General Principles - Cruise — Page 263, Lesson 316

Let's pick up right where the formula left us. We've got the specific range equation for a jet: SR equals TAS divided by (SFC times DRAG). Now I want to walk you through what happens to each of those three variables as we climb. First, the specific fuel consumption, or SFC. As the aeroplane climbs into colder air, and the engines need increasing rpm to maintain thrust, the SFC actually decreases. That's a benefit — a lower SFC in the denominator means the specific range goes up. Next, true airspeed, TAS. Remember our earlier work on altitude effects: if we hold a constant indicated or calibrated airspeed of 1.32 VMD — that's 1.32 times the speed for minimum drag — the true airspeed increases as we climb. So both the falling SFC and the rising TAS are pushing specific range upward. So far, so good. But now the third variable: drag. Here's where it gets tricky. As altitude increases, TAS rises and the local speed of sound falls. That means the Mach number climbs. The aeroplane is approaching the speed of sound, heading toward its maximum operating Mach number, MMO. Beyond a certain Mach number, the compressibility factor and the approaching shock wave cause drag to increase sharply. And since drag sits in the denominator, that hurts the specific range. So we have a tug-of-war. Climbing gives us more TAS and less SFC, both good. But if the Mach number gets too high, the drag penalty outweighs those benefits. At that point, specific range stops increasing and starts to fall. Look at the left-hand blue line in Figure 5.25 — you can see specific range rising with altitude at first, then peaking and dropping off above a certain altitude. That's the core of it: for a jet, there's an optimum altitude for range, and it's set by the balance between the SFC and TAS benefits against the compressibility drag penalty.