Sciencemadness Discussion Board

spherical magnet falling in Aluminium tube

D4RR3N - 12-12-2013 at 14:41

Hoping someone might know this or have some ideas how I could find the answer I seek.


So most of you will have seen an experiment in which you drop a magnet through a copper or aluminum tube and if falls very slowly due to eddy currents induced in the tube.

Lets say I have a 12mm dia spherical magnet, several aluminum tubes with an internal diameter of 14mm,300mm long but varying wall thickness from 0.5mm to 12mm thick.

We drop the magnet through the 0.5mm tube and time how long it takes to come out the end and then move onto the next tube with 1mm wall thickness. As the wall thickness increases the rate of fall will decrease but I assume at some point increasing wall thickness will have no effect on the speed of the falling magnet....that's what I want to find out, but I don't want to pay someone to machine 50 aluminum tubes. Can it be calculated?


phlogiston - 12-12-2013 at 17:00

yes

D4RR3N - 13-12-2013 at 12:12

Quote: Originally posted by phlogiston  
yes


you know how to calculate optimal wall thickness ?

WGTR - 13-12-2013 at 17:19

Is this something where you are looking for an exact answer, or a "rule of thumb"?

I don't have the time to figure out how to calculate it precisely, but I would think that after you pass a 1:1 ratio (wall thickness
to internal diameter) that you pass the point of diminishing returns. Technically no matter how thick the tube already is,
making it thicker will always help, even if it has a miniscule effect.

There are more than just eddy currents that you're dealing with. The tube itself acts like a shorted turn. If you cut a slit
all along the length of the pipe, the magnet will fall much faster.

other variables

quantumchromodynamics - 13-12-2013 at 20:45

orientation of spherical magnet
rotation of the magnet
flux density of the magnet
and others...

D4RR3N - 15-12-2013 at 06:26

Quote: Originally posted by WGTR  
Is this something where you are looking for an exact answer, or a "rule of thumb"?

I don't have the time to figure out how to calculate it precisely, but I would think that after you pass a 1:1 ratio (wall thickness
to internal diameter) that you pass the point of diminishing returns. Technically no matter how thick the tube already is,
making it thicker will always help, even if it has a miniscule effect.

There are more than just eddy currents that you're dealing with. The tube itself acts like a shorted turn. If you cut a slit
all along the length of the pipe, the magnet will fall much faster.



I want a rough idea so I don't waste material, basically this device I am making must be light weight and any wall thickness over what is required is extra weight that is doing nothing.

"I would think that after you pass a 1:1 ratio (wall thickness
to internal diameter) that you pass the point of diminishing returns"

I had actually thought this too but its simply a guess on my part and don't know if it is correct or not. Whats your logic behind this 1:1 ratio?

Actually correction my guess was that 1:1 for radius not diameter, so for a 12mm dia sphere that would be a wall thickness of 6mm. Its a pure guess and don't know if it is correct or not.

[Edited on 15-12-2013 by D4RR3N]

WGTR - 15-12-2013 at 13:43

Edited: stupid math mistake.

Looking at a cross-section of the tube, if the tube were divided up into a number that approaches
infinity of insulated concentric rings of a thickness that approaches zero:

A tube with an internal diameter of 10mm and an outer diameter of 30mm would have a
DC resistance around the outer surface that approaches three times that of the inner surface.
That would mean that additional increases in thickness would not decrease the overall resistance
much. This is rather subjective, though.

The assumption that there is an infinite number of insulated concentric rings, however, is not
accurate, since the tube is a solid piece of metal. Therefore, the above estimate doesn't account
for eddy currents and skin effect, which among other things, depend on the speed of the magnet
travelling past the metal. This is pretty much where my ability to help falls flat.

[Edited on 16-12-2013 by WGTR]

D4RR3N - 16-12-2013 at 06:08

Quote: Originally posted by WGTR  
Looking at a cross-section of the tube, if the tube were divided up into a number that approaches
infinity of insulated concentric rings of a thickness that approaches zero:

A tube with an internal diameter of 10mm and an outer diameter of 20mm would have a
DC resistance around the outer surface that approaches three times that of the inner surface.
That would mean that additional increases in thickness would not decrease the overall resistance
much. This is rather subjective, though.



The assumption that there is an infinite number of insulated concentric rings, however, is not
accurate, since the tube is a solid piece of metal. Therefore, the above estimate doesn't account
for eddy currents and skin effect, which among other things, depend on the speed of the magnet
travelling past the metal. This is pretty much where my ability to help falls flat.


Thanks WGTR! With an internal dia of 10 and an external dia of 20 that is a 1:1 ratio of radius to wall thickness which was also my guess, interesting at least that we came to the same conclusion but for me it was more of a gut feeling then actually using logic to work it out...still two heads is better then one!

Another thing I was thinking of was instead of using a solid bar which is heavy to segment the bar by running deep grooves at regular intervals on a lathe, so for example 2mm grooves 2mm wide spaced 2mm apart and leaving 1mm wall thickness at the bottom of each groove.

[Edited on 16-12-2013 by D4RR3N]

Master Triangle - 25-12-2013 at 01:05

For giving it the maximum fall time you should use copper, it gives quite noticeably longer fall time for the same or thinner walls. If you are going for low cost however I would recommend getting a catalogue from a local aluminium supplier and finding the thickest one that matches your magnet (up to about a diameter of about twice the magnet). And machining groves in the wall will increase the resistance and reduce the electromagnetic opposition that it can provide.

Have look at the conductivities of aluminium alloys, as far as I know the more pure the metal the lower the resistance. Consider using a smaller magnet as that will require a smaller and cheaper tube.

MrHomeScientist - 7-1-2014 at 08:06

Try a silver tube for maximum effect :) It has the highest conductivity of all metals, and will sustain the best eddy currents. Another fun thing to try is cooling your tube with liquid nitrogen (or dry ice, easier to come by). As you cool the metal its resistance goes down, further increasing eddy currents and slowing the magnet even more.

In a completely different application of Lenz's Law, my friend built an electromagnetic coil gun using some scary-looking capacitors and a flat coil of thick copper wire. Placing an aluminum hard drive platter atop the coil and discharging the capacitors into the coil creates a huge, short duration electric field. This induces eddy currents in the aluminum disk in opposition, and the corresponding magnetic fields cause the disk to launch into the air. One time we had access to liquid nitrogen and cooled the disk with it, then tried a launch. It easily flew 100 feet straight into the air, probably double the height we were able to achieve at room temperature.

phlogiston - 7-1-2014 at 17:23

Quote: Originally posted by MrHomeScientist  
Try a silver tube for maximum effect :) It has the highest conductivity of all metals, and will sustain the best eddy currents.


Without wanting to hijack this thread, this made me wander if it might be possible to separate particles of different metals with a rapidly varying magnetic field.
Consider a stream of vertically falling metal powder with a magnetic field of increasing magnitude (in time), with the flux horizontally and perpendicular to the stream of metal powder. Would particles of different metals be deflected differently, effectively separating them?
If so, this might be a quite useful method for recycling metal-containing waste.

Metacelsus - 7-1-2014 at 19:27

The difference in particle size and shape would probably swamp the difference in conductivity among metals.

MrHomeScientist - 10-1-2014 at 12:31

Interesting idea, though. If your recycling center had several grinding steps to shred the metals into uniformly-sized small particles, I'd bet there would be some effect. That would be an awesome experiment if practical - ball mill several different metal powders together (or just buy all the same mesh size), then subject them to such an electric field as they fall down a long tube and see what happens.

Master Triangle - 14-1-2014 at 18:30

That is definitely an interesting idea but I believe that the induced magnetic field in each particle would attract them together in clumps like iron filings rather than separate them. I believe that I have heard of an electromagnetic "kicker" being used to separate high-conductivity metals from low-conductivity ones though, it would be used in metal recycling and I guess would push the items out of falling rubbish?