The Machmeter — Page 19, Lesson 18

I want to walk you through the Machmeter and, more importantly, the relationship between CAS, TAS, and Mach number as an aircraft climbs or descends through the standard atmosphere. This is a critical concept for operating high-performance aircraft. Let's start with a climb at a constant CAS in the standard ISA atmosphere. If we were to climb at 330 knots CAS from sea level to 36,000 feet, here's what happens: TAS will increase from 330 knots to 593 knots, and Mach number will increase from M0.5 to M1.05. That's a rapid rise in Mach number — in this example, it actually exceeds Mmo, which is the maximum operating Mach number. This rapid rise is exactly why high-performance aircraft are flown on CAS, or sometimes IAS, for the first part of the climb. Then, they transfer to a constant Mach number for the rest of the climb. Similarly, in a descent at constant CAS, both TAS and Mach number reduce, but Mach number reduces at a greater rate. Let me explain what Figure 7.2 shows you diagrammatically. For a constant CAS — that's 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 this relationship between CAS, TAS, and Mach number, and it gives us an idea of the magnitude of these changes. Now let's consider the opposite: a descent at a constant Mach number. Take a descent at M0.8 from 40,000 feet down to sea level in the jet standard atmosphere. At 40,000 feet, M0.8 is 450 knots TAS. At sea level, it has increased to 528 knots TAS. But look at 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 indicated airspeed. So here's the key takeaway: although Mach number is used at altitude, CAS will be used in the descent. You don't want to exceed Vmo. You may have 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. Figures 7.2 and 7.3 are actually the same — just tilted to one side or the other. So when we consider a climb or descent through an isothermal layer or an inversion, only the constant TAS figure will be shown. Let me now explain the physics behind a descent at a constant Mach number in standard conditions. During a descent in the ISA, the LSS — that's the local speed of sound — will be increasing, because temperature increases as we descend. Therefore, if Mach number is being kept constant, the TAS must be increasing. Remember the formula: Mach number equals TAS divided by LSS. During the descent, air density increases. And if TAS is also increasing, the CAS must increase at an even greater rate. That's because dynamic pressure equals one-half rho times V squared — half the air density times the velocity squared. This is shown in Figure 7.3. Similarly, in a climb at constant Mach number, both TAS and CAS reduce. So to summarise what I want you to take away: in a constant CAS climb, Mach number rises faster than TAS. In a constant Mach number descent, CAS rises faster than TAS. And that's why we switch between CAS and Mach number control at different phases of flight — to stay within the aircraft's operating limits.