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

I want to walk you through how we calculate true altitude from indicated altitude when the temperature on the day differs from the standard ISA atmosphere. This is a critical skill for terrain clearance when you're close to the ground. Let's start with the problem. Your altimeter is calibrated against the ISA atmosphere, which assumes a particular set of temperature values at each level. If the actual temperatures at those levels are different from ISA, your indicated altitude will not match your true altitude. At higher flight levels, this isn't a safety issue because all aircraft in the same airspace experience the same temperature error, so vertical separation between aircraft is maintained. But when you're close to the ground, you need to know your true altitude to ensure you clear the terrain. Now, if you've already corrected for position error and instrument error, and you have the correct QNH set on your altimeter, the remaining difference between indicated altitude and true altitude is purely due to temperature error. We can correct this using a formula or with the navigation computer. The formula is: True Altitude = Indicated Altitude + (ISA Deviation / 273) × Indicated Altitude Let me explain what each part means. Indicated Altitude is what you read on your altimeter. ISA Deviation is the difference between the actual temperature at your level and the ISA standard temperature for that altitude — it can be positive or negative. The number 273 comes from the absolute zero reference in Kelvin, relating the temperature change to the expansion or contraction of the air column. Now, in practice, we use a simplified version. If you treat 1/273 as approximately 1/250, you can rewrite it as 4/1000. This gives us the "4% rule" used in Meteorology: True Altitude = Indicated Altitude + (ISA Deviation × 4/1000 × Indicated Altitude) Let me work through the example from the book. Say your indicated altitude is 20,000 feet, and the SAT — that's Static Air Temperature, the actual outside air temperature — is -35°C. First, we need to find the ISA standard temperature at that altitude. At FL200, which is 20,000 feet, ISA standard temperature is -25°C. Your SAT of -35°C is therefore ISA -10°C — that's an ISA Deviation of minus 10 degrees. Plugging into the 4% rule formula: True Altitude = 20,000 + (-10 × 4/1000 × 20,000) Let's work that step by step. 4/1000 times 20,000 gives you 80. Then -10 times 80 gives you -800. So True Altitude = 20,000 - 800 = 19,200 feet. That means your true altitude is 800 feet lower than what your altimeter is indicating, because the air is colder than standard. Cold air is denser and compresses the pressure levels closer together, so you're actually lower than the altimeter says. This is why the temperature correction is so important near the ground — in cold conditions, you could be significantly lower than you think. shows an example of this kind of correction on the navigation computer, and shows the relationship between calibrated airspeed and true airspeed, which uses similar correction principles.