The Machmeter — Page 19, Lesson 20

I want to walk you through the Machmeter and how it behaves during climbs and descents through different temperature layers. This is a key instrument for high-speed flight, and understanding its indications is essential for professional piloting. Let's start with the concept of an isothermal layer. This is a layer of air in which the temperature does not change as altitude changes. Because the temperature is constant, the Local Speed of Sound (LSS) will also remain constant. Now, if we fly through an isothermal layer at a constant Mach number, the True Airspeed (TAS) will not change — that's because Mach number equals TAS divided by LSS, and if both the Mach number and the LSS are constant, the TAS must stay the same. However, the Calibrated Airspeed (CAS) will change. This happens due to density error: as you climb, air density decreases, so the CAS reduces; as you descend, density increases, so the CAS increases. So in an isothermal layer at constant Mach, TAS stays steady but CAS drops on the way up and rises on the way down. Now, if instead you climb through an isothermal layer at a constant CAS, both the TAS and the Mach number will increase, and they increase at the same rate. Let's move to an inversion. In an inversion, the temperature of the air increases — it gets warmer — as altitude increases. So during a climb through an inversion, the Local Speed of Sound increases. If you maintain a constant Mach number during that climb, the TAS will increase, because Mach number equals TAS divided by LSS, and if LSS is going up, TAS must go up to keep the ratio the same. Meanwhile, the CAS will reduce as air density reduces. If you descend through an inversion at a constant Mach number, the TAS will reduce and the CAS will increase. If you climb through an inversion at a constant CAS, both the TAS and the Mach number will increase, but here's the key difference: the TAS increases at a greater rate than the Mach number. Let me give you the climb/descent summary that pulls all this together. First: TAS will always increase when an aeroplane climbs at a constant CAS. Second: climbing at a constant TAS, the CAS will always reduce. The reason is that pressure has a greater effect on air density than temperature does. Third: climbing at a constant CAS, the Mach number will always increase. Fourth: climbing at a constant Mach number, the CAS will always reduce. The reason for that last point is that the CAS/TAS density error dominates over the change in LSS due to temperature variation. Now, the excerpt also moves into a completely different topic: The Direct Indicating Compass, specifically acceleration on a northerly heading in the northern hemisphere. Let me teach that. When you accelerate on a northerly heading in the northern hemisphere, the centre of gravity of the compass lags, and the north-south tilt of the magnet assembly changes. However, the magnets are tilting in the vertical plane of the magnetic meridian through the pivot — so no error occurs. Similarly, with deceleration on north/south headings, there is again no error; you only get a reduced north-south tilt due to the inertial forward swing of the magnet assembly. Here's the summary of acceleration errors. Acceleration errors are zero on north/south magnetic headings in both hemispheres. They increase to a maximum on headings of 090° magnetic and 270° magnetic. Acceleration causes an apparent turn towards the nearer pole — that means an apparent turn north in the northern hemisphere, and an apparent turn south in the southern hemisphere. Deceleration causes an apparent turn towards the further pole — an apparent turn south in the northern hemisphere, and an apparent turn north in the southern hemisphere. Whenever the magnet assembly is displaced clockwise, the readings will decrease and the compass will under-read. Whenever the magnet assembly is displaced anticlockwise, the readings will increase and the compass will over-read. The size of a linear acceleration error depends on four factors: the heading, the magnitude of the acceleration, the design of the magnet system, and the magnetic latitude — which affects the relative strengths of the horizontal component H and the vertical component Z. The errors are maximum near the magnetic poles, and they decrease to zero at the magnetic equator.