Pacenotes, racing line and Vittorio Caneva

31.05.2016. / Knowledge

We've built iPACENOTES wheel in the last blog and we've invited you to make one and start measuring corners on public roads. If you did so, you've most probably noticed that there is at least one big problem which we didn't mentioned yet: if two corners are close to each other, you cannot drive through both of them using ideal racing line. Well, we've actually never mentioned ideal racing line in any context. This blog is all about pacenotes and its correlation to ideal racing line.
In short, ideal racing line is the route that must be taken through the corners in order to minimize the time taken to complete the course. In other words, ideal racing line should be the fastest way through the corner. When analyzing a single corner, the optimum line is the one that minimizes the time spent in the corner and maximizes the overall speed (of the vehicle) through the corner. Optimum line runs from the outer edge of the corner over its inner edge at the apex and ends on the outer edge of the corner at the end. The following picture shows ideal racing line through U-turn corner:
For those of you which are more curious about physics involved with racing line, here's the link to very good formal explanation of it (authors are MIT guys).
The fun fact about ideal racing line is that it is not the fastest way through the corner. It becomes the fastest way when you put braking and acceleration into the equation. Otherwise, shortest path would be the fastest (ideal racing line is not the shortest path!). In other words, ideal racing line allows later braking and earlier acceleration then the shortest line. Points of braking and acceleration have the most significant influence on overall speed through the course. Among these two, acceleration point is more important.
Ideal racing line through every single corner is the same: from outer edge to apex then again to outer edge. However, what happens to the racing line when two corners are so close to each other so that it is impossible to take ideal line on both of them? Consider the example from the following picture:.

The ideal racing line in the first corner positions your car adversely for the next corner, which implies more braking when taking the next corner and low exit speed out of the next corner. Low exit speed also implies greater delay. So, what is the fastest way through these two corners? Or more generally, whenever we have two, three or more consecutive corners, which driving line is the fastest one?
There is no analytical answer to this question. The fastest line ultimately depends on points of braking, corner's geometry and points of acceleration, but it also heavily depends on the road surface. It is not possible to make generic formula which would calculate ideal racing line for every given course. To make things even worse, ideal racing line differs slightly for front and rear driving cars.
One of the basic goals of any pacenotes system is to provide driver very clear and unambiguous picture of corners in from of him. Driver must know what to do with the car whenever he hears something like "L2 into R3". But how to determine ideal racing line from "L2 into R3" instructions?
Many racing drivers will tell that finding ideal racing line is an art. But we need something solid, easily explained and good enough to start with. Saying that something is "an art" unfortunately doesn't help.
We've decided to use a rules for determining an approximation of ideal racing line which was formulated by Vittorio Caneva, a famous Italian rally driver and racing educator. Here are the Vittorio Caneva's 3 simple rules:
  1. 1. Whenever possible, take the standard ideal racing line through the corner (this means that there are long enough straights both in front and after the corner)
  2. 2. For two connected corners, sacrifice ideal line through the faster corner in order to take ideal line through the slower corner
  3. 3. If two connected corners are equally fast (they have the same curvature radius), sacrifice ideal line through the first one.
The first rule is just standard ideal racing line which we've discussed above. The second one is the rule which explains how to drive through two adjacent corners. The third rule explains how to apply the second rule in the case when adjacent corners are equally fast.
Let's apply second rule to the case we've illustrated earlier:

As illustrated in the visual, you take a fast corner at lower speed later (in comparison with the ideal racing line in such corner when taken separately) to position your car for the ideal racing line in the slower corner at its entry. But such racing line carries the highest speed out of the second corner and is significantly faster than the dotted line in the previous example and thus also brings a better result.
Interestingly enough, by adopting these rules we don't need to add anything in pacenotes in order to describe racing line. For example, when we apply Caneva's rules to instruction "L2 into R3" we get the following: L2 (left 2)  into (is adjacent to) R3 (right 3). 2 is faster than 3. Therefore, we shall sacrifice ideal line through L2 in order to take ideal line through R3. In other words, it is perfectly clear where the car should be at any moment during the drive through these two corners.
To sum up: iPACENOTES themselves will not contain information about ideal line. There will be no instructions which describe position of a car on the road in the iPACENOTES. Racing line should be determined from the corners curvature, how close they are and finally by applying Vittorio Caneva's rules.

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