journey into space research - nasa · monographs in aerospace history number 40—journey into...

Journey Into Space ResearchContinuation of a Career at NASA

Langley Research CenterW. Hewitt Phillips

Monographs in Aerospace HistoryNumber 40July 2005

NASA/SP-2005-4540

Journey Into Space Research

Continuation of a Career at NASALangley Research Center

byW. Hewitt Phillips

NASA History OfficeOffice of Policy and Plans

NASA HeadquartersWashington DC 20546

Monographs in Aerospace HistoryNumber 40July 2005

Cover photograph (L-05136): Little Joe rocket being launched fromWallops Island. Several of these rockets were launched to studyseparation of the escape capsule from the Mercury capsule.

The use of trademarks or names of manufacturers in this monograph isfor accurate reporting and does not constitute an official endorsement,either expressed or implied, of such products or manufacturers by theNational 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


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


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/ft

2

; 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/ft

2

.

10

FIGURE 2.5.

Effect of entry angle,

γ

o

, on heat-transfer rates for entries at 90° angle of attack. Wing loading, 20 lb/ft

2

; 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


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 ofinterest both to scientists and to thegeneral public. Science fiction becamepopular with the works of Jules Verne,whose fanciful stories of space exploitsinspired many later science fiction publi-cations. These stories were usually notbased on valid science and technologyor they were ahead of the developmentsthat might have made them possible.These works, however, served to stimu-late thought on space flight for manyyears. Some groups, such as the BritishInterplanetary Society, made seriousstudies of the requirements for spaceflight. These efforts failed to lead topractical developments because of lackof financial support or interest from gov-ernmental organizations or from thepublic. These early studies had littleeffect on actual developments in thespace program because, with greatersupport and larger numbers of investi-gators, the results were quickly redis-covered and not until later was it foundthat some important results had beenworked out previously.

Studies of the possible military applica-tions of space flight were started by mili-tary organizations in the United Statesabout 1950, but these studies wereclassified secret. I, like the general pub-lic, was unaware of any activity in this

field until the nation was startled by theRussian launching of Sputnik. The lastchapter of the preceding volume on thehistory of my work at Langley (ref. 1.1)describes how the nation was galva-nized into action and started a nationalspace program. These developmentsare described in more detail in the bookSpaceflight Revolution (ref. 1.2).

The advent of the space program was awelcome event to many of the researchgroups at Langley. One reason for thisattitude was that aeronautical researchhad reached a plateau at this time.Many of the research contributions ofLangley and other National AdvisoryCommittee for Aeronautics (NACA) cen-ters had reached fruition in the designand production of advanced airplanes.These airplanes included jet bombersand transports, and supersonic fighterairplanes. Research and design workon the supersonic transports, theBritish Concorde and the RussianTU144, had progressed to a point thatconstruction could proceed with someassurance of success. No really revolu-tionary advances for atmospheric air-craft were envisioned at that time orhave occurred in the ensuing years.Some of the wind-tunnel organizations,however, expressed concern that theirwork might be cut back or otherwise

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

Introduction

affected by the emphasis on spaceresearch.

In the case of my work and that of theFlight Research Division, another eventoccurred that required a change indirection. A NACA Headquarters edict,published in 1958, stated that no furthertesting of high-speed airplanes would

be done at Langley. All future flightresearch on such airplanes was to bedone at the Edwards Air Force Base inCalifornia (now called the Dryden FlightResearch Center). The engineers in mydivision therefore were available forassignments in the field of spaceresearch.


CHAPTER 2 Blast Off Into Space

With the start of the space program, arapid transition occurred in the types ofresearch performed at Langley. Atfirst, the emphasis was on educatingresearch personnel so that they couldbecome acquainted with the new disci-plines and skills required in spaceresearch. Second, there was a diverseeffort in space research, applying thenewly acquired knowledge to the solu-tion of problems that were recognizedas being important in this field. Soon,however, a national space program wasestablished, involving both unmannedand manned satellites. Space flight cen-ters were established to take the leadin specific types of work, such as scien-tific satellites, interplanetary probes,and manned space flight. The variousgroups at Langley generally initiatedwork that would contribute to a specificphase of the national space program,and general research programs werephased out. In some cases, researchprograms were stopped by manage-ment because they did not fit in thenational space program or because thework being done had been assigned toother centers.

The discussion that follows appliesmainly to the work being done under my

direction in the Guidance and ControlBranch of the Flight Research Division(1959–1962), the Aerospace MechanicsDivision (1962–1963) and the SpaceMechanics Division (1963–1970). Noattempt has been made to presentthe dates or time periods of differentresearch programs. Because over40 years has passed since the start ofthe national space program, however,many readers today may be unfamiliarwith the progress of space flight and thetimes at which certain goals wereaccomplished. To assist the reader inrelating the work described to theprogress in space flight, an abbreviatedchronology of space launches and mis-sions, both Russian and American, ispresented in appendix I. These datawere obtained from the TRW Space Log(ref. 2.1). Much more detailed discus-sions of the various NASA space pro-grams are available in the NASAHistorical Publications that have beenprepared to describe each major pro-gram. Some of these publications aregiven in references 2.2, 2.3, and 2.4.Others are given in the lists of referenceworks included in these publications.




The start of the space program was atime of rapid transition for most aero-nautical research organizations in thecountry. The Russian feats of orbitingSputnik satellites had captured the inter-est of the general public, first from asense of wonder that space vehiclesactually existed and second from asense of fear that these vehicles, withunknown capabilities, might signal thestart of an era in which the enemy wouldhave technical expertise exceeding ourown. The engineering community wasperhaps less alarmed but neverthelessrealized that a great deal of study andresearch was necessary to becomefamiliar with the disciplines involved inthis relatively unknown field.

The effect on the administrators inWashington, as is well known, was tocause them to initiate the change of theNACA, the National Advisory Commit-tee for Aeronautics, from a small gov-ernment organization reporting directlyto the president, to the NASA, theNational Aeronautics and Space Admin-istration, a large government agencyreporting to Congress and involvingmany new research centers and opera-tional centers in addition to those in theoriginal NACA. This change, however,did not immediately affect the researchprograms at the Langley Research Cen-ter. The change in research emphasis atthis center came primarily from theinterest of the center personnel in newfields of work involving flight in spaceand the desire to learn as much as pos-sible about a promising new area ofresearch.

In the Flight Research Division, I wasstill assigned as Head of the Stabilityand Control Branch. At this time,Henry A. Pearson, Head of the AircraftLoads Branch, initiated a program in

which various engineers would lookup some subject involved in spaceresearch and give a lecture on it to thewhole division. The notes on theselectures were collected in a volume(ref. 2.5), the table of contents of whichis given in figure 2.1. These notes werewidely distributed in the NASA centersbut were never published. A copy of thisvolume is available in the LangleyResearch Center Library. As stated inthe preface of the volume, the initialdemand for the notes was so great that,“for the sake of expediency, this goal (ofrapid distribution) is best achieved bymaking the material available in itspresent unedited form instead of follow-ing the usual NACA editing procedure.”Later, most of the engineers involvedhad become involved in specific spaceprojects and therefore had no time forthe work of preparing the volume formore formal publication.

Similar studies and lectures were con-tinued after the distribution of the vol-ume. Among the subjects I studied werethe rotational motion of a free body inspace and later, the relative motion oftwo bodies, a subject of importance inconnection with space rendezvous.Many other research organizations, inthis period, were equally involved in anintense educational effort to learneverything possible about space flight.These organizations included the aero-nautical departments of engineeringcolleges and government researchgroups in the Army, Air Force, and Navy.

In studying these problems, it wasimpressive to find how much famousmathematicians centuries ago, who hadno idea of applying their theories tospace travel, had learned in studyingthe motions of planetary bodies. Thesebrilliant men had studied these prob-lems as pure academic exercises, with-out modern computing facilities andwithout the incentive provided by experi-mental research with artificial satellites.



In many cases, they originated mathe-matical techniques used in spaceresearch, particularly the techniquesrequired for the calculation of satelliteorbits.

I was also impressed by the progressmade by astronomers. These scien-tists, who devoted their lives to abstractstudies to understand the nature of theuniverse, soon realized that they hadknowledge of value in the space pro-gram. An example of this research,which could be classed as an engineer-ing study as well as a scientific effort, isgiven in a brief note entitled Explorationof Space from the University of Virginia,published in the University of VirginiaNews Letter in January 1959 (ref. 2.6).This note points out that the explorationof space there had been going on for75 years, since the acquisition of a largetelescope in 1888. The main object ofthese studies is the field known as

astronometrics, the study of the dis-tances to and relative positions of thestars and other heavenly bodies. TheUniversity of Virginia at Charlottesville,Virginia is one of the colleges closest toLangley with an astronomy department,and valuable contacts were establishedthere that later aided in the work on theApollo program.

The subjects presented in these lec-tures included many disciplines thathad little relation to the aeronauticalwork previously conducted by thesebranches. For example, a lecture onhypersonic flow was included becausesuch flow conditions would be involvedin the flight of rockets or space vehicleswhile entering or leaving the atmo-sphere. Orbital mechanics was con-sidered important because vehiclesoperating in space would be subjectto the same laws that had been devel-oped for planets and other heavenly

FIGURE 2.1. List of top-ics covered in Henry A. Pearson’s lecture series.

III

III

IVV

VI

VIIVIII

IXX

XIXII

XIIIXIV

XVXVI

XVII

W. B. Huston and J. P. MayerT. H. Skopinski

J. P. Mayer

A. P. MayoA. P. Mayo

J. J. Donegan

D. C. CheathamC. W. Mathews

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

W. B. HustonW. S. Aiken, Jr.

E. M. FieldsC. R. Huss

W. J. OʼSullivan and J. L. MitchellP. A. Gainer and R. L. Schott

D. Adamson

W. A. McGowan

Elementary Orbital MechanicsSatellite Time and Position With Respect to a Rotating Earth SurfaceThe Motion of a Space Vehicle Within the Earth-Moon System: The Restricted Three-Body ProblemOrbital TransferReentry With Two Degrees of FreedomSix Degree of Freedom Equations of Motion and Trajectory Equations of a Rigid Fin Stabilized Missile With Variable MassInertial Space NavigationGuidance and Control of Space VehiclesElements of Rocket PropulsionCharacteristics of Modern Rockets and PropellantsAerodynamic Heating and Heat TransmissionHeat ProtectionProperties of High Temperature MaterialsThe Solar SystemAppendix on the Earthʼs AtmosphereCommunication and TrackingSome Dynamical Aspects of the Special and General Theories of RelativityEnvironmental Requirements



bodies. The theory of relativity wasconsidered important because it hadbeen involved previously in astronomi-cal studies. This theory becomes impor-tant when the motion of the bodiesinvolved approaches the speed of light.Such speeds were not contemplated inthe type of space operations required inthe early years of the space program.Nevertheless, the desire to understandthe laws governing the universe maderelativity a subject of interest in the newfield of space flight. It was known that aslight motion of the perihelion of theplanet Mercury had been detectedthat was not explained by Newtonianmechanics and was one of the exam-ples presented by Einstein as a methodof verifying his theory of general relativ-ity. Thus, relativity might have an effecteven on the motion of objects in thesolar system. In later space projectsinvolving precise measurements of timeor in the use of spacecraft for navigationpurposes, inclusion of relativistic effectswas found necessary to obtain thedegree of precision desired.

Fortunately, an engineer with a knowl-edge of Einstein’s theories, workingin the Physical Research Division atLangley, was available. He was DavidAdamson, an Englishman who studiedphysics at Durham University but wasemployed at the Royal Aircraft Estab-lishment (RAE) in England during WWIIin research on airplane handling quali-ties. After the war he came to work atLangley. As a result of his experience inengineering as well as in physics, hislectures on the complex subject of rela-tivity were presented to the engineerswith unusual clarity.

Item 3 in the list of topics in figure 2.1 isa lecture by J. P. Mayer on the subject ofthe three-body problem. This notableproblem concerns the motion of threebodies in space, such as, for example,the Sun, Moon, and Earth, under theinfluence of their mutual gravitational

attraction. This problem has been stud-ied by many famous mathematiciansover the centuries. Despite the amountof effort expended in its solution, thisproblem, in all its generality, has neverbeen completely solved. As often hap-pens when brilliant mathematicianswork on a very difficult problem, how-ever, the work led to advances in manyfields of mathematics. As an aside,John P. Mayer later joined the SpaceTask Group working on the MercuryProject and was later in charge of all thecomputing facilities at the JohnsonSpace Center during the Gemini andApollo programs. Practically all the engi-neers in the Aircraft Loads Branch laterjoined the Space Program, either inthe Space Task Group or at the newGoddard Space Flight Center. In thelist of lecturers given in figure 2.l,these engineers include Wilbur B.Huston, John P. Mayer, Ted H. Skopin-ski, Alton P. Mayo, James J. Donegan,and Carl R. Huss. Others on the list,who worked in my branch, are DonaldC. Cheatham and Charles W. Mathews.Mathews later moved to NASA Head-quarters in Washington and becamehead of the Gemini project, one of themost successful space flight projects.Cheatham worked at the JohnsonSpace Flight Center and did importantwork in the design of the Space Shuttlecontrol system.


One of the main objectives of manyresearch organizations both in theNACA and in the armed services wasto beat the Russians in a race to placea man in space. The Air Force hadits MISS program (Man in Space Soon-est). At Langley, the Pilotless AircraftResearch Division (PARD) was incharge of Robert R. Gilruth, formerly my



boss in the Flight Research Division.Members of PARD, who had developedexperience in handling rockets by usingthem to propel test vehicles used inaeronautical research, proposed placingthe astronaut in a capsule that could belaunched into space by the existingAtlas Rocket and recovered by para-chute with a splashdown in the ocean.This imaginative program, largely theconcept of Maxime A. Faget, an engi-neer in PARD, later won the approval ofNASA and developed into the MercuryProject. The Air Force Program, mean-while, continued with several studies ofvehicles called the Robo, Brass Bell,and Hywards. Finally these studieswere consolidated into the Dynasoarproject, also called the X-20. This pro-gram received considerable support andreached an advanced state of engineer-ing development, but was cancelled in1963. The reasons for the cancellationwere that no well-defined military mis-sion for the vehicle could be found, thatthe cost was excessive, and thatby 1963 the NASA Gemini programplanned to accomplish many of theobjectives of the Dynasoar program.During the early stages of the Mercuryprogram studies, there was much con-cern that the ocean splash-down wouldbe impractical and that the vehicleshould allow the astronaut to land“like a gentleman,” with a conventionalairplane-type landing at an airport.

In considering this problem, I triedto take advantage of the conceptdeveloped by H. Julian Allen and A. J.Eggers, Jr. of the NASA AmesResearch Center that a blunt-facedobject would be much more suitable forentry into the atmosphere than apointed, rocket-like object (ref. 2.7). Thisconcept was based on the fact that suchan object would dissipate the tremen-dous energy of the vehicle entering theatmosphere in the form of shock wavesthat carried the energy away from the

vehicle, rather than in the form of heatthat would produce temperatures highenough to melt or decompose mostmaterials. The same concept wasemployed in the Mercury project by hav-ing the capsule enter the atmosphereblunt end first, with a suitable heatshield on the blunt end.

In considering the application of thisconcept to an airplane-like configura-tion, I visualized that the airplane couldenter the atmosphere at near 90° angleof attack, then pitch down to normalgliding attitude after the speed haddecreased sufficiently that heatingwould not be a problem. A delta-wingconfiguration seemed suitable for thispurpose, but controls had to be pro-vided to control the attitude of the vehi-cle during entry and to pitch the airplanedown to normal attitudes for landing. Asketch of the resulting vehicle is shownin figure 2.2. To pitch the airplane downafter entry into the atmosphere, a set oftail surfaces was provided that foldedinto the shielded region behind the vehi-cle during entry, but unfolded for thepitch-down maneuver and subsequentglide. In addition, four hinged surfaceswere provided around the outline of thevehicle, which, by suitable combinationof deflections, could provide pitch, yaw,and roll control during entry. Such con-trols are now known as controllablestrakes and are now being used on thenose of a fighter airplane to assist incontrol at high angles of attack. Theadvantage of these controls for an entryvehicle was that they simply extendedthe outline of the vehicle at angles ofattack near 90° and were not subject toany more heating than the lower surfaceof the vehicle, on which the heating wasreduced because of its large area.

Soon, considerable interest was gener-ated in further studies of a vehicle of theproposed type. I made a small model toillustrate the concept. Many engineersin my branch, with some assistance



from others in the Aircraft Loads Branchand the Performance Branch, madedetailed studies of such aspects asheating, structural loads, and stabilityand control. The vehicle was sized toweigh about 2000 pounds, the same asthe Mercury capsule, so that it could becarried on the nose of the Atlas Rocket.Preliminary calculations showed that avehicle capable of carrying a singleastronaut could be made within thisweight limitation.

The heating studies were made byJohn A. Zalovcik of the PerformanceBranch. He had previously gained con-siderable familiarity with this branch ofaerodynamics in his studies of airspeed

measurements and heating problems ofsupersonic aircraft.

Among the phases of flight studied werethe orbital phase, the atmospheric entry,the transition from flight in the vacuumof space to flight in the atmosphere, andthe control of the vehicle as the air-speed decreased from hypersonicspeed during the initial entry to super-sonic speed and finally to low subsonicspeed for landing. Most of these opera-tions were unfamiliar to aeronauticalengineers who had previously dealtwith conventional airplanes. Some ofthe newly acquired knowledge of thedynamics of orbital flight was applied inthis work.

FIGURE 2.2. Drawing of concept for entry vehi-cle studied by mem-bers of Flight Research Division.

(a) Reentry.

(b) Landing.



The return from an orbit around theEarth required firing a rocket to causethe vehicle to change its orbit from anear-circular path around the Earth toan orbit that entered the atmosphere.Though the initial thought based on air-plane experience would be to fire arocket perpendicular to the flight path,studies showed that a much smallerrocket impulse would be required if therocket were fired along the path in adirection to slow the vehicle down. Thenthe force of gravity would take over tobring the vehicle down into the atmo-sphere. This rocket was therefore calleda retro-rocket, a term now familiar in dis-cussions of space flight operations. Astudy was made of the effect of themagnitude of the retro-rocket impulseon the angle at which the vehicleentered the atmosphere and thedistance traveled before entering theatmosphere.

With too shallow an entry angle, thevehicle would skip back out of the atmo-sphere, whereas with too steep anentry, the vehicle would experienceexcessive deceleration, resulting inintolerable loads on the human pilot.Tilting the vehicle from an attitude inwhich the lower surface was perpendic-ular to the flight direction to one in whichthe longitudinal axis of the vehiclemade a smaller angle with the flightdirection, provided a lift force to slow thevehicle’s entry into the denser region ofthe atmosphere and a desirable reduc-tion in the deceleration of the vehicle. Ingeneral, the entry angle needed to bebetween –0.5° and –1°. Some of theseresults are illustrated in figure 2.3. Therange of –0.5° to –1° appears small, butthe accuracy of the direction and magni-tude of the retro-rocket burn was wellwithin the capability of existing rocketsand control systems. A fortunate effectof the laws of orbital motion is that theentry angle is very insensitive to the tiltof the deorbit impulse. Variations of this

angle by as much ±10° from the flightdirection produced less than a 0.02°change in the entry angle. In general, atshallow entry angles, the entry anglehad little effect on the variation of decel-eration, which reached a maximumvalue of about 8 g for the conditionsconsidered. Tilting the vehicle longitudi-nal axis from the perpendicular positionby just 10° shortly after the start ofthe buildup of deceleration reducedthe maximum value to the more desir-able value of about 5 g, as shown infigure 2.4.

The effects of variation in the entryangle of the vehicle on the aerodynamicheating were also investigated. Some ofthese results are shown in figure 2.5.The maximum heating rate remainedabout the same for entry anglesbetween –1° and –0.25°, but this maxi-mum occurred later in the entry at theshallower angles.

At that time, some studies had beenmade of the effects of different heatshield materials for use on the researchairplanes such as the X-1; heat resis-tant alloys such as Rene 41, a nickel-chromium alloy, withstood temperaturesup to 1600 °F. This material would allowthe use of a steeper entry with less totalheat input to the vehicle because thehigh temperature surface would radiatemuch heat. On the other hand, berylliumhas a high heat capacity, so that a rea-sonable thickness of the material wouldabsorb the heat of entry. These twomaterials typified what were called radi-ative and heat sink type heat shields,respectively. A combination of thesematerials was at that time thought suit-able to protect the vehicle from aerody-namic heating. At that time, ablativematerials, such as Teflon®, had shownpromise in tests in hypersonic wind tun-nels, but the amount of data availablewas not sufficient to allow considerationof their use on a vehicle. Ablative mate-rials decompose at high temperatures.



FIGURE 2.3. Effect of entry angle on varia-tions of deceleration, velocity, and flight-path angle, γγγγ, with alti-tude. Wing loading, 20 lb/ft2; angle of attack, 90°.

FIGURE 2.4. Time histo-ries 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.

–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

0350 300 250 200

Altitude, ft150 100 × 103

× 103

Deceleration,g units

Velocity,ft/sec

90 t > 0 s90 t < 370 s80 t > 370 s

4

2

0

468

10

100

2030

1000

200300

400

Altitude,ft

Velocity,ft/s

Deceleration,g units

Flight-pathangle, deg

Distance,miles

20

–40–60

–80

–100

–200

0 200100 300 500400Time, s

600 700

× 103

× 103

× 103

{



This process absorbs heat and theouter layers turn to gaseous productsthat carry the heat away from the vehi-cle. Later, many additional develop-ments were made both in ablative andradiative heat shields, as typified by theheat shields on the Apollo capsule andon the Shuttle Orbiter, respectively.

The studies associated with the wingedentry vehicle were published as NASATechnical Memorandum X-226 entitledA Concept of a Manned Satellite Reen-try Which Is Completed With a GlideLanding by the Staff of LangleyFlight Research Division, compiled byDonald C. Cheatham (ref. 2.8). Thismemorandum was originally classifiedconfidential but has since been declas-sified. Also, a patent was issued inmy name entitled Variable GeometryWinged Entry Vehicle. At that time, per-sonnel at many of the wind tunnels atLangley wished to contribute to thespace program, but not many designs

for entry vehicles had been proposed.The results of the Flight ResearchDivision study, however, had beendiscussed with personnel involved inaerodynamic research. As a result,independently of my efforts, branchheads in a number of the wind tunnelsoperating in different speed ranges hadmodels with folding wing tip panels con-structed and ran tests.

A large model of the Flight ResearchDivision vehicle was built for tests in thespin tunnel. A picture of the model beingtested is shown in figure 2.6. Thesetests were intended to study the abilityof the four-hinged surfaces around theborder of the vehicle to provide stabilityand control during descent at 90° angleof attack. These tests showed that thecontrol was easily accomplished. Later,an air jet was fitted to the rear of thefuselage and the model was mounted ina vertical position in the test sectionof the NASA 30- by 60-Foot Tunnel to

FIGURE 2.5. Effect of entry angle, γγγγo, 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 200100 300 500400Time, s

600



study the use of the folding tail surfacesto provide transition from 90° angle ofattack to a glide attitude. This maneuverwas again easily accomplished by grad-ually deploying the tail surfaces as the

tunnel speed was increased from zeroto the speed for horizontal flight. In fact,the configuration showed promise as atail-sitter vertical takeoff and landing(VTOL) airplane.

FIGURE 2.6. Large model of entry vehicle being tested in Lan-gley Spin Tunnel to study control at or near 90° angle of attack.



This configuration, or some variations ofit, for a time acquired the most completeset of aerodynamic data of any wingedentry configuration, covering the entirerange of Mach numbers within the capa-bilities of the Langley wind-tunnel facili-ties. A Langley committee called theSteering Committee for Manned SpaceFlight served to communicate theresearch results among the variousgroups. Several of these wind-tunnelstudies were published as NASA Tech-nical Memorandums (refs. 2.9–2.11).These reports also contain long lists ofreferences containing additional testson these and other configurations madeduring the same time period. By thetime these data were published, theSpace Task Group had been formed toimplement the Mercury project. Thisgroup was relocated in Houston, Texasto form the nucleus of the JohnsonSpace Flight Center. Before the groupmoved to Houston, however, theyrequested a presentation of the resultsof the Flight Research Division study tocompare the relative advantages of thetwo approaches. The presentation hadlittle effect on the planning for the Mer-cury project, mainly because, with thedesire to put a man in space as soon aspossible, the Mercury development wasobviously simpler and involved lessdevelopment. In addition, Mercuryincluded the feature of an escape towerthat was considered essential for astro-naut safety in case the Atlas rocket mal-functioned on the launch pad.

The beneficial results of the FlightResearch Division study included edu-cational background for many of theengineers who later joined the SpaceTask Group and early analysis of trajec-tory and heating problems that providedresults applicable to most types of entryvehicles. In addition, the later develop-ment of the Shuttle Orbiter involved aconfiguration somewhat similar to thatstudied by the Flight Research Division.

As a result, the engineers who hadjoined the space task group and laterworked at the Johnson Space Centerwere able to apply this experience in thedesign of the Shuttle Orbiter.


Just as the Flight Research Divisionrapidly changed its emphasis fromresearch on airplanes to research onspace vehicles, all the other divisions atLangley attempted to use their expertiseto investigate many problems of spaceflight. This research was not confined tostudies of the initial brief orbital mis-sions but included studies of unmannedsatellites and of manned orbiting spacestations intended for long durations inspace. Many problems confronting thecrew of a space station were immedi-ately recognized. They included numer-ous biomedical problems, such as theeffects of zero gravity, protection fromthe vacuum of space, protection fromionizing radiation (already discovered byVan Allen in his initial orbital experi-ments), and provision of food, water,and oxygen over long periods. In con-nection with the vehicle itself, therewere problems of temperature control,generation and storage of energy, pro-tection from meteoroids, and effects ofthe space environment on materials andstructures. It is remarkable that muchbasic knowledge of many of these sub-jects was obtained in the first two yearsof the Space program.

A brief discussion of some of the workdone at Langley on these space-relatedproblems is now presented. I was notconnected with these projects butlearned of them through participationin committee meetings and visits tosee items of research equipment.These comments are based on my rec-ollections and may not be historically



accurate, but they reflect the opinions ofthe research that I formed at that time.

In the areas of biomedical research,Dan Popma of the Instrument ResearchDivision (ref. 2.12) headed an extensiveprogram. He proposed ingenious ideasfor methods to purify the atmosphere ofa space station, to provide oxygen, andto recycle wastewater and urine. Meth-ods of testing these devices in ground-based facilities were suggested. He alsoconsidered the medical effects of zerogravity and studied centrifuges, rotatingspace stations, and other ideas, manyof which were finally tested in spacemany years later. This promising workcame to an abrupt halt when NASAHeadquarters ruled that all biomedicalresearch should be conducted in a newfacility at the Ames Research Center,manned mainly by medical doctors. Iconsidered it a mistake to place thiswork in the hands of doctors rather thanengineers. Dan Popma was an engi-neer, and his approach was much morelogical and could have produced therequired information for manned spaceflight much more quickly than the pro-gram that actually evolved. The doctors,who frequently lacked research experi-ence and had no experimental data togo on, feared that unknown effects inspace might cause a human being tobecome disoriented or might even provefatal, and they therefore proposed thatdifficult and inconclusive animal experi-ments should be performed before aman was allowed to go into space. Testpilots, on the other hand, had experi-enced, in high-altitude flight, many ofthe problems that at least approachedthose expected in space and did not seeany reason to delay placing a man inorbit. The eventual program representeda compromise of these views. After afew manned space flights had beenmade, the Ames group became involvedin other research, such as theories ofthe origin of life. Such theories are an

important subject for scientific research,but they have little bearing on the prob-lems of manned space flight.

Other groups at Langley were con-cerned with methods of overcoming theeffects of zero gravity. An obvious con-cept was the use of a rotating spacestation to allow the centripetal accelera-tion to simulate gravity. Paul Hill andothers in the PARD conceived an inflat-able rotating toroidal space station, likea large inner tube. This design wouldallow the device to be folded compactlyfor launching and then to be deployed inspace. A contract was given to theGoodyear Corporation to build an engi-neering model of this concept. Themodel was about 15 feet in diameterand was set up to study inflation,strength, puncture resistance, and leak-age. When Charles Donlan, at that timethe Deputy Director of Langley, heard ofthis work, he immediately ordered itstopped because a large space stationwas not at that time part of the NASAspace program. This and other experi-ences made it clear that the freedom topursue new ideas that had existedunder the NACA was curtailed underNASA, and projects had to fit the overallspace program as established by NASAHeadquarters.

Several groups studied the problem ofdurability of materials and electronicequipment in the space environment.An electron accelerator of the Van deGraaf type was acquired for thisresearch. Later, a large laboratory,called the Space Radiation Effects Lab(SREL) was built in Newport News andrun in cooperation with the College ofWilliam and Mary. A large cyclotron sup-plied the required radiation. This workcontinued for many years, but after theend of the Apollo Program, funds for thisproject were discontinued. Later still, thecyclotron was removed, but the buildingwas used as part of the ThomasJefferson Research Laboratory, which



contains a large, continuous beam elec-tron accelerator for basic research innuclear physics. My rather surprisinginvolvement in tiding over the use of thefacility during the lull in funding betweenthe Apollo era and the development ofthe electron accelerator is described ina later chapter.

Engineers at Langley also foresaw theneed for studies of other aspects of thespace environment on many types ofmaterials. Some work could be con-ducted in vacuum tanks. An example ofthis research is the study of friction ofmoving parts in the vacuum of space.Despite the desire to conduct muchresearch of this type, very little wasdone because instead of first puttingup a space station and later proceed-ing with more complex missions, Presi-dent Kennedy initiated the Apollo pro-gram, which required a relatively short-duration mission. As a result, the effectsof long exposure to space have beenstudied extensively only in recent yearsby using the Long Duration ExposureFacility (LDEF) satellite launched andrecovered by the Space Shuttle.

A number of engineers at Langleyinvestigated space power systems.About the time these studies were beingstarted, I learned about rechargeablenickel-cadmium batteries for poweringthe transmitters, receivers, and servosof radio-controlled model airplanes. Thegreat advantage of these batteries isthat they can be charged and dis-charged many hundreds of times with-out deterioration. I contacted one of theengineers working on the space sys-tems and found that he had not yetheard about these batteries. This expe-rience shows that hobbyists are some-

times more alert to new developmentsthan professionals. Nickel-cadmium bat-teries, or NiCads as they are called,have since been used extensively inspacecraft power systems.

Another engineer who turned his atten-tion to space power systems was AlbertE. Von Doenhoff, a former airfoil expertwho was mentioned in reference 1.1 forhis aircraft landing study. Assisted byRoland Ohlson and Joseph M. Halissy,he made an analysis of solar regenera-tive space power systems (ref. 2.13). Inthis type of system, a solar collectorheats and vaporizes a working fluid,which drives an engine similar to asteam engine or steam turbine. Theworking fluid is then condensedfor reuse by a radiator that radiatesheat to the blackness of space. Thesteam engine, of course, may then drivean electric generator. I thought thatVon Doenhoff’s analysis was excellent,but in that same period, solar photo-voltaic cells were developed to a usablestage. These cells, together with NiCadbatteries to store the energy, have beenused since then on practically all spacemissions. The weight and complicationof the regenerative power systems havediscouraged their use. Such systemsstill might be candidates for power onvery large spacecraft or on planetarybases.

Roland Ohlson, who formerly worked inthe NACA towing tank testing seaplanesand flying boat hulls, complained to meafter his retirement that nothing he hadever worked on was used anymore. Isuppose that many research engineersmust expect this outcome of their careerspecialties in this time of rapid develop-ment of scientific and technical ideas.


CHAPTER 3 Stability and Control of Space Vehicles

This historical document is not intendedto present a theoretical discussion ofthe problems encountered in designingspace vehicles. The conditions in space,however, are so different from the famil-iar Earth-based environment that someappreciation of the effect of these condi-tions on the dynamics and control ofspace vehicles is required to under-stand the reasons for the research stud-ies conducted in the course of thespace program. In flight in free space,far removed from any influence of otherheavenly bodies, a vehicle experiencesno disturbances. This condition is notattainable on Earth. In the solar systemand in particular in Earth orbit, somevery small disturbing influences exist.These influences include effects of grav-ity, forces due to flight through rarifiedgas, moments from magnetic fields, andeffects of solar radiation. Although theseeffects are small, they are of greatimportance because they provide theonly means of controlling a spacecraftwithout the expenditure of fuel orenergy. This chapter is thereforeintended to give a discussion of theseproblems with as little dependence aspossible on mathematical derivations.Primary emphasis is placed on a physi-cal appreciation of the phenomenainvolved.

A term used in analyzing the rotationalmotion of a body is the moment of iner-tia about some specified axis. Themoment of inertia resists rotationalacceleration of the body, just as its massresists linear acceleration. The momentof inertia of a small element of mass inthe body is determined by multiplyingthe mass of the element by the squareof the perpendicular distance from theaxis. The moment of inertia of the entirebody is determined by summing thecontributions of all the elements ofmass.

To allow calculation of the motion of thebody resulting from torques (also calledmoments) applied about arbitrary axes,the moments of inertia are first deter-mined about three mutually perpendicu-lar axes through the center of gravity ofthe body. In all rigid bodies, these val-ues of inertia serve to define an ellip-soid, called the ellipsoid of inertia, theformula for which is given in the follow-ing text. The axes defining the maximumand minimum values of inertia, togetherwith the third axis perpendicular tothese two, are called the principal axesof inertia. These axes are of specialimportance in determining the rotationalmotion of bodies.

The ellipsoid of inertia may be the samefor many different bodies that have the



elements of mass distributed differently.The angular motion of all these bodiesin response to a given applied torquewould be the same.


One of the most obvious problemsencountered in studying the motion ofrigid bodies is the motion of an arbitrarybody when it is started with a rotatingmotion. Students of elementary physicslearn that the translational motion of thecenter of gravity of a body depends onthe external forces applied at this pointand that the rotational motion about thecenter of gravity is independent of thetranslational motion. The problem of therotational motion can therefore be stud-ied independently of the forces acting atthe center of gravity of a body.

Although the rotation of a rigid body inthe absence of all external momentswould appear to be the first problem tostudy in this field, the solution of thisproblem is not well-known. In my gradu-ate course at MIT, Introduction to Theo-retical Mechanics, I do not recall thisproblem being mentioned. There areprobably two reasons for this neglect.First, for bodies rotating on the Earth,there are always eternal momentsapplied during the course of the motion.A rather complex mounting systemwould be required to reduce thesemoments to very small values. Actualfreely rotating vehicles, such as base-balls, airplanes, boats, etc. have rela-tively large moments applied by thesurrounding air or liquid medium. Sec-ond, the solution to this problem ofmotion with no external moments is verycomplex, and little was to be gained byteaching this solution when no practicalexamples existed.

Many problems of rotating bodies occurwhen external moments are applied.The equations for the solution of theseproblems are known as Euler’s dynami-cal equations. These equations aretaught in standard courses in mechan-ics. I used these equations in the analy-sis of the effect of steady rolling onstability of airplanes, a problem laterknown by the name “roll coupling”(ref. 1.1).

In 1957, before the start of the spaceprogram, I had some introduction to theproblem of rotation of rigid bodies with-out external moments. I became familiarwith a report by G. W. Braün, an engi-neer at the Wright Air DevelopmentCenter, on an analysis of the spinning ofairplanes (ref. 3.1). Braün assumed thatat high altitudes, the aerodynamicforces on a spinning airplane would besmall compared to the inertial forces. Asa result, the equations with no externalmoments appeared to be a good start-ing point for the studies of such spins.With the advent of space flight, bodiesin space outside the Earth’s atmosphereexperience extremely small externalmoments. The rotational motion of thesebodies in space is therefore a problemof practical importance. I also looked upfurther information in a book on classi-cal mechanics by Goldstein (ref. 3.2), onwhich the subsequent discussion isbased.

Although the mathematical details ofthis problem are too complex to presentherein, a novel geometric solution ofthis problem obtained in 1834 by LouisPoinsot, a French mathematician, ispresented. To describe this solution, abrief discussion of the method of speci-fying the applicable characteristics of arigid body is considered desirable.

For studying the rotational motion of arigid body, the detailed distribution of theelements of mass in the body or theshape of the body is not required. The



body may be described by the momentsof inertia about three mutually perpen-dicular axes, with their origin at the cen-ter of gravity, called the principal axes ofinertia. These values of moments ofinertia, represented as vectors IX, IY,and IZ along the three principal axes,can be used to determine the axes of anellipsoid, called the ellipsoid of inertia.The shape of the ellipsoid is determinedby the mathematical formula for an ellip-soid:

where a, b, and c represent the dis-tances from the center of the ellipsoid toits surface along the X, Y, and Z axes,respectively. The ellipsoid of inertia isdefined by setting

, , and

Vectors drawn from the origin to otherpoints on the ellipsoid may be used tocalculate the values of moments of iner-tia about any other axes through thecenter of gravity by using similar formu-las. Different bodies with different

detailed distribution of mass elementsmay have the same ellipsoid of inertia.

For any given ellipsoid of inertia, a solu-tion of Euler’s dynamical equations withthe external moments set equal to zeroallows the calculation of the motion fol-lowing a disturbance in terms of ellipticintegrals. A closed-form solution is thusavailable, but the calculations requiredare quite lengthy. Poinsot gave a veryingenious method of visualizing themotion of a freely rotating body inspace. During the motion, in which thebody rotates about the center of gravity,the ellipsoid of inertia rolls on a plane,called the invariable plane. Poinsotcalled the curve on the invariable planetraced out by the point of contact of theellipsoid and the plane the herpolhode,and the curve on the ellipsoid traced outby the point of contact the polhode.Thus, the brief explanation of themotion, as quoted in Goldstein’s bookon Classical Mechanics (ref. 3.2) is “Thepolhode rolls without slipping on theherpolhode lying in the invariable plane.”A sketch of this construction is shown infigure 3.1.

The assumption that no externalmoments 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

xa

yb

zc

2

2

2

2

2

21+ + =

a Ix=1/ b I y=1/ c Iz=1/



there are no damping moments. Amotion once started, therefore, will con-tinue indefinitely. The only steady rota-tions occur when the body is rotatingabout one of its principal axes, as seenfrom the fact that the tip of the axis thentouches the invariable plane in just onepoint. In general, the motions started inany other manner would be highly oscil-latory; that is, the principal axes wouldoscillate through large angles withrespect to a fixed reference system.Such oscillatory motions would bevery undesirable for most practicalapplications.

A question also arises as to the stabilityof the motion when it is started aboutone of the principal axes. The momentsof inertia may always be classified asminimum, intermediate, and maximum.If the body is rotating about the axes ofminimum or maximum moment of iner-tia, and is slightly disturbed, it willacquire a small oscillation or wobble. If itis rotating about the axis of intermediateinertia, however, and is slightly dis-turbed, it will immediately swing througha large angle and continue in a large-amplitude oscillation. The rotation aboutthe axis of intermediate inertia maytherefore be considered statically unsta-ble and is unsuitable for a vehicleintended to perform a steady rotation.

In the early days of the space program,there was considerable discussion ofthe design of rotating space stationsintended to provide a centrifugal forceon the bodies of the astronauts to simu-late the gravitational force existing onEarth. Once, in a meeting of one ofthe research coordinating committeeschaired by Eugene Draley, an AssistantDirector of Langley at that time, a pre-sentation was made for the design ofa rotating space station that rotatedabout its axis of intermediate inertia. Ipointed out that the vehicle would beunstable as a result of the consider-ations described previously. This fact

was not known to any other member ofthe committee. The design of the vehiclewas stopped at this point for furtherstudy. As a result, we avoided someembarrassment to Langley that mighthave occurred had the design been pro-posed to NASA Headquarters.

A simple method of visualizing the ten-dency of a rotating body to rotate aboutits axis of maximum inertia is to con-sider that each element of mass in thebody experiences a centrifugal forcetending to pull it into the plane of rota-tion. The body as a whole will then tendto move to a condition in which its ele-ments are as close as possible to theplane of rotation. This tendency willcause a pancake-shaped body, forexample, to approach a condition inwhich the rotation is about an axis nor-mal to the plane of the pancake. With nosource of damping, however, the body, ifstarted in an orientation displaced fromthe plane of rotation, will overshoot thisorientation and continue to oscillateback and forth about it.

To illustrate these points further, I hada model constructed, sketched in fig-ure 3.2, in which a flat slab of aluminumwas pivoted on a universal joint andcould be rotated about a fixed axis byturning a handle. The aluminum slabrepresented the dynamic characteristicsof a rotating space station. If the rotationwere started with the plane of the slabin the axis of rotation, a condition ofrotation about the intermediate axis ofinertia, the slab performed a large-amplitude oscillation. The oscillationdamped out fairly quickly because of airresistance and bearing friction, and theslab ended up with its plane normal tothe axis. In space, where the dampingforces are much less, such an oscilla-tion would continue much longer. If therotation is started with the plane of theslab perpendicular to the axis of rota-tion, corresponding to rotation about its



axis of maximum inertia, the steadyrotation continues.

The theory discussed so far assumes arigid body. All space vehicles, in prac-tice, have some flexibility, or some mov-able parts. When the body distorts, orwhen parts move, some energy is dissi-pated by internal damping or friction.This energy can come only from therotating body itself.

Newton’s laws state that the angularmomentum of a body will remain con-stant in the absence of externalmoments. If energy is dissipatedthrough internal causes, however, thenature of the motion must change. Ifthe rotating motion continues for along time, the motion will eventually

change to a rotation about the axis ofmaximum inertia, because this motion,for a given angular momentum, has theleast energy. Detailed consideration ofhow damping forces act on variousparts of the body might be extremelycomplicated, but the end result isalways the same. The body assumes asteady rotation about the axis of maxi-mum inertia. This condition results evenwhen the body starts rotating about itsaxis of minimum inertia, a stable condi-tion for a rigid body. So far as I know,this result has been known to designersof satellites launched by the UnitedStates, and in some cases intentionaldamping devices have been installed tospeed the settling down to a steadyrotation 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 iner-tia. 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.



inertia. Goldstein, in his book, ClassicalMechanics, however, states: “This factwas learned the hard way by earlydesigners of spacecraft.” In other words,there must have been some spin-stabilized satellite that was launchedspinning about its axis of minimum iner-tia and was intended to continue spin-ning in this manner, but which, becauseof internal energy dissipation, ended ina flat spin about its axis of maximuminertia.

Moments Acting on a Satellite

Moments acting on a satellite may comefrom the following sources that areinherent in the environment or motion ofthe vehicle. These moments are in addi-tion to those supplied intentionally bymechanisms 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 momentsto members of the Flight Research Divi-sion as part of the Pearson lectureseries. Information on these topics wasobtained from then current technicalpapers. Since then, textbooks andreports that discuss these subjects ingreater depth have become available(ref. 3.3). These texts, however, neces-sarily present derivations involvingrather complex mathematics. To avoidthe need for such derivations, I will con-fine this presentation to discussion ofthe illustrative examples worked out inmy lecture.

For convenience, the moments are des-ignated as rolling, yawing, and pitchingmoments in a way analogous to theusual definitions for aircraft. Thus, if asatellite is in an orbit, a rolling momenttends to rotate the satellite about a hori-zontal axis in the orbital plane, a yawingmoment about a vertical axis in theorbital plane, and a pitching momentabout an axis normal to the orbitalplane.


Consider first the effects of gravity andcentrifugal force on the pitchingmoments of a satellite in an orbit abouta planet. A dumbbell-shaped satellite isused as an example. The dumbbell con-sists of two equal concentrated massesconnected by a weightless rod. Thisconfiguration is used because it experi-ences the greatest gravitational andcentrifugal moments of any body of thesame total weight and size.

If such a body is aligned with the direc-tion of flight and rotated to variousangles about an axis normal to theorbital plane (a pitching motion), thecentrifugal forces due to the angularvelocity of orbital rotation may be shownto be zero, but the gravitational forcestend to hold the body in a vertical atti-tude. This effect is usually called thegravity gradient effect; it results becausethe lower mass of the dumbbell isnearer to the center of the planet thanthe upper mass. The gravitational attrac-tion, which varies inversely as thesquare of the distance from the centerof the planet, is therefore greater on thelower mass. The moment tending toalign the dumbbell vertically is zerowhen the dumbbell is horizontal or verti-cal and reaches a maximum at a pitchangle of 45°.



The rolling moment on a dumbbell-shaped body is discussed for the casein which the body is aligned normal tothe orbital plane and is rotated to vari-ous angles about a horizontal axis in theorbital plane. The analysis for the gravi-tational effects is identical to that for thepitching moments, but in this case, thecentrifugal effects due to orbital angularvelocity also tend to align the dumbbellwith its long axis vertical. The magni-tude of the rolling moment due to cen-trifugal forces is 1/3 that due to thegravity gradient. As a result, the totalrolling moment is 4/3 that of the pitchingmoment.

The yawing moment on a dumbbell-shaped body is discussed for the casein which the body is aligned with its longaxis horizontal and is rotated to variousangles about a vertical axis. In thiscase, gravity gradient effects are zero,but the centrifugal forces create amoment tending to align the body withthe flight direction. The magnitude ofthis effect is the same as for the rollingmoment, that is, 1/3 the magnitude ofthe pitching moment. This effect iscaused by the tendency, discussed pre-viously, of all elements of mass of arotating body to move into the plane ofrotation.

All pitching, rolling, and yawingmoments on a satellite do not reallydepend on the fact that the satellite is inorbit. A body on the surface of theEarth, located on the equator and expe-riencing the Earth’s rotation, would feelthe moments from the same sources.These moments are so small, however,that only in the weightless condition ofspace are they noticeable. On Earth, itwould be very difficult to mount the bodyon a bearing supporting its weight thatwould be sufficiently close to its centerof gravity or sufficiently frictionless toavoid masking these effects.

To give an idea of the small magnitudeof these moments, the period of oscilla-tion of the dumbbell about its equilib-rium attitude in orbit may be calculated.The period is given as a fraction of theorbital period.

Pitch

Roll

Yaw 1.0

The orbital period of a satellite in a lowEarth orbit is about 90 minutes; there-fore, the period in minutes for thesethree cases is

Pitch 51.96

Roll 63.6

Yaw 90

The periods for any other satellite wouldbe longer than those of the dumbbell-shaped body considered.

Another comparison of the magnitude ofthese effects may be made by compar-ing the periods of the motion with thoseof a more familiar vehicle such as an air-plane. For a typical light airplane, theperiod of the lateral oscillation in thecruise condition would be about 3 sec-onds. For a dumbbell-shaped satellitewith the same moment of inertia in yawas the light airplane, the period of thelateral oscillation would be 90 minutesor 5400 seconds. For a given moment ofinertia, the restoring moment in yaw var-ies inversely as the square of theperiod. The restoring moment on thebody in orbit is therefore (3/5400)2 or3.1 × 10–7 times as great.

The very small magnitude of themoments acting on a vehicle in space

13

12



requires the development of new con-cepts for stability and control. Despitethe very small magnitude of momentsproduced by gravity gradient effects,such moments may be used as thebasis of a stabilization system for a sat-ellite. Usually, such moments are usedto keep an elongated vehicle in a verti-cal orientation, to keep an antenna orsensor pointed at the Earth. In additionto the restoring moment provided by thegravity gradient, damping devices mustbe used to damp out oscillations aboutthe equilibrium attitude. Without the pro-vision of damping, oscillations wouldcontinue indefinitely.

Magnetic Moments

Magnetic moments may arise from theinteraction of the Earth’s magnetic fieldwith a permanent magnet or other mag-netized material on a satellite, or fromeddy-current damping of a rotating sat-ellite made of conducting material. Theinteraction of the Earth’s field with amagnet on a satellite in orbit is similar tothat of the Earth’s field on a compassneedle. This problem is discussed inmany available textbooks and is there-fore not considered further herein.

If any conducting body is rotated in amagnetic field, currents are induced inthe body. These currents generate mag-netic flux that interacts with the originalmagnetic flux to produce a torque. Thetorque is always in a direction to opposethe rotation. The energy required tomaintain the rotation is lost in the formof heat generated by the ohmic resis-tance to the current in the body.

The moments due to eddy-currentdamping are quite important in manysatellite applications because of thepractice of spinning bodies to provideattitude stabilization. An estimate of thetime for the original rotation to decay is

needed. This problem can be solvedanalytically only for simple geometricshapes, such as cylinders or spheres(ref. 3.4). As an example, consider analuminum cylinder that is long com-pared to its radius spinning about itslong axis in a low Earth orbit. If the rota-tion is such as to cut the magnetic linesof force at right angles, the rotation isshown to damp to half its initial angularvelocity in about 3.1 days. To determinethe effect of the Earth’s field on anactual spinning satellite, however,experimental measurements are usuallyrequired. The accuracy of these mea-surements may be increased and thetime for the test may be greatly reducedby spinning the satellite in an artificialmagnetic field many times the strengthof the Earth’s field. If the actual satelliteis too large to test in this manner, ascale model simulating the inertial andelectrical characteristics of the full-scaledevice may be used.

Effect of Radiation Pressure

Frequently, persons unfamiliar withspace research do not realize that sun-light shining on a surface exerts a pres-sure. The magnitude of this pressure ona black surface normal to the incidentradiation is

where W is the intensity of the incidentenergy and c is the velocity of light. Thispressure may be approximately doubledby the use of an aluminized surface toreflect the radiation. At the Earth’s

radius, ergs/s cm2 and

cm/s. Hence P for a reflect-

ing surface is dyne/cm2.

A moment tending to point a satellitetowards the Sun may be obtained by

P W c=

W = ×1 3 106.

c = ×3 1010

0 866 10 4. × −



equipping the satellite with a fin ofreflecting material supported on a lightstructure. The moment provided by sucha fin varies as the sine squared of theangle between the sunlight and the fin.The fin is therefore quite ineffective atsmall angles of deviation. This problemmay be overcome by using a pair of finsin the form of a V. The maximum effectis obtained by setting each fin at anangle of 45°.

The magnitude of the restoring momentprovided by such an arrangement maybe illustrated by the following example.Consider a 20-inch-diameter satelliteequipped with a V-shaped pair of finseach 1 m2. Assume the following char-acteristics:

The period of small oscillations aboutthe equilibrium position is 13.5 minutes.The period is a much smaller fraction ofthe orbital period than that obtained bygravity gradient or centrifugal effects.

The effect of radiation pressure actingon large, light “solar sails” has beenstudied as a means of propulsion inspace. The acceleration produced bythis method is small, but because of thelack of aerodynamic resistance inspace, large changes in velocity may beobtained by allowing this force to actover a long period of time.


The forces and moments acting on anobject in the rarified atmosphere athigh altitudes above the Earth are gov-

erned by aerodynamic effects existing ina flow condition called Newtonian flow.The laws for aerodynamic forces inNewtonian flow are equivalent to thosefor radiation pressure. The density of theatmosphere falls off continuously withincreasing altitude. A point of interest isthe altitude at which the impact pres-sure due to this rarified gas on a satel-lite traveling at orbital speed would beequivalent to the radiation pressure. Arough calculation indicates that thiscondition exists at an altitude of about420 miles. The satellite with V-shapedfins discussed previously, flying at thisaltitude in the shadow of the Earthwould have the same oscillation perioddue to aerodynamic forces alone(13.5 minutes) as that of the satelliteexposed to solar radiation in a com-plete vacuum. At lower altitudes, theperiod due to aerodynamic forceswould decrease until at an altitude of200 miles; the period would be about48 seconds.

At an altitude of 420 miles, assuming anearly circular orbit, the loss in altitudeper orbit due to aerodynamic drag onthe fin-stabilized satellite would be only0.0058 miles (30.6 feet) while at an alti-tude of 200 miles, the loss would be1.47 miles. These figures illustrate thataerodynamic forces can have a largeeffect on the angular motions of a satel-lite while they are still small enough tohave a minor effect on the trajectory.

Another application of this effect isthe ability of aerodynamic forces toalign an entry vehicle in the correctdirection before aerodynamic heatingand deceleration become large. Forexample, consider a vehicle weighing4000 pounds and having directional sta-bility equivalent to a fin area of 18 feet2

acting at a moment arm of 3 feet fromthe center of gravity. If the vehicle entersthe atmosphere at a sideslip angleof 90°, the aerodynamic forces at analtitude 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



to produce an angular acceleration ofabout 0.5° per second2. The vehiclewould pick up an angular velocity of5° per second in 10 seconds and wouldpass through zero sideslip in about20 seconds. Other studies have shownthat the aerodynamic heating rate doesnot start to build up, at least in a flatentry (flight path angle less than –3° at300,000 feet) until about 100 secondsafter this point. The deceleration doesnot build up until a later time. For suc-cessful alignment of the vehicle, how-ever, artificial damping would probablyhave to be provided; otherwise, it wouldoscillate back and forth through a largeamplitude with very little damping.

At the time the Mercury capsule wasunder consideration, Mr. Robert Gilruth,then Chief of PARD, expressed concernthat if the retro-rocket on the capsulefailed to fire, the capsule might be left inorbit so long that the oxygen and othersupplies onboard the vehicle would beexhausted. I proposed a device thatcould be deployed to add a sufficientlylarge amount of aerodynamic drag onthe vehicle to cause it to enter the atmo-sphere in a reasonable time. A sketch ofthis device is shown in figure 3.3. My

thought was that an ordinary parachutemight fail to open because of the smalldynamic pressure. In the device pro-posed, a series of curved vanes wouldbe attached to thin cables wrappedaround a bobbin. The bobbin would beexpelled from the vehicle by a spring ora small explosive charge. As it traveledback, the vanes would unwind from thebobbin, forming a train long enough toadd the required amount of drag. Gyro-scopic effect would keep the bobbinitself in a stable attitude, and it would fallfree at the end of the deployment. Thisdevice would allow placement of thetrain of drag vanes in a straight linebehind the vehicle without relying on thevery small aerodynamic drag to stretchout the thin cables and vanes. I made asmall model of the device using a bob-bin for sewing thread and vanes ofpaper. The model illustrated the princi-ple successfully. The idea was neverused, possibly because the attitude con-trol rockets could serve as a backup tothe retro-rocket.

The methods mentioned previously forapplying moments to satellites are usu-ally slow acting and limited to applica-tions 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 retro-rocket. Many small vanes could produce required drag.

Part of spacecraft

Vanes

Bobbin

Side view

Top view



applications requiring larger moments,rockets or flywheels may be used. Bothof these techniques have a limited totalimpulse. For example, the rocket canbe used until its fuel is used up, afterwhich it can no longer provide amoment. The flywheel can be spun upby a motor, producing a moment on thesatellite in the opposite direction. Themotor turns the flywheel faster andfaster until it reaches its limiting speedor the flywheel fails due to excessivecentrifugal stresses. Alternatively, theflywheel can be run at a constant speedand mounted in gimbals like a gyro-scope. A moment applied to an axis per-pendicular to the axis of rotation willthen cause the gyro wheel to precess,while the gimbal to which the moment isapplied will not move. As a result, anopposite moment will be applied to thesatellite. The gyro wheel will precess

until its axis is in alignment with the axisabout which the moment is applied. Atthis point, the gyroscope is said to besaturated and will no longer resist theapplied moment.

A combination of a gyroscope and arocket may be used so that when thegyro is approaching saturation, amoment may be applied to the satellitewith a rocket to precess the gyro so thatit its gimbals rotate back to the originalorientation. In this way, the gyro maycontinue to be used until the rocket fuelis exhausted, or perhaps some otherslower acting source of torque may beused to desaturate the gyro. The gyro-scope method, in some cases, has anadvantage that its ability to hold the sat-ellite in the desired orientation is practi-cally unlimited except for effects ofstructural flexibility.


CHAPTER 4 Rendezvous

Rendezvous of a spacecraft with a tar-get vehicle means maneuvering thespacecraft in such a way that it comes inclose to the target vehicle with small orzero relative velocity. Docking, a maneu-ver that often follows rendezvous,means that the spacecraft is attached tothe target vehicle to allow transfer ofequipment or personnel.

In this chapter, three aspects of my workon rendezvous are discussed. From theearliest days of the space program, theimportance of rendezvous in conductingspace operations was realized. If thespace program had been influenced pri-marily by scientific and technical think-ing rather than by political considera-tions, a logical development would havebeen to test some small manned satel-lites and then place a space station inorbit. Such a space station would haveallowed much basic research on prob-lems of space flight with application tolater missions to the Moon or planets.Obviously, rendezvous of supply ves-sels with the space station would havebeen necessary to conduct these oper-ations. Many researchers in the spaceprogram made studies to determinehow a spacecraft should be controlled ina rendezvous maneuver. A brief reviewwill be given of the work that I did in thisfield.

In an effort to overcome the perceptionthat the Russians were ahead of theUnited States in space research, and,by implication, in all scientific and tech-nical developments, president John F.Kennedy, on May 25, 1961, made hisbold commitment that the United Statesshould place a man on the Moon withina decade. This extraordinarily difficulttask required new developments inmany fields. As it turned out, rendez-vous was an important consideration intwo of the three mission plans that wereconsidered. The three mission planswere direct ascent, Earth orbit rendez-vous, and lunar orbit rendezvous. Thepart played by engineers in my divisionand by others at the Langley ResearchCenter in reaching the decision to usethe lunar orbit rendezvous technique isdescribed in this chapter.

The third subject discussed in this chap-ter is the development of the actualguidance and navigation systems usedin the Apollo mission. Although the orig-inal Langley research was effective inconvincing officials of the space pro-gram that the lunar orbit rendezvousmode was the correct technique to use,later developments showed that theoriginal Langley concepts were oversim-plified, and that much more sophisti-cated methods were used in the actual


Rendezvous

Apollo mission, both in the theoreticaldevelopments and in the design of hard-ware.

Effect of Orbital Mechanics

In the early stages of the space pro-gram, I and many other researchersmade studies to determine how aspacecraft should be controlled to per-form a rendezvous maneuver. Becauseof the relatively short time usuallyallowed for such a maneuver, thespacecraft is assumed to be maneu-vered by use of jets or rockets that allowcontrol of rotation about three axes andcontrol of velocity along three axes.

If two vehicles are in the vacuum ofspace and are sufficiently far from otherheavenly bodies that the effects of grav-itational fields of these bodies are negli-gible, then rendezvous is a relativelysimple procedure. In a two-dimensionalanalogy, it would be much like oneskater on ice maneuvering to catch upwith and move along with anotherskater. Obviously there are many pathsthat could be followed in such a maneu-ver. Other constraints would have to beimposed to specify a definite maneuver,such as the time for the maneuver, theenergy (or fuel) expended, or vehicledirection and motion as limited by visualor other constraints.

In maneuvers within the solar system,the effects of gravitational fields of theSun and planets are always of someimportance. In most practical cases,both vehicles are in orbit about thesame planet. If the two vehicles are atthe same altitude and speed, but dis-placed in different positions in a circularorbit, they continue to move in thesame relative position because bothvehicles are subject to the same gravita-tional acceleration. Any attempt to per-form a rendezvous, however, places

the vehicles in different orbits, requiringthe application of more complex varia-tions of force to perform the desiredmaneuver.

If the vehicles are in sufficient proximityand are moving with small relativevelocity, differences in accelerationcaused by differences in gravitational orcentrifugal force are small. In this case,the maneuver required to perform a ren-dezvous is only slightly different fromthat required in space far from the influ-ence of heavenly bodies. As the relativevelocity of or displacement between thevehicles increases, the required maneu-ver becomes different. My initial studieswere concerned with calculation of thepaths required of the rendezvous vehi-cle at larger values of the displacementand relative velocity.

Although the derivation of the equationsfor the motion of the vehicle requires theuse of mathematics, in this presentationan attempt is made to give only themethod involved. The equations for theorbit of a body around a planet may beset up considering the initial conditionsof the body and the acceleration due tothe gravitational field of the planet. Add-ing small increments to the variables inthese equations gives the equations ofa second vehicle that can be consideredthe rendezvous vehicle. Subtracting thefirst set of equations from the secondthen gives the equations describing therelative motion of the rendezvous vehi-cle and the orbiting vehicle. Readersfamiliar with differential calculus willrealize that this procedure incorporatesthe derivation of the methods of calcu-lus. The procedure may be simplifiedusing the methods of calculus by simplytaking the differential of the originalequation.

The resulting equations are nonlinearbecause the gravitational force variesinversely as the square of the distancefrom the center of the planet. In general,



there is no closed-form solution of theseequations. A closed-form solution is onethat can be expressed in terms ofknown functions, such as trigonometricfunctions or other tabulated functions.To obtain a closed-form solution, thevariables may be expanded in powerseries and terms higher than the firstorder may be neglected. If the relativedisplacements and velocities of thevehicles are sufficiently small, thehigher order terms will be very smalland the solution of the linearized equa-tions will be reasonably accurate.

As explained in the book Journey inAeronautical Research (ref. 1.1), the lin-earized equations for the motion of anairplane for small disturbances arehighly accurate because the aerody-namic forces and moments vary linearlywith the displacements and velocitiesin the range used in normal flight. Itis natural, then, that I should try thesame method in the problem of rendez-vous. Many other research groupsderived these linearized rendezvousequations about the same time that Idid. A paper by W. H. Clohessy andR. S.Wiltshire of the Martin Company,containing these equations, was pre-sented in June 1959 (ref. 4.1). As aresult, these equations were usuallyreferred to as the Clohessy-Wiltshireequations, although these authorsacknowledge that an earlier paper con-taining these equations was brought totheir attention after the presentation ofthe paper. My work was never publishedbecause of the earlier appearance ofthese other papers in the literature.


A complete chapter devoted to simula-tion of space operations will be pre-sented subsequently. At this point,however, some early work on simulationof rendezvous is introduced because it

was one of the first simulation studiesconducted, and because it had animportant bearing on subsequent devel-opments in the space program.

The purpose of the simulation was toinvestigate whether a spacecraft pilotcould rendezvous with a target vehicleby observing the illuminated vehicleagainst a star background. Simulationequipment at that time (about 1959) didnot have the advantage of computer-generated displays and digital computersolutions of vehicle dynamics that wereavailable in the nineties. Considerableingenuity was required to provide a real-istic simulation in a short time at lowcost.

A planetarium can provide a visualscene of the stars and heavenly bodies,but planetarium projectors and sphericalscreens of the type used in museumsand observatories are quite expensive.Max Kurbjun and other engineers in mydivision provided the necessary spheri-cal screen by obtaining a hemisphericalinflatable radome, about 50 feet in diam-eter, of the type that was used for pro-tecting radar equipment in Alaska. Asufficiently complete star backgroundwas provided by using a point lightsource to project beams of light throughsmall lenses, providing simulatedstars on the inside of the radome. Origi-nally, the simulation was performedunder conditions of free space, withoutthe effects of gravitation of a nearbyplanet. Later, an early type of analogcomputer was obtained that allowedincluding the effects of orbital mechan-ics as represented by the Clohessy-Wiltshire equations.

Carrying out a rendezvous in space wasa maneuver that had not beenattempted at that time, and many peopleexpressed doubt that such a maneuverwould be sufficiently safe to be practical.The main result of the simulation studywas to show that the rendezvous could


Rendezvous

be made quite simply with a minimum ofguidance equipment or instrumenta-tion. These runs were made at relativelyclose range, so that the visual cuesplayed an important role providing therequired information to the pilot or astro-naut. Furthermore, the rendezvous sim-ulator provided a convenient tool fordemonstrating such a maneuver toother personnel involved in the spaceprogram.


The Lunar Orbit Rendezvous mode wasselected as the design basis of theApollo Mission. In this mode, the LunarModule (LM) must take off from theMoon and rendezvous and dock withthe Command Module (CM) that is inorbit around the Moon. Some of thelengthy arguments and conferencesinvolved in selecting this mode of opera-tion are discussed later. For the presentpurpose, a brief comparison is madebetween the methods employed inthe simulation described previously andthe actual guidance and navigationtechniques used in the Apollo mission.These methods are discussed in detailin the excellent book by Richard H.Battin (ref. 4.2).

The Apollo mission managers selectedthe Draper Lab in Cambridge, Massa-chusetts to design the Apollo guidanceand control system. This organizationhad extensive previous experience indevelopment of inertial navigation sys-tems and in missile guidance. The engi-neers in this organization obviouslyhad much more experience in thedesign of sophisticated guidance equip-ment than the Langley engineers inmy division, who just a year or so ear-

lier had been working on stability andcontrol of aircraft.

The Apollo mission could be controlledby radio guidance from the ground or bythe astronauts onboard the vehicle byusing the navigation instruments pro-vided. The main reason for the onboardnavigation capability was to give theastronauts a guidance capability whenthe vehicle was on the back side of theMoon and as a backup in the unlikelyfailure of the radio guidance system.Both the LM and the CM were providedwith onboard computers of an unusualand advanced (for that time) design thatprovided a high degree of reliability.These computers were hard-wired tosolve the equations representing theorbital motions of the vehicles duringthe rendezvous operation as well as inall the other phases of the mission.

The lunar orbit rendezvous techniquerequires that the LM take off from theMoon and rendezvous and dock withthe CM that is in orbit around the Moon.At the time, other engineers in the Aero-space Mechanics Division at Langleyand I were deriving the rendezvousequations, we were unaware that theexact solution of these equations hadbeen obtained over two centuries agoby famous mathematicians, includingCarl Frederich Gauss, Joseph-LouisLagrange, and Johann HeinrichLambert. In fact, the equations for deter-mining the orbit of a body to go from onegiven point in space to another givenpoint with a specified transfer time areknown as Lambert’s equations. Aspointed out previously, these equationscannot be solved in closed form, but theearly mathematicians had derived itera-tive solutions to solve the equations toany desired accuracy. Such iterativesolutions, improved by modern develop-ments, were programmed into the com-puters used in the Apollo mission.Inertial platforms used in conjunctionwith radar equipment were used to



measure the relative positions of thevehicles. Sextants operated by theastronauts were used to determine thelocation of the vehicles with respect tothe Earth, Moon, and other referenceobjects. Thus the rendezvous navigationwas performed in a highly sophisticatedmanner, taking into account all the grav-itational influences of nearby heavenlybodies and allowing accurate calcula-tion of rendezvous trajectories of anylength or orientation.

The same equations and navigationalequipment were used in all phases ofthe Apollo mission, such as insertioninto translunar orbit, midcourse correc-tions in all phases of the mission, inser-tion into lunar orbit, and so on. Many ofthese mission phases required takinginto account gravitational influences ofthe Sun, Earth, and Moon. In addition,the locations of over 50 navigationalstars, as well as the corrections to theposition of the Earth and Moon whenusing the sextant to track the horizons,rather than the centers of these bodies,were all programmed into the Apollocomputers. In using these data, theastronauts were required to punch intothe computer on a keyboard the dataobtained in celestial readings. The com-puter would then automatically solve theequations to obtain the present and

future positions of the vehicle and itsdeviation from the planned trajectory.

One young engineer in my division,Robert Collins, had learned enough inhis college studies to know of Lambert’sequations. He devised an iterative tech-nique of solution, using the Langleycomputer complex, to solve the rendez-vous problem using Lambert’s equa-tions. This solution brought thepossibility of an exact solution to theattention of Langley engineers but wastoo late to influence the Apollo guidancesystem. The experience gained in theearly simulation studies proved veryhelpful to the Langley engineers wholater joined the Space Task Group andtook part in the actual design of theApollo system. For example, Walter J.Russell, who operated a small analogcomputer in the Langley rendezvousstudies, was later placed in charge of allanalog computer equipment at theJohnson Space Center. John Mayer,one of the Langley engineers who par-ticipated in the lecture series conductedby Henry Pearson, was later in chargeof all digital computing equipment atthe Johnson Space Center. John M.Eggleston, who made studies of optimalrendezvous at Langley, participated inthe design of the Apollo control systemand held important administrative posi-tions at the Johnson Space Center.

journey into space research - nasa · monographs in aerospace history number 40—journey into...

Documents