[amsat-bb] Torque Coil turns vanish?

[Luke Stras]

Yes, that's right -- it turns out that, given a target dipole (or
torque), and volume, you can adjust the coil resistance by selecting
the right wire gauge.  If you run twice as many turns, you get twice
the resistance, and so (for a fixed voltage) half the current.  That
gives you the same dipole, regardless.  Fundamentally, the dipole is
proportional to the mass of copper that's in the coil.

It also turns out that the power required to generate a given dipole
varies as the square of the dipole, given constant geometry.  Let that
guide your ADCS sizing!

-- Luke Stras (VA3LNS)

On Mon, Oct 27, 2014 at 4:35 PM, Robert Bruninga <bruninga at usna.edu> wrote:
> I keep coming up with the number of turns of a torque coil vanishing with
> respect to torque (for a given wire size).
>
>
>
> Given that Torque = A x B x I x n where A is area, B is field, I is current
> and n is number of turns.
>
> But I is inversely proportional to the length of wire (resistance). I = V/R
> but R is proportional to n.
>
> Hence the number of turns.  So I is proportional to  V/n.
>
>
>
> But V is fixed in the cubesat, (5v) area is fixed (where we can put the
> coil) and so plugging in,
>
> T = A x B x V/n x n and the n’s cancel.
>
>
>
> So I can get the same torque with –any- number of turns for a given size
> wire.
>
>
>
> What changes with turns, of course, is the current.  So to save spacecraft
> power, the more turns, the less current, and thus, the least power for the
> same torque.
>
> Interesting result.
>
>
>
> We ended up with 600 turns of #34 wire to keep the current at 25 mA so we
> can drive it directly from a CPU pin.
>
>
>
> I wonder where’s the limit?  Infinitie number of turns… Zero current?  I
> guess you run out of space.
>
>
>
> AH HA!  Yes, that was it.  We started with #30 wire but it took so many
> turns to get to below the 25 mA, that there wasn’t room for the coil.  So
> we went to smaller wire and ended up with the #34 to give us a ¼” thick
> coil with 600 turns to give 25 mA.
>
>
>
> But I just always found it interesting that once you have chosen the wire
> size, the number of turns is only determined by the current you want.  The
> Torque is constant.
>
>
>
> Bob, WB4APR
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