FAA Private Pilot Airplane (PAR)Weather Theory and ServicesHard
An airport has a field elevation of 3,000 feet. The current altimeter setting is 30.42 inches Hg, and the outside air temperature is 30°C. Using the standard lapse rate of 2°C per 1,000 feet from a sea-level standard of 15°C, what is the approximate density altitude?
- A2,500 feet
- B6,900 feet
- C4,900 feet
- D3,000 feet
Show answer & explanationAnswer & explanation
Correct answer: C. 4,900 feet
First find pressure altitude: PA = field elevation + (29.92 − altimeter setting) × 1,000 = 3,000 + (29.92 − 30.42) × 1,000 = 3,000 − 500 = 2,500 ft. Standard temperature at 2,500 ft PA = 15°C − (2,500/1,000 × 2°C) = 15 − 5 = 10°C. The actual temperature (30°C) is 20°C above standard. Using the approximation of 120 feet of density altitude per degree Celsius above standard, DA ≈ 2,500 + (120 × 20) = 2,500 + 2,400 = 4,900 feet.
Why the other options are wrong
- A. This is only the pressure altitude, before correcting for the non-standard temperature.
- B. This overstates the correction by using field elevation instead of pressure altitude as the starting point.
- D. This is simply the field elevation and ignores both pressure and temperature corrections.
Density Altitude Calculation
Density altitude is pressure altitude corrected for non-standard temperature; it represents the altitude in the standard atmosphere where the aircraft's true performance would be experienced.
- PA = field elevation + (29.92 − altimeter setting) × 1,000
- Standard temp decreases 2°C per 1,000 ft from 15°C at sea level
- Approx. rule: DA = PA + (120 × °C above standard temperature)
Memory trick: Pressure altitude first, then add 120 ft per degree hot