That is a beautifull piece of mathematical work done there, and sure that these were the kind of things the guys that worked on the TDC were doing.
But honestly, do you think the skippers had those equations in mind in the middle of a real patrol and playing with their lives? To start with, you need a calculator to solve the angle equations, which were non existence, or the TDC which was their calculator. It you want to be realistic and not use the TDC in the pigboats, then just use stadimeter, and guestimate angle on the bow and speed, or use the clock, the stadimeter and the nav map to get the measures (assuming playing with map updates off).
In any case, is a very good work of maths...hats off. I do appreciate your effort and mathematical skills.
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