What is the drag coefficient in an F-1 car?

[Ciro Pabón]

This thing (Mercedes Benz Bionic: http://www.wired.com/wired/archive/14.02/play.html?pg=9) has a wind-drag coefficient of 0.19 "less than that of the Honda Insight, which at 0.25 is the most aerodynamic car in mass production". It imitates the body of a box-fish (and I am not making this up).

So: Do you know, geniuses , the wind-drag coefficient of a typical F-1 car? Thanks to you all, in advance.

[se7725]

The drag coefficient of a F1 car is about 1.30 from what I've read. That was a few years ago so with the reduction in areo from the rule changes and the development of the cars it probably has gone down.

[se7725]

Oh yeah, And it depends heavily on the track and the set up

[ginsu]

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[pompelmo]

f1's drag coeficient varies from 0,75 (monza) to 1,25 (monaco)...but is always arround 1!

[Bender]

That merc is a crazy car.

I like this Citroen C-Sportlounge
http://www.citroen.com/CWW/en-US/CONCEP ... UNGE_2.htm

It has some very interesting Aerodynamic features, like the MEMS "virtual spoiler", or the active wing underneath (!) the car.

Anyone think that the MEMS spoiler could make it into F1?

[Ciro Pabón]

Are you crazy? Or am I? What kind of units are you using? Imperial gallons of drag? I may be only a highway engineer, but I am PRETTY SURE Cd is around 0.3 for a well designed car. And I mean Cd like in:

F = 1/2 * rho * Cd * A * V^2

Where, of course, F is drag force, rho is air density, A is the frontal area and V^2 is velocity squared. I HAVE measured Cd between 0.5 (for a sphere) and 1 (for a box).

So, please, explain to me how could an F-1 car have a Cd of 1 point something? Do you, F-1 aerodynamicists, use another equation?

[bernard]

Are you crazy? Or am I? What kind of units are you using? Imperial gallons of drag? I may be only a highway engineer, but I am PRETTY SURE Cd is around 0.3 for a well designed car. And I mean Cd like in:

F = 1/2 * rho * Cd * A * V^2

Where, of course, F is drag force, rho is air density, A is the frontal area and V^2 is velocity squared. I HAVE measured Cd between 0.5 (for a sphere) and 1 (for a box).

So, please, explain to me how could an F-1 car have a Cd of 1 point something? Do you, F-1 aerodynamicists, use another equation? [/url]

F1 cars are not designed for minimal drag. If they were, we wouldn't see any wings on the cars. It's a compromise between drag, the needed downforce and the power with which the engine can pull on the straights. Therefore you would not expect to see a perfect drag coefficient in an f1 car.

[Ciro Pabón]

Thanks, Bernard. Very reasonable. But, again: are not Cd and Cdi (coefficient of drag, induced) measured independently? Like in an airplane. Cdi equation is a different one, as you surely know.

Cdi = (Cl^2) / (pi * AR * e)

where: Cl = coefficient of lift, pi=pi, e = efficiency factor and AR = s^2 / A (s = span, A = wing area).

And, of course, Cd total = Cd + Cdi. And I would presume you want both coefficients as low as possible and a Cl as high as possible. Could you clarify it for me, please? [-o<

[Guest]

Of course, the Lift/Drag ratio is always changing in an F1 car, and they are definitely not the most aerodynamic cars, the wheels alone count for 35% of the drag. Closed wheel racers like LeMans cars will destroy an F1 car in Top Speed due to drag alone.

Here's some stats on the Ferrari F2000 at peak efficiency (different top speeds require different L/D ratios):

Cl: -2.381
Cd:0.779
Balance: 38.05%
L/D Ratio: 3.05

Now, the overall L/D ratio is all we can really use to compare with other cars.

Bentley EXP Speed 8 LMGTP, '01

Lift-to-drag ratio: 3.70:1
Coefficient of drag: .5038
Coefficient of lift: -1.87

1999 Ferrari 360 Modena

Lift-to-drag ratio: .73:1
Coefficient of drag: .34 (factory claim)
Coefficient of lift: -.25 (factory claim)

2003 Lister Storm LMP

Lift-to-drag ratio: 4.81:1 (peak L/D better than 5.0:1)
Coefficient of drag: .5499
Coefficient of lift: -2.65

[schumiGO]

F = 1/2 * rho * Cd * A * V^2

I don't know exectly situation now but in 2000 and 2001 in soe track not so fast and slow maclaren has Cd that used in F = 1/2 * rho * Cd * A * V^2 formula near 0.67 and 0.65


So now it must be a little mort 'cause aero rules had been changed..

So now range [0.75:1.25] is realy possible.

[bernard]

Thanks, Bernard. Very reasonable. But, again: are not Cd and Cdi (coefficient of drag, induced) measured independently?

Yes, correct, they are. You still end up with the same final CD in the end, which in f1's case is hightened due to the induced drag from the airfoils on the car. As I mentioned, it's a compromise, and a higher drag coefficient to a certain limit doesn't matter as much as grip when you have a strong engine to chew through it.

wothLike in an airplane. Cdi equation is a different one, as you surely know.

Cdi = (Cl^2) / (pi * AR * e)

where: Cl = coefficient of lift, pi=pi, e = efficiency factor and AR = s^2 / A (s = span, A = wing area).

And, of course, Cd total = Cd + Cdi. And I would presume you want both coefficients as low as possible and a Cl as high as possible. Could you clarify it for me, please? [-o<

Seems ok, this is pretty much kindergarden stuff.
The real issue is not getting the CD and especially the CDI as low as possible, I could do that, but rather how to lower it without losing that ever precious downforce.

[ginsu]

Cdi = (Cl^2) / (pi * AR * e)

where: Cl = coefficient of lift, pi=pi, e = efficiency factor and AR = s^2 / A (s = span, A = wing area).

And, of course, Cd total = Cd + Cdi. And I would presume you want both coefficients as low as possible and a Cl as high as possible.

Using the equations we don't have much choice on how to reduce drag and maintain a high Cl. Either increase the AR or the efficiency. I know that deep endplates effectively increase the AR so that is one way.

As for the efficiency factor:

Lifting line theory shows that the optimum (lowest) induced drag occurs for an elliptic distribution of lift from tip to tip. The efficiency factor e is equal to 1.0 for an elliptic distribution and is some value less than 1.0 for any other lift distribution. The outstanding aerodynamic performance of the British Spitfire of World War II is partially attributable to its elliptic shaped wing which gave the aircraft a very low amount of induced drag. A more typical value of e = .7 for a rectangular wing.

Does this account for 'spoon-shaped' rear wing profiles?

[bernard]

And, of course, Cd total = Cd + Cdi. And I would presume you want both coefficients as low as possible and a Cl as high as possible. Could you clarify it for me, please? [-o<

Actually this slipped past my eyes, so I take it was a mistake from you too, but that's actually Cdo + cdi=cd total, as in cd at zero lift. Otherwise it's correct.

Does this account for 'spoon-shaped' rear wing profiles?

I take it that means this type of elliptical distribution of lift?
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[Reca]

First of all a premise.

It’s not the Cd per se that matters, it’s the SCd.
So to say that a car has a Cd of 0.19 is absolutely useless if you don’t know the reference surface used to calculate it, and notice, I don’t want to know “it’s the frontal surface” because there are several ways to define the frontal surface, I want to know the number, X m2.
The Cd is just an arbitrary number, you measure the SCd, divide it by an arbitrary, reference surface and you have a Cd. Historically that reference surface for cars is the frontal surface (although as I said there are different way to define it), but it could equally be the plan area of the roof, of the bonnet, whatever, it doesn’t matter because at the end of the day you still need to know the SCd, hence both the Cd and the reference surface.

So, what’s that Cd useful for ? Besides to make up a suitable number for advertising fooling ignorant (in the good meaning, ie people who don’t know) people pretending to have established a worldwide record, it’s useful only to know that, if you make a scale model, say at 50%, of the same car, exactly the same shape, exactly in proportion, then the SCd of that model will be 50% of the SCd of the real car, hence it’s useful for example, for wind tunnels. Alternatively the Cd is useful for wing sections, but that’s again because for these shapes, the reference surface is well defined.
But while comparing two very different shapes, for example two different cars like that Mercedes and a F1, the Cd per se is absolutely useless, you need to know the SCd, as a unit, because it’s that number that matters.

To not understand that leads to one of the biggest misconceptions in aero, you hear/read it everywhere... do you want to reduce the drag ? Reduce frontal surface, like if the frontal surface per se had something to do with drag... I even heard someone saying that the Tyrrell P34 had the same drag of the other 4 wheels cars because the frontal surface, due to the rear tyres, was the same...
Generally, while talking about similar shapes it could make sense, but not necessarily because working on the reduction of the frontal surface you are also changing the shape, and if you do it in the wrong way that could easily lead to an increment of the SCd, even if the plan area of the frontal surface is greatly reduced.
An example is the dimension of sidepods of a F1 car, how often you read that bigger sidepods isn’t good because of drag ? Well, it’s false, just look at the Williams, for years they had the smallest sidepods and likely the smallest frontal surface of the cars on the grid, does it mean that they had the car with the lowest drag ? Not necessarily, and in fact with the FW28, in an year when, with drastic power reduction the drag limitation is fundamental, they adopted a different approach.

Now, end of the, long, premise and back more specifically to the topic, to calculate the SCd of a F1 car, at least in first approximation, is quite easy, just take the formula for the drag (force), multiply it for the velocity and you have the power required.
Let’s use now 2005 data just because we don’t have idea yet about the peak speeds they’ll reach with the V8.
Assume the power, spent only for aero (hence removing transmission losses and tyre rolling resistance), was something in the order of 730-750 hp = 530-550 kW, use standard air density (1.225 kg/m3) and assume we are talking about Monza where peak speed was about 360 km/h = 100 m/s, and the SCd of a F1 car, in Monza trim, is :

SCd = (2 * Power) / (density * v^3) = (1100 * 10 ^ 3 [W]) / (1.225 [kg/m3] * 100 [m/s] ^3 ) = 1.1/1.25 = 0.88 [m2] => I said 530-550 so let’s say 0.85-0.88.
(what’s the Cd ? it depends by the reference surface I use, but we don’t care about it)

As for that Mercedes, I don’t know the reference surface but it’s probably between 2 and 2.5 m2, that would mean SCd = 0.38-0.475 m2.

Assuming that the right numbers are 0.85 m2 and 0.4 m2 then that means that, at a given speed, the Mercedes needs roughly 0.38/0.85 = 47 % of the power required (for aero only) by the F1. Nevertheless we should remember that F1 is a open wheel car designed first of all to generate downforce, the Mercedes is a car designed solely to reduce drag, so, at the end of the day, the F1 isn’t that bad.

Obviously with the right numbers you would have better accuracy, that’s just an example to show the method and the method doesn’t change.

At the end just a note. I assumed that the SCd of the car is constant with speed. But... it really is ? Well, better if we avoid to open that can of worms