The Machmeter — Page 92, Lesson 105

Let’s start with the Machmeter and the single most important idea behind it: the relationship between CAS, TAS, and Mach number as you climb or descend through the standard atmosphere. I want you to picture a climb at a constant 330 knots calibrated airspeed, or CAS, from sea level up to 36,000 feet in the standard atmosphere. Two things happen. First, your true airspeed, TAS, increases from 330 knots to 593 knots. Second, your Mach number increases from M 0.5 to M 1.05. That is a dramatic jump — and notice that 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, before transferring to a constant Mach number for the rest of the climb. In the descent at constant CAS, the reverse happens: TAS and Mach number both reduce, with Mach number reducing at a greater rate. Let me make sure the terms are clear. CAS is calibrated airspeed — the indicated airspeed corrected for instrument and installation errors. TAS is true airspeed — the actual speed of the aircraft through the air. Mach number is the ratio of true airspeed to the local speed of sound. That ratio is the heart of the Machmeter. Now, the diagram in Figure 7.2 shows this beautifully. For a constant CAS, drawn as 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 show the relationship between CAS, TAS, and Mach number, and it gives us an idea of the magnitude of these changes. Now let’s flip it around and 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, that same M 0.8 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. So even though Mach number is used at altitude, CAS will be used in the descent. That is the practical rule: climb on CAS first, then Mach; descend on Mach first, then CAS. Here’s a subtle but important observation. You’ve probably noticed by now that the relationship of CAS, TAS, and Mach number as an aeroplane climbs or descends through the standard atmosphere remains the same. Figure 7.2 and Figure 7.3 are actually the same — just tilted to one side or the other. So when we consider the climb or descent through an isothermal layer — a layer where temperature is constant — and through an inversion — where temperature increases with altitude — only the constant TAS figure will be shown. Now let’s dig into the descent at a constant Mach number in standard conditions. During a descent in the ISA, the local speed of sound, or LSS, will be increasing, because temperature increases as you descend. Therefore, if Mach number is being kept constant, the TAS must be increasing. Remember the formula: Mach number equals TAS divided by LSS. So if the denominator, LSS, is increasing and the ratio stays constant, the numerator, TAS, must increase too. During the descent, air density also increases. And if TAS is increasing as well, then CAS must increase at an even greater rate. That comes from the dynamic pressure formula: dynamic pressure equals one-half rho times V squared — half the air density times the velocity squared. Since density is rising and velocity is rising, the dynamic pressure, and hence the CAS, rises faster. This is shown in Figure 7.3. Similarly, in a climb at constant Mach number, both TAS and CAS reduce. So the key takeaway is this: the Machmeter isn’t just a separate instrument — it’s the expression of a fundamental relationship. In a climb at constant CAS, Mach number rises faster than TAS. In a descent at constant Mach, CAS rises faster than TAS. And the reason we switch between CAS and Mach during climb and descent is precisely to stay within the operating limits — MMO on the high side, VMO on the high-speed side. That’s the whole logic of the Machmeter in everyday airline operation.