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The Earth's atmosphere is an extremely thin sheet of air extending from the surface of the Earth to the edge of space. If the Earth were the size of a basketball, a tightly held pillowcase would represent the thickness of the atmosphere. Gravity holds

the atmosphere to the Earth's surface. Within the atmosphere, very complex chemical, thermodynamic, and fluid dynamics

effects occur. The atmosphere is not uniform; fluid properties are constantly changing with time and place. We call this

change the weather.

Variations in air properties extend upward from the surface of the Earth. The sun heats the surface of the Earth, and some of

this heat goes into warming the air near the surface. The heated air is then diffused or convected up through the

atmosphere. Thus the air temperature is highest near the surface and decreases as altitude increases. The speed of sound

depends on the temperature and also decreases with increasing altitude. The pressure of the air can be related to the weight of the air over a given location. As we increase altitude through the atmosphere, there is some air below us and

some air above us. But there is always less air above us than was present at a lower altitude. Therefore, air pressure

decreases as we increase altitude. The air density depends on both the temperature and the pressure through the equation

of state and also decreases with increasing altitude.

Aerodynamic forces directly depend on the air density. To help rocket designers, it is useful to define a standard

atmosphere model of the variation of properties through the atmosphere. There are actually several different models

available--a standard or average day, a hot day, a cold day, and a tropical day. The models are updated every few years to

include the latest atmospheric data. The model was developed from atmospheric measurements that were averaged and

curve fit to produce the given equations. The model assumes that the pressure and temperature change only with altitude. The particular model shown here was developed in the early sixties, and the curve fits are given in Metric units. Curve fits are

also available in English units.

The model has three zones with separate curve fits for the troposphere, the lower stratosphere, and the upper stratosphere. The troposphere runs from the surface of the Earth to 11,000 meters. In the troposphere, the temperature decreases linearly

and the pressure decreases exponentially. The rate of temperature decrease is called the lapse rate. For the temperature T

and the pressure p, the metric units curve fits for the troposphere are:

T = 15.04 - .00649 * h

p = 101.29 * [(T + 273.1)/288.08]^5.256

where the temperature is given in Celsius degrees, the pressure in kilo-Pascals,and h is the altitude in meters. The lower

stratosphere runs from 11,000 meters to 25,000 meters. In the lower stratosphere the temperature is constant and the

pressure decreases exponentially. The metric units curve fits for the lower stratosphere are:

T = -56.46

p = 22.65 * exp(1.73 - .000157 * h)

The upper stratosphere model is used for altitudes above 25,000 meters. In the upper stratosphere the temperature

increases slightly and the pressure decreases exponentially. The metric units curve fits for the upper stratosphere are:

T = -131.21 + .00299 * h

p = 2.488 * [(T + 273.1)/ 216.6]^-11.388

In each zone the density r is derived from the equation of state.

r = p / [.2869 * (T + 273.1)]

This is the atmosphere model used in the RocketModeler II simulator. An interactive simulation for the atmosphere model is

also available. With the applet, you can change altitude and see the effects on pressure and temperature.

Guided Tours

Standard Atmosphere Model: Atmosphere Simulator:

Activities:

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Earth Atmosphere Model - Metric Units 12/19/2013

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