Re: Inductance of a conical coil

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

Original poster: "Antonio Carlos M. de Queiroz by way of Terry Fritz <teslalist-at-qwest-dot-net>" <acmq-at-compuland-dot-com.br>

Tesla list wrote:

 > Original poster: "Godfrey Loudner by way of Terry Fritz 
<teslalist-at-qwest-dot-net>" <ggreen-at-gwtc-dot-net>
 >
 > Hello Antonio
 >
 > Using numbers from Bart's old 12.75" coil, I have a comparison chart for k
 > below. I used the acmi numbers for Lp and Ls. Nice engine you have!
 >
 > height  measured   acmi      Godfrey   Antonio
 >     3"      0.1255     0.1238   0.1263    0.1262
 >     2"      0.1395     0.1384   0.1408    0.1408
 >     1"      0.1567     0.1542   0.1565    0.1565
 >     0"      0.1730     0.1708   0.1728    0.1730
 >   -1"      0.1878     0.1874   0.1891    0.1894
 >   -2"      0.2031     0.2032   0.2047    0.2051
 >   -3"      0.2174     0.2177   0.2191    0.2196
 >
 > Not a bad beginning for both of us. No matter how accurately M is
 > computed, there is still the problem of Lp. It will be interesting if you
 > can effect a numerical integration scheme for Lp. As for myself, I'm
 > going after an approximation formula for Lp. But first I must feel that
 > I have control over M. I feel that, whatever ideas give me control
 > over M, will also give me control over Lp.

It seems that we are integrating the same equation. I didn't find
yet a good method to calculate self-inductances. The fundamental
problem is that the current distribution must be taken into
consideration in some form. It is possible to obtain something
good by calculating the mutual inductance between two filamental
coils at small distance, but there is a "right" value for the
distance, that depends on how long are the segments used in the
integration. This method would be inpractical for a coil with
many turns.

I have updated the Inca program, correcting a subtle problem in the
drawing, allowing less than 1 turn in the coils (M is calculated
correctly. L1 and L2 aren't), and incorporating the improvement
in the inductance of conical coils mentioned in other post. I also
precomputed several terms that appear many times, what accelerates
the calculation significantly.

Antonio Carlos M. de Queiroz