Notes to Chapter III

1]

Arthur Beiser.  Physics.  Cummings Publishing Company, 1973.

2]

Francis Weston Sears and Mark W. Zemansky.  University Physics.  Addison-Wesley Publishing Company, third edition 1963.

3]

Irving H. Shames.  Engineering Mechanics, Vol. II: Dynamics.  Prentice-Hall, second edition 1966.

4]

R. C. Hibbeler.  Engineering Mechanics, Vol. II: Dynamics.  Macmillan Publishing Company, fourth edition 1986.

5]

Harry Pollard.  Celestial Mechanics.  The Mathematical Association of America, 1976.  Number eighteen in the Carus Mathematical Monographs.

6]

Pollard [5], pages 6-8.

7]

This assumes that gravity is the only force capable of directly accelerating every particle of mass in the body, regardless of its composition, without propagating stresses through it.  For certain types of bodies in certain environments, other accelerating forces - such as electromagnetism - may also have to be discounted.  However, habitat design is primarily concerned with human bodies and their perceptions.  Also, tidal stresses in the human body are assumed to be negligible - I leave it to others to speculate on the perceptions of a person in the vicinity of a black hole or neutron star in the final moments before annihilation.

8]

Carl C. Clark and James D. Hardy.  "Gravity Problems in Manned Space Stations."  Proceedings of the Manned Space Stations Symposium, April 20-22, 1960, page 109.  Institute of the Aeronautical Sciences, 1960.

9]

Albert Einstein.  Relativity: The Special and the General Theory, pages 66-70.  Authorized translation by Robert W. Lawson.  Crown Publishers, 1961.

10]

R. Esnault-Pelterie.  "Consideration on the Results of Indefinite Decrease in Weight of Engines."  J. de Physique, 1913; translated as Appendix I in A. G. Haley, Rocketry and Space Exploration, D. Van Nostrand and Co., 1958.  Cited by Clark and Hardy [8], page 109.

11]

Saunders B. Kramer and Richard A. Byers.  "A Modular Concept for a Multi-Manned Space Station."  Proceedings of the Manned Space Stations Symposium, April 20-22, 1960, pages 48-49.  Institute of the Aeronautical Sciences, 1960.

12]

Shames [3], pages 507, 518-521.

13]

Barry Tillman.  "Human Factors in the Design of an Artificial Gravity Research Facility," unpaginated, figure 4.  Unpublished report prepared under contract with Lockheed, 1987.

14]

Wilfred Kaplan.  Advanced Mathematics for Engineers, page 455.  Addison-Wesley Publishing Company, 1981.  Kaplan writes:  "Here u, v, w (in that order) form a positive triple if in the order given they roughly determine a right-handed coordinate system; more precisely if u, v, w in the order given can be obtained from i, j, k by continuously changing the lengths and directions of these vectors without ever reducing one vector to 0 or making the vectors coplanar (linearly dependent)."

15]

Kramer and Byers [11], pages 48-49.

16]

Tillman [13], figures 4, 8.

17]

Shames [3], page 507.

18]

Hibbeler [4], pages 300-301.

19]

Clark and Hardy [8], pages 109-110.  They use the term "coriolis acceleration effects" rather loosely, to include cross-coupled rotations as well.

20]

Eugene F. Lally.  "To Spin or Not To Spin."  Astronautics, vol. 7, no. 9, page 57, September 1962.  American Rocket Society.

21]

Ashton Graybiel.  "Some Physiological Effects of Alternation Between Zero Gravity and One Gravity."  Space Manufacturing Facilities (Space Colonies): Proceedings of the Princeton / AIAA / NASA Conference, May 7-9, 1975, pages 137-149.  Edited by Jerry Grey.  American Institute of Aeronautics and Astronautics, 1977.

22]

Peter R. Kurzhals and James J. Adams.  "Dynamics and Stabilization of the Rotating Space Station."  Astronautics, vol. 7, no. 9, pages 25-29, September 1962.  American Rocket Society.

23]

Kurzhals and Adams [22], on page 26, state the formula as:

[math]

(without taking the absolute value, and with the subtraction in the denominator reversed, relative to equation 3.50).  They assume that Izz is always greater than Ixx, but Ixz will be positive or negative depending on the direction of motion in the xz plane.  It's not necessary to take the absolute value as long as one doesn't mind dealing with negative wobble angles.  They do not discuss the fact that there are two supplementary solutions to this equation in the range ±π (corresponding to acute and obtuse wobble angles), but assume that the smaller of the two (the acute one, in the range ±π/2) is the correct one.  Considering the relative masses of the space station and its "live load" contents, this is probably a reasonable real-world assumption.

24]

Kurzhals and Adams [22], page 26.

25]

Kurzhals and Adams [22], page 29.

26]

Kramer and Byers [11], pages 52-54.

27]

Hermann Oberth.  Man into Space, pages 202-217.  Translated by G. P. H. De Freville.  Harper and Brothers, 1957.  Published in Germany under the title Menschen im Weltraum.  Oberth divides the tidal forces into "i-forces" (inertial) and "g-forces" (gravitational).  His i-forces are simply the centripetal forces associated with rotation, which have already been discussed.  The tidal forces discussed in this section correspond to Oberth's g-forces.

28]

Oberth [27], pages 84-85.

29]

The Coriolis acceleration of a person walking along the circumference of Oberth's station (perpendicular to the axis of rotation) would be approximately eight times as great as the tidal acceleration:

[math]

The additional centripetal acceleration that would result from walking on a curved floor with a 4000 meter radius is insignificant:

[math]

30]

NASA Office of Space Flight (Advanced Programs).  "Tethers in Space Handbook," pages 2·3-2·10.  August 1986.

31]

Ivan Bekey.  Keynote address.  Applications of Tethers in Space, volume 1, page 1·25.  NASA Scientific and Technical Information Branch, 1985.  Conference publication 2364: proceedings of a workshop held in Williamsburg, Virginia, June 15-17, 1983.

32]

NASA [30], page 3·59.

33]

Paul A. Penzo.  "Tethers for Mars Space Operations."  The Case for Mars II, pages 445-465.  Edited by Christopher P. McKay.  American Astronautical Society, 1985.  Paper no. AAS 84-174.  Penzo includes a figure showing "orbital tower and sky hook concepts" by Tsiolkovsky (1895), Artsutanov (1959), Clark (1963), Isaacs et al. (1966), Colar and Flowers (1969), and Pearson (1975).  The figure implies that Tsiolkovsky's concept is a tower reaching up to space, while the others are geosynchronous tethers reaching down from space.

34]

Arthur C. Clarke.  The Fountains of Paradise.  Harcourt Brace Jovanovich, 1979.  Although this is a work of science fiction, Clarke cites eight technical papers on space elevators, sky hooks, and related topics in his "sources and acknowledgements" (pages 258-261).  Clarke gives credit for the original concept to Leningrad engineer Y. N. Artsutanov, whose article in Komsomolskaya Pravda, July 31, 1960, contemplated a "heavenly funicular" lifting twelve thousand tons a day to synchronous orbit.

35]

Jerome Pearson.  "Ride An Elevator Into Space."  New Scientist, vol. 121, no. 1647, pages 58-61, January 14, 1989.  Pearson is also the author of two of the technical papers cited by Clarke [34].

36]

Gerard K. O'Neill.  "Maximum-Strength, Minimum-Mass Structures."  Space-Based Manufacturing from Nonterrestrial Materials, pages 161-171.  Edited by Gerard K. O'Neill and Brian O'Leary.  American Institute of Aeronautics and Astronautics, 1977.

37]

Edward Bock, Fred Lambrou, Jr., and Michael Simon.  "Effect of Environmental Parameters on Habitat Structural Weight and Cost."  Space Resources and Space Settlements, pages 33-60.  Edited by John Billingham, William Gilbreath, and Brian O'Leary.  NASA Scientific and Technical Information Branch, 1979.

38]

Bock, Lambrou, and Simon [37], pages 41-46.

39]

Oberth [27], pages 180-185.

40]

Oberth [27], page 182.

41]

Gerard K. O'Neill.  The High Frontier, pages 64-65.  Anchor Books, 1982.

42]

Bekey [31], page 1·25.