DeTomaso Mailing List: June 97, Message #337
     



From: "D.Jones" <m203253@ws2200.mdc.com>

Subject: Part 1 of 2 - Aero Stuff

Date: Thu, 26 Jun 1997 15:41:49 CDT



Mad Dog,



> In the August issue of Hot Rod Magazin, there is a good article on 

> backyard aerodynamics. In the quest for added stable high speed at the 

> upcoming Silverstate event in September I read this brief article. Is 

> there anyone out there who has calculated the combination of the front 

> drag area on the Pantera and the drag and lift coefficient?? The last 

> input quantifies turbulant rearend body lift indigenous to high speed. . 

> Someone who better understands aerodynamics help me out here!



I haven't read the article or calculated lift or drag for the Pantera

but I do have some info that might help you sort out your car's 

aerodynamics (or it may just confuse you).  A while back there was a

discussion on the fordnatics list about aerodynamics and I wrote a

lengthy follow-up to clear up some misconceptions.  I've included the

first of two parts here and I'll include the second part in another

post.  I had to break it up since the whole post was too big for Shane's 

mail program.



> Specifically, I am now looking at ways to additionlly decrease front end 

> lift by re-routing air around (and not under) the car. . .Quess this 

> means an air dam which is the only thing I haven't yet modified.    Your 

> input will be appreciated.



You might consider a slanted lip spoiler type front air dam.  In addition

to re-routing the air around the car, it will also provide positive

downforce.  You can tune the amount of downforce by change the angle.



Later,

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!  <g> 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.  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 windshied,

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 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 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. 



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