The main features of this bike are that we used an electric hub-integrated motor, and we used the front fork as the battery compartment.
metalwork and assembly: saul
battery mounts: dan
Step 1: Parts!
These hub-motors are standard equipment on the Zappy3 Electric Scooter (http://www.zapworld.com/products/zappyIII_scooter.asp). the entire zappy scooter is about $500, you can scavange everything you need from one of them, or you can order just the hub-motor and electronic controller from Zappy as spare parts, which will run you around $250 i think. The zappy scooter works great, but 3 wheels is SOOOO lame.
The zappy motor is 36V, 250W, and their controller has a key-switch and variable-speed thumb-trigger. By their specs, you'll get about 12 miles on a charge, at a speed of about 12 mph - although there are plenty of options for increasing those numbers.