LSS = TAS — Page 92, Lesson 109

Let's pick this up with the worked problem, because it ties the whole idea together. We have an aircraft at FL360, TAS 467 knots, Mach 0.8, and the temperature deviation from ISA is +9. The question asks: what's the temperature deviation at FL320 if Mach 0.8 still gives a TAS of 467 knots? First, let's set the standard. At FL360, ISA temperature is -57°C. With a deviation of +9, the actual temperature is -48°C. Now here's the key logic: if Mach number and TAS both stay the same, then the local speed of sound must be the same. And since LSS depends only on temperature, the temperature must be the same. So we're flying in an isothermal layer — the temperature stays at -48°C all the way down to FL320. Now at FL320, ISA temperature is -49°C. If the actual temperature is -48°C, the deviation from ISA is +1°C. That's the answer: +1. Let me make sure the relationship is crystal clear. The local speed of sound, LSS, equals TAS divided by Mach number. So LSS = TAS / MN. In the example, 80 divided by 0.12 gives 667 knots. That's the speed of sound at that temperature. Since TAS and Mach stay constant, LSS stays constant, and therefore temperature stays constant. Now let's move to the Mach/Airspeed Indicator. Many commercial aircraft need both IAS and Mach number, so we combine both instruments into one. The basic principles of each still apply — the Machmeter side and the airspeed indicator side work exactly as they do separately. The combined instrument inherits the errors of both. That means instrument error, position error, manoeuvre-induced error, density error, and compressibility error. All five are present. There are two types of construction. First, a self-contained instrument fed directly from pitot and static sources. Second, a combined instrument fed from the Air Data Computer. Here's how you read it. The airspeed pointer moves clockwise over a fixed scale. From Mach 0.5 upward, the Mach number is read off the same pointer, but now it moves over a moving Mach number scale. That scale rotates anticlockwise beneath the pointer as Mach number increases. And there may be a second striped needle to mark VMO — the maximum operating speed. So the takeaway: LSS = TAS / MN, temperature drives LSS, and the combined instrument gives you both IAS and Mach on one dial with all the associated errors.