Calc max available HP% by altitude

[AA5Bman]

I feel like I know - or should know - the answer to this question, but how would you go about calculating the maximum available horsepower for a normally aspirated engine at a given (density) altitude?

I’m curious about calculating the crossover point or altitude where a smaller turbocharged engine is more powerful than a larger NA engine, and I can’t quite remember how to do so!

 

[PeterNSteinmetz]

The max power available should be proportional to air pressure since the max power will be achieved at the stoichiometric ratio for fuel/oxygen. This given that the fraction of oxygen isn’t changing much with height in the troposphere and assuming proper leaning.

So about 1 inch of Hg pressure per 1000’ is just about 1/30 ~ 3% near sea level as given in a prior post. If you want to be a bit more accurate, use a better formula for pressure as a function of altitude, but I believe the linear approximation is usually used at altitudes where normally aspirated engines are usually flown.

There is a graph and are more accurate formulas in the Wikipedia article at https://en.m.wikipedia.org/wiki/Barometric_formula

 

[PeterNSteinmetz]

Just for fun here are two plots. The first is the pressure as a function of altitude for both the more accurate formula and the linear approximation. The second is the percent error in the linear approximation as a function of altitude. Reaches 5% at about 12,000 feet.

 

[PeterNSteinmetz]

These are just graphs of the predicted pressure, using both the 3% rule and the more accurate rule, as a function of height above MSL in the standard atmosphere. So if the temperature is standard, then I think the performance should be proportional to the pressure if the engine is leaned properly. If you go to the height corresponding a given density altitude, I think that should give engine performance for that DA fairly well.