Introduction
My name is Adam Brouillard. I am head instructor for Paradigm Shift Driver
Development and author of the Science of Speed Series books. In this video, we are going to be looking
at the physics of the racing line. We’ll first go over some different types
of cornering techniques and then identify the four main elements of a perfect corner. Next we’ll learn to use these elements to
work up a corner and identify mistakes. Finally we’ll end by looking at a training
exercise designed to improve your overall driving ability. We are going to be analyzing different techniques
so first we need to establish a good testbed to make comparisons. The Charlotte Legends track in iRacing is
great for our purposes for a few reasons. It consists of just two, flat nearly identical
180 degree corners and they are separated into one sector each. This allows us to easily isolate just a single
corner to get some feedback as to how our different techniques affect the exact time
it takes to complete a standard corner. Plus the corners take nearly 10 seconds to
get through, which is very long for a standard corner. A mistake that might cost you a 10th of a
second in an average length corner will cost you significantly more here so variations
in performance will be easier to see. The primary vehicle we are going to be using
is the Global Mazda Mx-5, which is a relatively low-powered car. Both the car and track are also part of the
base iRacing content so even with just a trial subscription I encourage you to follow along
with these exercises. We are going to be using the default weather
and car setup for all laps. Let’s start by setting a baseline corner
to which we can make comparisons. The fastest lap for this combination that
I happen to have a replay of is a 17.527. The second corner’s sector time is 8.799
and this is the corner we will focus on. Unfortunately, I didn’t record any telemetry
for that lap so I’ve also done a quick session to grab some and the best I did in our testbed corner was
an 8.831 which is about 3 one hundredths of a second slower. This will make a good baseline from which
we can make comparisons and it also allows us an opportunity to identify some mistakes
later on in the video. Beyond just looking at the time, let’s note
a few things that happen in the corner. The minimum speed reached is about 42 mph
and this happens near the inside of the track at the apex right as I go to full power. I also reach 64 mph as I cross the start/finish
line. I did this baseline corner and I will be doing
all comparison corners on the out lap so that the tires are always the same temperature
and condition as we enter the corner. This way the only variations that will affect
our time is driving technique. The geometric line
For our first comparison, let’s take a look at the classic geometric line. The geometric line is the widest arc we can
take through a corner and is driven at near constant speed. It’s often stated that this is the fastest
way through just a single corner when we aren’t worried about maximizing exit speed for a
following straightaway. Let’s put this idea to the test in our isolated
corner and see what we come up with. W hile a perfectly geometric line is not actually
possible because it would require instantaneous changes of direction I think I came pretty
close. I was able to increase the minimum speed through
the corner by 4 mph to a slowest of 46 at the apex. I also started the corner about 1 mph faster
than our baseline and the speed at the end of the corner as we cross the finish line
is the same as the baseline at 64 mph. So we lost less speed in the corner, we ended
at the same speed and started slightly faster. So It seems that this might really be the
fastest way through an isolated corner, but if we look at our sector time, it took 9 seconds
to complete the corner which is almost 2 tenths of a second slower than our baseline. Let’s load up the telemetry so we can take
a closer look at this comparison. We will start both our baseline and geometric
line at the beginning of the corner at the exact same point before braking and turn-in
and then play the telemetry in slow motion so we can see what happens. While the lines look pretty similar you can
see that the geometric line is not only slightly longer than the baseline, but more importantly,
in order to maintain a higher minimum speed at the apex, the geometric line is slower
primarily during the entry, but also during the exit of the corner. Shortly, we’ll come back to this and look
at it from a physics perspective to understand what it is about the geometric line that makes
it slower, but right now we want to point out an important lesson from this. To evaluate the usefulness of a racing line,
you have to look beyond just the speed achieved at any certain places on the track. While the individual speeds in our geometric
line seemed faster, the time through the corner was actually slower, and time is what matters
on a racetrack. The Late Apex
For our next comparison, we’re going to examine the late apex. While an ideal apex is almost always later
in a corner than the geometric apex, what we are actually referring to here is the technique
of tightening up the radius at the entrance of a corner so that you can accelerate earlier. The key difference from our baseline is that
the acceleration point is before your line reaches the inside of the track. The strategy being that the time lost during
corner entry is more than made up for by the extra speed that is carried down a long straightaway. So as not to confuse this approach with discussion
of simply adjusting your acceleration point to a later apex along the inside of the track,
we often refer to this method as the super late apex. Looking at the super late apex line, we can
see that I’ve tightened up the radius at the entrance to the corner so that we can
accelerate earlier. I did this while still maintaining a minimum
speed of 41, which is only 1 mph slower than our baseline. But this has allowed me to increase the speed
as we cross the start/finish line by 3 mph up to 67. Looking at the line from overhead we can see
how the profile matches the illustrations depicting this technique. Our time through the corner is 9.2 seconds,
which is slower than our baseline, but this was to be expected as we compromised the entrance. The strategy however, is that if we have a
long enough straight afterwards that 3 mph advantage will make up the difference and
then some. So let’s look at the telemetry to see how
long the straight would have to be for this strategy to be viable. As before, we’ll start the two cars at the
same point and have them go through the corner so we can see what happens. You can see that while the super late apex
car is able to achieve full throttle at an early position in the corner, both cars achieve
full throttle at nearly the same point in time. So while the super late apex car has reached
67 and is going 3 mph faster at the same position on track that they cross the start/finish. At the same point in time, the baseline car
already has a several car length advantage and has also reached the same speed of 67
mph. So regardless of the length of the straight,
a super late apex line will never make up the difference. The baseline method will always be faster. We’ll look at the physics behind this shortly,
but as in the geometric line, the principle that we’re learning here is that your speed
at any certain position in a corner is not important, only the amount of time it takes
to achieve that speed. Again, time is what matters on a racetrack. The perfect corner
Let’s take a step back now so we can look at our corner from a physics perspective. We’ll see if we can identify the problems
with our two alternate lines and what exactly it means to drive a perfect corner. Every standard corner can be broken down into
three basic obstacles. The corner entry edge, the corner exit edge,
and the most limiting point along the inside of the track, which we will simply call the
apex. To navigate these obstacles in the minimum
time possible, a driver must maximize the force the vehicle can generate decelerating
it in the same direction as the corner entry edge and then accelerating it in the same
direction as the corner exit edge. As the angle of a corner changes, the ideal
directions of force will simply follow the outside track edges
So at the apex of our test bed corner, our goal is not to accelerate the car forward
as quickly as possible. From the very instant we cross the apex all
the way to the track edge, our actual goal is to best use all four tires to constantly
maximize the acceleration of the car’s center of gravity in the same direction as the corner
exit edge. Likewise, from the braking point all the way
to the apex we should maximize our tire forces decelerating the car in a direction which
parallels the entry edge. The greater the total net force produced in
the ideal directions, the lower the time will be through the corner. A driver has more to go on that just the basic
physics alone however. If you are successful in maximizing force
in the ideal directions, four primary things will happen. We call these the four elements of a perfect
corner. You will be able to use these to work up a
corner and identify your mistakes. These four elements apply to all corners,
but advanced combinations such as chicanes and double apexes will require some additional
elements to optimize correctly. So let’s go through the four elements one
by one in increasing order of how important they are to achieving a good lap time. #4 The corner entry spiral
Starting at number 4 we have the corner entry spiral. During corner entry, your line should have
a smooth, spiral shape from the edge of the track to the apex. The vehicle’s path will steadily become
tighter and it will lose speed from the braking point all the way to your acceleration point. In comparison, our geometric line is much
more circular shaped and so the speed and steering position remain mostly unchanging
well before the apex. If we look at the speed traces, you can see
the baseline with a distinct slope whereas the geometric line’s deceleration rate is
inconsistent. Remember, both of these were driven at the
limit for the entire corner, the only difference was the direction of the tire forces acting
on the vehicle. To achieve this spiral shaped entry will require
trailbraking for the vast majority of cars, but this not always the case. The goal is to maximize the tire force pushing
the vehicles center of gravity in the ideal direction so a driver must work out how each
car makes its best grip. In a Rally car for example, a typical trailbraking
maneuver generates poor grip at certain angles and so offroad driving will typically require
other techniques such as hand brake turns or Scandinavian flicks to spiral to the apex
and decelerate efficiently. From a laptime perspective however, a spiral
shaped corner entry is the least important of the four elements. While it is the fastest way if done properly,
trail braking can be very difficult in certain situations whereas arriving at the apex with
the correct momentum is critical for a good laptime. A driver that takes a more constant speed
, but easier to drive entry will usually only lose a 10th of second at most per corner if
their corner exit is ideal. When a driver is looking for that last little
bit of time however, corner entry is usually where they will find it. #3 Maximum Acceleration
Arriving at the apex with the correct momentum is critical because only the correct amount
will allow us to maximize acceleration. Too much or too little momentum will compromise
our corner exit. Let’s take a look at our geometric line
again. At the apex, we have a speed of 46 mph, but
at that very moment the only thing that 46 mph is doing is sending us directly toward
the wall. Our goal however is to accelerate as quickly
as possible in the same direction as the exit edge. In this case, we actually have too much momentum
and you can see this evidenced as not being able to apply full throttle until much later
in the corner. This hurts our exit because now we must use
some of the tire force that could be used to accelerate us in the ideal direction to
counteract our excessive momentum. If instead, we had too little momentum at
the apex, although we would be able to achieve full throttle right away, our corner exit
would still be slower than ideal. We wouldn’t need to use the entire track
during corner exit, which means the total tire force generated to accelerate us in the
ideal direction was compromised. If we draw arrows showing the direction the
tires are pushing the car throughout the geometric line you’ll notice how they point inward. Much of the tire force generated during the
corner entry is then simply cancelled out during the corner exit. This is wasted force and is the reason the
geometric line is slower. Comparatively, in an ideal line as much tire
force as possible is used to decelerate and then accelerate the car. Maximum acceleration does not always mean
full throttle however. Let’s take a different car through the corner,
the lotus 49, which has a similar amount of grip as the MX-5, but significantly more power. This time, we aren’t able to reach full
throttle at the apex without excessive wheelspin. As a general rule, to maximize acceleration,
if you can’t achieve full throttle at the apex you shouldn’t be able too until you
are going nearly straight. Instead you will apply progressive power as
you steadily reduce steering. It’s important to realize that progressive
power doesn’t necessarily mean progressive throttle though, it depends on the shape of
the car’s powerband. In the lotus, power climbs quickly with rpm
so even though it looks like we are very near full throttle for the entire exit, the power
going to the wheels is actually increasing progressively. Whether to apply full or progressive power
not only depends on the car, but also the corner. For example, the lotus in a faster corner
would be in a higher gear and so wouldn’t be able to accelerate as quickly. So Let’s now take the lotus through our
same corner in 3rd gear instead of 2nd so we have the exact same level of grip, but
less acceleration potential and we’ll see how this affects our apex and exit. Just as in the mx-5, we are now able to reach
full throttle right at the apex without excessive wheelspin. But in 3rd gear, we needed more momentum to
optimize the exit. Our minimum apex speed is now 44 up from the
previous 43, but the higher gear reduced our acceleration potential and so our time through
the corner is slower by about 2 tenths So in all corners, every different car will
have a certain amount of momentum, a perfect apex, that is required to maximize the force
pushing it in the ideal direction. For a given level of grip, more power will
need a slower apex and less power will need a faster apex, or put another way, if you
have you less power, you need more momentum to maximize acceleration in the ideal direction. This is why lower powered cars are often referred
to as momentum cars. #2 Using the whole track
Our second most important element of a perfect corner is that we must use the whole track. Often, one of the first things that a novice
learns, there is a bit more to this than going from the outside, to the inside and then back
to the outside of the track. Let’s look again at our super late apex
line. The biggest problem with this line and why
it is almost 4 10ths slower than our baseline is that we did not even come close to using
the whole track. While it looks like we go from the outside
to the inside and then all the way back out, the point we cross the inside of the track
is not really an apex. By accelerating much earlier, we have actually
created what we call a false apex out in the middle of the track. We are essentially optimizing the corner around
an obstacle that is not really there. This has effectively made the track much narrower
than it really is. This is why the acceleration point should
ideally be at the most limiting point along the inside of the track. If it is not, then you aren’t using as much
track as you could be. This does not mean that a driver should simply
wait to apply throttle as they pass the inside of the track however. In the baseline lap you can see that where
I begin accelerating is actually slightly before where it could be if I had used every
last bit of the track during corner entry. This indicated to me that my approach wasn’t
quite optimal, but if I had waited any longer to apply throttle, I would have made the laptime
penalty for the error even worse. This is because, no matter where a driver
is in a corner, they should begin maximum acceleration the very instant that it will
take them to the edge of track at corner exit. If I had delayed acceleration any longer,
I would have used even less of the track than I already was. Driving a track is a dynamic process. A good driver will constantly be creating
a new optimal line based on their current situation. I like to say, never give up on a corner. No matter how bad you feel you have messed
up a corner so far, you can always optimize the rest from that moment on. For example, if I had not driven the super
late apex line on purpose and I instead had just severely missed my braking point, the
super late apex line would no longer be a bad strategy, it would then be correct. The instant I realized that I went too deep,
I would need to create a new optimal line for the false apex I had just accidentally
created. Optimizing a corner is all about constantly
recognizing and correcting mistakes. Ideally catching them quickly before they
become big mistakes. If you ever think you just drove a mistake
free corner, it just means you haven’t developed the sensitivity yet to recognize the 100 smaller
mistakes you actually just made. 1 Find the Limit (The Universal Cue)
So in the baseline corner, we’ve seen that I started accelerating a bit early so that
I could at least optimize the rest of the corner by using the whole track during my
exit. But if we now look at my corner exit, I didn’t
quite use as much of the track as I had done in my other comparison laps. So why didn’t I go all the way out to the
wall as I was planning to? The reason is because of the most important
element of a perfect corner. Driving all the way out to the wall would
have dropped me below the limit and so I wouldn’t be maximizing the total force accelerating
me in the ideal direction. Which after all, is the ultimate goal of all
of this. Driving at the limit is not just about using
your tires to their absolute maximum though; it’s also about directing those tire forces
in the right direction, at the right time Let’s look again at our geometric line. My goal was to drive the corner at the maximum
limit of the tires, but I was intentionally directing all of that force sideways in relation
to the car for the whole corner. During our faster baseline corner however,
my goal was not just to drive at limit of the tires. I needed to be aware of my angle, speed and
position at all times because I needed to direct those tire forces in relation to the
track, not the car. Developing a sensitivity to how these forces
affect the car’s overall movement through a corner can allow a precision in your driving
that no other car control cue can match. If you learn to develop this cue properly,
it can absolutely transform your driving. While some drivers just do this naturally,
in others it must be trained. We call this sensitivity to the overall movement
of a vehicle the universal cue. The Universal cue is different from most other
car control cues in that your primary focus is not on things within the car such as listening
to the tires or the feeling you get through the steering wheel. Instead, it is about paying attention to how
your driver inputs affect the car’s overall movement through a corner. You aren’t focusing on the car to drive
at the limit, you’re focusing on the track. During my baseline corner for example, as
I approached the apex, my focus was simply on moving the car across the finish line as
quickly as possible. This is what guided my driver inputs and let
me know to go to full throttle early and not drive all the way out to the wall. Likewise, In the lotus, although my goal and
focus were the same, the driver inputs turned out quite different. Paying attention to the Universal Cue showed
me how much throttle and steering to give at every instant to maximize my movement toward
the finish line. Conversely, if I’m training in a rally sim,
maximizing movement down the track typically requires very high slip angles and large amounts
of wheelspin that would be very slow on tarmac. So even though these cars might all accomplish
it in a different way, a driver must work out how to maximize the force they can generate
in each one. While all the other car control cues are helpful
and can get you close, only learning to pay attention to the overall
movement of a vehicle through a corner will give you the final answer to where that last
little bit of time hides. This is because the universal cue is simply
the direct representation of the physics used to optimize a racing line. So while the Universal Cue guides your inputs,
you can then use the other elements to identify how to modify your approach to bring you ever
closer to the perfect corner. Of course, no one will never truly get there
because while we can understand in our minds what it takes to drive the perfect corner,
performance will always be limited by how well someone can control the car, and car
control ability has no upper limit. Driver Training
This brings us to driver training. While learning the four elements is the first
step, training them properly is how you will take your driving to the next level. There are dozens of different training exercises
we use to work on a driver’s different skills, but one we find the most useful is directly
related to what we’ve been discussing. In this exercise, what you will do is find
a way to isolate and time a single corner just as we have done for this video. Practically any sim, car, and track can be
used, but the MX-5 at charlotte legends is a great and easy to setup training combo to
start with. You will then turn off any live sector time
display and run the lap multiple times. Each time you complete the corner you will
predict whether that was your best time so far. If you believe it was you will stop and check
whether or not you are correct. This will force you to constantly self-analyze
your performance as you drive. Rather than seeing a new low sector time flash
up on screen and then going back to try to figure out what you did differently that time,
you will instead be learning to predict what elements of your driving create that low time. It’s a subtle, but very powerful difference. What you are actually training here is your
sensitivity to the Universal cue. Being able to accurately predict that you
just did your lowest time means you are beginning to recognize when you’ve best maximized
your tire forces moving you in the ideal directions. As we’ve learned, how well these forces
have been maximized and directed is the only thing that truly determines your time. This is not only about sensing when you did
your best time however, it’s about being able to identify mistakes and how much they
cost you. Highly trained drivers can often predict their
sector times to within a 20th of a second. It’s very important for this exercise that
the only variable be the driver. Any change in sector time should be caused
by something the driver did, not by a change in weather, car, or tire condition. Being able to set the exact same conditions
every time is why we highly encourage even real world racers to take advantage of simulators
to supplement their training. Understand however, that in a real car, the
universal cue is a combination of vision and g-forces, as they both provide a driver information
about a car’s movement. In a simulator, we lose those g-forces that
help us feel the amount of force, but our vision is the way that we track our position,
angle, and the direction that force is pushing us. While the g-force cue is helpful, the visual
cues are the primary ones that guide us in how to drive a corner. Since a simulator can accurately recreate
these visual cues, training on one provides a direct benefit in real world driving skill
as well. As this training exercise will develop your
ability to identify how well you are achieving all four elements of a perfect corner, you
should see an across the board improvement in your driving. It’s not uncommon for a driver to go back
to previous car and track combos after doing this exercise regularly for only a few weeks
and beat their own personal best times within the first few laps. I hope you found this video educational and
if you have any questions or comments you can contact me at paradigmshiftracing.com.
Fascinating video, but by god, his voice puts me to sleep. Did make it through it, however.
That.... Was surprisingly educational. When I heard the soothing voice and saw the 30 minutes duration I never thought I'd end up watching the whole thing.
Will be watching later.
Slow in, fast out > Fast in, dead out
I saw "The Racing Line" and came here expecting Randy Pobst, still a great video though.
Does anyone know a good forum or subreddit devoted to this type of stuff? The last book in this series is about optimizing complex track sections and has a few good examples, but I would love it if there were a common place to post pics of track sections and talk about how to optimize them in different types of cars using the principles discussed here and in the books.
Scariest part for me is setting up the entry and trying not to spin out on the exit. I have had my WRX blow traction powering out of a turn, scary as hell since I am not used to all four tires spinning.
Awesome video! Will you be putting more up on your youtube channel?