On 9/7/2013 1:20 PM, . wrote:

that cool tip follows from 6 degree thread pitch - 1/2 base times height
...

You mean 60 degree, of course. And "... 1/2 base times height" is the
area of a triangular thread cross section & has nothing to do with
diameters.

The height of the triangle is P/2 * SQRT(3)(where P = pitch), which is
the difference between the major & minor _radii_ of a _triangular_ form
thread. The difference in diameters is then P*SQRT(3) which is quite a
bit larger than P (1.7 times).

But the standard thread form is not a triangle - the crest and root are
both truncated. So by a happy cancellation of inaccuracies (the pitch
being to small a difference for triangular threads and the standard
thread not being triangular), the pitch is a close-enough difference
between major & minor diameters.

I suppose that if one went through the geometry of the truncations, the
difference would come out being (almost)equal to the pitch. But it
certainly does not come from the height of a 60 degree triangle whose
base is equal to the pitch.

Bob