# Speed of elevator on rotating wheel space station

Assuming a passenger was sitting in an elevator in a rotating wheel space station, as depicted in the movie 2001:A Space Odyssey and based on this question Elevator on rotating wheel space station, would there be any obvious structural or physiological limitations on how quickly an elevator could move from the central hub to the outer ring, assuming a station with a 600m radius was spinning at 1rpm producing .8G in the outer ring.

• I think your artificial gravity magnitude is off. I'm getting more like .67g, and spincalc seems to agree. Nov 13, 2019 at 12:14
• Yup. I had rounded down. I didn't realize .09 rpm would make that much of a difference. Nov 13, 2019 at 12:52

Note: a 600m radius station spinning at 1rpm gets an artificial gravity of about 0.67G, not the 0.8G mentioned in the question. The various bits of maths below assume that the 1rpm is correct, and that the 0.8G is wrong.

Passengers on the elevator will experience two forces: one, the centrifugal force, which depends on the distance from the axis, and two, the coriolis force the strength of which which depends on velocity relative to the rotation vector of the station. For an elevator travelling at a constant speed, the coriolis force effects will be constant and artificial gravity forces will vary smoothly.

The real-world Guangzhou CTF building is 530m tall. The elevator shafts are 440m long, and the elevators reach a top speed of 1200m/min (20m/s), which is (or at least recently was) the fastest speed of any normal passenger elevator in the world. Possibly specialist industrial elevators elsewhere might be faster, but lets stick with speeds meant for normal people, and regular rapid travel.

The strength of the coriolis force is defined as $$F^\prime = 2m\Omega \times v^\prime$$, where $$F^\prime$$ is the resultant force vector, $$m$$ is the mass of the moving object, $$\Omega$$ is the rotation vector of the station, and $$v^\prime$$ is its velocity vector relative to the rotation vector of the station.

Lets make a coordinate system with Z pointing radially inwards at the axis from the rim (ie. "up" in the artificial gravity field). $$\omega$$ is the angular velocity, and $$v$$ is the velocity of the elevator, which will be travelling along the z-axis.

$$F^\prime = 2m\begin{bmatrix}0\\\omega\\0\end{bmatrix}\times\begin{bmatrix}0\\0\\v\end{bmatrix} = 2m\begin{bmatrix}v\omega\\0\\0\end{bmatrix}$$

If the elevator goes up, the occupants will feel a force in the direction of the rotation of the station. If they go down, the force will be in the other direction. Your station rotates at ~0.11rad/s, so the acceleration due to coriolis effects in something like the Guangzhou CTF lifts will be a little over 2m/s2, or about a fifth of a g. This is quite fast... compare this with the accelerations of public metro trains. I share the opinion of the author of the linked post that the Moscow metro trains are get going pretty quickly, and they only have an acceleration of 1.3m/s2. If you want your lifts to move as quickly as the Guangzhou CTF lifts, you're going to want everyone to be sitting down, I think, and ideally facing away from the direction of the expected coriolis force.

For a more mild 1m/s2 coriolis acceleration (which might allow for standing passengers, with suitable handrails available), top speeds would have to be limited to no more than 9.5m/s. A fast, american-style elevator has a vertical acceleration of perhaps 1.2m/s2, so it'll take about 8 seconds to get up to speed (or slow back down) and about 55 seconds at cruising speed for a total of 71 seconds to cover the whole distance. Even a quite impatient person should be able to cope with that.

The force of the artificial gravity is given by $$F = -\omega^2rm$$, so it scales linearly with radius. It will obviously be zero at the hub. During the cruise phase of the elevator's travel, the radius will change by 9.5m/s, so the acceleration due to artificial gravity will change by about 0.104m/s3 or about 0.01g (a property called jerk). During descent, you start off with an acceleration of 1.2m/s2 towards the ceiling as the elevator accelerates downwards. By the time the acceleration phase has stopped 8 seconds later, you'll be experiencing an artificial gravity acceleration of 0.42m/ss towards the floor, and a coriolis acceleration of 1m/ss towards the wall of the lift.

This sounds mildly hazardous... there's some scope for the initial acceleration of the lift to cause freely-floating passenginers to smack into the ceiling of the lift, and anyone braced against the ceiling will find themselves lying on the wall and sliding down towards the floor, possibly headfirst, once the acceleration has stopped. The initial acceleration during ascent will be largely safe, but the final braking phase risks smacking unrestrained passengers into the ceiling.

It therefore seems prudent to require that all passengers sit down with suitable restraints to prevent accidents. It is probably also sensible to use much lower accelerations near the hub on either ascent or descent, which will obviously increase journey times somewhat. This seems better than the alternatives, which involve bumps, bruises and vomitus.

Because of the lateral acceleration, the lift shafts for your station will be quite different from those on planets. The whole lift might in fact be on rails, rollercoaster style. Coping with forces of this magnitude is fairly trivial for modern engineering, so I don't doubt your space station builders will cope with this just fine.

• "71 seconds...Even a quite impatient person should be able to cope with that." You're right, 71 seconds is not unreasonable. Actually I was looking for an excuse for the elevator to take longer to travel that distance. Nov 13, 2019 at 12:54
• @Bob516 I think the safety issues at the hub-end of the journey, for both ascent and descent, warrant a more sedate lift speed. I think my suggestion is probably at the upper end of the speeds you'd want to have to deal with. If you reduce speeds enough, coriolis forces go away and you might be able to get away without restraints and have windows without people getting travel sick, and so on. Nov 13, 2019 at 14:51