The Atmosphere — Page 10, Lesson 15

I want to walk you through how we use the International Standard Atmosphere, or ISA, to work out temperature deviations — because that’s what we need for true altitude calculations and for assessing aircraft performance data. First, let’s define what we mean by an ISA deviation. It’s simply the difference between the actual temperature you measure at a given altitude and the temperature that the ISA model says should be there at that same pressure altitude. To find that deviation, we have to do two things in order: first, work out what the ISA temperature is at that altitude; second, subtract that ISA temperature from the actual temperature. So how do we find the ISA temperature at a particular pressure altitude? The rule is this: we start from mean sea level, where the ISA temperature is 15 degrees Celsius, and we reduce that temperature by 2 degrees Celsius for every 1000 feet above the 1013 hPa datum. In other words, the ISA temperature equals 15 minus 2 times the altitude expressed in thousands of feet. Let me give you the example from the book. Suppose we want the ISA temperature at 18 000 feet. We take 15, subtract 2 times 18 — because 18 000 feet is 18 thousands of feet — and that gives us 15 minus 36, which is minus 21 degrees Celsius. So at 18 000 feet, the ISA temperature is minus 21°C. Now, there’s an important note here: above 36 000 feet, which is about 11 kilometres, the ISA temperature becomes isothermal — that means it stays constant at minus 57°C. So if you’re above that level, you don’t apply the 2°C per 1000 ft rule; you just use minus 57°C. Once we have the ISA temperature, the deviation formula is straightforward: ISA Deviation equals the actual temperature minus the ISA temperature. So if the actual temperature at 18 000 feet is minus 27°C, then the deviation is minus 27 minus minus 21, which is minus 6 degrees. That minus sign tells us the actual air is colder than the standard model by 6 degrees. The book gives you a table to practise with. For each height, you’re given the actual temperature, and you need to calculate the ISA temperature using the formula, then the deviation. For example, at 1500 feet, the actual temperature is plus 28°C. You’d work out the ISA temperature as 15 minus 2 times 1.5 — that’s 15 minus 3, so 12°C — then the deviation is 28 minus 12, which is plus 16. You can work through the rest in the same way. Then there are two practical questions. First: if the limiting deviation for your aircraft at an airfield 5000 feet AMSL is ISA plus 10, what is the maximum temperature at which you can operate? That means the deviation cannot exceed plus 10. So you find the ISA temperature at 5000 feet — that’s 15 minus 2 times 5, which is 15 minus 10, so 5°C — then add the maximum deviation of plus 10, giving a maximum actual temperature of 15°C. Second: if the deviation at 3500 feet is plus 12, what is the ambient temperature? First, ISA temperature at 3500 feet is 15 minus 2 times 3.5, which is 15 minus 7, so 8°C. Then the actual temperature is ISA temperature plus the deviation: 8 plus 12 equals 20°C. Now, the book also gives you a full table of the ICAO International Standard Atmosphere, showing height in kilometres and feet, temperature in °C, pressure in hPa, the height change per hPa, and density as a percentage of sea-level density. Let me walk you through a few key points from that table. At sea level — 0 feet — the ISA temperature is plus 15°C, pressure is 1013.25 hPa, and the height change per hPa is 27 feet. Density is 100 percent. As we go up, temperature drops steadily until we reach about 36 090 feet, which is 11 kilometres. At that level, temperature is minus 56.5°C, pressure is 228.2 hPa, and the height change per hPa has increased to 91 feet. Above that, the temperature stays constant at minus 56.5°C all the way up to about 65 620 feet, or 20 kilometres — that’s the isothermal layer I mentioned. Notice that the height change per hPa is not constant. At sea level, one hPa change corresponds to 27 feet of height change. At 10 000 feet, it’s 37 feet per hPa. At 30 065 feet, it’s 73 feet per hPa. At 38 662 feet, it’s 103 feet per hPa. This is because the relationship between pressure and height changes with altitude, and the table gives you the exact values under ISA conditions. But what if you’re not in ISA conditions? The book gives you a formula to calculate the height change per hPa at any level, using the actual conditions. The formula is: H equals 96 times T divided by P, where H is the height change in feet per hPa, T is the actual absolute temperature at that level in kelvin, and P is the actual pressure in hPa. Let me be very clear about what this formula can and cannot do. It is only valid for calculating the height change per hPa change in pressure at a specified altitude. You cannot use it to calculate a change in height between two pressure levels, and you cannot use it to calculate a change in pressure between two altitudes. It gives you a local rate of change at one specific level, nothing more. So to summarise: we have the ISA model giving us standard temperatures and pressures at each altitude. We calculate ISA temperature using 15 minus 2 times altitude in thousands of feet, remembering the isothermal layer above 36 000 feet at minus 57°C. We find deviation by subtracting ISA temperature from actual temperature. And when we need to work out how much height corresponds to a one-hPa pressure change in non-standard conditions, we use H equals 96 T over P, but only for that specific level.