Air Compressor Motor Size???

Using the figure I quoted you of 5cfm at 90psi, you'll see that is actually a solid 3hp compressor at best. They are calling it a four because at full output, you'll need a 5hp motor to drive it.

Let's get some basics down here. If you turn that compressor faster, it pumps more air. That's why the tank fills faster. Pumping more air requires more power, and power is virtually unlimited in the form of electricity out of the wires. Your motor converts electricity to power, but is limited on the amount of power it can continuously convert. That's why the motor draws twice its rated amperage tryig to pul the compressor that fast. You can drop the pressure shutoff point on the switch to help out a little, but not much. The compressor will then run almost continuously to maintain the lower pressure, because you are still using the same amount of air in your tools, just not holding anything in reserve.

A 2hp 3450 motor will be turning twice as fast, but have exactly half the torque of a 1700rpm 2hp motor. To make up that torque, you'll have to double the reduction to get twice the torque multiplication. Motor spins twice as fast, compressor spins the same speed as with the 1750 motor. It'll turn the compressor at the exact same speed in the end because it only puts out 2hp.

hp is a measurement of work. 2hp will only do so much work. Turning that compressor at 600rpm is work. Turning it faster is more work. You can increase the speed until you max out the amp rating of the motor, and then that's it. If you use a larger motor, it can handle the larger amp draw, thus converting more electricity to power, and can run the compressor faster.

The only way to do more work with that compressor (just like an engine, which is a compressor) is to make more air go through it in a given period of time. To do that, it has to spin faster, which is more work. If you want to do the work faster (fill the tank or recover faster), you need to get a bigger motor. No free lunch.