The Machmeter — Page 83, Lesson 98

Let’s start with the Machmeter. This is the instrument that tells you, at any given moment, how fast you are flying relative to the speed of sound. It’s not a luxury instrument — in high-speed aircraft it is essential, and I want you to understand exactly why before we touch the mechanism. Think about what happens as an aircraft approaches the local speed of sound. The airflow over some parts of the fuselage or wings may be accelerated up to the speed of sound, and a shock wave will form. Those shock waves are not just a noise event — they cause more drag, less lift, Mach tuck, buffeting, and a reduction in control effectiveness, or even loss of control. Let me define Mach tuck precisely, because it’s a specific and dangerous phenomenon: it is a downward-pitching sudden change of trim, and it can be severe. So the danger here is real, and it’s why we need this instrument. To avoid the dangers of high Mach number flight, each aircraft is given a limiting Mach number, based on flight trials. That limit must not be exceeded, and it is known as MMO. So the Machmeter’s whole job is to display the present Mach number so that you, the pilot, can keep your speed below the particular MMO for your aircraft and avoid all those high-speed problems. Now, before we can understand how the instrument works, we need to understand the speed of sound itself. Here’s the key fact: the speed of sound is not constant — it varies with air temperature. There’s a formula for calculating the local speed of sound, abbreviated LSS: LSS = 38.95 √T Let me unpack that. LSS is given in knots. 38.95 is a constant. And T is the absolute temperature, where 0°C equals 273°A, which equals 273 K. So the relationship is direct: the higher the air temperature, the higher the speed of sound, and vice versa. And since temperature normally reduces as altitude increases, the speed of sound normally reduces as altitude increases. Let me give you two concrete numbers so you feel this. In ISA conditions at mean sea level, at +15°C, the speed of sound is 661 knots. But at 30,000 feet ISA, at −45°C, the speed of sound has reduced to 589 knots. Same aircraft, same day, different altitude — the speed of sound drops by over 70 knots. That’s why the Machmeter matters: Mach number is a ratio, and the denominator changes with altitude. So now the principle of operation. The Machmeter uses two capsules and linkages to indicate the aircraft’s True Airspeed, TAS, as a proportion of the local speed of sound, LSS. The definition of Mach number is: Mach Number = TAS / LSS The first capsule is the Airspeed Capsule. It expands and contracts as a result of changes in dynamic pressure. The second capsule is a sealed Altimeter Capsule. It expands and contracts as the static pressure inside the instrument case changes. Now here’s the clever part, and I want you to follow the derivation because it’s the heart of the instrument. We said Mach number is proportional to dynamic pressure over static pressure, but let me write it properly. Mach number is proportional to the square root of dynamic pressure over static pressure — that’s the √(D/S) you see. But as density, ρ, cancels out, we can see that Mach number is proportional to the square root of (P − S) over S, where P is pitot pressure and S is static pressure. So the instrument doesn’t need to measure density at all — it just needs pitot pressure and static pressure, and it can derive Mach number. Let me tie that to the mechanism. The Airspeed Capsule receives pitot pressure, and the Altitude Capsule receives static pressure. The altitude capsule drives the main shaft, and there’s a ratio arm and a ranging arm with a hair spring that link the two capsules together. The whole assembly moves the pointer to show Mach number. And you’ll notice there’s an adjustable limiting Mach number index on the dial — that’s the pilot-set reminder of the MMO for your aircraft, so you can see at a glance how close you are to the limit. So to summarise the chain: temperature changes the speed of sound, the Machmeter compares your true airspeed to that local speed of sound using pitot and static pressure, and it shows you the Mach number so you can stay below MMO and avoid shock waves, Mach tuck, and loss of control. That’s the Machmeter.