| From: DECWRL::"matthews%[email protected]" "Michael C. Matthews 30-Sep-88 1736 GMT" 30-SEP-1988 14:54
To: [email protected]
Subj: Space Tethers Bibliography (VERY LONG)
Well, I'm glad to see that this discussion has finally turned to my area of
expertise. In response to Steve Abrams' request, I'm posting this bibliography
of tethered system applications. I'm working on a control system stability
analysis for the Tethered Satellite System program, and have access to tools
and documentation that would be useful to an amateur group trying trying to
build a probe using this technology. I'll post more on this topic soon, but
I'd rather not make this posting any longer than it already is.
Probably the best introductory reference to the space applications of
tethered systems of all types is the _Tethers in Space Handbook_, August
1986, put out by NASA Headquarters. I'm not sure exactly how to go about
getting this book, but you could probably write Headquarters about it. The
inside of the front cover reads:
> This document is the product of support from many organizations and
> individuals. General Research Corporation, under contract to NASA
> Headquarters, compiled and prepared the final document.
>
> Sponsored by: National Aeronautics and Space Administration
> NASA Headquarters
> Code MT
> Washington, DC 20546
>
> Contract Monitor: Edward Brazill
>
> Task Monitor: Paul Penzo
>
> Contract Number NASW-3921
> and Title: Planning and Analysis of Advanced Programs
>
> Contractor: General Research Corporation
> Space Systems Operations (McLean)
> 7655 Old Springhouse Road
> McLean, VA 22102
>
> Project Manager: T.G. Reese
>
> Handbook
> Coauthors: W.A. Baracat, C.L. Butner
>
If you write them, ask if they have a newer version of the Handbook, since
there has been a great deal of good work in this area in the last two years,
especially in support of the Tethered Satellite System program. The _Tethers
in Space Handbook_ has an excellent section on the fundamentals of dynamics and
astrodynamics of space tethers, a section on current programs in tethered
satellites, a lengthy section on proposed tether applications, a very
informative appendix with lots of good data on some of the proposed systems,
and a compendious bibliography section (see below).
-----------
The following is a partial listing of the references section of the _Tethers
in Space Handbook_. Note that this listing is dated August 1986, and there have
been many good papers published since then (many of them in support of the
Tethered Satellite System program.)
J.A. Carroll "Guidebook for Analysis of Tether Applications,"
Contract RH4-394049, Martin Marietta Corporation, March 1985.
Available from Mail Code PS01, MSFC, NASA.
J. Sisson, "Development Status of First Tethered Satellite
System," NASA/Marshall Space Flight Center, Alabama, January
1986.
M. Nolan, R. Hudson, J. Sisson, D. Crouch, M. Vignoli, "Shuttle
Tethered Satellite Program," June 1984.
E. Vallerani, F. Bevilacqua, F. Giani, "Tethered Satellite System
Present Program and Future Applications," AAS 85-124.
_Applications of Tethers in Space_, Vol. 1, Workshop Proceedings,
Williamsburg, Virginia, June 15-17, 1983, NASA CP-2364, March
1985.
_Applications of Tethers in Space_, Vol. 2, Workshop Proceedings,
Williamsburg, Virginia, June 15-17, 1983, NASA CP-2365, March
1985
J. Pearson, "Anchored Lunar Satellites for Cislunar Transportation
and Communication", _Journal of Astronautical Sciences_, Vol. 27,
No. 1., pp. 39-62, Jan-Mar 1979.
"Study of Orbiting Constellations in Space," Contract RH4-394019,
Martin Marietta, Smithsonian Astrophysical Observatory,
December 1984.
_Applications of Tethers in Space_, Workshop Proceedings, Volume 1,
Venice, Italy, NASA CP2422, March 1986.
_Applications of Tethers in Space_, Workshop Proceedings, Volume 2,
Venice, Italy, NASA CP2422, March 1986.
_Applications of Tethers in Space_, Workshop Proceedings, Executive
Summary, Venice, Italy, NASA CP2422, March 1986.
G. von Tiesenhausen, ed., "The Roles of Tethers on Space Station,"
NASA TM-86519, Marshall Space Flight Center, October 1985.
M.D. Grossi, "Spaceborne Long Vertical Wire as a Self-Powered
ULF/ELF Radiator," _IEEE Journal of Oceanic Engineering_, Vol.
OE-9, No. 3, pp. 211-213, July 1984.
P.A. Penzo "ELF/ULF Radio Wave Generation Using Tethers," _JPL
Tethers in Space Studies Report_, 1986.
G. von Tiesenhausen, ed., Tether Applications Concept Sheets, June
28, 1984.
F. Bevilacqua, P. Merlina, and A. Anselmi, "The Science and
Applications Tethered Platform (SATP) Project," Aeritalia Space
Systems Group, Torino, Italy, Tether Applications in Space
Workshop, Venice, Italy, October 15-17, 1985�
J. Laue and F. Manarini, "The Tethered Retrievable Platform
Concept and Utilization," IAF-82-13, 33rd IAF Congress, Paris,
France, September-October 1982.
S. Vetrella and A. Moccia, "A Tethered Satellite System as a New
Remote Sensing Platform," University of Naples, Italy, Undated.
"Tether Released Recovery," Final Report, NASA Contract
NAS8-35096.
"SATP Definition Study," Mid-Term Report, Aeritalia, TA-RP-AI-002,
March 21, 1986.
M.D. Grossi, "Theoretical Investigation of the Generation and
Injection of Electromagnetic Waves in Space Plasma by Means of
a Long Orbiting Tether," Final Report, Contract NAS8-33520,
February 1981.
"Selected Tether Applications in Space, Phase III," NASA Contract
NAS8-36616.
"Selected Tether Applications in Space, Phase III," NASA Contract
NAS8-36617.
G. Colombo, D.A. Arnold, M. Dobrowolny, M.D. Grossi,
"Investigation of Electrodynamic Stabilization and Control of
Long Orbiting Tethers," Contract NAS-33691, Interim Report,
Smithsonian Astrophysical Observatory, March 1981.
M. Martinez-Sanchez and S.A. Gavit, "Four Classes of
Transportation Applications Using Space Tethers," Space Systems
Laboratory, Massachusetts Institute of Technology in Contract
with Marin Marietta, March 1984.
M. Martinez-Sanchez, "The Use of Large Tethers for Payload Orbital
Transfer," Massachusetts Institute of Technology, 1983.
G. Colombo, "The Use of Tethers for Payload Orbital Transfer,"
NASA Contract NAS8-33691, Vol. II, March 1982.
D. Stuart, "Tethered Rendezvous and Docking," Draper Labs, NASA
Contract NAS8-36602.
V. Chobotov, "Gravity-Gradient Excitation of a Rotating Cable-
Counterweight Space Station in Orbit," _Journal of Applied
Mechanics_, Vol. 30, pp. 547-554.
A.C. Clarke, "The Space Elevator: 'Thought Experiment', or Key to
the Universe?," _Adv. Earth Oriented Appl. Space Techn._, Vol. 1,
pp. 39-48, 1981.
H.L. Mayer, "Swarms: Optimum Aggregations of Spacecraft,"
Aerospace Corporation, ATR-80(7734)-1, February 29, 1980.
"Tethered Orbital Refueling Study," Contract No. NAS9-17059,
Martin Marietta.
L.G. Napolitano and F. Bevilacqua, "Tethered Constellations, Their
Utilization as Microgravity Platforms and Relevant Features,"
IAF-84-439.
S. Bergamaschi, P. Merlina, "The Tethered Platform: A Tool for
Space Science and Application," AIAA-86-0400, AIAA 24th
Aerospace Sciences Meeting, Reno, Nevada, January 6-9, 1986.
P.A. Penzo, "Tether for Mars Space Operation," JPL, 1984
Conference Paper, University of Colorado, Boulder, Colorado,
July 10-14, 1984.
P.A. Penzo and H.L. Mayer, "Tethers and Asteroids for Artificial
Gravity Assist in the Solar System," JPL, AIAA Paper 84-2056,
August 1984.
P.A. Penzo, _JPL Tethers in Space Studies Report_, 1986.
_Proceedings of Tether Applications in Space Program Review_,
McLean, VA, General Research Corporation, July 1985.
V.B. Braginski and K.S. Thorne, "Skyhook Gravitational Wave
Detector," Moscow State University, Moscow, USSR, and Caltech,
1985.
B. Bertotti, R. Catenacci, M. Dobrowolny, "Resonant Detection of
Gravitational Waves by Means of Long Tethers in Space,"
Technical Note (Progress Report), Smithsonian Astrophysical
Observatory, Cambridge, Massachusetts, March 1977.
R.V. Statchnik, D.Y. Gezari, "SAMSI: An Orbiting Spatial
Interferometer for Micro-Arcsecond Astronomical Observations,"
Proc. Colloquium "Kilometric Optical Arrays in Space," Cargese
(Corsica), October 23-25, 1984 (ESA SP-226, April 1985).
G.J. Corso, "A Proposal to Use an Upper Atmosphere Satellite
Tethered to the Space Shuttle for the Collection of
Micro-Meteoric Material," _Journal of the British Interplanetary
Society_, Vol. 36, pp. 403-408, 1983.
James E. McCoy, "PMG Reference System Designs for Power &
Propulsion," abstract.
Unknown, "Utilization of the External Tanks of the STS," draft of
results from workshop held at the University of California, San
Diego, August 23-27, 1982.
"Preliminary Feasibility Study of the External Tank (ET) Deorbit
by a Tether System," Martin Marietta Memo 83-SES-665, May 24,
1983.
M.C. Contella, "Tethered Deorbit of the External Tank," Johnson
Space Center, April 24, 1984.
J.A. Carroll, "Tethers and External Tanks: Enhancing the
Capabilities of the Space Transportation System," Research and
Consulting Services, La Jolla, California, December 20, 1982.
L. Bright, "Saturn Ring-Rendezvous Mission Utilizing a Tethered
Sub-Satellite," JPL, Memorandum 312/84.8-938, May 7, 1984.
"Tether Assisted Penetrators for Comet/Asteroid Sample Return," by
Paul A. Penzo (JPL); peper submitted for 1986 AIAA/AAS
Astrodynamics Conference.
H. Alfven, "Spacecraft Propulsion: New Methods," _Science_, Vol.
176, pp.167-168, April 14, 1972.
K. Kroll, Presentation Package for the NASA Tether Working Group
Meeting at Marshall Space Flight Center, February 1986.
-----------
In addition, I have included the Electrodynamics section of the Selected
Bibliography:
H. Alfven, "Spacecraft Propulsion: New Methods," _Science_, Vol.
176, pp.167-168, April 14, 1972.
J. Anderson, D. Arnold, G. Colombo, M. Grossi, and L. Kirshner,
"Orbiting Tether's Electrodynamic Interactions," final report
on NAS5-25077, Smithsonian Astrophysical Observatory, April 1979.
D.A. Arnold and M. Dobrowolny, "Transmission Line Model of the
Interactions of a Long Metal Wire with the Ionosphere,"
submitted to _Radio Science_, 1979.
D.A. Arnold and M.D. Grossi, "Natural Damping in the Electro-
dynamic Tether," Smithsonian Astrophysical Observatory,
Cambridge, Massachusetts, January 24, 1983.
D.A. Arnold, "General Equations of Motion," Appendix A of
"Investigation of Electrodynamic Stabilization and Control of
Long Orbiting Tethers," Interim Report, Smithsonian
Astrophysical Observatory, March 1981.
P.M. Banks, P.R. Williamson and K.L. Oyama, "Shuttle Orbiter
Tethered Subsatellite for Exploring and Tapping Space Plasmas,"
_Astronautics and Aeronautics_, February 1981.
B. Bertotti, R. Catenacci, M. Dobrowolny, "Resonant Detection of
Gravitational Waves by Means of Long Tethers in Space,"
Technical Note (Progress Report), Smithsonian Astrophysical
Observatory, Cambridge, Massachusetts, March 1977.
V.B. Braginski and K.S. Thorne, "Skyhook Gravitational Wave
Detector," Moscow State University, Moscow, USSR, and Caltech,
1985.
C. Chu and R Gross, "Alfven Waves and Induction Drag on Long
Cylindrical Satellites," _AIAA Journal_, Vol. 4, p. 2209, 1966.
G. Colombo, D.A. Arnold, M. Dobrowolny, M.D. Grossi,
"Investigation of Electrodynamic Stabilization and Control of
Long Orbiting Tethers," Contract NAS-33691, Interim Report,
Smithsonian Astrophysical Observatory, March 1981.
M. Dobrowolny, "Wave and Particle Phenomena Induced by an
Electrodynamic Tether," Smithsonian Astrophysical Observatory
Special Report #388, November 1979.
M. Dobrowolny, G. Colombo, M.D. Grossi, "Electrodynamics of Long
Conducting Tethers in the Near-Earth Environment," Smithsonian
Astrophysical Observatory, _Reports in Geoastronomy_, No. 3,
October 1976.
S.D. Drell, H.M. Foley and M.A. Ruderman, "Drag and Propulsion of
Large Satellites in the Ionosphere: An Alfven Propulsion
Engine in Space," _Journal of Geophysics Res._, Vol. 70, No. 13,
pp. 3131-3145, July 1965.
P.M. Finnegan, "A Preliminary Look at Using a Tethered Wire to
Produce Power on a Space Station," NASA LeRC, May 10, 1983.
T.B. Garber, "A Preliminary Investigation of the Motion of a Long,
Fexible Wire in Orbit," Rand Report RM-2705-ARPA, March 23,
1961.
M.D. Grossi, "Spaceborne Long Vertical Wire as a Self-Powered
ULF/ELF Radiator," _IEEE Journal of Oceanic Engineering_, Vol.
OE-9, No. 3, pp. 211-213, July 1984.
M.D. Grossi, "Theoretical Investigation of the Generation and
Injection of Electromagnetic Waves in Space Plasma by Means of
a Long Orbiting Tether," Final Report, Contract NAS8-33520,
February 1981.
M.D. Grossi, "On the Feasibility of Electric Power Generation and
Electromagnetic Wave Injection by Electrodynamic Tethers,"
Tech. Note TP 83-003, Smithsonian Astrophysical Observatory,
January 1983.
M.D. Grossi, "A ULF Dipole Antenna on a Spaceborne Platform of the
PPEPL Class," Report on NASA Contract NAS8-28203, Smithsonian
Astrophysical Observatory, May 1973.
M.D. Grossi, "Engineering Study of the Electrodynamic Tether as A
Spaceborne Generator of Electric Power," NASA Contract
NAS8-35497, Smithsonian Astrophysical Observatory, Cambridge,
Massachusetts, April 1984.
R. Guidici, "Electrodynamic Tether for Power on Propulsion Design
Considerations," NASA MSFC-PD, March 20, 1984.
R.W.P. King, "The Thin Wire Antenna Embedded in a Magneto-ionic
Plasma," Harvard University, 1980.
J.E. McCoy, "Electrodynamic Tether Applications - Massive Tether
Dynamics Study," General Status Review, NASA JSC-SN 3, May 3,
1984.
J.E. McCoy, "Plasma Motor/Generator - Proof of Function
Experiment," NASA JSC-SN3, July 1, 1984.
J.E. McCoy, "Plasma Motor/Generator - Electrodynamic Tether
Applications in Space," NASA JSC-SN3, June 13, 1984.
R.D. Moore, "The Geomagnetic Thruster--A High Performance 'Alfven
Wave' Propulsion System Utilizing Plasma Contacts," AIAA Paper
No. 66-257.
J. Pearson, "The Orbital Tower, A Spacecraft Launcher Using the
Earth's Rotational Energy," _ACTA ASTRONAUTICA_, Vol. 2, pp.
785-799, Pergamom, 1975.
P.A. Penzo "ELF/ULF Radio Wave Generation Using Tethers," _JPL
Tethers in Space Studies Report_, 1986.
Wei-Yuan Tang, "Comparison of Three Kinds of Possible Power
Generators as Space Shuttle Power Extension Package,"
Smithsonian Astrophysical Observatory, Cambridge,
Massachusetts, December 31, 1981.
W.B. Thompson, "Electrodynamics of a Conducting Tether," Final
Report to Martin Marietta Aerospace Corporation, Research
Contract RH3-393855, California Space Institute and Department
of Physics, University of California, San Diego, December 1983.
P.R. Williamson and P.M. Banks, "The Tethered Baloon Current
Generator: A Space Shuttle Tethered Subsatellite for Plasma
Studies and Power Generation," Final Report, NOAA Contract No.
03-5-022-60, January 1976.
P.R. Williamson, et al., "Measurements of Vehicle Potential Using
a Mother-Daughter Tethered Rocket," Utah State University, NASA
Grant NSG-6027, 1982.
P.R. Williamson, P.M. Banks, and K. Oyama, "The Electrodynamic
Tether," Utah State University, Logan, Utah, NASA Contract
NAS5-23837, May 1978.
ULF/ELF Antenna, NASA Contract NAG-551.
Unknown, "Report of the Plasma Physics and Environmental
Perturbation Laboratory Working Groups, "Program Development
Contract NASA TM X-64856, March 1974.
----------------------------------------------------------------------------
Disclaimer: I only work | Mike Matthews
for Lockheed, I don't | Lockheed Engineering & Sciences Company, Inc.
speak for them. I don't | Avionics Systems Department
speak for NASA either, | Flight Control Systems Section
for that matter. Any | Tether Dynamics Group
opinions expressed here | Houston, Texas
are mine alone and are, | MATTHEWS%[email protected]
therefore, Truth. | [email protected]
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|
| From: [email protected]
Newsgroups: sci.space
Subject: Re:Space tethers and Arthur C. Clarke
Date: 21 May 89 07:26:00 GMT
Sender: [email protected]
Organization: The Internet
The Italian-NASA tethered ionospheric probe was scheduled to fly
this year until the Challenger explosion. I read a new date for it
recently, perhaps 1991. Here are some older references on orbital
tethers, technical and fictional:
--------------------------------
Y. Artsutanov, V Kosmos na Elektrovoze (To Space by Funicular Railway),
Komsomolskaya Pravda, July 31, 1960
(contents described in Lvov, Science 158, p 946, November 17, 1967).
J.D. Isaacs, A.C. Vine, H. Bradner, G.E. Bachus, Satellite Elongation
into a True "Sky-Hook", Science 151 p 682, February 11, 1966 and 152,
p 800, May 6, 1966.
Y. Artsutanov, (The Cosmic Wheel), Znanije-Sile (Knowledge is Power)
No. 7 p 25, 1969.
G. Polyakov, A Space "Necklace" About the Earth. NASA technical
memorandum TM-75174, (translation of "Kosicheskoye 'Ozhere'ye' Zemli "
in Teknika Molodezhi, No. 4, 197, pp. 41-43)
J. Pearson, The Orbital Tower: A Spacecraft Launcher Using the Earth's
Rotational Energy, Acta Astronautica 2, p 785, September/October 1975.
J. Pearson, Using The Orbital Tower to Launch Earth Escape Payloads Daily,
27'th IAF Congress, Anaheim, Ca., October 1976. AIAA paper IAF 76-123.
J. Pearson, Anchored Lunar Satellites for Cis-Lunar Transportation
and Communication, European Conference on Space Settlements and Space
Industries, London, England, September 20, 1977. in Journal of the
Astronautical Sciences.
H.P. Moravec, A Non-Synchronous Orbital Skyhook, 23rd AIAA
Meeting, The Industrialization of Space, San Francisco, Ca., October
18-20, 1977, also Journal of the Astronautical Sciences 25,
October-December, 1977.
Roger D. Arnold and Donald Kingsbury, The Spaceport,
Part 1: Analog v99 #11 November 1979 pp 48:67 and
Part 2: Analog v99 #12 December 1979 pp 61:77
J. Pearson, Lunar Anchored Satellite Test, AIAA/AAS Astrodynamics
Conference, Palo Alto, Ca., August 7-9, 1978, AIAA paper 78-1427.
H.P. Moravec, Skyhook!, L5 News, August 1978.
Arthur C. Clarke, The Fountains of Paradise,
Harcourt, Brace and Jovanovich, 1978.
Charles Sheffield, The Web Between the Worlds, Ace SF, 1979.
Charles Sheffield, How to Build a Beanstalk,
Destinies Vol 1 #4, Aug-Sep 79, pp 41:68, Ace books.
Charles Sheffield, Skystalk, Destinies Vol 1 #4, Aug-Sep 79, pp 7:39
H.P. Moravec, Cable Cars in the Sky, in The Endless Frontier, Vol. 1,
Jerry Pournelle, ed., Grosset & Dunlap, Ace books, November 1979, pp. 301-322.
R.L. Forward and H.P. Moravec, High Wire Act, Omni, Omni publications
international, New York, July 1981, pp. 44-47.
Charles Sheffield, Summertide, Destinies Vol 3 #2, Aug 81, pp 16:84
Report on the Utilization of the External Tanks of the Space
Transportation System, proceedings of a workshop held at the UC San
Diego, La Jolla, California, August 23-27, 1982, under NASA contract
#NAS 8-35037 from the Marshall Space Flight Center. ** Section III:
Tethers and External Tanks **
|
| Article: 1757
From: [email protected] (Charles Danforth)
Newsgroups: sci.space.tech
Subject: SkyHook Paper (long)
Date: Tue, 10 May 1994 09:55:35 -0500
Organization: Swarthmore College, Swarthmore, PA, USA
ORBITAL BEANSTALKS: A MATERIALS ENGINEERING EXAMINATION
Charles Danforth `95
Swarthmore College Dept. of Astrophysics
Swarthmore, PA 19081
610-690-2747
[email protected]
December 13, 1993
revised May 9, 1994
***INTRODUCTION TO THE CONCEPT AND KINEMATICS OF BEANSTALKS:
The idea is not a particularly new one, it simply requires a satellite in
geosynchronous orbit, two ropes, and a good deal of courage and skill.
Though the idea of beanstalks seems fantastic and implausible, it is really
a fairly simple exercise in classical mechanics and orbital dynamics.
An object in orbit around the earth travels in an
elliptical path with the gravitational acceleration exactly canceling
centrifugal acceleration. Since gravity is a force whose strength is
proportional to inverse radius squared, the closer the orbiting object
is to the earth, the shorter itUs orbital period. Orbital period, for
circular orbits, is described by T=2pir/(GM/r)^.5. If we use a period
of one day (86400 seconds), the radius can be found to be 4.224x10^7
meters or 42,240 kilometers--35,860 kilometers from the surface of the
earth. Since both the earth and the satellite make one rotation in 24
hours, the satellite appears to be hovering above a spot on the earth,
ideal for, among other things, beanstalks.
Now, from our satellite in geosynchronous orbit, a cable
is lowered down toward the earth and another extended in the opposite
direction. Because the center of mass does not change, the orbit of
the satellite does not change. If your cable is long enough, it can
reach all the way down through the atmosphere to the surface of the
earth where it can be used to lift cargo, elevators, or to relay
space-generated power. Such a system, along with many of the inherent
problems and implications, is very artfully described by Arthur C.
Clarke in his novel RThe Fountains of ParadiseS. Many other science
fiction authors have examined such a problem and these structures are
variously called RskyhooksS, Rorbital towers,S RbeanstalksS and more.
A hidden advantage of the beanstalkUs structure can be seen by
examining the velocities along its length. Already we have seen that the
velocity at a given point is a linear function of radius r
v(r)_tower=2pir/(84600)
while the velocity necessary for a circular orbit at radius r is
v(r)_orbit=(GM/r)^.5
At the end of the countermass, objects are moving at over 6 km/second. It
can be seen that orbital velocity at this radius is a mere 3 km/s and in
fact escape velocity at this distance is only 4.3 km/s. Therefore, an
object released from the far end of the beanstalk would fly away from the
earth on a hyperbolic trajectory.
Thus a practical use for beanstalks becomes apparent. By
departing at the correct time and radius, a body can attain many
orbits in the equatorial plane and, with a small energy expenditure,
in many other planes (such as that of the ecliptic). Furthermore,
appropriate trajectories may be chosen to take spacecraft to Luna,
Mars, and beyond, for zero initial energy expenditure by the
spacecraft.
Similarly, incoming spacecraft could, with sufficient piloting
finesse, be caught by the outward tip of the beanstalk and transferred down
to earth safely without spending huge amounts of fuel.
Conservation of energy demands, however, that the energy
being given to all these spacecraft come from somewhere. As objects
move outward on the stalk, they will gain angular momentum and, the
stalk will lose angular momentum. Presuming the beanstalk is far more
massive than the object being lifted (a fair assumption as we shall
see when we get into materials) its energy loss will be quite low.
Similarly, objects caught on the outside tip of the beanstalk would
have to lose angular momentum as they travelled inward. Hopefully
these two tendencies would make the net energy change of the beanstalk
small. Thrusters or solar sails at the center point could supply
extra impulse to keep the structure trimmed and working smoothly.
Unfortunately, beanstalks have certain undesirable
characteristics. They can only be anchored at the equator. This is
because the ground track velocity must be zero which only occurs for
equatorial geosynchronous orbits.
Another drawback is the extraordinary length of cable which
must be used, 35,000 kilometers on each side of the orbiting platform which
supports the structure. This represents a considerable mass which must be
boosted up the gravitational well. Clearly, lightweight materials are
important in both reducing the mass to be boosted as well as reducing the
kinetic energy of such a structure should it fall.
Which brings us to safety concerns. If the cable is
broken somehow, the two halves separate and fly apart. Besides
proving extremely unpleasant for anyone attached to the structure, if
the downward section of cable landed in populated areas, it would
undoubtedly cause serious damage.
[Note: Current data from the SEDS tether experiment show that collisions
with space junk are relatively common along even a small length of cable.]
But possibly, with advanced materials of today and tomorrow, as well
as some wise engineering, such structures can come into being.
***A MATHEMATICAL MODEL: ***
Let us model a beanstalk mathematically. We already have an idea of what
length and velocity it should have. What shape should the beanstalk be?
Since the cable will have mass, each successive part of it will have to
support more and more weight. Let us picture the structure divided into
tiny parts called dm. Each dm will have a force on it dF which, in the
rotating frame (where the beanstalk is stationary) must be equal to zero or
else it will move away from its fellows. The gravitational force and the
centrifugal force act oppositely and are balanced by the tension present in
the section.
dF_grav+dTension=dF_cent
The tension T(r) will be a function of the cross-sectional area A(r) and
the tensile strength B of the material.
T(r)=BA(r), A(r)=T(r)/B
so all together, the equation will look like
-(GM/r^2)(rho)A(r)dr+(omega^2)(rho)rA(r)dr+(dTdr)/dr=0
Where rho is the density of the material. This is a differential equation
which can more easily be dealt with in the form
[equation suppressed]
Integrating, we obtain a function for A(r) which will let us determine the
optimal shape for the beanstalk.
[equation suppressed].
We have a boundary condition implied. A(R) is the cross
sectional area at radius R, the center of the structure, and C is some
constant which must be determined.
As has been stated, the area at the center is A(R).
Therefore, the exponential term at that point must be equal to one.
Our final equation is
A(r)=A(R)exp((GM/R-(omega^2 R^2)/2)rho/B-(GM/r-(omega^2
r^2)/2)rho/B).
By simple inspection we can see that this is an
exponential curve increasing to r=R and then decreasing at r>R.
The parameter p/B has a great deal to do with the final
dimensions of the structure. Unfortunately it is determined by the
materials involved which places some limits on the structure. In the
third part of this paper, I will explore the properties of different
materials determine which one would be best for this application.
***DESIGN CONSIDERATIONS:
There are several design considerations to take into account. Since the
object will be moving through a large section of space, it will
occasionally encounter solid chunks of material from the size of dust
grains on up to defunct satellites and used rocket stages not to mention
natural junk such as micrometeoriods. While it is true that a very crowded
part of space is in the geosynchronous band (where the relative velocities
of the beanstalk and object are low or zero), there is still a sizable
amount of stuff lower down and even a little higher up where the velocities
are not trivial.
Should one of these particles hit the stalk, dangerous cracking and
even breakage could occur, with disastrous results. A break would turn one
solid object at equilibrium into two objects with large net forces upon
them. The outer section of the stalk would be flung away to either orbit
the earth or escape all-together carrying whatever people and cargo were
attached to it as well. The inner section would, in the worst case,
plummet to earth potentially causing extensive damage to anything in its
(considerable) path.
In the best case there would still be enough mass far
enough up to only alter the orbit of the inner segment by a little
bit. Instead of being stationary with respect to points on the earth,
the tip of the beanstalk would move around the planet causing
(relatively) minor damage. However, as it moved, atmospheric drag will
slow down the whole object causing it to eventually crash to earth
with disastrous effects. Possibly, the air friction would ablate away
the slim tip of the beanstalk sufficiently for the remainder to remain
in orbit, but this is not terribly probable given the materials which
will probably be necessary. If the material is at all conductive, the
chance is practically nil as the burning friction from the air will be
conducted upwards and radiated into space.
Clearly the structure must be made to resist impacts
and cutting. One way to do this is to make it thin and strong giving
it a low impact cross-section. This has the added advantage of using
less material as well. Another way to do it is to wrap some sort of
protective layer around a central core which provides the tensile
strength. This layer could hopefully absorb any damage dealt out by
the environment. It seems best to me to incorporate both of these
ideas.
A second design concern is that of thermal expansion. The
temperature ranges of space are much more extreme than here on earth
because of the lack of heat conduction by the air. Hence objects in direct
sunlight will grow immensely hot while objects in the shade will be very
cold. The beanstalk would experience these sharp and extreme temperature
gradients and would change in length as the constituent materials expanded
and contracted causing the tip to alternately retreat into the stratosphere
by night and coil itself upon the ground during the day.
The solution to this, it seems, would be to either make the
protective outer layer highly reflective or to add another layer on the
outside which would reflect most of the incoming radiation safely away
keeping the cable at some constant temperature. Add to this a material
whoUs coefficient of thermal expansion is sufficiently low and the problem
of length changing would disappear.
The final and several-orders-of-magnitude-more-important concern
with this structure is going to be the tensile strength of the material.
It seems logical from studying climbing ropes, cables and so forth that the
best structure is one with long continuous fibers running axially, much
like a rope.
TABLE 1 Tensile Density Specific tensile
Material MPa/m^2 g/cc ccMPa/gm^2
-----------------------------------------------------------
Carbon Thornel P55S 1895 2.02 938
Carbon Thornel P75S 2070 2.06 1004
Carbon Thornel P100 2240 2.15 1041
Carbon AS4 fiber 3100 1.75 1771
Boron 1005m fiber 3100 2.57 1206
Boron 1405m fiber 3600 2.49 1445
Aramid MH-50 fiber 3100 1.39 2230
Kevlar 49 high end 4100 1.45 2827
Spectra1000 high end 3300 0.97 3402
Ceramic (SiC) 3920 3.00 1306
Ceramic (Nicalon) 3200 2.55 1254
Ceramic (Tyrano) 3000 2.30 1304
E-glass fiber 3400 2.54 1338
High Tensile Steel* 2000 7.80 256
Titanium Alloy* 1400 4.50 311
Wood (Spruce)* 100 0.50 200
Theoretical Diamond* 90K 3.51 25641
Theoretical Carbon* 150K 2.26 66372
*For purpose of comparison
While something like steel cable seems very strong, the weight of tens of
thousands of kilometers of it is far more than it can bear. Table 1 shows
a wide variety of materials which might suit our purpose.
Since weight is a serious problem in a beanstalk, it can easily be
seen that some fibers are far better than others in terms of
strength/weight. Aside from the theoretical carbon and diamond (which
exist only on paper thus far), Spectra and Kevlar fibers hold the edge over
all others. These organic fibers are quite tough and would be resistant to
impacts. The problem with them is that they break down in high
temperatures, which might make them unsuitable if thermal shielding, as
discussed above, should for some reason prove unfeasible. [Note: I donUt
know about other space-resistant qualities of these fibers.]
Carbon, boron, and ceramic fibers surprised me with how poorly they
rated. However, the fibers tested here were all grown on earth under
gravity. Research suggests that space-grown fibers may be far better with
far fewer flaws than their terrestrial cousins. These fibers have the
additional disadvantage of being extremely expensive (especially boron) and
quite fragile.
As we shall see, traditional metals are out of the question due to
their extreme weight and the sheer mass/volume involved. Metals, on the
other hand, have the advantage of being conductive and could thus serve a
secondary purpose of generating huge amounts of electric power as the
beanstalk sweeps through the earthUs magnetic fields like a gargantuan
dynamo coil. But, as this is not the primary purpose of the structure, at
least as presented here, metals can be safely disregarded as a building
material.
LetUs now look at the actual dimensions involved for some different
materials. If we put a payload of mass m on the bottom of the tower at
itUs thinnest point, the cross-section at that point must be able to take
itUs weight. The force is equal to the mass times the gravitational
acceleration. The force per unit area of the cable is equal to the force
divided by the area and the area at the tip of the beanstalk needed to
support a certain weight mg can be found by
A(tip)=mg/B
If we use this as a boundary condition, the value of A(R) can be found.
This tells us what may well be a primary engineering concern of the
project--the dimensions of the thick part in the center of the structure.
[equation suppressed]
Table 2 presents the results of this calculation for the materials
presented in Table 1. A 10 metric ton mass was used to calculate A(tip)
which was then used in the formulation for A(R). The results surprised me
a great deal in their range and their sensitivity to rho/B; similar
materials yielded vastly different radius results (carbon in particular).
Please note that, due to computational numerical overflow, the results of
the two metals and the wood (which was ludicrous anyway) are not really
valid except to show that they are very big indeed.
TABLE 2 Tip Center
Material area(m^2) radius(m) area(m^2) radius(m)
-----------------------------------------------------------------------
Carbon Thornel P55S 5.18e-05 4.06e-03 1.86e+20 7.70e+09
Carbon Thornel P75S 4.74e-05 3.88e-03 3.99e+18 1.13e+09
Carbon Thornel P100 4.38e-05 3.73e-03 5.65e+17 4.24e+08
Carbon AS4 3.16e-05 3.17e-03 3.20e+08 1.01e+04
Boron 1005m 3.16e-05 3.17e-03 3.96e+14 1.12e+07
Boron 1405m 2.73e-05 2.95e-03 2.34e+11 2.73e+05
Aramid MH-50 3.16e-05 3.17e-03 6.75e+05 4.64e+02
Kevlar 49 high end 2.39e-05 2.76e-03 3.36e+03 3.27e+01
Spectra1000 high end2.97e-05 3.08e-03 1.76e+02 7.48e+00
Ceramic (SiC) 2.50e-05 2.82e-03 1.07e+13 1.84e+06
Ceramic (Nicalon) 3.07e-05 3.12e-03 6.97e+13 4.71e+06
Ceramic (Tyrano) 3.27e-05 3.23e-03 1.50e+13 2.18e+06
E-glass fiber 2.89e-05 3.03e-03 4.67e+12 1.22e+06
High Tensile Steel* 4.91e-05 3.95e-03 3.40e+38 1.04e+19*
Titanium Alloy* 7.01e-05 4.72e-03 3.40e+38 1.04e+19*
Wood (Spruce)* 9.81e-04 1.77e-02 3.40e+38 1.04e+19*
Theoretical Diamond 1.09e-06 5.89e-04 8.63e-06 1.66e-03
Theoretical Carbon 6.54e-07 4.56e-04 1.45e-06 6.80e-04
*the data for these three materials is inaccurate due to numerical overflow
The clear choice in this matter seems to be Spectra 1000 fibers. This
would result in a beanstalk only 15 meters across in the center, easily a
manageable amount considering that there would be, in all likelihood, some
sort of orbital station located there to support the building of the
beanstalk and the commerce it produced. The total amount of material
required for the cable would be about 3.3 million metric tons.
Keeping all the design considerations in mind, it is now possible to
design the actual structure of the beanstalk. The cable (from a suggestion
by Prof. Fred Orthlieb) would be hexagonal in cross-section for closer
packing on a deployment spool. A pair of slots would be inset in opposite
sides to support elevators which would ride up and down the shaft. One
side would be for up-bound cars while another would be for down-bound cars.
As the cable gets thinner toward the ends, a single, slower type of
elevator would be used which gripped the outside of the cable with a
rolling clamp mechanism. This would provide transport into and out of the
atmosphere where high speeds are not really feasible. (see ClarkeUs
Fountains of Paradise).
[diagram suppressed]
***CONCLUSIONS:
It does seem as if an orbiting beanstalk is possible. It would require
immense quantities of material, labor, and dedication. However, the
long-range possibilities presented by such a system are seductive. Cheap,
easy and non-polluting travel into orbital, translunar and interplanetary
space. Immense amounts of clean energy for an increasingly energy-hungry
society. A way for our population to get off this crowded sphere and put
our eggs in more than one basket. The engineering is quite daunting and
the construction time scale would undoubtedly be measured in decades. But,
all in all, it looks like it could be done with present-day materials.
***FUTURE WORK:
One issue I have not considered is the issue of fiber termination.
Presumably, the fibers used in the cable would be of constant
cross-section. If the cable is to be tapered over its length, there must
be more fibers in the center section than at the tips and these fibers must
terminate part way down. This presents a considerable design problem, one
which, lacking more detailed knowledge of the materials involved, I
hesitate to speculate upon. Engineers, however, are clever sorts, so I
expect they should have the issue figured out by the time anything on this
scale is to be built.
There is another solution to the problem which I have not tackled here
due to its much harder dynamics. If a satellite is placed in a lower
orbit, say one only a thousand kilometers from the surface instead of
35,000, a much thinner cable can be lowered. The ground track velocity of
the tip in this case would not be zero and the satellite would quickly lose
momentum and spiral inward. However, if the whole assembly is spun at the
proper rate, each end will in turn dip more or less straight down through
the atmosphere, pause for a moment at ground level, and then take off
skyward again. On the upward swing, objects could be released to attain
orbital and interplanetary trajectories. Incoming objects could be
similarly caught (requiring even MORE piloting finesse!). The tips would
move toward and away from the earth in an epicycloidal fashion with the
number of lobes per orbit determined by orbital altitude.
This RpinwheelS system has the advantages of being much
smaller (by an arbitrary, user-controlled amount). Unlike the
beanstalk it can touch down at many places on the globe both on and
off the equator. Elevators can still go inward toward the center to
achieve a stable circular orbit, or they can simply stay on the end
and be thrown outward toward distant targets (Indeed, if elevators are
not installed, it makes the cable that much stronger for being
unmarred by tracks.). There is also the issue of safety--if a
pinwheel is severed by some calamitous mishap, there is less material
to crash to earth and a much greater chance that both halves will
simply spiral away and miss the ground completely. Unfortunately, the
mechanics of pinwheels are extremely arduous and I have not yet
performed a quantitative exploration of them.
***SELECTED REFERENCES AND INSPIRATIONS:
Clarke, Arthur C., The Fountains of Paradise
Easterling, K. E., Advanced Materials for Sports Equipment,
Chapman and Hall, 1993.
Gordon, J. E., The New Science of Strong Materials, Princeton
University Press, Princeton, 1976.
Engineer Materials Handbook, Volume 1: Composites, ASM International,
1989.
International Encyclopedia of Composites, Volume1, Stuart M.
Lee, Ed., VCH Publishers, Inc. New York, 1990.
Special thanks to Professors Amy Bug and Terje Volde (Physics, Swarthmore)
and Professor Fred Orthlieb (Engineering, Swarthmore) for help provided
with the modeling of this system.
Comments and criticism are heartily encouraged.
_____
|\ /| Charles Danforth <'D / C /
| O | [email protected] ()-^ --+-\\
|/_\| 610-690-2747 / > | \
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