I just had to machine some grinder spindle hubs over the holidays. So I wrote a program (using Arts Gearotic/Auggie/Monkey C code) to help me understand the start and stop points for my lathe
Interested to see if these are correct for you; I used the major OD dimension and a length of a holder I'd found on the net.
24/7 = 12/3.5 = 3.5" per foot
I'd verified my grinder spindle taper dimensions with autocad.
the trick to my programming was to remember the taper is included angle not a right triangle. So the calculations had to take that into account.
I modified a Bridgeport spindle a few years ago with my tool post grinder on a manual lathe, still works great for my needs. Now handles both R8 and Cat30 collets.