Welcome, learning.
In addition to the excellent resources already mentioned, here are some general recommendations.
I believe three phase windings will always produce more power than single phase, assuming all other factors are equal, and the dual-rotor, air-core design is relatively easy to build.
For determining the optimum wire size, the largest that you have space for will have less resistance/losses.
In lieu of a fully engineered design, I recommend the following "trial-and-error" steps.
- Determine the voltage that you must have for your specific application.
- Build the rotors and the stator coil supporting structure first.
- Make and mount one coil, using, let's say #16 wire, with as many turns as you can fit within the physical space that will be available for a single coil.
- Connect a variable load to the coil, and spin the rotor at the desired "cut-in" speed, and measure the voltage and current.
- Evaluate the voltage at various loadings to determine if you need more turns of smaller wire to increase the voltage, or less turns of larger wire to increase the current, bearing in mind that you will be connecting the other coils in series, parallel, or even series-parallel, with the test coil. If a three phase winding is used, you have a choice of wye or delta connections.
- If you want to evaluate coil heating at this time, run the test setup for at least an hour under load, and check the coil heating.
- When you find a wire size/turns combination that works, wind the remaining coils.
Electric Ed