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Aircraft Performance Chart

Effects of Air Density

Most aircraft accidents occur during the take off and landing phase of the flight. Collisions with obstacles during climb out, runway overruns during landing do occur every now and then.

In this section of the site we will take a look at the various factors contributing to the performance of the aircraft during take off and landing. Hopefully we help the pilot ensuring safe operation during these phases of the flight as the rules require that of the pilot in command.

Our first performance factor, air density, should be of considerable interest to any pilot. For example, aircraft all up weight is something we can do about but the density of the air depends on other factors, as we will see shortly, and most of them we can not influence at all.

If your aircraft is equipped with a turbo- or supercharged engine then the variation of air density doesn't really affect the power output of the engine at all. Until it reaches a certain altitude where even the turbo can not compensate anymore for the loss in air density.

Remember that the engine can be technically compensated for a loss in air density with a turbo charger, but this will not apply for the propeller and wings. They will continue to see a loss in performance.

Air Density & Pressure Altitude

When air density decreases both engine and aerodynamic performance reduce. The reason being is that with lower density air molecules are further apart from each other (put a different way: there are less air molecules per m3 or ft3).

A number of factors (altitude/pressure, temperature and humidity) influence air density. A higher altitude, low pressure area, higher temperature and high humidity all have one result: they lower the density of the air. And as a result of that: a reduction in aircraft and engine performance.

International Standard Atmosphere

A standard atmosphere has been established by the aviation authorities to enable comparison of aircraft performance, calibration of instruments (altimeters, transponder encoders, etc) and even more so for meteorological purposes.

There are a number of hypothetical conditions set in this standard atmosphere (at 45 ° latitude). For example: sea level pressure is 1013,25 hPa (29.92 inHg), a sea level temperature of 15 °C, pressure lapse rate is 1 hPa per 27 feet at lower altitudes (1" per 1000 feet), mass of 1,225 kg/m3, temperature drop of 1,98 °C per 1000 feet (300 m) up to 36000 feet and the speed of sound is 340,3 m/s (1225 km/h or 661,4 kts).
With this, performance between aircraft can be compared and actual take off and landing data can be calculated for the day of the flight.

Pressure Lapse Rate, PLR

This formula: PLR = 96 × ( T in kelvin) / QNH (in hPa) is used to calculate the exact pressure lapse rate. For example at 15 °C and with ISA QNH the lapse rate will be: 96 × (15 + 273) / 1013,25 = 27,3 ft/hPa.

Pressure Altitude, PA

Density Altitude ChartDensity Altitude Chart
Density Altitude Chart

This is altitude or elevation corrected for non standard pressure. When in the aircraft: make a mental note of the current indication, set the Kollsman window on the altimeter to 1013 hPa / 29,92 inHg and you will have your PA.
Easy when you have an aircraft or altimeter nearby, but what to do when you only have the regional QNH and local elevation or altitude?
With a small but effective formula it is easy to calculate: Pressure Altitude = Altitude + (1013 - QNH) × 27.

Pressure Altitude Calculator
Temp (OAT): °F °C
QNH: hPa (mb) inHG
Altitude: feet
Pressure Altitude feet

When looking at this formula it becomes obvious that when QNH is higher than 1013 hPa (QNE) that result will be negative and deducted from altitude, or, put another way: add 27 ft for every hPa below 1013 hPa (common in low pressure areas) or when QNH is lower than 1013 hPa -> Pressure Altitude will be higher (27 ft/hPa) and vice versa.

The PAC form to the left will help you with this, enter the required values and press 'Calculate'.

Density Altitude, DA

This is the combined effect of the factors mentioned above. It is defined as: "Pressure altitude (PA) in the standard atmosphere corrected for non standard temperature". The performance of your aircraft depends on air density: which has a direct effect on lift, drag, engine performance and propeller thrust. Thus you can say that when air density decreases, aircraft performance also decreases.

Basic rule of thumb: DA can be calculated by taking PA and adding (or subtracting) 120 feet for each 1 °C temperature difference above (or below) the standard atmosphere temperature at that particular ISA altitude. The formula for dry air conditions is as follows:
Density Altitude = Pressure Altitude + (OAT - ISATpa) × 120.

Density Altitude Calculator
Temp (OAT): °F °C
Pressure Altitude: feet
ISAtemp (@PA): °F °C
Density Altitude feet

Where: OAT is the actual outside air temperature and ISATpa is ISA temperature at this pressure altitude. Or put another way: if OAT is lower than ISA -> Density Altitude will be lower than Pressure Altitude (120 ft/°C difference from standard) and vice versa.

The DAC form to the left will help you with this, enter the required values and press 'Calculate'.

When taking off at any DA above ISA sea level, you will still need the same indicated airspeed. But because air density is lower, true airspeed will be higher and as a result your groundspeed is higher. To get to the same indicated airspeed you will also need more runway for your groundroll.
Note: that your indicated stall speed is always the same regardless when DA is higher or lower. DA influences the true airspeed / groundspeed and not the indicated airspeed.

Normally aspirated engines

When your engine is not equipped with a turbo- or supercharger it will also suffer from the less dense air. Each intake stroke (which is by volume) will contain less air molecules and thus less power can be developed by the engine (due to the fixed fuel / air ratio). Propeller thrust (and wing) efficiency are also reduced at these higher density altitudes (for both fixed and controllable types). This explains the need for more runway at higher density altitudes.

High elevation airports

You will run into high density altitudes at high elevation airports in combination with high ambient temperatures. Should there also be a low atmospheric pressure system in the area, then this will accentuate the effect even more. Taking off in these conditions is not without problems. Our advise: calculate actual DA and make sure to check all related performance charts for your aircraft before attempting the flight.

written by EAI.

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