Producing Artificial GravityThe perception of gravity is caused by acceleration, and acceleration means change in the magnitude and/or direction of velocity. Thus, a space colony can either constantly speed up / slow down to produce artificial gravity, or have a torus that rotates (a torus is a doughnut-shaped structure), such that inhabitants within the torus experience artificial gravity. It is impractical to accelerate a structure larger than the empire state building at 1-g, but a rotating torus can easily create artificial gravity of 1-g.
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According to the equation above, acceleration is directly proportional to radius. Therefore, at a small radius, the acceleration at a person's head will become much smaller than that at the person's feet. This will cause blood to rush toward the legs and feet, depriving the brain of oxygen. For example, Skylab, a U.S. space laboratory in the 1970's, had a diameter of 6.6 meters, or a radius of 3.3 meters. Assuming a person is 1.65 meters tall, the gravity at that person's head would be half of that at their feet. Therefore, so reduce the effects of this artificial "tidal force", the radius of a rotating habitat must be large.
The video shows astronauts running inside the Skylab (00:27). Note how his head moves significantly slower.
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Let's assume that humans walk at about 1.4 m/s, and a 15% change in gravity will be noticeable (10% change is about what we feel when riding an elevator). This will put the minimum radius of the habitat at 38.2 meters. If the inhabitants are to run (about 5m/s), then the minimum radius will become 486.9 meters. A more comprehensive list is given in the following.
Interestingly, this also means that moving against the direction of rotation will reduce apparent acceleration. However, if your movement speed cancels out the rotation speed, you will no longer be constrained to the ground and begin to float, before being slowed by air resistance and crashing back down. So, a speed limit would probably be enforced in space colonies. Low-g sprinting would be a great source of entertainment, nevertheless.
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When inside a rotating frame of reference, if a person is to rotate their head in a direction that does not align with the habitat's rotation, they will experience nausea due to cross-coupled rotations messing with the brain. Thus the rotational speed of a habitat must be limited - and to produce 1-g, the minimum radius of the habitat is in turn limited.
Theodore W. Hall presented a brilliant paper at the 2016 ICES about finding the comfort zone in artificial gravity. The paper summarizes various prior research papers on the same topic, and says that the commonly agreed rotational limit is 2 rpm, or 30 seconds per rotation, although limits range to as high as 6 rpm (10 seconds per rotation). 30 seconds puts the lower bound of the radius to 223.4 meters, while 10 seconds demands only 5.0 meters. Wall's results are shown here.
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