Turbo vs naturally aspirated engine power band width around peak power

[gen x]

Which engine have wider "power band", more average power around max power rpm-s(rpm range that car use for max acceleration), high revs naturally aspirated engine or low revs turbo engine, if both engines have same peak power?(gasoline engines)
That can be calculated from area under power curve at that specific rpm range, divide by rpm interval(definite integral).

 

[Lnewqban]

The naturally aspired engine will always have a wider power band.

 

[gen x]

The naturally aspired engine will always have a wider power band.

Can you elaborate more, maybe put some power curves plots that support that?

 

[Baluncore]

The width of the power band will be determined by the tuning of the inlet and the exhaust. The turbo will be most important at high RPM, as it will extend the power at high RPM, when there is little time to induct air into the cylinders.

A turbo will enable more power from the same engine displacement, or the same power from a smaller displacement engine.

... high revs naturally aspirated engine or low revs turbo engine, ...

It is more likely that a low revs engine would have a supercharger than a turbocharger. A high revs engine will benefit from a turbocharger.

 

[jack action]

If both engines are identical and have the same peak power, it can be assumed that the turbo is bypassed at high rpms. Therefore, the turbo only kicks-in during low rpms, thus increasing the overall power band compared to the naturally-aspirated engine.

It is more likely that a low revs engine would have a supercharger than a turbocharger. A high revs engine will benefit from a turbocharger.

A turbocharger can work just as well on a low revs engine:

 

[Lnewqban]

Can you elaborate more, maybe put some power curves plots that support that?

It is all about breathing.
A naturally aspired engine that has a healthy breathing along a wide range of rpm's is said to have a flat performance curve, and can enjoy a transmission with three or four steps only.

Turbines are only efficient in certain narrow range of rpm's and delta pressures (which depends on good engine breathing), which limits the range of rpm's in which it is able to provide the best boost to its engine.

The case described in post #5 is a good example of a turbo specifically designed to make a peak curve flatter, which is opposite to the case of a turbo meant to increase the peak power of an engine (maximum breathing-rpm's combination).

 

[Baluncore]

A turbocharger can work just as well on a low revs engine:

Yes, but to get power across the widest RPM band, the turbo will need to function at the low end of the revs, where it is most inefficient. As I understand it, turbocharger efficiency follows an RPM⁴ power, while with a positive displacement supercharger, efficiency does better than RPM², and it follows closer to the stoichiometric air volume required.

I know the vast majority of the turbo compressed air can be dumped at the top end, but that does not relieve the requirement for a higher capacity turbocharger, that will work sufficiently well at the bottom end.