What sort of forces can be expected in the sudden stop of a rotating space station ring?

Question

This is a bit hard for me to put into to words, but it is an idea I have been working on for a few days, with input from a few other people. I have actually brought up part of this in a previous question that I asked.

The scenario is a large space station with rings that are not connected to the station by spokes, but by a magnetic rails similar to a maglev train. The goal of the scenario is to sabotage the station in a way that is both a complete catastrophe, but does not destroy the station entirely (some destruction is acceptable).

Excerpt from novel: "The station was essentially a stationary drum encased by four, counter-rotating rings. What could be considered the base of the drum faced away from the planet and acted much like a massive satellite dish. The other end of the station directly transmitted information to and from the surface. Rotating at just over 280 kilometers per hour, the rings were suspended and propelled around the station by magnetic rails."

If the saboteur were to cause the magnetic rails to lock up in a sort of emergency braking system, what sort of forces would be excerted on the station? How would I calculate them? What sort of effects might I see?

Further station details:

• Inner ring radius: 620m
• Outer ring radius: 650m
• Inner rotation speed: 280 km/h
• Rotations per minute: Approx. 1.2

Assuming a magnetic braking system similar to Linear Eddy-current Brakes found on high speed trains, I'm unsure of how to calculate what sort of deceleration I would see. On the other hand, if the momentum throwing all of the ring's occupants to the wall produces too much force for survival, I would need to know the maximum (reasonable) impact force survivable. I would then need to work backwards from that value for an appropriate breaking speed.

On top of all of that, I am aware that Eddy-current Brakes produce quite a bit of heat to conserve the loss of kinetic energy. I need to know how to calculate that heat, but can't seem to find any equations relating to it directly. This could be another major factor because I don't want to cook everyone inside, but I wouldn't mind melting or warping the magnetic rails.

Another factor to consider is that the sudden slowing of one ring will throw off the equilibrium of the station since the counter rotating rings are now at a 2:1 ratio instead of 2:2. I suspect this would force the entire station into an incalculable spin, simply because I don't have any really masses or measurements for torque. That said, if someone disagrees on that I would love to know how badly these people are screwed.

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Addition:

For anyone interested, here is a link to an early version of the chapter. It has been edited a few times and some parts have been changed to improve the flow of the story, but it's roughly the same for the most part. The part where this event takes place is at the end of the chapter, but please read the whole thing and let me know what you think.

Answer 1

There is some missing data to fully answer your question, but some things can be said:

• There are four counter-rotating rings, so I assume two are turning clockwise while the other two will be rotating at the same speed counter-clockwise.
• If above holds true then stopping all of them (presumably at the same time) will not make the hub start rotating (i.e.: the total momentum o Space Station is null throughout the event).
• Total energy to be dissipated is (as correctly says @pojo-guy) $ E = 1/2 m v^2$; we cannot calculate it because we miss $m$, which is the total mass of the four rings.
• Deceleration strongly depends on the magnetic field applied to generate the eddy-currents, among other things.
• Deceleration depends on relative speed.

• Complete formula appears to be: $F = \nu v B^2 \sigma$ where:

  • $F$: braking force.
  • $\nu$: Volume of the conductor.
  • $v$: Linear velocity.
  • $B$: Magnetic field.

  • $\sigma$: Conductor's conductivity.

  • Reference https://www.physicsforums.com/threads/calculating-the-magnitude-of-eddy-currents-retarding-force.822714/

• Without these data we cannot compute deceleration, time needed to stop rings and thus the expected smashing force (as said force is proportional to speed, so it will be maximal at start and then diminish; this is the worst possible because it means a sudden high deceleration with almost no warning).
• There won't be any rotational effect on hub, but it will be subject to a severe torque whose size will depend on the above applied force.
• The whole energy (see above) will have to be dissipated as the magnetic rail gets hot; that is quite difficult to do in space and you seriously risk it melting down, unless braking is very gentle.
• A magnetic rail doesn't mean you won't have "spokes" connecting the (stationary) rail to hub; this system will be severely stressed while braking.
• In general I expect all these variables to be computed by whoever designed the thing in the first place, so that any brake you may have would be compatible with structural strength. If you want something catastrophic you should think about some means to have the braking system work outside its specifications (e.g.: "enhance" magnetic field).

EDIT: to follow OP comment

If just one of the rings brakes then resulting disaster is much less severe because:

• just one ring and the hub will be affected.
• all other rings, assuming a frictionless rotation on magnetic rail, will not experience any disturbance.
• Ring has a much higher moment of inertia than hub (exact data needs mass and dimensions of the various components).
• braking effect would be to equalize rotation speed of hub and braking ring.
• angular momentum is preserved, so a part of ring momentum is transferred to hub, in proportion with their moments of inertia.
• rule of thumb would say they will both rotate ~1rpm after braking, so neither will have very high impact:
  • ring change in speed is small because angular speed does not change much.
  • hub change in speed is also small because it does not have a large arm to multiply angular speed.
• energy is not conserved, but the excess kinetic energy lost by ring and not transferred to hub will be turned into heat at brake; but it will be much less than in the first scenario (all rings brake).
• also stress on magnetic rail spokes is much reduced.
• the only scenario in which this would result in wild rotation is if main axis of moment of inertia of hub is not near the main axis of rotation.

Answer 2

A 50g impact/deceleration is going to cause injuries, possibly some fatal, but won't directly kill most people, 100g is usually fatal, thank you Mythbusters. I think you will see some rotation and some precession due to a partial shutdown. Other than that there's not enough data, mainly we need the Mass of the ring before we can start doing the math on the rotational mechanics side of things, this page has most of the equations you'd need to work things out. The other principle effect I'd watch out for is "pile up" the movement of unsecured mass, not least liquid fuels and water reserves, towards the direction of the rotation, depending on the structure and strength of the ring this could buckle the structure.

Answer 3

I posted this comment:

I just can't see a massive space station suddenly stopping. Even with brakes. Just too much momentum. If it comes with brakes to slow it to a stop then surely the engineers have already accounted for what would happen so that there's minimal if any damage. As for ship or asteroid impact: shoot it down before the impact. Its messed up in the case of the ship, but the needs of the many...

Which prompted the OP to object with:

@Len I don't see where there wouldn't be any reason not to have some sort of breaking system. It would make complete sense to bring the ring to a stop for repairs or the works would be flung away from the station, and it would need to stop quickly if there was sudden damage that might be more dangerous to continue spinning. The idea is that the saboteur would trigger the sudden braking and disable the safety measures meant to protect the people inside.

I get what you're saying. I just think there are better ways to do the same thing.

Briefly... The ring wouldn't need to stop for repairs because any works on it would be going at the same speed as it is. If an astronaut goes to work on the outside of the station he wouldn't fly away once he stepped outside. He would go along with the station.

Aside from say, a massive comet crashing into the space station, there could be no more dangerous thing to happen to it than stopping suddenly! Everything inside would get flattened against walls from the sheer momentum! Anything not secured would go flying and become a deadly projectile. A pen would become a bullet. Any liquid inside would get thrown around. Say you wanted to have a pretty lake in the middle of the space station, if the station suddenly stopped that lake would become a rushing mountain of water smacking you like an avalanche.

Also the energy required to suddenly a stop something as large as a space station (you did say it was a large one) would be astronomical. The engines that put the space station into its spin in the first place built that energy up over a long time. its not something that happens as easily as flipping a switch and voila now we have spin. And, just before it reached its desired speed it would already start a the slow down process so it would remain at the desired speed, instead of overshoot, making it too fast.

Its a very finely tuned balance with mathematical equations I wouldn't even begin to understand (I'm sure some genius here will chime in on that [and it might be good for both of us]). in other words the engines the put that station into its spin would have to go in reverse for just as long as it took for it to go forward, expending a ridiculous amount of energy for no benefit.

Imagine a set of beer cans back to back suddenly crushing into one another. That would happen to the body of the station ring. The stresses would be overwhelming. And contrary to popular belief space stations will most likely be built from quite the flimsy materials. Walls of aluminum are not out of the question (with some kind've radiation shielding inside, but that would be fairly minimal too) since all it has to do is keep air inside. A balloon could do that.

A braking system that stops a space station suddenly is not the good idea you think it is.

Here's my suggestions for how you can achieve a sudden stop:

Catastrophic damage. A huge explosion or collision. A saboteur could crash a ship into it, or smuggle an explosive aboard, or destroy a nuclear power plant that was already on board.

Space is filled with lots of objects that could crash into it. A swarm of particles would do lots of damage. A rock the size of a golf ball could puncture just the right thing that does lots of damage.

And even then the wreckage would still keep spinning for some time creating all sort of interesting and dangerous problems for your characters.

Good luck with your story. Sounds fun.