Quote:
A turbocharger is powered by the exhaust gas of the engine. Both perform the same general function, but use separate methods for the power needed to do so.
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Correct. The key difference being generation of power.
Superchargers are near instant power giving a pilot in a dogfight full use of the power band.
Turbochargers, especially in the early days, create more boost pressure but at the cost of lagging just like a jet engine.
That means you do not have instant power on demand.
The P47 was supercharged and turbocharged, however they did not operate independently. Instead, the normal use was to keep the throttle full forward and use the supercharger/turbocharger to change power.
Those power changes were not instant. You are not going to stall the airplane for example and then power out of it. It just doesn't respond that quickly.
If you try to use the throttle instead of the boost you will collapse the system and induce a compressor stall in your turbine.