In Part 1, we covered inductance calculations based on the fact that a coil can be approximated by a uniform cylindrical current sheet representing the entire coil, or as a series of rings each of which represents a single turn in the coil. These approximations simplifed the calculation significantly, and still provided very accurate results in the case of typical coils. And with the corrections given in Part 2a they become even more accurate.
Part 2b pointed out some of places where differences between real world coils and the approximations can lead to inaccuracy. It had been my intention to pursue the idea of corrections for turn length and pitch. However, to do that we need to know the true inductance of a real coil in order to have some idea of what the correction should be. That prompted me to research inductance calculations that are based on an accurate helical model of a coil. That was originally presented as Parts 2c and 2d. However, shortly after these two pages appeared on this site, I wrote a much longer more detailed article which combined everything on the Parts 2c and 2d pages, and expanded it into a more detailed discussion. For that reason, the information previously presented on this page and the following page (Part 2d) has been replaced with that article—a pdf document—which you can view here online, or download to read offline.
Part 3 – Optimizers, Solvers and Empirical Methods