Coriolis Deflection & Gravity Gradient Calculator

Calculate the gravity difference between head and feet inside a rotating space habitat.

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Gravity Gradient
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Gravity at Feet
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Gravity at Head
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g Difference
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Rotation Rate
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Understanding Gravity Gradients in Rotating Habitats

In a rotating space station, artificial gravity is generated by centripetal acceleration. However, because this acceleration depends on the distance from the center of rotation, different parts of a standing person's body experience different levels of gravity. This gravity gradient is one of the primary engineering constraints for rotating habitat design.

The Gradient Formula

The artificial gravity at any point inside the cylinder depends on its distance from the rotation axis:

gfeet = ω² × r

ghead = ω² × (r - h)

The gradient percentage is simply the height divided by the radius:

Gradient = h / r × 100%

Comfort Thresholds

Research on human tolerance to rotating environments has established several important thresholds:

  • Under 3% gradient: Imperceptible to inhabitants. Feels like standing on Earth.
  • 3% to 10%: Noticeable. Your head feels slightly lighter than normal. Adaptation period of days to weeks.
  • Over 10%: Nauseating for most people. Dropped objects visibly curve. Balance is impaired. Long-term habitation is problematic.

Coriolis Effects on Daily Life

Beyond the static gradient, the Coriolis effect causes moving objects to deflect. In a rotating habitat, if you throw a ball "straight up," it curves to the side. Walking against or with the rotation direction changes your effective weight. Water spirals when poured. These effects scale inversely with radius, making larger habitats significantly more comfortable.

Design Implications

For an O'Neill Cylinder with a 3,200-meter radius, a 1.8-meter person experiences only a 0.056% gravity gradient, essentially identical to Earth. For a more modest 100-meter station, the gradient jumps to 1.8%. At a tiny 10-meter radius, the gradient reaches 18%, making normal activities extremely disorienting.

Frequently Asked Questions

In a rotating habitat, objects moving radially appear to deflect sideways because different heights move at different tangential speeds. This Coriolis effect makes dropped objects curve and creates disorienting spatial perception for inhabitants.
Artificial gravity depends on distance from the rotation axis. Feet at the rim experience full gravity, while the head (closer to the axis) experiences less. The smaller the cylinder radius, the larger this percentage difference becomes.
Under 3% is imperceptible. Between 3-10% is noticeable but tolerable with adaptation. Above 10% causes significant disorientation, balance problems, and nausea for most people.
High gradients make walking feel strange (your head weighs less). Thrown objects curve instead of traveling straight. Sports, cooking, and pouring liquids all behave differently. The effect is most pronounced in small habitats.
For a 1.8m tall person: ~180m for under 1% gradient, ~36m for under 5%. Most studies recommend at least 500 meters for truly Earth-like conditions. The O'Neill Cylinder uses 3,200 meters for effectively zero gradient.