Other electric bikes seemed to use a battery in an aluminum case, which fit under the rear luggage rack or between the seat tube and rear wheel.
Trek Transport electric longtail with battery under rear rack. (Photo credit Trek)
These were usually 24 or 36 volt, and somewhere between 5 to 10 Amp hours capacity. (Volts is the zing, like the octane rating on gas, and Amp hours is like the gallons in a car fuel tank. Bigger numbers on either one can give you more range.) These batteries had a nice package that could take falling down, and also a built in key for turning the bike on and off, but they seemed kind of small, even though manufacturers were promising a 30 to 40 mile range. Then it occurred to me that range would depend greatly on how much extra the rider pedaled.
Another thing that influences range is drag. Bicycles have been in development for over two hundred years, and they roll pretty nicely now. Their main energy loss is air friction, which is proportional to size, and an upright riding posture is not very aerodynamic. A rule of thumb is about 300 watts of force to push an average size rider along in an upright posture at 20 mph. (This results in many electric bike motors being built at the 300 watt size, as many national laws use around 20 mph as the registration threshold.)
American Road Cycling's Cycling Performance Simplified
If the wind is blocked by a fairing so that air resistance is removed, it is possible to go quite fast using just human pedal power:
Fred Rompelberg (Netherlands) on a bicycle drafting a dragster at the Bonneville Salt Flats in 1995, setting a world bicycle speed record of 166.9 mph (photo credit Strausberg racing team)
Of course, since aerodynamic drag increases proportional to the square of speed, I could ride slow (5 to 10 mph, which is not very likely to happen) and not worry about the range...
After spending far too many late nights reading electric bike forums, I decided a step or two bigger battery was needed.