The transmission of alternating-current power with small eddy-current losses

Minimum loss sections of flat conductors

“…This is similar to the starting-point of Arnold's paper [11], in which 'equi-inductance lines' are normal sections through surfaces of constant A z .…”

“…As a increases, the lower-order terms in the polynomial gain strength, while the p 20 term becomes weaker, and for yet greater separations only the p x term would be required to describe a perfect circle. The original curves given by Arnold [11] were not represented by a formula. The curves in Fig.…”

“…It would appear, from the published literature, that there has been just one attempt to calculate the optimum shape of parallel conductor bars. In 1937, a remarkable paper [11], by A.H.M. Arnold of the National Physical Laboratory, showed that flat conductors, thin in comparison with the skin depth, can be constructed in parallel pairs, with particular shapes, such that the combined influences of skin effect and proximity effect are made to cancel each other out completely.…”

“…The shapes are neither easy to calculate nor easy to fabricate. The defining property of the shapes, minimum total power dissipation, has not led to analytical solutions, and the original curves [11] evidently were obtained by a process of trial and error, which must have been enormously time-consuming in the days before digital computers. In Arnold's original paper it was accepted that structural cross-sections, rectangular channels, may provide practical approximations to the optimum shapes.…”

“…The development of the theory given here is rather different. The original paper [11] used CGS units, and described the conductor shapes in terms of 'equi-inductance lines'. In this paper, we use rationalised MKS units, with all properties compared with those of flat parallel conductors of nonoptimum shape, and the inductive coupling is now described by the magnetic vector potential.…”