The Machmeter — Page 92, Lesson 105

Let’s start with the Machmeter and, more importantly, the behaviour it measures. I want you to picture a climb at a constant calibrated airspeed, or CAS, of 330 knots, from sea level all the way up to 36,000 feet, in the standard ISA atmosphere. Here’s what happens. Your true airspeed, TAS, will increase from 330 knots to 593 knots. And your Mach number will increase from M 0.5 to M 1.05. That’s the key point — at a constant CAS, both TAS and Mach number rise with altitude, but Mach number rises at a greater rate. Why does that matter? Because M 1.05 is far beyond MMO — the maximum operating Mach number. That rapid rise of Mach number is exactly why high-performance aircraft are flown on CAS, or IAS, for the first part of the climb, and then transferred to a constant Mach number for the rest of the climb. You don’t want to exceed MMO, so you switch your reference. Now, let’s look at the descent at constant CAS. The same logic applies in reverse. TAS and Mach number both reduce, but Mach number reduces at a greater rate. So the relationship is symmetrical — climb at constant CAS, Mach rises faster; descend at constant CAS, Mach falls faster. Let me show you this on Figure 7.2. For a constant CAS, shown by the blue line, as altitude increases, TAS — the green line — increases, and Mach number — the red line — increases at a greater rate. The navigation computer can also display the relationship between CAS, TAS, and Mach number, and it gives you an idea of the magnitude of these changes. Now, let’s consider a descent at a constant Mach number of M 0.8, from 40,000 feet down to sea level, in the jet standard atmosphere, using the navigation computer. At 40,000 feet, M 0.8 corresponds to 450 knots TAS. At sea level, it has increased to 528 knots TAS. But look at the CAS — it has increased much more markedly, from 242 knots at 40,000 feet to 528 knots at mean sea level. That would exceed VMO — the maximum operating speed in terms of CAS. So, even though Mach number is used at altitude, CAS will be used in the descent. That’s the operational rule: Mach at altitude, CAS in the descent. Now, I want you to notice something important. The relationship between CAS, TAS, and Mach number as an aeroplane climbs or descends through the standard atmosphere remains the same. In fact, Figure 7.2 and Figure 7.3 are the same — just tilted to one side or the other. So when we consider a climb or descent through an isothermal layer, or through an inversion, only the constant TAS figure will be shown. Let me explain the descent at a constant Mach number in standard conditions more carefully. During a descent in the ISA, the local speed of sound, LSS, is increasing, because temperature increases as you descend. So, if Mach number is kept constant, the TAS must be increasing. Remember the relationship: Mach number equals TAS divided by LSS. If the denominator increases and Mach stays constant, the numerator — TAS — must increase too. Now, during the descent, air density increases. And if TAS is also increasing, then CAS must increase at an even greater rate. Why? Because dynamic pressure equals one-half rho times V squared — ½ ρ V². As density and velocity both rise, the dynamic pressure, and hence the CAS, rises faster. That’s what Figure 7.3 shows. Similarly, in a climb at constant Mach number, both TAS and CAS reduce. So the whole picture is consistent: constant CAS means Mach changes faster; constant Mach means CAS changes faster. Let me tie this together. The Machmeter is the instrument that displays Mach number, but what you really need to understand is the relationship between CAS, TAS, and Mach number through the atmosphere. In a climb at constant CAS, Mach rises faster than TAS. In a descent at constant Mach, CAS rises faster than TAS. And the governing equations are Mach = TAS/LSS, and dynamic pressure = ½ ρ V². That’s the core of it.