Line Theory: Perfect Corner 1 & 2

In Perfect Corner 1 and 2, Adam Brouillard has made the most important contribution to racing line theory since the first technical book on the subject, Taruffi’s 1959 The Technique of Motor Racing.

A few months ago I started reading, studying and applying knowledge gained from these two books. They are an exposition of line theory, the theory of what driving lines are most efficient, i.e. the fastest, around a race track. Brouillard takes a physics-based approach.

With Perfect Corner 1 and 2 we can look at all the various permutations of line theory since 1959 and clearly understand what is right about each one and why and what is wrong about each one and why. When a new theory explains all the previous ones, that makes for a powerful theory.

Brouillard teaches that there are only three types of corners in all of road racing and autocross. (He tells me he began as an autocrosser.) The three are the standard corner, the chicane and the double-apex. That’s it.

A standard corner has enough space before and after to stand alone so that the entry and exit can be optimized without regard to the previous or following element. A chicane is defined as two corners in opposite directions that are so close to each other that they must be optimized together. (The autocrosser’s slalom is two or more chicanes end to end.) A double-apex is two corners in the same direction that are so close to each other they must be optimized together.

The books give rules for how to classify each corner you will encounter and rules for how to determine the most efficient line through each type.

My approach to autocross is now forever changed because of Brouillard. What I’ve realized in doing autocross events this year with his concepts and rules in mind is that many autocross courses are more complicated than most road-race tracks. Some autocross courses essentially have no stand-alone elements. Everything is connected in a series of chicanes and double-apexes with only the rare standard corner. So, applying the methods and rules he gives is not easy. Some of it is immediately applicable, some is not. He tells me he’s thinking of writing an autocross book. I hope he does. Soon!

In the meantime, get these books and start a new journey into autocross.

What Trail-Braking Looks Like

TAC3 180

Big Sweeper At TAC/TVR #3


One of the difficulties in learning anything is working through the trash. The ‘trash’ is what I call all the myths, supposed common-knowledge and just plain wrong stuff people tell you that can send you down less than optimal learning paths. If you’re someone like me that has to first get it in his head intellectually before the body can do it, you may be particularly susceptible to well-meaning but wrong advice or supposed facts that aren’t so factual. Even correct information delivered at the wrong stage of development can cause learning to go off track. We can’t start at the top. We have to start at the beginning. There’s always a progression.

I guess if you begin with a world-class instructor in a well-developed field (one where effective teaching techniques have been developed over time and are widely known, like music or golf) then the trash problem is minimized. I don’t think autocross is quite there yet, but the data revolution is changing that. If you’re Dad or Mom happens to be a great autocrosser, knows why she’s fast and can teach it, then you’re in the soup. Very few get so lucky.

In my case my Dad was a multi-sport athlete and tremendous competitor who could never understand this nutty autocross thing. He always wanted to come watch the event if I was racing in his city but he never, ever rode with me.  Not once. He just wouldn’t do it and I never understood the reluctance. He would say, “I don’t want to encourage you” and smile as if it was a joke.

Trash example: the purpose of trail-braking is to help get the car turned in a long corner, like the one shown above.

Maybe I heard it wrong (multiple times?) but this is what I remember people would say when discussing track driving and the difference between braking for a corner in a straight line then turning in for a late apex (Slow-in, fast-out) vs. the more advanced (and, OMG! dangerous!?!) technique of trail-braking into a corner. My problem was that I’d believe stuff like that and think it was the real reason for trail-braking when maybe it was just an easy thing to say, or it was being said by someone who didn’t really know why trail-braking was a technique for Saving Time. (Yes, I’m kinda slow like that.) I carried that idea into autocross.

It was in my head and wouldn’t come out without great difficulty, i.e. progress in learning that can replace the simple idea that trail-braking is for rotating the car with a more sophisticated idea.

I’ll tell you The Non-Trash Truth: no one can Save a lot of Time in autocross without trail braking the heck out of any long corner, like the one shown at the top. We see a lot of those in autocross and many tracks have something similar. The feature shown above didn’t even have an apex cone. Just an entry and an exit and you figure out how to get from one to the other as fast as you can.

Trail-braking has little to do with turning the car by putting weight on the nose and freeing up the back tires to slip more. Sure, you can use it for that and may need to, depending on the type and setup of the car, but it’s not the most important reason why you should trail the brakes entering most long turns.

The real reason is because of the physics of tire performance. Unlike me when I started out, tires can do two things at once. They can both brake and turn at the same time, just like they can accelerate the car forward and turn it at the same time, but that doesn’t seem as hard to understand. The two capabilities added together are more powerful than used separately. Proper use of trail-braking allows you to brake later into the corner, thus extending the time spent at a higher speed (extending the length of the previous straight for you track drivers), to take a shorter, elliptical path to the apex, and to take that path at a higher average speed. Those three things sound like they’d Save some serious Time, don’t they?

So, go learn how to trail-brake.

This isn’t a how-to article on trail-braking, but I will show you what it looks like in data. If you’re like me, you need some convincing first so you can really commit to learn it later. Read this article then go read some books on racing. I like Krumm’s Driving On The Edge. He’s a professional racer that figured out how to drive long corners by trail-braking into a double-apex by analyzing data of the same corner driven over and over again various ways by various drivers.

Then, go practice. Where? At the autocross event, of course, where a spin only costs you a little tire rubber.

The data below is for the turn shown at the top of this post. The top trace is speed, the middle trace is how hard the car is turning (lateral force) and the bottom trace is how hard the car is braking (negative) or accelerating forward (positive).

From the point marked ‘Lift’ the LongAcc goes steeply negative. This is hard braking. Notice that just above the LatAcc is turning positive. That means I started turning left at exactly the same time as I was braking. (This is a little unusual, but I was in a bit of a hurry.) And I keep it up.

In the section marked ‘Trail braking’ the negative acceleration is gradually trending up to zero, i.e. I’m gradually coming off the brakes. Meantime, the LatAcc continues to build up to well over 1g. The tires are providing the ability to brake and turn simultaneously. This is the data signature of trail-braking.

TAC#3 180data

TAC/TVR #3 First 180

The other thing to notice is the shape of the path. It’s an almost perfect portion of an ellipse. The physics of the situation dictate that it be this way if you do it correctly.

A Real World Comparison

At the Blytheville Pro-solo a few weeks ago I put my data device into another car and got data for three different drivers: Ryan, Tom and me.

Ryan and Tom were in a BSP Miata on race compound Hoosiers; I was in my BS Corvette on Bridgestone street tires. The course contained an almost perfect, more-than-180 degree sweeper, entered from a slalom just like in TAC/TVR #3, above, marked by an entry cone, a center “apex” cone and an exit cone. Each of us did this corner in his own way. You can see the path differences in the right of the figure and the data on the left. 

BPS180 data

2018 Blytheville Pro-Solo Turnaround (Left Side)


Looking at both the LongAcc (longitudinal force) and the LatAcc (lateral force) we see the trail-braking signature in the data. After braking hard, Ryan’s red line only very gradually heads back to zero, that is, he’s staying on the brakes as he turns in more and more, only very gradually releasing the brake pedal, taking best advantage of the tires’ ability to multi-task. This allowed him to maintain the highest entry speed and yet not overshoot.

The major difference as I see it was that Ryan, clearly the highest level driver of us three, did a much faster straight-in approach and a perfect trail-brake entry. His minimum corner speed was 38.7mph. I (green) did a slightly wider approach and a less than perfect trail-brake, attempting to agressively go shallow and accelerate to the apex.  (It’s a big corner, much larger than the corner from TAC/TVR #3, so big and with such a fast and difficult entry that everyone was accelerating to what would normally be called the apex. Effectively, we all double-apexed this monster.) My minimum corner speed was 35.8mph, almost 3mph slower than Ryan, not too surprising given the car/tire difference and the different strategy. Tom (blue) went widest for a classically best entry angle, did not trail-brake, but was able to accelerate to the apex sooner than I and catch back up to me. His minimum speed was 38.3mph, just slightly less than Ryan.

Once at the apex cone all three cars had speeds contained within a 1mph band. From entry to apex cone took a bit more than 4 seconds during which time Tom and I lost 0.25s to Ryan. This can be seen in the bottom trace, where Tom and I (blue and green, respectively) are compared to Ryan, the horizontal red line. The more the blue and green lines are above the red, the more time they’ve lost to red.

For my part, I think trail-braking is what allowed me to match another car to the apex that had greater grip but whose driver didn’t trail-brake. 


I’ve become aware that Brouillard claims that the shape of the trail-brake curve is an Euler spiral, not part of an ellipse as I stated above. I’ve now ordered all his books and will study on it. I don’t see how Brouillard can be correct (if this is actually his claim… I read it in Wikipedia) when the radius of curvature of such a spiral varies linearly. That’s the definition of an Euler spiral.

Euler spirals were first used in the railroad industry to transition from a straight to a curve without literally jerking the passengers around. They also reduce loads on the tracks. In autocross, of course, we’re not too worried about a little jerking, which is literally the time derivative of acceleration. Lots of little jerks in autocross.

The trail-braking curve seems a non-linear situation, even if we assume a perfect circle for the tire traction “circle” and a linear release of the brakes, since the radius varies with the square of the velocity. I think the the curve shape is more complicated, more like an ellipse with a non-linear variation of the radius of curvature. My assumption of an ellipse, based on what the path actually looks like in the data, may be an approximation that’s not mathematically correct. So far, I’ve not found a mathematical description of the trail-braking curve geometry. Maybe I’ll find it in Brouillard’s books. If so, I’ll come back and tell you about it.



Extra Twist?

Someone asked this question in an on-line critique of various run videos from our latest event: Not being the expert you guys are, I enjoy the critiques. What I notice is that I and others will start a turn, hold it for a while and then just as we [get] to the cone we give the wheel an extra twist to get around the cone and on the line we want. Or am I just seeing good technique?

While we all make mistakes, and we all have to make corrections (for instance, the level of grip is not necessarily constant in even a single turning element) Steve Brollier (multi-time national champ) taught in our autocross school last year that we should strive to turn once for each slalom cone, for instance, and once for each offset cone. I think this applies, in general, to all turns.

As someone pointed out in my video (which can be seen here TAC/TVR#3 Run video) at 1:07 in the final turn to the finish I make a preliminary turn and then the “real” turn. As a result, I have to turn sharper, which means slower, and I lost time there.

The “extra twist” being talked about may be a valid technique in certain situations. I’ve always called it taking advantage of the ability to dynamically shock the tires and get a little extra out of them. There aren’t many places where you can use it, however. If you’re doing it at every corner, it’s probably covering up a basic fault. You’re probably cornering too much under the limit over a large portion of the turn and only at (or above) the limit in the final phase. You may be turning too early and too slow, rather than turning later but with greater steering wheel speed.

I remember doing a lot of the “extra twist” technique when I was new. I think it may be caused by the lack of confidence in turning hard at higher speeds. We get comfortable with turning hard a low speeds first, so that’s where we do it. As our level increases we get more comfortable with quickly getting to the cornering limit at higher and higher speeds. Turning the steering wheel as fast as conditions allow reduces the transition time from one turn to the next, or from going straight to turning in, which has a direct effect on the speed you can carry, how late you can brake and ultimately elapsed time on course.

I think the process of “getting fast” is 1) learning how to evaluate the proper line to take, for your particular car and driving style, 2) developing the car control skills necessary to make certain maneuvers and be able drive the line you’ve decided to take, which again is highly dependent upon the type of car, and 3) gradually reducing the number and severity of mistakes, which implies that you have gained the knowledge of what constitutes a mistake. Making multiple inputs in what should be a single, smooth arc is definitely a mistake, but doesn’t by itself mean you won’t be “fast” in relation to someone else just because you’re not perfect. A lot depends upon the magnitude of the “mistake.” It does mean you have room for improvement. (I’m discounting the often-rapid corrections you have to make to keep a car on the limit of adhesion.)

Earlier this year I got to sit in on a video critique session with a group of accomplished autocrossers. One of the top drivers on the national circuit (another multi-time national champion) was watching his own video from the course we’d all run that day. The level and completeness of the critique he gave himself was impressive. “Oh, I got late there,” he says at one point, and I’m looking at it thinking the error was so incredibly slight that I would have never noticed it. Upon first view I would have said it was a flawless run. Only after repeated viewings could I see what he saw.

There are levels and levels.

$2 C5 Seat-back Flop Fix!

One of the most annoying and inexcusably dangerous aspects of the fifth generation Corvette are the seats. Specifically, I mean the tendency of the seat-back to flop to the fully reclined position when loaded. Such as during an emergency maneuver, at the worst possible time during an autocross run, or when pulling out onto a busy highway. Each has happened to me, starting from when I bought the car in pristine condition with 13,800 miles on it.

My seats got progressively worse over the next 40K miles. First, they occasionally let loose at any intermediate position. They gradually worsened until they would not hold any position at all other than fully upright, which is not at all comfortable. At any angle more reclined, one side would slip backwards under normal sitting pressure. Either side could let loose with more load, sometimes both sides at once. Yesterday the seat-back flopped from the fully upright position. I’d had enough.

I’ve searched the internet in vain for anyone who knew how the seat-back locks worked and how to fix them. No luck. Lots of people searching for a solution, but no one finding one. I found various people who had taken their new Corvette to the dealer, supposedly had it fixed with new parts (no longer available) only to have the problem reoccur. Today, I had a little time so I pulled out the seat determined to understand and fix the issue, even if I had to weld it into one spot. Turns out welding wasn’t necessary. Two $1 hose clamps did the trick.

Here’s what you see after removing the seat bottom cushion: two cylindrical mechanisms, one for each side of the seat-back. I call them angle locks. Since they are independent in operation (but actuated together) one can slip and the other hold, creating the common situation where one side falls back and not the other. (The fiberglass construction of the back is very flexible in torsion, so it has no problem twisting until one side falls waaaay back there.


Figure 1- Seat Mechanisms with Bottom Cushion Removed


The green springs you see in the figure above are what bring the seat-back up to touch you when you actuate the lever. This way, you don’t have to pull the seat up and you then just lean back to the preferred angle and drop the lever. The angle locks are supposed to hold it at your preferred angle. Now, let’s look a little closer at one angle lock device.


Figure 2- Angle Lock Device

The main body of the lock is a steel cylinder that is pinned at the forward end. (It has to rotate a little bit during the seat-back movement.) The cylinder is holding together two split sleeves that are inserted into it. Inside the sleeves is some sort of cam-lock device. I don’t know exactly what it is, but this is the bad-boy that slips. The cam-lock is locking the axial position of a shaft that runs from inside the cylinder all the way back to where it is pinned to the lever arm of the seat-back. (You can’t see it… it’s inside the green spring.) With the shaft locked into position, the seatback is prevented from rotating about the seat-back pivot which is fixed to the lower frame.

To release the cam-lock a cable pulls tangent to the lower edge, causing it to rotate inside the split sleeves. (Two cables are pulled at the same time, actuating both devices simultaneously, more or less.) It takes very little rotational motion, at least on both of mine, to release the shaft and allow it to move in or out.

Some have thought that the weight of the driver pressing down through the foam can deflect the pull cable and release one side. Nice theory, but I don’t think so. The cables do get pinched between the seat cushion support wires and the silver metal shaft you see in the picture above, but the cables have a good amount of slack in them. I tried, but, in spite of how little motion it takes to release the shaft, I could not create any cam-lock rotation and thus seat-back release by deflecting the cables unless I pulled them totally outside the volume of the seat.

I think there’s some sort of spring inside the cylinder that serves to pre-load the cam and thus lock the shaft at all times unless pulled by the cable. It’s theoretically possible that the green springs are doing this job, doing double duty. Maybe the spring(s) get weak? Maybe, but my buddy Glenn and I came to a different conclusion.

We noticed that the gap between the split sleeves wasn’t uniform. The gap was bigger in the middle where the pull cable comes in and smaller at the end where the shaft protrudes and smaller at the other end where the sleeves disappear into the cylinder. It looks like the split sleeves have dimples at the shaft end to lock them to a ferrule of some sort that carries the shaft and holds the split sleeves together.

Our theory is that the cam locks the shaft by squeezing on it. An equal and opposite reaction (expansion) within the split sleeves is therefore required. That expansion may spread the sleeves apart over time, such as during the delivery trip from the factory to the dealership. And they probably weren’t particularly close-toleranced to begin with. So, Glenn suggested that we squeeze the two halves together better. We put hose clamps around them as close to the pull cables as we could and tightened until they cried for their Mamas.

It worked!

The seat-back now locks firmly in any intermediate position, which it would not before. I slam back into it and Holy Toledo Pro-Solo! it holds. Driving the car is so much more comfortable, not to mention much safer.

We’ll have to see if this procedure is permanent, but I can dig deep and afford to put two $1 clamps on each side if I really have to. (Glenn thinks I should market a machined and anodized aerospace-grade aluminum two-piece clamp with thread-lockable screws. What do you think…$25? Hey, maybe titanium. Yeah, that’s it. Titanium! $99.95) If anyone wants to protest me, go ahead and try. I’m not removing those hose clamps! I hereby proclaim this to be the industry-standard repair for a safety issue that’s been vexing Corvette owners for nearly 20 years.

P.S. If anyone has ever cut up or otherwise disassembled one of these angle locks I’d love to see a picture.



First T&T: This thing feels good!

Just back from two days of testing & tuning down in Birmingham at the Hoover Met(ropolitan Stadium) parking lot. What a great site- big with very good, very grippy asphalt. As usual, the ALSCCA folks were very welcoming and did great job. The Iron City Match Tour scheduled for June 17-19 should be a fantastic event. Be sure to put it on your calendar.

But, before I get to how the car handled, let me catch you up. I borrowed a set of corner weight scales from a friend (Thanks Tom!) and got another friend (thanks Glenn!) to help me do the corner weighting. The empty car weighed 3043 lbs on 3/16 of a tank and the cross weights were way off somewhere near Saturn… around 1.5% out. We got it close to 50% but I’d only disconnected the rear roll bar, not the front. I felt like I was fighting the front bar, so I knew we’d have to do it again.

The next morning Clem Tire aligned the car. They found that last years’ home alignment was good, but the big thing I had them do was reduce the toe-in in the rear. Up until now I’d wanted a very stable car so I ran 0.28 degrees of rear toe-in per tire which is 1/4″ total. This year I had them reduce it to 0.22 degrees per tire, which is right at 3/16″ total. Not a lot of difference, I grant you, but along with some other changes I was hoping to get a little more slithering from the back end this year. When a well-driven Corvette slithers like a big lizard through a slalom it looks from the rear like the car is bending in the middle around each cone.

That night Glenn and I measured the corner weights with both roll bars disconnected. We had to crank up the left-rear corner even more to get close to 50%. Here are the results, with driver and helmet in the car and 3/16 of a tank of gas:


Corvette Corner Weights After Adjustment

What does 50% cross weight mean, you may ask? For one thing, it doesn’t mean that there is equal weight on each tire. The values in the chart show that clearly and the % left and % rear numbers tell you what the static weight distribution is. Cross weight is something different.

What 50% cross actually means is that the differential left to right is equal front and back. (It’s calculated by adding the right-front weight to the left-rear weight and dividing by the total weight.) So, if the left-front has 51% of the front axle weight, then the left-rear will also have 51% of the rear axle weight when the cross weight is 50%. Per the numbers above the car actually has 51.5% on the left-front and 51.2% on the left-rear. So, the cross isn’t perfect (49.74%) but it’s less than 0.5% from 50, which is usually the target.

Why is cross weight percentage important? It helps make the handling of the car symmetrical. That is, it will have the same characteristics turning left as turning right. Equal cross can’t do this all by itself, however. Remember I said my car has more weight on the left side than the right with the driver in place? Most production cars are that way. And this condition will forever affect the handling. (Not to mention the 54% that’s on the front axle!)

How do you adjust the corner weights to get 50% cross? Well, in Street class, there’s only one way: adjust the ride height at a corner. (We can’t rearrange components.) Not all cars have such an adjustment from the factory. Luckily, the Corvette has an adjustment bolt at each corner. What I’ve done is set both fronts low and equal. Then, I adjust the rears. The right-rear was already as low as it would go and the left-rear about in the middle. So, I had to crank up the left-rear, physically lifting that corner of the car. Doing this also sends weight to the diagonally opposite corner, the right-front, and removes weight from the other two corners. Think of your car like a 4-legged table. If you shim up one leg, it teeters on that one and the diagonal. With a sprung suspension it’s not all or nothing like it is with the rigid legs of a table, so even a little air pressure difference in the tires has an effect. Set your pressures before you measure the corner weights!

Lifting the right front would have the same effect on the cross, and maybe I should have. I’ll have to think about that and what difference it might make. I had a specific reason for making all the adjustment at the rear. Raising the rear of a corvette increases the roll stiffness at the back, promoting more of that slithering talked about earlier.

So, now the car is aligned with healthy front toe-out set at the event, cross-weight balanced, shocks set stiff, more air pressure than last year, a narrower (better supported) front tire than last year… wow, it drove good!

I couldn’t believe the turn-in rate! I was early on every corner for the first three runs. The back end was wagging left and right way too much, but once I slowed the input to the steering wheel, it all came together for top PAX time for the day.

The car is definitely better in transition, slithering through the slalom the way a Corvette should. It is less stable but more fun to drive and more than one person commented to me how good the car looked on-course. I can’t tell if any peak lateral G has been lost… the site and courses didn’t allow me to figure that out, but I’m not worried. I’ve achieved what I set out to do, which was to improve transient response. If I can’t do well at Dixie Tour a month from now it won’t be the fault of the car.

With all the runs today (day 2 of the Test & Tune had very few cars) I was able to play with tire pressures and figure out the sweet spots. Minus 4 psi from baseline in the front didn’t seem to reduce peak grip, but it definitely slowed the transitions. Plus 4 psi in the front reduced front grip and induced understeer. Plus or minus 2 psi around the baseline in the front and I can’t tell the difference.

In the rear, minus 2.5 psi from the baseline was a disaster… totally uncontrollable at the 1-2 shift! Plus 2 psi and I could feel some loss of grip. So, I think I have a +/- 1 psi band figured out for the rear. Of course, this is all for one surface, on one particular day, without changing shock settings, but it gives confidence in the starting point to use in the next events leading up to Dixie Tour.