Coil shot current, intermediate fill factor

The two familiar coil formulas sit at the ends of a range. NI = 35 000/((L/D)+2) applies when the coil bore area is less than twice the part area (high fill), and NI = 45 000/(L/D) when it is at least ten times the part area (low fill). Most real coil shots land somewhere between those two, and the standards close the gap with a straight-line interpolation on the area ratio Y = coil bore area / part cross-sectional area.

Physically the interpolation reflects how far the part sits from the windings. Close in, the flux is dense and few ampere-turns are needed. Far out, the flux has spread across the bore and more magnetomotive force is required to reach the same field in the part. At Y = 2 the formula returns exactly the high fill answer; at Y = 10 it returns exactly the low fill answer.

The length-to-diameter ratio still governs the demagnetising field from the part's own end poles, so L/D enters through both endpoint formulas and remains restricted to the 2 to 15 band. For a round part in a round coil, Y is simply the square of the diameter ratio; for anything else, compare true cross-sectional areas and use the greatest cross-sectional diagonal as D.

Interpolated ampere-turns carry the same ±10% tolerance as the endpoint formulas and the same obligation to prove field adequacy on the part itself with a Hall-effect probe or an artificial flaw shim.

Y = coil bore area / part cross-sectional area = (Dc/D)² for round in round, limited to 2 to 10
NI(low fill)  = 45 000 / (L/D)
NI(high fill) = 35 000 / ((L/D) + 2)
NI = [ NI(high fill) x (10 - Y) + NI(low fill) x (Y - 2) ] / 8   ampere-turns, ±10%
I = NI / N