This could be an interesting project. In a way, the use of a capacitor for energy storage is much more elegant than using a battery. You aren't converting to and from chemical energy, which looks like a plus from the perspective of efficiency. Capacitors tend to lose their charge over time, but I don't suppose that really matters if you just want to make a rider's life easier over the course of a single journey. On paper I really like it!
Then comes the problem of energy storage. I'm a little rusty on this so I just used this little tool on the web:
http://hyperphysics.phy-astr.gsu.edu...ic/capeng.html
If you plug in 1,000,000uF (1 farad) and 12V, you get a total energy storage of something like 72J. If you idealize in a major way and pretend like you can convert it all to work, you are looking at 72N*m. For perspective, that's enough to lift my heavy 825N (190lb) rear end about 8cm vertically.
So let's say you want to build a system that can get you up a 10m hill unassisted and work backward. Working strictly from PE, that's 86kg*9.81m/s^2*10m = ~8400J. (Obviously, this is BS because I'm assuming 100% system efficiency.) By fiddling blindly with that calculator, it looks like a 1F capacitor at something like 130V will store the 8400J.
Yeah, I guess that passes a sanity test. You could achieve that voltage through some kind of transformer, and you would have to make sure that your capacitor is rated for that kind of voltage. But it should be feasible, I think. Yeah? Somebody should confirm that the calculation makes sense because it's been a while since I have worked with silly things like numbers and units.