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→The International Standard Atmosphere: fix typo
In the simplified model, it is assumed that the density of air is a constant. The Equation of State clearly says otherwise: density depends on pressure and pressure depends on density. Here we run into a problem and the problem can no longer be solved by simple algebra: the powerful mathematical tool of calculus must be used.
Even this is under the assumption that the temperature is a constant. The additional complexity is that the temperature in the atmosphere varies greatly, and you can feel this quite easily by climbing onto a hill and note the temperature drop (just make sure you use a thermometer instead of feeling, to isolate the effect of windchill). At low altitudesbefore the cloud base is reached, as a rule of thumb, the temperature will reduce by 0.6°C 3°C for every 100 meters1000 feet' raise s rise of altitude. This is known as the dry adiabatic lapse rate.
The temperature of the air greatly depends on the heat transfer between the ground and the air: it is the ground that absorbs the radiation from the sun and heats up, the air is transparent so the absorptivity is quite low in the visible spectrum. Generally, the higher the altitude, the less heat the air will get from the ground, and, as a result, the air will become cooler. This applies until the tropopause is reached, beyond which the temperature ceases to decrease and, in fact, starts to increase again at higher altitudes. Gliders almost never reach the tropopause, so we can ignore this complexity.
=== The International Standard Atmosphere ===
The '''International Standard Atmosphere (ISA)''' is a '''model''' for the atmosphere widely used in aviation. It is established based on extensive observations. It is not meant to be exact as the atmospheric conditions can vary actively (especially at low altitudes, knows known as weather). Also, the temperature in the atmosphere at low levels is subject to seasonality as we well understand. Despite these factors, the ISA is a good model and perhaps the most acceptable one to be used if some aviation equipment is to be designed.
The modelling approach of the ISA is to divide the atmosphere into several layers, within each layer the static temperature is assumed to vary linearly. If \(T\) is known, it is then possible to use the theories as described before to solve for the density and the static pressure simultaneously.
