CHAPTER 3: AERODYNAMICS AND AIRFOILS
“Isn’t it astonishing that all these secrets have been preserved for so many years just so that we could discover them!!”
3.1 DESIGN MOTIVATION
The Physics of Aerodynamic Forces
Figure 3.1 shows a cross section view of an aircraft wing. A wing cross section like this is called an airfoil. Lines drawn above and below the airfoil indicate how the air flows around it. The shape of the airfoil and the pattern of airflow around it have profound effects on the lift and drag generated by the wing. Aircraft designers choose a particular airfoil shape for a wing in order to optimize its lift and drag characteristics to suite the requirements for a particular mission. It is essential that an aircraft designer understand how the changes that occur in air as it flows past a wing create lift and drag, and how airfoil shape influences this process.
Figure 3.1. Flowfield Around an Airfoil
The Basis for Airspeed Indication
The changes which occur in the properties of moving air as it encounters obstructions provide the basis for the airspeed indicating systems used on most aircraft. An understanding of how these systems work is essential to anyone who designs, builds, or operates aircraft.
3.2 BASIC AERODYNAMICS
A number of terms must be defined to facilitate a discussion of aerodynamics. The lines in Figure 3.1 which indicate how the air flows are known as streamlines. Each streamline is drawn so that at every point along its length, the local velocity vector is tangent to it. A tube composed of streamlines is called a stream tube. In a steady flow, each streamline will also be the path taken by some particle of air as it moves through the flowfield (a region of air flow). A steady flow is defined as one in which the flow properties (pressure, temperature, density and velocity) at each point in the flowfield do not change with time. If, as in Figure 3.2, a streamline runs into an obstruction, the airflow along the streamline comes to a stop at the obstruction. The point where the flow stops is called a stagnation point, and the streamline leading to the stagnation point is called a stagnation streamline.
Figure 3.2. Stagnation Point and Stagnation Streamline
If, at each point along a streamline, there is no variation in the flow properties in a plane perpendicular to the flow direction, the flow is said to be one-dimensional. Figure 3.3 illustrates a flow that is one-dimensional at stations 1 and 2.
Figure 3.3. Flow Which is One-Dimensional at Station 1 and Station 2
The Continuity Equation
Figure 3.3 depicts a flow in a stream tube. Because the walls of the stream tube are composed of streamlines, the velocity vectors are everywhere tangent to the walls of the tube, so no air can pass through the tube walls. The rate at which mass is flowing through a plane perpendicular to a one-dimensional flow is given by:
where is the mass flow rate and A is the cross-sectional area of the stream tube. In nature, in the absence of nuclear reactions, matter is neither created nor destroyed. Therefore, mass which flows into the tube must either accumulate there or else flow out of the tube again. The case where matter is accumulating in the tube like air filling a balloon is an unsteady, time-varying flow. If the flow is a steady flow, then the rate at which mass is flowing into the tube at station 1 must just equal the rate at which mass is flowing out if the system at station 2:
Equation 3.2 is known as the continuity equation. It is a statement of the law of conservation of mass for fluid flows. Applying this equation to the flowfield shown in Figure 3.3 reveals a phenomenon which is...