General Principles - Cruise — Page 263, Lesson 316

Let's pick up with altitude and its effect on range for a jet aeroplane. This is where the performance picture gets really interesting, because altitude pulls the variables in opposite directions. I want to start with the formula that governs all of this. For a jet, the specific air range, which we abbreviate as SR, equals true airspeed divided by the product of specific fuel consumption and drag. So SR = TAS ÷ (SFC × DRAG). Let me define each piece. True airspeed, TAS, is the actual speed of the aeroplane through the air. Specific fuel consumption, SFC, is the fuel flow per unit of thrust — essentially how efficiently the engine converts fuel into thrust. And drag is the aerodynamic resistance the aeroplane must overcome. So the specific air range is, in plain terms, the distance you get per unit of fuel. The higher the TAS, the better the range; the higher the SFC or the drag, the worse the range. Now, as we climb to higher operating altitudes, two things happen that help us. First, the air gets colder, and the engine needs increasing rpm to maintain thrust. That combination causes the specific fuel consumption to decrease. A lower SFC helps increase the specific air range. Second, think back to our earlier analysis of altitude effects on speeds. If the aeroplane operates at higher and higher altitudes at a constant indicated or calibrated airspeed of 1.32 VMD — that is, 1.32 times the speed for minimum drag — the true airspeed increases. So the increasing TAS acts together with the reducing SFC to push the specific range up. That's why, initially, specific range increases with altitude. But here's the complication. The third variable, drag, eventually turns against us. As altitude increases, TAS rises and the local speed of sound decreases. That means the Mach number — the ratio of TAS to the local speed of sound — increases. The aeroplane is approaching the speed of sound, and approaching its maximum operating Mach number, which we call MMO. Beyond a certain Mach number, the compressibility factor and the approaching shock wave cause drag to increase sharply. And as you can see from the formula, increased drag is detrimental to specific range. So the full picture is a trade-off. As altitude increases, if the Mach number is allowed to get too high, the drag penalty starts to outweigh the benefits of increasing TAS and reducing SFC. It is exactly at that point that the specific air range starts to reduce. If you look at the left-hand blue line in Figure 5.25, you can see this clearly — specific range initially increases with altitude, but above a certain altitude it decreases. So the key takeaway is that for a jet, there is an optimum altitude for range, and it's not the highest altitude you can reach. It's the altitude where the gains from TAS and SFC are just balanced against the drag penalty from approaching MMO. That's the heart of cruise performance for a jet.