The Atmosphere

Understanding the details of the atmosphere is critical for manned flight since it provides the medium through which the aircraft moves. The lift provided by the wings and drag experienced by the aircraft vary greatly with different altitudes. In fact Sir Frank Whittle was largely motivated to design a jet engine due to his insight that aircraft would be able to fly faster and more efficiently at higher altitudes due to the lower density of air. The internal combustion engines at the time would not allow higher altitudes of flight, since the lack of oxygen was starving the engines thereby reducing power output.

In essence the atmosphere is a fluid skin that surrounds the entire earth to around 500 miles above the surface. Measured by volume the atmosphere at sea level is composed of 78% nitrogen, 20.9% oxygen, 0.9% Argon, 0.03% Carbon Dioxide and a trace of other gases. Up to about 50 miles the composition of the air is fairly constant, except for a variation in water vapour, which depends on the ambient temperature. The hotter the air the more water vapour it can hold (this is why you can see your breath on a cold morning as the cold air is saturated at this lower temperature). The heavier gases do not rise to high altitudes such that above 50 miles the atmosphere is largely comprised of hydrogen and helium. Above 18 000ft oxygen has depleted enough to prevent human’s from breathing and so oxygen is supplied mechanically to the cabin. At about 100 000ft oxygen is too low to allow combustion even in the most advanced turbojet engines.

In lower temperature latitudes the 36 000 ft of the atmosphere are generally known as the troposphere. In the troposphere the temperature decreases from about 20°C at sea level to -53°C. The tropopause is a hypothetical boundary between the lower troposphere and the higher stratosphere. In the stratosphere the temperature is initially constant and then increases to about -20°C at 35 miles. The separating tropopause is not a clear cut line but rather a hypothetical boundary that varies from around 30 000 ft over the poles to around 54 000 ft above the equator. As a result the temperature in the stratosphere is naturally warmer over the poles than over the tropics, since the higher altitude of the tropopause over the tropics allows the temperature to fall further before the constant temperature region of the stratosphere is reached. The atmosphere is divided further into regions such as the mesosphere, mesopause, thermosphere and the exosphere. However, these regions are outside of the realms of commercial and most fighter aircraft and we will therefore not deal with them here.

As originally observed by Sir Frank Whittle, the atmospheric conditions have a great effect on the performance of aircraft:

1. The local ambient conditions of the air influence lift, drag and engine performance. In particular the pressure, density and temperature of the local air define the performance characteristics.

2. The aircraft is moving relative to a fluid mass that in turn is moving relative to the surface of the earth. This introduces navigational problems that require special on-board equipment to control flight speed and direction.

3. Temperature variations within the atmosphere may cause adverse weather patterns such as strong winds, turbulence, thunderstorms, heavy rain, snow, hail or fog. These criteria influence the loads applied on the aircraft, safety and the comfort of the passengers.

4. The presence of the chemical compound ozone at high altitudes prevents cabin pressurisation with ambient air. This present the designer additional problems with air conditioning and prevention against pressure-cabin failure.

Air is a compressible fluid (i.e. it can change in volume and pressure in contrast to fluids which are largely incompressible). The compressibility of air allows it change shape and shear (flow) under the smallest pressure changes. The relation between pressure p, temperature T and volume v is governed by the ideal gas equation:

where R is the universal gas constant 287.07 J/kg/K and temperature is measured in Kelvin (T in °C + 273). In order to standardise calculations relating to the atmosphere the International Civil Aviation Organization has chosen a definition of the “standard atmosphere”. This states that air is a perfectly dry gas with a temperature at sea level of 15°C and 101.3 kPa of pressure. For the first 11 000km (i.e. in the troposphere) the temperature is assumed to change at a constant lapse rate of -6.5 °C/km, then stays constant at -56.5°C in the troposphere (11 000- 20 000 km) and then increases at different rates in the stratosphere. Another important metric for aircraft flight is the dynamic viscosity of “stickiness” of the air, which influences the drag imposed on the aircraft. You can imagine air being composed of thin layers of air that move relative to each other similar to multiple pieces of paper in a notebook. The dynamic viscosity is the constant of proportionality between the force per unit area required to shear the different sheets over each other and the velocity gradient between the layers. At ordinary pressures the dynamic viscosity generally depends only on the temperature of the air.

Finally the local atmospheric conditions is why aircraft engineers and pilots differentiate between the quantities of true airspeed (TAS), which is measured relative to the undisturbed air, and a fictional speed called the equivalent airspeed (EAS). The latter is of prime importance for aircraft design since it defines the forces that are acting on the aircraft. TAS and EAS are equivalent at sea level in the standard atmosphere but vary at altitude. As an aircraft moves through a mass of initially stationary air it imparts momentum to the surrounding air molecules by both impact and friction. The first molecules that hit the aircraft can be imagined to stick to the aircraft surface and are therefore stationary with respect to the aircraft. Every unit volume of air that has been accelerated to the velocity of the aircraft V, has therefore been imparted with a kinetic energy of

$Title: q = \frac{1}{2} \rho V^2 - Description: q = \frac{1}{2} \rho V^2$

where q is known as the dynamic pressure. Aerodynamic quantities such as lift and drag are typically expressed as non-dimensional parameters i.e. they are divided by the wing area and the dynamic pressure to give the lift coefficient and drag coefficient.

$Title: C_L= \frac{Lift}{qS}, - Description: C_L= \frac{Lift}{qS},$ $Title: C_D= \frac{Drag}{qS} - Description: C_D= \frac{Drag}{qS}$

The non-dimensional form of the parameters is important since it allows a performance comparison between different wings operating at different flying speeds or density conditions. Thus for an aircraft with a specific lift coefficient and wing area to generate the same aerodynamic forces at altitude as at sea level, the aircraft must be flown at a velocity that keeps the dynamic pressure a constant, regardless of any difference in air density. Thus, if the density at flying altitude is $Title: \rho - Description: \rho$ and the airspeed measured by the onboard controls is the TAS, then the equivalent speed at sea-level EAS with density $Title: \rho_0 - Description: \rho_0$ is defined by,

$Title: EAS = TAS \sqrt{\frac{\rho}{\rho_0}} - Description: EAS = TAS \sqrt{\frac{\rho}{\rho_0}}$

Therefore the EAS is a fictional quantity used in aerodynamic calculations to defined the speed that gives the same aerodynamic forces at sea-level as those experienced at altitude.