Pitch Diameter from Three-Wire Measurement
The inverse of the three-wire tile and the way it is actually used on the bench: the pitch diameter from the measurement read over three wires, E = M - 3W + 1.51553 x pitch. A 1/2-13 thread read at M = 0.4900 in over best wires gives E = 0.4734 in. Compare E to the thread-class limits for the fit. First-principles 60-degree geometry.
Formula and source
E = M - 3W + 1.51553 x P, the three-wire relation M = E + 3W - 1.51553 x P solved for the pitch diameter; best wire W = 0.57735 x P (range 0.560P to 0.650P) for a 60-degree thread.
The three-wire measurement-over-wires method for 60-degree threads solved for the pitch diameter, and the best-wire / 1.51553 constant - first-principles geometry as in Machinery's Handbook (Industrial Press), by name; public domain.
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