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In which Ben does the math on a hoverboard. - Adventures in Engineering — LiveJournal
The wanderings of a modern ronin.

Ben Cantrick
  Date: 2006-12-23 22:42
  Subject:   In which Ben does the math on a hoverboard.
Public
  Mood:innumeracy ensues
  Music:Chemlab (The Magnetic Field Remixes) - 21st Century


The equation for the magnetic force on a wire is:

F = BLI

B is the magnetic field, in Teslas
L is the length of the wire, in meters
I is the current, in amps

The earth's magnetic field is about .3-.6 Gauss. There are 10,000 Gauss in a Tesla. Let's be optimistic and call it .5 Gauss. Converting to Teslas, B = .00005

Let's say the wire is one meter long, because it makes the math easier. L = 1.

How much force do we need? Let's say a 200 lb person, call it 90 kg. Gravity pulls them down with an acceleration of 9.8 m/s^2. F = ma, so F = 90 * 9.8, or 882 Newtons.

882 = I * 1 * .00005

I = 882 / .00005

I = 17,640,000 amps

A little more than seventeen and a half million amps.

To get some sense of scale, most circuit breakers for houses are about 200 amps. Your whole house, everything in it, all the lights going full blast, stereo, fridge, washer/dryer, everything, takes less than 200 amps. (And requires a cable about 3/4 of an inch across.) Doing the math, we see that this is the electrical equivalent of 88,200 houses going full bore.


In terms of energy, P = I^2V, so this comes to 3.7 x 10^16 Joules per second. In more familiar terms, this about the same energy as you would produce if you exploded 40 million tons of TNT. Per second.


As your lawyer, I advise you to stick with Inductrack. ;]
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  User: nickhalfasleep
  Date: 2006-12-26 21:29 (UTC)
  Subject:   (no subject)
Not quite, since it could operate on ground effect it needs somewhat less power than a helicopter.
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