# What is the minimum Radius required for an O'Neil or McKendree Cylinder?

This is a follow up to this question. Dimensions of an O'Neill cylinder with gravity and coriolis force like surface of Earth

I read different things like football field length, 200km or 4000km.

• Are you sure you mean coriolis force? Or do you mean Eötvös effect? Nov 10, 2020 at 2:40
• @Corey I'm just using the original title. Nov 12, 2020 at 2:21

## 225m

For 1g and achievable comfort for trained humans, a centripetal gravity system need to have a radius of 225m or greater

Assuming you are completely addicted to having exactly 1g of apparent gravity under your feet, and live only at the rim of the cylinder. (otherwise this becomes a question of how much gravity is needed to stay healthy/comfortable/unmutated?)

There are two factors to consider: The gravity gradient between your head and feet, and the angular velocity. Both of these are affected by the rate of rotation, but the gravity gradient is also affected by the radius and is much easier to satisfy for human needs.

The human balance system depends on the movement of fluids in the inner ear. If your head is under gravity and rotating all the time, these signal you all the time, causing extreme disorientation and nausea among unadapted humans, and even for trained and experienced professionals it produces constant discomfort if the level exceeds a certain rate. Experimentally, this rate seems to be about 2 rotations per minute, for acclimatized personnel. (best results from military pilots, as it happens)

The website at Spincalc has a handy interactive tool to calculate results for inputs of radius|rotation rate|gravity. It also had much discussion on the relevant comfort criteria, including citations galore. (so much so that if there is a way, and permission, that whole website should be embedded in here)

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About the second bit of your leadup question "...and coriolis force like surface of Earth" The absolutely only way to achieve this is to live on a spherical planet with 1g surface gravity, radius of 6 371km, and rotation rate of one per 23 hours, 56 minutes and 4.09053 seconds. The coriolis force in an o'neill will always be in the "wrong" direction, because you are living on the inside rather than the outside of the skin. And the rotation rate will always be greater than the planet, thus making coriolis effects vastly greater than on the planet.

According to sources listed on this page, the minimal safe comfortable radius of a spinning habitat is ~12 meters. This is due to the gravitational gradient between the head and the feet of the person living in such habitat: in a small diameter drum, it becomes too pronounced (The feet experience greater centrifugal force than the head), and the result ranges from noticeable to absolutely nauseating.

– L.Dutch
Nov 9, 2020 at 14:49
• I've edited my answer a bit more but I don't exactly sure how else to expand it. I felt it would be even weirder if I'd just claimed that it's 12 meters. Nov 9, 2020 at 14:55
• Say what bad stuff happens at less than 12m radius. Nov 9, 2020 at 15:11

Size does not matter - differences in forces between head and feet does

Let's start simple - both size and speed will be determined by a pretty simple equation.

$$a = r*w^2$$

On earth a = 9.8, so just change radius (r) and spin speed (w), until you get 9.8.

And now for all the gotchas.

The cylinder needs to be big enough you can't jump from one side to the other. This is super bad. From your perspective the other side is moving at double gravity speed in the other direction!

In a small tube, you'd also have to deal with differences in centripetal force between your feet and head

$$a = w^2*r$$

Assuming your head is at the center of the cylinder (r=0) acceleration/velocity would be 0. Your feet, on the other hand, will be experiencing A LOT of g-forces if w is large enough and r is small enough. The human body can handle max "9g's". After that, your heart can't pump blood out of your feet, it's simply too heavy.

You'll have to make the tube big enough the difference between acceleration at your head and feet are about equal if you want a remotely earth like experience.

Using your examples (a=9.8 at the feet) and assuming a human is about 3 meters tall.

$$w = \sqrt[2]{\frac ar}$$

Football Field -> 100ish meters

w = .313

$$a(head) = .313^2 * (100 - 3) = 9.5$$

200km

w = .007

$$a(head) = .007^2 * (200000 - 3) = 9.799$$

So a football field would probably be good enough, but 200km would likely be much better.

The answer depends on how much training your cylinder dwellers are prepared to go though. What matters most appears to be the tolerable spin rate, high spin rates make you feel sick. To counteract this you can lower the spin rate ( and hence lower spin-gravity), increase the radius or train more (to an extent).

This is all covered in great detail on the Atomic Rockets - Spin Gravity page.
To summarise

At 1G:

• Well trained people should be able to handle 6RPM.