Introduction to Flight Testing. James W. Gregory

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The atmosphere becomes thinner as the altitude increases, and there is no clear boundary between the atmosphere and outer space. However, the Kármán line has been defined at 100 km and is often used as the border between the atmosphere and outer space. Atmospheric effects become noticeable during atmospheric reentry of spacecraft at an altitude of around 120 km. Aircraft propelled by internal combustion engines and propellers are generally limited to operating in the troposphere, while jet‐propelled aircraft routinely operate in the stratosphere.

Schematic illustration of the layers of Earth's atmosphere.

      In contrast with the temperature–altitude profile, the variation of pressure with altitude is highly repeatable and deterministic. Air pressure continually decreases with altitude from Earth's surface all the way to the edge of the atmosphere. The primary reason for this is the action of Earth's gravitational acceleration on air, causing a given mass of air to exert a force on the air below it. Air at a given altitude must support the weight of all of the air mass above it, and it balances this force by pressure. As altitude increases, there is less air mass above that altitude, so there is less force (weight) acting on the air at that point and the pressure decreases. Thus, pressure decreases as altitude increases. We will discuss this physical mechanism in greater detail in Section 2.2, when we derive an expression for the variation of pressure with altitude.

      2.2.1 Hydrostatics

      (2.1)upper W equals italic m g equals rho left-parenthesis italic d x italic d y italic d h Subscript upper G Baseline right-parenthesis g period

Schematic illustration of the forces acting on a hydrostatic control volume.

      (2.2)p italic d x italic d y minus left-parenthesis p plus italic d p right-parenthesis italic d x italic d y minus rho g italic d x italic d y italic d h Subscript upper G Baseline equals 0 period

      Canceling terms leads to

      which is the hydrostatic equation as a function of geometric altitude. This expression mathematically expresses the physical explanation that we presented earlier for the variation of pressure with altitude. As altitude increases (positive dhG), the minus sign indicates that the pressure decreases (negative dp). The ρg term is an expression of the weight of the air inside the control volume, which is the reason for the pressure difference.

      2.2.2 Gravitational Acceleration and Altitude Definitions

      As we proceed with the development of the standard atmosphere, we must consider how gravitational acceleration varies with altitude. From Newton's law of universal gravitation, we know that gravitational acceleration varies inversely with the square of the distance to the center of the earth. Thus, we have

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