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George,
1) The centrifugal compressor efficiency will not likely be anywhere
near 80%. Many are as poor as 55 to 65% unless you happen to be at just the
right mass flow and the right RPM.
Choosing incorrectly sized equipment will almost always get a poor result. The unit should be designed to have "just the right mass flow and the right RPM" at the desired operating point. Operating off peak results in poor efficiency even without supercharging.
Typical turbine/compressor combinations I have seen operate at around 70% combined efficiency. Of course a fraction of that efficiency is reclaimed from the proverbial "waste heat" of the exhaust. Centrifical compressors are commonly 80% or better.
2) The belt drive has a significant penalty in lost horsepower.
The typically accepted efficiency range for a "properly designed and maintained" V-belt drive is 95% to 98%. Flat and synchronous belts are slightly better, gears slightly worse at about 92% to 96% I think.
Certainly, poor design and maintenance can make the losses substantially worse.
3) The gear drive in the compressor has another significant drop in
efficiency.
See above.
4) To get the air temperature back down to tolerable (detonation
margins) ranges requires an intercooler
All sorts of engines run without intercoolers, without damage. Detonation is a function of temperature AND pressure in the cylinder at, or near, full compression, not the temperature in the intake. Besides, if you are flying up high, where an add on system makes sence, the air starts out colder so it isn't all that much warmer than it would have been at ground level.
The principle reason for adding an intercooler is the same as for adding a supercharger, to make the intake air denser and increase the mass flow through the engine.
5) The losses across the intercooler and through the induction
plumbing
to accommodate the twists and turns to make the intercooler fit in the system
extract a substantial further penalty requiring still more boost - - but at
the penalty of all of the efficiencies noted in 1-3, above.
Granted, all of these losses exist. I alluded to them in my original post. However, substantial is a relative term and these losses aren't exactly huge (another relative term). From my knowledge of intercooled, turbocharged auto aplications, the induction efficiency is around 90%, ignoring the filter. I would expect that an aircraft application would be at least as good, but you would certainly know far more than me on this.
And consider the engine I was referring to was a 400 hp engine, not a 300
hp.
I wasn't trying to prove anything with respect to the specific engine you refered to. I simply wanted to show the basic math governing the subject that anyone could use to get an idea of the likely benefits of forced induction for an given application. If your freind simply tried to install a spare supercharger he had lying around, it is entirely possible that the result wouldn't be to his liking.
Since you asked, the calculation results with your suggested inputs follow. You didn't provide a design boost pressure or a cruise altitude so I will reuse those I suggested and scale the volumetric flow by the horespower change.
Mass flow air is 0.301 kg/sec
Ideal compressor power is 16.2 hp
System efficiency is .55 (compressor) * .95 (belt drive) * .9 (intake) = 47%
Corrected compressor power is 34.5 hp
The net supercharged power at 18k is 336.8 hp
The net gain from the supercharger at 18k is 91.5 hp
Regards,
Rob
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