Physics of the Atmosphere
The ISA model, pressure, temperature, density and lapse rate with altitude, and how density altitude drives performance.
Physics of the atmosphere, summary notes
- 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.
- 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
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.
The ISA standard atmosphere
Atmosphere concept map
Physics of the Atmosphere
Physics of the atmosphere quiz
Physics of the Atmosphere, quiz
1. Using an ISA lapse rate of 2 °C per 1000 ft and a sea level temperature of 15 °C, the temperature at 10 000 ft is:
−5 °C+5 °C−20 °C2. The ISA sea level pressure and temperature are:
1013.25 hPa and 15 °C1000 hPa and 20 °C1013.25 hPa and 0 °C3. ISA sea-level conditions are:
15 °C, 1013.25 hPa, 1.225 kg/m³0 °C, 1000 hPa, 1.0 kg/m³20 °C, 1013 hPa, 1.5 kg/m³4. The ISA temperature lapse rate up to the tropopause is approximately:
2 °C per 1000 ft10 °C per 1000 ft0.5 °C per 1000 ft5. The ISA tropopause is at about:
36 090 ft, −56.5 °C10 000 ft, 0 °C50 000 ft, −20 °C6. Above the tropopause, in the lower stratosphere, temperature:
Stays constant (isothermal)Continues to fall at the same rateRises rapidly7. Compared with dry air at the same pressure and temperature, humid air is:
Less denseMore denseExactly the same density8. A 'high, hot and humid' day degrades performance because it:
Lowers air densityRaises air densityHas no effect on density