RE: New Inductance Formula

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "David Thomson by way of Terry Fritz <twftesla-at-qwest-dot-net>" <dave-at-volantis-dot-org>

Hi Terry,

             (N * R)^2
mH = ---------------------------
     L * c * Cd * 16 *pi^2 *10^-4


= (1175.5 * 0.053975)^2
  -----------------------------------------------
  401.117 x (2.99 x 10^8) x (2.112 x 10^-4) x 16 x (3.14159^2) x (10^-4)

= 4025.6 / 127322.65 == 0.0100640 mH

When I did the above math I came up with 10.036 mH.  Did you multiply the
numbers I outlined in parenthesis above before multiplying with the rest of
the equation?

>My coil is:

26.125 inches long
1175.5 turns of #24 enamel wire
4.25 inches in diameter
1316 feet of wire
inductance is 22.1mH

I have a question on your coil.  Are your turns counted?  Is the wire gage
right?  According to the dimensions you gave, your coil is space wound or
has about 10% space between the windings.

>The actual inductance is 22.1mH

The value for the Wheeler formula that I got was 22.156 mH.

I went back to see why the values were so far off and I discovered I had not
finished cleaning up my fudge factors (I used them as markers while trying
to get the right unit proportions.)  I concede, the formula I presented is
wrong.  I still have the right idea, though.

The Wheeler formula gives inductance as length.  His values are correct but
his units are incomplete.  If you look at inductance in relation to
Coulomb's constant it is:

                    m
henry = --------------------------
        c * Cd * 16 * pi^2 * 10^-7

What this equation says is that 1 meter is equal to 1 henry.  Also .003
meter is equal to 3 mH and so on.  So looking at inductance from Coulomb's
constant it makes sense to express inductance in length (just as long as we
realize there is a denominator that converts the length to inductance.)

Wheeler's formula gives inductance in henry as inch times 1,000,000.
Wheeler did not see that inductance was related to Coulomb's constant.  If
he did he would have written the full equation for inductance as...

                         (N*R)^2
henry = ------------=-----------------------------
        ((X*R)+(Y*H)) * c * Cd * 16 * pi^2 * 10^-7

where

           (N*R)^2
      m = ---------
	   (X*R)+(Y*H)

and X and Y are factors for meters instead of inches. N, R, and H are as in
Wheeler's formula.

It's getting late, but I came up with some close factors for X and Y.  They
are not correct.  I'll give this more time tomorrow.  Maybe others on this
list would like to take up the challenge and come up with the correct
conversion factors?

                                (N*R)^2
henry = --------------------------------------------------------
        ((354331*R)+(3937001.79*H)) * c * Cd * 16 * pi^2 * 10^-7

Dave