How do you compare outside-air temperature with the model ISA temperature?

Standard temperature in the app

Crabwise computes the ISA temperature at a pressure altitude as ISA = 15 − 1.98 × PA ÷ 1000, in °C. The deviation is ΔISA = OAT − ISA: positive on a warmer-than-standard day, negative on a colder one. The same pressure altitude then feeds the density-altitude steps, so the deviation and the density altitude always describe one consistent condition.

The 1.98°C per thousand feet lapse is the rounded standard value the app uses for this display; the density calculation itself uses the pressure ratio and the absolute temperature.

Worked example

At 5200 ft pressure altitude, this approximation gives 4.704°C standard temperature. An entered 30°C is therefore 25.296°C above that comparison temperature.

Model standard temperature (°C)

4.704

Entered temperature above model standard (°C)

25.296

Find the deviation

1. Get pressure altitude first, from elevation and altimeter setting or directly.
2. Enter the outside-air temperature in °C.
3. Read the ISA temperature and the deviation lines in the results.
4. Keep the sign: +2.84 and −2.84 describe opposite conditions.

A slightly warm day at 8000 ft

At 8000 ft the ISA temperature is 15 − 1.98 × 8 = −0.84°C. With an OAT of 2°C the deviation is 2 − (−0.84) = 2.84°C. The pressure ratio is about 0.742782, the temperature ratio about 0.954885, and density altitude comes out at about 8335.79373 ft, a little above the pressure altitude.

ISA temperature at 8000 ft (°C)

−0.84

ISA deviation (°C)

2.84

Density altitude (ft)

8335.79373

ISA temperature at 12000 ft (°C)

−8.76

At 12000 ft the standard drops to −8.76°C, so the same 2°C OAT would be more than 10°C above standard.

Entered at 12000 ft, the same 2°C reading is 10.76°C above standard and density altitude comes out at about 13246.625304 ft, roughly 1247 ft above the pressure altitude instead of about 336 ft at 8000 ft.

Common mistakes

• Using field elevation instead of pressure altitude for the ISA lookup.
• Subtracting in the wrong order and reversing the sign.
• Comparing an OAT in °F with an ISA value in °C.
• Assuming a positive deviation at one altitude means a positive deviation at every altitude.

Scope

The deviation compares two temperatures in a dry standard model; humidity and the aircraft's performance tables are outside it. The FAA handbook and NASA pages below describe the standard atmosphere used.

Primary sources and related work

• FAA Pilot’s Handbook of Aeronautical Knowledge
• NASA: isentropic flow relationships