![]() ![]() We could look at the upper and lower surface velocities at several points along the chord and find that at any point we can model that local flow by a “uniform” flow and a circular type flow as shown in Figure 3.3. This, in fact, works very well and is the basic idea behind the way an aerodynamicist would model the flow around an airfoil. If these two flows can be said to end up giving the same result, the flow shown in Figure 3.2 can be said to be a way to model the flow around an airfoil. Figure 3.2: Model of Upper/Lower Surface Speed Difference Figure 3.1: Upper/Lower Surface Speed Difference Gives LiftĪnother way to represent this same flow would be with a combination of a “uniform” flow and a circular flow, such that the velocities add on top of the wing and subtract on the bottom as shown below. If we look at the flow at a point some distance behind the leading edge of an airfoil we will find that we could represent it somewhat as shown in the figure below with a large velocity vector on top of the airfoil and a smaller one on the bottom. If this occurs, Bernoulli’s equation would tell us that the faster flow over the upper surface will give a lower pressure than the slower flow over the lower surface and this pressure differential will produce lift. 3.1 Airfoils (2-D Aerodynamics)įor an airfoil or wing to product lift the flow over its upper surface must move faster than the flow over its lower surface. Let’s begin by looking at the flow around a lifting airfoil. In order to develop the desired “back of the envelope” methods of looking at some basic influences of airfoil and wing shape on aerodynamics and performance we need to first take a quick look at how an aerodynamicist would make a mathematical model of a wing or airfoil. We will do this, not through the type of thorough analysis that would be found in most good aerodynamic textbooks, but with a couple of somewhat over simplified approaches that are, nonetheless, often useful. In this chapter we are going to take a very elementary look at these two fundamental wing and airfoil configuration effects, just enough of a look so we will have at least one or two basic tools that might help us find out something about the effects of wing design on aircraft performance should we need to do so. We learned that there is a certain type of spanwise lift distribution on a three dimensional wing that will give “optimum” aerodynamic performance by giving “minimum induced drag” and we found that higher aspect ratio wing planforms also give better performance than wings with low AR. We might be curious as to how much of a change camber can give in the zero lift angle of attack. We learned, for example, that the camber of an airfoil will determine the angle of attack at which the airfoil lift coefficient is zero and that we can temporarily change camber with things like wing warping or its modern equivalent, “morphing”, or, in a more conventional manner with flaps. We looked at some of the basic conclusions that come from an analysis of two and three dimensional flow around airfoils and wings. In chapter one we looked at a few basic concepts relevant to the first three topics above with an emphasis on the incompressible flow regime and, hopefully, enough discussion of the assumptions involved for the reader to recognize when he or she is in danger of the need to account for transonic or supersonic flow effects. Other, even more specialized, segments of the aerodynamics field might include such topics as rarefied gas dynamics and magneto-hydrodynamics.
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