Re: Inductance of a conical coil

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Original poster: "Barton B. Anderson by way of Terry Fritz <teslalist-at-qwest-dot-net>" <classictesla-at-netzero-dot-com>

Hi Antonio,

Tesla list wrote:

>I have run some tests. The correction factor 1/sqrt(cos(a)+sin(a))
>works well. It has a maximum value of 0.841 for a 45 degrees coil.
>I notice, however, that the sqrt factor reduces the factor excessively
>when the angle is close to 0 or to 90 degrees.

Yes, At the time I was looking at this, I had graphed out several 
geometry's and remember seeing the same.

>I propose then this correction factor: 1-k*sin(2*a)
>k is a constant chosen so the calculation is "exact" for some particular
>geometry. For example, consider a coil with:
>minimum radius=0.1 m
>winding length=0.1 m
>angle varying between 0 and 90 degrees with the horizontal.
>100 turns, 1 mm wire.
>My formula requires a factor k=0.1466 to match Fantc exactly at a=45
>degrees. The correction factor is then (1-0.1466*sin(2*a))
>A comparison (sizes in meters, L in mH):
>a     rmin  rmax    h       Fantc  cone   Bart  Antonio
>0     0.1   0.2     0       3.78   3.85   3.85  3.85
>22.5  0.1   0.1924  0.0383  3.64   4.03   3.52  3.61
>45    0.1   0.1707  0.0707  3.26   3.82   3.21  3.26
>67.5  0.1   0.1383  0.0924  2.70   3.02   2.64  2.71
>90    0.1   0.1     0.1     2.07   2.08   2.08  2.08
>For your coil (rmin=0.1445 m, rmax=0.3838 m, h=0.0871 m, n=13.6), I
>obtain L=0.103 mH (Fantc: 0.102; Your correction: 0.101).

I see closer agreement with this correction factor. The only limitation is 
obtaining k, which we need a measurement or one of the higher order 
programs to resolve.

>Note that there is still a problem with Wheeler's formula for flat
>coils, that doen't match Fantc well.

No, Wheeler's flat coil equation does not fair well. I suspect the reason 
is due to turn-to-turn inductance is non-linear simply due to the geometry 
of the flat spiral as opposed to a helical coil where turns are linear to a 
far greater degree (all turns are of the same size). I believe the formula 
is not accounting for this fact and is assuming internal coil inductance is 
similar to that of a helical. Just a guess.

Take care,
Bart