Gentlemen,
I have been following this friendly, yet heated, debate on the merits of belt and turbine driven superchargers for the past few days. While I have found it interesting as well as humorous, I would like to ad my two bits to the discussion.
First, the thermodynamic principles behind supercharging and engine power output need to be understood. The fundamental advantage of supercharging is that it allows an engine of smaller displacement to develop the power of a larger model, by improving its volumetric efficiency. Obvious enough.
Unfortunately, you seldom get something for nothing, and the “main” price here is the power required to compress the intake air. Assuming the compressor to be adiabatic (no heat loss), the power required is P = [(p1*v1)/(k-1)]*[1-(p2/p1)^[(k-1)/k]*kg/m, where P = power, p=pressure, v =specific volume, and k = the ratio of specific heats, or 1.4 for air near atmospheric conditions. Of these variables, we can obtain p1 and v1 directly from the air tables and p2 is manifold pressure. Without an intercooler, the only thing left is to divide by the efficiency of the supercharger.
Without an intercooler the power imparted to the pistons as a result of the supercharger is roughly equivalent to the non supercharged power multiplied by v1/v2. v2 is given by v1*(p1/p2)^(1/k).
The discharge temperature of the compressor is given by
T2=T1(p2/p1)^[(k-1)/k]
Assume you are flying at 18k, (50.5 kPa) with a supercharger that puts out 50.5 kPa, an engine that consumes 0.2 cubic meters of air per second (cms) and makes 300 hp at sea level manifold conditions. (I just invented the engine, don’t try to look it up)
v2 is 1.45 cum/kg * (50.5 kPa/101 kPa)^-1.4 = .884 cum/kg
note: while MAP is equivalent to sea level, v2 is 8.3% higher due to compression heating. In other words the manifold air is less dense.
Mass flow is 0.2 cms /.884 cum/kg = 0.226 kg/sec
P=[(50.5 kPa*1.45 cum/kg)/.4]*[1-(101/50.5)^(.4/1.4)]*.226 kg/sec
= 9061 watts or 12.15 hp.
Assuming an efficiency of 80% results in about 15 hp to run the supercharger
The normally aspirated power at altitude is roughly sea level power multiplied by the ratio of manifold specific volume:
300 hp * 0.816 / 1.45 = 169 hp
The supercharged power at the piston is 169 hp * 1.45/.884 = 277 hp
The net supercharged power is then 277 hp – 15 hp = 262 hp
So the net gain from the supercharger is 262-169 = 93 hp
George, am I missing anything here?
The compressor discharge temp is 252 K (101/50.5)^(.4/1.4) = 307 K
or 34.2 C, or 93.5 F, however you like it.
At this point, I doubt if there is a great deal of difference between a turbo, a belt or a gear. The added complexity of the turbo, including increased lubrication and cooling requirements, probably offsets much of the benefit of using that waste energy from the exhaust.
Fly down low and things get a tad more interesting. If the engine was not modified for the supercharger installation, then I can’t see how it will be able to utilize much boost without self destruction. The cylinder compression ratio just isn’t that far from the detonation limit when the factory sells the engine. Burning a higher octane fuel will allow a little more boost, but we’re still not looking at huge gains before detonation makes worm food out of the aircraft. If someone knows better, I would like to hear the explanation. Rick, what MAP are you running around the pylons with your stock engine?
In a pylon race I would be surprised if there was a major difference between the turbine and the belt driven supercharger. The belt supercharger installations I have seen (all cars) don’t have space for an intercooler, which should probably give the edge to the turbo in an engine modified for pressurized induction. At low boost, the pressure drop across the intercooler, combined with the cooling drag might offset the density increase.
In an airplane used for typical GA flight, a turbocharged engine has to make the most sense. A wastegate is simply much more efficient than either a pop off valve or a throttle. Yes, you could use a clutch on the belt or gear drive but you then are left with an all or nothing configuration and belts and gears use some power even when they are unloaded. Then again, as an afterthought / add-on feature the simplicity of a belt driven supercharger, combined with a lower price tag might make it the more attractive option.
I will grant that the above calculations are simplified, but they should be in the ball park. Of course we still haven’t looked at the drag losses associated with cooling the turbo, intercooler or the additional heat load from the engine. And then there is the additional mass of the supercharger installation.
It has been suggested that belt driven superchargers are foolish because a calculation of a certain supercharger on a certain engine in a certain aircraft showed that it would be slower with than without. Perhaps a certain combination of components will be slower at low altitude. This does not make the concept of the mechanically driven supercharger fundamentally flawed. It simply shows the importance of properly sizing the components. Remember that the P38 used mechanically supercharged engines back in the 40’s. The first batch sold to England were delivered without the supercharger, as it was considered to be sensitive technology in the day. The Britts considered these first planes to be totally useless. I think the capability of the mechanical supercharged models speaks for itself.
It has also been suggested that racing to within 5 feet of first place is proof that a belt driven supercharger is the best way to go. First, let me commend Rick on his success on the course. I really respect anyone who refuses to follow the crowd, especially when they are competitive. However, there is a whole lot more to racing than horsepower, and there is a lot in racing that doesn’t apply to everyday operation.
While there may be some magic in Rick’s supercharger, it is just as likely that his airplane is a little bit slicker or that he is a better pilot. Let’s face it, a 1% reduction in drag will buy just as much speed as a 1% increase in power.
That may have been a little more than two bits worth.
Rob