Been having a terrible time trying to figure out the motor pulley sizes for the two speed countershaft drive on a Heavy 10 from scratch. Thought I had a spreadsheet set-up for the job but it turned out to be a backwards calculation, good for verification only. No way can I get a sensible result matching the published speed tables.
According to the books the effective diameter of a 5L Vee (motor) pulley, used for belt length and speed calculations, is 0.3" less than the measured overall diameter and the effective diameter of the flat (countershaft) pulley is the measured diameter plus twice the belt thickness. As a 5L belt is 3/8 thick that's 3/4" more. I presume that the Vee pulley effective diameter correction takes into account the the narrowing due to the reduced groove angle used with smaller pulleys which clearly must act to increase the effective diameter.
After sorting out a spreadsheet with the correct formulae I got a decent result using the pulley sizes recorded off my Heavy 10 before I sold it. Namely 9.125" and 10" OD flat sheaves on the countershaft with 4 3/16" and 2 13/16" OD Vee sheaves on the motor. Calculated belt lengths for the two cases vary by less than 0.1" so tension won't be a problem. Bummer is that the speeds come out high, 3.7 to 4.8 % up on the high range and 18 to 19 % up on the low range with a US 1720 rpm motor. Interestingly my 1440 RPM British motor gave almost the right low range speeds but was slow in high range. Which worried me not a jot.
I know that in the great scheme of things that result is probably good enough but it would be nice to know why the result comes out wrong. Obvious guess is that the Vee pulleys are slightly modified in angle and OD to alter the effective diameter. The SouthBend speeds given in How To Run A Lathe are very precise and, given the need for equal tension, the solutions are pretty specific for any given pair of flat sheaves. 35 years or so ago it might have been fun to figure this lot out from nothing but there's no point in getting older if you don't get more sensible and mathematics is too close to masochism.