"N_Cook" wrote in message
...
Perhaps a bit of integral calculus. In a coil winding manual I have a
table
of wire gauge v the minimum excess advance per turn to avoid upsetting of
wound layers. Then sum the layers in terms of the number of turns per
width
and this excess , including in a notional paper layer per turn (p), out to
the outer layer set an average value . Including p being negative (layers
settling into the gaps of the previous layer) and determine what value of
p
gives the right length of wire to fill that volume, then that gives the
number of turns. At the first approximation ignoring curvature at the
"corners".

You don't need integral calculus to calculate this, any more than you need
calculus to determine the number of "layers" in a recording-tape "pancake".
The approximation assuming the "discreteness" of each layer is good enough.