LSS = TAS — Page 92, Lesson 109

Let’s pick this up right where the math left off. We’ve just worked through the idea that LSS equals TAS divided by Mach number, and we saw that with a Mach of 0.12 and an LSS of 80 knots, the TAS comes out to 667 knots. Now I want to walk you through Problem 5, because it ties together temperature, Mach number, and true airspeed in a way that really matters for how you read your instruments. Here’s the setup. An aircraft is flying at FL360, that’s flight level 360, which is 36,000 feet pressure altitude. Its TAS is 467 knots, and its Mach number is 0.8. The temperature deviation from ISA, the International Standard Atmosphere, is plus 9 degrees. The question asks: what is the temperature deviation at FL320, that’s 32,000 feet, if Mach 0.8 still gives a TAS of 467 knots? Let’s work the solution step by step. At FL360, in the standard atmosphere, the temperature would be minus 57 degrees Celsius. If we have ISA plus 9, that means the actual temperature is minus 48 degrees Celsius. So far, so good. Now here’s the key insight. If the Mach number stays at 0.8, and the TAS stays at 467 knots, then the local speed of sound, the LSS, must also stay the same. Why? Because LSS equals TAS divided by Mach number. If both TAS and Mach are unchanged, their ratio is unchanged. And since the local speed of sound depends only on temperature, a constant LSS means a constant temperature. So we must be flying in what we call an isothermal layer — a layer of the atmosphere where the temperature doesn’t change with altitude. That means at FL320, the temperature is also minus 48 degrees Celsius. Now, what’s the standard temperature at FL320? In the standard atmosphere, it would be minus 49 degrees Celsius. So if the actual temperature is minus 48, the deviation from standard is plus 1 degree. That’s your answer: at FL320, the temperature deviation from ISA is plus 1 degree. Let me make sure that logic is crystal clear, because it’s a classic trap. The question gives you a temperature deviation at one altitude, but the real clue is that Mach and TAS are both constant. That forces the temperature to be constant, regardless of altitude. So you don’t just carry the plus 9 down; you recompute the deviation against the new standard temperature at the new altitude. Now, let’s move on to the instrument that actually displays these values. We’re looking at the combined Mach and Airspeed Indicator. Since many commercial aircraft need to show both indicated airspeed and Mach number, it makes sense to combine both into a single instrument. The basic principles of both the Machmeter and the airspeed indicator still apply — we’re just putting them together in one case. But combining them means we also combine their errors. The combined instrument will have the errors of both the Machmeter and the airspeed indicator. And those errors are specifically: instrument error, position error, manoeuvre induced error, density error, and compressibility error. Let me name each one so you know what we’re dealing with. Instrument error comes from the mechanical imperfections inside the instrument itself. Position error comes from the way the static and pitot sources are mounted on the aircraft, disturbing the airflow. Manoeuvre induced error happens when the aircraft’s attitude or acceleration disturbs those pressure sources. Density error is the difference between the actual air density and what the instrument assumes. And compressibility error arises because at high speed, the air compresses ahead of the aircraft, affecting the pressure readings. All five of those apply to the combined instrument. Now, construction. There are two types of Mach and Airspeed Indicator. The first is a self-contained instrument, fed directly from the pitot and static sources. The second is a combined instrument fed from the Air Data Computer. So one is standalone, taking raw pressures; the other gets its data from the computer that processes all the air data. Let me walk you through how you actually read this instrument, because the display is a bit unusual. The airspeed pointer moves clockwise over a fixed scale — that’s your conventional airspeed readout. But from Mach 0.5 upward, the Mach number is read off the same pointer, as it moves over a moving Mach number scale. That scale rotates anticlockwise beneath the pointer as the Mach number increases. So the pointer does double duty: below Mach 0.5, it’s purely airspeed; above that, the same pointer also indicates Mach against a scale that’s sliding the other way. And there’s one more feature. A second striped needle may be present to mark VMO, which is the maximum operating speed. That striped needle is a fixed reference that shows you the limit you must not exceed. Let me tie this back to the earlier problem, because it all connects. The reason we care about Mach number and TAS and temperature is that the Mach number tells you how close you are to the speed of sound, and the speed of sound depends on temperature. In a cold layer, the speed of sound is lower, so a given TAS gives you a higher Mach number. That’s why the temperature deviation matters — it changes your Mach for a given airspeed, and it changes what your instruments show. So to summarise what we’ve covered: we solved the isothermal layer problem, where constant Mach and TAS force constant temperature, giving a plus 1 degree deviation at FL320. Then we looked at the combined Mach and Airspeed Indicator, its five errors, its two construction types, and how the pointer reads both airspeed and Mach with that moving scale, plus the optional striped VMO needle. That’s the full picture for this section.