11 replies to this topic

[Greg Locock]

With the exception of the change in downforce as the ride height changes, am I right in thinking that for all practical calculations concerning circuit cars the lift and the drag from a given setup will be proportional to v^2 ?

I can't see it being any other way, just wanted to check.

[desmo]

As I understand it, it is a pretty good approximation but the high degree of vorticity and seperated flows around a race car makes the actual relationship much more complicated and harder to predict. If it were as simple as v^2, aeromapping would be far easier as one could get a value at one velocity and extrapolate for all other velocities.

[fattogatto]

Parasitic (form) drag is often expressed as directly related to speed squared. Induced drag (that drag created by the production of lift/downforce) is another, much more complicated matter.

[wegmann]

The lift and drag change significantly for F1 cars with ride height, pitch, yaw angle, steer angle, etc. ... so I guess it depends on how "practical" you want to be.

[DOHC]

Pressure difference is proportional to v^2 (Bernoulli's law).

The problem is that this is a local characterization. "Pressure" is force per unit area, therfore "force" is the integral of pressure (difference) over an area. So "force" is an aggregation of a "pressure field."

Downforce from a wing is then the integral over the wing area, of the pressure difference above and below.

If we want this to be proportional to v^2, you first have to ask "what v?" What is the velocity? Is that the car's velocity (supposedly equal to free field flow speed)? Because the car has many other body work features that interfere with free flow, the "velocity" may actually be quite different. Also, in today's complex wings, you have many flap elements or "slots" between the wing elements, and these accelerate the flow over certain areas, which means the "velocity" varies a lot. So does pressure difference, and the resulting force may not be porportinal to the square of the free flow speed.

In addition to this, F1 wings have realtively small spans, with big and often complex endplates creating significant vorticity at the wing tips. Vorticity has an impact on "velocity", so again: what velocity?

I think that aero mapping is very complex, and that discussing it in terms of aggregate or averaged parameters such as "force" and "velocity" is useful to establish crude measures of the downforce, but the finer points will certainly be missed.

[pabs]

Potentially you can measure a coefficient of lift and simply make lift scale with V^2 which is a pretty good first-order approximation asumming your CL is not changing (big assumption sometimes). This will take into account your pressure distribution and hence resultant force. The same can be said for drag. So from a practical point of view, V^2 should get you in the ballpark of the actual numbers.

[Greg Locock]

As a first approximation you are right, but I've just had a look at SAE 2001-01-2072 (for a completely different reason), and it shows a change in Cd for a truck and trailer of about 10% for a doubling of speed.

That's bigger change than I'd expected, to say the least. However, to put it into context, that is the difference between extrapolating a force of 3.6 N instead of 4N at 120 kph, from a result of 1 N at 60 kph, so it isn't too bad.

So to answer my own question, it is close, but perhaps not close enough.

[DOHC]

Originally posted by Greg Locock
As a first approximation you are right, but I've just had a look at SAE 2001-01-2072 (for a completely different reason), and it shows a change in Cd for a truck and trailer of about 10% for a doubling of speed.

That's bigger change than I'd expected, to say the least. However, to put it into context, that is the difference between extrapolating a force of 3.6 N instead of 4N at 120 kph, from a result of 1 N at 60 kph, so it isn't too bad.

So to answer my own question, it is close, but perhaps not close enough.

I would have thought that a 10% deviation from a plain proportionality is quite accetable. The flow might change character quite a bit when speed is doubled for that truck and trailer. For example, what is the flow like between the truck's cabin and the trailer? One might expect that it depends significantly on the speed. Similarly, the flow under the trailer probably also depends strongly on the speed.

BTW, that's 3.6 kN, 4 kN and 1 kN, right?

[wegmann]

DOHC-

You seem to have some good aerodynamic info, so if I may ask you a question ...

The truck that Mr. Locock brought up appears to have reduced it's drag coefficient with speed. In other words, the drag force went up *less than* proportionally with velocity squared.

Is this typical behavior, for say, a winged car? And for both drag and downforce? For example, if an F1 car produced 400kg at 150kph, would we tend to expect something less than 1600kg at 300kph?

-Weg

[pabs]

Cd also has a Reynolds number dependence. A good case is a cylinder in a crossflow. My guess is this is what causes the decrease in Cd in the truck case. Recall that for a cylinder in a cross flow, Cd decreases approximately linearly up to Red=100, then it stays constant up to Red=1*10^5, then there's a sudden decrease (when Red is high enough to have a turbulent BL), and the Cd increases again for the higher Re.

[DOHC]

Originally posted by wegmann
DOHC-

You seem to have some good aerodynamic info, so if I may ask you a question ...

The truck that Mr. Locock brought up appears to have reduced it's drag coefficient with speed. In other words, the drag force went up *less than* proportionally with velocity squared.

Is this typical behavior, for say, a winged car? And for both drag and downforce? For example, if an F1 car produced 400kg at 150kph, would we tend to expect something less than 1600kg at 300kph?

-Weg

I think I would expect more than a factor of four, because at low speeds I would expect interference from bodywork drag to be more significant. At high speeds, bodywork drag goes up too, but in spite of this, wings really come to the fore as the speed increases. At low speeds, you wouldn't worry too much about having wings. Karts don't have any...

For a truck, it's perfectly sensible that it goes the other way, because a truck rarely has a design which is primarily "aerodynamic." I think one must expect a certain deviation from what happens to a simple geometry such as a sphere or a single, undisturbed wing profile. As pabs points out, there's a dependence on Re as well.

My info is not particularly exquisite -- I'm not an F1 insider -- it's only based on a long experience with computing, some of it with CFD.

[wegmann]

Very interesting. Thanks for the reply!