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Andrew Choutka
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Density altitude at KLAF

Purdue University Airport, where I fly, is 606 feet above sea level. On a 34 °C afternoon with a 23 °C dewpoint, the air over its runways is as thin as standard air at about 3,250 feet, and the wing and the engine perform as if they were up there. Here is the same calculation for the latest KLAF observation.

METAR KLAF 251854Z VRB04KT 10SM CLR 23/07 A3039 RMK AO2 SLP289 T02330067

Observed .

Density altitude1,310ft

  • 704 ft above the field at 606 ft
  • 1,180 ft if the same air were dry
  • 1,210 ft by the 120 ft per °C rule of thumb
Density altitude in feet against temperature in °C, at a pressure altitude of 180 ft
−6,000−4,000−2,00002,0004,0006,000−30−20−10010203040Field, 606 ftSaturatedDry1,310 ft
Dry airSaturated air, dewpoint equal to temperatureCurrent conditionsStandard temperature

Conditions

°C
°C

Relative humidity 34 %.

inHg
ft
kt
Pressure altitude
180ft
standard temperature 14.7 °C
Station pressure
29.73inHg
1006.9 hPa
Air density
1.179kg/m³
σ = 0.962 of standard sea level
True airspeed
76.5kt
at 75 KIAS
Engine power
95%
of sea-level rated, full throttle

The calculation

  1. Station pressure from the altimeter setting A and the field elevation H. ASOS reports A = (p0.1903 + 1.313 × 10−5 H)5.255, in inHg and feet, and this inverts it.
  2. Pressure altitude, the height in the standard atmosphere with that pressure: 145,442 ft × [1 − (p / 1013.25 hPa)0.190263].
  3. Vapor pressure from the dewpoint Td, using Bolton’s fit: e = 6.112 hPa × exp[17.67 Td / (Td + 243.5)].
  4. Air density, treating dry air and water vapor as ideal gases: ρ = (p − e) / (287.05 T) + e / (461.5 T), with T in kelvin.
  5. Density altitude, the height in the standard atmosphere with that density: 145,442 ft × [1 − (ρ / 1.225 kg/m³)0.234969].
  6. True airspeed. The airspeed indicator measures impact pressure, so the indicated airspeed and the static pressure give a Mach number, and true airspeed is the equivalent airspeed divided by √σ.
  7. Engine power at full throttle for a normally aspirated piston engine, from Gagg and Farrar’s 1934 fit: P / P0 = 1.132 σ − 0.132. Water vapor displaces oxygen, so σ here counts only the dry air.

Assumptions and sources

Indicated airspeed is taken as calibrated; the POH has the correction for a particular airspeed indicator. The power figure is an approximation, and the POH’s performance charts are the numbers to plan with.

The field elevation, 605.8 ft, is from the FAA’s airport record for LAF. Observations come from the Aviation Weather Center and this page refreshes them at most every 10 minutes.

The Pilot’s Handbook of Aeronautical Knowledge, chapter 11, says there is no rule of thumb for humidity’s effect on density altitude. The “if the same air were dry” line above is that effect. The formulas reproduce the handbook’s standard-atmosphere and altimeter-correction tables, and agree with the NWS density altitude calculator to within 20 ft. That calculator rounds the standard sea-level temperature to 288 K and reads about 17 ft high on a standard day.

Vapor pressure: D. Bolton, “The computation of equivalent potential temperature”, Monthly Weather Review 108 (1980), equation 10. Engine power: R. F. Gagg and E. V. Farrar, “Altitude performance of aircraft engines equipped with gear-driven superchargers”, SAE paper 340096 (1934).

Also in the lab: Wind tunnel, Why airplanes bank and Flying in moving air.