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But exhaust is a byproduct of a running car and does not steal any horsepower.
But they do indeed cost horsepower, they create back pressure.
Nothings for free in this world, if you spin the turbo with an electric motor you’re going to need a bigger alternator, which is more drag on the crankshaft. This is why people that modify engines for a living use dynos to see where the gains and losses are. And without a turbine spinning the drive, I believe you are left with a supercharger…