Sounds like a sophomore's proof.
What you will not be able to recover is a) the heat lost to resistance. b) radiated energy.
I mention the second because it is less obvious than the first.
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One improves the efficiency of radiation by adding the correct length of antenna to the circuit above and then you call it a transmitter.
More personal research would be needed to recover the | proof, but that would imply something like 40% of the KE absorbed by | the regenerative brakes could be recovered.
If the objective is to burn fuel then cars are 100% efficient. If the objective is to convert chemical energy to mechanical energy then cars are 18% efficient, measured as lifting its own weight (and that of its passengers) against gravity. By driving the car off a cliff most of that energy can be recovered. If the car is used as a pile driver that would be useful work. A brake does not assist the car in doing useful work. The question asked was: " What is the efficiency of regenerative brakes? "
Firstly we have to decide if stopping the car is efficient, because clearly if that is the only purpose then a friction brake is 100% efficient for succeeding or 0% efficient for wasting useful kinetic energy. Indeed, locking the brake will result in no heat loss at all, that will be transferred to the tyres skidding against the road surface, but few would call that efficient. A regenerative brake returns some of the energy to the battery without the corresponding heat loss and is therefore
82% efficient, the other 18% being lost to air resistance. This can be improved upon by streamlining all cars to look like aircraft. Of the 82%, 1-2% will be lost heating the cables between the brake and the battery. The figure of 80% is necessarily approximate since an identical brake fitted to a different vehicle will change the overall efficiency.
| | An Analysis of Hybrid Electric Propulsion Systems for Transit Buses | Milestone Completion Report by O'Keefe and Vertin of the | National Renewable Energy Laboratory |
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gives the efficiency of regenerative braking | as 49-50% at best and 39% as current practice. If you look at figure 46 of that document you'll see many variable parameters including vehicle dimensions, location, time of year etc. and we can argue the efficiency of brakes on roller coasters in the Swiss Alps or kids burning rubber and doing wheelies on motor cycles or the space shuttle deploying a parachute on landing.
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Regenerative braking on Airbus 308 would not be efficient, lifting batteries to 30,000 feet is a waste of fuel and it doesn't have electric turbo fans to recover the energy. A Prius is not a transit bus and a transit bus is only efficient when fully laden, it serves no purpose when driven around empty.