RE: New Inductance Formula

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

Original poster: "Terry Fritz" <twftesla-at-qwest-dot-net>

Hi Dave,

At 11:36 PM 4/28/2002 -0500, you wrote:
>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?

For some reason I though the answer was in mH.  You have the result in "mH"
in you original equation.  If the equation gives full henries, then it
would be 10.0640mH for an answer.  The factor of 1000 is no big deal...
We'll say it is 10.064mH then...

>
>>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?  

Yep!  I put tape along the coil with marks at every inch.  The coil was
then digitally photographed and the images were blown up large so each
little turn could be counted.

>Is the wire gage
>right?  

It is #24 wire but it's diameter is 0.0218 inches (with insulation) via
calibrate Starrett micrometer.  The next chart list this wire (#24) as 46.3
tuns per inch which works out to 0.0216.  Pretty close considering I buy
plain motor wire (cheap) that can vary quite a bit.

http://hot-streamer-dot-com/TeslaCoils/Misc/WireGaugeChart.gif

>According to the dimensions you gave, your coil is space wound or
>has about 10% space between the windings.

My coil is 26.125 inches long with 1175.5 turns so we get 0.02222 inches
per turn.  0.02222 / 0.0218 = 1.9% extra for spacing and slope between
turns.  Pretty darn close ;-))

>
>>The actual inductance is 22.1mH
>
>The value for the Wheeler formula that I got was 22.156 mH.

Those values have been measured and tested many times, in different ways,
over a span of years, with a variety of pretty close calibrated
equipment...  Trust me, it IS 22.1mH...  Of course, we are not trying to
resolve a 0.01% error here but rather an error of 219.6% =:O

>
>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.

"Fudge factors" always scare me =:-)  I thought it worked for your coils.
It is +219.6% for mine...

>
>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

Wheelers formula is a purely "empirical" formula derived by studying many
coils.  The constants in it may have "odd" dimensions.  He tested a large
number of coils and found a simple equation that "fit".  It fit pretty darn
good too!

>
>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.)

In a way, the dimensional analysis does not matter much unless the equation
is truly derived from first physical principles.  If it relies and curve
fitting, all kinds of dimensional liberties can be taken.  Simply the fact
the "any" equation consistently gives "the right answer" is enough for
most.  Wheelers is a curve fit thing so dimensions of the constants are
assumed to be "odd".  In your case, it looks like you are using first
physics in the derivation so your dimensions "should" work out.  1m = 1H is
sort of a "stretch" but we'll give you more time to work that nasty stuff
out :-))  Fudge factors are a wild card...

>
>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
>


Wheelers formula works as is.  It does not need to be fixed.  Maybe if you
set your equation equal to wheelers the constants would fall out easily.
This is especially true since you both use a pretty similar form of the
inductance equation.  However, I wonder if you might just end up right back
at Wheelers form.  Hey! Its only 1:37am!  What with this "it's getting
late" stuff :o))))

Cheers,

	Terry


>Dave
>