Re: formulas (fwd)

---------- Forwarded message ----------
Date: Tue, 14 Jul 1998 22:29:44 -0700
From: "Antonio Carlos M. de Queiroz" <acmq-at-compuland-dot-com.br>
To: Tesla List <tesla-at-pupman-dot-com>
Subject: Re: formulas (fwd)

Jim Monte wrote:

> The formulas you gave are accurate, but not exact.  If you compute
> the arc lentgh for the wire, you come up with a log term.  The
> program I sent in an earlier post uses the exact formula and works
> for soleniodal coils, pancakes, or anything between these, including a
> straight piece of wire.

I keep that my formulas are exact. For a solenoid it is just a question
of "unrolling" it. The expression gives the diagonal length of a rectangle
with width n*2*pi*r and heigth m. The formula is correct for any n, r, or m. I
verified the formula with a line integral too:
Wire length=sqrt((n*2*pi*r)^2+m^2)
The formula for the spiral coil I derived with an integration (rather long
to post here), and appears to work correctly for any n, r1, or r2:
Wire length=sqrt((n*pi*(r1+r2))^2+(r2-r1)^2)
I didn't try a derivation for a conical coil. Maybe this case includes a
log term, or maybe we are talking about the same expressions written in
different ways. I would guess that the general formula is (not checked,
but reduces to the other cases with r1=r2 or m=0, and works for n=0):
Wire length=sqrt((n*pi*(r1+r2))^2+(r2-r1)^2+m^2)

Can you comment on the derivation of your expression (off list if there is
too much math)? I can't see from where the expressions came.

Antonio Carlos M. de Queiroz