Talk:Racing line

Things to Do

1. Find a drawing tool suitable for producing an improved version of the diagram, or find a better pre-prepared diagram, with suitable copyright provisions. The straight line segments, starting "early apex" and ending "late apex", in the current diagram are incorrect.--SportWagon (talk) 18:38, 25 August 2008 (UTC)
2. Decide on structure for article, so as to imply necessary source materials for reference, and then see if they can be found. would be good for a "what would one do with a single corner, then refine that into a total circuit" approach. Alternatively, we've got to decide whether there's really enough citable (web-citable?) material to base a NPOV digested article on. We seem to have ideas, but not a lot of citable references.--SportWagon (talk) 18:38, 25 August 2008 (UTC)
3. For me the article is unnecessary theoretical - seldom the racing line follows the "theoretical" ideal line as derived - AFAIK, nowadays - by simulations. Weather, grip laid on the track, local road roughness, tire condition, puddles, even sun position are often much more important. And if we'll be going theoretical - the road is a 2-dimention surface and the curbing might (end up being) variable across the width of the turn (like at most ovals). A sim driver will never consider most of these - but it's the common chatter in track racing briefs, and that's why every "resurfacing" of this and that section brings so much buzz. — Preceding unsigned comment added by Kerguelen Rogue Avon (talk • contribs) 08:27, 24 September 2022 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for speedy deletion

The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for speedy deletion:

• Racing Line showing earlier and later apex.jpg

You can see the reason for deletion at the file description page linked above. —Community Tech bot (talk) 18:23, 14 April 2023 (UTC)

Where is the math?

The article makes claims about optimal trajectories, but does not justify them from a theoretical viewpoint. Why is it, for an isolated "corner", *always* better to start from the outer edge and follow a circular arc at the highest possible speed, even as that trajectory is longer than the shortest one possible? This principle cannot possibly hold across all road widths and corner angles. Elias (talk) 15:55, 11 April 2025 (UTC)

If you have any reliable sources that make this case or present the math, they could be added. Barte (talk) 00:00, 12 April 2025 (UTC)

Theoretical Issues with this Article

Not to start an argument with someone who devoted their time to this topic 18 years ago, but this article appears to share quite a lot of common myths and misconceptions, due in one part to the questionable theoretical basis of the source from Ross Bentley, and in another part to the previous editor's erroneous readings thereof. I'm not sure if this is a consequence of the information being outdated or just overly simplified to the point of being misleading, but either way I am going to try my hand at using some more current sources to fix it up.

Here are some sections I take issue with:

"In theory, the optimal path around a race course follows a geometric line, which takes the widest possible arc through a corner. The line starts at the outside of the road, clips a point on the inside, and finishes back outside while maintaining a constant radius throughout."

This is not true, even in theory. I consider Adam Brouillard to be a very reliable source when it comes to the theory behind racing dynamics, and in this article he points out that the "optimal" line into a corner (treating the car as a point mass, and regardless of what follows the corner) is always a path of constantly decreasing radius (an Euler spiral), as a result of the car decelerating towards the apex.

For what it's worth, Bentley also never refers to this as a description of an optimal racing line in any way, so this seems to simply be a misreading of the source.

"But while this line theoretically represents the fastest way through the corner, it may result in longer overall track times due to slower speeds on the straightaways. To compensate, drivers often delay the point where they begin to turn, thereby shortening the radius when entering the corner and lengthening the radius when exiting. This late apex line allows for earlier acceleration when exiting the corner into the straightaway, but requires slower speeds going in."

This part is substantiated by Bentley. The previous editor also seems to have backed up this claim, by suggesting that the "the tightest, minimum speed part of the line [tends] to occur earlier [than the apex]. Brouillard explains that this is not only a misunderstanding, but a very common mistake that newer racers make, commonly called a "false apex". In reality, aside from very specific exceptions (e.g. double apexes), the tightest part of the turn, the point closest to the "center" of the turn, and the acceleration point should always be the same. Even when a car is taking a late apex, the optimal point of acceleration is at the apex, never earlier. This means that the correct way to take a late apex almost always involves accelerating later than you would at an earlier apex. The benefits of a late apex are not in being able to accelerate earlier, but in being able to transition towards the acceleration end of the traction circle much more quickly.

Additionally, whether a later apex is "ideal" is not an absolute fact of racing, not even with regards to the track boundaries, but is determined by the characteristics of the car. For example, modern Formula 1 cars often take an early apex, since their deceleration is much more limited by tire grip than their deceleration is.

I don't want to rely on Brouillard's work to refute all of the work done so far on this article, but the mathematical basis of racing lines is quite well understood and well researched, so I will be including other such sources as I make my changes. Amatmilen (talk) 19:18, 9 May 2026 (UTC)

I've removed the references to the "geometric line" from the article. As stated, the contents of the article in reference to this concept were not substantiated by the source from Bentley, and while Bentley's usage of the geometric line may be useful as a tutorial topic, from an encyclopedic standpoint I think it's best to get to the point. Amatmilen (talk) 19:37, 9 May 2026 (UTC)

The article has been substantially changed by me and others over the years. By me, not remotely an expert, because what I found had zero or few cites, as well as material not directly related to the topic. Looks to me like you've further improved it. Barte (talk) 04:33, 10 May 2026 (UTC)

I'm also definitely not an expert (at least, not outside of simulations!) although it's a topic I've had an interest in for long enough to find decent sources on. I apologize if my little essay here sounded critical, I'm just the type to give overly wordy explanations for my changes. I'm probably going to focus on expanding the section on theory for any future changes. Amatmilen (talk) 05:21, 10 May 2026 (UTC)