1.7 Density

Density is defined as the mass per unit volume of a substance, at a specified temperature and pressure.

     Density = Mass / Volume

Density is expressed in grams, or kilograms per cubic metre for metric or SI units, respectively. The Imperial unit for density is pounds per cubic feet. Factors affecting density when considering a gas are:

       Density = Pressure / (Gas constant x Absolute temperature)

For a given temperature, therefore, an increase of pressure increases density, or, at a given pressure, a decrease in temperature increases density.

Density of air depends on atmospheric Temperature and Pressure. As the altitude increases the density decreases.

Variation of Density in the Atmosphere

At sea level, density vary between 1.20 and 1.55 kg per cu m, the higher values being usually associated with the colder temperatures of higher Altitudes, and the lower values typical of Equatorial Altitudes.

Air at lower levels in the atmosphere is compressed by the mass of the overlying air. With increasing altitude, the overlying mass reduces and air can now expand, resulting in further reduction of pressure. With increasing altitude the temperature also decreases, but at a rate lower than the pressure. Density, therefore, decreases with height.

Density values of the International Standard Atmosphere are shown below: 

Altitude (ft)	Density (Kg/m3)
40,000	0.301
30,000	0.458
20,000	0.653
10,000	0.905
0 (Sea Level)	1.225

At about 22,000 ft, the density is half the sea level value. We have already seen that density at sea level tends to be higher at the Poles than at the Equator. However, at 26,000 ft, the density value is similar at all Altitudes.

Variation of Density with Humidity

The total pressure of the atmosphere is equal to the sum of the individual pressures of the gases. The pressure of moist air is less than that for dry air, and so humidity decreases the total pressure. From the gas equation, it can be seen that the reduction in pressure results in a lower density. The greater the humidity, the lower the density.

Density Altitude

This is defined as the altitude in the International Standard Atmosphere at which a given density is found. Aircraft performance is largely dependent on density altitude as opposed to true or pressure altitude.

Density and Performance

The effects of density on lift, drag, power and thrust have been considered in the section concerning temperature. There are, however, additional effects of density performance.

Above about 300 kt TAS, air becomes significantly compressed, and locally increases the density. At much higher speeds this may give a marked increase in drag, and when increasing altitude, this can offset the otherwise reducing drag value. A similar compressibility effect increases drag on a propeller blade, reducing its efficiency, particularly at higher altitudes. A jet engine's performance, however, is enhanced by this compressibility effect as mass flow is improved.

Air Density and the Human Body

The reduced density of air with increasing altitude means that in a given volume of air breathed in, the oxygen content has decreased. Above 10,000 ft this reduction leads to hypoxia, its effects ranging from lack of judgement to sleepiness or collapse, according to height. At night, the reduced intake of oxygen impairs night vision at altitudes of 4,000 ft and above.

To counter these problems, aircraft operating above 10,000 ft must have an enriched oxygen supply, either in conjunction with a pressurised cabin, or through face masks. At night, ideally, oxygen should be available from ground level upwards.