rear wing aerodynamics

I'm sure you will get as many opinions here as there are reasons for liking or hating the delta wing.

I don't know if the factory did any testing. I'd assume it was a cosmetic upgrade following the Countach.

Anyhow, from personal experience I would expect that the wing just adds drag until you get to speeds over 100 mph. I have noticed the car squat down at very high speeds and expect that's when it works. Most Pantera race cars have a different type of wing. I don't know of many that use the original delta wing for racing.

Where are you located in Ontario? Do you own a Pantera? Looking for one? Building one?

Thanks for the reply,
I own 2016...recent purchase...haven't even driven it yet. Twin turbo E85 flex fuel set up. Goal is the 200mph mile. I do not have the wing, but am torn whether or not to put it on. I like the look, but don't want to find out a high speed it ruins the aerodynamics.
North of Toronto

It'll work just fine getting to 200. Better with than without it nearing those speeds.

There are a bunch of Canadian Pantera owners near you that can be very helpful. Check us out here:

http://www.teampanteracanada.c...astern_Panteras.html

From what I understand, the rear isn't a problem at speed, it's the front.
Junior Wilsons Silver State ORR car (200mph) didn't have a rear wing.
Will

I agree with Will. The delta wing will ultimately reduce top speed runs. At 200 mph I would spend all my concentration on keeping the nose pressed down, not the back. Just my 2cents.
Welcome, another Canada pantera. Great

Doug M

I've heard it said a few times that the car goes faster without the delta wing ... the drag it creates is not off-set by the amount of downforce it creates. Downforce would make the car faster in corners.

long winded explanation:

There are aerodynamic devices designed to prevent lift, and there are aerodynamic devices designed to create down force. The rear wing, if it works, is not a lift-prevention device. Its not there to fix a problem. It would be there to create downforce, to push the car downward, giving a Pantera better grip in high speed corners.

On the negative side, all spoilers & wings create some amount of drag. Wings are mounted on race cars because the downforce is needed in the corners more than the top speed is needed in the straights. The goal is to design the spoiler in such an aerodynamically efficient way to create as much downforce as possible while creating as little drag as possible.

You don't see many spoilers at the Bonneville salt flats, because the salt flats are all about going as fast as possible in a straight line, no cornering.

I see two problems with the delta wing: (1) its not shaped like the wings you'll find pictured in race car engineering books and (2) its not high enough to be in "clean air", its about at the level where the air tumbling off the roof is. In other words, its not a "serious" aerodynamic device. However, even the little flip-up spoilers you see on the back edge of race cars in NASCAR, Trans Am, etc creat some useful amount of down force, so there is a possibility that even though the delta wing isn't shaped right, and it isn't high enough, it may still generate some useful amount of downforce. Just not as much as it would if it were shaped better and mounted higher. The $64 question is ... does the delta wing create enough down force to justify the aerodynamic drag it creates?

I'm not aware of any serious Pantera race cars equipped with the delta wing. Greg Esakoff's, Dennis Quella's, Larry Stock's, Jerry Sackett's; none of them use the delta wing. How about the Group 4's racing in Europe, do any of them use the delta wing? Have you noticed the wing mounted on the back of the Adler's Pantera ... now that's a serious aerodynamic device.

-G

I believe that the wing was commandeered from the Countach. Lamborghini is a little unique in that it does not have a test track. They test on the street.
The test drivers have some kind on an agreement with the local police that they do not have to respect the posted speed limits. I suppose it is the equivalent of being issued a 00 number by the Secret Service?

I remember a road test article on the Countach in which the writer remarked that according to the Lamborghini test drivers, the wing limited the top speed of the car to under 200mph vs about 205 without it. What freaking kind of roads do they drive on in Italy? Geeze.

I would expect the same limitations with the wing on the Pantera.

You should ask the Canadian Pantera owners though. Many of them have them strangely enough. Maybe they have the same agreement as the Lamborghini test drivers do? LOL! After all, most of them live like 2 miles from where they work, so they NEED a car that does 200mph?

The nose of the Pantera tends to lift at speeds over 170mph. Not only does that mean that the steering gets spooky light, it means that the cars steers where it wants up there. Kind of like a speedboat though getting momentarily light which makes it dart uncomfortably left and right. Possibly lethally.

For function, down force needs to be added to the front of the car, not the rear.

The rear isn't a problem. Personally I agree with Coz. The thing is for putting your beer on the back, your barbie for tailgate parties and seemingly is put there to impress the 12 year olds. I would go as far to say that it's probably what an Italian pimp would want on his car?

OK. Who wants to take the first slug at me now? I didn't say anything is wrong with being a pimp...or a 12 year old. I was one once too. A 12 year old that is. Oh geeze, am I gonna get it now?

quote:

Originally posted by PanteraDoug:

OK. Who wants to take the first slug at me now?

Hey, I live 4 miles from work.
And my insurance won't let me take the car anyway. So I'm stuck in the truck.

Doug M

quote:

Originally posted by PanteraDoug:
.... I suppose it is the equivalent of being issued a 00 number by the Secret Service? ...

Aye carumba! Double naught spy's were under the jurisdiction of the British "Secret Intelligence Service" SIS. AKA MI6. The name is Bond, James Bond.

quote:

Originally posted by INZOWHO:
Hey, I live 4 miles from work.
And my insurance won't let me take the car anyway. So I'm stuck in the truck.

Doug M

But Doug, you have no wing? You CAN do 205 on the way to work?

Hey don't get me wrong. we played a lot of hockey against you guys and when I would get stopped by the RCMP for exceeding the limit the cop would ask why I was going so fast.

All I had to say in my best Canadian accent was, "I'mwitdagoalie A?" He would look at the pads in the car and usually would just nod me on.

Worked like a charm every time! LOL!

Hi guys,
Thanks for all the replys...It seems the wing will stay off. I was 50-50 in the looks department whether I liked it or not. just a thought...if you feel something has too much drag, you simply need more power. as for PanteraDoug using his quaint "Canadian" accent, let him know to start working on his Punjabi....most of our RCMP are now for India and wear Turbans

quote:

Originally posted by Made it:
Hi guys,
Thanks for all the replys...It seems the wing will stay off. I was 50-50 in the looks department whether I liked it or not. just a thought...if you feel something has too much drag, you simply need more power. as for PanteraDoug using his quaint "Canadian" accent, let him know to start working on his Punjabi....most of our RCMP are now for India and wear Turbans

OMG! What is the world coming to? WTF do punjabs know about hockey?

> Would anyone know if the rear delta wing helps or hinders at high speeds?

It will hinder top speed due to additional drag. When thinking about automobile
aerodynamics, you need to consider drag (for top speed in a straight line),
downforce (for increased speed through corners) and stability (for safety).
There's also internal aerodynamics for cooling and to feed the engine.

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.

Stability is determined by the both the ratio (front to back) and the total
lift or downforce. The downforce a wing generates (assuming the wing actually
generates downforce as installed) can be used simply for downforce for grip or
to reduce lift for stability reasons. You must think about this in a dynamic
sense (e.g. lift the nose generates when cresting a hill or encountering a
gust).

For a wing to be functional, it needs to be in clean air and have an angle
of incidence and/or camber. Also, the load bearing structure needs to be
able to support the amount of downforce generated. Flow over the top of a
Pantera separates coming off the roof, so a wing mounted in the separated
flow will not generate meaningful lift. If the wing is mounted far enough
back or high enough it will be back in useful flow. Also, flow can come
around the sides of the vehicle and flow over the wing. A quick glance at
a Pantera delta wing shows that it was likely designed for asthetics and not
function. The leading edge is swept back. Leading edge sweep is used to
reduce drag at transonic and suspersonic speeds and is of no use on a subsonic
automobile. Looking at the wing in David B's picture, it appears the wing is
roughly parallel with the top of roof. If so, there's a chance the some
clean air is flowing over the wing but you'd really want to tuft (tape short
segments of yarn and see if they all align themselves with the flow) the wing.
You could also use a hang glider airspeed inidcator on a short pole to see
where the flow reaches freestream (in the vertical axis). Also, a load cell
on the latch will register the amount of downforce versus speed. As I understand
it, the delta wing is attached to the decklid. I'd look to see what sort of
weight can be supported by the decklid before it starts to bend.

If I were to design a rear wing, it would have a straight leading edge, an
adjustable angle of incidence (so the downforce can be tailored) with a Liebeck
air foil shape. You'll find race car wings are usually designed not to minimized
drag for a given lift but rather to maximize lift (downforce) within the rule
limitations (usually some sort of a physical constraint on the allowable dimensions
like width). Bob Liebeck is a fellow Boeing engineer and designed a series of
race car airfoils ("Liebeck Airfoils") that go back 20 or 30 years and stem
from research on the maximum pressure gradient a boundary layer can sustain
without separation. As I recall, they were inverse airfoil designs with
Stratford pressure-recovery on the aft end and laminar flow forward sections.
Liebeck's airfoils were designed to provide maximum lift (downforce) but do
so at the cost of drag. Depending upon the application, there may be lower
drag airfoils that can produce similar downforce in a larger physical space.
Of course, the wing would need to be mounted up and/or back far enough to be
in clean air.

For a top speed run, you are worried about minimizing drag while retaining
stability. To understand the stability, you need to know what the lift is
on the front and rear of the vehicle at various speeds. Style Auto published
that data for an early (non-flared, no wing) Pantera in issue 29:

Speed Speed Lift Lift Lift Drag HP required
(KPH) (MPH) Front Rear Total (lb) due to drag
(lb) (lb) (lb)
----------------------------------------------------
260 162 300 112 412 556 238
225 140 229 86 315 426 159
190 118 170 62 232 313 100
160 99 115 49 164 218 58
130 81 75 33 108 139 30
----------------------------------------------------

I imagine the forum software won't presrve the spacing so the table format
above will likely get screwed up.

Notice that front lift is nearly 3 times that of rear lift. Remember
that lift acts in conjuction with the weight of a car. Using Pantera
specification information from the August 1971 issue of Car and Driver
(curb weight = 3123 lbs, weight distribution = 40.9% front, 59.1% rear)
you'd have 1277.3 lbs of weight on the front and 1845.7 lbs on the rear.
At 162 MPH, subtract the aero lift and you'd have 977.3 lbs total on the
front and 1733.7 lbs total on the rear. Couple that with the angle of
attack changes that happen at the front when you crest a hill or encounter
a bump and it's obvious the front needs to be addressed first. Several
caveats apply here: we're using curb weight of a stock vehicle without
driver, the wind tunnel used a fixed ground plane and not a rolling mat,
and the numbers for 162 MPH were extrapolated from lower speed data but
the trend is still there. You can reduce lift at the front of the vehicle
by giving the vehicle some nose down rake, ading a simply flat plate type
lip spoiler (mounting leading edge down at prehaps 30 to 45 degrees),
installing a front air dam and side skirts (to prevent pressure build up
under the car). A flow through GT-40 style nose will also help but requires
some radical sheet metal work. Also, weight works just as well as downforce
and has no drag penalty so you can mount steel or lead (or depleted uranium)
in the nose, preferably down low.

Drag at the rear can be reduced by minimizing pressure separation at the
rear of the roof, perhaps by installing a set of slats or a fill panel to
mimic a fastback shape.

I wrote a primer on automobile aerodyamics years ago that I've attached below,
along with several segments from follow up discussions. I don't have the time
now to better organize it but perhaps it will be of some use.

Dan Jones

Subject: Auto Aerodynamics 101

Hi All,

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 110 mph, 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 efficent 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. One of nature's best stream-
lined shapes is the tear drop shape that a water droplet assumes as it falls
under the pull of gravity. A tear drop is a very low drag shape and has a
blunt, rounded, leading edge with a long gently tapered, pointy, tail. A
couple of problems arise when applying this shape to an autombile. On large
shapes, a boundary layer builds up at the surface of the object which tends
to disturb the flow so that it detaches from the body. The resulting
separated flow is very draggy. Kamm (Von Kamm?) showed you could reduce
drag with a properly designed short tail almost as much as with a long
tapered tail. The abrupt separation provided by the cropped tail induces
the flow to continue as if it were flowing over a long tail. 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 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.

> 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 uneducated guess.
>
> 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

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.

> 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 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 the back of of the car. Inducing this effect
> earlier at the windshield and providing a bigger arear for low pressure
> and flow destabalization 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 applies
to 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 spilt 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
cancelling 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 bundary 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 bondary 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)

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.

> * 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 windsheild
> 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)

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 ways 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 conditiong 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/airdam
- 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
Just My 2 Cents Worth,
Dan Jones

Eugene,

> ... 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 Dan's 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

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.

> So on most production cars - are the wings cosmetic or do they help
> decrease lift at high speeds? More specifically how about the Mustangs?
> Anyone know? At a glance I'd think they might create a LONGER path over
> the top of the car and actually create more lift.

With the wing, the distances to be concerned with are local (i.e. over and
under the wing itself and not over the whole car). This why the wing is
raised off the body of the car on your '93 Cobra (and my '87 GT). What the
rear wing is attempting to do is create downforce (negative lift) on the
rear of the car, presumably to balance out a rear-biased lift tendency of
the car without wing (assuming it's not just cosmetic).

Also, the path the air actually travels may be quite different from the
contour of the vehicle. For instance, a flat shape with equal distances over
and under can produce a lot of lift. If you don't believe me, try this
experiment at home (just don't sue me if you do). Step into the bed of a
pick-up truck and lift a 4'x8' sheet of plywood over your head. Be careful
to hold the sheet of plywood parallel to the ground, while the driver slowly
accelerates to 60 mph or so. Now comes the fun part. Grip tightly to the
sides of the plywood and quickly tilt the leading edge upward. What happens?
Instant lift (and an impressive, if short lived, Peter Pan imitation).

What you've just experienced is the influence angle-of-attack has on lift.
Take a symmetric (top-to-bottom) airfoil shape that does not produce lift
when it is aligned parallel to the air flow (i.e. is at zero angle of attack)
and point it up. It produces lift. Point it down and it produces downforce.
While the physical distance over the top and bottom of the plywood are the
same, the distance the airflow travels is not. Likewise, you don't need
angle of attack or even thickness to produce lift/downforce. A thin curved
shape like a Venetian blind slat will also produce lift. This is an extreme
example of wing camber.

A little wing theory and several definitions are in order here. This would
be easier to explain with illustrations, but I'll give it a shot with words.
An airfoil is the 2-dimensional cross-sectional shape obtained by the
intersection of a wing and a perpendicular plane. The mean camber line of an
airfoil is the locus of points halfway between the upper and lower surfaces
(measured perpendicular to the mean camber line itself). The chord of an
airfoil is the straight line connecting its leading edge to its trailing
edge. Camber is the maximum distance between the mean camber line and the
chord line, measured perpendicular to the chord line.

An airfoil's angle of attack is the angle between the relative wind (the
local airflow direction) and the airfoil's chord line. Drag is the component
of aerodynamic force parallel to the relative wind and lift is the
perpendicular component.

If an airfoil is symmetric (top-to-bottom), it has no camber. A sheet of
plywood has no camber. A Venetian blind slat is a shape that has camber but
(practically) no thickness. The camber, the shape of the mean camber line,
and the thickness distribution of an airfoil determine its lift and moment
characteristics. Surface roughness also plays a roll but is usually treated
as a separate design issue.

Because of camber, wings can have lift at zero degrees angle of attack and
because of angle of attack, wings (and sheets of plywood) with no camber can
still produce lift. To separate these effects, aerodynamicists break an
airfoil's lift into two components:

Cl = Clo + (Cla * alpha)

where:

Cl = coefficient of lift
Clo = coefficient of lift at zero angle of attack
Cla = lift curve slope (the slope of Cl versus alpha)
alpha = angle of attack

On low speed circuits where downforce is very important, Formula 1 race cars
will have multiple, highly cambered, wings, oriented at a relatively large
negative angle of attack. All of this is done in an attempt to generate
downforce. Since this approach is a relatively high drag method of
generating lift, you won't see similar set-ups on aircraft (they are not
limited by wing size rules).

Front lip spoilers (like those on a Boss 302) produce downforce because they
are mounted at a relatively large negative angle of attack. They have all
the aerodynamic elegance of that piece of plywood, but they work. A pedestal
mounted, cambered, wing would be more efficient but probably wouldn't look
too good mounted on top of your hood. Some versions of the Lamborghini
Countach have a pedestal mounted front wing on the nose.

By the way, car spoilers really aren't spoilers at all. On aircraft,
spoilers are devices which intentionally promote pressure separation. They
are called spoilers because they "spoil" lift when they are deployed. They
are generally mounted flush on top of a wing and pop-up to reduce lift
and increase drag. You can watch these devices at work on airliners when
they decelerate in preparation for landing.

Rear mounted spoilers (like those on Cobra Daytonas), look more like a fixed
version of an aircraft trailing edge flap. Trailing edge flaps generate
lift/downforce by altering the effective length of a wing and its camber line
shape.

Since real wings exist in three dimensions, there are three-dimesional effects
to be concerned with. Lateral flow along a wing is called span-wise flow and
is usually undesirable. Guides, called fences, are often employed on aircraft
to reduce span-wise flow. The circulation around the ends of wings is
particularly strong and creates large vortices and substantial drag. The
flow wants to circulate laterally from the high pressure region underneath
the wing to the low pressure region on top of the wing (in the case of lift).
Race cars usually employ large vertical end plates on the sides of their
wings to reduce this circulation.

Unfortunately, most of this is probably academic since I have reason to
believe the rear wings on late model Mustangs don't see all that much flow.
A couple of guys at work (McDonnell Douglas Aerospace), tufted an '87 LX from
the center of the roof to the taillights. They were trying to use vortex
generators to increase the flow attachment on the rear glass. Vortex
generators are devices which are put in the flow field to intentionally
induce turbulent flow. They are often used on aircraft to re-attach and
direct flow (especially over control surfaces). Their vortex generators were
based on aircraft designs and they used a hang glider airspeed indicator on a
pole to measure the boundary layer thickness across the roof. They made the
vortex generators two inches tall to be conservative (the boundary layer was
approximately one inch thick and a rule of thumb is to make the generators 1.5
time the boundary layer thickness). They didn't see an improvement in coast
down times, but the tufts did appear a little better behaved with the vortex
generators. They believe the turn at the back of the roof may be too sharp to
permit attached flow. Some sort of fairing might help there (or maybe a
switch to a Capri hatch). They also noted that much of the clean wing flow
appeared to be coming from around the sides of the car.

From watching the flow patterns in the rain, one of them concluded that the
flow over the hatch of his 1986 Camaro was still attached, though it flowed
laterally as well as longitudinally.

Taller wings or wings that are mounted farther aft will see cleaner air.
Rear wings on race cars tend to be mounted high to get them out of separated
flow and into clean flow. The wing on the Dodge Daytona Chargers and
Plymouth Superbirds (the ones that made them look like shopping carts) are
examples of this. It would be interesting to tuft the various rear wings
(LX, GT, Cobra, SVO biplane, etc.) to see if any of them are useful.

On a related note, some of the racing Shelby GT-350's had a noticeable gap
between the fastback window and the roof. Does anyone know if this was for
aerodynamic reasons?

I previously mentioned trying to estimate drag from coast down measurements.
By taking measurements at several speeds, you should be able to separate the
effects of rolling resistance (roughly proportional to speed) from
aerodynamic drag (proportional to the square of speed). Data scatter would
be a real problem, but you could do a least squares curve fit. Also, making
runs with and without winds (at the same speeds) could be used to isolate the
aerodynamic contribution. Supposedly, NASA has done some work on coast down
drag equations as part of an effort reduce drag on tractor-trailers. They
even put a full size tractor-trailer in the 80' x 120' Ames wind tunnel.

I dug up some information on Mustang and Thunderbird drag coefficients from
a couple of old magazines. The January 1984 issue of Sports Car Graphic
claimed a Cx of 0.39 for a 1984 SVO Mustang (the model without flush
headlights) and s 1987 issue of Sports Cars of the World had these numbers:

0.35 for a 1986 base Thunderbird
0.38 for a 1986 Turbo Coupe Thunderbird
0.34 for a 1987 base Thunderbird
0.36 for a 1987 Turbo Coupe Thunderbird

One of the guys who did the vortex generator experiment, also relayed some
information on an AIAA presentation made by Corvette engineers about the
'Vette's aerodynamics. They claimed the 'Vette has a Cx of 0.30 and said it
was a difficult number to achieve with such wide tires. Note that GM tests
without mirrors, so this number may be a bit optimistic. There was also
a drag hit with the externally mounted 3rd taillight. GM used to test at
several tunnels, including one at Lockheed Georgia and one in Canada, but has
since built its own tunnel. Interestingly, it does not have a rolling mat.
The engineers admitted this is a compromise but noted they use a boundary
layer suction device near the front tires. This arrangement apparently yields
useful data with less scatter than a rolling mat facility.

The 'Vette engineers also noted that more aerodynamic testing is done for
acoustic (noise) and cooling reasons than for drag reasons. At first glance,
since it takes energy to make noise, you might think a quiet car is a slick
car. This is not necessarily so. Turbulent boundary layers are noisier than
laminar ones, but they often provide lower drag. Of course, you need to
trade this off against pressure separation noise.

Dan Jones

The generation of lift occurs when a flow stream is turned. This is
consistent with Newton's 3rd Law of Equal and Opposite Action. When
an airfoil turns the flow, an equal and opposite reaction occurs which
imparts a force to the airfoil. The lift and drag components of this
force can be determined by integrating the pressure distribution over
the airfoil surface. Without going in to a lot of detail, let me state
that a proper theory of lift can not be arrived at without considering
the considerable effects of viscosity which introduce friction into the
flow. It is viscosity that introduces circulation into the flow. This
circulation reaches an equilibrium when the stagnation point reaches the
trailing edge. This is known as the Kutta condition (see the
Kutta-Joukowski theorem) and is why the flow over the top and bottom
meet at the trailing edge (nature abhors a vacuum).

>We're dealing in semantics, here. I came from the school that
>presupposes that if there is airflow toward an airfoil, then there
>is an angle which it approaches the chord of that airfoil, hence
>the definition of angle of attack, even if zero.

In every aerodynamics text book I've ever seen, the definition of
geometric angle of attack is the angle from the chord line to the
undisturbed freestream velocity vector. This is the definition that
all the NACA/NASA airfoil data assumes. Perhaps you are refering to
induced angle of attack, which is a consequence of wing finiteness?
For three-dimensional wings, downwash, induced by trailing wingtip
vortices, alters the local flowfield, resulting in an effective
angle of attack which is less than the geometric angle of attack.
The difference between the geometric and effective angles of attack
is termed the induced angle of attack:

AOAi = AOA - AOAeff

where:

AOA = geometric angle of attack
AOAi = induced angle of attack
AOAeff = effective angle of attack

For an elliptical lift distribution, the induced angle of attack
can be calculated as

AOAi = Cl/(pi*AR)

This occurs in both symmeric and cambered airfoils, and is a three-
dimensional effect. Air foil sections are two-dimensional and therefore
the geometric and effective angle of attacks are the same (i.e. the
induced angle of attack is zero). Even for 2-D airfoil sections, in
general, there is a non-zero lift component at zero angle of attack
for cambered airfoils. See the NACA air foil section 2408 I mentioned
previously for one example. Note that air foil data can be applied to
finite wings since flow over an inifinite wing at geometric angle
of attack is similar to a finite wing at effective angle of attack.
Also, since it can be measured directly, wind tunnel data for finite
wings is generally taken at the geometric angle of attack.

> Paul Jaray developed streamlined car body work in the 1920s. His innovative
> body design featured a low-profile teardrop shape with a long tail to
> minimize the air resistance of passenger cars. The long tapering tail bent
> the air, it induced the air into following the gently tapering bodywork of
> the vehicle, thus preventing the formation of a negative pressure area
> behind the vehicle.

Hungarian engineer Paul Jaray was the first to promote the full-on
teardrop shape for an automobile. Jaray had designed a new series of
Zeppelins that featured the teardrop shape and applied his ideas to
automobiles, applying for a patent in 1922. Jaray tested a series of
streamlined automobiles in the Zeppelin work's wind-tunnel in
Friedrichshafen, achieving drag coefficients as low as 0.2. He went
on to design a variety of aerodynamic bodies for Tatra, BMW, Benz,
Adler, Mayback, Audi and Hanomag and influenced a number of others.
Chrysler was forced to pay royalties for the Airflow to Jaray, as was
Peugeot (for the 402). IIRC, the Tatra T87 was designed by Hans Ledwinka
with the body based upon proposals submitted by Jaray. Ledwinka's Tatras
were rear engined (the T87 was an OHC V8 and the T97 was a flat four) and
air cooled and the designs would heavily influence Ferdinand Porsche.

Jaray's patent was contested by another aeronautical engineer, Edmund
Rumpler but was ultimately upheld. Rumpler had debuted a mid-engined,
aerodynamic automobile (the Tropfen) at 1921 show in Berlin. Benz used
Rumpler's ideas in a 1923 race car but Rumpler returned to aviation.
Rumpler was later arrested by the Nazis because he was Jewish but was
protected by Goering who knew of his aircraft designs. Rumpler's
design was wind tunnel tested in the late 1970's at VW and recorded a
Cd of 0.28.

While aerodynamically efficient, the Jaray teardrops were long and not
always easily applied to practical shapes. Based upon experimental
research conducted on buses, Reinhard Koenig-Fachsenfeld applied for
a patent on the chopped tail as a practical alternative. At around the
same time, Professor Wunnibald Kamm (head of the Automotive Research
Institute at Stuttgart Technical College) published a textbook that
described a similar truncated tail. Fachsenfeld was persuaded to sell
his patent to the German state and Kamm was funded to develop the concept.
Another university professor, Everling was onto the same idea and his
design was among those tested by Kamm. Kamm's research showed that a
properly truncated Jaray tail had less drag than a shortened tapered
tail. The full length tear drop is still a lower drag shape, of course.

When fairing in and truncating the tail, you want to do it in a manner
that raises the base pressure (the pressure acting on the aft end of
the vehicle) while making the base area (where the pressure acts) as
small as possible. There's a point of diminishing returns where
increasing the tail length has progressively less effect. Kamm's
research led him to the conclusion that you should find the point where
the tail is half as wide as the maximum width of the vehicle and cut it
off there. This Kamm truncated tail is what Pete Brock applied to the
Cobra Daytona from above and from the side, you'll see it tapers in both
dimensions. Fairing in the Pantera sugar scoop will help in one dimension
only so will not be as effective as a true Kamm tail.

Somewhere around here I have a copy of "The Aerodynamics of Land Borne
Vehicles" which details some of the early wind tunnel research on cars,
trucks, and trains.

> I do remember a drag coefficient being quoted for the Pantera of .29.
> Was it from this test? That's an impressive number even today.

I don't think that number was quoted in the Style Auto test.
I have one reference that shows a 1972 Pantera Pre-L as having:

Cd = 0.34
A = 18.23 square feet
Cd * A = 6.20

Assuming they ignored rolling resistance, I can get a decent match to
the HP required numbers in Style Auto for a value of Cd * A = 8.2035.
It may be the case they figured in a rolling resistance in the data.
I think the frontal area is in right ballpark. We can bracket the
frontal area on the high end by width times height and on the low end
by track times height. Using the specs on Pantera Place (from an August
1971 Car and Driver article):

A = 43.4 inches * 58 inches = 17.48 sq ft
A = 43.4 inches * 67 inches = 20.19 sq ft

Averaging the two numbers yields 18.835 which is close to the referenced
18.23 value. That area value would imply the coefficient of drag is 0.45
for the Style Auto data. That's relatively high so I wonder if they figured
in some sort of rolling resistance.

The Pre-L Pamteras had the chrome bumperettes and narrow tires. The later
L models had the rubber safety bumpers and may have been a bit slicker.
GT5-S had the Countach-like wings and flares. Those would have considerably
higher drag as well as larger frontal area.

If you ignore rolling resistance, the following easily derived formula
can be used to estimate a car's top speed:

/------------
15 / 1100 P
Vmax = ---- \ 3 / -------------
22 \ / Cd A rho
\/

where:

P = rear wheel power in horsepower
Cd = drag coefficient
A = frontal area in square feet
Vmax = drag limited speed in miles/hour
rho = density of air in slug/cu. ft.
= 0.002378 slug/cu ft. (at standard sea level density)

Note this only considers aerodynamic drag and not rolling resitance
and will underestimate the power required to go a given speed.
However, if you use coast-down times (at multiple speeds) to estimate
CdA, it will overestimate the required horsepower as rolling resistance
will be assumed to vary as speed squared when it actually varies to
the 1.X power. Using both calculations will allow you to bound the
power needed. Of course, this assumes optimal gearing such that
rear wheel torque peak occurs at the intersection of the drag/speed.
In general, aerodynamic drag dominates so the answer isn't that far
off.

If we assume Cd * A = 8.2035, we get a decent match to the HP required
numbers in Style Auto at 99, 118, 140, and 162 MPH. Plugging in
200 MPH and solving for HP required (at the rear wheels) indicates
447 HP:

If we assume Cd * A = 8.2035, we get a decent match to the HP required
numbers in Style Auto at 99, 118, 140, and 162 MPH. Plugging in
200 MPH and solving for HP required (at the rear wheels) indicates
447 HP:

Speed Drag HP required Calculated
(MPH) (lb) from Style HP
Auto
------------------------------------------
200 -- --- 447
162 556 238 238
140 426 159 153
118 313 100 92
99 218 58 54
81 139 30 30

Adding downforce through rake, wing, or diffuser will only increase
drag. wider wheels tires, etc.


I used to have a NASA paper that characterized rolling resistance but
can't seem to find it. I searched a bit on the 'net and came up with
an equation of the form:

fr = fo + 3.24 * fs * (v_mph / 100)**2.5

where:
v_mph = speed (mph)
fo = basic coefficient
fs = Speed effect coefficient

Assuming the tires are rolling on clean concreter, warmed up and inflated
to proper pressure the following coefficients were suggested:

fo = 0.008
fs = 0.0018

Plug these back into the equation for rolling resistance:

fr = 0.008 + 3.24 * 0.0018 * (v_mph / 100)**2.5

For weight in pounds:

drag_rr = fr * weight

where:
drag_rr = drag due to rolling resistance

For velocity in ft/sec:

HP_reqd = drag_rr * v_fps / 550.0

where: HP_reqd = horsepower required to overcome rolling resistance for a
given speed and weight

V_fps = v_mph * 3600 / 5280

I wrote a little program and for the Pantera example used above:

Enter drag coeficient: 0.45
Enter frontal area in square feet: 18.23
Enter velocity in miles per hour: 200.
Enter vehicle weight (including driver and fluid weights): 3100.

It calculates the following:

Drag due to aerodynamic drag (pounds) = 838.8860086847279
Drag due to rolling resistance (pounds) = 127.0713993474226
Horsepower required due to aerodynamic drag = 447.4059065147985
Horsepower required w/rolling resistance = 515.1773209689964

If the assumptions are correct, it looks like a stock bodied '71 would
need on the order of 515 RWHP to turn 200 MPH on a level concrete surface.

> Does anyone know the HP at 8000+ RPM the Bloomberg's Pantera delivered
> for their 209MPH run at Bonneville?

Remember that land speed cars routinely tape seams, remove mirrors, lower
ride height and use ballast instead of wings for stability to reduce aero
drag.

Dan Jones

> If the issue is that droppong the nose creates increased frontal area, air
> dams would also be bad. I thought that keeping air from getting under the
> car is a good thing. I thought a lot of new cars have air dams just for
> that reason..

Somewhere in the database, I have some info on 76 individual wind tunnel
tests that were carried out in the Maryland University wind tunnel on
a 3/8 scale model to arrive at the original GT40 MKI body shape. Based
upon those tests, a full-size model was built and tested at Ford's own
wind tunnel in Dearborn. Ford used the Lola GT as a baseline, comparing
it to various revisions of the baseline GT40 shape. Some results are
presented below:

Vehicle Yaw Speed Lift Lift Lift Drag
(MPH) Front Rear Total (lb)
(lb) (lb) (lb)

-----------------------------------------------------------------
Lola GT 0 200 528 168 696 503
15 200 768 384 1152
-----------------------------------------------------------------
GT40 with 0 200 540 108 648 519
High Nose 15 200 844 362 1206 614
-----------------------------------------------------------------
GT40 with 0 200 445 199 644 507
Low Nose 15 200 704 422 1126 596
-----------------------------------------------------------------
Front Spoiler 0 200 326 266 592 513
#1
-----------------------------------------------------------------
Front Spoiler - 200 --- --- --- 531
#2
-----------------------------------------------------------------
Front Spoiler 0 200 236 272 508 488
#3 15 200 309 343 652 591
-----------------------------------------------------------------

Front spoiler #1 was 2.67 tall and was added below nose, behind the
air intake. Front spoiler #2 was in the same location but twice as
tall. It reduced lift but was deemed to not have enough ground
clearance. Front spoiler #3 was 3 1/2" tall and faired in. Recessed
headlights were chosen as raised headlights resulted in "marked increases
in lift and drag".

Many of the tests were directed towards trying to find the lowest drag
way to provide air flow for the cooling system, the induction, engine
compartment ventilation, interior ventilation, and brake and shock
absorber cooling air. The designers originally wanted to use twin side
radiators mounted in the engine compartment but tests on the full scale
wind tunnel model indicated 8000 CFM would be required which was deemed
not possible with the side intake duct layout. A conventional front
mounted radiator with intake and outlet beneath the nose was a little
better. The final solution was to take air in at the high pressure
region below the nose, let it flow past an angled radiator and exhaust
out the low pressure region at the top of the nose bodywork. Anti-dive
and squat were designed into the suspension to keep the cars more level
so as to not upset the aerodynamics.

Even with all the wind tunnel work, Ford was learning as they went and
the GT40's airflow management proved insufficient once the cars got out
in the field. The wind tunnel models were not fitted with the internal
ducting so it was only later discovered that 76 horsepower were being
consumed up just trying to ram air through the car at high speed. The
cars were modified in the field to fix one problem like cooling only
to change another, like the aerodynamic balance resulting in yet another
problem. Ken Miles spoke of the problem:

"The aerodynamic problems we've had with the car were essentially ones of
air flow within the car being affected by external details. For example
we were getting very little air flow to the brakes, although they had huge
ducts ostensibly directing vast quantities of air at them. In fact, the
brakes were overheating badly. The engine was getting too hot. The
engine compartment itself was getting too hot. The cooling water was
getting too hot. The engine and gearbox oil was gettting too hot. All
this in spite of a large number of aperatures which should have supplied
them with more than enough air. We discovered that what was happening was
that due to design changes that had been made over a period of time,
probably without reference to the original specifications practically all
of the ductwork was at a "stall " condition" i.e. no air was moving in the
ducts".

Ford's aeronspace division Aeronutronics was brought in to instrument a
GT40 with pressure and temerature sensors on various parts of the body
(externally and inside the ducts). From this data, the Shelby team was
able to modify the cars properly. Even when the MKII's appeared, Ford
still had some aerodynamic lessons to learn. Phil Hill wrote "The second
year at LeMans we were in deep trouble when we first arrived, thanks
to a diabolical instability that had been supposedly eliminated in
stateside testing. The MKII's were simply terrifying down the Mulsanne
Straight. We ended up tacking on little eyebrow spoilers as well as an
additional little spoiler across the back to solve the problem. I also
remember early Ferraris with so much front end lift that the steering
became progressively lighter as speed climbed until finally the rebound
stops were a factor... we could have called it up-force."

Dan. You mentioned an interesting point, that you would think that the L front bumper could be slicker?
Well I presume that you mean less nose drag but I am wondering if you recall seeing any nose lift numbers with that bumper and or with any of the front spoilers like the little GTS or the Revson?

It's a long time ago and I don't think I ever saw any numbers on it but I think Pete Revson made that front spoiler after taking the first Pantera he drove, on one of his little joy rides? LOL.

I know the steering feels light over 150 with no nose spoiler. I didn't actually realize how light it was getting around 170? Something like 314 pounds lighter? Wow? Makes sense to me.

I know the little GTS front spoiler helps a little at that speed but I wouldn't attempt 200 without very serious help in the front.

Is there anyone who would care to share their knowledge about solving the aerodynamic front lift at speed on the Pantera? I promise I'll be quite and listen...and not interupt...and not be abusive. Really.

Wow...amazing stuff Dan....my head just expolded

I hope there won't be a test?

Dan,
Remind me to never ask you what time it is. Ha ha ha.
Forest

Thank you, Dan!

Does the 'std' rear wing create lift, drag or actually do anything?
To my knowlege no one has actually checked in a wind tunnel or with any instrumentation, but a few observations:
First, the 'std' wing is also used by the Lambo Countache, and in a road test a few decades ago, a magazine pitted the Ferrari Boxer against a Countache at Mid-Ohio road course. The Ferrari was slightly faster so Lambo technicians removed the wing; the Countache then gained about 15 mph and beat the Ferrari's time.... but there were big black spots on the track where rear end lift had caused the Lambo to twitch sideways some 3 ft at a time... at 180 mph. The test driver, pale and shaking, declined to make another run. With the rear wing, the car was stable and easy to drive but slower.

Second; a British magazine ran an informal test on a then-new '87 GT5-S both with and without the 'std' wing on one of their famous race courses. The article noted that lap times were several seconds faster with the wing, although the car 'felt' stable in both configurations, according to the driver.

Third, Larry Stock says that when he was drafting Hennessey's Viper at 180mph during a Silver State event a few years back, rear end lift caused his '73 Pantera to wheelspin noticably: the tach suddenly climbed. He now runs a small NASCAR-style blade spoiler attached to the trunk lip, not the decklid, to go with his big air-dam & splitter. The combo seems to balance the Pantera better at very high speeds.

Bottom lines: Aerodynamic balance at 170 and above is different than at 150. Pushing down really hard on one end of a car will cause the other end to rise, pivoting around the center of balance. No hard facts but it seems advisable to carry some 'Depends" if you attempt to go real fast with no aerodynamic aids on either end of your Pantera!

When people ask me if I need the spoilers on my Pantera, I have always said it "Depends" on you point of view?

> Well I presume that you mean less nose drag

Yes.

> I am wondering if you recall seeing any nose lift numbers with
> that bumper and or with any of the front spoilers like the little
> GTS or the Revson?

The Style Auto numbers are the only ones I've seen. It's hard to
tell from the pictures I've seen but the Revson spoiler doesn't seem
to have much of an angle of incidence. It looks more or less flat.
Anyone know what the angle is? Kirk Evans has a similar front spoiler.
I have the "no holes GTS spoiler" to try on one of my Panteras one of
these days. You can see its angle of incidence (also Kirk's front
spoiler and Revson's) in this thread:

> I hope there won't be a test?

Heh, heh, heh. No tests.

> Remind me to never ask you what time it is.

Don't get me started on space-time :-)

Dan Jones

Tomorrow Dan will have our rocket science seminar.

I was reminded the other day of a conversation had at one time with Mike Cook about aerodynamics on the Pantera.
Hall took one of his Panteras to Bonneville and had Mike drive it.
The rules limited the car to factory stock or at most factory add ons.

The configuration of the car they ran had the fiberglass L front bumper, late model (lamborghini) "Hibatchi" grills, and the GTS chin spoiler.

Each added to the stability in their own way and this combination made the car stable to it's top speed which was something like 212 mph.

This may be the day they blew the elephant ears off of the car too? I seem to remember a picture of the drivers side scoop laying on the salt with silver duct tape on it? Should have tried the black duct tape?

Of course no one was going around turns with it but frankly even if you know of some 212mph turns, you had better drive. I'll just watch and take pictures ok?

Angle of incidence sounds like a serious moving violation offense that I'd expect the NYS Police Trooper to hit me with? You can't fart in the car here either. It's a serious violation. They should only know?

You know the Police are required to have 62 college credits to apply. They tend to throw that in your face a lot.

I have the GTS spoiler on my car. What angle are you looking for? The variation from horizontal? I can put a level on it and use my trig?

> Tomorrow Dan will have our rocket science seminar.

I've had the classes from one of our Germans.

"Our Germans are better than their Germans."

> The variation from horizontal?

Yes.

Dan Jones

The angle varies on the GTS spoiler depending on where you measure it.

In the center it is something like 0-2 degrees down.
By the time you are under the headlamps it is down in the 2-5 degree area.

To a casual look, it appears to be completely horizontal until the ends where it's incline accelerates more briskly to something like 15-20 degrees.

So I suppose that it has some function of downforce but cosmetics are also a consideration in the appearance?

Under the presumption that it is 100% functional, then I would have to think then that the downforce is then intended to be more concentrated towards the corners or I suppose to the vicinity of the front tires.

These are the approximations for now. If you require more precise measurements I'll have to verify the car is sitting level, etc.

I do play with a lot of cars and therefore sometimes my memory from one confuses the actuality on another, BUT I want to say that this spoiler provides something like 70 pounds of downforce to the nose. At what speed? 100mph.

Where do these numbers come from. Beats me but apparently there are a couple of cities in the Midwest where a lot of the children look like me and yet I have never been there? Everything came from somewhere?

Memory can sometimes be convenient Dan?