### No, Cars Are Not Wings

It’s a
common refrain: “Cars are shaped like wings, so they make lift.”

Shockingly, one of these was published by a major automotive magazine. |

*airfoils*). Here’s why.

**Airfoils**

The
behavior of airfoils is described by a branch of aerodynamics called Thin
Airfoil Theory (TAT) that is well-developed and characterized by straightforward math
that can, to a surprisingly high degree of accuracy, predict the performance of
wings. Theodore von Kármán wrote in 1954:

“Mathematical
theories from the happy hunting grounds of pure mathematicians are found
suitable to describe the airflow produced by aircraft with such excellent
accuracy that they can be applied directly to aircraft design.”

This is
possible because any low-speed airfoil, so long as it is thin (i.e. has a
thickness 20% or less the length of its chord;

-have a
sectional lift slope (lift coefficient

-conform to the Kutta condition (upper and lower surface velocities are equal in magnitude and direction at the trailing edge) and Kutta-Joukowski Theorem (lift is proportional to circulation—a property related to the difference in velocities along the upper and lower surfaces—around the airfoil)

-can be approximated as flat and horizontal, allowing the prediction of lift solely based on pressure

The Kutta
condition has been interpreted incorrectly by many people unfamiliar with TAT,
and consequently has led to the idea that the “equal transit theorem” explains
the lift of airfoils (and cars). The equal transit theorem states that two
fluid elements adjoining one another before splitting to travel over the
airfoil’s upper and lower surfaces must come together at the trailing edge, the
upper element having traveled a slightly further distance in the same time (due
to the curved upper surface and flat lower surface—similar to a car),
therefore moving faster and resulting in pressure less than on the flat lower
surface. There are a few problems with this: if it were true, airplanes could
not fly upside down; most airfoils have curved upper

In
reality,

*h*≤ 0.20*c*), operates at low angle of attack (i.e. about 12° or less), and has a rounded leading edge and sharp trailing edge, behaves basically the same way. Various mathematical derivations and extensive wind tunnel tests demonstrate that these airfoils conform to certain rules:*c*as a function of angle of attack_{l}*α*) of 2*π*rad^{-1}-have zero-lift angle of attack determined by maximum camber height from the chord line and position of that maximum height along the chord-conform to the Kutta condition (upper and lower surface velocities are equal in magnitude and direction at the trailing edge) and Kutta-Joukowski Theorem (lift is proportional to circulation—a property related to the difference in velocities along the upper and lower surfaces—around the airfoil)

-can be approximated as flat and horizontal, allowing the prediction of lift solely based on pressure

*and lower*surfaces; and there is absolutely no physical reason that two adjacent fluid elements which split to travel over the airfoil must come together at the airfoil’s trailing edge. The equal transit theorem is a fourth grade explanation of lift (literally—that's where I first learned it) that is fundamentally incorrect but which appears to underpin the whole "cars look like wings" assertion.*any*thin airfoil—positive cambered (upside down “u” when viewed from the side), negative cambered (right side up “u” when viewed from the side), or symmetrical—can be made to generate positive lift, negative lift, or no lift depending on its angle of attack. Yes,*any*thin airfoil. Take a negative cambered wing from an F1 car, for example, that is used to make huge amounts of negative lift (“downforce”). Angle it differently with respect to the airflow and the same wing can make positive (upward) lift! Conversely, take a positive cambered airfoil. Flip it over and it doesn’t make as*much*positive lift as angle of attack increases before stall, but it*does*make positive lift. The right-side-up airfoil doesn’t make as*much*negative lift as angle of attack decreases before stall, but it*does*make negative lift (left side of the second plot below).As camber height decreases, zero-lift angle of attack α grows. A negative cambered airfoil has positive _{L0}α, meaning it makes negative lift over a wider range of angles of attack._{L0} |

Like this: the wing section spans the width of the flow volume. |

*much*more complex. On airplane wings, it is possible to mathematically determine this

*induced drag*and design a lift distribution and wing shape that will result in lowest drag (if that is an engineering requirement) by incorporating geometric (varying chord line orientation along the wing) or aerodynamic twist (varying airfoil profiles along the wing) into the wing design. On cars this is not possible to do with simple math. While the same mechanism of pressure differences between the upper and lower surfaces explains the trailing vortices and lift-induced drag of cars, cars also 1) have a lot of thickness and surface area between those upper and lower surfaces that also affect vortex formation, 2) have a flow field complicated by the influence of the ground, 3) form other vortex types in various places due to their bluff shapes, and 4) can be designed for high positive lift, high negative lift, or anything in between depending on requirements whereas airplane wings

*must*generate positive lift to function.

**Cars**

*h*≤ 0.20

*c*; cars can have thicknesses of anywhere in the range of

*h*= 0.23

*c*(for a long, low sports car like the Lamborghini Revuelto) to

*h*= 0.36

*c*(for a tall SUV like the Chevrolet Tahoe), and even more extreme for things like box vans and heavy trucks.

Despite being fairly low for a crossover, this Subaru Solterra is still quite thick compared to an airfoil—h = 0.35c. |

*bluff*rather than

*streamlined*; their flow is characterized by separation of the airflow from the body, and it can happen at any number of locations on the top, sides, back, and underside of the car. When this happens on a wing it is called

*stall*and TAT no longer mathematically predicts the wing’s performance; in fact, it goes out the window. The same is true of cars. Once you have separation over an aerodynamic shape—due to its bluff nature or a high angle of attack—aerodynamic parameters are strongly influenced by viscosity, for which TAT does not account (it assumes an inviscid model). The inviscid model works just fine for predicting airfoil performance; it does not work for cars.

Multiple things are wrong here, especially the random arrows “showing” airflow and pressure that have no basis in reality (image credit: ebay.com). |

Here’s Calypso on display at the Chicago Auto Show earlier this year. |

*That*is perhaps the fundamental reason that, contrary to what you’ll hear a lot of people say,

**cars are not wings**.

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