BASIC AERODYNAMICS

In order to understand the characteristics of his aircraft and develop precision flying tech­niques, the Naval Aviator must be familiar with the fundamentals of aerodynamics. There are certain physical laws which describe the behavior of airflow and define the various aerodynamic forces and moments acting on a surface. These principles of aerodynamics pro­vide the foundations for good, precise flying techniques.

WING AND AIRFOIL FORCES

PROPERTIES OF THE ATMOSPHERE

The aerodynamic forces and moments acting on a surface are due in great part to the prop­erties of the air mass in which the surface is operating. The composition of the earth’s atmosphere by volume is approximately 78 percent nitrogen, 21 percent oxygen, and 1percent water vapor, argon, carbon dioxide, etc. For the majority of all aerodynamic con­siderations air is considered as a uniform mixture of these gases. The usual quantities used to define the properties of an air mass are as follows:

STATIC PRESSURE. The absolute static pressure of the air is a property of primary importance. The static pressure of the air at any altitude results from the mass of air supported above that level. At standard sea level conditions the static pressure of the air is 2,116 psf Cor 14.7 psi, 29-92 in. Hg, etc.) and at 40,000 feet altitude this static pressure decreases to approximately 19 percent of the sea level value. The shorthand notation for the ambient static pressure is “p” and the standard sea level static pressure is given the subscript "0" for zero altitude, p0. A more usual reference in aerodynamics and perform­ance is the proportion of the ambient static pressure and the standard sea level static pressure. This static pressure ratio is assigned the shorthand notation of 8 (delta).

Altitude pressure ratio

_____ Ambient static pressure

Standard sea level static pressure

5 = p/po

Many items of gas turbine engine perform­ance are directly related to some parameter involving the altitude pressure ratio.

TEMPERATURE. The absolute tempera­ture of the air is another important property. The ordinary temperature measurement by the Centigrade scale has a’datum at the freezing point of water but absolute zero temperature is obtained at a temperature of —273° Centi­grade. Thus, the standard sea level tempera­ture of 15° C. is an absolute temperature of 288°. This scale of absolute temperature using the Centigrade increments is the Kelvin scale, e. g., 0 K. The shorthand notation for the ambient air temperature is “T” and the stand­ard sea level air temperature of 288° K. is signified by T0. The more usual reference is
the proportion of the ambient air temperature and the standard sea level air temperature. This temperature ratio is assigned the short­hand notation of в (theta).

Temperature ratio

Ambient air temperature ""Standard sea level air temperature e=T/r0 „ C°+273

Many items of compressibility effects and jet engine performance involve consideration of the temperature ratio.

DENSITY. The density of the air is a prop­erty of greatest importance in the study of aerodynamics. The density of air is simply the mass of air per cubic foot of volume and is a direct measure of the quantity of matter in each cubic foot of air. Air at standard sea level conditions weighs 0.0765 pounds per cubic foot and has a density of 0.002378 slugs per cubic foot. At an altitude of 40,000 feet the air density is approximately 25 percent of the sea level value.

The shorthand notation used for air density is p (rho) and the standard sea level air density is then po. In many parts of aerodynamics it is very convenient to consider the proportion of the ambient air density and standard sea level air density. This density ratio is assigned the shorthand notation of cr (sigma).

, . . ambient air density

ensity ratio stan(jar(j sea level air density

<r = p/po

A general gas law defines the relationship of pressure temperature, and density when there is no change of state or heat transfer. Simply stated this would be "density varies directly with pressure, inversely with temperature." Using the properties previously defined,

_ pressure ratio temperature ratio

-да

=&/e

This relationship has great application in aerodynamics and is quite fundamental and necessary in certain parts of airplane perform­ance.

VISCOSITY. The viscosity of the air is important in scale and friction effects. The coefficient of absolute viscosity is the propor­tion between the shearing stress and velocity gradient for a fluid flow. The viscosity of gases is unusual in that the viscosity is gen­erally a function of temperature alone and an increase in temperature increases the viscosity. The coefficient of absolute viscosity is assigned the shorthand notation ц (mu). Since many parts of aerodynamics involve consideration of viscosity and density, a more usual form of viscosity measure is the proportion of the co­efficient of absolute viscosity and density. This combination is termed the “kinematic viscosity” and is noted by v (nu).

kinematic viscosity

coefficient of absolute viscosity
density

v = n/p

The kinematic viscosity of air at standard sea level conditions is 0.0001576 square feet per second. At an altitude of 40,000 feet the kinematic viscosity is increased to 0.0005059 square foot per second.

In order to provide a common denominator for comparison of various aircraft, a standard atmosphere has been adopted. The standard atmosphere actually represents the mean or average properties of the atmosphere. Figure 1.1 illustrates the variation of the most im­portant properties of the air throughout the standard atmosphere. Notice that the lapse rate is constant in the troposphere and the stratosphere begins with the isothermal region.

Since all aircraft performance is compared and evaluated in the environment of the stand­ard atmosphere, all of the aircraft instrumenta­tion is calibrated for the standard atmosphere.

Thus, certain corrections must apply to the instrumentation as well as the aircraft per­formance if the operating conditions do not fit the standard atmosphere. In order to prop­erly account for the nonstandard atmosphere certain terms must be defined. Pressure altitude is the altitude in the standard atmosphere corresponding to a particular pressure. The aircraft altimeter is essentially a sensitive barometer calibrated to indicate altitude in the standard atmosphere. If the altimeter is set for 29-92 in. Hg the altitude indicated is the pressure altitude—the altitude in the stand­ard atmosphere corresponding to the sensed pressure. Of course, this indicated pressure altitude may not be the actual height above sea level due to variations in temperature, lapse rate, atmospheric pressure, and possible errors in the sensed pressure.

The more appropriate term for correlating aerodynamic performance in the nonstandard atmosphere is density altitude—the altitude in the standard atmosphere corresponding to a particular value of air density. The computa­tion of density altitude must certainly involve consideration of pressure (pressure altitude) and temperature. Figure 1.6 illustrates the manner in which pressure altitude and tem­perature combine to produce a certain density altitude. This chart is quite standard in use and is usually included in the performance section of the flight handbook. Many subject areas of aerodynamics and aircraft performance will emphasize density altitude and temperature as the most important factors requiring con­sideration.