Corner Radius for Corners of the Gilles Villeneuve Circuit

[Ciro Pabón]

What looks really strange for me on this speed plot is the changing slope in braking area

I think it's because you change car speed under braking (duh) and wing height and thus downforce.

[Lycoming]

My actual aim is once i have calculated the required downforce levels for each corner is to complete CFD/FEA simulations on my front wing model to select the optimum angle of attack for this circuit.

I chose the Gilles Villeneuve circuit due to the medium downforce requirements, preventing the requirement to make changes to my front wing model

The optimum angle will be different depending on the design of the wing and the rest of the vehicle. Just setting your angle of attack such that you get the same amount of downforce as Mercedes was producing will not necessarily be the optimum for your design.

I have calculated the radii for each corner as i know the g force and velocity at each corner and were found using the following equations.

Radius=Velocity^2/Lateral Acceleration

where Lateral Acceleration= g force * 9.81


Using these Radii i can calculate the centripetal force for each corner using Fc=mass * Velocity^2/Radius.

This is where the problem arises whilst using the following tyre friction force equation...

Fc= Tyre Friction Coefficient * Fnormal


Fnormal consists of two parts. The weight of the car, Mass*gravity, and the downforce. Therefore rearranging this equation to find downforce results in the following.

Downforce=(Fc/tyre friction coefficient)-(mass of car*gravity)

As the tyre friction coefficient varies from corner to corner this is providing me with negative values on several corners. This is where my problem lies

As somebody else has already mentioned, not every corner is traction limited, in which case you'll get a negative number for normal load since you're assuming the tire is operating at peak lateral force, whereas in reality it's not, because it's a really gentle curve. Look at the run into turn 1. It's obviously not traction limited.

Here a plausible racing line computer generated, using speed data of Rosberg’s 2014 pole (from analysis of engine noise) and track’s boundaries (from satellite image), with the aim of minimizing an opportune fitness function of the resulting lateral acceleration and other parameters:
http://i.imgur.com/lMfZv1U.jpg

What looks really strange for me on this speed plot is the changing slope in braking area, especially for the last 2 corners, the hairpin and the final chicane. If I would have seen such a graph not knowing that is was Rosberg, I would assume that we are dealing with a very inexperienced driver.
What might be the reason for this? Just expected inaccuracy of Mercedes engine noise analysis?

If your model includes aerodynamic downforce, which is proportional to speed, then you will not have constant deceleration under braking. Signal noise doesn't look like that.

[Tim.Wright]

If the goal is to calculate the tyre friction coefficient and the downforce, there is a much simpler way:


3. Fit a squared polynomial to the data in the form: LatAcc = a.Speed^2 + b

4. Then you have:
Tyre friction coefficient: mu = b/9.81
Downforce: SCz = (2 x mass x a)/(mu x AirDensity)

Thanks for your help everyone.

Tim I was wondering if you expand on point 3 and 4 for me please?

If you write out the equation for the maximum lateral acceleration of a simple car as a function of mass, friction coefficient and downforce (like I think you have already done) then you will find it has the form:
LatAcc = a x Speed^2 + b
Where "a" and "b" are constant coefficients.

If you take an onboard lap, and find the lateral acceleration and the speed at the centre of all of the grip limited corners (in the gap between the release of the brake pedal and the application of the accelerator pedal) you should find that you will get a roughly polynomial curve when you plot speed vs lateral acceleration for all the points on the lap.

Then you use some curve fitting techniques to find a polynomial in the form LatAcc = a x Speed^2 + b which best fits the data from the onboard lap. This will give you "a" and "b". Then from there you can calculate the tyre friction coefficient and the Cz.

[al_garnett]

If the goal is to calculate the tyre friction coefficient and the downforce, there is a much simpler way:


3. Fit a squared polynomial to the data in the form: LatAcc = a.Speed^2 + b

4. Then you have:
Tyre friction coefficient: mu = b/9.81
Downforce: SCz = (2 x mass x a)/(mu x AirDensity)

Thanks for your help everyone.

Tim I was wondering if you expand on point 3 and 4 for me please?

If you write out the equation for the maximum lateral acceleration of a simple car as a function of mass, friction coefficient and downforce (like I think you have already done) then you will find it has the form:
LatAcc = a x Speed^2 + b
Where "a" and "b" are constant coefficients.

If you take an onboard lap, and find the lateral acceleration and the speed at the centre of all of the grip limited corners (in the gap between the release of the brake pedal and the application of the accelerator pedal) you should find that you will get a roughly polynomial curve when you plot speed vs lateral acceleration for all the points on the lap.

Then you use some curve fitting techniques to find a polynomial in the form LatAcc = a x Speed^2 + b which best fits the data from the onboard lap. This will give you "a" and "b". Then from there you can calculate the tyre friction coefficient and the Cz.

I think this is going to be the best method to calculate the tyre friction force,mu and subsequently downforce. I did consider looking into deriving the mu value for each corner but i think it is going to be pretty much impossible.

[Tim.Wright]

The coefficient of friction doesn't really change much from corner to corner. Its a relatively small source of error given the other simplifications of these calculations.

Anyway its a calculation that you can't do corner per corner, because the equation for each corner has 2 unknowns. You need at least 2 corners to solve the equations but its better to use as many as possible because other factors like track banking will affect what you calculate for the friction coefficient.

[Blanchimont]

Maybe these 2013 Caterham data can help a bit as speed and lateral acceleration is part of it.

[Tim.Wright]

Does anyone have a collection of all of these telemetery printouts from Caterham? They are quite difficult to find on their website. Could come in handy one day.

[Blanchimont]

Yes, i have a copy of them on my computer. A google search with "caterham telemetry previews XX" (XX between 01 and 19) helps if you want to look them up.

Here is an older one for Korea: http://caterhamf1.com/previews/korea/index.html

Lotus also provides some fact files: https://www.flickr.com/photos/lotus_f1team/

[al_garnett]

[quote="Reca"]Here a plausible racing line computer generated, using speed data of Rosberg’s 2014 pole (from analysis of engine noise) and track’s boundaries (from satellite image), with the aim of minimizing an opportune fitness function of the resulting lateral acceleration and other parameters:
http://i.imgur.com/lMfZv1U.jpg

And here the corresponding radiuses (numbers are only to give you an easy visual correspondence between the graphs, not corner’s “names”):
http://i.imgur.com/sUDiAvt.jpg

Hi Reca, Would it be possible for you to send me the file for the corner radius graph please? Just so i can read off the exact radii for each corner?

Thanks Alex

[Reca]

As the tyre friction coefficient varies from corner to corner this is providing me with negative values on several corners. This is where my problem lies

That’s why I said that Canada wouldn’t be my first choice (or even in top 10...) for a similar work, it lacks proper high speed corners, negotiated at limit of grip, let alone sustained for a meaningful time interval.

Reca!

I'm so happy reading your post.

Best post of the year, no doubt.

Ciro! Good to “see” you around still too, hope you’re doing well.

As always you are being too kind.

Fair play Reca, nice post! Did you do the sound analysis directly in your matlab script as well in an (semi)automatic fashion?

As for the track boundaries, what was your methodology? Manually picking point on the satellite picture? I recon it would be great to just give matlab 1 point on a satellite view which is on the track, and let matlab find the boundaries, knowing that the track is of a gray-ish colour (escape roads and tarmac run-off areas might be a problem tho).

Thanks Matt.
Yes, the script takes the wav file with the engine audio and processes it automatically, it’s always been like that since the start, years ago. A bit of manual intervention on post-processing is required as sometimes it identifies some wrong peaks giving incorrect reading. Usually though the incoherencies are quite obvious looking at the rpm plot, couple of clicks on the relevant area to redo a local search limited to a narrower rpm range around the expected correct value, and the problem is solved.

As for the layout, I highlight/select the track borders of the image in photoshop and fill in a single color, and then give that colored layer to a small Matlab routine I made that converts the edges in the two input vectors of coordinates representing the borders for the racing line optimizer, scaled using a measured distance on the satellite image.

It’s all rather straightforward, and quick enough that, for the few times I have to do that work, there’s no need to waste time programming something more complex.