exactly how does KERS “convert” braking energy into battery power.

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Does pressing the pedal mechanically/hydraulically move spinning magnets on the hub nearer other magnets to create electricity?

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The technology is more commonly known as regenerative braking. Even the term KERS is outdated. But you are sort of correct, although the magnets do not physically move. Rather these are electromagnets that is turned on and off by a switch controlled by a computer. The computer can therefore control exactly where the magnetic field should be at any time. When coasting freely the magnetic field of the electromagnets match the magnetic field of the rotating permanent magnets exactly. So no force is applied through the electric motor. But when you apply the regenerative braking the computer moves the magnetic field of the electromagnets slightly behind the magnetic field of the permanent magnets. So the electromagnets are pulling the rotating magnets back slowing down the rotation. This also produces a current in the electromagnets which is fed back to the batteries charging them.

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