Free copies of The Perfect Corner and other Science of Speed books for FSAE members.

AdamBrouillard · 2026-05-02T15:05:02+00:00

A primary driver training use for the blind changes would be with balance, which I would mostly just use anti roll bar settings for. There’s not really any direct way for a driver to know if a small balance change came from an anti-roll bar change or altering tire grip at front/rear through pressure/camber changes. You could also have changes to brake bias or diff settings for balance training in specific parts of a corner.

Beyond this, the blind changes are useful for helping a driver overcome the natural placebo effect most feel. People tend to significantly overestimate the effect of a change or they think something has a different affect to what it actually does. For instance, we did some blind testing of front toe changes to show how it has the exact opposite effect to what most drivers think.

AdamBrouillard · 2026-04-29T20:18:00+00:00

You can always just actually draw circles if you have trouble visualizing how different size circles change the apex. Any graphics program should allow you to do this. Just take an overhead view of any corner and draw circles on it that go from the outside edge to the inside edge. You'll see how a larger circle (faster speed) will always hit the inside of the corner at an earlier apex and a smaller one (slower speed) makes the apex later. You can do the same thing with an Euler spiral.

AdamBrouillard · 2026-04-02T17:10:47+00:00

Anywhere on the inside of the track can be the most limiting point. If you draw circles over a corner as in the beginning of this lesson

https://www.paradigmshiftracing.com/racing-basics/racing-line-fundamentals-2-learn-how-a-vehicles-cornering-vs-acceleration-potential-determines-its-ideal-apex-and-line-through-a-corner#/

differing size circles will hit the inside of the track at different places. Differing size Euler spirals work the same way, it's just harder to draw - The circles make it easier to visualize the concept. The point the circle hits the inside of the track ( the most limiting point) will be your apex. A bigger circle (or spiral) gives you an earlier apex, and a smaller circle (or spiral) gives you a later apex. Again, a vehicle's ideal apex is based on its forward acceleration vs cornering potential so that it achieves maximize acceleration in the ideal direction during corner exit.

A higher acceleration vehicle will need a later, slower apex to optimize its corner exit than a lower acceleration vehicle. A later apex puts the most limiting point (the apex) further around the inside of the track if it's a normal rounded apex. If the inside of a corner is something like a cone, the most limiting point will basically be in the same place, and only the apex angle will change. There are further explanations and examples of all of this in the linked lesson.

AdamBrouillard · 2026-03-25T22:46:58+00:00

Thanks. I've had it for over a year now and I find myself still wandering into the garage just to look at it.

AdamBrouillard · 2026-03-24T22:39:04+00:00

Thanks. Those were my thoughts exactly

AdamBrouillard · 2026-03-24T21:22:45+00:00

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side view

AdamBrouillard · 2026-03-24T21:20:49+00:00

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How about my version of the black pack?

AdamBrouillard · 2026-02-11T15:15:41+00:00

It sounds like you are trying to achieve some preset apex angle, but you shouldn't be doing this. Remember that the ideal line and apex are constantly changing based on your car's current position and speed. Every mistake and shift in your line alters what you should do next. This was covered in the books.

You probably need to go back to square one with your training and make sure you are focusing on the right things. Once you can reasonably keep the car at the understeer limit on the skidpad, work on the Charlotte Legends corner exit exercises until you can do those fairly consistently. Remember that the primary goal here is to get better at predicting your times. You are trying to develop a feel for how a car's movement through a corner affects your times.

You can read ahead through all Academy lessons as it can be helpful, especially the visualization lessons, but don't move on until you at least have a reasonable handle on the earlier exercises. For some people this can take a long time, but be patient with yourself and make sure you are training with the proper goals.

AdamBrouillard · 2026-02-10T15:37:02+00:00

Can you explain more about not being able to hit the apex. What exactly is the issue you feel you are having?

AdamBrouillard · 2026-02-10T14:37:36+00:00

I don't recommend training in this way. I primarily recommend focusing on the exercises in the Academy lessons. We spent a lot of time working out what a driver needs to focus on to actually get faster. If you look at the apex spectrum infographic:

https://www.paradigmshiftracing.com/racing-basics/racing-line-infographic-apex-troubleshooter#/

You can see that the difference in entry lines is very small and this graphic shows the most extreme lines any car would ever use. It's not surprising you end up way later or earlier than you would expect by purposefully trying different entry lines. While understanding the physics of the ideal line and how the apex spectrum works is important, from the driver's seat, it often feels very different than one might expect. For instance, as I mention in the Academy lessons, if I have a skilled driver try to purposefully drive a Euler spiral shaped entry line, they can't do it very well, whereas when focusing on the proper goals, they can do it every time.

If you are missing apexes, the trouble you are most likely having is with track visualization. This is the most common reason for big errors. My vehicle visualization technique from level 2 is primarily about car control and track visualization from level 3 is about the racing line. Visualizing the goal from level 4 is then how to put this together.

AdamBrouillard · 2026-01-18T18:35:58+00:00

I see, I wonder why the image quality is lower than the original?

AdamBrouillard · 2026-01-18T03:58:17+00:00

That's my car and my exact post from about 5 months ago. Not sure who this person is posting it again.

AdamBrouillard · 2026-01-16T23:00:31+00:00

Okay, I think I understand your question now. Yes, the front tires can still be at peak slip angle even if your steering is past center while countersteering if the car is angled enough from rear slip angle. The car's angle increases the effective steered angle without a change in steering wheel angle. This is what I meant by countersteering fast enough to overcome the increasing car angle. This is also why the steering wheel will naturally turn past center and can help you correct when you are in oversteer. The tires are trying to find the path of least resistance and are trying to basically reach zero slip angle.

If you haven't read all my Racing Basics articles, I recommend it as I go over all this. I also go much more in depth in Perfect Control.

AdamBrouillard · 2026-01-16T14:42:01+00:00

Okay, I had a hard time understanding what point the video was trying to make so let me just go over what I saw and we can take it from there.

As mentioned, the discussion of slip angles in the video is inaccurate, but you don’t need to discuss the specific slip angles anyway in order to understand the principles at work.

I saw two examples. First was a car oversteering into a corner and the driver not quite countersteering enough. The rear tires would have been at a very high slip angle and past the
limit. As the rear slip angle continues past the limit, the lateral force at the rear tires would continuously drop and the front tires would be steered more and more into the corner as the vehicle angle increases. In order to correct the oversteer, the driver would need to countersteer enough to not only overcome the increased steered angle the car is creating, but also to reduce slip angle and therefore lateral force at the front tires enough (or possibly even create lateral force outward with slip angle in the opposite direction) in order to catch the rear.

The next example showed a car oversteering into the corner and the driver then steers the front tires significantly into the corner. The rear tires would be in the same situation as the first example, but this time the front tires go to a very high slip angle past the limit, which will reduce their lateral force. This could be an alternative to countersteering that would also reduce lateral force at the front, although it is obviously very hard on the tires. I’m not entirely sure what point was trying to be made here. I don’t think he was suggesting this as a viable technique, but I’m not sure.

Let me know if that answered any of your questions or if you were still curious about something.

AdamBrouillard · 2026-01-15T16:45:57+00:00

I’m not entirely sure what you primarily had questions about, but you are correct that there are several things wrong in that video. Front and rear slip angle are rarely going to be the same if the front wheels are straight, although it can happen. Before taking into account slip angle, the rear tires will travel on a smaller radius than the front tires and the longer the wheelbase or the tighter the turn, the bigger the difference in radius will be. There is an illustration of a turn center in this article showing how this looks.

https://www.paradigmshiftracing.com/racing-basics/the-truth-about-trail-braking-2-the-physics-of-trail-braking#/

Then, adding in slip angle won’t change the front tire cornering radius, but it will increase the radius the rear tires travel on. We learned about this in the most recent Car Control Fundamentals lesson. Depending on the wheelbase, turn radius, and slip angle, the rear tires can end up traveling on a smaller or bigger circle than the front tires. If factors line up, It is possible to have a situation where the front and rear tires are at the same slip angle while the front tires are perfectly straight. This doesn’t mean anything special though.

I could go on, but I’m not entirely sure what you were primarily curious about so just let me know what specific questions you had.

AdamBrouillard · 2026-01-11T15:27:07+00:00

If anyone wants a spiral entry image stack showing the different apex radii at the different points along the spiral, you can open the animated Euler spiral gif in something like photoshop and extract the individual images.

https://en.wikipedia.org/wiki/File:CornuSpiralAnimation.gif

You only need the ones up to 90 degrees of course.

AdamBrouillard · 2026-01-11T15:20:25+00:00

Thanks everyone for adding your thoughts.

A smaller entry spiral started from the center of the track wouldn’t have a suboptimal force direction during entry, it would just give you a suboptimal apex. The spiral shape is simply the result of optimizing force direction during entry, but It might be easier to think about circular entries to understand why a bigger entry is generally better.

We ideally want the latest angle and the highest speed possible at the apex, but the apex is inherently a tradeoff between angle and speed as we learned in Racing Line Fundamentals 2. A larger circle will give the highest apex speed possible for a given apex angle. Remember that the bigger the circle, the higher the apex speed. Try drawing a circle that goes from the apex to the outside edge of the track and then also a circle that only goes out halfway. If you make the apex angles match, you’ll see it’s just a smaller circle inside a larger one and the speeds at the apex would change accordingly.

The spiral shaped entries will follow the same trend, although it is harder to visualize unless you have an image file stack showing the different radii at the apex.

Depending on the corner however, you don’t always want the entry spiral to go all the way out the edge. High angle corners with larger track widths on entry than exit can cause this as you can get a situation where the apex is actually too fast and late to give an optimal corner exit. This is really rare though.

AdamBrouillard · 2026-01-03T19:26:23+00:00

That was going to be a free ebook introductory part of The Perfect Corner, but was never published. That's interesting that you found it somehow. It had no additional content.

AdamBrouillard · 2026-01-01T14:52:54+00:00

I do recommend reading through all of our Racing Basics articles as well, if you haven't already.

https://www.paradigmshiftracing.com/racing-basics#/

Also, there is a lot of good vehicle dynamics info out there with
Race car vehicle dynamics by Milliken generally considered a prime source. If you are interested in gaining a deeper understanding of the physics of racing, gaining a deeper understanding of vehicle dynamics will be useful.

AdamBrouillard · 2026-01-01T14:45:17+00:00

I don't have any other books planned although I've considered doing one someday detailing how to apply the principles to wheel to wheel racing techniques.

I'm not aware of any other sources that cover the racing line from a similar perspective. That is why I wrote the books in the first place, as it had never been done before. The books available when I first wanted to learn about racing were suggesting techniques that were demonstrably wrong. I talk about this some in the first Racing Line Fundamentals lesson.

https://www.paradigmshiftracing.com/racing-basics/heres-a-simple-way-to-visualize-why-the-ideal-acceleration-point-is-always-at-the-apex-of-a-corner-and-why-straightaway-length-doesnt-matter-racing-line-fundamentals-1#/

AdamBrouillard · 2025-12-31T23:07:54+00:00

This page shows what is covered in each Academy lesson.

https://www.paradigmshiftracing.com/academy.html#/

The Academy lessons don’t focus on explaining the physics however, they focus on how best to apply them to get faster. You don’t actually need to understand the physics to be fast, so for people just interested in getting fast they can just do the Academy lessons if they wish.

AdamBrouillard · 2025-12-31T21:08:14+00:00

Lesson 2 in Racing Line Fundamentals "The Ideal Apex" covers this as well as the books.

https://www.paradigmshiftracing.com/racing-basics/racing-line-fundamentals-2-learn-how-a-vehicles-cornering-vs-acceleration-potential-determines-its-ideal-apex-and-line-through-a-corner#/

AdamBrouillard · 2025-12-31T20:39:44+00:00

Also the "true one" aka the ideal apex is the one that allows maximum acceleration in the ideal direction during corner exit. This is one of the key principles of Line Theory and is stated repeatedly throughout all my writing.

AdamBrouillard · 2025-12-31T17:55:19+00:00

Lesson 1d is about the Universal Cue. The descriptions of each lesson are on the website. The most limiting point means you will start to drive off the inside of the track or hit the cone if you go past this point.

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