More boost = more power
You might not be able to get more boost (i.e. because you're already running WOT at max rpm). But if you could get more boost then it would result in more power.
If you want to get technical then the chain was something like
IHP>SHP>BHP
IHP would just be a function of boost & rpm
SHP is the actual mechanical power produced by the piston engine itself
BHP is the power available to do useful work after the power required to drive the supercharger has been subtracted.
As a general rule, if you improve the fuel available and use this improvement to increase the maximum boost of an engine, the maximum TAS that the aeroplane can achieve doesn't change much. What happens is that the minimum altitude at which it can attain that maximum TAS decreases to the new FTH associated with the increased maximum boost.
So you basically drop a vertical line on the TAS/altitude diagram from the old FTH to the new FTH. This approach makes all manner of implicit assumptions and is therefore somewhat quick & dirty. But it's generally quite close to the truth for WWII fighters.
Obviously, the IAS at the new FTH will be considerably higher.
The extra power will also dramatically improve acceleration and rate of climb at or below the new FTH.
The increased ROC was one of the main attractions of 100 octane fuel for fighters during the Battle because it reduced the amount of warning time required to make a successful interception.
If I put a bigger supercharger onto the engine but maintain constant boost, then SHP stays basically the same (it probably goes down a little due to increased compressor delivery temperature, but piston engines aren't generally explicitly T4 limited like gas turbines, so this is a second order effect).
FTH obviously goes up.
BHP at FTH goes down, because of the increased power required to drive the supercharger.
However, neglecting transonic dragrise and assuming reasonable compressor efficiency, the max TAS will always go up, because the increased FTH means that the density of the air that the aeroplane is trying to move out of its way has decreased.
power required = 0.5*roh*v^3*Cd
So long as roh decreases faster than BHP, you're winning.
Eventually, if you take the process to the extreme, you find that at some very high FTH, the BHP available is only just sufficient to sustain the aircraft in flight at its maximum endurance speed; at this point you need to start looking to the airframer for further improvements. Additionally, low altitude performance will be extremely marginal due to throttling losses, but this may be improved simply adopting a multi-speed supercharger drive system of some sort (or possibly by using VIGVs in the supercharger if that's your bag).
You also find that simply bolting a bigger supercharger onto the engine stops working well once the pressure ratio required exceeds 3-4ish for a single centrifugal stage due to the fact that the tipspeed required becomes mechanically challenging. It's therefore expedient to use multiple stages.
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