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

We’re in the middle of the compressibility correction on the navigation computer. We had a CAS of 280 knots, and we’d already worked out an initial TAS of 500 knots. But that 500 is too high, because at that speed the air is compressing around the aircraft, which makes the airspeed indicator read slightly high. So we need to correct for compressibility. Here’s how we do it. Under the COMP CORR window on the computer, you’ll see a small equation printed. It reads: TAS divided by 100, minus 3. So we take our initial TAS, which is 500, divide it by 100, that gives us 5, and then subtract 3. That leaves us with 2. So the correction is 2 divisions. Now, in that COMP CORR window, we move the arrow 2 divisions to the left. The window has a small arrow, and we shift it left by those 2 divisions. What this does is move the inner scale to the left, which alters the relationship between CAS on the inner scale and TAS on the outer scale. That’s the correction for compressibility. Once we’ve moved that arrow, we read off the new value of TAS on the outer scale, corresponding to our original 280 knots CAS on the inner scale. And that gives us a revised TAS of 480 knots. So the compressibility correction has taken us from 500 down to 480. Now, let’s move on to a different and easier calculation: finding TAS from Mach Number. This is easier than from CAS because there’s only one variable involved — temperature — and there’s no compressibility correction needed. There are two methods: a formula, or the navigation computer method. The formula is this: TAS equals Mach Number times 38.95 times the square root of the temperature in degrees Kelvin. So TAS = Mach No × 38.95 × √T°K. That 38.95 is a constant. And for the temperature, we need it in Kelvin. Absolute zero is -273.16°C, though -273°C is a good enough approximation for our purposes. Let’s do an example. Say the COAT, which is 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. Then we plug it into the formula: TAS = 0.82 × 38.95 × √226. And that works out to 480 knots. Now let’s do the same calculation using the navigation computer. First, we move the AIRSPEED window round until the Mach No. index appears. That index is a small marker on the inner scale. Then we set the COAT of -47°C against the index arrow. That sets up a relationship between Mach Number on the inner scale and TAS on the outer scale. Finally, we read off the TAS on the outer scale against the Mach Number of 0.82 on the inner scale. And that gives us 482 knots. Notice it’s slightly different from the formula’s 480 — that’s just the rounding in the computer’s scale, but it’s close enough for navigation purposes. So to recap: for compressibility correction, we use that COMP CORR window with the TAS/100 minus 3 rule, moving the arrow left by that many divisions. And for TAS from Mach Number, we either use the formula with the Kelvin temperature, or we set the COAT against the index arrow on the computer and read the TAS directly.