Cobra drag co-efficient....is it a "barn door"?

[xb-60]

Every now and then (ie regularly) I see a comment comparing a Cobra at speed to "pushing a barn door through the air", or "pushing a brick....." etc
Wouldn't almost any Cobra have an impressive enough power to weight ratio that would overcome however much aerodynamic drag a Cobra is lumbered with?
Does anybody know what the drag co-efficient (Cd) of a Cobra is?
Cheers,
Glen

[tkb289]

Glen,

Great question and I bet some of our members will have some good information.

For precise answer, I wonder if it also depends on what exact model of Cobra we are talking about… 289 or 427, with or without hood scoop or oil cooler scoop, so forth and so on.

Then compare that to what Peter Brock did to streamline that 'brick' … what's the co-efficient of drag for a Daytona Coupe ?

[mdross1]

This has been discussed for sure.Useless info for me since there is nothing I would ever do to change the look of the Cobra all for the sake of a high speed run.Was once warned of running a Cobra over 140mph because of brass windshield mounts.So the brick thing aint such a bad thing.

[RICK LAKE]

xb-60 Glen, With the large radiator opening, windshield rake, front duct openings for brakes, and hood scoops. These are all drag killers of the cobra.
Couple of the pros here have enclosed the radiator opening like nascar. Taped the hoods, no or small hood scoops only, full belly pans, no or a small wind deflector( windshield ) side exhaust close to body or even stuck into the lower rocker panels with alot of heat barrier protection.
Horse power to weight ratio is great for a cobra but body style is not. There maybe 1-4 cars here in the club that MIGHT be able to break the 200 mph range. The power on these cars are all over 750hp. I know from my car that it gets happy and lite in the front end at 128 mph with the paxton hood scoop on. This is why there is no way the 2 paxton cars could ever hit this number. It was a great market selling idea. 180's seam to be about as far as some guys have gone.

If you enclosed the cockpit, closed off the front opening, belly pan, no hood scoop, tallest tires you could find, a beast of a motor, and a guy with BIG B@LL$ to drive, rake the cars front end to the ground, 200 mph is possible. Need to under stand that airplanes can take off and 140 mph to 160 mph after that, it's all ground effects to keep you on the ground. I think you could punch the car to this speed but not be able to maintain it long.

I have thought about going after the 198 mph record but the MAN that owns it was the first and a legend in the Cobra world. It should be easier today than back in the 60's with less engineering envolvement. You can break the record but never be the first. I think that this is the way it should stay. I might take a shot at it in an event at Maxon in a couple of years. Need to finish a motor with about 800hp first with higher compression in the 14.0 range. CD for a cobra, a guess of 2.0-4.0. Rick L.

[SunDude]

I posted this question a few years ago. You can read through the old thread HERE if you want.

[joyridin']

I think it was one of the Top Gear programs on the Veyron where they made a comment that it took 250 horsepower to get the car to 150 mph, and the other 750 horsepower to get it to 253 mph. It has a normal cd of .41 and a cd of .36 when lowered for a high speed run.

You can push a brick through the air, but you need a lot of hp!

[Dwight]

I save this article several years ago by L.E. Mayfield.
The charts don't copy paste as they should. Go to his web site for the charts. Don't forget Dick Smith's 198 mile per hour run in his Cobra in 1967 I think.
Dwight




Automotive Analyses
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FFCobra Forum Question: How fast is my Cobra with this much horsepower?
This also works for all vehicles, shhhh!
INTRO
Once upon a time, in a land far away, I was a huge fan of the original Cobra and it's final originator, Shelby. I went to the plant is Southern California, but at the time was a starving student or just out of school at Cal Poly, SLO. I could not swing the 6 grand or so, so I quietly walked away. Then I bought a used Tiger. Jeeze, I am off track and have just started this. Well, anyway, I spent an entire career with the Boeing Company doing odd jobs. Some of them involved aerodynamics and such.
Now I know how you all feel about your cars, Cobras, whether or not original or a reproduction. I know that many of you are true performance fans and have hopped up your cars to the n th degree. But, after all that hopping up, you find that there is little in the way of knowing just how fast it is or can be. Roads with the public on them just aren't the way to go and the drag strip just isn't quite enough either. What I have done for my Tiger, I am gonna try and do for you. I am going to develop a set of tools that you can use to figure it all out: "Just how fast will my Cobra go?"
BASIC EQUATIONS
The math is generally pretty easy and has been developed many times by many people, so I wont go into the derivations of the equations or where they come from. At the end, I'll give you a reference text that you may or may not want to purchase (no, I don't sell books).
There are only three things that need to be considered in determining how fast you car can go. Now, mind me, in each of these things there is a plethora (I love that word!) of other factors that have to be found first.
Total Road Loads
The summation of all the forces is called road load. It is made up of rolling resistance, aerodynamic forces, and road grade. When you have determined these then you have found the power requirement for the interface between the tire and road. Here is what this equation looks like:
Total Load (pounds) = fr * W + � * rho * V * V * Cd * A + W * sin(theta)
where:
fr = is the rolling load coefficient (dimensionless)
W = the vehicle weight (pounds)
rho = air density (slugs)
V = speed (ft/sec)
Cd = drag coefficient (dimensionless)
A = frontal area of vehicle (sq ft)
theta = road grade (degrees)
Subordinate equations
Each of the terms in the above have some underlying equations that must be used. Some can be complex, but I will make some assumptions to simplify.
Tire Rolling Resistance
The rolling resistance is very complex and has to do with the road surface and the tire itself. Most work has been done in the speed regime where we drive mostly and for heavy trucks. So I am going to use the equation that fits you best: nice clean concrete roadway, tires well aired up and at the proper temperature. That equation is:
fr = fo + 3.24 * fs *( v / 100) 2. 5
where:
v = speed (mph) {note that this is little v not big V}
fo = basic coefficient
fs = Speed effect coefficient
I am going to make an assumption here that you all have warmed up the tires for about 20 miles or so and have the tires really aired up: 50 psig or so at least! Then the two coefficients fo and fs are approximately:
fo = 0.008
fs = 0.0018
Plug these back into the equation for rolling resistance:
fr = 0.008 + 3.24 * 0.0018 *( v / 100) 2. 5
Let's try a couple of examples, say 100 mph and 200 mph
fr = 0.008 + 3.24 * 0.0018 (100/100)2. 5 = 0.0138 for 100 mph
and
fr = 0.008 + 3.24 * 0.0018 (200/100)2. 5 = 0.041 for 200mph
If we multiply the coefficients by the gross vehicle weight, then we have the Tire Rolling Resistance!
for 100 mph, Tire Rolling Resistance = 0.0138 * 2700 lbs = 37.26 lbs
for 200 mph, Tire Rolling Resistance = 0.041 * 2700 lbs = 110.7 lbs
So now we know how to determine Tire Rolling Resistance.
Air Density
Air density, rho, can be rather hard to determine from what the weather news on the local station gives us. They typically use some corrected barometric pressure values and this hoses up the ability to correctly determine air density. So we will start from first principles and develop a way to get air density from real pressure and real temperature.
P = rho * g * R * T
where:
P = absolute pressure (lbs/sq ft or psf)
rho = air density (slugs)
g = local gravity (32.174 ft/sec2)
R = universal gas constant for air (53.3, you figure out the units)
T = temperature (degrees Rankine = 458.6 + F)
F = temperature (deg Fahrenheit)
Solving for rho
rho = P / (g * R * (458.6 + F))
Now I use an absolute pressure gage to measure absolute pressure, but it reads in psia, not psf. So we need to multiply the P by 144 to convert it to psf. Then rho will be in slugs:
rho = 144 * P / (g * R * (458.6 + F))
which is what we wanted in the first place. Now this is an interesting equation because it can be used to tell how much your horsepower is reduced at any altitude and any temperature and ditto for aerodynamic losses. You need only multiply the hp or drag number by the ratio of the new density divided by the old density to effect the change. Say you had your motor dynoed at (or corrected to) standard seal level conditions where the density is 0.002377 slugs and the temp is 60 degrees F. Now you are at Denver (mile high) and the temperature is about 41 degrees out. Here is how to find the ratio:
rho/rho0 = (144* 12.27psia/ (32.174 * 53.3 * (458.6 + 60)) / 0.002377
= 0.001989 / 002377 = 0.8368 or a loss of 16.32%
See how that works? If your gee whiz wham bam motor produces 550 hp at std conditions, then it will make on 460 hp at Denver on a standard day there. The above can be used for any pressure and temperature conditions.
Drag Coefficient
Boys and girls, this can be beastly to figure out, but if you want to try then see my article, drag coefficient, for how to determine the Cd using a coast down method. Analytically it is a booger! So I am going to use a published Cd of 0.42 for the open bodied Cobra. A top might reduce it a little bit, but, not much.
Frontal Area, A
This is not much of a mystery, but people always seem to get it screwed up. If you went out in front of your car and hunkered down to look straight on at it and drew an imaginary line around the perimeter of what you saw, you would see frontal area. But, how do you get it? Well, one way is to take a photograph with a ruler for scale, overlay that with a gridded paper you can see through and count squares. Another way, not as effective but a whole lot quicker and good enough is to measure the tallest point and the widest point, convert these to feet, multiply to get square feet, then take 80% of that. This will be good enough for comparisons. With the wind screen up, this amount to about 18.5 square feet for the frontal area (A) for the Cobra 427.
Theta
This is the road grade. I am assuming that most of you are smart enough not to be racing up hill or down but are on level ground. Theta in this case is 0 degrees. But if for some reason you want to go either up or down, theta is equal to the grade in percent (close enough, anyway).
Mechanical losses
There are losses between the flywheel and where the rubber meets the road. I assume that the clutch is locked up and if you are using an AOD (yeeewww, you say, but, they handle more torque) and it is in OD and torque converter is locked up, a manual tranny is in top gear, and a Fox body 8.8 inch rear end. Some of the loss numbers are: Auxiliary equipment about 2%, Manual trans about 6%, auto trans about 8%, torque converter about 3 %, rear end about 4%. Lots of variables here like fluids, temperature, so we are going to use an average of 15% for all examples to get from flywheel hp to rear wheel hp. And vice versa..
Horsepower and Drag Relationship
As torque and horsepower are related, so to are drag and horsepower. The relationship is simple and I merely present it here.
HP = Drag * V /550
SOLUTIONS!
Ok, I think we got enough to go on now. I had planned on using horsepower in the equation and solving for the maximum speed, but this quickly gets beyond the math or spreadsheet capabilities of a lot os us in a really big hurry. So what I am going to do, is finalize the equation in a manner that you can use your own particular data. I am going to solve the equation for speeds from 10 to 250 mph (yeah, right...) so that you can simply find your flywheel horsepower go accross the chart and find your top speed. Ok?
Total Load (pounds) = fr * W + � * rho * V * V * Cd * A + W * sin(theta)
Putting in all the stuff we found above, we get:
Drag = 0.008 + 3.24 * 0.0018 *( v / 100) 2. 5* W + � * rho * V * V * Cd * A + W * sin(theta)
But remember, we are racin' on flat surfaces so the last term, the theta term goes to zero and drops out.
Drag = 0.008 + 3.24 * 0.0018 *( v / 100) 2. 5* W + � * rho * V * V * Cd * A
Also remember that
HP = Drag * V / 550
So if we multiply Drag by V / 550 on each side of the equation, we have a solution for Horsepower vs the independent variable, V.
Drag * V / 550 = HP = {0.008 + 3.24 * 0.0018 *( v / 100) 2. 5* W + � * rho * V * V * Cd * A} * V / 550
I programmed this into my Excel spread sheet to find HP vs Speed. The results are shown below.
Speed (mph) Rolling Drag (lbs) Aero Drag (lbs) Total Drag (lbs) RWHP FWHP
10.0 18.0 2.0 19.9 0.53 0.61
20.0 18.1 8.0 26.1 1.39 1.60
30.0 18.6 17.9 36.5 2.92 3.36
40.0 19.2 31.8 51.1 5.45 6.27
50.0 20.2 49.7 70.0 9.33 10.73
60.0 21.6 71.6 93.2 14.91 17.15
70.0 23.3 97.5 120.8 22.55 25.93
80.0 25.4 127.4 152.8 32.59 37.48
90.0 28.0 161.2 189.1 45.40 52.21
100.0 31.0 199.0 230.0 61.34 70.54
110.0 34.5 240.8 275.3 80.77 92.88
120.0 38.5 286.6 325.1 104.05 119.66
130.0 43.1 336.3 379.4 131.55 151.28
140.0 48.2 390.0 438.2 163.65 188.20
150.0 53.9 447.7 501.7 200.71 230.81
160.0 60.2 509.4 569.6 243.10 279.57
170.0 67.1 575.1 642.2 291.21 334.90
180.0 74.7 644.8 719.4 345.41 397.22
190.0 82.9 718.4 801.3 406.08 466.99
200.0 91.8 796.0 887.8 473.60 544.64
210.0 101.4 877.6 979.0 548.35 630.60
220.0 111.7 963.2 1074.8 630.71 725.32
230.0 122.7 1052.7 1175.4 721.08 829.24
240.0 134.5 1146.2 1280.7 819.83 942.81
250.0 147.0 1243.7 1390.7 927.36 1066.47

The data for Speed vs Flywheel horsepower is plotted below:

I hope this helps all of you settle many debates and/or starts a lot of new ones!
Copyright (C) 1998 - 2004, all dates inclusive, L.E. Mayfield - All Rights Reserved
Return to Mayfield Motor Sports Homepage

[twin turbo]

I would guess the drag coefficient is around .6 based upon some coast down testing another member did (Dominik) with a hard top installed. I think it would take around 600 rwhp to hit 200 mph with a windscreen (no windshield).That's assuming you could find a long enough straight and you didn't become airborn or lose control. Cheers.

[tirod]

Open coupe, 289, about 145mph, .41+ cd.
Lemans coupe, 289, with roof, about 155mph, the roof helped a bit, without adding frontal area, and reduced drag, maybe .38.
Daytona Coupe, 289, tagged on Mulsanne at over 190mph, about .24.
Daytona Coupe, F5 (closer to the Italian design,) 650hp plus, 216mph.

The difficulty is that to go ten mph faster, you need double the hp, or reduce the cd by a lot more.

Tilt the windscreen, some help. Track roadsters were commonly slanted back as much as they could get away with. Remove the windscreen and add a small bubble, significantly more. Lower the car, go faster, add a dam, splitter, and tray under the nose, even more. Recontour the rear trunk and control the adhesion of air to keep it on the deck, faster yet.

A good example is the Audi TT, which at speed had some serious instability issues. They were recalled and a wing/spoiler added by the factory. Cute design, horrible aerodynamics. The problem was the center of air pressure on the car being ahead of the center of gravity. It pushes the nose around and it resolves by swapping ends.

Look at the LSR cars at Bonneville, the 249mph Studebaker coupe, for example. Very similar frontal area and cd compared to the roadster. They added a wing with side boards to increase the swept air surface on the side, and control the air coming off the roof and tail. It keeps the center of air pressure behind the center of gravity and makes it more stabile.

The Coupe with more aero work underneath and with a different rear air device should go a lot faster with 700 hp. The traditional spoiler was an expedient piece of aluminum tacked on at the last minute at a race to generate some vortex and reattach flow along that sloping roofline, plus enhance the affects of the Kamm tail. As designed, it needs more work to reduce lift overall. The side profile is still a wing - air has to go over it faster than what gets under it, and it creates lift. The original wing would have likely worked better if they had stuck with it and worked it out, even if it was tilted into a stall.

Here's some web sites to peruse: Bonneville and Land Speed Racing Links

Just one article of dozens here: http://www.autospeed.com/cms/A_2159/article.html

The entire history of the Daytona Coupe is basically the understanding by Shelby American in the day that they simply couldn't keep up on long Euro courses, even with 2 more liters of engine displacement. The result was the Coupe, which ran the same motor as the roadster, but ran 40mph faster on the top end.

Essentially, free hp because they didn't have to push a wall of air in front of it. The concept is reproducible and proven, lower the cd and you go much faster with the available horsepower. It's where that speed is needed - above 100mph - where the most engineering has taken place. Which leaves out the bulk of us. We simply don't go that fast due to a number of reasons, so we have little to no familiarity with the concepts involved.

And since the factories can't sell gas mileage to us yet, we also don't care. But it's starting to change. Wait for 2016 and the mandatory 33.5 mpg the CAFE jumps to, aero will get popular again because we will be buying it like it or not. Expect serious reductions in frontal area and a lot more attention to airflow.

So, is the roadster a barn door, yes, emphatically. Shelby knew it, and only saw success with it on short tracks that emphasized acceleration, not aerodynamics. When it came to top end, the roadster was a brick, and there was no doubt about it, it had to go. The Coupe won the GT Championship, not the roadster, something the 427 S/C fans don't like being reminded. Hence, the fascination with one lone 427 making it over 190. It takes another 2 liters of maximum power to push it that fast. The Coupe did it with a 289.

[rpatton3]

That was an incredible amount of "ciphering" which shows aerodynamic drag is the enemy. Huge horsepower can't compensate for that.

I fell in love with the 427 body style in the middle 1960's.
The Venus de Milo doesn't need to pump iron either!

Russell

[xb-60]

I'm thinking along the lines that it's a little unkind to call the Cobra a 'barn door' or a 'brick' when the drag force is related to the drag coefficient multiplied by the frontal area.
OK, given that the drag coefficient of the Cobra is probably north of 0.42, but its frontal area has to be quite small (we're not talking about a big barge here).
Multiply Cd x A for a Cobra and it can't be deserving of the 'barn door' tag, can it?
The first road test of the Shelby's 260 engined Cobra (OK, hotrodded no doubt) gave a top speed of 152mph. Not bad for a 'barn door'
Cheers,
Glen

[xb-60]

The theorists and the practical results don't always line-up...,,
There's the documented story about Shelby bringing in Benny Howard (aeronautical engineer, test pilot, airplane racer, airborne bootlegger) to give an opinion on Pete Brock's Cobra Daytona prototype. Howard's expert opinion was that the Daytona would need 450hp to achieve 150mph (interesting, compared to what the roadster could already achieve).
Shelby had around 380hp available, and wanted 170mph from the Daytona.
Brock said "trust me", and we know the rest of the story
Cheers,
Glen

[tirod]

Uncharitable or not, the roadster was never designed with aerodynamics much in mind. AC just copied a Ferrari Barchetta body and went from there. That same chassis was used under the Daytona, which did manage another 40 mph with the same 289. The roadster, 152 tops, Coupe, 190+. No contest. It took the Coupe to win the GT Championship, and it wasn't brute force that did it. It was aerodynamics. Exactly what Shelby American intended and achieved.

The populist notions of the Cobra don't really hold up in the historical record or the track.

[Ralphy]

So now I know why the crappy fuel mileage! It's not the 433 cubes.



If I remember right the hardtops were part of improving the aero.

Ralphy

[Dominik]

Cd changes from 0.55 to 0.65
Frontal area is 16.6 sqft.

You need "about" 466hp (DIN, about 600 "hot rod" hp) to 200mph with Cd 0.51.
I'm not going into the 466 vs 600hp definition...

BTW, 350hp DIN should suffice with the single seater windscreen.
The frontal area drops to about 12.5 sqft. The Cd changes to...?

Now, that 350Hp is something to discuss!

[twin turbo]

Dominik, what is DIN?

[strictlypersonl]

Originally Posted by twin turbo

Dominik, what is DIN?

Deutsches Institut für Normung - Wikipedia, the free encyclopedia

Back when things were a bit looser, DIN ratings were about 10% lower than SAE. Engines were tested under more realistic conditions than the US allowed. Now, I think that the US methods are very similar to the DIN methods.

[Dominik]

Yes, DIN and SAE came closer in the early 70s. But the typical hot rodder likes the "old" SAE. Now, let me get into this:

A rear wheel horsepower reading of 500Hp does not translate into:
500x1,2 (20% drivetrain loss) = 600Hp, plus 80Hp exhaust and accesory loss = 680Hp. Let make it 700...

It does translate into 550Hp DIN (in my car, most cars).

Sorry, to burst your bubble: There is no 20% drivetrain loss (in direct drive, 4th gear).
Just imagine 100Hp which is about 70 kiloWatt (240000Btu) which would be the same as 70 off 1.000Watt electrical heaters, or blow dryers.

Your transmission would almost be glowing red hot.

[Dwight]

In a conversation with Keith Craft I asked what was the hp loss for a Cobra. Keith said they saw typical a 20% loss. He dyno's his motors before they ship out. Sometimes he installs them into Cobra and then dyno's the Cobra.
Some of the CC members have dyno'ed their Cobras with different sidepipes and report losses of 40 to 100 hp.
I think Keith's experience is of value because he dyno'ed the same motor out of the car and installed.
I have hear loss numbers of 15% to 27% for a Cobra. But for most of us it's a guessing game. I had mine dyno'ed on a chassis dyno for rear wheel hp. I can only guess at the flywheel power.

Several of my buddies have motor that were dyno'ed before they were installed into their Cobras. They can only guess at their rear wheel hp.

Dwight

[Dominik]

I agree on various numbers for losses due to poor exhaust design, but one shouldn't add 80 - 100Hp as a default to rwHp just to make it sound good at the next bench racing session.

And I don't agree on the 20% losses for the drivetrain. Your transmission engineers would kill you for that bad percentage. Also, nobody rated a Nascar 750Hp 358cui at 1.000Hp just because the valve train and friction took away 250Hp at max rpm.

Fact is, the 427 has a very bad drag coefficient. We tested it in 1995 with GM's (OPEL) engineering team on the German A5 Frankfurt-Darmstadt (no speed limit).

+/- 570Hp (DIN) to get to 198mph in the late 60s? Very much achievable by Dick Smith's engine builder. What windshield did he use??

But we will never change this SAE/DIN debate :-)