If we drive a car at a fixed speed, while rotating as much as the car can handle without understeering too much or oversteering too much, right on the limit, the car will produce a fixed radius circle. As long as the speed is constant, the rotation is constant, the four tires are on the limit and the car is sliding perfectly in a consistent line.

Speed and Radius Relationship

If we increase the speed and then maintain it, then the car will start doing a bigger circle with the higher speed. It's not going to be able to maintain the same rotation that it had before, so it's going to create an increasing radius while accelerating, and then as soon as we stop accelerating and maintain the new speed, a new fixed but bigger radius will show up.

If we decrease the speed and then maintain it again, same thing will happen but the opposite—the car will start doing a smaller circle like in a spiral, and then as soon as we stop decelerating and keep the speed consistent, it will go back to creating a fixed circle but a much smaller one because the speed is now slower.

If we decelerate and continue decelerating all the way into the car stops, then we create this spiral, and if we continue accelerating all the way into the top speed, it's going to create an opening spiral until we reach the top speed.

The Maximum Rotation Point (MRP)

In corners where deceleration is required, the rotation then should reach its peak at the minimum speed, and this is one of the most important things we're going to talk about in this course, because everything else, all the next lessons will depend on you having a clear idea of what we're going to call the maximum rotation point.

From Geometric Line to Racing Line

As a beginner, you learn to brake on a straight line, then to build the biggest radius possible that fits that corner as a fixed radius, so in the end, the geometric line looks like a circle. But now you know that at entry you're going to have, for example, 100 kph, but then it's still going to continue to go down to let's say 60 at the apex. This means that the amount of rotation that you get at entry should be smaller than the amount of rotation that you get at the apex, so the line will not be a circle.

Instead of having a fixed circle, we're going to drag it down and create an ellipse, because now this line matches the fact that we are rotating less at entry because we are fast, but then we are decelerating, decelerating, decelerating and getting the peak rotation right at the MRP. This is what we're going to call the maximum rotation point, the MRP.

MRP and Apex Relationship

Right now you can see that the MRP matches exactly the apex, because we are decelerating at a fixed rate and then accelerating at that same fixed rate. But you know that cars are much more effective in deceleration and much less effective in acceleration. If we create a speed graph of a race car, we know that it's able to decelerate a lot more quickly and then it accelerate a lot less.

If the speed decreases more quickly than it increases, in order to actually benefit and create the fastest line, we are going to have more rotation on the deceleration part and less rotation on the acceleration part. So instead of having a racing line that is super symmetrical like that, a symmetrical ellipse, we now know that there's going to be more rotation happening on the first half and less rotation happening on the second half.

Asymmetrical Racing Line

In real life we are going to decelerate more aggressively, so the line is then going to look asymmetrical. We have a car that is more efficient at decelerating, so we concentrate a little bit more rotation to the first half and then have the car more pointed towards the exit and accelerate a little bit earlier, because we will gain a lot of time if we accelerate a little bit earlier and carry more speed throughout the entire exit.

In this situation we get more rotation on entry and our maximum rotation point now is not at exactly the same place as the apex. If we divide this on the middle, you can see that there is a small distance between the place where we accelerate and the apex. This is why we always want to accelerate a little bit before the apex.

There will be rare occasions where you actually accelerate at the apex, because of this natural behavior of 100% of the race cars—we brake more efficiently than we accelerate, therefore we get more rotation on the initial part and a little bit less rotation on the exit.

Distance Between MRP and Apex

Of course this is a subtle thing. In some situations you're going to have an obvious distance between the MRP and the apex. Basically the distance between the MRP and the apex depends on how early or late the apex is.

• If you're taking an early apex approach then you're pretty much going to accelerate almost at the same point, although we always want it to be a little bit where you accelerate a little bit before

• If it's a very late apex approach because it's a very low speed corner that leads into a long straight, then we can stretch this more and more and more to have a very late apex approach

• The later the apex the earlier we're going to accelerate, which means the earlier the MRP is going to be, which increases the distance between the MRP (which is the point where you accelerate) and the point at which we touch the inside of the track

Downforce Effects on Racing Line

A car with absolutely no downforce quickly loses the ability to turn when they gain speed. But if the car has downforce, the extra cornering grip that comes with the speed makes the opening spiral look more gradual. Although we continue to lose the ability to turn with extra speed, we lose a lot less of it, and the car is still able to do a lot of rotation on high speeds in comparison to low downforce cars that lose drastically their ability to turn on high speeds.

This is why high downforce cars have a more U-shaped line, and low downforce cars have a more V-shaped line. And no matter how much downforce you have, your optimal line will never be a circle, but always an ellipse.

Practical Application of the MRP

Learning New Tracks

The MRP, or the idea of an MRP, is useful as a better way to figure out what is going to be the actual line of a corner. When I'm learning a new track, I don't need to figure out the entire line. I can just figure out the braking point, then this smallest radius, which is where the MRP is more or less going to be located, and then from those two points—the braking point and the MRP—I already know everything else.

I know where the turning point is going to be, depending on how much downforce the car has, and how the car is going to behave on exit, because I know it's going to lose rotation from there. So by knowing more or less how much speed I need to carry into the corner (workable speed range) and where the peak rotation is going to be (which is the maximum rotation point), everything else kind of happens naturally.

So I don't have to overthink when I'm learning a new track. I just figure out those things. Of course you're going to learn the MRP after you get used to the workable speed range, which is the understeer exercise from the beginning of the course.

Using the MRP at the Limit

The MRP is a lot more useful when you're getting closer and closer and closer to the limit, because after I get on that understeer area, I already have a better idea of how much speed I'm going to carry. I'm going to start getting as much rotation as possible on the lowest speed, because I know that the maximum rotation point is the minimum speed point.

If I know where that bit is, I can start building a much more consistent approach, because when you know where the MRP is, you will know that you have to gain more and more and more and more rotation until that point. So it's not only the peak, but it also shows you that that entire duration until there, you should only be gaining rotation.

Common Mistakes

It's a very common mistake to see drivers coasting or just getting back on power a little bit too early, way before the actual half of the corner and losing rotation in the process. But if you think about an MRP, you know, I'm going to continuously gain rotation all the way until that point.

The MRP is the pillar of the corner. It's going to divide the entry from exit in a very practical way that you can use in absolutely every corner.

Telemetry Analysis of the MRP

It's possible in telemetry to identify whether you're doing a very good MRP approach or not. This is how we can analyze in our own telemetry whether we have a very clear development of rotation until the peak, which is the MRP (maximum rotation point) and then losing rotation from there.

Telemetry Example

In a telemetry analysis of a short oval lap with the Porsche Cup car, you can see the driver starting to brake and adding steering, so we're gaining rotation. We're still trail braking a little bit and then adding more steering, gaining more rotation until we reach a specific point. This is beautiful because everything kind of fits together.

You can see in the same point in time, we have:

• The peak steering

• The minimum speed

• The peak yaw rate (yaw rate is literally how many degrees per second the car is rotating; if you have 360 degrees per second, that means every second you're doing a full circle)

• The moment where we start accelerating

• The end of our braking

So the MRP is all this: the peak steering, minimum speed, peak rotation, point of acceleration, end of braking—all in the same spot. Look at how useful thinking of one point on your corner can be.

MRP Variations

Every corner will have an MRP. Of course there will be variations depending on corners, compound corners, and whether you brake or not on that corner. For example, if the corner is flat then the MRP is going to be in a different place—it's not going to be in the middle of the corner, it's actually going to be way before.

But just by placing an MRP you divide the corner, you structure the corner in a much more useful practical way that you can apply everywhere in any car, in any track.

MRP Application Throughout a Lap

Here's a breakdown of a lap to show how to really think about MRPs everywhere and how you can divide the corner from entry to exit:

Corner Entry to Exit Pattern

Start braking, add steering. Still braking, speed is going down, steering is increasing, rotation is increasing, and then throttle—that's the peak steering. The steering goes back as you get back on power. You're not gaining rotation, the car is on the limit, but if you gain rotation and speed at the same time, you're going to lose the car, either spin or just understeer and go off, because you were at the limit at the MRP.

After the MRP you should never gain rotation. This is a very common misconception that you have to rotate the car in power. Be careful with that, because you should just maintain the rotation that you had before and then the rotation should go down. So power means less steering, and then the car is rotating less and less and less while gaining speed.

Consistent Cornering Process

The cornering process is very simple when you divide the corner into the first half and the second half. The pattern for each corner follows:

• Start braking (on a straight line, dealing with elevation changes)

• More steering, more steering, more steering while still trail braking

• MRP (maximum rotation point)

• Unwind the steering with a little bit of corrections here and there

• The car loses rotation on that opening spiral naturally

Different Corner Types

For corners where you don't have to brake hard on the straight line, you already start turning in and touch the brakes a little bit (perhaps 20% brakes), then add steering as the speed goes down until the MRP. Then start accelerating—now it's less steering, and the car is opening out on the spiral.

You can see the pattern: closing spiral (gaining rotation), opening spiral (losing rotation). This is how all corners are divided.

Full Speed Corner Breakdown

At full speed, the pattern becomes: more steering, more steering, more steering, more, more, more until the MRP. Then less steering, less steering, less steering, less, less, less, less as the car opens up.

The MRP concept will be discussed in practically all the other lessons, because it's a way to divide the entry from the exit and provides a fundamental framework for understanding and executing corners consistently.