It’s a
common refrain: “Cars are shaped like wings, so they make lift.”
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| Shockingly, one of these was published by a major automotive magazine. |
The only
problem is, it isn’t true. Cars are entirely different from wings (or 2D
sections of wings used for analysis and design called airfoils). Here’s
why.
Airfoils
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| Plot of a NACA 0012 airfoil. The numbering system gives us information about the airfoil: it has no camber (curve), there is no position of maximum camber, and its thickness is 12% of its chord. Moving at 60 m/s, and with an angle of attack of just 1.7°, this symmetric airfoil with a chord (length) of 2.0 m will generate a massive 820 N lift per meter of wing width! |
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; h ≤ 0.20c), 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:
-have a
sectional lift slope (lift coefficient cl as a function of
angle of attack α) of 2π 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
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 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.
In
reality, 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).
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| Camberline plots of NACA 4-digit airfoils. m is maximum camber height as a percentage of chord; p is position of maximum camber as a percentage of chord. Note that the scale of the vertical axis here is exaggerated; a real airfoil, even with relatively large camber, will appear to have only a slight curve. |
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| As camber height decreases, zero-lift angle of attack αL0 grows. A negative cambered airfoil has positive αL0, meaning it makes negative lift over a wider range of angles of attack. |
TAT
applies strictly to wings which can be approximated as infinite, so that 3D
effects can be ignored. In wind tunnel and CFD tests, this means using a wing
section the width of the test section, so that each end abuts a wall (a real
wall in a wind tunnel, which will affect results due to the no-slip condition,
but a slip wall in a CFD simulation).
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| Like this: the wing section spans the width of the flow volume. |
In real
wings (and cars), of course, this is not possible; wings (and cars) must be
finite in width. This complicates things and means that 2D airfoil theory does
not strictly apply to wings without compensation for three dimensional
peculiarities.
These
peculiarities arise from the difference in pressures between the upper and
lower surfaces of a wing, which results in longitudinal trailing vortices. The
vortices shed from wingtips change the angle of attack the wing “sees” at any
station along its width so that the onset flow no longer aligns with the
airfoil’s direction of motion, tilting the resultant force vector (which we
approximate as acting only in the vertical direction—normal to the flow
direction—for a 2D airfoil) backward and resulting in a component
upward (lift) and backward (drag). Voilá: pressure drag. The same thing happens
on cars but is much, 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
Let’s look
at the flow around cars in more detail, specifically how it differs from that
of airfoils.
The first
and obvious difference is the very different shape of cars compared to
airfoils, even using just a centerline cut of a given car. The car may have any
number of front bumper and hood shapes, windshield angles and curvature,
rooflines, backlight angles and curvature, trunk or trailing edge shapes, and underside
shapes (usually far from smooth)—and these shape details affect the lift
distribution. Airfoils are all the same general shape
in that they have a gentle, tapered curve from a rounded nose to a sharp edge with
smooth surfaces (considering low-speed airfoils only). Airfoils, as I noted
above, typically have a thickness h ≤ 0.20c; cars can have
thicknesses of anywhere in the range of h = 0.23c (for a long,
low sports car like the Lamborghini Revuelto) to h = 0.36c (for a
tall SUV like the Chevrolet Tahoe), and even more extreme for things like box
vans and heavy trucks.
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| Despite being fairly low for a crossover, this Subaru Solterra is still quite thick compared to an airfoil—h = 0.35c. |
This wide
range of possible shapes and rather tall heights has an important implication.
Cars, unlike airfoils, are 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.
Now,
expand from that centerline cut (which only schematically represents a car) to
a three-dimensional car shape. Compared to a wing, which has very long span
compared to its length, cars have very short spans or widths, much smaller than
their lengths. This, coupled with their characterization by flow separations,
creates a strongly three-dimensional flow field, where flow properties vary
considerably in each of the three orthogonal directions used to define the vector subspace of the real world.
Where wing design, and especially first approximations, can rely on a 2D
assumption and come pretty close to an accurate prediction, this is not
possible on cars—despite what you may see online!
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| Multiple things are wrong here, especially the random arrows “showing” airflow and pressure that have no basis in reality (image credit: ebay.com). |
Then, add
in the fact that airfoils are smooth surfaces and wings are too (aside from a
few excrescences like pylons for nacelles or flaps, and lighting) while cars
have numerous body details that create complex surfaces which are far from
smooth. These body and styling details include grills, heat exchangers, air
inlets, ducts and vents for internal flows, fascia elements, seams and panel
gaps, antennae, window indents, styling creases and lines, door handles, axles,
rotating wheels and tires, brakes and hardware, everything in the engine bay,
suspension, driveshafts, exhaust components and other underside
elements—especially important since they are not seen and consequently don’t
get a lot of attention—and more. All these perturb flow and affect the flow
field.
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| One of the major benefits of the current shift toward electric vehicles is the relative ease of smoothing the undersides of these cars. Here, for example, is the BMW i5, looking forward from the rear; notice the fairing attached to the lower control arm. |
Next, a fundamental
difference between wings and cars is the presence of the ground. Where airfoils
and wings operate mainly in free air (except during takeoff roll and landing),
cars move in ground effect all the time, unless something goes drastically
wrong. The ground plane, through which a car’s traction force
is applied and without which it cannot move, constrains the car’s motion to two
dimensions (neglecting the movement of the body on the suspension system, which
includes the wheels and tires). The ground also affects the flow around the car
in important ways. Complicated flow patterns develop underneath the car, where
the boundary layer on the ground interacts with the elements under the car as
well as the rotating wheels and tires. But more fundamentally, the presence of
the flat ground imposes a constraint on the streamlines around the car,
introducing an inherent asymmetry to the flow pattern. This
asymmetry is at least partially responsible for the separation that is
characteristic of the flow field of an otherwise streamlined shape in free air
(a phenomenon identified very early on in car aerodynamics), and also for the
positive lift that such a body experiences in ground proximity (bring the body
into contact with the ground—the logical extreme case—and, as Barnard points
out, lift will be enormous).
Finally,
cars must satisfy packaging and dimensional constraints (related to my second
point, above, about width) that wings do not, in order to fit humans and
whatever they want to carry with them inside in practical positions that allow
for comfortable driving over long distances. Even purpose-built low drag cars,
like our solar car, must make concessions to this: what
started out as an airfoil becomes something more like a “tub” with a bubble
canopy so that it can fit a driver with sightlines that satisfy specific
American Solar Challenge regulations.
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| Here’s Calypso on display at the Chicago Auto Show earlier this year. |
That’s an
extreme case, and most cars—including all production cars—actually have a shape
and details dictated by styling and packaging rather than aerodynamics. 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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| There are papers that argue that the camberline of car bodies affects their lift in the same way as a cambered airfoil; you can plot it yourself by taking a photo from far away (to minimize distortion) and then marking a series of points halfway between the upper and lower surfaces. You will find that most cars, like my Prius above, have positive camber. However, even this car could easily be made to generate negative lift overall by fitting wings, spoilers, splitters, undertrays, or other devices to it—because a car does not behave the same as an airfoil. One important difference: the massive rear face here means the Kutta condition cannot be satisfied. |
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