I'm not sure if I posted this before, but a few years ago, I took an electric bicycle and built a series hybrid range extender for it. It worked but was quite loud. This is a different bike than the one posted above.
Series Hybrid with Hubmotor - MotoredBikes.com: Motorized Bicycle Forum
The range extender was not really practical, however I learned how to put one together, and I think I know how to do it right, if I ever were to do it again.
I would use a HuaSheng 50cc four stroke with a governor, and connect it to a high voltage (60 to 100V) permanent magnet motor rated at 15 to 20 amps. It could be controlled so that it only starts on acceleration (large voltage drop) or on low battery conditions. I would hope that this combination would provide enough power to run the bike even with a low voltage battery, in other words, with all power coming from the generator.
I had an arduino programmed and ready to control the motor, but found that the range extender needed to be run at full throttle most of the time, so abandoned the arduino controller. It was essentially a voltage detector with a voltage divider to bring the battery voltage down under 5V so the arduino could read it directly, and a large relay to turn power on and off to the electric motor/generator. There was also a gas motor kill switch in there too. The electric motor/generator would start the gas motor when it was connected to the battery, they were directly coupled at the driveshafts.
The downside is that this system is fairly heavy, especially together with the lead acid batteries. I don't know enough about the LiPo charging regimen to know if this hybrid system would work with lighter batteries. My guess is that this system would provide performance of 30 mph. It is not easy to find the right electric motor/generator. I'm not even sure one is available, although an outrunner type might be rewired to create one.
After this experiment I decided that a well made gas motor system is simplest and easiest to build and gives great results if you focus on design for efficiency. At my level of engineering capability (low) a gas motor is a better choice. But I was able to build a working series hybrid bicycle on a very low budget and could build a much better one with about $3,000.