BOOSTERBRAKE – strong coil spring built into back wheel of pushbike to push you up hills
Simply press the brake to store energy when going down a hill or stopping at lights and then release the break or flip a switch on it to reverse the rotation and give you a major boost up the next hill!
Great idea, but I think a simple dynamo has been invented for this, rather than waste the energy lost when breaking, it just charges up a battery, then press the button to release the energy and it gives you a boost. I prefer your idea of the simple coil though, less things could go wrong.