12-11-2012, 04:04 PM
Race Car Aerodynamics
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Introduction
First racing cars were primarily designed to achieve high top speeds and the
main goal was to minimize the air drag. But at high speeds, cars developed
lift forces, which affected their stability. In order to improve their stability
and handling, engineers mounted inverted wings profiles1 generating negative
lift. First such cars were Opel’s rocket powered RAK1 and RAK2 in 1928.
However, in Formula, wings were not used for another 30 years. Racing in
this era 1930’s to 1960’s occured on tracks where the maximum speed could
be attained over significant distance, so development aimed on reducing drag
and potencial of downforce had not been discovered until the late 1960’s.
Flow over an airfoil
Properties of an airfoil can be measured in a wind tunnel, where constant-
chord wing spannes the entire test section, from one sidewall to the other.
In this conditions, the flow sees a wing without wing tips. Such wing is
called infinite wing and streches to infinity along the span. Because the
airfoil section is identical along the wing, the properties of the airfoil and the
infinite wing are identical. Therefore the flow over an airfoil can be described
as a 2D incompressible inviscid flow over an infinite wing.
Thin airfoil theory
Here we discuss thin airfoil in freestream of velocity V∞ under small angle
of attack . Camber and thickness are small in relation with chord length c.
In such case, airfoil can be described with a single vortex sheet distributed
over the camber line(Figure 4). Our goal is to calculate the variation of
(s), such that the chamber line becomes streamline and Kutta condition at
trailing edge,
© = 0, is satisfied.
Finite wings
Properies of airfoils are the same as the properties of a wing of infinite span.
However, all real wing are of finite span and the flow over finite wing is 3
dimensional. Because of higher pressure on the bottom surface of the wing,
the flow tends to leak around the wing tips. This flow establishes a circulary
motion that trails downstream of the wing. A trailing vortex is created at
each wing tip. These wing-tip vortices induce a small downward component
of air velocity, called downwash .
Prandtl’s classical lifting-line theory
The idea of lifting line theory, is to use two dimensional results, and correct
them for the influence of the trailing vortex wake and its downwash. Let’s
replace a finite wing of span b, with a bound vortex2 extending from y = −b/2
to y = b/2. But due to the Helmholtz’s theorem, a vortex filament can’t end
in a fluid. Therefore assume the vortex filament continues as two free vortices
trailing downstream from the wing tips to infinity(Figure 8). This vortex is
due to it’s shape called horseshoe vortex. Downwash induced by such vortex,
does not realistically simulate that of a finite wing, as it aproaches −∞ at
wing tips.
Instead of representing the wing by a single horseshoe vortex, Prandtl su-
perimposed an infinite number of horseshoe vortices, each with an infinites-
imally small strength d