The Navigation Computer - TAS and Altitude Conversions — Page 118, Lesson 110

I want to walk you through how we handle compressibility correction on the navigation computer, and then how we calculate True Airspeed from Mach Number. Let's start with the compressibility correction. We had a situation where our initial TAS came out to more than 300 knots — in the example, 500 knots. Above about 300 knots TAS, compressibility effects start to distort the relationship between Calibrated Airspeed and True Airspeed, so we need a correction. Under the COMP CORR window — that's the "compressibility correction" window on your navigation computer — you'll see an equation printed. It reads: - 3 DIV. Here's how we apply it. First, take your initial TAS — 500 knots in this case — and divide it by 100. That gives you 5. Then subtract 3 from that result. So 5 minus 3 equals 2.0. That number — 2.0 — tells you how many divisions to move the arrow inside the COMP CORR window. Now, in the COMP CORR window, move the arrow 2 divisions to the left. What does that do? It shifts the inner scale to the left relative to the outer scale, which alters the relationship between CAS and TAS. That shift is the correction for compressibility. Once you've moved the arrow, read off the new value of TAS on the outer scale that lines up with 280 knots CAS on the inner scale. In this example, that gives a revised TAS of 480 knots. So the compressibility correction reduced the TAS from 500 to 480 knots. Now let's move to a different method — calculating TAS from Mach Number. This is actually easier than from CAS, because there's only one variable involved: temperature. And there's no compressibility correction needed when you start from Mach Number. There are two methods: a formula, and the navigation computer method. Let me give you the formula first: TAS = Mach Number × 38.95 × √T°K Here, T°K is the temperature in Kelvin. Remember, 0 Kelvin is -273.16°C, though -273°C is a good enough approximation for our purposes. Let's work through an example. Suppose the COAT — that's the Corrected Outside Air Temperature — is -47°C, and the Mach Number is 0.82. What's the TAS? First, convert -47°C to Kelvin. That's 273 minus 47, which gives us 226 Kelvin. Now plug into the formula: TAS = 0.82 × 38.95 × √226 The square root of 226 is approximately 15.03. Multiply that out: 0.82 × 38.95 × 15.03 gives us 480 knots. Now let's do the same calculation using the navigation computer. First, rotate the AIRSPEED window — that's the window on the computer's inner disc — until the Mach Number index appears. That's a special mark on the scale. Next, set the COAT of -47°C against the index arrow — that's the fixed arrow on the outer scale. This action sets up a direct relationship between Mach Number on the inner scale and TAS on the outer scale. Now read off the TAS on the outer scale against the Mach Number of 0.82 on the inner scale. You'll get a TAS of 482 knots — very close to the 480 we got from the formula. The small difference is just rounding. So to summarise: compressibility correction uses the COMP CORR window with a simple division-and-subtract procedure to shift the inner scale left. And for Mach Number to TAS, you either use the formula with temperature in Kelvin, or set COAT against the index arrow on the computer and read TAS directly against Mach Number.