions of vehicle dynamics that were

available in the nineties. Considerable

ingenuity was required to provide a realistic simulation in a short time at low

cost.

A planetarium can provide a visual

scene of the stars and heavenly bodies,

but planetarium projectors and spherical

screens of the type used in museums

and observatories are quite expensive.

Max Kurbjun and other engineers in my

division provided the necessary spherical screen by obtaining a hemispherical

inflatable radome, about 50 feet in diameter, of the type that was used for protecting radar equipment in Alaska. A

sufficiently complete star background

was provided by using a point light

source to project beams of light through

small lenses, providing simulated

stars on the inside of the radome. Originally, the simulation was performed

under conditions of free space, without

the effects of gravitation of a nearby

planet. Later, an early type of analog

computer was obtained that allowed

including the effects of orbital mechanics as represented by the ClohessyWiltshire equations.

Carrying out a rendezvous in space was

a maneuver that had not been

attempted at that time, and many people

expressed doubt that such a maneuver

would be sufficiently safe to be practical.

The main result of the simulation study

was to show that the rendezvous could
32 Monographs in Aerospace History Number 40—Journey Into Space Research

Rendezvous

be made quite simply with a minimum of

guidance equipment or instrumentation. These runs were made at relatively

close range, so that the visual cues

played an important role providing the

required information to the pilot or astronaut. Furthermore, the rendezvous simulator provided a convenient tool for

demonstrating such a maneuver to

other personnel involved in the space

program.

Implementation of 

Rendezvous in Apollo 

Program

The Lunar Orbit Rendezvous mode was

selected as the design basis of the

Apollo Mission. In this mode, the Lunar

Module (LM) must take off from the

Moon and rendezvous and dock with

the Command Module (CM) that is in

orbit around the Moon. Some of the

lengthy arguments and conferences

involved in selecting this mode of operation are discussed later. For the present

purpose, a brief comparison is made

between the methods employed in

the simulation described previously and

the actual guidance and navigation

techniques used in the Apollo mission.

These methods are discussed in detail

in the excellent book by Richard H.

Battin (ref. 4.2).

The Apollo mission managers selected

the Draper Lab in Cambridge, Massachusetts to design the Apollo guidance

and control system. This organization

had extensive previous experience in

development of inertial navigation systems and in missile guidance. The engineers in this organization obviously

had much more experience in the

design of sophisticated guidance equipment than the Langley engineers in

my division, who just a year or so earlier had been working on stability and

control of aircraft.

The Apollo mission could be controlled

by radio guidance from the ground or by

the astronauts onboard the vehicle by

using the navigation instruments provided. The main reason for the onboard

navigation capability was to give the

astronauts a guidance capability when

the vehicle was on the back side of the

Moon and as a backup in the unlikely

failure of the radio guidance system.

Both the LM and the CM were provided

with onboard computers of an unusual

and advanced (for that time) design that

provided a high degree of reliability.

These computers were hard-wired to

solve the equations representing the

orbital motions of the vehicles during

the rendezvous operation as well as in

all the other phases of the mission.

The lunar orbit rendezvous technique

requires that the LM take off from the

Moon and rendezvous and dock with

the CM that is in orbit around the Moon.

At the time, other engineers in the Aerospace Mechanics Division at Langley

and I were deriving the rendezvous

equations, we were unaware that the

exact solution of these equations had

been obtained over two centuries ago

by famous mathematicians, including

Carl Frederich Gauss, Joseph-Louis

Lagrange, and Johann Heinrich

Lambert. In fact, the equations for determining the orbit of a body to go from one

given point in space to another given

point with a specified transfer time are

known as Lambert’s equations. As

pointed out previously, these equations

cannot be solved in closed form, but the

early mathematicians had derived iterative solutions to solve the equations to

any desired accuracy. Such iterative

solutions, improved by modern developments, were programmed into the computers used in the Apollo mission.

Inertial platforms used in conjunction

with radar equipment were used to
Implementation of Rendezvous in Apollo Program

Monographs in Aerospace History Number 40—Journey Into Space Research 33

measure the relative positions of the

vehicles. Sextants operated by the

astronauts were used to determine the

location of the vehicles with respect to

the Earth, Moon, and other reference

objects. Thus the rendezvous navigation

was performed in a highly sophisticated

manner, taking into account all the gravitational influences of nearby heavenly

bodies and allowing accurate calculation of rendezvous trajectories of any

length or orientation.

The same equations and navigational

equipment were used in all phases of

the Apollo mission, such as insertion

into translunar orbit, midcourse corrections in all phases of the mission, insertion into lunar orbit, and so on. Many of

these mission phases required taking

into account gravitational influences of

the Sun, Earth, and Moon. In addition,

the locations of over 50 navigational

stars, as well as the corrections to the

position of the Earth and Moon when

using the sextant to track the horizons,

rather than the centers of these bodies,

were all programmed into the Apollo

computers. In using these data, the

astronauts were required to punch into

the computer on a keyboard the data

obtained in celestial readings. The computer would then automatically solve the

equations to obtain the present and

future positions of the vehicle and its

deviation from the planned trajectory.

One young engineer in my division,

Robert Collins, had learned enough in

his college studies to know of Lambert’s

equations. He devised an iterative technique of solution, using the Langley

computer complex, to solve the rendezvous problem using Lambert’s equations. This solution brought the

possibility of an exact solution to the

attention of Langley engineers but was

too late to influence the Apollo guidance

system. The experience gained in the

early simulation studies proved very

helpful to the Langley engineers who

later joined the Space Task Group and

took part in the actual design of the

Apollo system. For example, Walter J.

Russell, who operated a small analog

computer in the Langley rendezvous

studies, was later placed in charge of all

analog computer equipment at the

Johnson Space Center. John Mayer,

one of the Langley engineers who participated in the lecture series conducted

by Henry Pearson, was later in charge

of all digital computing equipment at

the Johnson Space Center. John M.

Eggleston, who made studies of optimal

rendezvous at Langley, participated in

the design of the Apollo control system

and held important administrative positions at the Johnson Space Center.