An engineering question, for anybody that wants to solve itS

I've had an idea for a hybrid drive bicycle/moped, but it's feasibility depends upon a question that I don't know how to find an answer to. Could a small* tank of compressed air, hooked up to some sort of generator/dynamo thing, be able to provide electricity for longer than a battery pack of similar size?

If not, we can just toss this idea in the trash but I don't know enough about this sort of stuff to be able to determine whether this is a plausible solution to the alternative power dilemma.

In the simplest form of this contraption, there would be no batteries involved. Current from the dynamo would directly drive the electric motor. The rider would throttle the air flow to control the rate at which the motor spins.

At home the owner could possibly have a solar powered air compressor, making this a sustainable method of personal transportation.

*about the size of a paintball air tank, maybe?

ADDENDUM: I came up with this idea while thinking about diesel-electric trains. They use a similar setup, a power source creating electricity rather than mechanically driving the wheels, to great effect, so why can't this be scaled down and adapted to use different methods of creating the electricity?