First, Mach number — Page 83, Lesson 96

This is the start of a brand-new chapter — the Machmeter. So let me set the scene properly, because this instrument is really about one idea: flying fast enough that the speed of sound itself becomes part of your instrument readings. The chapter opens with a contents list, and I want to walk you through what we're going to cover, because it tells you exactly how the subject hangs together. We start with High Speed Flight, then the Speed of Sound, then the Machmeter's Principle of Operation, its Construction, its Errors, and Blockages. Then there's a section on Abbreviations, a Machmeter Summary, and then a whole series of practical scenarios — Climb at a Constant CAS in Standard ISA Atmosphere, Descent at a Constant Mach Number in Standard Conditions, Climb and Descent through an Isothermal Layer, Climb and Descent through an Inversion, and a Climb/Descent Summary. After that come Example Problems Associated with the Machmeter, then the Mach/Airspeed Indicator and its Construction, and finally the Questions and Answers at the end of the chapter. Now, before we dive into the physics, let me define the key terms you're going to meet, because they're the vocabulary of this whole chapter. First, Mach number. That's the ratio of the true airspeed of the aircraft to the local speed of sound. It's a pure number — no units — and it tells you how fast you're going relative to the speed of sound in the air you're actually flying through. Mach 1 means you're travelling at exactly the local speed of sound; Mach 0.8 means you're at 80 percent of it. Second, the speed of sound itself. This is the speed at which pressure disturbances propagate through the air. And the critical thing to remember — the thing that makes the Machmeter necessary — is that the speed of sound is not constant. It depends on the temperature of the air. In warmer air, sound travels faster; in colder air, it travels slower. So a given true airspeed might be well below Mach 1 at one altitude and dangerously close to it at another, purely because the temperature changed. Third, CAS — Calibrated Airspeed. That's the airspeed shown on your airspeed indicator after correction for instrument and position errors. It's the reading you get from the dynamic pressure of the pitot-static system. The chapter is going to ask you to think about what happens when you climb at a constant CAS — and the answer hinges on how temperature changes with altitude. Fourth, ISA — the International Standard Atmosphere. That's the model atmosphere we use as a reference: sea-level temperature 15 degrees Celsius, and a lapse rate of about 1.98 degrees Celsius per 1,000 feet up to the tropopause. When the chapter says "standard conditions," it means ISA. Now, the Machmeter itself. Its principle of operation is elegant: it's essentially an instrument that computes Mach number from two pressures — pitot pressure and static pressure. The Mach number is a function of the ratio of pitot pressure to static pressure. The instrument takes those two inputs and mechanically solves that relationship, so the pointer reads Mach number directly. That's why it's a self-contained instrument — it doesn't need a separate temperature input, because the pressure ratio already encodes the temperature effect. The construction follows from that. The Machmeter is built around an aneroid capsule — that's a sealed, flexible metal bellows — which is connected to the pitot pressure. That capsule sits inside a sealed case that's connected to static pressure. So the capsule expands and contracts with the difference between pitot and static pressure, and that movement is geared to the pointer. The scale is non-linear, because the relationship between pressure ratio and Mach number is not a straight line — the pointer sweeps across a scale that's compressed at low Mach numbers and expanded at high ones. Now, errors. The Machmeter is subject to the same pressure errors as any pitot-static instrument — position error, where the static source isn't sampling true static pressure, and instrument error from the mechanical linkage. And there's a specific failure mode: blockages. If the pitot line blocks, the capsule can't sense the dynamic pressure properly, and the reading goes wrong. If the static line blocks, the case pressure is trapped, and again the reading is corrupted. The chapter covers these blockages explicitly, because recognising a blocked line from the instrument's behaviour is a real pilot skill. Then we get to the operational scenarios, and this is where the Machmeter really earns its keep. Let me walk you through each one. Climb at a constant CAS in standard ISA atmosphere. As you climb, temperature decreases with altitude. Since the speed of sound decreases with temperature, the local speed of sound is falling. But you're holding CAS constant — and CAS is related to true airspeed, which actually increases with altitude for a given CAS, because the air is less dense. So both effects push the same way: your true airspeed is rising while the speed of sound is falling. The result is that Mach number increases during the climb. That's why, in a jet, you often climb at a constant Mach number once you're high enough — because holding CAS would push you toward Mach 1. Descent at a constant Mach number in standard conditions. Coming down, temperature increases, so the speed of sound increases. To hold Mach constant, your true airspeed must increase as you descend — you have to speed up in absolute terms to keep the same fraction of a rising speed of sound. And since CAS increases with true airspeed at lower altitude, your CAS reading rises during the descent. Now, an isothermal layer. That's a layer of the atmosphere where temperature stays constant with altitude — it doesn't lapse. In such a layer, the speed of sound is constant. So if you climb through an isothermal layer at constant Mach, your true airspeed stays constant too, because Mach times a constant speed of sound is a constant. And if you climb at constant CAS through an isothermal layer, the Mach number stays constant as well, because the pressure ratio that defines Mach is unchanged when temperature doesn't change. The key insight: in an isothermal layer, Mach and CAS behave as if altitude doesn't matter, because the temperature — the thing that drives the speed of sound — isn't changing. Then an inversion. That's where temperature increases with altitude, the opposite of normal. So as you climb through an inversion, the speed of sound increases. If you're climbing at constant Mach, your true airspeed must increase to keep pace with the rising speed of sound. And if you're climbing at constant CAS, the Mach number actually decreases, because the rising temperature raises the speed of sound faster than the true airspeed is rising. So an inversion flips the normal behaviour — that's the trap to watch for. The chapter then gives you a Climb/Descent Summary, which pulls all four scenarios together into one table — the direction of Mach change for each combination of climb or descent, constant CAS or constant Mach, in standard, isothermal, and inversion conditions. That summary is your revision tool. Then come Example Problems — worked numerical questions that apply all of this. And finally, the Mach/Airspeed Indicator. That's a combined instrument that shows both airspeed and Mach number on one dial — typically an airspeed pointer and a separate Mach pointer, or a drum and pointer arrangement. Its construction is essentially the Machmeter mechanism plus the airspeed mechanism sharing the same case and the same pitot-static inputs. So the whole chapter is really one story: the speed of sound varies with temperature, the Machmeter measures your speed relative to that varying speed of sound, and the operational scenarios teach you how to predict what the instrument will do as you climb and descend through different temperature structures. Let me pause there. That's the map of the chapter. When you're ready, we'll go into the detail of the speed of sound and the Machmeter's principle of operation.