Lenz's Law for Fire-pole?

[Erina]

Although it would be a leap of faith, how reliable would it be for a human to strap on an easy to wear magnetic jacket/belt and jump down a strait tube of which the temporary Eddie current would slow the person down according to Lenz's Law so they would reach the end of the tube at ground level reliably and without injury?

Sort of life a Fireman's Pole, only without the pole.

[swansont]

I think there's a chance you could do it. You need strong magnets and thick metal walls. I have a neodymium magnet ( ~2.5 cm on a side) that takes about 3 sec to drop half a meter in a thick-walled aluminum pipe (about 10x longer than in freefall) and it hits terminal speed pretty quickly. It makes for a nice demonstration.

You're adding mass to that, which increases the gravitational force and speeds it up. This would increase the resistive force, since B would be changing faster (and makes this a tad more complicated to model)

What kind of speed do you consider to be safe? That's got to be known.

 

[swansont]

Since the induced field depends on the rate of change of the field in the material, that means the retarding force should be proportional to speed. That gives us a behavior like F = kv - mg

k is some negatively-valued number (because the retarding force is up and v is down, kv > 0) and it depends on the magnet and the surrounding material and geometry. I assume that will be the same for all magnets (we have a platform with magnets around the rim, tightly fitting inside the tube)

 

Terminal speed means kv = mg, and if my magnet is 0.1 kg (tough to measure, since it would tend to stick to a scale and it's hard to manipulate) and we approximate g as 10 m/s^2, we get mg = 1 N

My estimate of the speed was 0.5 m in 3s, so that's 0.167 m/s (assuming it hits terminal speed quickly), and k is then 6 N-s/m

And now, adding mass should result in a faster speed, but that should scale linearly, at least over some range of values. So if you increase the mass by 10x (0.9 kg of load per 0.1 kg magnet), you get a speed of 1.67 m/s

Jumping from 1m gives a landing speed of 4.4 m/s, so you can tolerate a load of 2.5 kg additional mass per magnet (4.4/0.167 = 2.6 and subtract 0.1 kg for the magnet)

If you are jumping into a tube that's 0.4m in radius, the circumference is 2.5 m, and you could fit ~100 magnets around the rim of your disk. Which should support 250 kg of load. More if you use stronger magnets

So this back-of-the-envelope model suggests this would work.

[Erina]

Many thanks for your help !

Assuming if the magnets were woven into an upper body jacket (to better distribute the forces on the human body) could there be another chute with magnets arranged to zip the jacket back up to the top for the next person without power?

Similar to how a battery moves around the inside of a coil, but without a current.

[swansont]

12 hours ago, Erina said:

Many thanks for your help !

Assuming if the magnets were woven into an upper body jacket (to better distribute the forces on the human body) could there be another chute with magnets arranged to zip the jacket back up to the top for the next person without power?

No. Lenz's law will not result in a force larger than that of gravity. The best it can do is balance it. Otherwise you have a violation of conservation of energy.

You could make two tube + platform systems and couple them with a pulley + cable, so one goes up while the other goes down. It would double the slowing effect (so you could use fewer magnets on each platform) and the empty one would rise while the other one descended.

 

(In reality there are a number of technical issues with this system if one wanted to actually build it. Platform tipping and jamming, for example. If it's the harness as you describe, there would be the worry that the magnets get too far from the metal and decrease the retarding force, plus the practical consideration of making a jacket full of magnets without them sticking to each other as you put it on or took it off)