How much horsepower was required to run the supercharger impeller in the R-2800 engine at cruise conditions, as used in the DC-6?
For compounding see below. The R-2800 was not compounded. From information available in print, the power absorbed by the supercharger turbine was about 400 horsepower. This is comparable to the power required by the compounding supercharger. A comment below gives the source in print for the noted supercharger power requirement of 400 hp. This was a very interesting question!
The caption explains these diagrams. On the right, (b) shows the equivalent work produced by the supercharger and compounding turbine. The excess hatched area is equivalent to power produced at the propeller. Since compounding will realize equivalent power at the propeller with 25 pct less fuel, the portion of the power at the propeller produced by the compounding is equivalent to the total shaft power from the turbine less that portion of the shaft power consumed by the compressor. If we make the rough assumption that the area of the turbine curve (hatched area in b) is about twice that of the compressor curve, then the power consumed by the compressor would be equivalent to the half the power produced by the turbine. The other half of the power from the turbine is given to the propeller. In other words, if the engine is operated at 65 pct power, approximately one-fourth of that power is produced at the propeller by the turbine, and equivalent power is consumed by the compressor in boosting the engine.
If we do the math we will find the turbine produces about 910 hp, of which half is given to the propeller and half is given to the compressor. These do not seem to be unreasonable approximations for the engine operating at 65 pct of its rated 2800 horsepower.
Source of the illustration -
Dommasch, et. al, Airplane Aerodynamics, 3rd ed. 1961, or 4th ed. 1967, Pitman Publishing, New York.