Understand the relationship
The reasoning behind the result
Uniform rotation ties radius to acceleration
ω=2πn/60; a=ω²r; v=ωr; T=60/n
Here n is rotations per minute, ω is angular speed in radians per second, r is distance from the rotation axis, v is tangential speed, and T is the rotation period. A point moving in a circle needs an inward centripetal acceleration of magnitude ω²r. Contact forces from a rotating structure supply that acceleration.
In the rotating frame, the apparent outward centrifugal loading has the same magnitude for a stationary point. This is the rotation-induced contribution calculated here; it does not include gravitational fields, habitat translation or other accelerations. Dividing m/s² by the fixed 9.80665 m/s² standard gives a dimensionless g0 comparison.
Two points have different acceleration at the same rpm
ainner=ω²(r−h); Δa=ω²h; Δa/aouter=h/r
An inward radial separation h reduces the distance from the axis. Uniform angular speed means acceleration decreases linearly toward zero at the axis, while tangential speed also decreases. The live profile shows this relation, with the entered inner and outer points on the same line.
The percentage gradient compares the magnitude difference with the outer acceleration. When rotation is stopped both accelerations are zero, so that relative comparison is undefined. The geometric separation remains meaningful but does not create an acceleration. No head-to-foot physiological effect or acceptable gradient is inferred from the comparison.
Radial motion introduces a separate rotating-frame term
|aC|=2|ω×vrelative|=2ωvradial for radial motion
The general Coriolis term depends on the direction of velocity relative to the rotating frame. For the specifically radial motion accepted here, velocity is perpendicular to the rotation axis and the magnitude is 2ω times the entered radial speed. The term is transverse to that radial motion; its direction depends on motion and rotation directions.
It is not added as a scalar to the rim acceleration. Arbitrary three-dimensional motion, walking orientation, spin-up transients, human adaptation, comfort, structural forces and control behavior need additional models and are not solved here.
Follow the numbers
A 100 m radius rotating three times per minute
- Three rpm gives ω=2π×3/60=π/10 rad/s and a 20 s rotation period.
- At 100 m, acceleration is (π/10)²×100=π²≈9.8696044 m/s². At 98 m, it is 0.98π²≈9.67221231 m/s², a 2% decrease.
- Rim speed is 10π≈31.4159265 m/s. A separately entered 1 m/s radial motion has Coriolis magnitude 2×π/10×1≈0.628318531 m/s².
The radial gradient and motion-induced Coriolis term describe different relationships and are reported separately.
Quick guide
How to use this calculator
- Choose the quantity to solve and enter the two quantities actually known.
- Measure radius from the rotation axis to the outer comparison point. Enter an inward separation no greater than that radius.
- If useful, enter a motion speed specifically along the radius; zero omits its Coriolis acceleration.
- Compare the rim, inner point, period, speed and gradient. The g0 conversion is a unit reference, not a habitability target.
Calculation method
Calculation and interpretation
Connect rotation geometry with local acceleration while keeping human tolerance and habitat engineering outside the arithmetic.
ω=2π·rpm/60; a(r)=ω²r; rpm=60√(a/r)/(2π); r=a/ω²; v=ωr; |aC|=2ωvradial.
Worked example
A 100 m radius rotating three times per minute
The radial gradient and motion-induced Coriolis term describe different relationships and are reported separately.
ω=2π·rpm/60; a(r)=ω²r; rpm=60√(a/r)/(2π); r=a/ω²; v=ωr; |aC|=2ωvradial.
Supported inputs
Precision and limits
Uniform rigid rotation model
The geometry assumes a fixed axis and uniform angular speed. Structural loading, spin-up, wobble, stability, external gravity and translational acceleration are excluded.
No human-tolerance prescription
Acceleration targets and motion speeds are entered scenarios. The calculation does not establish comfort, medical suitability, an acceptable rotation rate or a safe habitat design.
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