# Is true altitude vertical separation between airplanes dependent on temperature?

Does the "true" altitude vertical separation between airplanes (using the same altimeter setting) vary as the temperature changes?

( I fully realize that the "true" altitude of both airplanes is lower when it's colder than ISA and higher when it's warmer than ISA)

Yes, the vertical geometric separation is temperature dependent.

If it cooler than ICAO Standard Atmosphere (ISA) conditions, the geometric vertical separation is lower than the pressure altitude separation. If the temperature is above ISA temperature then the geometric separation is higher.

The ICAO atmosphere assumes a sea level temperature of 15 degrees Celsius and a lapse rate of -6.5 degrees per 1000 geopotential meters altitude. At FL250, according to the model, the temperature is -34.5° Celsius, at FL260 it would be -36.5°C.

Because the ISA is based on geopotential height, the geometric separation between FL250 and FL260 under standard temperature conditions would be slightly over 1000 feet. In fact it would be 1002.1 feet, because gravity is about 0.2% lower at that altitude.

If we would take the same mathematical model as in ISA, but would offset the temperature by -20° Celsius (-5°C temperature at sea level), the geometric difference between FL250 and FL260 would be only 932.7 feet.

If we offset the temperature by +20°C, the difference would be 1072.7 feet between FL250 and FL260.

This can be approximated by looking at the ratio of temperatures expressed in Kelvin. The average temperature between FL250 and FL260 is -35.5° C or 237.7 Kelvin. For 20 degrees below ISA temperature a rough estimate would yield:

$$\frac{237.7 - 20}{237.7}×1000$$ft = 915 feet.

For separation between aircraft and terrain, temperature effects are taken into account by adjusting the minimum safe altitude.

For vertical separation between aircraft no adjustments are made by ATC, but the effect is taken into account in safety cases.

• Thanks for the info. But I was wondering why then does ATC not take into consideration that the two airplanes (in the illustration above) are closer than 1000 (actual) feet apart? If it is extremely colder than ISA, how much less than 1000 ft actual separation is there? – 757toga Nov 10 '18 at 21:03
• I am working on an example, I'll update in a few minutes – DeltaLima Nov 10 '18 at 21:03
• so, if the temp at fl250 is -54.5 C and -56.5 C (-20 C offset) at fl260, the actual (true) altitude vertical separation would be about 932 ft. instead of the desired 1000 ft. true vertical separation between the aircraft? – 757toga Nov 10 '18 at 22:30
• The desired pressure altitude difference is 1000 feet. Not sure where you get that the desired true separation is 1000ft, but the rest is correct – DeltaLima Nov 10 '18 at 22:52
• 1000ft is just a convenient number; if the true separation is slightly less, it doesn't really matter because it's still far more than actually required for safety. – StephenS Nov 11 '18 at 5:47