New formula to calculate the skin effect in isolated tubular conductors at low frequencies

The exact solution of the AC/DC resistance ratio of an isolated tubular conductor involves the calculation of values from 12 Kelvin functions. Previous approximate solutions are complicated, and graphical solutions require interpolation from sets of curves. A simplified solution, based on a new formula, is presented. The values of the resistance ratio derived from this formula are within ±1% of those derived from the exact solution in the practical ranges 0.05 ≤ (thickness/diameter) ≤ 0.40 and 0 < √(frequency/DC resistance) ≤ 3000, except for t/D2 = 0.40 and √(f/Rdc) > 2000. For practical tubular conductors, the formula can be used for frequencies up to about 10 kHz, depending on the thickness t and the outer diameter D2. The application of the skin effect formula to a steel-cored conductor can result in significant error.