# Traction circle myths

I recently discovered a really cool website/service: Race Optimal. They use a genetic algorithm to compute the theoretical fastest lap around a race track. One of the primary components of the model is the g-force limits of the vehicle. By this I mean cornering, accelerating, and braking. The combination of these is often called the traction circle. The topic is an introductory chapter in nearly ever recent racing book. The idea is that you only have so much grip in your tires. You can use this for cornering, accelerating, braking, or some mixture. As a safety example, if you’ve used all of your grip for braking, there’s none left for cornering (panic braking understeer).

One of the lessons taught to novice drivers is to separate braking from cornering. That’s because mixing the two can lead to a spin. But mixing them allows you to transition from full braking to full cornering without any lag between the two. The practice of releasing brakes while increasing cornering is called trail-braking, and is one of the most important skills for a racing driver.

Let’s imagine some mixtures of braking and cornering.

1. 100% braking, 0% cornering
2. 75% braking, 25% cornering
3. 50% braking, 50% cornering
4. 25% braking, 75% cornering
5. 0% braking, 100% cornering

Let’s call throttle/brake the Y-axis and cornering the X-axis. There are two ways to plot these values. We can plot the raw values or plot them as force vectors. Plotting the raw values will make a straight line. Plotting force vectors will make a circular arc. That’s right, there are two valid ways to draw a traction diagram: as a diamond or a circle. In theory anyway. But what about in practice?

In the traction plot below, focus on the blue dots. This is the output from a TraqMate from the people at Race Optimal. I have overlaid a circle and a diamond. As you can see, neither one fits. Is TraqMate plotting the sum of the accelerations (diamond expected) or computing the sum of force vectors (circle expected)? I don’t care. Neither one is correct. The true nature of traction isn’t that simple.

So let’s talk about some things that are different in theory and practice starting with the most obvious differences.

1. The graph has a flat bottom because acceleration is mild compared to braking.
2. The car has more cornering grip in one direction than the other.
3. Cornering and braking have different maxima (1.3G vs 1.1G).
4. Under high brake pressure, cornering follows the diamond line.
5. Under low brake pressure, cornering follows the circular line.

What does all this mean? The notion that you have the same amount of grip for braking and cornering isn’t true. There is more traction available for cornering than braking. Under heavy braking, you can’t do much cornering, but under light deceleration you can corner just as well as not braking at all. In practical terms, this means that the very end phase of trail-braking is critical because it allows the greatest mixture of braking and cornering. Although it’s hard to tell because the bottom of the graph is so flat, it also looks like mixing throttle and cornering is also a good idea. So maintain a little brake pressure on the corner entries and add a little throttle as soon as possible. Neither one really impacts your cornering ability, but they do affect your Y-axis.

Does this apply to your car on your favorite track with you driving? Only one way to find out…

## 6 thoughts on “Traction circle myths”

1. Eric H says:

Simulations found in Race Optimal aren’t too useful on tracks like The Ridge and Oregon Raceway Park. ORP is like a paved roller-coaster and doesn’t have a single flat corner on it making the simulated lines entertaining at best.

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1. What I admire about Race Optimal is what it attempts to do, not its accuracy. I contacted them about why their track time at Sonoma was so far off. I had expected it was elevation and they sort of confirmed this. Nice people doing interesting stuff. The model isn’t perfect, and like all models, it can be improved. I look forward to that.

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1. Ian,
Have you driven the Ridge or ORP?
If you ever make it up here we’ll have to share a beverage together.

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2. ORP, PIR, and The Ridge have all been outside my tow range (3.0L Ranger with single axle trailer and no brakes). But now that I have a street legal B-Spec, I plan on making the trip. Thanks for the invite, I’ll have to take you up on it.

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2. sean says:

I use VBox on track. My anemic car does produce a flat bottom but at my best I get close to a circle at the top. My max braking and turning g’s are similar if on a flat surface.

Also, I have rarely heard others note what I noticed as well: if one is able to produce a traction circle with the car, the max grip in transition from braking to turning (as expressed by the sum of g longitudinal + lateral) far exceeds the max of either. I see this as one of the reasons trail braking leads to fast laps (along with the increased ability to turn via loading fronts, and from brake release).

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3. sean says:

I just reviewed my Sonoma data and found that VBox seems to have removed the G-G plot graph (support email pending). I do have a G circle on video, and can see the little dot tracing the G circle (when trail braking well). I can see time graphs of lateral, longitudinal, and combined g’s. My combined g never exceeds my max lateral or longitudinal g, which I guess makes sense (a circle with max vector length constant). VBox website notes that combined g is derived using Pythagorian Theorem a^2 + b^2 = c^2. But the SUM of my lateral and longitudinal g’s do exceed either maxed alone, which also makes sense:
If a car did 1g max, and was able to trace the traction circle to 45 degrees, then while combined g would measure 1g, the magnitude of longitudinal AND lateral g each equal 0.707g, with the sum of them = 1.414g. I’ll keep pushing to see if I can get there!

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