Notes to Chapter IV

1]

The simulation is in the form of an interactive graphic computer program that I call "G-man".  The program displays the rotation of the environment and the relative trajectory of the ball in real time.  A control panel allows specification of radius, angular velocity, and centripetal acceleration of the environment, and initial height and velocity of the ball.  Currently, the program runs only on Apollo computers, using Apollo Graphics Primitives (GPR).  I hope to port it to other systems, but not until after this dissertation is complete!

[As of 2002, I've put a version compiled for IRIX, SunOS, and Mac OS X workstations on the web for free download, under the name "SpinDoctor".  My next goal is to port it to Linux, or rewrite it in Java.]

2]

A conic section is an ellipse, parabola, or hyperbola depending on whether its eccentricity is less than, equal to, or greater than one.  The eccentricity is defined as the (constant) ratio of distances to a fixed point (the focus) and a fixed line (the directrix), from any point on the conic.

3]

Paul R. Hill and Emanuel Schnitzer.  "Rotating Manned Space Stations."  Astronautics, vol. 7, no. 9, pages 14-18, September 1962.  American Rocket Society.

4]

Robert R. Gilruth.  "Manned Space Stations - Gateway to our Future in Space."  Manned Laboratories in Space, pages 1-10.  Edited by S. Fred Singer.  Springer-Verlag, 1969.

5]

Theodore J. Gordon and Robert L. Gervais.  "Critical Engineering Problems of Space Stations."  Manned Laboratories in Space, pages 11-32.  Edited by S. Fred Singer.  Springer-Verlag, 1969.

6]

Ralph W. Stone.  "An Overview of Artificial Gravity."  Fifth Symposium on the Role of the Vestibular Organs in Space Exploration, pages 23-33.  Edited by Ashton Graybiel.  NASA Scientific and Technical Information Division, 1973.  Special Publication 314: proceedings of a symposium held in Pensacola, Florida, August 19-21, 1970.

7]

D. Bryant Cramer.  "Physiological Considerations of Artificial Gravity."  Applications of Tethers in Space, vol. 1, pages 3·95-3·107.  Edited by Alfred C. Cron.  NASA Scientific and Technical Information Branch, 1985.  Conference Publication 2364: proceedings of a workshop held in Williamsburg, Virginia, June 15-17, 1983.

8]

NASA.  Man-System Integration Standards.  NASA-STD-3000, vol. 1, sec. 5.3.2.3, March 1987.

9]

Hill and Schnitzer [3], page 15.  It is not evident that this is the best comfort chart - it is certainly not the most recent - but it does seem to be the most frequently cited.  My use of it here is not intended as an endorsement, but rather as a reexamination of a well-known icon of artificial gravity research that has been widely circulated over the past thirty years.

10]

Gilruth [4].

11]

J. Peter Vajk, Joseph H. Engel, and John A. Shettler.  "Habitat and Logistic Support Requirements for the Initiation of a Space Manufacturing Enterprise."  Space Resources and Space Settlements, pages 61-83.  Edited by John Billingham and William Gilbreath.  NASA Scientific and Technical Information Branch, 1979.  Special Publication 428: technical papers derived from the 1977 Summer Study at NASA Ames Research Center.

12]

Steven Welch.  "Mission Strategy and Spacecraft Design for a Mars Base Program."  The Case For Mars II, pages 345-375.  Edited by Christopher P. McKay.  American Astronautical Society, 1985.  Paper no. AAS 84-169.  Volume 62 of the Science and Technology Series, Advances in the Astronautical Sciences.

13]

Robert L. Staehle.  "Earth Orbital Preparations for Mars Expeditions."  The Case For Mars III: Strategies for Exploration - General Interest and Overview, pages 373-396.  Edited by Carol Stoker.  American Astronautical Society, 1989.  Paper no. AAS 87-205.  Volume 74 of the Science and Technology Series, Advances in the Astronautical Sciences.

14]

J. M. Snead.  "Space Base I: Building a Large Space Station Using External Tank Technologies."  Space Manufacturing 8 - Energy and Materials from Space: Proceedings of the Tenth Princeton / AIAA / SSI Conference, May 15-18, 1991, pages 233-247.  Edited by Barbara Faughnan and Gregg Maryniak.  American Institute of Aeronautics and Astronautics, 1991.

15]

Eugene W. Meyers.  ET-Solutions: Detroit's Competitive Secret.  Space/Life Project (Box 814, West Covina, CA 91793), 1990.

16]

Snead [14], page 245.

17]

BOCA.  The BOCA National Building Code, 1990, eleventh edition, sections 817.6, 1306.3.2.  Building Officials and Code Administrators International, Inc., 1989.

18]

BOCA.  The BOCA National Plumbing Code, 1990, eighth edition, sections P-602.1, P-803.1.  Building Officials and Code Administrators International, Inc., 1989.

19]

John Templer.  The Staircase: Studies of Hazards, Falls, and Safer Design, page 149.  MIT Press, 1992.

20]

Sven Hesselgren.  The Language of Architecture, page 163.  Studentlitteratur, Lund, Sweden, 1969.

21]

Willy Ley.  Rockets, Missiles, and Space Travel: Revised Edition, page 372.  Viking Press, 1957.

22]

Rene A. Berglund.  "AEMT Space-Station Design."  Astronautics, vol. 7, no. 9, pages 19-24, September 1962.  American Rocket Society.

23]

Richard D. Johnson and Charles Holbrow, editors.  Space Settlements: A Design Study.  NASA Scientific and Technical Information Office, 1977.  Special Publication 413: authored by the participants of the 1975 Summer Faculty Fellowship Program in Engineering Systems Design at Stanford University and NASA Ames Research Center.

24]

L. G. Lemke.  "VGRF Technology Overview and Strawman Design."  NASA Ames Research Center, March 27, 1988.

25]

L. G. Lemke and R. B. Welch, editors.  "Workshop on the Role of Life Science in the Variable Gravity Research Facility."  NASA Ames Research Center, March 27-30, 1988.

26]

Templer [19], pages 3-5.

27]

Gary Scott Nelson.  "Engineering-Human Factors Interface in Stairway Tread-Riser Design."  Master's thesis, Texas A&M University, 1973.  Cited by Templer [19], page 113.

28]

Gerard K. O'Neill and Gerald W. Driggers.  "Observable Effects In and Human Adaptation To Rotating Environments."  Space-Based Manufacturing From Nonterrestrial Materials, pages 173-176.  Edited by Gerard K. O'Neill and Brian O'Leary.  American Institute of Aeronautics and Astronautics, 1977.  Volume 57, Progress in Astronautics and Aeronautics: technical papers derived from the 1976 Summer Study at NASA Ames Research Center.

29]

Actually, O'Neill and Driggers seem to have rounded-up significantly in calculating the "angle of lean".  Including (as they apparently did) only the tangential component of Coriolis acceleration associated with radial motion, the formula is:

[math]

where vr is the radial component of velocity.  If Ω^2*r is 32.2 ft/s2 (1 g), vr is 1 ft/s, and Ω ranges from 0.105 to 0.314 rad/s (1 to 3 rpm, as tabulated in their example), then the lean angle ranges from 0.4° to 1.1°.  Though significantly less than the 1.8° tabulated by O'Neill and Driggers, the upper end of this range still exceeds the 1° maximum considered acceptable in terrestrial design.

30]

Templer [19], page 105.  The prediction equation for rate of ascent that best fits the available data is:

vr = 76.98 + 2.106 riser - 2.543 tread

where riser and tread are measured in inches and vr is the rate of vertical ascent in feet per minute.  For a 6" riser and 12" tread, this predicts an average rate of ascent of 59.1 feet per minute, or 0.985 feet per second.

31]

Ley [21], pages 368-370.

32]

Wolfram Research, Inc.  Mathematica ® NeXT release 2.1, NeXT system release 3.0.  Solutions to the differential equations were computed and plotted with the functions NDSolve and ParametricPlot.

33]

The relative acceleration a associated with the curvature of the path is still not accounted for in this approximation.  Weightlessness in retrograde tangential motion actually occurs at:

[math]

34]

This assumes that each flight of stairs is spiral rather than straight.  If the flights are straight, then the relative acceleration a is zero, and equation 4.27 should be used instead of 4.34.  In the station depicted in figure 4.13 it makes little difference: the relative acceleration a of the spiral curvature is small compared to the Coriolis acceleration ACor, which is present whether or not the stairs are curved.

35]

Don B. Chaffin.  "Graphical Predictions of Human Strengths for Two-Handed IVA/EVA Tasks: Two-Handed Lifting, Pushing, and Pulling Strength Predictions for Differing Gravities, Populations, and Space Suit Conditions."  Engineering Human Performance Laboratory, University of Michigan, under contract to NASA Manned Spacecraft Center, NAS9-10973, phase one report, April 1971.

36]

Chaffin [35], page 5.

37]

Stone [6], pages 29, 31.

38]

Cramer [7], page 3·101.

39]

Stone [6], page 27.

40]

David N. Schultz, Charles C. Rupp, Gregory A. Hajos, and John M. Butler.  "A Manned Mars Artificial Gravity Vehicle."  The Case For Mars III: Strategies for Exploration - General Interest and Overview, pages 325-352.  Edited by Carol Stoker.  American Astronautical Society, 1989.  Paper no. AAS 87-203.  Volume 74 of the Science and Technology Series, Advances in the Astronautical Sciences.

41]

Stephen Capps, Robert Fowler, and Matthew Appleby.  "Induced Gravity Mars Transportation Systems: Configuration and Hardware Penalties."  Space Manufacturing 8 - Energy and Materials from Space: Proceedings of the Tenth Princeton / AIAA / SSI Conference, May 15-18, 1991, pages 126-131.  Edited by Barbara Faughnan and Gregg Maryniak.  American Institute of Aeronautics and Astronautics, 1991.