Density Altitude

Density altitude is the altitude in the International Standard Atmosphere (ISA) at which the air has the same density as the air the aircraft is actually in. The altimeter does not show it, yet it is the altitude at which the airplane performs: the wing, the engine and the propeller all respond to the mass of air they work on, not to the height above the sea. On a hot afternoon at a high aerodrome the altimeter may read 5,000 ft while the airplane accelerates, climbs and lands as though it were near 8,000 ft.

The idea links the International Standard Atmosphere, the altimeter and the performance chart. It is examined from the EASA PPL and the FAA private pilot test, where candidates compute it, to ATPL performance, where it explains why hot and high airports limit the takeoff mass of jets.

Pressure altitude and density altitude

Pressure altitude is the altitude in the ISA at which the measured pressure would be found. An altimeter set to the standard setting, 1013.25 hPa or 29.92 inHg, displays it. At an aerodrome it is worked out from the elevation and the QNH or altimeter setting, allowing about 27 ft per hPa near sea level, rounded to 30 ft in many exam questions, or 1,000 ft per inch of mercury in FAA practice. A QNH below standard puts the pressure altitude above the elevation: an aerodrome at 1,500 ft with a QNH of 983 hPa is at a pressure altitude of about 1,500 + 30 × 30 = 2,400 ft.

Density altitude goes one step further and corrects pressure altitude for non-standard temperature. Warm air at a given pressure is less dense than standard, so the density altitude is higher than the pressure altitude. Cold air is denser, and the density altitude is lower; at a low aerodrome on a very cold day it can be below sea level. When the temperature is exactly ISA, the two are equal.

Pressure altitude is the datum for flight levels and the entry to performance charts; density altitude describes the air itself, and with it the airplane's performance.

Temperature, ISA deviation and humidity

The ISA assumes 15 °C at mean sea level, falling by 1.98 °C per 1,000 ft, rounded to 2 °C, up to the tropopause at 36,090 ft. The ISA deviation is the difference between the actual outside air temperature and the ISA temperature at the same pressure altitude. At 3,000 ft the ISA temperature is 15 − 2 × 3 = +9 °C, so +29 °C there is ISA +20.

The commonest mistake, in exams and in the cockpit, is to measure the deviation from 15 °C rather than from the ISA temperature at the pressure altitude. In the example above that error gives ISA +14 and understates the density altitude by about 700 ft.

Each degree of deviation is worth roughly 120 ft of density altitude, so ISA +20 adds about 2,400 ft and the airplane performs as if it were at 5,400 ft. Temperature is usually the largest variable: a summer afternoon can be 25 °C or more above ISA. Because density altitude follows the temperature, it is highest in the afternoon and lowest around dawn.

Humidity lowers the density further. Water vapor has about five-eighths the density of dry air at the same pressure and temperature, so moist air is less dense than dry air. The effect is small next to that of temperature: the FAA's Pilot's Handbook of Aeronautical Knowledge treats humidity alone as usually not an important factor in calculating density altitude, though a contributing one, and offers no simple rule of thumb for it. The standard calculation and most performance charts leave it out. Water vapor also displaces oxygen, so a piston engine loses some power on a humid day. The FAA's density altitude pamphlet sums up the worst case as high, hot and humid, and when the humidity is high it advises adding 10 percent to the computed takeoff distance and expecting a reduced rate of climb.

Calculating density altitude

Without a chart or a computer, density altitude takes four steps:

1. Pressure altitude: elevation + (1013 − QNH) × 30 ft, or elevation + (29.92 − altimeter setting) × 1,000 ft.
2. ISA temperature at that pressure altitude: 15 °C minus 2 °C per 1,000 ft.
3. ISA deviation: outside air temperature minus ISA temperature.
4. Density altitude: pressure altitude + 120 ft × ISA deviation.

The 120 ft figure is an approximation. The exact standard-atmosphere formulas give slightly less on hot days, about 110 to 116 ft per degree at typical aerodrome altitudes: for 5,000 ft and ISA +25 they give about 7,800 ft against the rule's 8,000 ft, and the PHAK's own example puts a 5,048 ft field at 30 °C at 7,855 ft. In summer the rule therefore errs on the safe side. Exam questions state the figure to use, sometimes 118 ft.

The illustration works one case through: a 5,000 ft aerodrome with a QNH of 1003 hPa and +30 °C. At 27 ft per hPa the pressure altitude is about 5,270 ft, where ISA is about +4.5 °C; the deviation of ISA +25.5 adds about 3,060 ft, for a density altitude of about 8,300 ft.

View full schematic

An E6B-type flight computer does the same calculation graphically: the outside air temperature is set against the pressure altitude, and the density altitude is read in a window. In the United States, the ATIS broadcast includes a density altitude advisory when appropriate (AIM 4-1-13).

The Koch chart, a nomogram reproduced in the FAA's density altitude pamphlet (P-8740-2), skips density altitude altogether. A straight line from the aerodrome temperature to the pressure altitude crosses two scales: the percentage increase in takeoff distance and the percentage decrease in rate of climb, compared with sea-level standard conditions. At 100 °F and a pressure altitude of 6,000 ft, for example, it adds 230 percent to the takeoff distance and takes 76 percent off the rate of climb. It gives typical values for light airplanes only, and the airplane's own flight manual charts are authoritative.

Effects on engine and propeller

A piston engine's power depends on the mass of air, and so of oxygen, drawn into its cylinders. A normally aspirated engine, one without a turbocharger, loses roughly 3 percent of its sea-level power for each 1,000 ft of density altitude, by a common rule of thumb. About 85 percent remains at 5,000 ft and about 75 percent at 8,000 ft, the PHAK's figure for a typical engine, even at full throttle.

The mixture also becomes richer as density falls, because the fuel is metered by the volume of air while its mass shrinks, so at full rich the engine is over-rich and gives less than the power available. Flight manuals therefore call for leaning before a high density altitude takeoff, typically to a specified maximum static rpm or fuel flow. Near sea level full rich remains correct, because the surplus fuel cools the cylinders at full power (see mixture control and abnormal combustion).

A turbocharged engine holds its rated manifold pressure, and so its power, up to its critical altitude, which makes its takeoff power far less sensitive to density altitude. The airframe still flies in thin air, with the higher true airspeeds described below (see supercharging and turbocharging).

The propeller is also less efficient in thin air, because it has less air to work on. Turbine engines also produce less thrust as density falls, because the mass flow through them is lower; jet thrust falls roughly in proportion to density.

The wing and true airspeed

The airspeed indicator and the wing respond to the same quantity, dynamic pressure, which depends on air density and the square of the true airspeed. In thin air both need a higher true airspeed to give the same reading or the same lift. The indicated stalling, rotation, climb and approach speeds therefore do not change with density altitude, and the pilot flies the flight manual's indicated speeds at any aerodrome. What changes is the true airspeed behind them, and in still air the groundspeed.

True airspeed is equivalent airspeed divided by the square root of the density ratio. At 8,000 ft density altitude the air has about 79 percent of sea-level density, so 60 kt indicated is about 68 kt true. A common rule of thumb adds 2 percent per 1,000 ft, which slightly overstates the difference in standard conditions. The higher true airspeed also widens turns: at the same indicated speed and bank angle the turn radius grows with the square of the true airspeed, so a turn in a valley needs more room (see turning flight).

Effects on takeoff, climb and landing

A high density altitude hurts the takeoff twice. The airplane must reach a higher true airspeed, and so a higher groundspeed, before it lifts off, and it accelerates more slowly because thrust is reduced. The ground roll and the distance to 50 ft both lengthen markedly, and on a light twin the accelerate-stop distance grows for the same reasons.

The climb suffers most. Power available falls with density, while the power required at the climb indicated airspeed rises, because the same drag is overcome at a higher true airspeed. The excess power that drives the climb is squeezed from both sides, so the rate of climb falls, and the climb gradient with it, just where terrain is often close. For a jet, the gradient, thrust minus drag divided by weight, falls because thrust falls while the drag at the same indicated speed stays about the same. For a light twin, the FAA's one-engine-inoperative service ceiling, the density altitude at which the best single-engine rate of climb has fallen to 50 ft/min, may lie below the minimum en route altitude on a hot day (see light twin engine-out performance and climb performance).

On landing, the approach is flown at the normal indicated speed, but the higher true airspeed means a higher groundspeed at touchdown. The kinetic energy to be absorbed rises with its square, so the landing roll is longer and the brakes work harder. A go-around is weaker for the same reasons as the climb.

For transport airplanes the takeoff calculation uses the actual pressure altitude and temperature, and a high density altitude can lower the maximum takeoff mass through several limits at once: the climb limit, usually set by the one-engine-inoperative second segment; obstacle clearance; the tire speed limit, because the lift-off groundspeed is higher; and the maximum brake energy speed. On landing, the approach and landing climb gradients and brake energy can limit the mass (see takeoff mass limitations).

Hot and high aerodromes

A hot and high aerodrome combines elevation with heat. Denver, Nairobi and Sana'a are classic high examples, where many airplanes are weight-limited on hot days. Hot aerodromes such as Bahrain and Khartoum produce high density altitudes mainly through temperature. Aircraft limitations add a ceiling of their own: the Airbus A320, for example, has a maximum runway altitude of 9,200 ft.

Mountain aerodromes add terrain that a weak climb may not clear, and often a sloping runway. A föhn wind warms the lee side of a range and raises the density altitude there (see local winds and mountain flying).

Nothing in the cockpit announces the problem: the altimeter shows the familiar elevation and the airspeed indicator the familiar speeds. Only the long ground roll and the shallow climb reveal it, when stopping or turning back may no longer be possible.

Planning for high density altitude

• Calculate it for the departure, the destination and any high ground on the route, at the time of flight.
• Use the flight manual charts. Enter them with pressure altitude and outside air temperature, never with the elevation, at the actual mass and wind, then apply the slope and surface corrections. Expect real performance to be somewhat worse than charted on a humid day.
• Keep margins. Commercial Class B flights apply the Part-CAT factors described in factors affecting takeoff and landing performance. On private flights EASA's NCO.POL.110 requires adequate performance, and 14 CFR 91.103 requires the pilot in command to know the airplane's takeoff and landing distances; a personal margin serves the purpose of the factors.
• Reduce the demand. Depart early in the morning or late in the evening, carry less fuel, baggage or passengers, and use the full runway length.
• Lean as the flight manual directs, and check the static rpm or fuel flow before releasing the brakes.
• Fly the book indicated speeds, and plan a climb path that clears the terrain at the reduced gradient.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.