How does an Airfoil Generate Lift ?

How does an Airfoil Generate Lift
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Any moving object through fluid creates a velocity and pressure field around itself and generates a resultant force. This force can be considered to be composed of two components, one normal and another one tangent to the flight path of that object. These forces are called lift and drag force respectively in aerodynamics.

lift drag force

Force Representation around an Airfoil

Flow around some special group of geometries generates more lift force compared to drag force. These geometries are called airfoils and they are characterised with their droplet shaped geometry. Such a geometry generates lift efficiently.

Generation of lift and drag is related to how the fluid particles around an object are deflected due to presence of the geometry. By experiments and nondimensionalization analyses, these forces are considered to be a function of  the dynamic pressure of the flow and wing area. According to that function, as wing area and/or dynamic pressure increase(s), lift and drag force increases. A coefficient ties these factors and the generated force in the form of the equation below:

Force = Coefficient x Dynamic Pressure x Area 

In the case of lift force

L=0.5\rho V^2SC_L

and drag force

D=0.5\rho V^2SC_D

The factors are defined as lift and drag coefficients. These coefficients are dimensionless and are functions of flow regime and configuration of airfoil. Configuration of airfoil is represented by the angle of attack of airfoil, and flow regime is represented by the Reynolds and Mach numbers. Reynolds number is a measure of dominance of the effect of viscosity over an airfoil. The higher the Reynolds number is, the lower the viscosity dominated area in the flow is. Mach number is a measure of how close the flow around airfoil to the sonic speed. This number represents the compressibility of flow. Shockwaves can occur in the flow regions where Mach number is beyond unity.

In early times, aerodynamicists simplified the calculation of lift by the assumption of incompressible inviscid flow and  found mathematical expressions which model the flow. In one of these models, the geometry is replaced by a vortex sheet, which bends the fluid particles the same as the geometry does. This vortex distribution in the geometry boundaries models the velocity distribution around an airfoil. This velocity distribution gives us the pressure distribution according to Bernoulli’s principle. At the same time, integration of that velocity distribution over the airfoil gives circulation which gives us the lift coefficient.

lift generation

Generation of Lift Induced by the Vortices

When upper and lower part of an airfoil is symmetrical by the horizontal axis, vortex distribution on the upper side is same in magnitude but different in terms of sign. Therefore there is no net circulation when the resultant velocity distribution is integrated which corresponds to the zero lift. However, when the airfoil is cambered, or there is an angle of attack, it generates an asymmetry in the vortex distibution in such a way that there is a net positive circulation, which creates a velocity difference accompanied by a pressure difference on the upper and lower surfaces, or vice versa. If the airfoil is positively cambered and/or there is a positive angle of attack, the circulation is positive. Imagining the direction of such a circulation as the clockwise direction, the effect of the circulation is to accelerate the flow on the upper part and to make the opposite effect on the lower part in average corresponding to lower pressure on the upper surfaces in comparison with the lower surface in average terms. This pressure imbalance is responsible for the generation of lift.

Here is a great video to learn about how does an airfoil generate lift?

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I am an aerospace engineer specializing on aerodynamics. My aim is to introduce the basic concepts of aerodynamics to aviation enthusiasts as simple as possible.
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