General Principles - Cruise — Page 246, Lesson 298

Let’s pick this up right where the jet discussion left off, because the propeller aeroplane endurance story is almost the same — with one crucial twist in the formula. For a jet, the engine produces thrust directly from the fuel. For a propeller aeroplane — and I mean both turboprops and piston engines — the process is two-step. The engine first converts the chemical energy in the fuel into power output on a shaft. Then the propeller takes that shaft power and converts it into thrust. That distinction is everything. Because the fuel is being used to generate power, not thrust directly, the fuel flow formula changes. It becomes: fuel flow equals fuel flow per unit of power, multiplied by the total units of power. Let me write that out clearly: FUEL FLOW = FUEL FLOW PER UNIT POWER × TOTAL POWER. Now, that "fuel flow per unit power" — you already know this term from the jet work — it’s called specific fuel consumption, SFC. So the propeller formula reads: FUEL FLOW = SFC × TOTAL POWER. To minimise fuel flow, you want both terms small: the SFC and the total power. But here’s the practical reality — for the majority of propeller aeroplanes, the SFC value is more or less fixed. It doesn’t move much. There is a general rule though: for piston engines, SFC is a minimum at lower altitudes. For turbo-propeller engines, SFC is a minimum at middle to high altitudes. So altitude behaviour differs between the two engine types, but within each, SFC is fairly constant. That leaves you with only one lever to pull to minimise fuel flow: use the minimum amount of power. And the speed at which the power required is at its minimum is called VMP — the speed for minimum power required. So here is the key contrast I want you to lock in: for a propeller aeroplane, the speed for maximum endurance is VMP. For a jet, it is VMD — the speed for minimum drag. Two different speeds, two different aircraft types, same goal of maximum endurance. Now let’s move to the factors that affect endurance, starting with weight. You’ll recall from earlier work that increasing the weight of the aeroplane increases induced drag. That increase in induced drag moves the total drag curve — and the power required curve — up and to the right on the graph. Think about what that means for a jet: at higher weights, the aeroplane has more drag, which requires more thrust, which requires more fuel flow. And more fuel flow for the same fuel on board means the endurance decreases. So heavier aeroplane, shorter endurance — that’s the direct cause-and-effect chain. That figure shows the pressure waves building up as the aeroplane approaches the speed of sound — we’ll come back to that when we discuss compressibility effects on cruise. For now, hold onto the endurance picture: propeller aeroplanes maximise endurance at VMP, jets at VMD, and weight pushes the drag and power curves up and right, which costs you endurance.