General Principles - Cruise — Page 246, Lesson 291

Let’s start with the Mach number, because it’s the heart of everything we’re about to discuss. Mach number is not a speed in the way we normally think of one. It’s a ratio — the ratio of the aeroplane’s true speed to the local speed of sound. The formula is simple: Mach number equals true airspeed divided by local speed of sound. So, Mach number = TAS ÷ LSS. Let me give you a concrete example. At sea level in ISA conditions — that’s International Standard Atmosphere — the local speed of sound is 661 knots. If your true airspeed is 510 knots, then your Mach number is 0.77. In other words, you’re travelling at about three quarters of the speed of sound. If you fly faster, the Mach number increases. If you accelerate to 661 knots, your speed equals the speed of sound, and you’re at Mach 1. Now, here’s a critical point: the speed of sound is not constant. It varies with temperature. As altitude increases, temperature decreases, and that causes the local speed of sound to fall. For example, at 30,000 feet, the speed of sound is 590 knots. So if you keep your true airspeed constant at 510 knots while climbing, the local speed of sound is dropping, and that means your Mach number will increase — even though your indicated airspeed hasn’t changed. That’s a relationship you must understand cold. Why does this matter so much? Because as your 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. Because of these effects, 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. It’s a hard limit you must respect. Now, let’s talk about the speed ranges. Aeroplanes flying between Mach 0.8 and Mach 1.2 are said to be in transonic flight. That’s the regime where you start encountering those compressibility effects and shock waves. Let me show you what’s happening physically. This figure illustrates pressure waves emanating from an aeroplane flying at the speed of sound. As the aeroplane approaches the speed of sound, those pressure waves pile up ahead of it, forming a shock wave. Now, having discussed all the relevant speeds, it’s important to understand how they relate to one another as altitude changes. That’s best illustrated on a graph. This shows the relationship of the various speeds with altitude. And here’s the companion graph. This one shows what happens if true airspeed is kept constant with altitude. And finally, these graphs can also be used to see the relationship between the speeds. The key takeaway is this: Mach number is a ratio, not a fixed speed. It changes with altitude because the speed of sound changes with temperature. And it’s the Mach number — not your indicated airspeed — that determines when you hit those dangerous compressibility effects. That’s why MMO exists as your ceiling.