For range, we flip it — Page 251, Lesson 305

We're moving from endurance into range now, and the key shift is in the formula. For endurance, we were dividing fuel flow by something—essentially asking how long we can stay up. For range, we flip it. We want to know how far we can go, so the formula now reads true airspeed divided by fuel flow. That gives us specific range. Let me write that out clearly. Specific range, abbreviated SR, equals true airspeed divided by fuel flow. So SR = TAS ÷ FUEL FLOW. That's the definition of specific air range—it's the ratio of true airspeed to the fuel flow. Think of it as nautical miles per unit of fuel. The higher that number, the more distance you squeeze out of every pound of fuel. Now, you might remember from the endurance section that fuel flow isn't just a single number. For a jet, fuel flow is specific fuel consumption multiplied by drag. For a propeller-driven aeroplane, it's specific fuel consumption multiplied by power required. So we can expand our formula. For a jet, specific range equals TAS divided by the product of specific fuel consumption and drag. For a propeller aeroplane, it's TAS divided by the product of specific fuel consumption and power required. Looking at these formulae, it's obvious what we need to do to maximize specific range. We want true airspeed to be high, and we want fuel flow to be low. That's the fundamental goal. Let's focus on the jet first. We said TAS must be high, and specific fuel consumption and drag must be low. Look at Figure 5.17, which shows a drag curve for a jet aeroplane. If the aeroplane flew at VMD—that's the speed for minimum drag—the drag force would be at its lowest. That seems to solve the drag problem. But here's the catch: the drag curve is fairly flat at the bottom. So you can increase the speed significantly above VMD for only a small drag penalty. So what happens? Drag increases a little, which is bad for range. But airspeed increases significantly, which is good for range. The overall effect is an increase in specific range. The speed at which the speed-over-drag ratio is maximized can be read from the graph at the point where a tangent from the origin touches the curve. You may recall this speed is 1.32 times VMD. So it's 1.32VMD that is the speed for maximum range for a jet aeroplane. Now there's one item left in the formula to resolve. To increase range even more, we must decrease specific fuel consumption. For a jet, the only way to do that is to operate at as high an altitude as possible. Operating high gives a higher true airspeed for any given indicated airspeed, which again improves specific range. Now let's look at the propeller aeroplane. The goal is the same—maximize specific range—so TAS must be high, and specific fuel consumption and power required must be low. Look at Figure 5.18, which shows the power required curve for a propeller aeroplane. If the aeroplane flew at VMP—the speed for minimum power required—the engine would be delivering minimum power required for level flight. That solves one component: making power required as small as possible. So we've set up both cases. For the jet, we fly at 1.32VMD. For the propeller aeroplane, we're starting with VMP. The next step is to see how the speed-over-power ratio behaves for the propeller machine, just as we did for the jet.