Auto Aerodynamics 101
by Dan Jones
It's been over a decade since I had my aerodynamics courses (basic aerodynamics, gas dynamics,
fluid flow, and boundary layer theory), so I probably remember just enough to be dangerous.
Still, I think I may be able to add some insight to this discussion and correct some erroneous
assumptions. I found it necessary to toss in quite a bit of theory to support my points, but
there's also some practical stuff towards the end.
"I recently experienced an interesting phenomenon while racing a Z28. Some
relevant data...I was driving my 94 Steeda Mustang convertible with the top down
when I encountered a 94 Z28 convertible running with his top up. We both had a
single passenger. My car is running about 305 HP with his a stock 275HP as far
as I could tell. We went from a 60 mph rolling start up to about 110mph when we
both backed off. I did quite well and won but I also recall that right about 110mph,
it felt like I had hit a wall in that the air resistance seemed to go up exponentially.
Given that my top was down, and the downforce of the wind hits the back seat, I
guess this is not surprising. I had never experienced this before with the top up,
but then again 110 mph is the fastest I've ever driven it with the top down!
But, it did get me to thinking about the impact of aerodynamics on the Mustang's
top end and high speed highway performance.
To initiate the discussion, here's a couple observations:
The 94/95 look a bit sleeker, and thus are presumably a bit more aerodynamic
than the earlier Mustangs."
Looks can be deceiving. A sleek looking car may actually generate more drag than a blunt car.
If you look at a sleek airplane like the Concorde, you'll find it has thin wings with sharp
leading edges and a pointed nose. While this is an aerodynamically efficient shape for a
supersonic transport, it is not an efficient shape for a subsonic one. Subsonic aircraft,
like Boeing 747's, tend to have thick wings with blunt, gently rounded leading edges and a
similarly blunt, rounded nose. The point is that aerodynamics is a complex field of study
and it takes a well educated eye not be misled.
The 4th gen Camaros look sleeker than the 94/95 Mustang, and thus presumably more
aerodynamic than the new Ponies. (??)
Here's some data I've obtained from a knowledgeable person:
Coefficient of drag (CD) on the 94/95 is .37 whereas the late 80s'/early 90s
Mustangs are about .41 or so. I don't know what this really means engineering
formula wise, but presumably the lower the CD, the better. Better in this case
means less HP needed to overcome drag and wind resistance."
Yes, lower is better, though strictly speaking it's not really horsepower that's overcoming drag.
I'll save explaining the subtleties of horsepower and torque for another post. For now I'll just
note that drag has the units of force, while horsepower does not. I'll also note that horsepower
is really only useful as a measurement of the potential to produce a motive force, in this case
A car will continue to accelerate until the total external resistive forces (aerodymamic drag
and rolling resistance) cancel out the motive force provided by the drivetrain via the tires.
This is, of course, a simple example of Newton's Second Law of Motion which states that the
sum of the external forces acting on a body is equal to the rate of change of momentum of the
body. This can be written in equation form as:
F = d/dt(M*V)
F = sum of all the external forces acting on a body
M = the mass of the body
V = the velocity of the body
d/dt = time derivative
For a constant mass system, this reduces to the famous equation:
F = M*A
F = sum of all the external forces acting on a body
M = the mass of the body
A = the resultant acceleration of the body due to the sum of the forces
So acceleration stops when the resistive and propulsive forces cancel each other out. In the case
of an automobile, aerodynamic drag is the major resistive force. Drag is usually expressed in
terms of non-dimensional coefficients. In the aircraft industry, the coefficient used is Cd:
Cd = D / (q*S)
Cd = coefficient of draq
D = aerodynamic drag force in lbs
S = wing planform area in square feet (ft**2)
q = dynamic pressure in lbs/ft**2
q = (rho * V**2)/2
V = velocity
rho = air density (a function of temperature and altitude)
In college, we used Cx to distinguish automobile drag coefficients from aircraft drag coefficients
(Cd), since the automobile industry uses a different normalizing area (frontal as opposed to
planform). So for an automobile:
D = Cx*q*A
Cx = D/(q*A)
Cx = automobile coefficient of draq
D = aerodynamic drag force in lbs
A = automobile frontal area in square feet (ft**2)
q = dynamic pressure in lbs/ft**2
Note that while drag is directly proportional to both frontal area and Cx,it is proportional to
the square of velocity. If you double a vehicle's speed, you will quadruple its drag. If you
formulate the problem in terms of the power required (Preqd = F*V) to overcome drag, you'll find
that it varies with the cube of velocity since power is a rate (the rate of doing work) and thus
carries with it another velocity term.
"While we are on this topic, what about a roadster that doesn't have a windshield,
or just a very small low-profile one? I would think that this would be better than
even a coupe, since the actual frontal area is much less, but then this is a total
My plan for my '63 Falcon SuperStreet car is to make it a roadster like this, but
I might reconsider if it slows it down in the 1/4-mile by a big amount."
Using the equation above, you'll see that you have two variables to trade off, shape (Cx) and size
(A). To have low drag, you want the product of these two quantities to be small. Cutting the
windshield down will reduce area but probably won't help the Cx, though canting it back may help a bit.
You might want to consider chopping the top on a coupe. This will reduce the frontal
area while not incurring the large Cx penalty of an open roadster. Alternatively,
you could fit a top to the roadster when you're racing. Of course, you'll need
to factor in any weight penalty. If you plan on running a roll bar, you'll definitely
want to get it out of the breeze. Also keep the body work narrow (no flares) and
the tires within the fenders.
"I'm told that some of the things that can be done to reduce drag on the 94/95 is
to use a vented cowl hood. What is a vented cowl hood, what does it really
do, and where can I get one for a 94/95?"
A vented cowl hood looks like a cowl induction hood from the 1960's but doesn't
do the same thing. Cowl hoods like those on late 1960's Z28s were used to make
more horsepower. Vented cowl hoods are designed to allow cooling air an easy escape
path, allowing the engine to run cooler and possibly increasing stability by reducing
the high pressure area under the nose of a car. The old cowl induction hoods used
raised center section that ran back to the base of the windshield. Instead of having
the opening on the front of the hood scoop, it was on the back. This allows the
carb to pull its air from the relatively high pressure area at the base of the
windshield, providing a very mild passive supercharging effect and possibly a few
more horsepower. When a moving gas like air is brought to a halt, there is an
attendant rise in pressure (the kinetic energy is converted to static pressure).
Bernoulli's equation illustrates this:
P + (rho*V**2)/2 = constant
P = air pressure
rho = air density
V = air velocity
When you decrease the air velocity, pressure must increase to keep the quantity
"The vented hood allows air that enters the engine compartment a route to escape.
It has to go SOMEWHERE after it's cooled your radiator, and without an explicit
exit, it will go under the car, creating lift and more drag."
Probably so, but with the cost of wind tunnel time, you can bet they didn't do any
testing to prove their hood works.
Swirling effect = turbulence. Turbulence requires more energy as the random motion
of the particles has been induced. This will increase drag on the next surface
hit (rear of the car), but most importantly is the back pressure the windshield
will provide. With the top up, the airflow gets time to stay in a laminar like
flow up until the end of the trunk, after that the flow separates, and the only
real low pressure zone in the back of the car. Inducing this effect earlier at
the windshield and providing a bigger area for low pressure and flow destabilization
will increase drag many times.
The swirling effect creates air resistance and turbulence therefore creating drag.
The same reason an airplane wing will stall at a high angle of attack.
"To be more technical on this, you need to preserve "laminar" flow on the car, and
avoid any "turbulent" flow. Any air flow separation form the body will create an
offset in surface pressure (thus creating a lower pressure area and inducing drag)."
I disagree with these explanations. The laminar flow argument only works for slender
bodies, like airfoil sections, which can maintain laminar flow, and then only sometimes.
A major conceptual error has been made in the statements above. Flow separation and
turbulence are NOT the same thing.
For low drag on a shape that will not sustain laminar flow, you want to eliminate
flow separation. Inducing turbulence is a great way to do this.
The profile drag of an object can be split into two components:
Cd = Cdf + Cdp
Cd = profile drag coefficient
Cdp = pressure drag coefficient due to flow separation
Cdf = skin friction drag coefficient due to surface roughness
in the presence of laminar/turbulent flow
The drag which comprises the Cdf component is caused by the shear stress induced
when air molecules collide with the surface of a body. A smooth surface will have
a low Cdf. Also, the Cdf is lower for laminar flow and higher for turbulent flow.
Cdp, on the other hand, is caused by the fore-and-aft pressure differential created
by flow separation. Often (usually?) Cdp is lower for turbulent flow and higher
for laminar flow. In many cases, inducing turbulence will dramatically decrease the
pressure drag component, decreasing the overall drag. Airplanes use this trick all
Back in the 19th century, when scientists were just beginning to study the field of
aerodynamics, an interesting observation was made with respect to the drag of a
cylinder. Since a cylinder is symmetric front-to-back (and top-to-bottom), their
early theories predicted it should have no drag (or lift). If you plot the (theoretical)
pressure distribution along the surface of the cylinder (remembering that pressure acts
perpendicular to a surface) and decompose it into horizontal (drag) and vertical
(lift) components, you'll find that the pressure on the front face of the cylinder
(from -90 to +90 degrees) and the pressure on the rear face ( from +90 to +270 degrees)
are equal in magnitude but opposite in direction, exactly canceling each other out.
Therefore, there should be no drag (or lift).
However, if you actually measure the pressure distribution, you'll find there are
considerably lower pressures on the rear face, resulting in considerable drag. This
difference between predicted and observed drag over a cylinder was particularly
bothersome to early aerodynamicists who termed the phenomenon d'Alembert's paradox.
The problem was due to the fact that the original analysis did not include the
effects of skin friction at the surface of the cylinder. When air flow comes in
contact with a surface, the flow adheres to the surface, altering its dynamics.
Conceptually, aerodynamicists split airflow up into two separate regions, a region
close to the surface where skin friction is important (termed the boundary layer),
and the area outside the boundary layer which is treated as frictionless.
The boundary layer can be further characterized as either laminar or turbulent.
Under laminar conditions, the flow moves smoothly and follows the general contours
of the body. Under turbulent conditions, the flow becomes chaotic and random.
It turns out that a cylinder is a very high drag shape. At the speeds we're talking
about, a cylinder has a drag Cd of approximately 0.4. By comparison, an infinite
flat plate sets the upper limit with a Cd of 1.0. An efficient shape like an airfoil
(that is aligned with the airflow, i.e. is at 0 degrees angle of attack) may have
a Cd of 0.005 to 0.01. Think about what this means. An airfoil that is 40 to 80
inches tall may have approximately the same drag as a 1 inch diameter cylinder.
Luckily, there are easy ways of reducing a cylinder's drag. Another thing the early
aerodynamicists noticed was that as you increased the speed of the air flowing over
a cylinder, eventually there was a drastic decrease in drag. The reason lies in
different effects laminar and turbulent boundary layers have on flow separation.
For reasons I won't get into here, laminar boundary layers separate (detach from
the body) much more easily than turbulent ones. In the case of the cylinder, when
the flow is laminar, the boundary layer separates earlier, resulting in flow that
is totally separated from the rear face and a large wake. As the air flow speed is
increased, the transition from laminar to turbulent takes place on the front face.
The turbulent boundary layer stays attached longer so the separation point moves
rearward, resulting in a smaller wake and lower drag. In the case of the cylinder,
Cd can drop from 0.4 to less than 0.1.
You don't have to rely on high speeds to cause the boundary layer to "trip" from
laminar to turbulent. Small disturbances in the flow path can do the same thing.
A golf ball is a classic example. The dimples on a golf ball are designed to promote
turbulence and thus reduce drag on the ball in flight. If a golf ball were smooth
like a ping pong ball, it would have much more drag. So instead of waxing your car,
maybe you should let it get hail damaged :)
If you look closely, you'll notice that some Indy and F1 helmets have a boundary
layer trip strip to reduce buffeting. It seems odd but promoting turbulence can
reduce buffeting by producing a smaller wake.
Another consequence of skin friction on a cylinder is that you can generate substantial
lift with a spinning cylinder. By spinning a cylinder you can speed up the flow over
the top and slow down flow under the bottom, resulting in a lift producing pressure
differential. I think this phenomenon is known as the Magnus effect. BTW, the
spinning tires on F1 and Indy cars are huge sources of drag.
I felt I needed to correct this statement. A waxed surface is NOT slipperier than
a non waxed surface. We have determined this empirically with Sailplanes and wing
surface prep. A lightly sanded (400-600 grit) smooth (.002" max ripple) surface
will cause the least amount of drag (and maximum laminar airflow). (On the other
hand, we still wax our ships (the increase in surface life and durability more
than offset the increase in L/D).
To follow up on this, do the following experiment: Take a piece of 4-600 grit
sandpaper and a sheet of glass. Place a small drop of water on each and then blow
on the drop of water. Kind of makes you wonder why people spend big dollars polishing
ports on engines!!
If you pour water on a slightly inclined portion of a non-waxed car, it may not
run off. However if you pour water onto to same car after a waxing it may indeed
slide right off the car. This does not necessarily mean a waxed car will slip through
the air easier. As explained above, skin friction is only part of the story. Also,
the dynamics of fluids (like water) and gasses (like air) are considerably different.
The surface tension of liquids make them different animals.
"Well let's just say an "infinite sheet" would have a CD of 1. A real sheet in practice
has a CD of greater than 1, ex 1.1, due to the edges."
Yes, for simplicity I've illustrated my points using mainly 2-dimensional shapes.
Things get more complicated with 3-dimensional flow, but the same principles apply.
"Does anyone know of any enhanced rear wings for the 94/95...ie where could I
get a "good one" that does in fact improve air flow, reduce drag significantly and/or
help to better plant the rear end? The stock 94/95 rear wing looks more cosmetic than
anything else to me."
Wings are not drag reducing devices, they are lift (negative lift or downforce,
in the case of automobiles) producing devices and will generate substantial drag
if they are effective. Wings produce drag as a direct consequence of generating
lift/downforce. This drag is in addition to the wing's basic profile drag (the drag
at zero lift) and is termed induced drag. Induced drag is proportional to the square
of the lift/downforce produced:
Cdi = Cl**2/(pi*e*AR)
Cdi = induced drag coefficient
Cl = coefficient of lift
AR = the aspect ratio (wing span squared/wing area) of the wing
pi = mathematical constant (approximately 3.14159)
e = wing efficiency factor (1 for an elliptical wing planform like
that used on the WWII Spitfire fighter planes, less than 1 for
When they are not strictly cosmetic, wings are added to cars for stability and
downforce reasons. The wings on a Formula 1 race car generate incredible amounts
of drag because they generate equally incredible amounts of downforce (4 to 5
times the weight of the vehicle - the primary reason these cars are able to pull
4 to 5 lateral g's on high speed corners). Obviously, F1 cars are willing to trade
a lot of top speed for increased corner speeds.
The bodies on most production cars generate de-stabilizing lift. Nature abhors
a vacuum, so the air flowing over the top, under the bottom, and around the sides
of a car will at some point (aft of the vehicle) re-join. Since the paths over,
around, and under a car are different lengths, the air must flow at different speeds.
The longer the path is, the higher the air flow speed must be and from Bernoulli's
equation, we know that higher speed means lower pressure. Usually, the path over the
top is longest and the result is lift.
Getting the air to go around the car rather than under it makes a huge difference.
As already mentioned, a big factor is getting the air coming in from the front-grill
out of the engine compartment. In really fast door-slammer drag cars, they use solid
front-ends (no grill openings) so air doesn't get in. I've read in some of the drag
mags that cars with open grills can loose control of the car from the air coming
in the grill at 150+ mph.
This is a big stability concern. If the cooling air cannot exit quickly enough,
there will be a big pressure increase underneath the front of the car. This is
very destabilizing and at 150+ mph, can make the front end of the car want to fly.
"Does anyone know at what speeds the coefficient of drag really starts to become
a limiting factor for the 94/95 Mustang? (i.e. is there a speed at which drag starts
to become exponential, thus requiring a significant power increase to overcome resistance,
or is the drag pretty much linear up to top end speed?)"
As shown earlier, drag varies with the square of speed and the power required varies
with the cube of speed. The drag coefficient is relatively constant for the range
of speeds a typical automobile sees. Over wider speed ranges (subsonic, transonic,
and supersonic) this is not the case.
"Does anyone know what the coefficient of drag is for other performance cars such
as the Z28, Firebird, 300ZX or whatever?"
You'll have to take these numbers with a grain of salt. Back when I was in college,
a friend worked at the Lockheed wind tunnel where some of the auto manufacturers
tested. He claims the advertised numbers were often lower than the tested numbers.
That said, the lowest claimed numbers I have seen are in the 0.29 to 0.30 range.
The performance versions of cars generally have a higher Cd due to the added drag
of wider tires and any added wings. I think the 1980's Audi 5000 claimed a Cx of 0.30.
It's not sleek looking, but it does have an efficient subsonic shape (smooth, rounded, and blunt).
"I'm building my own homemade wind tunnel to test out my new windshield design
for my '63 Falcon. I've found a good deal on Fans from Sears that should give enough
air flow to get meaningful results. (no flames Dan) I've cleared all the parts and
stuff out of the garage and have ripped out the backwall. I'm working on the computer
and getting the bugs out of the visual image processing system that will analyze
the way the attached ribbons tussle from the wind. If all goes well, it should lower
my ET's by 2 tenths."
I know you're only joking, but I'll offer a tunnel tip anyway. The proper way to measure
an automobile's drag is in a rolling mat wind tunnel. The rolling mat simulates
the "ground effects" of the road passing under an automobile and also takes into account
the considerable aero drag generated by rolling tires. So when you're shopping for
fans at Sears, see if you can find a really big belt sander. :)
To see if your rear wing has any air flow to work with, tape several pieces of yarn
to your trunk lid and wing - they'll tell you what's up. Check your roof while you're
at it. Then tape a bunch to a yard stick and use it as a probe with the roof down
- see where the air is "clean". Of course, this is a 2 person effort. ;-)
Yes, when you don't have a wind tunnel at your disposal, yarn tufts are a good way
to visualize the flow field. Tape them all over the car and have a chase car shoot
some video of your car at speed. You can also use them to test the placement of
boundary layer trips.
So what can you do if you don't have access to a wind tunnel? Several years ago I
copied down this coast down formula which can be used to test aerodynamic and rolling
resistance drag. I've never tried it, so caveat emptor.
CDHP = (WEIGHT*MPH)/(823.3*CDTIME)
CDTIME = coast down time in seconds
CDHP = coast down horsepower (i.e. the horsepower required to maintain a given speed.
This formula can be used in determining the effects of changes made to a vehicle
to alter its aerodynamic drag or rolling resistance. As an example, assume you
have taken coast down measurements from 65 to 55 mph (under similar atmospheric
conditions) before and after making changes to reduce aerodynamic drag (e.g. lowered
the vehicle and added an air dam). In the before case, it takes 15 seconds to
coast down. In the after case it takes 20 seconds. Assume the vehicle weighs 3400 lbs.
Plugging this data into the formula yields:
Before: CDHP = (WEIGHT*MPH)/(823.3*CDTIME)
= 16.51 hp
After: CDHP = (3400*60)/(823.3*20)
= 12.39 hp
Net Change: 16.51 - 12.39 = 4.12 hp @ 60 mph.
This formula indicates that the changes result in 4.12 hp less required to maintain
the vehicle at 60 mph. Since aerodynamic drag varies with the square of speed,
the effect will be greatly accentuated at higher speeds. To minimize the effects
of internal engine drag, coast down times for aerodynamics effects should be taken
with the transmission in neutral. When testing the effects of lubricants or the
effects of accessory drag (an air conditioning compressor, for instance), leave
the transmission engaged.
Coast down time should be measured on a flat, smooth, road with no wind or drafting,
using a 2 way average, under similar atmospheric conditions. I wouldn't put much
faith in the absolute numbers provided by this formula, but I think it might be
a good tool for assessing relative changes.
Off the top of my head, I can think of several things that might be worth testing
using these formulas:
*lowering the car
*adding a lip spoiler/air dam
*raking the body with a slight nose down attitude (primarily for stability)
*fitting a Capri hatch (supposed to be more aerodynamic than a Mustang one)
*fitting a belly pan to the rear skirt on GT's (factory skirt looks draggy)
*taping over door and hood seams
*convertible top up and down
"...so the 800 pounds of force at 180 mph drops to 200 pounds at 90 mph and
50 pounds at 45 mph (not what I originally wrote, which were based on a cubic function).
But this implies that even at 45 mph, the down force gained by that wing seems significant.
My only questions now are generated by descriptions of laminar vs turbulent flows:
Do those sport slats cause enough turbulence so that they totally nullify any
effects that the rear wing might have?"
I believe you'll find that the boundary layer is fully turbulent before it ever gets
to the sport slats. The real question is whether or not the turbulent boundary layer
is still attached by the time it gets back to the rear wing. If the flow has not
detached from the body, the wing will likely see clean air, since it's raised off
the body enough to clear the turbulence of the boundary layer.
Technically speaking, separated flow is not turbulent, even though it is random and
chaotic (and very draggy). The laminar and turbulent concepts apply only to the boundary
layer, which is only a few inches thick. Beyond the boundary layer, flow is treated
as frictionless (inviscid). The boundary layer is very important since it determines
skin friction drag and the tendency towards pressure separation (turbulent boundary
layers are *less* likely to detach). There is a drag increase associated with the
transition from laminar to turbulent flow but it is usually small compared to the drag
increase associated with separated flow.
This brings up another important aerodynamic term, the Reynolds number, which is defined as:
Re_x = (Rho * V * X)/Mu
Re_x = Reynolds number at location x (a dimensionless quantity)
Rho = freestream air density
V = freestream flow velocity
x = distance from the leading edge
mu = freestream viscosity, a physical property of the gas (or liquid)
involved, varies with temperature, at standard conditions mu is
approximately 3.7373x10E-07 slug/(ft*sec) for air.
The location along the body at which the flow transitions from laminar to turbulent
determines the critical Reynolds number. Below this number, the flow is laminar,
above it's turbulent. Since the Reynolds number varies linearly with the location
along the body and with velocity, the faster you go, the farther forward the transition
point moves. At cruising speed on a typical jet airliner, only a small region near the
leading edge may be laminar. Slow speed gliders with very slender (but still with
rounded, blunt, leading edges) may maintain laminar flow over most of the wing surface but
this is not the case for most practical aircraft. Note that glider wings are typically
designed with very short chord lengths (x distances) to help promote laminar flow.
Laminar flow is desirable when there is no pressure separation.
Automobiles operate at relatively slow speeds like gliders, but have much longer
x distances and shapes that are less likely to maintain laminar flow. The bottom line
is the flow is fully turbulent before it gets to the slats.
Assuming the Motor Trend article is true, the flow stays attached for the race car
without slats so the wing sees clean air and produces downforce. We can theorize
as to whether the street car's slats disturb the flow enough to detach the turbulent
boundary layer, but the only way to tell for sure is to test it. Anyone want to
volunteer to tape some tufts of yarn to a Boss 302 wing and watch the flow patterns?
The guys at work who did it on the '87 LX, did it with Scotch tape and some thick yarn.