The accurate computation of forces between circular coils

A new approach for the computation of the forces between coaxial single-layer coils is introduced. It is based on the direct application of Bartky´s transformation to the basic force expression in terms of the axial derivative of the mutual inductance. Differentiation and integeration in the axial direction are done analytically and the transformation is applied successively to reduce the integrand to a form that can be analytically integrated in the angular direction. The iterative process is fast and simple and can yield results to any specified accuracy. The algorithm is applicable over the entire range of coil sizes, shapes and degrees of coupling. It extends an earlier algorithm that has been developed for the computation of inductances. The new algorithm has been checked over the whole range against the numerous results available in the literature. The accuracy of the results is only limited by the word length of the computer used and the loss in significant figures incurred in the computations is usually less than three. In the extreme cases, Grover´s tables were found to be correct to one significant figure only.