Lesson 2: Aerodynamic Forces
Section 3 - Physical Quantities of Aerodynamic Motion, Dimensions and Aeronautic Terms
There are a number of physical properties of the air which affect the way it flows and which have to be measured and allowed for. The study of these properties is important to understanding aerodynamics.
FUNDAMENTAL PROPERTIES OF AIR
Three fundamental properties of air are its temperature, density, and pressure.
Temperature, denoted as T, is proportional to the average kinetic energy of the air molecules. The higher the temperature, the greater the molecular motion. At extremely high temperatures associated with high air-speeds energy, this can also be absorbed internally by the molecules causing them to rotate and vibrate.
When this occurs, the air can no longer be considered as an “ideal gas.” Here, the term “real gas effects” is applied to represent the state where internal energy changes also have to be considered.
Density, denoted by the symbol ρ, is the mass per unit volume. Density decreases with altitude and its ratio to sea-level density is the relative density, or:
s = ρ/ ρo
Pressure, p, is the force per unit area exerted on or by the air.
These three quantities are related in the Ideal Gas Equation which is
P/ ρ = R*T/w
Where R* is the universal gas constant, and w is the molecular weight of air.
Gravity, represented by g, involves heating and buoyancy as well as several other phenomena. It is the acceleration which would be experienced by an unrestrained surface arising from the pull of the earth’s gravity. At sea level, this value is approximately 32.2 ft/s2
At high speeds, the air becomes compressed when encountering an object. Other quantities are involved at this point which can be derived from the gas equation. These include:
Compressibility, k, which is the proportional decrease in volume resulting from the application of external pressure on a mass of air.
Coefficient of thermal expansion, ß, which exists in convection and buoyancy effects.
And Specific heat, C, which is the quantity of heat needed to raise the temperature of a unit mass of air by a unit temperature difference.
PROPERTIES OF MOVING AIR
Three other properties of moving air are related to the mechanisms by which momentum, energy and mass are transported on a molecular scale. They are viscosity, thermal conductivity, and diffusivity.
Viscosity, µ, is the measure of the resistance of air to a shearing deformation. The viscosity is the force per unit area needed to maintain a unit velocity difference between layers a unit distance apart. The viscosity of air increases with temperature, but is virtually independent of pressure.
In Kinematic viscosity, v, units used include those of length and time only. V varies with temperature and pressure.
Thermal conductivity, λ, or k, is the quantity of heat that flows through a unit of area per unit of temperature difference.
For the diffusion coefficient, represented by D12, this term expresses the rate of diffusion of one gas or 1 through another or 2. This mixing occurs with water vapor in sweating, or in transpiration cooling when hydrogen is passed through a porous surface in contact with a hot boundary layer to produce a relief in temperature.
DIMENSIONS AND UNITS
The use of Dimensions and Units apply to the study of aerodynamics, but it is important to first establish the difference between the two.
A dimension represents the definition of an inherent physical property which remains independent of the particular scheme used to denote its measure. For example, the quantity of matter present in a lump of metal has the dimension of mass and the physical size of the edge of a book has the dimension of length.
A unit represents the particular, arbitrary scheme used to denote the magnitude of a physical property. In this case, the mass of matter in the lump of metal may be expressed in kilograms or slugs and the length of the book expressed in meters or feet depending on the system of units selected.
Usually the quantity to be measured influences the choice of units to be employed, that is, meters or feet to measure the length of the book rather than kilometers or miles.
Basic Dimensions
There are four basic dimensions of general interest to aerodynamicists. These are called the basic or primary dimensions and are length, mass, time, and temperature. They may be abbreviated by using, respectively, L, M, T, and ø [Greek letter theta].
Derived Dimensions
The dimensions of all other quantities may be found to be combinations of quantities expressible in terms of the basic or primary dimensions. These are known as derived or secondary dimensions. For example, area may be represented as a length times a length or L2.
Angular Measurement
The measure of the central angle of a circle is defined as the ratio of the subtended arc of the circle divided by the radius, that is, a ratio of two lengths. This measure is dimensionless but is assigned a special name of radians.
You can also express the angle in degrees by noting that an angle of 1 radian equals about 57.3°. The fact that both radian measure and degree measure are dimensionless means that the numerical value of an angle does not change from one system of units to another. Systems of Units
There are two basic engineering systems of units in use in aerodynamics. They are the International System of Units (SI) and the British Engineering System of Units (B.E.S.). In 1964 the United States National Bureau of Standards officially adopted the International System of Units to be used in all of its publications. Table I lists the SI and B.E.S. units for both the basic dimensions and some of the more common aerodynamic quantities.
Vectors and Scalars
Vectors are quantities that have both a magnitude and a direction. Examples of physical quantities that are vectors are force, velocity, and acceleration. Thus, when one states that a car is moving north at 100 kilometers per hour, with respect to a coordinate system attached to the Earth, one is specifying the vector quantity velocity with a magnitude (100 kilometers per hour) and a direction (north). Scalars are quantities that have a magnitude only. Examples of physical quantities that are scalars are mass, distance, speed, and density. When one states only the fact that a car is moving at 100 kilometers per hour one has specified a scalar, speed, since only a magnitude (100 kilometers per hour) is given (that is, no direction is specified).
Vectors may be added together (composition) to form one vector (the resultant) or one vector may be broken down (resolution) into several components. The resultant can be resolved back into the lift and drag components. As we continue with this course, there are some definitions which may be helpful to outline. These terms can be found in the following:
General Definitions
AIRCRAFT any machine or weight-carrying device (whether lighter or heavier than air) designed to be supported by the air, either by buoyancy or by dynamic action.
AERODYNE that class of aircraft being heavier than air and deriving it lift in flight chiefly from aerodynamic forces.
AIRPLANE(aeroplane) a subset of aerodynes, specifically, a mechanically driven fixed-wing aircraft, heavier than air, which is supported by the dynamic reaction of the air against its wings.
AERODYNAMICS the science that deals with the motion of air and other gaseous fluids, and of the forces acting on bodies when the bodies are in relative motion with respect to such fluids.
AEROSTAT that class of aircraft being lighter than air and deriving its support chiefly from buoyancy derived from aerostatic forces.
AIRSHIP a subset of aerostats, specifically, an aerostat provided with a propelling system and with a means of controlling the direction of motion.
AEROSTATICS the science that deals with the equilibrium of gaseous fluid and of bodies immersed in them.
AERONAUTICS the science and art of designing, constructing, and operating aircraft.
Bibiliography
Aerodynamics and G. Forces. www.voodoo.cz/falcon/agf.html.
Allen, John E. Aerodynamics: A Space Age Survey. New York: Harper & Row, 1963.
Glenn Research Center. Beginner’s Guide to Aerodynamics. www.grc.nasa.gov/www/K-12/airplane/bga.html.
Taley, Theodore A. Introduction to the Aerodynamics of Flight. Science and Technical Information Office. Wash, D.C.: NASA. 1975.
Von Braun, Wernher, Ordway, III, F. I., and Dooling, D. Space Travel: A History. New York: Harper & Row, 1985.
Wegener, Peter P. What Makes Airplanes Fly? New York: Springer-Verlag, 1991.
