Temperature, Pressure, Density and Their Altimetry Implications
The relationships
Temperature, pressure and density are linked through the gas law and the hydrostatic equation. Density falls with altitude, with rising temperature (at constant pressure) and with rising humidity. Pressure falls with altitude and with cold, dense air columns. These relationships explain altimetry errors and performance changes.
Altimetry
The altimeter is a pressure gauge calibrated to ISA. Set QNH and it reads elevation when on the ground; set QFE and it reads height above the reference; set 1013.25 (standard) and it reads pressure altitude, used above the transition altitude. Errors follow the rule "high to low, look out below": flying from high pressure to low pressure without resetting makes the aircraft lower than indicated; flying from warm to cold air makes true altitude lower than indicated. Temperature error is largest at high altitude and low temperature; the 4% per 10°C rule approximates the true-altitude correction.
Performance
High altitude, high temperature and high humidity all reduce density and therefore lift, thrust and propeller efficiency, while increasing take-off and landing distances. Pressure altitude and temperature combine into density altitude. Cold air increases density and improves performance but can cause altimeter over-reading.
Traps
Questions mix QNH, QFE and standard settings, or ask which way the aircraft drifts when pressure changes en route. Distinguish indicated from true altitude, and remember that the transition level is not fixed - it varies with QNH.
Worked example
Cruising at 5000 ft indicated with QNH 1003 hPa (10 hPa below standard). 1 hPa ≈ 30 ft, so true altitude is about 5000 + 10×30 = 5300 ft. The aircraft is higher than indicated.