The Machmeter — Page 83, Lesson 98

I want to walk you through the Machmeter now. This is a brand-new instrument for you, and it's one of the most important ones for high-speed flight. Let's start with why it exists. In high-speed aircraft, the Machmeter is an essential instrument. Here's the problem it solves: 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 bad news. 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 for you precisely: it's a downward-pitching sudden change of trim, and it can be severe. So, to avoid the danger associated with flight at high Mach numbers, a limiting Mach number is specified for each aircraft, based on flight trials. This must not be exceeded. It's known as MMO — that's the maximum operating Mach number. The Machmeter displays the present Mach number so the pilot can keep his speed below the particular MMO for his aircraft and avoid all those high-speed problems. Now, before we get to how the instrument works, we need to understand the speed of sound itself. The speed of sound is not constant — it varies with air temperature. There's a formula for calculating the local speed of sound, which we abbreviate as LSS: LSS = 38.95 √T Let me read that carefully. LSS is given in knots. 38.95 is a constant. And T is the absolute temperature. Now, absolute temperature — you'll see it written as 0°C = 273°A = 273 K. So 273 Kelvin is absolute zero on the Celsius scale. The key relationship here: the higher the air temperature, the higher the speed of sound, and vice versa. 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 can feel this. In ISA conditions at mean sea level, which is +15°C, the speed of sound is 661 knots. But at 30,000 feet ISA, which is -45°C, the speed of sound has reduced to 589 knots. So you can see the drop — colder air, slower sound. Now, the Machmeter 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. And that's exactly what Mach number is: Mach Number = TAS / LSS So Mach number is your true airspeed divided by the local speed of sound. If you're flying at Mach 0.8, you're at 80% of the local speed of sound. Let's look at the two capsules. The first capsule is an Airspeed Capsule. It will expand and contract as a result of changes in the dynamic pressure. Dynamic pressure is the pressure you feel from the aircraft's motion through the air — that's what the pitot system measures. The second capsule is a sealed Altimeter Capsule. It will expand and contract as the static pressure inside the instrument case changes. Static pressure is the ambient pressure of the surrounding air at your altitude. Now here's the clever part — the derivation. The excerpt shows that Mach number is proportional to a ratio involving dynamic pressure and static pressure. Let me write this out. We have: MN is proportional to D / S where D is dynamic pressure and S is static pressure. But then, because density, which we write as the Greek letter rho, ρ, cancels out, we can see that Mach number is proportional to: (P - S) / S Let me unpack that. P is pitot pressure — that's the total pressure from the pitot tube, which is the sum of static pressure and dynamic pressure. So P minus S gives you the dynamic pressure, D. And then you divide by S, the static pressure. So the ratio (P - S)/S is really just dynamic pressure over static pressure. And because density cancels out in that ratio, the Mach number can be derived purely from pitot pressure and static pressure — you don't need a separate temperature measurement. Now let me walk you through the physical instrument using Figure 7.1. The instrument has a main shaft. Connected to it are the two capsules. The airspeed capsule receives pitot pressure — that's the dynamic pressure input. The altitude capsule receives static pressure. These two capsules work through linkages to move the main shaft. There's a ratio arm and a ranging arm — these are the mechanical linkages that combine the motions of the two capsules. There's also a hair spring, which provides the restoring force to keep the mechanism stable and return it to a consistent position. And importantly, there's an adjustable limiting Mach number index. This is the pilot's reference marker — it's set to the MMO for the aircraft, so the pilot can see at a glance whether the Mach number needle is approaching or exceeding the limit. So the whole system works like this: the airspeed capsule responds to dynamic pressure from the pitot system, the altitude capsule responds to static pressure, and through the ratio arm and ranging arm, the main shaft position indicates the Mach number — which, as we derived, is proportional to (P - S)/S. The hair spring keeps it all stable, and the adjustable index marks your MMO limit. That's the complete Machmeter — why it exists, how the speed of sound behaves, and how the two capsules and linkages turn pitot and static pressure into a Mach number reading.