What is the drag coefficient of a Cobra roadster?

[dynoroom]

Why do you want to know?

[eschaider]

Originally Posted by Excaliber

...Man, wasn't Peter Brock something when "back in the day" with a limited understanding of CD he designed the Coupe!

Ole Pete was one sharp dude. He actually did a great deal of personal research into airflow and clean automotive design before he implemented it in the real world we know as the Daytona Cobra.

He studied the work of Professor Kamm quite thoroughly before the Daytona design was put to chalk on the floor and plywood on the chassis. To have the insight and also the where-with-all to go from concept to real world vehicle while part of an active racing effort is extraordinary. To do it in 90 days is unbelievable!

The concept and actual car design are a testament to both the vision and also just how far ahead of the pack Peter Brock was in those years. To knock on the door of 200 mph in that type of vehicle in the middle sixties speaks volumes about just how good those hotroders that took on Ferrari and the rest of the European racing elite really were.

Three other men played pivotal roles during that brief but intense development period. One was Shelby's Chief Engineer Phil Remington who could make anything out of almost nothing and one was Ken Miles who shook down and sorted the bugs out of the concept car that became one of the actual race cars.

Ken Miles was one of those very special drivers that had enormous talent, stamina and the ability to put into words what he discovered driving the car. Peter and Phil would take those cockpit reports and translate them into design refinements that continuously improved the car.

The Daytona exceeded everyone's expectations but not right out of the gate at the first track test. It took about a thousand miles of Ken Miles test driving and the third man John Collins who would ride shotgun without a seat to get the bugs worked out. When they were about done Ken lapped Riverside with a 183 mph pace that no one believed especially Ken, when the crew told him the car had a 3.73 (reported) ring and pinion.

When the axle ratio was verified back at the shop that was all it took. The new Daytona would go to Europe to do battle with Ferrari. By the time they got to Le Mans the last few reliability problems had been sorted out and the 180 mph Ferraris had a 196 mph Daytona to deal with on the Mulsanne straight.

Peter Brock's design came within a whisker of 200 mph in 1964. Impressive by any standard and a testament to the skills and ingenuity of those hotrodders from Southern California who wrote those special pages of automotive history.

A much better rendition of the Daytona and the rest of the Cobra story is on the Snake and Stallion DVD from Spirit Level Films.

Ed

[SunDude]

Originally Posted by dynoroom

Why do you want to know?

Two reasons, really.

Firstly, I'm just curious to know. It's one of those little trivial bits of info on the Cobra that I like to have in mind.

Secondly, I was trying to calculate the theoretical top speed for my SPF and needed these figures (see http://vlsicad.ucsd.edu/~sharma/Potpourri/perf_est.html). I realize that aerodynamic drag would be a major factor for the Cobra in roadster form (as we all know the Daytona Coupe's vastly improved aerodynamics resulted in huge speed gains at the top end).

I think I read somewhere that the Dodge Viper roadster's cd was in the neighborhood of 0.45-0.49, which would suggest that the Cobra's is nearer to 0.55 or so as eschaider points out.

[COBRA427]

I am by no means an engineer, but based on what all of you have said, which BTW, sounds very credible and logical to me, I just couldn't help thinking of Dick Smith's car reportedly going 198mph. I just find it too difficult to accept and believe that Dick was actually able to drive his car that fast.

As mentioned, if it takes a substantial amount of hp just going 110mph, and at 160mph, the Cobra, due to its shape, is hitting the aerodynamic wall, then how could it be possible, back in the 60's, that Dick could go faster by almost another 40mph?? Morris Clement in his well engineered car with air splitter, wing, flat belly pan, and tons of hp, I haven't heard that even he has been able to reach the speeds claimed by Smith. Something just doesn't add up.

I'm not trying to take anything away from Dick, but physics is physics. If I'm missing something important facts, I'd like to know.

[Bob In Ct]

On more than one occasion the cars were raced with a small piece of plexi in place of the standard windshield.

Bob

[Excaliber]

Cobra427, your right, Dick most likely didn't do 198 mph. It's pretty clear he actually exceeded 200 mph unofficially, with 198 being the official time.

Seriously, the evidence and support for Dick's run is substantial, I have no doubt he did it. What is really interesting to me is that Dick did not necessarily set out to break any speed records. This occured during a RACE, with other cars on the track at the time, he was just trying to win.

[Argess]

I still think the Miata is bad due to the sidemirrors.......

Look at those things....like the ears on Dumbo the Elephant......like wing flaps on a 747...

Seriously, the CObra does have a rather blunt front and steep windshield, but isn't the vacuum drag from not having a roof one of the more significant problems, (like the Miata). If that is the case, I wonder how the Cobra CD fairs when a roof is installed.

[SunDude]

Originally Posted by Argess

...I wonder how the Cobra CD fairs when a roof is installed.

Probably not much better, judging from the fact that in 1963 they installed a hardtop on the LeMans Cobra roadsters and decided they weren't fast enough for this track, which is what prompted Shelby American to design the Daytona Coupe for 1964.

[Excaliber]

Additional drag with a convertible top down is increased. I recall one of the magazine's ran a top speed test with a new Dodge in the late 60's or early 70's. Convertible, they ran about 150 mph with the top up, less with it down, but not by a lot.

The Le Mans Cobra picked up a few mph with the hardtop, not nearly enough to make a difference. The Ferraris were running the 180 mph range, matching or exceeding that was the target.

[DMXF]

I have fairly extensive data which supports the premise that a Cobra roadster in "aero" race trim (tonnau, race windscreen, lowered, open side exhaust, etc) will do 200mph with 600 flywheel HP. The Cd shown in my analysis is somewhere around .61, although I don't know how accurate that is because I was using correlation factors to match the actual data.

My opinion, for what it's worth here but based in large part on real data, is that Dick Smith probably did 198mph. It's doubtful he had 600hp (which he said he did), given the single four barrel MR he was running and what was state of the art in '66. It's more likely he was around 530-540 (if he had a HR that would have added roughly 20hp), but that alone could have got him approaching 190mph and the other 8mph or so was likely due to the draft of cars in front of him and maybe some tailwind.

[mdross1]

Put enough horsepower to a brick it and becomes very fast.

[Silverback51]

Originally Posted by mdross1

Put enough horsepower to a brick it and becomes very fast.

That defines the F4 fighter too.

[greg schroeder]

Originally Posted by jon@harrison.ne

The drag coefficient Cd has nothing to do with the size of the car,only the shape. The total drag force is proportional to the frontal area times Cd times speed squared.

Here's that formula again. It's pretty cool to see the HP loss value at speed.

http://www.gtechprosupport.com/support/AeroDragCalc.php

[Dominik]

Good morning!

Sorry to reanimate an old thread, but years ago we had a nice discussion about all of this. That thread got lost, but the frontal area is 16.6 sqft, the Cd of drag is about 0.6.

We couldn't determine the real value because it's a part of total drag and it's changing when the car lifts at speed (as does the frontal area).

In essence, Cd (coefficient of drag) is a variable, most likely from 0.55 to 0.65 for a Cobra.

To go 180mph you need 430Hp, with a hardtop and open windows (that's how we tested in 1995). Side note: If you reduce your windshield size to a single seater you need only about 320Hp to drive 180mph. That should improve your 1/4-mile time too.

[SunDude]

How coincidental that you should dig up this old thread, as I was thinking about it the other day.

It turns out that there's an FFR owner in my city who happens to be an aerodynamicist, working at the National Research Council's wind tunnel. I don't know if he's ever been able to estimate or measure the Cobra's Cd, nor have I met with in person yet, but when I do it's a topic I'll be sure to raise with him.

[Dominik]

We worked it out by accelerating and coasting down on a road with known profile using a manufacturers data and resources for it (GM/OPEL).

We were mainly after the torque, but the rest was a by-product. Interesting note back then: Your tires' losses can quadruple above the speed they were designed to.

It was 40 deg F then. That's why I mounted the hardtop.

[mdross1]

Doesn't matter much to this cat since most of the work my car does is from my rowing the gears and the big blocks problems are from traction or the lack of.Besides what a fine looking piece of masonary.

[Dominik]

Incidentally the photo taken from my car IS outside the OPEL mother plant.
Tire friction losses are a major factor at higher speeds, even with 500cui+ ;-)

[Dwight]

I found this in my old files from a few years back

Dwight


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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
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[Jerry Clayton]

Damn, I'm going to go faster than I thought