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Here's a rule of thumb: I have been told that you require 1 hp for every 10 cubic inches of first stage displacement. Since you have a two cylinder pump: ((Pi/4) X (Diameter ^ 2) X Stroke) X 2 Pi /4 is always .7854. When you multiply it by the diameter squared, you have the area of the piston in square inches. When you multiply it by the stroke, you then have the volume in cubic inches. Multiply it by two, since it is a single stage pump, and divide it by 10. I have used this formula several times and it seems to work out quite well. You will still have to sheave it correctly for proper RPM and amp draw. If in doubt, I would put a little larger motor on in than you calculate for. Example: 2 cylinder single stage pump, 4" bore X 2" stroke Pi/4 X diameter squared = area of piston .7854 X 16 = 12.566 square inches X 2" Stroke = 25.1328 Cubic inches per cylinder X 2 Cylinders (single stage) = 50.2656 Cubic inches in total divided by 10 = 5.026 HP motor required. Therefore, for a 2 cylinder, single stage 4" X 2" compressor, you would need a 5hp motor to get the rated capacity of air out of it. Of course, you could run it slower with a 3.5 HP motor, or a bit faster with a 7.5 HP motor. Ultimately, within reason, sheave sizes can allow you to work with either a smaller or larger motor. It all comes down to a balance of amp draw, rpm and pressure. Most cheapie units now use larger motors to run the heck out of small pumps to produce impressive numbers, totally leaving out considerations like the longevity of the pump. One example of sheaving for required output is a DeVilbiss 445, v-4 industrial compressor pump. I have seen them turning very slowly with a 7.5 hp motor in HVAC applications where pressure and CFM requirements are modest. I have also seen them turning about 1000 RPM with a 15 hp motor in heavy duty applications such as bodyshops. These ranges are all well within acceptable limits for this pump. But obviously, you can't expect 200 psi or 50 cfm from the same pump when running it with a 7.5 hp as compared to a 15 hp motor. Remember, you can turn a pump too slowly, as well as too quickly. If it is running too slowly, the oil will not splash correctly, and you will starve the wristpins and crankshaft of oil. Anything over 500 rpm should be ok.
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