I've read from a few different sources (some on this board) that Richmond and Ford Racing gears are made by the same company, so I'm assuming that this method of setting pinion depth should work for me.
Basically, I don't know where to find the pinion depth measuring tool yet, so I'm going to try this method if I don't find the tool.

Basically, I don't know where to find the pinion depth measuring tool yet, so I'm going to try this method if I don't find the tool.
Shimming the new pinion head to equal the measurement of the factory pinion head and shim
This is the method that I think makes the most sense - if you are installing Ford Racing Performance Parts. After removing the stock pinion gear from the housing you would measure the thickness of the pinion head and shim with a dial caliper. Then you would measure the thickness of the new pinion head. Subtract the latter from the former, and you come up with your pinion shim thickness.
For example, you measure the factory head and shim and find a measurement of 1.975". You then measure the new pinion head and get a measurement of 1.945". By subtraction you find that you need to use a shim which is .030" thick. Put that sized shim on the new pinion and take another measurement with the dial caliper to be sure you reach the stock number.
If this method is used, pay particular attention to the wear pattern measured with white gear marking compound after installation.
