Let’s pick this up right where the endurance work left off — Page 251, Lesson 305

Let’s pick this up right where the endurance work left off. We’ve already established that endurance is about time in the air, and now we’re flipping that idea to talk about range — how far the aeroplane can travel. And the key shift is that instead of thinking about fuel per hour, we now think about fuel per mile. That’s why the formula changes. So here’s the core definition we’re working with: Specific Range, abbreviated SR, is defined as the ratio of true airspeed to fuel flow. The formula reads: SR = TAS ÷ FUEL FLOW Let me unpack each symbol. TAS is true airspeed — the actual speed of the aeroplane through the air. Fuel flow is, as the name says, the rate at which fuel is being consumed, typically in mass per hour. So specific range is, in plain terms, the distance you get per unit of fuel — the miles per gallon of the aviation world, if you like, but expressed properly as airspeed divided by fuel flow. Now, you’ll recall from the endurance section that fuel flow isn’t just a standalone number. For a jet, fuel flow equals specific fuel consumption multiplied by drag. For a propeller-driven aeroplane, fuel flow equals specific fuel consumption multiplied by power required. So we can expand the specific range formula into two forms. For a jet: JET SPECIFIC RANGE (SR) = TAS ÷ (SFC × DRAG) For a propeller aeroplane: PROPELLER SPECIFIC RANGE (SR) = TAS ÷ (SFC × POWER REQUIRED) Here SFC is specific fuel consumption — the fuel burned per unit of thrust or power per hour. So looking at these formulae, it becomes 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 trade-off we’re chasing. Now let’s focus on the jet aeroplane range in detail. We’ve said we want TAS high, and SFC and drag low. Look at Figure 5.17 — that’s a drag curve for a jet aeroplane. If the aeroplane flew at VMD — that’s the speed for minimum drag — then the drag force would be at its lowest. That seems to solve the drag part of the problem. But here’s the subtlety. The drag curve is fairly flat at the bottom. That means you can increase the speed significantly from VMD for only a small drag penalty. So yes, drag increases a little — which is bad for range — but the airspeed increases significantly — which is good for range. The net effect is that specific range actually increases. The benefit of the higher speed outweighs the cost of the slightly higher drag. So what’s the actual speed for maximum range for a jet? It’s the speed at which the speed-over-drag ratio is maximized. You can read that off the graph at the point where a tangent from the origin touches the curve. And you may recall from earlier work that this speed is 1.32 VMD. So it’s 1.32 VMD that gives maximum range for a jet aeroplane — not VMD itself, even though VMD gives minimum drag. Now there’s one remaining item in the formula to resolve: specific fuel consumption. To increase range even more, we need to decrease SFC. And for a jet, the only way to do that is to operate at as high an altitude as possible. Why does that help? Because operating high gives a higher true airspeed for any given indicated airspeed — and that higher TAS improves the specific range. So altitude is the lever we pull to reduce SFC and boost range. Now let’s switch to the propeller aeroplane range. The logic mirrors the jet, but the curve we look at is different. For a propeller aeroplane, we want TAS high, and SFC and power required low. Look at Figure 5.18 — that’s the power required curve for a propeller aeroplane. If the aeroplane flew at VMP — the speed for minimum power — then the engine would be delivering minimum power required for level flight. That solves the power-required component, making it as small as possible. So the structure is parallel: for the jet we minimised drag, for the propeller aeroplane we minimise power required. And just as with the jet, the speed for maximum range for the propeller aeroplane won’t be VMP itself — it’ll be a higher speed where the trade-off between speed and power works out best. That’s where we’re headed next.