The Atmosphere — Page 32, Lesson 36

We're starting a new topic now: the atmosphere, and I want to walk you through the ICAO Standard Atmosphere and then the concept of dynamic pressure, which is the foundation for all aerodynamic loads. First, the ICAO Standard Atmosphere. This is a model we use to compare aircraft performance. It assumes a uniform temperature lapse rate — that's the rate at which temperature decreases with altitude — of 2°C per 1000 ft, which is 1.98°C precisely, from mean sea level up to a height of 36,090 ft, which is 11,000 metres. Above that height, the lapse rate becomes zero, meaning the temperature stops decreasing and remains constant at -56.5°C. Let's look at the table of standard values. At sea level, the temperature is 15°C, pressure is 1013.25 hPa, density is 1.225 kg/m³, and relative density is 1.0. Relative density, symbol sigma (σ), is the ratio of the air density at altitude to the sea-level density. As we climb, temperature, pressure, and density all decrease. At 10,000 ft, temperature is -4.8°C, pressure is 696.8 hPa, density is 0.905 kg/m³, and relative density is 0.74. At 35,000 ft, temperature is -54.3°C, pressure is 238.4 hPa, density is 0.386 kg/m³, and relative density is 0.31. And at 40,000 ft and above, temperature holds constant at -56.5°C, as we said. At 50,000 ft, pressure is 116.0 hPa, density is 0.186 kg/m³, and relative density is 0.15. There's an important note here about high density altitude. High density altitude means that the conditions that actually exist at the airport of take-off or landing represent those of a higher altitude in the International Standard Atmosphere — in other words, less air density. So if it's a hot day at a high field, the air is thinner, and the aircraft behaves as if it were at an even higher altitude. Now let's move to dynamic pressure. The unit for dynamic pressure is N/m², and the symbol is lower case 'q' or upper case 'Q'. Because air has mass, air in motion must possess kinetic energy, and it will exert a force per square metre on any object in its path. The kinetic energy is given by KE = ½ m V². It's called DYNAMIC pressure because the air is moving in relation to the object being considered — in this case, an aircraft. Dynamic pressure is proportional to the density of the air and the square of the speed of the air flowing over the aircraft. An aircraft immersed in moving airflow will experience both static AND dynamic pressure. Remember, static pressure is always present — that's the pressure of the air around you even when it's not moving. The kinetic energy of one cubic metre of air moving at a stated speed is given by the formula: Kinetic Energy = ½ ρ V² joules, where ρ is the local air density in kg/m³ and V is the speed in m/s. If this cubic metre of moving air is completely trapped and brought to rest by means of an open-ended tube, the total energy will remain constant, but by being brought completely to rest, the kinetic energy will become pressure energy which, for all practical purposes, is equal to: Dynamic Pressure = ½ ρ V² N/m². Let's work through the example. Consider air flowing at 52 m/s, which is 100 knots, with a density of 1.225 kg/m³. The conversion: 100 kt = 100 NM/h = 100 × 6080 ft/h = 608,000 ÷ 3.28 = 185,366 ÷ 60 ÷ 60 m/s = 52 m/s. So dynamic pressure = 0.5 × 1.225 × 52 × 52 = 1656 N/m², which is 16.56 hPa. Here's the key relationship: if speed is doubled, dynamic pressure will be four times greater. Let's check: 0.5 × 1.225 × 104 × 104 = 6625 N/m², which is 66.25 hPa. Exactly four times. That's because of the V² term. If the cross-sectional area of the tube is 1 m², a force of ½ ρ V² newtons will be generated, since Force = Pressure × Area. Dynamic pressure, ½ ρ V², is common to ALL aerodynamic forces and determines the air loads imposed on an aeroplane moving through the air. The symbol for dynamic pressure is q or Q, so Q = ½ ρ V². This is the single most important quantity in flight — lift, drag, all of it scales with dynamic pressure. And you can see the airspeed indicator schematic in the figure if you want to see how we actually measure it.