Originally Posted by
BeBerlin
Big fat warning: I hate maths. Always have, always will. It's a truly mutual relationship, by the way.
That said, I am not entirely certain that what you said is entirely accurate. Take a look at the drawing again. We measure B, which is the total spine thickness. Suppose we did not calculate the taped bevel, but just measure the taped spine, in the same fashion as we measure the un-taped spine. Obviously, we are then measuring 2 extra layers (I tried to illustrate that in the drawing as well). So when using the same formula, in the taped version the spine thickness is B+2 layers of tape. It is true that you can easily rewrite the formula (B+2T)/2 = B/2+T. Both are correct. I believe my variant stays closer to what would happen if you were to measure the taped spine instead of calculating it. Quite honestly, I thought that would be simpler.
The rest is, I'm afraid, slightly beyond me. I think that by widening B, also A will become very marginally longer. However, a spine is usually rounded and neither does tape create a sharp corner where it is folded over the rims of the spine. I couldn't think of a formula that completely correlates with how exactly the tape folds around the rim. Moreover, I think this factor will only alter the outcome in amounts far beyond the precision of our measurements (using the Verniers calipers) and far beyond the normal variations in spine thickness and blade width that can be found along the same blade. Variations in thickness of the tape itself will nullify the intended extra precision.
I'm sure this will be an interesting exercise for you mathematicians (and, of course, the Polymaths), but for practical use in real life on real razors, it seems a bit over the top. Personally, knowing the bevel angle within half a degree is more than accurate for my purposes. ;)
I think it would be fun to have that in the Excel spreadsheet for practical purposes.
Thanks a lot!
Robin