SpinCalc

an artificial-gravity calculator in JavaScript
[About the Calculator]

Copyright © 2000
Theodore W. Hall

Last revision: 2003/05/05

About the Calculator

Artificial gravity, as it is usually conceived, is the inertial reaction to the centripetal acceleration that acts on a body in circular motion.  Artificial-gravity environments are often characterized in terms of four parameters:

• Radius from the center of rotation.
• Angular Velocity or “spin rate.”
• Tangential Velocity or “rim speed.”
• Centripetal Acceleration or “gravity level.”

These four parameters are interdependent: specifying values for any two of them determines the values of the other two as well.

The calculator assigns a priority to each parameter.  Whenever you input a value, that parameter receives the highest priority.  The calculator recomputes the two parameters with the lowest priorities – the two values least recently specified by you.  It displays text beneath each parameter to describe how it determined the value.

The calculator doesn’t update anything until your input is complete.  Depending on your browser, you may need to press <Tab> or <Enter>, or click the mouse outside the text input area, to trigger the update.

You can select the measurement unit for each parameter.  When you change a parameter’s unit, the calculator converts the numeric value while holding the physical quantity constant.  If you want to specify a parameter value in a unit other than the current selection, select the unit first, and then input the numeric value.

The calculator displays the formulae as proportions, designated by the symbol .  If the angular velocity unit is radians/second, and if the other three parameter units are consistent (all meters and seconds, or all feet and seconds), then the proportion is actually a numeric equality .  (You can verify this by selecting consistent units.)  Else, there’s a constant multiplier (not displayed) to account for the unit conversions.

The colored “LED” in front of each parameter indicates how its value compares to the “comfort zone” for artificial gravity, as proposed by several authors:

The value is too high for comfort.

The value may be too high for comfort – authors disagree.

The value is in the comfort zone.

The value may be too low for comfort – authors disagree.

The value is too low for comfort.

If you resize the browser window, the formulae and LEDs may disappear temporarily.  They’ll reappear as you continue to change parameter values.  You can also reset everything by reloading the page.

Known bugs:

• Microsoft Internet Explorer 5 on Macintosh:  When it loads the page, IE5 scrolls the numeric fields so that the most significant digits and the decimal point are clipped out of view to the left.  Click in the input field and drag to the left to expose the full true value.  Other than that, the JavaScript runs correctly.

• Netscape 4.7:  Poor support for CSS style sheets causes a misalignment of the form fields and incorrect coloring.  But the JavaScript runs correctly.

• Netscape 6.2 on Macintosh OS X:  When it loads the page, NS62 fails to convert the initial acceleration value from units of meters/second^2 to units of g, although g is the selected unit.  Selecting g again corrects the numeric value.  Neither Netscape 4.7, Netscape 7, nor Mozilla 1.0 have this problem.

Comfort Criteria

Radius
Because centripetal acceleration – the nominal artificial gravity – is directly proportional to radius, inhabitants will experience a head-to-foot “gravity gradient”.  To minimize the gradient, maximize the radius.

Angular Velocity
The cross-coupling of normal head rotations with the habitat rotation can lead to dizziness and motion sickness.  To minimize this cross-coupling, minimize the habitat’s angular velocity.

Graybiel [6] conducted a series of experiments in a 15-foot-diameter “slow rotation room” and observed:

In brief, at 1.0 rpm even highly susceptible subjects were symptom-free, or nearly so.  At 3.0 rpm subjects experienced symptoms but were not significantly handicapped.  At 5.4 rpm, only subjects with low susceptibility performed well and by the second day were almost free from symptoms.  At 10 rpm, however, adaptation presented a challenging but interesting problem.  Even pilots without a history of air sickness did not fully adapt in a period of twelve days.

Tangential Velocity
When people or objects move within a rotating habitat, they’re subjected to Coriolis accelerations that distort the apparent gravity.  For relative motion in the plane of rotation, the ratio of Coriolis to centripetal acceleration is twice the ratio of the relative velocity to the habitat’s tangential velocity.  To minimize this ratio, maximize the habitat’s tangential velocity.

Centripetal Acceleration
The centripetal acceleration must have some minimum value to offer any practical advantage over weightlessness.  One common criterion is to provide adequate floor traction.  The minimum required to preserve health remains unknown.  For reasons of cost as well as comfort, the maximum should generally not exceed 1 g.

Hill & Schnitzer don’t explain their minimum limit of 0.035 g.  Compared to the others, it’s an outlier that appears to be an arbitrary lower bound on their logarithmic graph.

Gilruth doesn’t explain his maximum limit of 0.9 g.  It may be to allow for additional Coriolis accelerations without exceeding a total of 1.0 g.  This would be better addressed by minimizing the Coriolis accelerations, by maximizing the tangential velocity.  In particular, in a large rotating colony with high tangential velocity and low Coriolis acceleration, there should be no comfort problem with a centripetal acceleration of 1.0 g.

I have no data on the upper limit of “comfortable” acceleration.  I’ve guesstimated values at which the indicator should transition from green to yellow to red.  You may think that I’ve set these limits too low.  However, I’m interested in the maximum acceleration that would be comfortable for normal activity within the habitat.  This is undoubtedly less than the maximum acceleration tolerable while seated in a padded chair.

References