General Principles - Cruise — Page 256, Lesson 307

Let’s pick this up right where the jet aeroplane left off, because now we are switching to the propeller aeroplane, and the whole logic flips. For a propeller aeroplane, the key curve is the power required curve, not the drag curve. And here is the crucial point: for the propeller aeroplane, the speed for maximum range is VMD — the speed for minimum drag. Let me explain why, because it is not obvious. Look at the power required curve. It is fairly flat at the bottom, just like the drag curve was for the jet. That flatness means you can increase your airspeed significantly above VMP — the speed for minimum power — for only a small penalty in power required. So you trade a little extra power, which is bad for range, against a big gain in airspeed, which is good for range. The net effect is an increase in range. Now, where exactly is that best point? It is the point where the speed power ratio is at a maximum. Geometrically, that is the point of contact of the tangent drawn from the origin to the power required curve. And that point, you may recall, is exactly VMD — the speed for minimum drag. So for a propeller aeroplane, VMD is the speed for maximum range. That is the direct contrast with the jet, where the speed for maximum range was 1.32 times VMD. Now, there is one remaining item in the range formula we still need to resolve: specific fuel consumption. To maximize range even further, we want specific fuel consumption to be as low as possible. And here the behaviour depends on the engine type. For a piston aeroplane, specific fuel consumption is more or less best — that is, lowest — at low altitudes. But for a turbo-propeller aeroplane, which uses a jet engine, specific fuel consumption decreases with altitude, up to a point about halfway up the troposphere. So the altitude you choose for cruise depends on which engine you have. Now let us move to the factors that affect range, starting with weight. You will recall that increasing the weight of the aeroplane increases induced drag. That moves the total drag curve, and the power required curve, up and to the right. Look at Figure 5.19, which is for the jet aeroplane. At higher weights, the aeroplane is subject to a higher drag force, and therefore it requires a higher rate of fuel flow. That decreases the specific range — the distance flown per unit of fuel. But notice something important: the speed for maximum range, which is 1.32 times VMD, is now higher. So a heavier aeroplane cruises at a higher speed for maximum range, but it burns more fuel per unit of distance. So to summarise the contrast we have built: for the jet, maximum range is at 1.32 times VMD, and weight pushes that speed higher while reducing specific range. For the propeller aeroplane, maximum range is at VMD itself. And specific fuel consumption — the last piece of the range formula — behaves differently with altitude depending on whether you have a piston engine or a turbo-propeller.