United Autosports European Le Mans Series - Portimao Race Track [1]

Driving Lines

By Trav Mays

In this post I thought it would be fun to look at driving lines and how to pick the best one. The complex nature of our sport means that any analysis we do is really only for exact or very similar conditions. Changing the car set up, weather, tyres, driver, etc all could change the best line to drive the corner. Whilst it might sound like a useless exercise, we can still get extremely important information from it, especially over a race weekend and for any races in future that have a similar corner. Doing this sort of analysis on a stand alone corner, one that has a straight before and after it, will have the greatest payoff as consecutive corners adds more variables and therefore more complexity.

Theory

We’ll start off with a little theory about driving lines and how we can use data to analyse what we or our drivers are doing. The data I will be using is from a Aim Sports Race Studio Webinar on Youtube, the file is the Hanna Race, the car is a Swift DB2, the track is Mid Ohio, you can go and watch the video or download the data from here [1]. Below you can see the google maps image overlaid with the fastest lap’s GPS data.

Mid Ohio Raceway with Aim GPS data overlaid onto a Google Earth image

The corner we are going to be looking at is the second corner, the one just after the short straight and just before the long straight. If we zoom in a bit, we can see a lot more detail about the driving line they took on their best lap.

The driver begins to turn in for the corner at point 1, the point of minimum corner radius (42m) is at point 2, my guess is the apex is around point 3 and they stop exiting the corner at point 4. If we create a maths channel that plots the corner radius, we can see this graphically and get a more accurate approximation of where the apex is located. Below I have done this in yellow, I have also plotted the speed trace in blue and the curvature in green. If we mark the point of minimum corner radius, point 2, and measure to where the driver begins to enter the corner and where they have exited the corner, we can use this info to determine what type of apex the corner has. A late apex corner will have a shorter first section as they will be turning in sharper at the beginning, a mid corner apex will have them equal to one another, and an early apex will have the second section shorter than the first. As you can see, ours are fairly similar, 100m in the first section and 114m in the second section, so a mid to slightly late apex in my book. We can also determine the type of apex from the steepness of the curves, but with a lot less accuracy. If we look at point 1, we can see that the steepness of this portion of the curve is far greater than that of corner exit, typically this indicates that the corner is a late apex, they have done most of the turning at corner entry and hence the steeper curve.

Click here to learn about the different corner apexes

There are three broad categories of apexes, the early, in green below, the middle, in yellow, and the late, shown in red. Each has their own pros and cons and are therefore used at different times and different corners throughout a race.

Typically for a corner the late apex is the quickest, the early braking allows for the bulk of the turning to be done fairly early, this allows the driver to apply the throttle sooner, the sooner they are on the throttle the fast they will be going at the corner exit and therefore the faster they will get to the next corner.

Whilst this is typically the fastest, it’s not always the best line, we need to think about the track as a whole. The early or middle apex lines might be best given what comes after the corner, isolating a corner to find the fastest lap is good, but comparing a driving line to a sector or overall lap times is better.

The early apex line might be the best option if you are overtaking someone, dive bombing under braking. You will exit the corner slower, but assuming you have been able to block on the exit you should be able to stay in front.

The middle apex also has its advantages, whilst it isn’t the fast entry or exit of the corner, it can have the fastest middle section speed, which could be high enough to be the highest average corner speed, making it the best line.

As you can see they all have their advantages, we will be covering driving lines more indepthly in the future, stay tuned to read them as they come out.

To calculate the corner radius is fairly simple, all we need is a Lateral acceleration and the speed, the formula is below

The curvature graph is really just the same thing shown in another way, all values are positive and it doesn't go off to infinity, so it is a bit nicer to look at in my opinion, especially when you have a few lines on the screen. It also highlights where the car is turning the most, if you look above, it is far easier to see the high vehicle turning and straightening points on the curvature garah than on the corner radius graph. The equation for it is below

Click here to learn a little more about the above 2 equations

Just in case anyone isn’t aware, the two straight lines beside the R in the curvature equation represent an absolute value, that is, irrespective of the sign, it can be either positive or negative, it only shows the positive value, eg |7| = 7, |-7| = 7 etc.

The SI units for the above equation are

Depending on what units your devices record in, you might need to convert them. I have put a conversion chart with the most frequent conversions below in case you need it.

Example

Now that we have had a little better understanding of corner apex’s and two of the cornering equations, let's have a look at a real world example. The corner we are going to be using for this analysis is the final corner at Sebring, Florida, you can see a google earth image of the track with 4 laps overlayed below.

Sebring Raceway with 4 driven lines overlaid onto a Google Earth image

The data I have used for this analysis is again from an Aim Webinar, the data files are Test3_Alex and Test4_Alex, you can watch the webinar and get the data for yourself here [3]. We are going to be looking at the final corner, that is the corner at the bottom left of the above image, you can see a close up with four driven lines overlaid below.

Sector under analysis with each driving lines minimum corner radius highlighted

As you can see above, we have three very different lines, all from the same driver, in the same car, on the same day. The red line, a early apex, was recorded at 1:15, whilst the yellow, midcorner apex, green, midcorner apex and blue, late apex, lines were all recorded at 6:30pm. Unfortunately we don’t have any weather data from the Aim file, but using a historical weather archive we can see that in Sebring on March 4th 2017 at 1pm, it was sunny, with a temp of 23℃, a wind speed of 26 km/hr, and a humidity of 33%. At 6pm we had similar weather conditions, scattered clouds, 21℃, a wind speed of 30 km/hr (blowing in the same direction) and a humidity of 39%. I think it is fairly safe to rule out weather playing too large a role in our analysis. The drop in temp and scattered clouds might have unleashed a horse or two and maybe increased the stickiness of the tyres, but I think it’s about as close as we can get. We unfortunately don’t have any tyre dat or any notes on changes done to the vehicle, so we will have to assume all is equal (compound, level of wear, temperatures, aero, ride heights etc).

Below I have created a table with some data for each of the four lines. As you can see, the green line is able to get through the sector the quickest of the three, 0.2 seconds quicker than the yellow line, and 0.4 seconds quicker than the other two lines. It also had the highest average speed of the sector and as is typically the way, it had the lowest curvature area value.

The curvature area is the area under the curvature curve for the corner. When determining the best driving line for a corner in isolation, typically the line with the lowest curvature value is the quickest, less of the tyre’s grip is being used to turn the car, so the car is able to go through the corner faster.

The A distance is the point from where they begin to turn in and the lowest radius point (100m in the image in the theory section), whilst the B distance is the lowest radius point to where they stop turning the corner (114m in the image in the theory section). As explained earlier, doing this allows us to determine what type of line the driver took. As you can see, we have fairly textbook early, mid, and late apex corners. The late apex line has the highest end of sector speed, which isn’t surprising, as this is the main reason this driving line usually is the quickest through a sector.

Despite it having the fastest end of sector speed (the sector is the section of track picture above), it had the slowest average sector speed of the three, this was partly because it had the lowest minimum radius, the driver turned the car in harder. As you know, a car’s speed around a corner is governed by the centrifugal equation (see this post to find out more), a tighter radius means a slower speed. If we look below, we can see this strategy does result in the slowest minimum speed in the corner, 109.0 km/hr, the yellow’s lowest was just 114.7 km/hr, the green’s lowest was just 116.5 km/hr, and the red line only slowed down to 123.1 km/hr, 13.41 km/hr quicker than the blue line.

Below I have plotted the distance of the minimum radius vs the average sector speed time, with each of the driving lines we are looking at coloured accordingly. The distance of the minimum radius is measured from the start line, so the smaller the number, the earlier they hit their minimum corner radius. We can see that the two are correlated, the earlier the minimum radius point is reached the higher the average speed through the sector, except for the blue point, maybe they turned in too early?

Location of minimum corner radius vs average sector speed

If we then plot the distance of the minimum radius vs the sector time, it’s no surprise that along with the faster average speeds, the earlier the car reaches its minimum radius point the faster the sector.

Location of minimum corner radius vs sector time

Obviously there is a point where turning in early is no longer the quickest line, maybe the blue line has gone past that point? Unfortunately we only have one data point that is before 5310ms, so let's have a look at that lap and to try and see anything unusual about this specific lap, did something go wrong, or could it still be the best option?

If we have a look at the speed trace below, it becomes pretty obvious what happened, for one reason or another the driver started to brake a lot earlier, 78m earlier, and a lot gentler, over 100 bar/sec less than the green and yellow driving lines. The blue, green, and yellow laps were all driven in the same session, the blue lap was actually the lap just before the green lap. Maybe the tyres weren’t up to temp, the driver wasn’t in the zone, or maybe there is less grip further out off the racing line, so they were a little more cautious? Unfortunately we won’t know without talking to the driver, but assuming it was just a mistake, it would be good to get a couple more data points for the early turn in.

I can hear what you’re saying, “Trav, corners aren’t in isolation”, and you’re right, this one has a large straight after it, so perhaps the blue line could actually be better if we evaluate all the way up to the next braking point. But no, the green line is still the winner, the blue line is a little quicker at the braking zone, but it’s not enough to get back the time lost at the corner.

This corner is a story of two corners, if we look at the curvature trace, we can see that after the initial peak, the car begins to straighten up, it then turns sharply again to get around the final section of curve. Whilst the corner looks fairly symmetrical in the above image, it is anything but, the car generates the highest lateral acceleration of anywhere on the track at this point, 1.6g.

It’s this second turning point of the track that makes me think the blue line probably still won’t be the fastest line around it. But we won’t ever know without more data. If anyone has any, feel free to send it in, it would be great to have a look at it.

That wraps it up for this post, I hope you have enjoyed it. If you have any comments, suggestions, or noticed I made a mistake, write it down in the comments or get in contact via email or using the contact page, I’d love to hear it. Thanks for reading, don’t forget to sign up so you don’t miss out on any of our upcoming posts, and I hope you have a great day.

By Trav Mays

Previous Post Next Post

What to look at when you just have 20 mins Are you braking hard enough?

References:

[1] Link to original image here 
[2] Link to Aim webinar and data here 
[3] Link to Aim webinar and data here