Food for thought in that lot.
I must admit I'd often wondered the same problem, such as only yesterday when cutting a 1/4" X 19tpi BSP thread and had to creep up on the last bit beyond the theoretical feed depth for the commercially-made union nut to fit.
I was using an insert tool, squared to the chuck face, and direct in-feed, starting from and allowing for a slightly under-diameter surface so as to give a little flat along the crest.
Unusually for me I'd also set the cross-slide to count up to 0, rather than starting from 0 and counting up to depth value. This clearly showed a considerable discrepancy which I put down to accumulations of slight setting error, springing and wear in the lathe (a Myford ML7)… and wear in me.
It had just not occurred to me to consider the geometry. Usually I close-cut a thread then finish with a die but of all the dies I lack or cannot find, 1/4" BSP is one.
So Thank-you, Jim, for asking!
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I have only once had to analyse thread geometry to any extent.
This was to tap the hold-down holes in the four feet on my Harrison L5 lathe cabinet for the levelling-screws the Manual reckons are there, at 1" BSW. Unable to drill the holes that little bit larger through the 5/8" thick steel, I resorted to partially tapping the holes M24, easing the developing thread to Whitworth, taking another bit out at M24… Took all day, lying on my side in a very cramped position, turning the taps barely a 1/4 turn at a time…. I won't make a habit of such antics.
To prepare for it I drew the thread profiles, ignoring the roots and crests, to establish the interferences and errors. I forget if I drew them completely or in fact plotted them as a pair of traces on an "Excel" graph, but it worked.