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The Science of Air Foils



Air layers in vicinity of tiny flat foil.
Note 1.
The is a fluid stream front
Note 2. There are 2 types of friction:
a) Friction between the lowest air stream and the foil. The friction bends the layer front into foil surface. This results in "dynamic sticking to the surface".
b) Friction between different layers of streams (dynamic viscosity). The lower layer of the stream drags and bends down the upper neighboring layer.


Note 3. The stream layers have velocities gradient along the normal to foil surfaces.
Note 4. The figure is simplified - the foil is considered to be very thin. Air flow is laminar. The stream bending (and little compression for air only) is exaggerated in order to show it.
Note 5. The Coanda effect has a dynamic origin - it appears at nonzero relative to fluid and foil speed.



Boundary Layer. Ref.

When the air hits the airfoil leading edge, it will separate into the upper and lower airstrea; which meets again at the trailing edge.





It is obvious that the air, very close to the airfoil, "rubs" against the solid surface and is slowed down. In other words, starting downstream of the impact point, the air loses some of its momentum, or velocity. In addition, it loses more and more momentom as we follow it along the path close to the solid airfoil. We can see that friction creates an area where there is less speed. The reduced speed area, just outside of the airfoil, becomes thicker and thicker as we follow it from the leading edge to the trailing edge. This area is called the boundary layer. Its thickness is increasing as described, and is defined as the thickness at which the local free stream speed is finally reached. A typical boundary layer thickness is 1/2" near the trailing edge. The friction, which obviously is a loss, results in the friction drag of the airfoil.



Ref. Glenn Research Center

Again the theory of fluid dynamics shows that there are two possible types of stable boundary layers Ref. : The first to build up is called 'laminar," because the flow is nice and steady while the friction drag is relatively low.
The second is called 'turbulent," because the flow is rather rough and the friction drag is higher.
Unfortunately, the "laminar boundary layer" will automatically become turbulent (with associated higher drag) close to the leading edge of the airfoil unless very special precautions are taken. These precautions are:



A very smooth airfoil surface: Slight construction defects (or bugs as they stick to the airfoil leading edge) will change the laminar boundary layer into a turbulent one. Unless you have a perfect airfoil and keep it this way, forget about the possible gain with a laminar flow!
A special shape of the airfoil: The pressure distribution on the airfoil is related to the airfoil shape. Today, we can calculate (with high speed computers) airfoils, which maximize the length of the laminar boundary layer. Still, what is mentioned in a) applies. But, do not get desperate. The friction drag of the airfoil with a laminar boundary layer is .08, whereas in turbulent flow it becomes .12. Sure, this is a 50% increase but only on the friction drag of the airfoil.



Lift force of airfoil
Lift depends on the density of the air, the square of the velocity, the air's viscosity and compressibility, the surface area over which the air flows, the shape of the body, and the body's inclination to the flow. In general, the dependence on body shape, inclination, air viscosity and compressibility are very complex.
One way to deal with complex dependencies is to characterize the dependence by a single variable. As for the lift, this variable is called the lift coefficient, designated "Cy." The lift equation states that lift L is equal to the lift coefficient Cy times the density rho times half of the velocity V squared times the wing area A.



Lift force= 1/2*Cy * A * rho * V^2



For given air conditions, shape and inclination of the object, we have to determine a value for Cy to determine the lift. For some simple flow conditions, geometries and low inclinations, aerodynamicists can determine the value of Cy mathematically. But, in general, this parameter is determined experimentally. The combination of terms "density times the square of the velocity divided by two" is called the dynamic pressure.





Actually, the coefficient Cy hides a mechanism of lift (also physics of aerodynamics), but this allows us to collect all the effects, simple and complex, into a single equation. The question, what kind of mechanisms convert the drag force into the lift one, still remains under discussion. If you would like to prepare further research about this issue, you can find useful information in Weltner, Klaus and Ingelman-Sundberg, Martin paper "Physics of Flight".
Notes:
The amount of air diverted by a wing is proportional to the speed of the wing and the air density.
The vertical velocity of the diverted air is proportional to the speed of the wing and the angle of attack.
The lift is proportional to the amount of air diverted times the vertical velocity of the air.

 

Information courtesy of Saulius Pakalnis, Research Support Technologies (researchsupporttechnologies.com)



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