The Perfect Corner 2: A Driver's Step-by-Step Guide to Optimizing Complex Sections Through the Physics of Racing

Beyond the Standard Corner

While the basic principles of Line Theory that we learned in The Perfect Corner will take you far, there are some unique track situations that take special rules. While the eventual answer is not any harder to execute than a standard corner, how we get there can be a little complex. This will be worth the effort however, because while trial and error will often eventually lead you to at least close to the right answer with standard corners, understanding how Line Theory works in more complex track sections can give you a significant advantage. Even in the higher levels of motorsport, some drivers misunderstand how to optimize complex track sections and will debate various ways to handle them. Being able to quickly determine how to optimize a complex section can be a great benefit and we can do this with just a few new rules.

We’ll start out with a summary of basic Line Theory and then we will push your understanding of its rules to the limit. Next, we will look at the new rules needed when combining corners, as well as the surprising science of optimizing straights. Finally, we will end by breaking down some of the most complex corner sequences in the world. If you can learn how to solve these puzzling track sections, you will be able to figure out how to drive anything.

You can also be assured that these rules provide a complete solution. They work with virtually every vehicle, on any track. You sometimes hear discussion about which corner on the track is most important or the concept of grading corners, but while certain corners will certainly have greater potential to change your lap times, this doesn’t affect how you should drive them. There is time to be gained and lost in every corner and you can use the same principles to optimize them all.

Standard Line Theory Summarized

To get started, let’s lay out a basic summary of everything we learned about Line Theory so far in The Perfect Corner.

A driver should set their braking point based on how their entry spiral carries them to the apex. If their spiral does not reach the apex, they need an earlier braking point. If their spiral would carry them off the inside of the track, they need a later braking point.

Once the driver starts turning into their entry spiral, they will try to reduce their radius as quickly as possible by maximizing their tire forces pushing them in the ideal direction. The pre-apex ideal direction is basically at the same angle as the track during corner entry.

An entry spiral’s starting speed determines its size and therefore where in the corner it needs to start. For a given corner, a larger, faster, and earlier starting spiral will create an earlier apex. A smaller, slower starting spiral will create a later apex, but will need to start later.

With an earlier apex, the vehicle will be at a higher speed and will have turned less as it passes by. A later apex will have a lower apex speed and the vehicle will have turned more as it passes.

The shape of the inside of the corner will determine the exact location of the apex. This will create a steady progression of a certain speed and angle attainable as the apex moves from earlier to later along the inside of the track.

As they pass the apex, the driver will maximize the vehicle’s acceleration in the ideal direction. The post-apex ideal direction will be in the same direction as the track exit.

If maximum acceleration would carry the vehicle off track, the driver needs a later, slower apex. If there is space left at trackout, the driver will need an earlier, faster apex. This new apex will require a different spiral and thus a different braking point.

Often the best line for an off-road motorcycle is wherever the rut has formed.

But are there no exceptions? What about off-road driving? What about racing on a wet track? What about elevation changes and banking? These situations don’t actually change the rules, but they will test how well you understand them. As an example, while racing in the rain, it is often standard practice to avoid driving on the standard line if on a well-worn track where the racing line is very slippery when wet. If the grip on the standard line is only half what driving off the line produces then this will just effectively change where the edges of the track are. Those curbs are no longer the edge of the track. Now the edge is where the track grip level significantly changes and you must use Line Theory principles to optimize around these new track limits. If you used your car control abilities to find this area of high grip, you might discover that now your apex is out in the middle of the track or it could even turn a standard corner into a double apex. You still want to maximize your movement in the ideal direction before and after the apex, but the results are completely different now from when the track was dry.

Changes in track geometry work the same way. Off-camber corners, high banking, crests, dips. They might change the grip you have at any moment, but the rules stay the same. For example, consider a corner that is off-camber near the apex and then transitions to have some banking near the corner exit. A car would gain extra force production capacity (grip) as it progressed through its acceleration arc. This would change its lateral vs longitudinal force generating capability to be as if it was a less powerful car. So just like a less powerful car, this would create a more circular acceleration arc, but only for that specific corner. A driver goes through this same line finding process on every corner however. Different cars, setups, pavement grip levels, track geometry, weather. These will all create a unique solution each time. The process and the rules however, will always be the same.

Beyond just modifying a line, track geometry can also progessively change the efficiency of different lines and minimize or magnify mistakes. For example, a well designed curb will cause a car to progressively lose grip the farther off track it drives. The more curb used however, the more ideal the line so there can be a range of lines where using more and more curb won’t change lap times very much. A well marbled track causes the opposite to happen where a car progressively loses grip the further off line and into the marbles it drives.

Bristol Motor Speedway has actually used track geometry on purpose to promote close racing. The track has a progressive banking where the higher line is more angled. This evens out the efficiency of multiple lines to make passing easier. Sometimes track geometry can even be so extreme however, that the best line might be completely different from what the ideal line would normally be. Often the best line through a corner for an off-road motorcycle is wherever the rut has formed. The force generating potential in the rut is so much higher that it could be far from a normal ideal line for a fresh track, but still be faster.

Bristol Motor Speedway’s progressive banking promotes close racing by increasing the efficiency of alternate lines.

Line Theory Tested

Whether it was the track designer’s intention or not, a racetrack will sometimes fool you. The track edges can be a red herring. As we move beyond standard corners, you’ll learn how the key to navigating complex sections is often to find the real limits of the track. To visualize your own perfect racetrack within the real track and optimize around the ideal points, which are not