Updated: Never Late Apex!

In the post here back in July of 2015 I argued that autocrossers should almost never drive a late apex line. I was almost on to something.

Since then I read Adam Brouillard. (I’ve talked about him several times and exchanged some nice emails with him.) He explains why for each standard corner and each particular car, corner and set of conditions there is only one correct apex location. Not late, not early, just one correct apex which is defined as both a location and an angle.

Here is some of what I said back then:

Late-apexing is done on track for various good reasons, but the only one related to saving time is to increase exit speed off the corner by “lengthening” the straight. The increased exit speed is carried down the ensuing straight whose average speed is now increased, reducing lap time. This is the only occasion to use a late-apex: when the length of the ensuing straight is long enough to save more time than lost in the corner.

This was wrong. It doesn’t matter how long or short the straight is. It’s wrong. My only excuse is that Brouillard’s books Perfect Corner and Perfect Corner 2 hadn’t been published when I wrote it!

While “lengthening the straight” can be done, and while it does increase the “exit speed off the corner” and while this increased speed is “carried down the ensuing straight” a late apex (an apex intended to increase the exit speed and later than the correct apex) does not decrease your lap time. Never did, never will.

I will not try to explain Brouillard and the physics. I recommend you go read him. I will say this in way of explanation, however: Suppose a corner had an off-ramp just long enough so that you could accelerate down it, turn around and then race back to the exit of the corner achieving the top speed of the car at corner exit. Your corner exit speed might go from, say, 45mph to 150mph. Your average speed down the straight might increase from 90mph to 150 mph. Could taking this exit ramp ever, under any circumstances, save time?

I don’t think so either.

When we late apex this is what we’re doing, just to a smaller extent. The more we do it the more time we lose.

 

Here’s my rule of thumb: it rarely pays to go in the wrong direction, no matter how fast.

When you create a late-apex, you have gone in the wrong direction (continuing toward the outside of the corner when you could have been heading more directly toward the exit), taken a longer path and actually done it slowly because of the smaller radius turn you had to make to get pointed toward the exit. Brouillard’s analysis shows that the time lost can never be made up.

It. Never. Pays. Off.

Slithering

All you great autocrossers out there already know everything about the title of this post. I know I’ll be preaching to my betters and you folks can stop reading right about here.

But, I got some good data last Saturday that doesn’t show anything about how to go fast and I wanted to share it with those who maybe don’t have a lot of autocross experience and those who maybe don’t have a lot of experience with data either. I want to share it because of what it doesn’t show. It’s a good example of the limitations of limited data. And I’ll also say something about how to be fast in a slalom that has little if anything to do with being early or late or how fast your car can change direction (Transient Response) or how hard it can corner.

I just completed a set of posts about transient response and a lot of it concerned slaloming. I was criticized by some for focusing only on the math and not how people really go fast through slaloms in the real world. Well, math has its place and I’ve always tried to put numbers to anything I can. I find people who criticize trying to put numbers to autocross, well, a little weird. Many couldn’t see the value in it. I guess I’ve done so much mining for meaning in data during my engineering career that I can’t relate well to those that haven’t.

This post, instead, concerns a real-world way of going faster through a slalom that I can’t put numbers to and seems not to come up in discussion as often as maybe it should. Lots of people learn it quickly, of course. I was sort of slow on the uptake. I remember trying to learn this about year five or so which is probably the equivalent of learning to walk when you’re a teenager.

The car I co-drove this past event was a C-Street Honda S2000 owned by someone just two years into the sport. I’ve got ten years in. The owner is much faster than I was at the two year mark. I barely managed a better time for the event.

The course began with a 5-cone slalom with an immediate turn around the 5th cone, so only a moderate ability to accelerate near the end. The data below begins just as the cars have turned around the first cone shortly after the start. Both cars are going identical speeds of 31.9 mph at the cursor location A. (The direction of travel is from A to C.) Both cars have already short-shifted to 2nd. I’m the red trace, my co-driver the blue. I’ve drawn in the approximate location of the five cones on the path trace. The Delta-T data trace begins at zero at the start of the data so the interval from the start to point A is not counted.

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Figure 1- 5-cone Slalom Data

The first thing to note: by time we’re at B Red is 4 mph faster. Red maintains a speed advantage all the way to C, at which point Blue has lost 0.29s to Red, as you can see on the Delta-T trace.

Second, note that Blue is turning harder around each cone. I’ve marked the Blue peaks on the LatAcc trace with three little arrows. The Blue peaks are earlier and each about 0.15G higher than the Red peaks. (I know that my 20Hz GPS data is missing the actual value of these peaks but the relative differences should be real.) Does this seem a little strange to you? Strange that the faster car is pulling less G’s? It did to me.

The explanation could be that Red (me) was under driving the car as compared to the owner. I was under driving the car yet faster than the owner in the slaloms? Doubtful. Especially since the Red run shown in the data was my 6th. I think I was working the car pretty hard by then.

Thirdly, how Red got to a higher speed is clearly shown on the LongAcc trace where you can see Red continuing to accelerate into the first part of the slalom while Blue uses only maintenance throttle. Does this really explain anything? OK, yes, using more throttle makes the car go faster. Got it. But how the heck does Red go faster than Blue through the same slalom with the same car and pull less lateral G’s doing it?

You might think that Red must have been closer to the cones. That could be one explanation, but I think we were both quite close to the cones. I certainly didn’t notice any issue when I rode with my co-driver on three of his seven runs.

You might think that Blue could be driving bigger loops in between the cones even while being close to each cone when passing it. The GPS-derived path is probably not accurate enough to see such a small difference, especially with drift over time. It’s possible that this is part of the explanation, but not the complete explanation. I do remember trying to make my crossovers in the middle between the cones, as explained in this earlier post here. My co-driver was probably following the standard instructions to “backside” the slalom cones, at least in the beginning of the slalom. This would put Blue’s peaks earlier than Red and make him drive a wider path, if only very slightly.

[Edit: I just compared the zero lateral G crossover points in the data with respect to distance travelled. Red consistently crossed over between 5 feet and 10 feet later than Blue.]

The complete answer is down to slithering. By the end of the day I was comfortable enough with the car, its handling and its limits to slither it consistently. I don’t think the owner knows how. Not yet.

OK, so what exactly do I mean by slithering? It’s very simple. It means to a) speed up, b) turn in and aim at the cones as if you intend to hit them, and c) allow the car (by virtue of the higher speed) to drift both front and rear so that the front tire just misses the cone in question and the rear of the car rotates just enough (by sliding) to also miss the cone. Only the higher speed will show up in the limited data with limited resolution that I take and show above.

The rear of the car can’t step out too much or uncontrollably, of course, or disaster will occur. So, this requires a well-setup car that you can trust while repeatedly exceeding the peak cornering ability of the tires as you intentionally create controlled slides around each slalom or offset cone. The result is a straighter, faster path from cone to cone.

I remember the first time I became aware of slithering. I watched a slalom directly from the rear at Dixie Tour many years ago. Sam Strano’s Corvette looked like a lizard bending in the middle as it miraculously wrapped itself around each cone.

It was beautiful.

Another great example is from an earlier post here where Matthew Braun shows an even more sophisticated form of slithering while negotiating offsets than I’m describing.

I can slither most any “good-handling” RWD car given a few runs to get to know it and the surface. I suspect slithering a FWD car is more difficult because I see fewer people do it, but the top drivers do slither FWD. (I know nothing about driving FWD.)

Fast hands, good timing, entering early and leaving late… all these things will only carry you so far. I think you have to learn to slither to be really fast through a slalom.

Transient Response 6.3- Final Answer

How much does transient response really contribute to Saving Time on the autocross course? Time to answer that question.

Turns out we already have what we need to get a first-cut approximation. Back in Transient Response 5, if you’ll recall, I found out three things.

Thing 1: All typical slaloms, no matter the length between cones, take almost exactly the same time in the gaps between cones for a given car

…therefore it doesn’t matter what size slalom we get data from, as long as the spacing is consistent, or we average over enough different designs

Thing 2: I showed data for my BS Corvette that indicated 1.05s between cones

Thing 3: I showed data for a Street Prepared car that indicated 0.98s between cones.

I think we can safely conclude that any properly prepared Street Touring car will be similar, on average, because of the similar amount of suspension  preparation allowed (springs and bushings) which I think are the key factors. Car to car variations can be big, of course.

So, we now have all we need except one thing: how many gaps between slalom cones are there on a typical autocross course? If we count them up we can calculate a first-cut approximation.

Here’s the map for the 2019 Nats East course with the slalom gaps counted.

East count

Figure 1- 2019 East Course Slalom Gap Count

I get 15 slalom cone gaps. Multiply this number by the difference between the Street time number and the ST/SP time number gives 15 x (1.05s – 0.98s) = 1.05s

Here’s the 2019 Nats West Course counted:

West count

Figure 2- 2019 West Course Slalom Gap Count

 

I count 14 slalom cone gaps. So, 14 x (1.05s – 0.98s) = 0.98s.

Both results are right at 1 second.

Assuming these courses are typical I conclude that the increased transient response of ST and SP classes over Street classes is worth about 1 second on a Solo Nationals course. I think this result is exclusive of weight differences, power differences or grip differences to any great extent. Just transient response. It’s also conservative in that it doesn’t take into account the gain into each standard corner where a high TR car can turn in later, thus extending the previous straight.

I really don’t know what to make of this. I don’t know if it’s more or less than I expected or more or less than generally understood. Let me know what you think.

Also, I’d love for people to post their data for average time between slalom cones along with the car and prep level. If we could create such a database we might have something very useful.

 

Transient Response 6.2 Rev A

Additional charts and info has been added at the end.

Now I owe you the explanation for the statement: “The fastest way through any generic, non-infinite slalom is probably achieved by starting early and ending late.”*

I’ll try to illustrate the idea. Let’s assume we are negotiating an 80′ slalom, meaning 80′ between cones. It might look like Figure 1, below.

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Figure 1- Car And Path In An 80′ Slalom

There are two little blue dots… those are the cones at 40′ and 120′, so 80′ apart. The path in the picture crosses at the 80′ mark, exactly half-way between the cones.

If the slalom is infinite, then trying to be early or getting late is the equivalent of shifting the path (and car) left or right with respect to the cones and results in hitting a cone. So to be early or late you must alter the path. The different path could be one with more (wider) lateral movement or it could be one with smaller radius curves connecting straight sections. If you think about it for a while and maybe even draw it I think you will come to the conclusion that any of the possible alternate paths that would allow the car to be early will take at least a little bit more time than the perfect path that crosses exactly in the middle.

But, of course, infinite slaloms are rare. (That’s a joke.) More importantly, the entry and exit of non-infinite slaloms can take all sorts of forms. Let’s look at a fairly common non-infinite slalom as shown below in Figure 2.

6point2fig2

Figure 2- A Non-infinite (5-cone) Slalom With Same-Side Entry And Exit

Here’s the same 80′ slalom, showing 5 cones, with the same red line showing the infinite-slalom perfect path. But now let’s assume that we enter from point A and exit at point B.

We could enter from A and get on the red path and follow it faithfully to the end.

But, because of the entry location at point A something more interesting has become possible. We can be early on the first cone without losing anything. (Let’s assume that’s true, though it’s not really, quite absolutely positively true.) I’ve drawn a dashed line path that shows the cross between the first and second cone at 10′ from the first cone, which is the 50′ mark on the chart.

What if we now follow the dashed path and make our next crossing at 20′ beyond the second cone, at the 140′ location. And then the next crossing is at 30′ past the third cone and the crossing after that is 40′ beyond the fourth cone. Do you see what’s going on?

In the infinite slalom we cross every 80′. In the non-infinite slalom we cross every 90′ (or more.) Necessarily the non-infinite slalom path (dashed line) must have a bigger radius than the original path (red solid line.) Therefore, the car can travel faster through the slalom for the same lateral acceleration and transient response capability.

I know that many of you are saying that I’ve missed a key point, which is that we can start accelerating early to the exit, somewhere about the fourth cone. That’s true for almost all non-infinite slaloms (except ones where the course designer is really obtuse and prevents us from doing that via what comes next) and of course we can and should do this, but that’s not my point here. I assume you already know about accelerating early.

There’s a possible glitch, however. The dashed-line path cannot actually be a series of perfectly smooth and efficient curves, circular, sinusoidal, or otherwise. We still have to modify it somewhat to not hit the cones. There’s just no way to perfectly fit the path with 90′ nodes into an 80′ slalom without altering the path somewhat due to the finite size of the cone and the finite width and length of the car. A little bit of a wider line is required. How much this degrades the net result I don’t know.

In any case, I think that in many real-world situations the start-early and end-late path Saves Time but I recognize that I’ve certainly not proven it.

Rev A Addition

Maybe an easier way to think about this is to start with the 3-cone slalom, known in some circles as the Chicago Box.

The figure below shows the situation with the infinite slalom driving line in red.

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Figure 3- The 3-cone Slalom

If we were entering at A and exiting at B would we try to find the infinite slalom, midpoint-crossing driving line? I don’t think many people would. I think most everyone understands that the 3-cone slalom is a special case where we should enter as early as possible and exit as late as possible to produce the biggest radius path, as shown below.

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Figure 4- The Correct Path Thru The 3-Cone Slalom

We tend to treat the 3-cone slalom as a special case and it is. A special case of what? It’s a special case of the generic start-early and end-late path shown above in Figure 2.

Here’s another one, a 4-cone slalom, shown below.

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Figure 5- The 4-Cone Slalom

With a 4-cone slalom we necessarily enter on one side and exit on the other, but the principle is the same. We make the first cross as early as possible, make the 2nd cross at the midpoint between cones and make the third cross as late as possible. This creates a path with the maximum radius curves possible, which means the highest speed.

  • *I must give credit to Steve Brolliar who teaches this start-early, end-late concept at our Advanced Autocross school each year. I hope I’m presenting his point faithfully.