The ISA model — pressure, temperature, density and lapse rate with altitude, and how density altitude drives performance.
Notes
Physics of the atmosphere — summary notes
Free
Main ideas
The International Standard Atmosphere (ISA) is the agreed reference: sea level 15 °C (288.15 K), 1013.25 hPa (29.92 inHg), density 1.225 kg/m³ — every performance chart is corrected back to these datum conditions.
Temperature falls at a lapse rate of about 1.98 °C per 1000 ft (≈2 °C/1000 ft, 6.5 °C/km) up to the tropopause at 36 090 ft (11 km), where it reaches −56.5 °C and then stays constant through the lower stratosphere.
Pressure and density both fall with altitude — pressure roughly halves every ~18 000 ft — because there is progressively less air above pressing down.
Density is set by pressure, temperature and humidity through ρ = P/(RT): hot air and (counter-intuitively) humid air are LESS dense, so a 'high, hot and humid' day degrades lift, thrust and climb — high density altitude.
Aerodynamic force and engine mass flow both depend on air density via the dynamic pressure ½ρV²; as density falls with height, true airspeed must rise to hold the same indicated airspeed, and the aircraft eventually reaches its service ceiling.
⚠ Exam trap: the lapse rate STOPS at the tropopause — above it the stratosphere is isothermal at −56.5 °C, temperature does not keep falling. And humid air is less dense than dry air, not more.
Key formulas
Air density
ρ = P / (R·T) (R = 287 J/kg·K for dry air)
ISA lapse rate
≈ 1.98 °C per 1000 ft, to 36 090 ft
Dynamic pressure
q = ½·ρ·V²
Solved examples
On a hot day the airfield reports 35 °C at an elevation of 3000 ft. Qualitatively, how does take-off performance compare with an ISA day?
ISA temperature at 3000 ft is about 15 − 6 = 9 °C, so 35 °C is roughly 26 °C above ISA. The high temperature lowers density, raising the density altitude well above 3000 ft. Lift and thrust both fall, so the take-off run lengthens and climb rate drops — the classic 'high, hot and humid' performance penalty.