Wait I think I understand. The baseline is just an arbitrary line that feels about right, the specifics don't really matter because it's just a starting point. It could be any line really. But from that point you then adjust where you want the apex to be and where you want the braking and acceleration areas to be little by little until the line is optimal. Do I have that right?

The "4 elements" of the video explain the baseline, but you can read more about the rules for a standard corner here. www.paradigmshiftracing.com/racing-basics/the-rules-of-the-racing-line#/ We also have a new Racing Line Fundamentals lesson series that will cover this more in depth www.paradigmshiftracing.com/racing-basics/heres-a-simple-way-to-visualize-why-the-ideal-acceleration-point-is-always-at-the-apex-of-a-corner-and-why-straightaway-length-doesnt-matter-racing-line-fundamentals-1#/

At the point in time the super late apex car crosses the line, both it and the baseline car are going 67 mph, but the baseline car is 46 feet ahead. From that point on, they would both accelerate at the same rate (from 67 mph) and so the baseline car would maintain that 46 foot advantage. Does that help explain it better?

@ParadigmShiftDriverDevelopment well, firstly, even if the time gap were to remain the same down the straight, that 46 feet will change as they both accelerate. And, there will be a fixed distance to the next corner that they both need to drive to. 2 cars, each driving down a straight, will NOT do so in the same amount of time if they each start at different velocities. The whole point about leaving a corner with a higher speed is to shorten the time needed to reach the next corner. If that involves losing time in the corner itself, then it becomes a trade off ... time lost in ghe corner vs time gained afterwards. If there is no straight after the corner, then overall you've lost time. If there is a straight, then ghe question is - how long is it, and will you make up the time lost, and more. And, of course, this would also have to take on board the respective power, gearing and drag etc of the two cars involved. I rallied, not raced, and it was never about one corner on its own, but where each corner sat in relation to what was before & after it.

@@garyrowe58 It is the time gap that will change as the two different cars continue down the straight. The 46 foot difference will remain the same. Consider two equal cars that take off from zero, but one is 46 feet in front of the other. They will always remain 46 feet apart, but the time difference will shrink as they accelerate. 46 feet takes longer to traverse at 10 mph than at 100 mph. In the video example, the baseline car will always reach the next corner 46 feet in front of the super late apex car no matter how long the straight is. How much time difference this makes will depend on the length of the straight. We have an upcoming article that delves into this topic more that might help you understand it better so keep an eye out.

​@ParadigmShiftDriverDevelopment while the example video is correct, the car chosen and the extremely large radius is the reason this is true. The smaller the radius and or the more powerful the car the more advantageous a late apex becomes assuming a long straight follows. I'm sure you already know all this but it seems a bit misleading for those that may take this as a general rule.

@@H8MadXeroLater in the video we show the ideal line for the Lotus 49 which is a more powerful car. A later apex than the MX-5 is ideal, but not a "super late apex" with acceleration prior to reaching the inside of the track and the straightaway length doesn't factor in.

Thanks for the kind words

This is something that will always develop and is primarily related to how well you can see the exact placement of your car on track. Vision provides the upper limit to driving skill. As your vision improves, your car control skill will rise to meet it. Adam likes to say, "The better you see, the better you drive." Check out our Academy lessons for exercises teaching you how to develop this.

Thanks, glad you liked it!

It looks like he just had trouble getting it into gear the first time and was trying again. You wouldn't need to double clutch the NSX as it has a syncro transmission.

This video is meant to be a general overview. For more in-depth explanations, please check out the books, training program, and free articles available through our website at www.paradigmshiftracing.com.

Thankse

Thanks, glad you liked it.

El tipo es el más grande de la historia

The Universal Cue is a driver’s sense of where the car is and how it is moving through the corner. It could be visualized in a similar way to how you would see an RC car being driven on a miniature racetrack as you tried to drive it through the corner as quickly as possible. This is an external car cue, as opposed to internal car cues such as steering forces or tire noises.

A driver is always making small corrections when driving at the limit. Earlier during entry, these corrections would primarily be with just steering and braking. As you get closer to the apex though and less braking is needed, you will sometimes see throttle as part of those corrections. This is because even with no brakes applied, a car will slow down (sometimes too much) and this needs to be counteracted with throttle. You don’t want to actually be accelerating before the apex though and a good way to check is to look at your speeds in relation to the apex. Another reason you will see throttle combined with braking sometimes is that it allows a driver to dynamically alter brake bias and therefore balance during entry. Michael Schumacher was one of the first to popularize this technique and depending on the car and setup, it might be needed. This is a more advanced technique though, and is not the primary reason I would be doing it in this car. Hope this answered your question, Adam.

I was curious, if we maximize forces in the ideal direction on exit, wouldn't that also be a euler spiral in reverse?

​@@gregoryj99 From my understanding yes, but only if you have a car powerful enough to reach the grip limit (from the apex). Otherwise keeping higher speed from the apex of the corner on a rounder trajectory is better

Man I was going to write a comment but you took the words right out of my mouth! This truly is an invaluable video!

I understand what you are saying, but I try to keep my explanations as simple as possible as I know it can already be a bit overwhelming. I'm not trying to explain horsepower vs torque here, I'm primarily trying to explain that you don't necessarily want a steady increase in throttle. For anyone reading this who is curious about power and torque here is a good video kzbin.info/www/bejne/i3q0m6ykbpqWY9E

I'm not sure I completely follow your example, but have you read this article. www.paradigmshiftracing.com/racing-basics/the-corner-exit-drag-race-racing-line-physics-explained#/ It might answer your question. I talk about AWD in this as well as in the later books more if you've only read the first one. Let me know if that article didn't answer your question and we can dig into it more.

@@ParadigmShiftDriverDevelopment thanks for a very quick response! That article is awesome, thank you. I wish I read it before the book. Do you plan to republish the book with corrections, and/or maybe redo this video? I wish I had a "one stop" place I could refer my friend to.

Also curious if you can point me at some explanation why the right shape of the entry is a Euler Spiral. I have a major in math and physics, and I studied control theory, but Euler Spiral isn't obviously an optimal line to me. Something like it - possibly, but curvature as a linear function of distance feel suspicious if the speed changes.

@@TimurIskhodzhanov Maybe at some point although I don't feel any of it is wrong, I just think of different ways of explaining things. Some might work better for some than others. I'm glad that one helped you.

@@TimurIskhodzhanov I talked about in the books how I primarily use the Euler spiral to illustrate the concept that the ideal entry line is one of continually reducing radius. You would need a lap simulator programed to find the exact radius change rate for a given car and corner if you wanted something exact. This wouldn't have much use though as a driver shouldn't be concentrating on trying to follow a preset line regardless. They are concentrating on other cues, but we've found that the entry line for a top driver in a typical car matches the Euler spiral so closely that it's also useful when charting out a line on a track map.

That may or may not be ideal if this corner was done perfectly, but inputs are not preplanned. A driver gets to the point they are paying attention to the vehicle movement and constantly updating their line and inputs to give the best possible result based on their current situation.

@@ParadigmShiftDriverDevelopment I watch all your reference laps of Lime Rock. It seems that the controls are similiar. Their horse powers are much different, so I think the controls should be more different. Can you explain more?

@@r88522726 The biggest differences you are going to see is on slower corners where a higher horsepower car will be wheelspin limited and therefore oversteer limited on exit and need a progressive throttle application whereas a lower power car will be going to full throttle at the apex.

Thanks, you can find some discussion of the double apex in our Lime Rock Park video.

I'm not braking past the apex, the Lotus double apexes a bit here in the middle as it needs a fairly late final apex.

@@ParadigmShiftDriverDevelopment ok, that was my second guess, but I wanted to be sure because the transition on braking is so smooth. It s been a while since I thought that 180 degrees turns are in fact double apex because of the 90 degree limit and the apex angle needed. Would you say they are necessarily decreasing radius?

@@loicludwig429 The ideal radius change would depend on the car and exact shape of the apex area, but a high angle rounded apex corner will typically be very close to constant radius. Plus, even the best drivers have slight line variations that will need to be compensated for during the double apex portion. The double apex portion of a corner like this is very much about car control and maximizing force, not necessarily trying to follow a perfect radius change. I wouldn't call out a driver for a definite mistake here unless they are accelerating before they reach the inside of the track or braking after they have left it.

@@ParadigmShiftDriverDevelopment i get it. Thanks again Adam!

Also the MX5 doesn't have enough power to force its tires above the limit when accelerating out of a long, wide corner like this one, so the finding should vary greatly when looking at really high power cars like F1 cars or Indycars.

I'm not sure I follow you. The comparison starts with both cars in the same place and time in the corner.

@@HexlGaming Yes, a higher acceleration car would have an even larger differential loss between the geometric and baseline. For the super late apex, the loss is simply based on how far from the ideal apex the false apex is.

@@ParadigmShiftDriverDevelopment I was referring to data like 12:33. the way the graph is set up there is off, making it much harder to compare, because at the same timestamps the cars are at different stages of the track, even just in the acceleration part of the graph. So it’s not „Zeroed“ if you will

@@HexlGaming Yes, sorry if that is confusing. You are right, we didn't start them from the same point for that part of the video. They were just zeroed from the lap start. That part was just showing the shape of the line to look for. If you want to see a direct overlay go to 4:56 for the geometric comparison and 7:54 for the super late apex comparison.

Hi Björn, this is Adam. Sorry if that part was confusing. I go into this in much more detail in the books. I do use a 180 degree corner as an example because the ideal directions are both the same. For a corner like turn 6 at Laguna, however you are essentially cutting out the middle and spreading apart what you do in the 180 degree corner. The key point I'm trying to get across is that you do want to maximize the total force in the ideal directions throughout the corner, not entry and exit separately. This will primarily be set by what you need to do to maximize corner exit. If you completely stopped during corner entry, although you might be maximizing deceleration on entry, the ability to produce acceleration in the ideal direction during exit would be severely reduced. Maximized acceleration during exit is a combination of sideways and forward acceleration that the car can create. This will vary by car and effectively sets what you ideal apex is. A higher acceleration car can use a later, slower apex and vice versa. This part will effectively set your apex. Then during corner entry you want to get to this ideal apex while also maximizing the car's deceleration in the entry ideal direction. This is where you get the Euler spiral shaped entry. You do technically "waste" force by needing to drive across the track, but this is necessary. The idea is to minimize this force needed while maximizing the forces pushing you in the ideal directions. Hope this made more sense. Let me know if it doesn't. You might also want to give this article a read. www.paradigmshiftracing.com/racing-basics/the-corner-exit-drag-race-racing-line-physics-explained#/

​@@ParadigmShiftDriverDevelopment Hi! Thanks for the very quick reply! Maybe I'm misunderstanding something here, so let me clarify what I mean and ask some questions. "The key point I'm trying to get across is that you do want to maximize the total force in the ideal directions throughout the corner, not entry and exit separately." <= This I completely agree with. They key question is what the ideal direction is at all points during the corner to minimize the time through it. "Then during corner entry you want to get to this ideal apex while also maximizing the car's deceleration in the entry ideal direction." <= This I don't agree with, or I'm understanding you wrong. Take a 90 degree corner, for example. Let's remove the straight braking part since that is basically just preparation for the corner and start the scenario at the turn in point. From this point and forward, you want to minimize the time it takes to go to the corner exit. This is done by maximizing force in the corner exit edge direction, where more early is better than more later since that gives a high mean velocity in that direction. The shedding of speed in the corner entry edge direction is a restraint of this optimization problem to not go off track, where shedding it early is better than late for the same reason as before (we can brake later giving higher mean velocity). But, since the goal is maximizing force in the exit direction, braking is secondary. If you look at the traction bubble of the car on your link, the forward max force is lower than any other direction. That means we have spare grip at the end of the corner where we are already at full throttle, which we then can use for braking, releasing some grip at the beginning of the turn to be used for acceleration in the exit edge direction. So, we DON'T want to maximize force in the entry edge direction before the apex because we have spare grip at the end, and at the start is where we have the biggest possibility to accelerate in the exit edge direction, with all four tires able to give full traction in the lateral direction, which is the same direction as the exit edge direction. Just as your drag race example. A little background here. I have a masters in applied physics so I'm not new to physics, however, I've never studied any race theory before so I'm fairly new to all the details here. I've done some racing before, mostly on sportsbikes. I found your section about the super late apex really revealing about what are the important parts when racing. Usually when discussing getting on the throttle early people refer to position on track as a reference, but position on track is irrelevant, it's early in TIME that is relevant (but hard to keep track of). If you not earlier in TIME you will never make up the loss from slow entry. So thanks for that insight!

@@ZartaxtheWise In regarding the 90 degree corner, you need to take into account how the radius of the line will increase with speed and how we are going to be limited by the apex. By accelerating in the corner exit ideal direction starting at turn in we would need to severely compromise our entry speed. You would need a much later, slower turn-in to still make it through the apex and corner exit. You've essentially added a little cone right at your turn in point where you achieved minimum speed further constricting your line. This is the definition of a super late apex. The apex should always be the point of minimum speed in the corner where deceleration changes to acceleration. Consider that an ideal apex speed is 100. Is it faster to get to 100 by decelerating to it, or accelerating to it? Does this make sense now?

​@@ParadigmShiftDriverDevelopment ​I think you are misunderstanding what I mean by "accelerating". When you turn, you accelerate perpendicular to your current velocity. So in a 90 degree turn, as soon as you turn your steering wheel you are accelerating in the direction of the exit edge, in some part. Regardless of entry speed. Note that accelerating in the direction of the exit edge doesn't mean your speed is increasing. It's probably decreasing since you are probably also accelerating in the direction of the entry edge (that is, braking). Your drag race is the perfect example of this. Both cars are accelerating in the direction of the goal, from start, even though one starts perpendicular to the goal. It even wins, because it's possible acceleration in the direction of the goal (the exit edge) is higher when limited by grip and not engine power. I see when I read by previous comment that I was unclear in my use of terms. "If you look at the traction bubble of the car on your link, the forward max force is lower than any other direction. That means we have spare grip at the end of the corner where we are already at full throttle, which we then can use for braking, releasing some grip at the beginning of the turn to be used for acceleration in the exit edge direction." <= In this comment, when I say "braking" I mean accelerating in the entry edge direction. Not by using the brake, but by turning the car. So the goal is to reach the end of the turn as quick as possible with as much speed as possible in the exit edge direction, with the speed in the entry edge direction going to 0 sometime during this, but before we reach the track edge. That is the limitation. Where we reach 0 speed in the entry edge direction is actually irrelevant to the optimization problem, but since acceleration in the exit edge direction is better earlier we probably want to reach 0 speed in the entry edge direction as late as possible. Which is why we reach the track edge at the end of the turn. So this is why the focus on maximizing deceleration before apex seems like the wrong focus. You always want to maximize force in the exit direction throughout the turn while allowing for just enough traction budget to stop the speed in the entry direction, and you want to allow this budget where it hurts the acceleration in the exit direction the least. Which is before turning in (straight line braking) and at the very end of the turn, where there is some free traction budget due to the shape of the traction bubble. Now, what complicates things is that earlier turn in is better (due to what we are optimizing, time to end of turn and speed at end of turn), as long as you can manage the constraints. Trail braking means you can turn in earlier because it allows for higher speed at turn in point etc. etc. I don't know, maybe all this was just a very long way to say that the apex might not be the slowest point of a corner. Getting to the ideal apex of 100 in the desired direction might not be possible by only decelerating to it. Oh, and sorry for an extremely long and wordy answer! :p

Okay, I understand what you are saying now. I need to walk you through a few steps, which I’ll try to do briefly. If you haven’t read my books, you really should. It would probably clear everything up for you. They are written for people who really like to understand racing at the level you are trying to. First try to understand why the apex is the point of minimum speed. The apex is your primary restraint. Consider your 90 degree turn with a cone as the apex. The highest minimum speed attainable in the corner would be by driving a perfectly circular line. You could pass the cone at a higher speed than this, but only by severely reducing your speed earlier or later in the corner. Your instant radius and speed is linked so that means that if you achieve a lower speed anywhere other than the apex you will need to tighten up your line there more than had you done this at the apex. You have effectively added another cone at your point of minimum speed. Once we understand the cone/apex is the point of minimum speed/radius we can understand we will pass it at exactly 45 degrees. The highest speed we can do this at would be with a perfectly circular line. This will make the velocities of our corner entry edge direction (X) and our corner exit edge direction (Y) equal. Driving at the limit, we can still pass the cone going slower if we wish by driving a spiral shaped line on entry however. Our x and y velocities would still be equal and it would still be at 45 degrees though. Now the question is how fast do we want to pass the cone? Just consider an idealized car with a perfectly round traction circle for now. Our goal from the point we pass the cone is to maximize acceleration in the Y direction while bringing our X speed to zero. With the apex speed from our circular example, we can’t add any additional acceleration in the Y direction because we are already at the limit. We need to use significant amount of the available grip just to bring our X velocity to zero. Our exit line will remain a circle at best. If we pass the cone going slower however, we can bias toward our Y direction acceleration as we have less X direction velocity to bring to zero. There will be an ideal apex speed that allows us to maximize our Y direction acceleration while only using the absolute minimum force necessary to bring our X speed to zero. This will create a spiral shaped exit line of expanding radius. Once you understand this, realize that entry is simply the mirror image. Your maximizing force in the X direction while only using the minimum force needed in the Y direction. You end up with a spiral shaped line of reducing radius.This gets you to the ideal apex you have determined in the minimum time possible.

Thanks, a lot of work and thought went into this video so it's good to know new people are still finding it.

Sure thing, although it would help if you had a specific question. The basics however is simply that a rotating object wants to continue rotating, but during a chicane you need to stop the rotation of the car and reverse it. The rotating object (car) resists this.

HI Luis, sorry for the late reply. Could you explain a little bit more about what you are asking? A super late apex is a line where acceleration starts prior to reaching the inside of the corner. A normal apex would be one where acceleration begins along the inside and then there is a spectrum between earlier and later. HIgher acceleration cars will need a relatively later apex than lower acceleration ones.