WOW! I get home from teaching this stuff all day and BANG! Here it is on my home computer! The internet... I hear they are gonna have it on computers soon!
Chad, ummmm, well... Where do I start? Maybe a bulletized list? Okay...
Pro's
1) Cheap (that is good 'cause hooking it up is gonna be a DOOZIE in a residential area!)
2) No other pro's
Con's
1) Need 3-phase power (in a residential situation, you just can't get it.)
2) No other con's
That was easy!
Seriously, the question is... What is 3 phase power and how do I get it?
It is where you have 3 "hot legs" 120 degrees out of synch with each other. Essentially a phase shift in the sine wave of the AC magnitude.
Each one starting a climb to max voltage after the next. This makes for a very EFFICIENT motor. Not necessarily any more powerful. You can have an equally powerful (output horsepower-wise) in a single phase motor. A three phase motor is akin to log splitting. A single man striking a maul on a wedge cannot be compared to three men with mauls 120 degrees apart, striking the same wedge. One BIG, strong man could potentially beat the three... meaning there is more "power" there. Kinda like the single/three phase "thing".
How do you get it?
Well, you could buy a phase converter. That is the UL approved, thouroughly engineered, dependable, safe way to go. Buuuut, what is so fun about that!?! We are tinkerers! Let's do some "Ghetto FAB!"
Here is a simple THREE PHASE GHETTO CONVERTER!!!
Need:
1-3 Phase load (your compressor)
1-3 Phase motor of equal size (or better)
1-Everything else to hook it up
Concept:
Make Three Phase power from Single. Single phase power is 180 degrees out of phase.
Net result due to vectoring, less leg to leg voltage.
We need to create (by induction) a THIRD leg!
How? Well, we get another three phase motor and hook it up to the TWO legs we have in a single phase system. It has higher voltage and can limp along on two legs, but not enough to really have much torque.
Soooo, we tie the three legs of the limping motor to the three legs of the compressor motor. There will be an "INDUCED" voltage present in the third leg of the liming motor. It will be roughly 20-35% lower, but nevertheless... will BE THERE!
This induced "Phantom" leg is enough to make the compressor run at nearly full power!
DANGERS:
1) No UL testing HAS EVER BEEN DONE on this!
2) Overload protection needs to be in place!
3) No manufaturer has ever made anything to set this up.
4) Depending on phase rotation, reverse operation could result.
Nuisances:
1) Limp motor may need a twist to get going. This means that you will need to stop work and give it a spin to start the motor. "HASSLE"!
2) Fabbing up the motor starting gear is complicated at best.
I HAVE done this in my lab at school for demonstrations and it DOES work!
I would only hook it up at my house or someplace where someone FULLY understands what is going on.
Disclaimer: This is TOTALLY GHETTO! Don't do it!
With that said, give it a try!
Sorry for the long read.

CJ