GHIT extra: decreasing vs. increasing radius

I was recently interviewed on the Garage Heroes in Training podcast and they asked me a lot of really interesting questions. I want to follow that up in a series of posts on YSAR where I get into a little more depth on a few topics.

“Increasing or decreasing radius?”

That was the question. Which do I prefer? Decreasing. And off camber if possible. Why? Because I like the challenge of balancing traction, and there’s more challenge to do that with brakes (decreasing radius) than throttle (increasing radius). Later, as I was thinking about this again, I came to an important realization: all corners are decreasing radius. Also, all corners are increasing radius.

Geometric line is a fantasy

The geometric line described in nearly every racing book is (a) not possible (b) not optimal.

There is no way to instantaneously go from driving in a straight line to a curve with constant radius. If you turn your steering wheel super fast, as would be required, the car doesn’t respond at the same speed. If you took a snapshot in the middle of a corner, you would see the rubber in the contact patch twisted to some degree and the suspension have a certain compression. But they had to get there somehow. It takes some time for the vehicle to take a set. During that time, the radius is probably not constant, but tightening whether you want to or not.

Not only does every racing book describe the geometric line, they also show the late apex line. The reason why the racing line is faster than the geometric line is because cars have engines. If they didn’t, the racing line would look very different. In fact, it would be decreasing radius. But since cars do have engines, and sometimes very powerful ones, the more time you can spend using that engine, the better. The late apex line trades corner speed at the beginning for corner speed late. In other words, the radius at the start is tighter than the radius at the end.

Every corner is decreasing radius (and increasing)

Let’s break up the corner into 2 parts.

  1. The first half of the corner. This is defined as the moment you turn the steering wheel until the moment you release the brake.
  2. The second half of the corner. This is defined as the moment you step on the accelerator until the moment you are no longer actively steering.

The point between the two halves of a corner is sometimes called the EoB or “End of Braking” but I call it the “nadir” because if every corner has an apex (top), it should also have a nadir (bottom). In some corners, the apex and nadir are really close to each other. That’s because the apex is the point at which the car is closest to the inside of the track and the nadir is the point of lowest speed. Usually, the nadir is a little before the apex. In really long corners, or two corners connected by an inconvenient distance, the nadir may be a stretch of track rather than a single point.

If you’re taking the usual racing line, the first half of most corners has a decreasing radius. You start out with the steering wheel straight. As the car trail-brakes to the nadir, the corner gets tighter. As grip transitions from braking to steering, more steering gets done. Also, speed is decreasing, so it’s possible to drive a smaller radius with the same grip. At the nadir, all grip is use for cornering at the slowest speed. Therefore, the radius is tightest. Even if you weren’t aware of it, the first half of the corner is supposed to be decreasing radius.

In the second half of the corner you’re mixing steering and throttle. As the steering is unwound, more throttle can be applied. The radius increases both because there is less steering and because there is more speed. From nadir to exit, the corner is increasing in radius.

Here’s an illustration to help you picture what I’m talking about. Whether you’re taking the single late apex or the double apex, there is decreasing and increasing parts, even in a carousel. The circles represent the halfway point of the corner as described above. The A’s represent the apexes on the single apex (blue) and double (red) apex lines.

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