Good luck. You're really gonna hafta gear that thing up to get any speed. I think a standard gearing set will get you to ~12MPH without any excess strain, or about 18 feet per second. If you want to achieve about 600 fps to get a good cut on wood, and with a workpiece diameter of 3", that'd be ~8 - 900 rpm. 600/18=33.3:1 gear ratio from the bike wheel. Of course, YMMV. I'd recommend using either a gear belt or a serpentine belt like today's cars use to minimize friction loss.
Have you thought about using the bicycle wheel as a mounting point for some ballast attached to the spokes to act as a flywheel?
I gotta ask, will this be a 2 man operation, or will the 'cyclist' also be doing the turning?
Oh, and WE GOTTA SEE PICTURES!:icon_thum