A hybrid car trivially improves total energy input needed, since it replaces braking by generating heat by braking by storing energy later to be reused.

The same should he true here, right? The added energy needed to carry the weight of the motor would be easily overcome by the gains from regenerative braking?

Only if the motor were in the hub of the wheel, which given the typical size of the hubs, seems even less likely. Remember that bicycle drivetrains are typically one-way due to the ratchet, so you can't apply braking force via the chain.

Broadly speaking electric bikes don't use regenerative braking. It's not possible with a road bike drive train.

In any case, the weight of the motor is overcome by the motor itself, using the power stored in the battery.

These guys are not using their brakes nearly enough to make up for the amount of power they would use on the climbs, even on the descents.

Are you saying the physics of a bicycle are somehow different than a car going up and down hills? Or are you saying actually hybrid cars use more gasoline driving in hilly terrain as well, and their benefits only accrue in stop-go city traffic?

Physics and practical concerns are way, way different. You want to go as fast as possible down the descents in a bike race. You don't want to lose any kinetic energy and fall behind your opponents, so the only time you'd be using it is when you actually want to slow down. In a car, you might be braking/slowing down going downhill anyway, so that energy is better captured than used that moment.

There's also the matter of mass: lot more momentum/energy to be gained from a 1500kg car versus a 70kg bike + rider. That said, less energy needed for the motor so don't know how the math works out there.

Edit: all of this is moot anyway because of the point zettabomb made as well.

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