well all that can said is that The Turbo's will run off the Exhaust/air.. where as the supercharger will run from the engine and will respond instantly to throttle.. where a s a turbo needs certain rpm's and air to actually perform
yeh, a roots type supercharger will have virtually instant response and can make decent enough power, so isnt a bad choice for a low-boost street car.
The only issue is that if you want to go further than a low-boost street car, and look for a larger power increase, the supercharger is less efficient than a turbo and simply doesnt work well at higher boost levels.
A centrifugal type supercharger has lag just like a turbo, as it also needs to get to a certain speed to start compressing the air
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