Some auto makers have made use of the turbocharger (and to an extent the Supercharger in Mazda miller cycle) mostly for efficient reasons rather than outright performance for many many years, not just this recent burst we are seeing now (Ecoboost anyone), Saab is an example of this.
Turbochargers can/do give a higher efficiency over a similar powered NA engine for a couple main reasons.
One is thermal efficiency, all that heat energy that normally is wasted out of the exhaust to some extent is used assisting for a intake charge rather than just fully expelled, some of this effiency is lost at higher boost where the intake charge itself is overheated from the compressing, needing a intercooler to remove some of that excess heat energy for combustion and compression temps to remain at safe level (bit of a two way dagger)
Another is the fact the turbocharger at idle, low RPM's and low loads (cruising) is really not doing much and is hardly a restriction at all, this means the engine off and at low boost can be tuned to run almost stoich, behaving much like a usual standard tuned NA engine. While a NA engine to provide a similar power and torque curve would need a displacement increase and or compression increase thus increasing other inefficiencies like extra pumping and friction losses.
Supercharging on the other hand can have advantages like in the miller cycle assisting the intake charge during a small period of time to reduce pumping losses (in one of the important time periods of the cycle BDC) by allowing the intake valve to stay open someway through the compression cycle, this design is not for outright power, but rather extra efficiency, which is greater than the losses of the supercharger.
One main disadvantage of the miller cycle is it is not a power chasing engine, infact if you try to increase boost you will just loose the efficiency that was gained.
Superchargers also have the disadvantage of mechanical friction losses all the time from idle and small loads/throttle inputs (cruising), much like having the aircon running all the time but worse, there is clutch systems for superchargers that can disengage at will, so it could be shut off at low rpm, low loads but long term reliability will suffer.
Some superchargers can be boost adjustable without changing pulleys, some have a aggressive pulley ratio with having a boost bypass to control boost similar to a turbochargers wastegate, which can aid in steady broad flat torque curves.
Doesn't forced induction = higher compression = hotter explosion? I'd think that you'd be able to lean out the mixture because of that.
Hotter explosion also means higher combustion temps, there is only so high you can go before given pump fuel pre-detonates, fueling (enriching) is one of a few ways to reduce combustion temps to a safe level without dropping a ton of power.
where in their "non-performance" naturally-aspirated versions, they just stick on a "safe" (super-rich) map and leave it.
Interesting, most factory NA tunes I have l looked at have a pretty good map, it's the aftermarket chipping I have seen some odd examples of.
A lean mix is more air and less fuel?
Well same air, less fuel.
And your saying that the power would only come on at higher throttle?
Power will come on (on a turbocharged engine) when ever you have setup to provide boost not how you fueled it, you then have to fuel the engine accordingly on the rev's vs load axis map. The fueling is to make the most effeicent possible (closest to stoich is possible with some exceptions) while keeping the combustion temps in the correct safe ranges.
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