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Considering the actual thrust or power delivered by the prop to the airframe, what are examples of power-available and thrust-available curves for piston and turboprop engines, with constant-speed propellers in each case? The x axis should be airspeed.

Is it safe to assume that less power is available at low airspeed than at some higher airspeed both in the case of the piston engine and the turboprop engine? Because the prop is never optimized for maximum efficiency at zero airspeed?

Assume the throttle or power level and rpm controls are being manipulated as needed to to give the maximum thrust and power that is safely allowable, as the airspeed varies.

This is not intended to be a question about cooling. If the curves reflect power reductions that are required to prevent the engine from overheating at low airspeeds, please make a specific note of that. It's fine if the curves include a part of the envelope where sustained operations would not be possible, due to gradually rising engine temperatures. The question is just intended to get at the maximum and thrust and power that may be safely delivered at various airspeeds, even if only for a few minutes.

For the piston engine, start by assuming there is no turbocharging or supercharging-- feel free to include extra curves showing the effects of turbocharging or supercharging.

Feel free to also include examples of the power-available and thrust-available curves for piston engines with fixed-pitched props, and pure jets, for comparison.

Some related ASE questions --

Why isn't Vy lower than the speeds for best L/D ratio and best glide ratio in an airplane with a piston engine and a variable-speed prop?

On a constant speed propeller, how is blade pitch related to airspeed and efficiency? -- the lower diagram is of special interest, but it's not clear whether this is intended to be for a constant-speed prop or a fixed-pitch prop.

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