# Is there a simple formula for estimating supercharger throttling losses?

I’ve noticed that in both Aerodynamics for Naval Aviators, and most old WWII engine power charts, power vs altitude seems to be composed almost entirely of linear relationships: at a given supercharger speed, (assuming a single stage supercharger with no aftercooler, Water Injection, or other additional power boosting system active), power from sea level increases in a linear fashion until critical altitude, and from there, power decreases at a linear rate

I already know the basics of why power increases, then decreases: the engine must be throttled below critical altitude to prevent overboost, and this results in a loss of efficiency in accordance to the amount of throttling. And above critical altitude, the supercharger simply cannot provide enough of an increase to pressure to achieve the desired manifold pressure

I also understand that roughly, 1,000ft increase in altitude will correspond to a 1”HG decrease in air pressure, so that gives me some clues to work out the relationship above critical altitude. But I don’t understand how to determine how much power a given supercharger speed gives BELOW Critical Altitude, where Max manifold pressure is available, but must be throttled