General Principles - Cruise — Page 246, Lesson 298

We’ve just finished how a jet achieves maximum endurance, so now I want to walk you through the propeller aeroplane version, because the logic is nearly identical — but there’s one crucial difference in the formula, and it changes the speed you fly. For a jet, fuel is burned to produce thrust directly. For a propeller aeroplane — whether it’s a turboprop or a piston engine — the fuel is first converted into power output on a shaft, and then the propeller converts that shaft power into thrust. So the fuel isn’t being used to generate thrust directly; it’s being used to generate power. That means the formula for fuel flow changes. Instead of fuel flow being tied to thrust, for a propeller aeroplane the fuel flow equals the fuel flow per unit of power, multiplied by the total units of power. Let me write that out: FUEL FLOW = FUEL FLOW PER UNIT POWER × TOTAL POWER. Now, you already know the term for fuel used per unit of power — that’s the specific fuel consumption, or SFC. So we can rewrite the formula as: FUEL FLOW = SFC × TOTAL POWER. To minimize fuel flow, you need 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 needs to be small, but you can’t really change it much in flight. There is a general trend worth remembering though: for piston engines, specific fuel consumption is a minimum at lower altitudes, whereas for turbo-propeller engines, SFC is a minimum at middle to high altitudes. So the altitude behaviour differs between the two engine types. Since SFC is essentially fixed, the only way left to minimize fuel flow is to use the minimum amount of power. And that is achieved by flying at the speed for minimum power required — which we call VMP. So here’s the key contrast: for a propeller aeroplane, the speed for maximum endurance is VMP. For a jet, it’s VMD — the speed for minimum drag. Remember that distinction, because it’s a classic exam trap: propeller aeroplanes fly at minimum power speed for endurance, jets fly at minimum drag speed. Now let’s move on to the factors that affect endurance, and the first one is weight. You’ll recall that increasing the weight of the aeroplane increases induced drag, and that moves the total drag curve — and the power required curve — up and to the right. So for a jet aeroplane at higher weights, there’s more drag, which requires more thrust, which means more fuel flow. And in that situation, endurance decreases. The same logic applies to the propeller aeroplane — more weight means more power required, more fuel flow, and shorter endurance. So to summarise what we’ve covered: propeller aeroplanes burn fuel to make power, so fuel flow equals SFC times total power; SFC is roughly fixed, so you minimise fuel flow by flying at VMP, the minimum power speed; and increasing weight raises the drag and power curves, increasing fuel flow and decreasing endurance.