inductance calculations again

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

Hi:

While the list was down I continued to work on inductance and
mutual inductance calculation methods.
Newmann's formula with true spirals and numerical integration
works perfectly for mutual inductances, but is a bit slow.
An approximation using circular turns and Maxwell's expression
for mutual inductances between turns, with elliptic integrals,
works well too, and is fast.
Maxwell's method with true spirals and numerical integration
continues to give the best values for inductances, but is slow.
The approximation with turns considered as closed circles works
well too, and is fast, but requires complete turns.
I found a formula derived by Kirchhoff (in 1864!) that gives
practically the same results and speed. The method looks very
similar to the ones used in Acmi and Fantc, considering complete
circular turns, but uses Maxwell's closed form solution for the
mutual inductances between turns and an approximate formula
for the self-inductance of a turn (and gives precise values for
inductances of coils with widely spaced turns).
The paper is in the "Annalen der Physik", 121, 1864.
I found also an interesting closed solution for the mutual
inductance between a true solenoid and a closed circular turn,
in a paper by John Viriamu Jones. Phylosophical
Transactions of the Royal Society, 63, 192, 1898. A simple
summation computes the mutual inductance between a true
solenoid and a coil decomposed into circular turns.
These formulas, and several others, are all implemented in
the Inca program: http://www.coe.ufrj.br/~acmq/programs
Still missing is a fast and precise method for the calculation
of inductances and mutual inductances when numbers of turns
are noninteger. For awhile, this problem must be solved by
slow numerical integration. I didn't work also in the problem
of nonuniform current along the coils.
The research is being interesting. Everything was known by the end
of the XIX century, and then forgotten. Several recent papers
derive the same old formulas, without references to the old
works...

Antonio Carlos M. de Queiroz