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the best ultracapacitors have a power density of 30wh/kg, which is four times worse than simple Lion cells (a 0.5kg laptop battery stores about 60wh).
So let's say you put a 2kg (4.5 pound) ultracapacitor on a bike. That's 60Wh - the same energy capacity as the aforementioned laptop battery. A typical bus will use about 60kw of power on average for ~30mph city use. For one hour that's 60Kwh, or 60,000 watt-hours. Divided by the ultracapacitor capacity of 60wh, a fully charged bike can provide the bus with 1/1000th of an hour of power, or precisely 3.6 seconds. To fully power one city bus for one hour, you would need 1000 fully charged bicycles, which would save you a grand total of four gallons of gas (assuming a 45% efficient diesel drivetrain). Given the expense of producing bicycles with this capacity, and factoring in the weight penalty to riders, this idea is completely invalid.