Spin-Gravity Formulas

Introduction

So just how fast will your newest starship have to rotate its spin habitat to provide a reasonable level "gravity"? The following formulas should be of help to you.

In the following formula, please remember that the number of RPMs ( revolutions per minute) is an important factor:

• One RPM can be handled by just about everyone ( except those most sensitive to motion sickness).
• Three RPM is about the maximum tolerance for an active human.  Everyone moving about will be suffering to some extent from disorientation ( a few have mild, but many have incapacitating cases of motion sickness).  Even simply turning your head to one side can trigger nausea/disorientation due to the effects spin forces have on fluid in the inner ear.
• Civilians ( "green" passengers) would want RPMs closer to one.  Only professional spacers, with selected crews ( to weed out those overly sensitive) would operate at/near three RPM.

Variables:

  g   = in terms of earth gravity ( earth = 1.0)

  RPM = "Revolutions Per Minute" of the spinning habitat

  d   = diameter ( in meters) of the spinning habitat ( more 
        useful than radius when using Star Cruiser's design 
        system).

  v   = velocity of rotation ( in meters/second)

  Pi  = 3.141592654 ( or use button on your calculator)

Formulas:

  g   = Pi * Pi * d * RPM * RPM / 17640

  RPM = SquareRoot( ( 17640 * g) / ( Pi * Pi * d) )

  d   = 17640 * g / ( Pi * Pi * RPM * RPM)

  v   = Pi * d * RPM / 60

Simplifying the first three formulas further:

  Letting "k" = ( 17640 / ( Pi * Pi)) then
              = 1787.305679 in the following equations

  g   = d * RPM * RPM / k

  RPM = SquareRoot( ( k * g) / d )

  d   = k * g / ( RPM * RPM)

Pre-calculated Table

Note: Unfortunately GDW used unrealistically small, but artistically more pleasing, spin diameters ( witness the Kennedy on the Star Cruiser box cover).  So don't be surprised by the low gravity generated by their starship designs, which came in the various game supplements.

      RPM   RPM   RPM   RPM   RPM  |  RPM   RPM   RPM   RPM
      1.0   1.5   2.0   2.5   3.0  |  3.5   4.0   4.5   5.0
Dia     g     g     g     g     g  |    g     g     g     g
 18  0.01  0.02  0.04  0.06  0.09  | 0.12  0.16  0.20  0.25
 21  0.01  0.03  0.05  0.07  0.11  | 0.14  0.19  0.24  0.29
 24  0.01  0.03  0.05  0.08  0.12  | 0.16  0.21  0.27  0.34
 27  0.02  0.03  0.06  0.09  0.14  | 0.19  0.24  0.31  0.38
 30  0.02  0.04  0.07  0.10  0.15  | 0.21  0.27  0.34  0.42
 33  0.02  0.04  0.07  0.12  0.17  | 0.23  0.30  0.37  0.46
 36  0.02  0.05  0.08  0.13  0.18  | 0.25  0.32  0.41  0.50
 39  0.02  0.05  0.09  0.14  0.20  | 0.27  0.35  0.44  0.55
 42  0.02  0.05  0.09  0.15  0.21  | 0.29  0.38  0.48  0.59
 45  0.03  0.06  0.10  0.16  0.23  | 0.31  0.40  0.51  0.63
 48  0.03  0.06  0.11  0.17  0.24  | 0.33  0.43  0.54  0.67
 51  0.03  0.06  0.11  0.18  0.26  | 0.35  0.46  0.58  0.71
 54  0.03  0.07  0.12  0.19  0.27  | 0.37  0.48  0.61  0.76
 57  0.03  0.07  0.13  0.20  0.29  | 0.39  0.51  0.65  0.80
 60  0.03  0.08  0.13  0.21  0.30  | 0.41  0.54  0.68  0.84
 63  0.04  0.08  0.14  0.22  0.32  | 0.43  0.56  0.71  0.88
 66  0.04  0.08  0.15  0.23  0.33  | 0.45  0.59  0.75  0.92
 69  0.04  0.09  0.15  0.24  0.35  | 0.47  0.62  0.78  0.97
 72  0.04  0.09  0.16  0.25  0.36  | 0.49  0.64  0.82  1.01
 75  0.04  0.09  0.17  0.26  0.38  | 0.51  0.67  0.85  1.05
 78  0.04  0.10  0.17  0.27  0.39  | 0.53  0.70  0.88  1.09
 81  0.05  0.10  0.18  0.28  0.41  | 0.56  0.73  0.92  1.13
 84  0.05  0.11  0.19  0.29  0.42  | 0.58  0.75  0.95  1.17
 87  0.05  0.11  0.19  0.30  0.44  | 0.60  0.78  0.99  1.22
 90  0.05  0.11  0.20  0.31  0.45  | 0.62  0.81  1.02  1.26

For a good discussion of spin gravity see: http://www.npl.washington.edu/AV/altvw18.html