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Comment by dsfyu404ed | Hacker News Reader

TL;DR Yes but not very well. A spring made from magnets doesn't have a close to linear spring rate like a traditional coil spring does.

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But is it linear, from the data? They had two datapoints and projected from that sparse data a regression line.

There are far more than two data points on all of the charts in the article. What chart are you looking at?

The youtube video mostly.

No, it's linear from basic physics.

Within a certain operating region (stress and strain, i.e. the straight bit on the stress/strain graph), a spring will behave linearly e.g. F = kx.

In real life it should be pretty close to linear, but it would be worth checking as I could imagine there being non-linearity or time dependence of a spring under what is probably a decent amount of load being applied quickly and repeatedly.

Yes, that would have been fair. The electromagnets are also (close to) linear if you look at small intervals.

Hook's law[1] states that the force of a spring scales linearly with the distance it is stretched.

[1] https://en.wikipedia.org/wiki/Hooke%27s_law

And magnets repel with an inverse cube law. So there is no simple way to replace a spring with magnets.

You could "linearise" an electromagnet with distance sensors and code, but that's a bit of a Franken-Solution - not least because any delay in the closed loop could make the system unstable.

In this case a couple of minutes of research - or maybe asking a physicist - would have saved a lot of essentially rather pointless tinkering.

I mean - if you enjoy tinkering more than you enjoy producing an elegant solution, then tinker away. But this is noodling around for the sake of it, not solid engineering.

You coukd linearize it using a meta-material of small magnets, though it would probably end up being a cylinder lined with magnets of varying density.

You can also linearize it by making the displacement small enough -- which is how Hooke's law actually works.

Coil spring + magnets = success?

You're fundamentally going to be limited by the fact that magnetic force is roughly exponential with regard to distance whereas coil springs are roughly linear. By stacking a bunch of magnets in the article they reduce the travel of any one magnet pair so it's closer to linear. If you look at short enough segment of a graph of an exponential equation it will look linear, this is basically what they're doing.

You mean quadratic, not exponential.

Actually, the answer is probably "it's complicated". https://en.wikipedia.org/wiki/Force_between_magnets#Force_be... gives an approximation in the x >> R case, but in the pogo stick situation we're not in that case, especially once we get to 5 magnets or so. But even there, if x >> L also holds (which it would in this case, since the magnets shown have R and L of about the same size), the force goes as 1/x^3 or so, because the 1/x^2 terms cancel out if you go through the small-L approximation. Which, again, is not relevant to the problem because our case has small x.

For small separations, the exact geometry of the magnets starts to matter. http://www.magnetsales.com/design/faqs_frames/FAQs_2.htm has some experimental results that show the field going up a bit over 3x when distance drops from 1 to 0.5, then ~2x when going to 0.25, then ~1.5x when going to 0.125 and only changingby 1/8 when going to 0.063... all distances in inches from _surface_ for a magnet that's radius 0.5 and length 0.5 in the same units. Note that this means that the distances from the _center_ are approaching 0.5.

All that said, the force is almost certainly not exponential, I would guess.

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