Flight Theory and Aerodynamics. Joseph R. Badick

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2 Atmosphere, Altitude, and Airspeed Measurement

      CHAPTER OBJECTIVES

      After completing this chapter, you should be able to:

PROPERTIES OF THE ATMOSPHERE

      The aerodynamic forces and moments acting on an aircraft in flight are due, in great part, to the properties of the air mass in which the aircraft is flying. By volume, the atmosphere is composed of approximately 78% nitrogen, 21% oxygen, and 1% other gases. The most important properties of air that affect aerodynamic behavior are its static pressure, temperature, density, and viscosity.

It is important to remember at this point that air is a fluid, and like other gases takes on the shape of its container. Just as a liquid can fill a container, air has the capacity to expand and fill the container as well, though the density will differ significantly. Throughout this textbook, we will expand on this introduction to the fluid properties of air, especially as it relates to an airfoil and ultimately the impact on aircraft performance calculations.

      Static Pressure

The static pressure of the air, P, is simply the weight per unit area of the air above the level under consideration. Air has mass and as we have discussed thus has weight, which means it exerts a force. For instance, the weight of a column of air with a cross‐sectional area of 1 ft² and extending upward from sea level through the atmosphere is 2116 lb. The sea level static pressure is, therefore, 2116 pounds per square foot (psf), or 14.7 pounds per square inch (psi). Another commonly used measure of static pressure is inches of mercury. On a standard sea level day, the air’s static pressure will support a column of mercury (Hg) that is 29.92″ high (Figure 2.1). Weather reports express pressure in millibars; standard atmospheric pressure is 1013.2 mb. In addition to these rather confusing systems, there are the metric measurements in use throughout most of the world. For the discussion of performance problems in this textbook, we will primarily use the measurement of static pressure in inches of mercury is the standard used unless stated otherwise.

Static pressure is reduced as altitude is increased because there is less air weight above. At 18 000 ft altitude, the static pressure is about half that at sea level, the higher you go the less air there is above. The accepted standard pressure lapse rate is approximately 1″ Hg decrease in pressure for every 1000 ft gain in altitude from sea level (Figure 2.2). This change in atmospheric pressure with altitude is an important concept during evaluation of aircraft performance as well as the operation of aircraft flight instruments.

Figure 2.1 Standard pressure.

      Source: U.S. Department of Transportation Federal Aviation Administration (2008a).

Figure 2.2 Properties of a standard atmosphere.

      Source: U.S. Department of Transportation Federal Aviation Administration (2016b).

      In aerodynamics, it is convenient to use pressure ratios, rather than actual pressures; thus the units of measurement are canceled out. When at sea level on a standard day, the pressure ratio can be determined using equation:

      (2.1)

      where P₀ is the sea level standard static pressure (2116 psf or 29.92″ Hg). Thus, a pressure ratio of 0.5 means that the ambient pressure is one‐half of the standard sea level value. At 18 000 ft, on a standard day, the pressure ratio is 0.4992.

      Temperature

      The commonly used measures of temperature are the Fahrenheit, °F, and Celsius, °C scales. Aviation weather reports for pilots, as well as performance calculation tables, will usually report the temperature in °C. In a standard atmosphere, the sea level surface temperature is 15 °C or 59 °F.

Since neither of these scales has absolute zero as a base, neither can be used in calculations; absolute temperature must be used instead. Absolute zero is −460 °F, or −273 °C. To convert from the Fahrenheit system to the absolute system, called Rankine, R, add 460 to the °F. To convert from the Celsius system to the absolute system, called Kelvin, K, add 273 to the °C. The symbol for absolute temperature is T and the symbol for sea level standard temperature is T₀:

      By using temperature ratios, instead of actual temperatures, the units cancel. The temperature ratio is the Greek letter theta, θ:

(2.2)

      At sea level, on a standard day, θ_0° = 1.0. Temperature in a standard atmosphere decreases with altitude until the tropopause is reached (36 089 ft on a standard day). The rate of change of temperature with altitude is known as the lapse rate. The standard lapse rate is approximately a 2 °C decrease in temperature for every 1000 ft increase in altitude from sea СКАЧАТЬ