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.

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.

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 
torque.  
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)
  where:
    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
  where:
    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)
  where:
    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 
  and:
    q  = (rho * V**2)/2
  where:
    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)
  where:
    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.

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.

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 
    where:
    P   = air pressure
    rho = air density
    V   = air velocity

When you decrease the air velocity, pressure must increase to keep the quantity 
a constant.

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.  

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
    where:
    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
the time.
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.

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.

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)
   where:
   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 
         other planforms)

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.

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.

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 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)
 Where:
   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)
                = (3400*60)/(823.3*15)
                = 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
*roll bar  

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
 where: 
   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.