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A Rotating Cylinder in a Moving Fluid
When the cylinder rotates in a fluid that is also moving, the result is a higher circulatory flow in the direction of the rotating cylinder. [Figure 3-3C] By adding fluid motion, the magnitude of the flow increases.
The highest differences of velocity are 90° from the relative motion between the cylinder and the airflow. Additionally, and as shown in Figure 3-4, at point “A,” a stagnation point exists where the air stream impacts (impinges) on the front of the airfoil’s surface and splits; some air goes over and some under. Another stagnation point exists at “B,” where the two airstreams rejoin and resume at identical velocities. When viewed from the side, an upwash is created ahead of the airfoil and downwash at the rear.
In the case of Figure 3-4, the highest velocity is at the top of the airfoil with the lowest velocity at the bottom. Because these velocities are associated with an object (in this case, an airfoil) they are called local velocities as they do not exist outside the lift-producing system, in this case an airfoil. This concept can be readily applied to a wing or other lifting surface. Because there is a difference of velocity above and below the wing, the result is a a higher pressure at the bottom of the wing and a lower pressure on the top of the wing.
3-6
A.
Flow of air against a nonrotating cylinderB. Rotating cylinder in a fluidD. Leading edge of wing C. Rotating cylinder in a moving fluidE. Leading edge of wing under 1,500x magnification BABALeading edge
Figure 3-3. A illustrates uniform circulation. B illustrates the increased airflow over the top of a rotating cylinder. The airflow speed is further increased when the rotating cylinder is in a moving stream of air (C). The air molecules near the surface of an object are slowed and almost stationary. D is an example of typical aircraft grade aluminum used in aircraft construction to include wings and leading edges of wings as shown in E (left). When magnified at 1,500x (E, right), polished aluminum is visibly rough. This demonstrates why airflow is affected by molecular irregularities of the surface.
3-7
F
igure 2-3. Air circulation.BATrailing edge stagnation pointLeading edge stagnation point
Figure 3-4. Air circulation around an airfoil occurs when the front stagnation point is below the leading edge and the aft stagnation point is beyond the trailing edge.
F
igure 2-4. Air pressure decreases in a venturi.86420I0VELOCITYOC86420I0PRESSURES86420I0VELOCITY86420I0PRESSUREPR86420I0VELOCITYOC86420I0PRESSURES
Figure 3-5. Air pressure decreases in a venturi tube.
This low-pressure area produces an upward force known as the Magnus Effect, the physical phenomenon whereby an object’s rotation affects its path through a fluid, to include air. Two early aerodynamicists, Martin Kutta and Nicolai Joukowski, eventually measured and calculated the forces for the lift equation on a rotating cylinder (the Kutta-Joukowski theorem).
To summarize the Magnus effect, an airfoil with a positive AOA develops air circulation about the upper surface of the wing. Its sharp trailing edge forces the rear stagnation point to be aft of the trailing edge, while the front stagnation point falls below the leading edge. [Figure 3-4]Bernoulli’s Principle of Differential Pressure
A half-century after Newton formulated his laws, Daniel Bernoulli, a Swiss mathematician, explained how the pressure of a moving fluid (liquid or gas) varies with its speed of motion. Bernoulli’s Principle states that as the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. This principle explains what happens to air passing over the curved top of the airplane wing.
A practical application of Bernoulli’s Principle is the venturi tube. The venturi tube has an air inlet that narrows to a throat (constricted point) and an outlet section that increases in diameter toward the rear. The diameter of the outlet is the same as that of the inlet. At the throat, the airflow speeds up and the pressure decreases; at the outlet, the airflow slows and the pressure increases. [Figure 3-5]
Since air is recognized as a body and it is accepted that it must follow the above laws, one can begin to see how and why an airplane wing develops lift. As the wing moves through the air, the flow of air across the curved top surface increases in velocity creating a low-pressure area.
Although Newton, Magnus, Bernoulli, and hundreds of other early scientists who studied the physical laws of the universe did not have the sophisticated laboratories available today, they provided great insight to the contemporary viewpoint of how lift is created.
Airfoil Design
An airfoil is a structure designed to obtain reaction upon its surface from the air through which it moves or that moves past such a structure. Air acts in various ways when submitted to different pressures and velocities; but this discussion is confined to the parts of an aircraft that a pilot is most concerned with in flight—namely, the airfoils designed to produce lift. By looking at a typical airfoil profile, such as the cross section of a wing, one can see several obvious characteristics of design. [Figure 3-6] Notice that there is a difference in the curvatures (called cambers) of the upper and lower surfaces of the airfoil. The camber of the upper surface is more pronounced than that of the lower surface, which is usually somewhat flat.
　
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