# [amsat-bb] Torque Coil turns vanish?

Robert Bruninga bruninga at usna.edu
Mon Oct 27 20:35:25 UTC 2014

```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
```