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LESSONS · PERFORMANCE · 15 MINUTES · AUSTRALIA

Density height and performance.

Hot air, low pressure and a high aerodrome all thin the air. Density height turns that into one number: the height the aircraft will perform as if it were at.

PREDICT FIRST

Your aerodrome is at sea level and QNH is 993 hPa. Using the VFRG's 30 ft for each hPa, what is the pressure height?

Pressure height

The VFRG and the FAA handbook call these pressure altitude and density altitude.

Put simply, pressure altitude is the height above the ISA datum of 1,013 hPa.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Pressure altitude considerations

In the VFRG's example the aerodrome is 1,000 ft above sea level, but 1,300 ft above the 1,013 hPa datum, because QNH is 1,003 hPa.

A 1,000 ft aerodrome elevation with a QNH of 1,003 hPa

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Pressure altitude considerations

You can also read pressure height straight off the altimeter.

As stated above, without making the above calculation, you are also able to read pressure altitude on the altimeter for the aerodrome (1,300 ft) of the aircraft at the aerodrome directly by setting standard pressure 1,013 hPa on the altimeter subscale.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Pressure altitude considerations

Density height

Pressure height leaves out temperature. The VFRG corrects for it with a second rule of thumb.

Density altitude can be determined by applying an ambient temperature correction to the pressure altitude. Each 1°C variation from ISA (15°C at sea level) is equivalent to a 120 ft variation in density altitude.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Density altitude considerations

The standard temperature itself falls with height, so first find ISA at your pressure height: 15 °C less 2 °C for each 1,000 ft.

A standard temperature lapse rate is one in which the temperature decreases at the rate of approximately 3.5 °F or 2 °C per thousand feet up to 36,000 feet.

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Atmospheric Pressure

Thus, for a 1,000 ft aerodrome elevation in the example above having a 1,300 ft PA, ISA equals approximately 12°C. If the aerodrome has a 30°C outside air temperature, this is 18°C hotter than ISA. Therefore, 120 x 18 equals 2,160 ft, plus PA 1,300 ft, equals a density altitude of 3,460 ft. So, the performance of the aircraft will be degraded. It will perform as if the aircraft were at 3,460 ft and not at 1,000 ft aerodrome level.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Density altitude considerations

The VFRG rounds ISA to about 12 °C in that example. The simulation keeps the decimal, 12.4 °C, so the same day comes out at 3,412 ft rather than 3,460 ft.

PREDICT FIRST

An aerodrome at sea level, QNH 1,013 hPa. The temperature climbs from 15 °C to 35 °C. Using the VFRG's 120 ft for each °C, what happens to the density height?

TRY IT

Heat the day and watch the air thin

Pressure height and density height are worked with the VFRG's rules of thumb, so they are approximate. At the hottest, highest settings the rules give a density height about 560 ft higher than the full standard atmosphere does. Humidity is left out.

Sea levelAerodromePressure heightDensity height

The faded aircraft sits at the density height worked by the VFRG's rules, close to the height in the standard atmosphere with the same air density.

Pressure height
1,300 ft
Density height
3,412 ft
Air density
90%
TAS for the same IAS
+5%
Standard sea levelThis air, 90%
  1. Pressure height = 1,000 + 30 × (1,013 − 1,003) = 1,300 ft
  2. ISA at 1,300 ft = 15 − 2 × 1.3 = 12.4 °C
  3. 30 °C is 17.6 °C warmer than ISA
  4. Density height = 1,300 + 120 × 17.6 = 3,412 ft

The aircraft performs as if it were at 3,412 ft, 2,412 ft above the aerodrome.

Try a day

What thin air does to take-off and climb

It is imperative that you are aware that the hotter the day gets, there is a decrease in air density. This, in turn, results in a decrease in aircraft performance. This decrease in air density markedly reduces engine power output, thereby having significant effect by reducing the aircraft’s take-off and climb performance.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Density altitude considerations

The FAA handbook lists what less dense air takes away:

As air becomes less dense, it reduces: • Power, because the engine takes in less air • Thrust, because the propeller is less efficient in thin air • Lift, because the thin air exerts less force on the airfoils

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Atmospheric Pressure

Regardless of the actual altitude at which the aircraft is operating, it will perform as though it were operating at an altitude equal to the existing density altitude.

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Density Altitude

The take-off roll

On the take-off roll, a higher density height works against you twice.

An increase in density altitude can produce a twofold effect on takeoff performance: 1. Greater takeoff speed 2. Decreased thrust and reduced net accelerating force

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Takeoff Performance

The airspeed indicator works from air pressure. In thinner air the aircraft has to move faster through it to make the indicator read the same.

Because air density decreases with an increase in altitude, an aircraft has to be flown faster at higher altitudes to cause the same pressure difference between pitot impact pressure and static pressure.

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 8, Airspeed Indicator (ASI)

Thus, the aircraft at altitude takes off at the same indicated airspeed (IAS) as at sea level, but because of the reduced air density, the TAS is greater.

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Takeoff Performance

The simulation's TAS for the same IAS shows by how much. It uses the square root of the density ratio, taking indicated airspeed as equivalent airspeed.

This can be done rather simply by using the square root of the density ratio (sea level to altitude) as discussed earlier to convert the equivalent speeds to actual speeds.

James F. Marchman III, Aerodynamics and Aircraft Performance (3rd edition, Virginia Tech University Libraries, CC BY 4.0), chapter 4, 4.12 Minimum and Maximum Speeds

PREDICT FIRST

In the FAA handbook's example, a flight manual gives a take-off ground run of 790 ft at a pressure height of 5,000 ft on a standard day. The day is then 20 °C above standard. What ground run does the handbook say to expect?

The climb

An increase in altitude also increases the power required and decreases the power available. Therefore, the climb performance of an aircraft diminishes with altitude.

FAA Pilot's Handbook of Aeronautical Knowledge (FAA-H-8083-25C), chapter 11, Climb Performance Factors

The aircraft performs as if it were at its density height, so a high density height costs climb performance as well as runway.

In practice

You do not always have to make a separate density altitude calculation because take-off and landing performance charts normally provide integral solutions for density altitude through entries of pressure altitude and temperature.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Density altitude considerations

Humidity thins the air further, and the simulation leaves it out.

Increased humidity also reduces the density of air.

CASA Visual Flight Rules Guide (VFRG) v8.3, CC BY-NC 4.0, Density altitude considerations

The flight computer works pressure height and density height with the full standard atmosphere, and shows the working.

Lock it in.

358 Australian practice questions on performance. The ones you miss come back sooner.

Practise performance

SOURCES FOR THIS LESSON

Source-checked, awaiting pilot review. Learning only. Your aircraft's flight manual and your instructor come first. Sources and licences