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Use air-core-coil resistance to estimate inductance
If the coil is tightly wound you do not need the number of turns to calculate inductance.
Peter Demchenko, Vilnius, Lithuania; Edited by Paul Rako and Fran Granville -- EDN, January 5, 2012
Because the length of an average turn is equal to π×D, the total length of the wire is (N×π×D). The square of the cross-sectional area of the wire is (π×d2)/4.
- This comment should not be taken as a criticism, but as an attempt to increase accuracy of quite cute estimation presented in the DI.
As the wire is assumed to have circular crossection,
the winding always contains empty (non-conductive) space;
even if the wire were not covered by an enamel or other insulation.
To determine the minimum empty space theoretically;
you can imagine three parallel conductive cylinders (wires); each of which is touchimg the rest two.
In the center of the crossection of this configuration, there is an empty area of:
In the winding with many turns two such areas can be counted per each turn.
Consequently, the filling factor of the winding drops from the value of 1, assumed in the DI, to the value of:
2x(1-(pi)/sqrt(3)) = 0.89734