| (Updated 8/18/24) Determining the ideal acceleration point is a key part of optimizing a racing line, so in this lesson, we’ll go over a simple way to visualize and understand why the ideal acceleration point is always at the apex and why straightaway length doesn’t affect the ideal line through a corner. This doesn't mean that a driver should accelerate at the apex every time however, so make sure to read through to the end of the lesson to learn about the compromises that must sometimes be made. |  1. The Acceleration Point 2. The Ideal Apex 3. The Chicane 4. The Double Apex 5. The Straightaway 6. The 90-Degree Limit |
The Ideal Acceleration Point - From Observation to Insight
This lesson starts a new series covering the fundamental principles of racing line optimization, and I wanted to start off with the acceleration point because, not only is it a central principle, but was also one of my first eureka moments in regards to the physics of racing.
This lesson starts a new series covering the fundamental principles of racing line optimization, and I wanted to start off with the acceleration point because, not only is it a central principle, but was also one of my first eureka moments in regards to the physics of racing.
| When I first started racing in the 2000s, I read everything I could in my pursuit of knowledge and speed. I delved deep into data analysis and vehicle dynamics, as well as going through all the driving technique books I could find. With my background in physics, my initial aim was to piece together the principles that governed the ideal racing line. As is depicted in this illustration from Going Faster, the Skip Barber book on race driving, one common theme in the driving technique books was that a driver should generally begin accelerating prior to the apex. The apex is the point on the inside of a corner that a car passes closest to. While some of the driving books didn't make a direct recommendation regarding the acceleration point, the ones that did usually showed that it was before the apex, but didn't seem to offer clear advice on where exactly this point should be. |  |
I had started sim racing as well, and in my search for more concrete answers, I found several fast lap videos by Greger Huttu of Team Redline, the top sim racer in the world at the time. I’ve held onto these videos and we’ve uploaded them to our YouTube channel so you can view them as well. I’ve linked Greger’s Road America video below, so take a moment to watch the lap while keeping an eye on the speedometer (near the bottom left) so you can see where he accelerates in a corner. It’s important to look at the point of minimum speed, not the throttle, to determine when a vehicle begins accelerating. Due to varying drag forces as well as advanced techniques such as combining throttle with braking, these are not always the same.
In all his laps, the point of minimum speed in a corner where the car begins accelerating was not before the apex as I had read. It was at the apex. To make sure this wasn’t just unique to Greger, I downloaded other Team Redline drivers’ videos as well. While their overall techniques did seem to vary slightly, the acceleration points were all the same. Excited by this revelation, I went searching for lap videos with data overlays for real world drivers as well. This was a good bit harder at the time then it is now, but after finding laps of top drivers in various different types of racing classes, I found one very common trait. They were all accelerating at the apex. While I wouldn’t discover the exact reasons for this until later, based on these observations, I did have one very important realization. The ideal acceleration point was most likely... at the apex.
Line Radius and Speed are Linked when Driving at the Limit
A common problem in driving technique books and elsewhere is that the racing line is often simply drawn as circular in shape or is hand sketched and sometimes includes radius changes that are not even possible if a car is driven at the limit. If however, the racing line is accurately depicted and shows the correct relationship between line radius and speed, a lot can be revealed.
| An important vehicle dynamics principle to understand is that when a vehicle is driven at the limit, its speed and line radius are linked. A higher speed requires a larger radius and this is an exponential relationship so double the speed requires four times the radius. This means that when a vehicle at the limit turns in during corner entry, its line radius will start to progressively decrease, but it must progressively slow down to do so. Then, at the point of minimum speed in the corner, the line reaches its minimum radius before it begins to progressively expand again as the vehicle accelerates. |  |
This process happens every time a vehicle goes through a corner at the limit with the driver influencing the rates of radius change as well as determining where the acceleration point will be, which is where the line radius and speed will reach a minimum. The ideal rates of radius change and therefore shape that the racing line will take is determined by a vehicle’s acceleration vs cornering potential, but we’ll cover that in the next lesson. For now, let’s just look at what the line for a given vehicle would look like if it were driven through a corner with an earlier and earlier acceleration point.
As you can see in the illustration, as the car reaches its minimum speed and begins to accelerate, the line radius shrinks and then expands again as it gains speed. For the earlier acceleration points however, in order to still clear the apex, the car must have a progressively tighter line and therefore lower minimum speed beforehand to do so. If a driver attempted to accelerate before the apex without doing this, their line radius expansion would cause them to miss the apex and start heading off the outside. So for any given vehicle, the earlier the driver wishes to accelerate, the lower their minimum radius and therefore speed must be. The illustration shows some very early acceleration points in order to more easily visualize this trend, but the key takeaway here is that since the apex is the most limiting point on the inside of a corner, optimizing the line around this point allows the largest minimum radius and therefore highest minimum speed possible.
The Straightaway Length Myth
So we've learned that accelerating before the apex causes a vehicle to have a lower speed through a corner, but a side effect of this early acceleration is that it can allow a higher straightaway speed afterwards. Because of this, it is sometimes suggested that if the straightaway is long enough, the distance spent at that higher speed will make up for the extra time spent in the corner, and a car can be faster overall. This is not true, however. The reason we don’t see top drivers like Greger Huttu accelerating early before long straightaways is that the acceleration point is not a balancing act between the corner and the straightaway. Instead, accelerating before the apex simply acts as if the driver is going through a corner that is earlier and tighter than it really is.
So we've learned that accelerating before the apex causes a vehicle to have a lower speed through a corner, but a side effect of this early acceleration is that it can allow a higher straightaway speed afterwards. Because of this, it is sometimes suggested that if the straightaway is long enough, the distance spent at that higher speed will make up for the extra time spent in the corner, and a car can be faster overall. This is not true, however. The reason we don’t see top drivers like Greger Huttu accelerating early before long straightaways is that the acceleration point is not a balancing act between the corner and the straightaway. Instead, accelerating before the apex simply acts as if the driver is going through a corner that is earlier and tighter than it really is.
In the image, you can see how the inside of the track has been shifted earlier and outward so that it meets the earliest acceleration point. This is effectively what happens with early acceleration because this line would be optimal if the corner did have this earlier, tighter configuration. With the real configuration however, this early acceleration point means the driver has made their line tighter and slower than necessary by essentially optimizing for an early false apex, an apex that is not really there that they are now going around in addition to the actual apex. The reason this can allow the speed achieved on the following straightaway to be higher is because the entire corner geometry from the braking point onward has effectively been shifted earlier. Length has essentially been removed from the previous straightaway and added on to the end of the corner, which gives the vehicle a greater distance to accelerate before it reaches any given point on the following straightaway. This is not an even trade however, because we've seen how this also progressively decreases the minimum line radius so it will always take more time for the vehicle to get back up to any given speed from the point it begins decelerating.
The key principle to understand here is that although a vehicle that accelerates before the apex can achieve a higher speed at a given position on the following straightaway, at that same point in time, the same vehicle driving on an ideal line would already be at an even higher speed while also being further down the track. Starting at 7:50 in the video linked below, you can see a demonstration of this principle where two different lines from the same car have been overlaid. You can see how the early acceleration car, which is called Super Late Apex in the video, reaches 67 mph as it crosses a given position at corner exit, while the ideal apex car, called Baseline, only achieves 64 mph at that position. The key however is that, at the same point in time that the early acceleration car reaches 67 mph, the ideal apex car has also already achieved 67 mph, but is 46 feet ahead. This actually represents a best-case scenario for the early acceleration car, as it was at least able to achieve the same speed at the same time as the ideal apex car, but since it traveled a longer distance around its false apex, it is 46 feet behind. Since both cars are identical and would be accelerating from the same speed of 67 mph at that point, the ideal apex car would maintain this 46 foot advantage down the straightaway, regardless of its length.
The key principle to understand here is that although a vehicle that accelerates before the apex can achieve a higher speed at a given position on the following straightaway, at that same point in time, the same vehicle driving on an ideal line would already be at an even higher speed while also being further down the track. Starting at 7:50 in the video linked below, you can see a demonstration of this principle where two different lines from the same car have been overlaid. You can see how the early acceleration car, which is called Super Late Apex in the video, reaches 67 mph as it crosses a given position at corner exit, while the ideal apex car, called Baseline, only achieves 64 mph at that position. The key however is that, at the same point in time that the early acceleration car reaches 67 mph, the ideal apex car has also already achieved 67 mph, but is 46 feet ahead. This actually represents a best-case scenario for the early acceleration car, as it was at least able to achieve the same speed at the same time as the ideal apex car, but since it traveled a longer distance around its false apex, it is 46 feet behind. Since both cars are identical and would be accelerating from the same speed of 67 mph at that point, the ideal apex car would maintain this 46 foot advantage down the straightaway, regardless of its length.
So although we've learned how accelerating before the apex can increase straightaway speed, but at the cost of overall lap time, this technique does have it uses sometimes, such as when a driver is doing a qualifying run. They can accelerate early in the last corner of a lap so that they cross the start/finish with as much speed as possible to reduce the time on the subsequent lap. They will lose time on the previous lap, but gain some on the qualifying lap when it really counts.
Before moving on, I do want to mention that once the distance between two corners is short enough, it does have an effect on cornering technique, as they must now be optimized together as a chicane or double apex. While the ideal acceleration points would still be at the apexes, the distance between the corners helps determine how early or late those apexes are. We’ll cover this in future lessons, but it’s important to understand that unless the corners are close enough for this to happen, the ideal apex and line will not change based on straightaway length. In the next lesson, we’ll also look at another way to understand why the ideal acceleration point should always be at an apex.
From Line Theory to Racing Reality
As we wrap up this lesson, I want to emphasize that while learning the theory behind racing line optimization can be an important first step as it is useful for analysis and understanding the ideal technique, a driver isn’t supposed to go out on track and apply these principles directly. Instead, we recommend a driver take a progressive approach where they gradually internalize these principles by learning to feel the physics at work out on track and that is what we teach in our Academy program. Part of this process is learning the relative time penalties for different types of mistakes. In this lesson for instance, it is important to understand that not accelerating until after the apex will generally have a greater time penalty than accelerating before the apex. Sometimes much greater, depending on the car and corner and this is most likely where the traditional advice to accelerate before the apex originated. While top talents like Greger Huttu show us what’s possible, attempting to mimic his technique without having the underlying skills can often result in worse times than starting with a more conservative approach. Then as skills improve, a driver can push closer and closer to the ideal.
It’s also important to understand that while a driver can understand and visualize the ideal line, they can never truly achieve it. Even the very best drivers will have constant imperfections in their line and every little imperfection will then change the ideal line for the rest of the corner. It is a constantly moving target and even though the ideal acceleration point is right at the apex, a driver can’t simply begin accelerating as they pass it because their line up to that point is not going to be ideal. Imperfections in their entry might cause their current best acceleration point to end up being slightly before, slightly past or even slightly outside the apex. While this wouldn’t be ideal if the entry was done perfectly, it was as close to the ideal as the driver was able to achieve that time.
Before moving on, I do want to mention that once the distance between two corners is short enough, it does have an effect on cornering technique, as they must now be optimized together as a chicane or double apex. While the ideal acceleration points would still be at the apexes, the distance between the corners helps determine how early or late those apexes are. We’ll cover this in future lessons, but it’s important to understand that unless the corners are close enough for this to happen, the ideal apex and line will not change based on straightaway length. In the next lesson, we’ll also look at another way to understand why the ideal acceleration point should always be at an apex.
From Line Theory to Racing Reality
As we wrap up this lesson, I want to emphasize that while learning the theory behind racing line optimization can be an important first step as it is useful for analysis and understanding the ideal technique, a driver isn’t supposed to go out on track and apply these principles directly. Instead, we recommend a driver take a progressive approach where they gradually internalize these principles by learning to feel the physics at work out on track and that is what we teach in our Academy program. Part of this process is learning the relative time penalties for different types of mistakes. In this lesson for instance, it is important to understand that not accelerating until after the apex will generally have a greater time penalty than accelerating before the apex. Sometimes much greater, depending on the car and corner and this is most likely where the traditional advice to accelerate before the apex originated. While top talents like Greger Huttu show us what’s possible, attempting to mimic his technique without having the underlying skills can often result in worse times than starting with a more conservative approach. Then as skills improve, a driver can push closer and closer to the ideal.
It’s also important to understand that while a driver can understand and visualize the ideal line, they can never truly achieve it. Even the very best drivers will have constant imperfections in their line and every little imperfection will then change the ideal line for the rest of the corner. It is a constantly moving target and even though the ideal acceleration point is right at the apex, a driver can’t simply begin accelerating as they pass it because their line up to that point is not going to be ideal. Imperfections in their entry might cause their current best acceleration point to end up being slightly before, slightly past or even slightly outside the apex. While this wouldn’t be ideal if the entry was done perfectly, it was as close to the ideal as the driver was able to achieve that time.
| I hope you enjoyed this first installment in our new Racing Line Fundamentals lesson series and if you have any questions, please use the comments section below. Up next, we’ll look at the factors that determine The Ideal Apex and line through a corner. If you are interested in a complete guide to the physics of racing, we also offer The Science of Speed book series, available through our bookstore or at popular retailers such as Amazon. We’ve also just released a new t-shirt that we are selling at cost so please check that out as well. Adam Brouillard |  1. The Acceleration Point 2. The Ideal Apex 3. The Chicane 4. The Double Apex 5. The Straightaway 6. The 90-Degree Limit |
