Fundamentals of Aerodynamics
Aerodynamics theory has its applications in both race cars and aircrafts. Their importance and principles in practice are equally significant.
This guide explores the fundamental theory behind aerodynamics and the simple characteristics of airfoils.
Airfoil Forces
When fluid flows past an object, the forces that act on the object are:
- Drag (Parallel to flow)
- Lift (Perpendicular to flow)
The stresses that act on the object are:
- Shear stress (tangential to surface)
- Pressure stress (perpendicular to surface)
Shear stress is caused by frictional forces from fluid viscosity. Pressure stress is caused by differences in pressure along the airfoil to create a pressure distribution.
A resultant force, which has components of lift and drag, is generated from shear and pressure stress.
Starting Vortex and Circulation
In hindsight, fluid viscosity is required to generate lift, otherwise there would be no shear stress. The effects of viscosity create a starting vortex close to the trailing edge of the wing in counter-clockwise direction, which produces the proper conditions for lift.
To satisfy the conservation of angular momentum, there is a counter circulation around the wing.
The addition velocity from the counter circulation results in a higher velocity above the wing and lower velocity below the wing.
Upwash and downwash are also generated by the counter circulation near the leading and trailing edge respectively.
The counter circulation is shown in the direction of curve C4 in the figure below.
Without the counter circulation, there would be an infinite change in velocity around the trailing edge, shown in the below figure, which is impossible.
Kutta Condition
The Kutta condition states that the flow at the trailing edge must be parallel to the airfoil surface since it is generating a counter circulation. By assuming flow is parallel to the surface, the unrealistic phenomenon of infinite velocity change at the trailing edge is eliminated and the right conditions are set for calculating the counter circulation.
Lift Generation
The difference in pressure above and below the airfoil creates lift. There are currently two popular and debated explanations for where the pressure distribution comes from:
- Bernoulli’s principle
- Newton’s 3rd law
Bernoulli’s principle states that as the velocity of a fluid increases, the pressure decreases. For an airfoil, the velocity of a fluid is greater on the top than on the bottom because of the counter circulation. Thus, the pressure at the bottom must be higher than the top, creating a pressure gradient pushing the airfoil upwards.
Newton’s 3rd law states that an airfoil must be creating a counter force to the downwash force near the trailing edge of the airfoil caused by the counter circulation. The counter force to the downwash is the lift force.
Airfoil Profiles
An airfoil is a cross section of a wing. The difference between an airfoil between any generic object is that an airfoil is optimized to produce less drag and more lift.
An airfoil profile is defined by the leading edge, trailing edge, chord, angle of attack, and camber line. The figure below shows the parameters that define the airfoil profile.
The leading edge is the forward most edge, and the trailing edge is the back most edge. The chord line is a straight line distance between the leading and trailing edges.
The camber line or mean camber line joins the two edges with a line that is equidistant to the upper and lower surfaces. The angle of attack is the angle between the chord line and the incoming opposing flow.
The camber describes how curved an airfoil is. A positive camber describes a concave airfoil and a negative camber describes a convex airfoil. The figure below shows the differences in camber.
Effect of Camber and Angle of Attack
Increasing the camber or angle of attack will allow the airfoil to deflect more fluid and change the pressure distribution, thus increasing the lift generated.
However, increasing the angle of attack past a threshold, typically around 16 degrees, will result in stall or a sudden decrease in lift. The high angle of attack creates a wake region or separation region behind the airfoil which affects the pressure distribution.
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