General Principles - Cruise — Page 246, Lesson 291

Let’s start with the Mach number, because it’s the heart of high-speed cruise. Mach number is not a speed in the usual sense — it’s a ratio. Specifically, it’s the ratio of the true speed of the aeroplane to the local speed of sound. Aerodynamicists named it after Ernst Mach, a late 19th-century physicist who studied gas dynamics. So when I say an aeroplane is flying at Mach 0.77, I’m saying it’s travelling at 77% of the speed of sound in the air around it. The formula is simple: Mach number equals true airspeed divided by local speed of sound. We abbreviate true airspeed as TAS, and local speed of sound as LSS. So Mach number = TAS ÷ LSS. Let me give you a concrete example. At sea level in ISA conditions — that’s the International Standard Atmosphere — the local speed of sound is 661 knots. If the aeroplane’s true airspeed is 510 knots, then 510 divided by 661 gives you a Mach number of 0.77. In other words, the aeroplane is travelling at about three quarters of the speed of sound. If it flies faster, the Mach number increases. If it accelerates to 661 knots, its speed equals the speed of sound, and it’s at Mach 1. Now, here’s a critical point: the speed of sound is not constant. It varies with temperature. As altitude increases, the temperature drops, and that causes the local speed of sound to fall. For example, at 30,000 feet, the speed of sound is 590 knots — noticeably lower than the 661 knots at sea level. So if you keep your true airspeed constant at 510 knots and climb, the local speed of sound falls, and your Mach number increases — even though your indicated airspeed hasn’t changed. That’s a relationship you must understand: Mach number rises with altitude for a constant TAS, purely because the speed of sound drops. Why does this matter so much? Because as the aeroplane’s speed approaches Mach 1, compressibility and the approaching shock wave can have very detrimental effects on performance — increasing drag, decreasing lift, and causing aeroplane buffet. That’s why pilots need to know when they’re approaching the speed of sound. Most commercial aeroplanes in service today have a limit on the maximum Mach number they’re allowed to fly at. That maximum operating Mach number is called MMO. Now, let’s tie all the speeds together. We’ve discussed the relevant speeds of an aeroplane, and it’s important to understand how they relate to one another as altitude changes. The best way to see this is on a graph, and that’s exactly what Figure 5.10 shows — the relationship of the various speeds with altitude. Let me walk you through what that graph is telling you. If calibrated airspeed, or simply indicated airspeed, is kept constant with altitude, the true airspeed increases as you climb — because the air gets thinner. But the Mach number also increases, because the speed of sound is falling. So on that graph, you’ll see the lines for CAS, TAS, and Mach number diverging as altitude increases. The key takeaway is that a constant indicated airspeed does not mean a constant Mach number — and a constant Mach number does not mean a constant true airspeed. Each speed behaves differently with altitude, and you must know which one you’re controlling. There’s also a second graph, Figure 5.11, which shows what happens if true airspeed is kept constant with altitude. In that case, as you climb and the speed of sound falls, the Mach number increases — exactly the relationship we discussed with the 510-knot example. And Figure 5.12 shows how these graphs can be used to see the relationship of the various speeds with altitude in a combined view. So the core idea for cruise is this: you have three speeds — indicated or calibrated airspeed, true airspeed, and Mach number — and they don’t move together as you change altitude. The speed of sound falls with temperature, so Mach number rises with altitude for a constant TAS. And because approaching Mach 1 brings compressibility, shock waves, drag, and buffet, you have a hard limit called MMO that you must never exceed. That’s the foundation of high-speed cruise performance.