James W. Gregory - Introduction to Flight Testing

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In this chapter, we will discuss the properties of the environment for flight testing – Earth's atmosphere. It is critical to understand the nature of the atmosphere, since aircraft performance depends significantly on the properties of air. For example, the lift produced by the aircraft is proportional to the air density, and the amount of power produced by an internal combustion engine also varies with density. For these two reasons, aircraft performance decreases as density decreases. We will see in this chapter that density decreases with altitude, so key aircraft performance metrics such as takeoff distance, rate of climb, acceleration, etc. all degrade with altitude. Since aircraft performance depends significantly on the local properties of air, we need some way to factor out altitude effects. We also need to be able to predict the performance of an aircraft as a function of altitude, once its baseline performance is known. Thus, we need an agreed‐upon standard definition of the properties of the atmosphere – this is the standard atmosphere. Definition of the standard atmosphere allows us to evaluate and compare aircraft performance in a consistent manner, no matter what the altitude is.

The important atmospheric parameters are the atmospheric temperature, pressure, density, and viscosity, which depend on the distance from the earth surface, geographic location, and time. In order to describe the atmosphere in a universal way, a standard atmosphere model has been developed, where the atmospheric parameters are determined as the univariate functions of altitude from sea level. Temperature exhibits strong variations with time of year, geographic location, and altitude. And, on a daily basis, temperature depends on current weather conditions in a stochastic manner. It is impossible to develop a first‐principles model that will capture all of these parameters that influence the temperature profile; thus, the standard temperature profile is determined from an average of a large ensemble of atmospheric measurements. The variation of pressure with altitude, however, is rigorously described by some basic physical principles – we will derive these here. In fact, pressure is so intricately and reliably linked to altitude that aircraft altimeters measure pressure and convert the measurement to an indicated altitude through the definition of the standard atmosphere. Density is related to the estimated value of temperature and the derived value of pressure via the ideal gas law. Finally, we will provide a relationship that determines the viscosity of air as a function of temperature. Based on these developments, we will define a standard atmosphere that can be expressed in tabular form, or equations coded for computational analysis. This chapter will start with a physical description of the atmosphere and then present a detailed development of the standard atmosphere. Most of the development of the standard atmosphere presented in this chapter will rely on SI units, since this was the unit system used to define the standard atmosphere and the boundaries of atmospheric regions. The input and output of the standard atmosphere can be easily converted from SI units to English units as needed.