Introduction to Flight Testing. James W. Gregory

Introduction to Flight Testing - James W. Gregory


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2.1, we can write expressions for the temperature profile throughout the standard atmosphere as

      Source: Data from NOAA et al. 1976.

Region h1(km) h2(km) a = dT/dh(K/km)
Troposphere 0 11 −6.5
Stratosphere 11 20 0.0
20 32 1.0
32 47 2.8
47 51 0.0
Mesosphere 51 71 −2.8
71 84.852 −2.0

      h1 and h2 are the beginning and ending altitudes of each region, respectively.

Graph depicts the standard temperature profile.

      2.2.4 Viscosity

      We also need to define an expression for dynamic viscosity, μ, which depends on temperature. The most significant impact of viscosity is in the definition of Reynolds number,

      (2.11)italic Re Subscript c Baseline equals StartFraction rho upper U Subscript infinity Baseline c Over mu EndFraction comma

      which is an expression of the ratio of inertial to viscous forces (here, U is the freestream velocity or airspeed, and c is the mean aerodynamic chord of the wing). Reynolds number has a significant impact on boundary layer development and aerodynamic stall, as we will see in Chapter 12.

      The viscosity of air is related to the rate of molecular diffusion, which is a function of temperature (Sutherland 1893). This relationship has been distilled down to Sutherland's Law,

      (2.13)nu equals StartFraction mu Over rho EndFraction period

      Source: Based on NOAA et al. 1976.

SI English
β 1.458 × 10−6 kg/(s m K1/2) 2.2697 × 10−8 slug/(s ft ° R1/2)
S visc 110.4 K 198.72 ° R

      2.2.5 Pressure and Density

      To derive an expression for the variation of pressure with altitude, we need to integrate the hydrostatic equation. Since density and gravitational acceleration also vary with altitude, we need to cast the hydrostatic equation in terms of only pressure and altitude, with all other variables being constant. We will work with the hydrostatic equation shown in Eq. (2.5), based on geopotential altitude and constant gravity. Density can be expressed as a function of pressure and temperature via the equation of state for a perfect gas,

      Equation


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