# What would the size and rotation of a station need to be to produce 1g gravity from head to toe?

A structure with a radius of 224m rotating at 2 rotations per minute will generate 1g of force on the inside (spincalc). It will generate that force on the feet, but as you travel up the body the amount of force applied reduces.

According to Wikipedia (citation needed) a larger radius and a slower rotation should be make the effect more consistent for a standing human.

Playing around with the spincalc tells me that with a 1000 meter radius and a rotation of 0.95 rotations per minute is also at 1g, but I have no idea how that will affect the reduction in inertia felt as you travel away from the outer edge.

What radius and rotation would be needed to produce 1g consistently from the floor to a height of about 6ft (2m) within a tolerance of a few percentage points (maybe 5%)?

• Define your margin of accuracy, You can never have exactly 1g of centrifugal force for two points separated as described. Commented Jul 17, 2013 at 16:52
• First you would need to specify your tolerance (what variation is perceptible/disorienting to the human body?). Otherwise this would be impossible. The force will always vary proportionately with the distance from the center of rotation. Commented Jul 17, 2013 at 16:55
• I added a tolerance of 5% Commented Jul 17, 2013 at 17:08
• Suggest the artificial tolerance of 5% be replaced with a more qualitative measure such as small enough to be generally unnoticeable, where the ideal answer would then define what that value is and back it up with a source. Commented Jul 18, 2013 at 0:16
• A quote from a somewhat related article: "At different points on Earth, objects fall with an acceleration between 9.78 and 9.83 m/s2 depending on altitude and latitude" en.wikipedia.org/wiki/Gravitational_acceleration Commented May 19, 2015 at 3:31

What radius and rotation would be needed to produce 1g consistently from the floor to a height of about 6ft (2m)?

Infinity. Technically there will always be a vertical gradient of artificial gravity. Realistically, people will not care. Even with a radius of 224 m the difference isn't much. The acceleration for anything attached to the structure will be:

This makes the problem simple because the rotation rate (omega) is constant, so the difference between your head and feet is r1/r2. For a person standing in a 224 m radius structure, that's 2/224 = 0.9%.

For reference, the tidal forces on Earth cause a difference in gravity of 0.00006 % from your head to your toe. Earth has an exceptionally constant gravitational field. If you like, you can calculate the radius needed to produce this degree of consistency. It is about half the radius of the Earth.

A percent difference in acceleration from head to toe shouldn't bother someone too much. The main concerns of discomfort in artificial gravity are dynamic Coriolis (false) forces. These are not static like the effect your mention. The terms depend on velocity, not position, so someone standing still will not feel them (discounting any moving fluid in their body). For normal motion, these are much more significant.

Here are some images of dropping an object in artificial gravity. For the 2 rpm case, there is significant noticeable deflection. But again, due to forces that only occur when something is moving relative to the ground. So you could have 1% difference in gravity due to radial location, but several centimeter displacement from dropping something. The latter will be more noticeable.

• Not that it matters but one could argue about the infinity argument, because on the earth surface, there is also a vertical gravity gradient. Commented Jan 3, 2015 at 10:03
• But I think the correct interpretation of the technicality is that the earth doesn't produce 1g consistently from head to toe. You have to separate this into two different questions and figure out which one you want to answer: Is it, how do you get exactly the same gravity at all points (infinitely large radius for rotation, or thrust gravity), or is it, how do you get gravity so close that the human brain can't tell the difference and thinks it's consistent (as, empirically, it does when we stand on the surface of the planet)? Commented Feb 15, 2019 at 20:24
• Gravity between two adjacent bodies is the two bodies influencing each other's performance in the speed of light, or time progression, iow warping each other's spacetime. Or space-time. Hence normalizing each other's, hence drawing each other together. It's a folly to say one manifestation of gravity is more "artificial" than another form of manifestation. "Artificial" is in the eyes of the beholder. Commented Aug 19, 2021 at 20:25