Density altitude

Density altitude (DA): pressure altitude (PA) corrected for temperature. Altitude in the standard atmosphere where air is this thin. Aircraft performs to DA, not altimeter reading.

Formula (TC AIM MET 8.4.3; ISA: TC AIM AIR 1.5.1):

• DA = PA + 118.8 × (OAT − ISA temp)
• OAT = outside air temperature
• ISA temp = 15 − 1.98 °C per 1000 ft
• DA rises about 118.8 ft per °C above ISA
• Colder than ISA: DA below PA

Unit trap: OAT 23 °F = −5 °C; at 4,000 ft ISA is 7 °C, so deviation is −12 °C, not +16 °C.

Humidity (TP 1102 ch.2; see air-composition):

• Raises DA slightly, minor next to pressure and temperature
• Dewpoint effect generally negligible (FAA AWH 8.4.1.5)

High DA effects (FAA AWH 8.4.1.5):

• Less thrust: propeller works less efficiently in thin air
• Less lift: thin air pushes less on the wing (PHAK ch.5, Lift)
• Airspeed indicator shows none of this; normal indicated airspeeds still flown
• True airspeed and groundspeed higher for a given IAS as DA climbs

Service ceiling (bites at cruise; altitude where climb drops to 100 ft/min, PHAK ch.11; FAA AWH 8.4.1.5):

• Published figure rated for ISA temperature
• Hotter than ISA: limit reached at a LOWER pressure altitude (performance follows DA, not PA)
• Practical ceiling today below published figure

Trap: high and hot means HIGH DA and worse climb, take-off, landing. Never read PA as DA.

Practice