Spirals in Racing: Understanding Dynamic Racing Lines

Introduction to Spiral Physics

The most essential physics involved in motorsports fundamentally affects the lines a car is capable of taking depending on speed. Understanding this relationship is critical to proper race craft and vehicle control.

Visualizing Spiral Dynamics

First, let's visualize a race car at a centripetal circuit at a constant speed. The path the car is capable of maintaining is a fixed circle. Now let's observe what happens when we modify the speed:

• Closing Spiral: When starting to decelerate slightly, the car is capable of rotating more and more towards the inside. With less speed, the car gains the ability to increase rotation.

• Opening Spiral: When increasing the speed slightly, the car naturally widens the line as long as the speed keeps going up. The car loses rotation capability as speed increases.

The Geometric Line vs. Real Racing Lines

When learning the basics of racing, we first learn the geometric line, which is a fixed radius circular arc throughout the corner touching the entry outside, apex inside, and exit outside. If we were to execute this by the book and stay on the limit, we would have to decelerate to a speed, stay on it on the limit as we do the whole corner, and then only start accelerating after the exit.

However, you gain way more time by carrying a little bit more speed on entry and decreasing that speed after we already start turning all the way until the apex, where we start regaining that speed out of the corner way before we hit the exit point.

With this in mind, we conclude that the line in corners where deceleration is required is not a fixed circle but rather a closing spiral on entry and an opening spiral on exit. This means we have to steer less on corner entry and consistently increase the steering as the speed decreases, and then decrease the steering as we gain speed towards the exit.

The Maximum Rotation Point (MRP)

What you should never forget from this lesson is that the minimum speed of a corner is your opportunity to rotate the car as much as it is capable of, because inertia will allow the car to rotate more there than anywhere else in the corner. We are going to call this the maximum rotation point or MRP.

The Danger of Hesitation

The danger lies in hesitating to rotate the car at this minimum speed and maximum rotation point. If you miss this opportunity, your car will start going wide too early. Remember, you're probably on throttle at this point and you're going wider and wider. What happens is you realize that you're going wide and you instinctively start turning the steering more, or you just don't unwind your steering.

At this point later towards the exit, your car is already too fast for the rotation that you're asking, and you risk losing the car and going over the limit—either understeering off track or spinning inwards.

Key Principles to Remember

• Closing spirals occur as your speed goes down

• Opening spirals occur as your speed goes up

• At the minimum speed, don't hesitate in rotating the car as much as possible

• Get the car rotated so that you can give yourself room to open the spiral as you gain speed on exit

Steering Angle and Speed Relationship

Another thing to never forget is that your steering angle should be related to how much speed you are carrying. This seems obvious, especially if we look at a traditional corner where we brake, turn, hit the apex with the minimum speed, then accelerate out of it in an open spiral.

This is a very good example of how you should patiently turn more and more and more as the speed goes down, meaning you're building that closing spiral. Then use that opportunity when those speeds are lower to really rotate the car as much as you can, because as soon as you accelerate, the car is going to want to rotate less and spiral out.

Again: closing spiral on entry, opening spiral on exit. The MRP divides the corner by two—one where you spiral down into more rotation, and the second where you spiral up away from the rotation, never ever gaining rotation on exit.

Understanding Oversteer on Entry

When you lose the rear on entry, the graph was supposed to show a normal closing spiral, but because you got more rotation than the car was capable of handling at that speed, the rear broke grip. That's why you had to do the countersteer before quickly bringing the car back to the limit and pointing to the right direction.

Reading Data Graphs

To make it clear how you should read these graphs:

• The steering goes right when it's negative and goes left when it's positive

• The speed is straightforward—more speed at the top, less speed at the bottom

• The yaw rate is the same as the steering—the graph goes down when the car is yawing to the right and left when the car is turning left

In an oversteer example, the speed goes down, then a little bit less slowly during trail braking (slowing down a little bit less during the corner compared to while braking in a straight line), and then it goes up. The steering turns a tiny bit, but then the yaw actually went a lot more than expected to the right. The car is now oversteering because we have less steering and a lot more yaw.

Understanding Oversteer vs. Understeer

The relationship between steering and yaw is always what's going to tell you if you have oversteering or understeering:

• Oversteering: If you have a little bit of steering but the car is yawing a lot, that's oversteering

• Understeering: If you have a lot of steering but the car is not yawing, that's understeering

Of course, it's very difficult to actually measure this because you don't know exactly what are the proportions of the graph. It's just so you can have some extra information. This is not necessarily how you're going to judge if you have understeering or oversteering—it's just a fun fact.

When oversteer occurs, you had a little bit of steering and you had a lot of yaw, more than necessary. You must do a quick correction with the steering to bring that yaw back, then quickly get back to where you wanted to be to not lose time. Do the correction and then bring the car to building that nice rotation until you reach the actual peak that you wanted, and then all the way back.

In the oversteer graph, you can see two peaks of rotation. One with the correct speed, which is exactly what was intended, but the other peak of rotation occurs at a higher speed, and the car is not capable of dealing with it.

Recognizing Patterns in Corner Sequences

In most corners, you'll start to see the same pattern emerge: closing spiral under braking, opening spiral on power. This pattern repeats across different corners: closing spiral under braking, opening spiral on power. In all these examples, the maximum rotation point or MRP is very close to the apex, where the intersection between these closing and opening spirals occurs.

Because many corners are like that, we associate turning the steering the most when the car is at the inside apex of every corner. But is it always like this?

When the MRP is NOT at the Apex

Let's look at a different type of corner. You are already slow because of another corner, and you don't actually have to decelerate for this one. Because you don't have to decelerate and your speed is only going up, where should your peak steering be? At the very turn-in phase.

Notice how at the change of direction, you immediately go to the peak steering of that second corner because your speeds are only going up. So far in all the previous examples, the peak steering was very close to the apex or very close to the inside of the corner.

Example: Sequential Corners Without Braking

On the first apex, it is still true that the peak steering occurs at the minimum speed, which is very close to the apex. You get back on power a little bit before the apex, but then on the second corner, the MRP is not very close to the right apex anymore.

This time, as soon as you change direction, you jump straight to the actual MRP. If you look at the graph, you actually jump straight to the peak steering way, way before the actual second apex. The reason for doing this is because you are not braking towards the second corner—you are accelerating.

If you're accelerating, you're gaining speed, so you have an opening spiral. Yes, you have an opening spiral very early into that corner because if you're gaining speed, you should be losing rotation.

The Common Mistake

This is such a common mistake on this type of corner: 90% of all the drivers on the planet will increase the steering towards the apex. Because so many corners have peak steering near the apex, we are wired in our brains to add more steering when we see that we're getting closer to an apex.

But you have to add steering if you're decreasing your speed. If you're on power, you should be opening up your steering, which means if you're doing an entire corner on power and gaining speed, the peak steering is at the very beginning of it.

This is where many drivers get caught increasing the steering towards the apex and ignoring the physics of racing because they are so used to just adding steering towards the inside. Remember: if your speed is going up, your line is an opening spiral and your steering should only straighten up more and more.

Practical Analysis: LMP3 at Nürburgring GP

Here's a quick analysis on a lap in an LMP3 at Nürburgring GP in Germany. We are going to focus on the relation between speed and steering and see where in the corners we are doing closing spirals versus opening spirals.

Hairpin (Traditional Corner)

At first, pretty basic: we have a very traditional hairpin where we do a closing spiral on entry and an opening spiral on exit. More, more, more, more steering, and then opening, opening, opening.

Turn with Delayed Trail Braking

Then we're going to open up for the next corner. Here you can see how quickly you already get into somewhat 45 degrees of steering. The reason is that trail braking doesn't happen right away—you're actually turning into the corner and then adding the brakes because you're still on power and your speeds are still not going down, so you can afford to turn in more quickly.

Then you're going to add a little bit of brakes right here and start adding more steering after. You can see now a little bit of correction and then adding, adding, adding, adding—peak steering at the minimum speed, your opportunity to rotate the car as much as you can, your maximum rotation point or MRP.

Now getting back on power, you can see how you start relaxing your hands, opening the steering. The car wants—because it's gaining speed—to do an opening spiral. It wants to run wider and rotate less and less and less as speed is gained.

Sequential Left-Right Combination

Then preparing the next corner, you start braking quite relaxed with the hands, and then you can see again closing spiral—turning more and more and more and more in a closing spiral all the way until the minimum speed and maximum rotation point of this left-hander.

Then we get into something very interesting: we have a change of direction now to the right. Let's look at what happens with the steering. As you can see, the change of direction was not so slow—it was a little bit quicker. Why? Because you're already at that speed, so you can quickly change now to what's going to be very close to the peak steering of the right-hander now.

Because your speeds are only going to be maintained or going up (you're not trail braking to this right-hander), you're not doing a closing spiral here. You're actually doing a fixed radius and an opening spiral because you're already on power. Peak steering occurs now. You pretty much maintain a little bit of half throttle, kind of waiting for the car to turn, maintaining your speed. Now as you get back on power more aggressively, you really let the car spiral out all the way to the outside.

More Traditional Corners

Then we have another corner: brake, relaxed hands, start turning very progressively—closing spiral, closing spiral, closing, closing, closing, closing, closing—peak. Now get back on power and start relaxing hands and opening the spiral. Same thing.

Then for the next corner, same pattern: braking, slow turn-in because of trail braking right away from the beginning, and then adding more and more and more and more and more steering—peak steering. Get back on power, and going a little bit wide, so kind of hold it. Obviously because of that, you cannot go full power. Trying your best to bring the car as much as you can to the outside of the next corner. Now finally able to bring the car to where you want.

Long Closing Spiral Corner

Then change direction: you're going to be closing spiral for a long time—closing, closing, closing, closing, closing, closing, closing, closing, closing, closing. Now power, and now starting to open and open and open, relaxing hands as you hit that curb and let the car spiral out all the way to the outside.

Chicane with Change of Direction at Minimum Speed

Then we have the chicane, which is also going to be a little bit different because there's a change of direction at the very minimum speed. You're probably going to see the change of direction being pretty aggressive. Starting to brake, turn in progressively more and more and more and more and more and more—we already have a change of direction right here.

You're not going to trail brake to the right. Trail braking from here, then getting back on power and changing direction at the same time. That means when you change direction at the minimum speed and the speed is only going up, you will have to turn the most at the very change of direction—boom, very quick change of direction as you can see. And then from here just opening and opening and opening and opening and opening.

Final Corner

A closing spiral, and then we have the last corner: going to start braking, light hands initially, closing spiral all the way until the minimum speed, maximum rotation point. Then back on power, relax hands, open spiral. A little bit of a correction there that was probably easier to be done because hands were relaxed.

Additional Example: Lime Rock

Here's another very good example at Lime Rock. We're doing this left-hander corner, and this is an acceleration part, so we're adding, adding, adding, adding steering until we accelerate. Now we decrease a little bit the steering, right? Because we're gaining speed.

But then we're changing direction to the right, and the next corner is flat. That means we should already reach the peak steering as soon as we change direction. There you go—change right away, and then getting less and less.

The Wrong Approach

But like all the other corners, a lot of people tend to add steering here because they see this curve and they think, "Oh okay, that's a curve, that's the apex—increase steering on the way to that apex." And that's not correct. This is how you should NOT do it.

You see, this is exactly what was talked about: at this point, he's steering this much right here—he has more speed than before but also more steering. He is definitely going to be over the limit at this point and destroying the front tires if he wasn't at the limit right here. You can hear the tires just suffering and struggling and understeering and scrubbing and crying because he is asking for way too much from the car by expecting more rotation with more speed.

The reason he's doing that—he's not even noticing it—is just seeing the apex on the right, seeing the curb. Again, like was said, we are wired to add more steering when we see an apex. When we go from the outside on entry towards the inside mid-corner, we are doing more steering in 95% of the corners, and that's why we don't realize that there are moments where this is wrong.