The Navigation Computer - TAS and Altitude Conversions — Page 118, Lesson 112

We're moving into a new part of the navigation computer work now: converting indicated altitude into true altitude. This is a critical safety calculation, so let's take it step by step. First, the core problem. Your altimeter is calibrated against the ISA atmosphere—that's the International Standard Atmosphere, a fixed model of temperature, pressure, and density at each altitude. The altimeter assumes a particular set of temperature values at each level. But on the actual day, the temperatures at those levels will almost certainly be different from ISA. When that happens, the indicated altitude will not equal the true altitude. Now, here's an important distinction. At higher flight levels, this temperature error doesn't threaten safety, because every aircraft in that part of the atmosphere experiences the same temperature error. They all read the same wrong value, so they can still maintain vertical separation from each other. The problem becomes serious close to the ground. There, you need true altitude, not indicated, because you must maintain terrain clearance. If the air is colder than ISA, your altimeter over-reads—it says you're higher than you actually are—and that's how you can hit high ground. So, let's set up the conditions. We assume you've already corrected for position error and instrument error, and you've set the correct QNH. Once those are done, the only remaining difference between indicated and true altitude is the temperature error. You can fix it with a formula or with the navigation computer. Let's work the formula. Here it is. True Altitude equals Indicated Altitude plus the quantity: ISA Deviation divided by 273, all multiplied by Indicated Altitude. Let me read that as an equation: True Altitude = Indicated Altitude + (ISA Deviation / 273) × Indicated Altitude. Now, the ISA Deviation is the difference between the actual temperature at your level and the ISA temperature for that level, in degrees Celsius. It's positive if the day is warmer than ISA, negative if colder. Now, there's a handy simplification. If you treat 1/273 as 1/250, you can rewrite it as 4/1000. That's the basis of the "4% rule" used in Meteorology. So the formula becomes: True Altitude = Indicated Altitude + (ISA Deviation × 4/1000 × Indicated Altitude). Let me walk you through a worked example. Say your Indicated Altitude is 20,000 feet, and your SAT—that's Static Air Temperature, the actual outside air temperature—is -35°C. What's the true altitude? First, find the ISA temperature at FL200. FL200 is Flight Level 200, which is 20,000 feet. ISA at that level is -25°C. Your SAT of -35°C is therefore ISA minus 10°C. So the ISA Deviation is -10. Now substitute into the equation. True Altitude = 20,000 + (-10 × 4/1000 × 20,000). Let's compute that. 4/1000 times 20,000 is 80. Then -10 times 80 is -800. So True Altitude = 20,000 - 800, which is 19,200 feet. So on a day 10 degrees colder than ISA, your true altitude is 800 feet lower than indicated. That's the terrain clearance error you must correct for. That's the heart of this calculation—knowing that cold air makes you lower than the altimeter says, and by exactly how much.