What minimal radius is needed for rotation to simulate gravitation without adverse effects on humans?
A quite common idea to provide "gravitation" in space stations is to make them rotate, so the centrifugal force gives an effective gravitation. A possible design is a ring-shaped space station.
Now of course it is easy to calculate how fast a space station has to rotate, as function of the radius, in order to provide a given g-value. Of course, the smaller the radius, the larger the needed angular velocity to provide the gravitation:
$$\omega = \sqrt{\frac{g}{r}}$$
However, a small, fast rotating a space station has two disadvantages:
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Due to the dependence of the centrifugal force of the radius, there's a difference in the gravitational strength between head and feet. For a human of height $h$, when the floor is on radius $r$ (assuming $r>h$, of course) you get
$$\Delta g = \frac{g h}{r}$$
This difference might give problems; but I doubt they will be the main problem. Also, it falls off quite quickly with $r$, so with any halfway reasonable size of the space station, I guess it should be no issue.
Due to the rotation you get a Coriolis force. This should mess with the human sense of balance. Moreover, since it is proportional to $\omega$ (more exactly, for running perpendicular to the rotation axis, it's $2\omega v$), it only falls off with the square root of the radius, so I guess that is the determining factor to decide which radius is needed.
Also an effect is that when moving, the direction of "gravitation" will change as you walk around the ring. This I guess will tend to cause you to stumble as soon as you walk, let alone run, if the radius is too low. I have no idea how well humans can adapt to this (or if that question has even been studied).
So my question is:
What would be the minimal radius for a space station, if there should be no problematic effects for humans?
Assume aiming for earth-like gravity ($g=10\,\rm m/s^2$), normal size humans (height up to not much more than 2 meters) and people may run (from 100 meter sprint times, one may assume a maximum speed of about 10 m/s). Also, we can assume there's only one floor (no "upstairs" with different radius).
Note that this is not really a question about physics (how to calculate the physical quantities is clear to me) but more a question about human physiology (how weak do we have to make the effects to not cause problems), thus the tag.
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