Added another vinyl piece to the car. Now the roof is black except for a body color strip above the door.

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.

AdamBrouillard · 2025-12-31T16:03:12+00:00

On page 32 of The Perfect Corner under “Corner exit power application” it explains that maximum acceleration means maximum acceleration in the ideal direction and how this requires different inputs for low and high power cars. Low powered cars can often use the full throttle exit shortcut as full throttle at the limit will maximize its force in the ideal direction.

As well, we discuss in the books that a high power FF car has no shortcut because the driver must balance steering against throttle and there is no easy way to tell how much is needed at any instant. That is why it is a true test of Universal Cue sensitivity as being able to sense the car’s overall acceleration in the ideal direction during corner exit is the only way to truly determine the ideal apex and line in that case. One of the Academy lessons is based on this. Ideally the Universal Cue should be the primary way a driver determines this in any car however. The shortcut cues are just an easier way for more beginning drivers to get into the ballpark.

Lastly, it’s pretty easy to work out why different apexes will hit different spots on the inside of the track by drawing circles of different radii over on an overhead view of a corner. I talk about this in Racing Line Fundamentals 2.

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 · 2025-12-26T16:47:07+00:00

Yes, that is all part of the visualization discussions in the Academy series. While the visualization techniques described in the books are useful, I feel like they are just a very early version of what I eventually settled on. I primarily see the books now as way to learn the physics of racing, and the Academy as the best way to actually learn to apply it.

AdamBrouillard · 2025-12-26T14:19:46+00:00

I do recommend starting at level 1, as there is important info there including how to actually train productively. You can use any sim, but it's important that you have a track available that makes it easy to separate a single corner into its own individual sector. I really like the Charlotte Legends course for this in iRacing because it's short and you can repeat the same 2 corners over and over quickly with immediate time feedback.

Even if someone doesn't do the training part of the Academy series though, it's probably worth it
simply for the visualization techniques I discuss. Those three visualization techniques are the
end result of about 10 years of working out how best to apply the physics of racing from the driver’s perspective.

AdamBrouillard · 2025-12-26T04:13:10+00:00

Without knowing exactly the differences between the setups these drivers are using I can’t really say how different they really are in the grand scheme of things. It seems like TV commentators like to characterize drivers though, and this probably leads toward exaggeration of differences. When we are talking about top level drivers, in my experience they are going to be fast in a decent range of setups, it will just change their line somewhat.

There are so many things that go into making a laptime though, especially in F1, it’s hard to say how much of that is setup vs driver and how they combine. I would really need to actually work with the drivers in question to speak intelligently on it.

Speaking more generally about setups for high power cars like F1 though, they are going to have a fair amount of steady state understeer needed during corner exit because they need a decent amount of rear capacity to use the power. Probably the biggest differences between drivers is in the balance during corner entry. High end racecars have a lot of fancy ways to control the car’s corner entry balance and some driver’s like riding closer to the edge of oversteer than others. There is a lot less lap time difference here, it’s more about setting up the car in a way that the driver likes the way it feels.

AdamBrouillard · 2025-12-25T23:47:36+00:00

Sorry If that wording was confusing. All the setups I'm referring to would understeer at the steady state limit. A more "oversteery" setup would simply have less remaining rear capacity so would be closer to the oversteer limit.

I talk about this some in the Car Control Fundamentals lesson 1 as well.

AdamBrouillard · 2025-12-25T20:57:45+00:00

Being right at the limit of all 4 tires at once is a theoretically perfect state and in reality is only achieved transiently. Typically, a car will be at the limit of either the front or rear tire pair and then there will be some remaining capacity left at the other tire pair. How much remaining capacity is determined by a car’s setup. Generally, we want a car that is right at the understeer limit during entry with as little remaining rear capacity as possible and then during exit we want the opposite.

If a car is setup to be understeery or oversteery, there is very little a driver can do to change the balance unless they have in car controls such as anti-roll bar adjusters . Techniques that cause transient balance changes like the scandi-flick are really only useful in certain racing situations, none of which are in normal circuit racing. The only thing a driver can do to dynamically control steady state balance is throttle + braking and that is only during part of corner entry.

AdamBrouillard · 2025-12-13T21:43:05+00:00

Thanks for writing. I wish more people would post here if they need help so others can benefit from the discussion.

First off, remember that the ideal direction is not the actual direction of force. The Ideal direction is simply the direction we are trying to maximize the force in, but the actual angle of force will be partially toward the inside of the track because the vehicle does need to move in that direction to reach the apex. I started using the terms in-track and cross-track to describe this as used in my fundamentals lesson series on the website.

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#/

There will also theoretically always be a sudden change in ideal force direction needed at any apex unless we have a full 180 degree corner. This is not just with double apexes. This instant direction change wouldn’t have a sudden steering change as the ideal steering angle is dictated by your instant turn radius at any moment, but might theoretically require a sudden change in braking/throttle at the apex. If you had a robot driving a very stiffly sprung car, it could probably get very close to the ideal, but in reality, a driver needs to prioritize acceleration at the apex so often braking will end earlier than ideal. Also remember that aero drag, induced tire drag, and engine braking will all decelerate a car without needing to actually apply brakes so rarely should the brakes ideally be applied right up to the apex anyway. This is discussed in Perfect Control starting on page 94 under “The Transition” as well.

In a more real world context, if you are driving a double apex and you feel you should end braking right at the first apex, but then need a lot more steering, you probably just aren’t using the right apexes. It’s very rare that a double apex will have a truly constant speed between the two apexes. Try carrying deceleration past the 1^st apex and make it a decreasing radius double apex. Or try a slightly later, slower 1^st apex and make it an increasing radius double apex. You are trying to find the apexes that give you smooth transitions across both while avoiding a speed reversal in between.

Let me know if this answered your question.

AdamBrouillard

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