GHIT extra: decreasing vs. increasing radius

I was recently interviewed on the Garage Heroes in Training podcast and they asked me a lot of really interesting questions. I want to follow that up in a series of posts on YSAR where I get into a little more depth on a few topics.

“Increasing or decreasing radius?”

That was the question. Which do I prefer? Decreasing. And off camber if possible. Why? Because I like the challenge of balancing traction, and there’s more challenge to do that with brakes (decreasing radius) than throttle (increasing radius). Later, as I was thinking about this again, I came to an important realization: all corners are decreasing radius. Also, all corners are increasing radius.

Geometric line is a fantasy

The geometric line described in nearly every racing book is (a) not possible (b) not optimal.

There is no way to instantaneously go from driving in a straight line to a curve with constant radius. If you turn your steering wheel super fast, as would be required, the car doesn’t respond at the same speed. If you took a snapshot in the middle of a corner, you would see the rubber in the contact patch twisted to some degree and the suspension have a certain compression. But they had to get there somehow. It takes some time for the vehicle to take a set. During that time, the radius is probably not constant, but tightening whether you want to or not.

Not only does every racing book describe the geometric line, they also show the late apex line. The reason why the racing line is faster than the geometric line is because cars have engines. If they didn’t, the racing line would look very different. In fact, it would be decreasing radius. But since cars do have engines, and sometimes very powerful ones, the more time you can spend using that engine, the better. The late apex line trades corner speed at the beginning for corner speed late. In other words, the radius at the start is tighter than the radius at the end.

Every corner is decreasing radius (and increasing)

Let’s break up the corner into 2 parts.

The first half of the corner. This is defined as the moment you turn the steering wheel until the moment you release the brake.
The second half of the corner. This is defined as the moment you step on the accelerator until the moment you are no longer actively steering.

The point between the two halves of a corner is sometimes called the EoB or “End of Braking” but I call it the “nadir” because if every corner has an apex (top), it should also have a nadir (bottom). In some corners, the apex and nadir are really close to each other. That’s because the apex is the point at which the car is closest to the inside of the track and the nadir is the point of lowest speed. Usually, the nadir is a little before the apex. In really long corners, or two corners connected by an inconvenient distance, the nadir may be a stretch of track rather than a single point.

If you’re taking the usual racing line, the first half of most corners has a decreasing radius. You start out with the steering wheel straight. As the car trail-brakes to the nadir, the corner gets tighter. As grip transitions from braking to steering, more steering gets done. Also, speed is decreasing, so it’s possible to drive a smaller radius with the same grip. At the nadir, all grip is use for cornering at the slowest speed. Therefore, the radius is tightest. Even if you weren’t aware of it, the first half of the corner is supposed to be decreasing radius.

In the second half of the corner you’re mixing steering and throttle. As the steering is unwound, more throttle can be applied. The radius increases both because there is less steering and because there is more speed. From nadir to exit, the corner is increasing in radius.

Here’s an illustration to help you picture what I’m talking about. Whether you’re taking the single late apex or the double apex, there is decreasing and increasing parts, even in a carousel. The circles represent the halfway point of the corner as described above. The A’s represent the apexes on the single apex (blue) and double (red) apex lines.

Beyond Thompson

At the last Lemons race at Thompson, I only got in 6 laps of practice. However, the AiM Solo was running then and during the race, so I got to do a little comparative analysis afterwards. In the graph below, the red line is my fastest practice lap while the blue line is the fastest race lap on Sunday. Click on the image to open it up in a larger window and then write down at least 3 things you notice that’s different about the two traces.

OK, so the most obvious thing is that the drive down the main straight was very different. I had an extra 200+ lbs of passenger and gear in the car and was driving in 4th gear. There may also have been traffic.
The second thing you probably noticed was the very low speed in T2. I was experimenting with the brakes seeing how good they were, so my braking point was very late and this caused me to botch the corner. No big deal, this is what practice laps are for. I had never driven the car before and I needed to experiment. I tried different lines and gears nearly every lap.
The thing I want you to notice next is that all the red lines are shifted left relative to the blue lines. The braking points are earlier and the acceleration points are earlier.
Because my acceleration is earlier, I tend to have higher speeds on the way to the next corner.
The most important area of the track is the 9-10 combination that sets up the main straight (6000-7000 ft). I take this as a single descending radius corner rather than two corners.
While the 7-8 carousel (5000-5500 ft) isn’t nearly as important, I have a very different line compared to everyone else on the team (who all take a line similar to the blue one).

We could go through each corner talking about the trade-offs of taking different lines. But the differences in the red and blue lines aren’t really about Thompson. We can summarize all the specific differences with two general strategies, which I’ll describe below.

Backing up the corner

In point #3 above, I noted that my driving style involves braking earlier and accelerating earlier. This is called “backing up the corner”. The earlier you can get the car pointed to the exit, the earlier you can get to full throttle. Getting the car rotated early is usually accomplished by trail-braking deep into the corner so that the steering and braking inputs overlap quite a bit. This has the effect of swinging the rear of the car around, and you may have to make a steering correction to prevent the car from oversteering into a spin. There are risks involved when driving with this style. That said, no matter how hard I tried, I couldn’t get the car to rotate. It was set up with a lot of understeer. While I could get on throttle early, the car was leaned over quite a bit, and the open diff caused the inside front tire to search for traction. But even without getting the rotation I wanted, you can see from the telemetry graphs that there are gains to backing up the corner.

Connecting combinations

There’s only one combination corner at Thompson: 9-10. The blue driver “sees” this as 2 corners with a small straight between them. You can see this as the hump in the speed graph. The red driver (me) sees this as one long corner. Why? It’s the most important corner of the track and my goal is to optimize the position, angle, and speed of the nadir (slowest part of the corner). So I focus all my attention on getting to the nadir with the best combination of grip and speed that I can, which means throwing away the first corner. By slowing down early and keeping the suspension quiet, I optimize grip. If I speed up too much, or turn too much, I’ll upset the car and lose grip. This costs me some time at the start of the corner, which you can see at 6100 ft. But the investment pays off as from then on I’m gaining time.

Summarizing

Next time you’re on track, try making a conscious effort to get your shit (braking, turning) done earlier. Stop optimizing the straight you’re on and start optimizing the straight coming up. Also try to get your connected corners more connected. Think about how the first corner affects the second. Try some different lines to see what works and what doesn’t. Make sure to bring a data acquisition device. Not only will it help you sort things out later, it also makes the downtime between track sessions a lot more interesting.

Ghosting the Aliens: part 3, driving harder

Imagine you’re heading down the main straight and the following thought enters your mind, “I want the next lap to be my personal best”. There are a lot of people who approach this problem with a solution that sounds like “I’m just going to drive it harder”. How can you drive harder?

Brake more aggressively
Hold more entry speed

If you’re a complete chicken-shit who coasts into braking zones or parks their car before the corner, these strategies might actually work. And if they do, you’ll think that by braking harder and hoarding speed, you’ll eventually become an alien. Not true. Your understanding about the nature of speed is fundamentally flawed. You can’t bluff or bully your way to expertise. It’s got to be earned.

Brake aggressively

As we did the last two weeks, we’ll load Alex Czerny’s fast lap into Lap 1 and choose Leon Jagusch (1:43.477) for Lap 2.

In nearly every braking zone, Leon is braking much later and harder than Alex. He’s also more than 3 seconds behind. Threshold braking is an important skill, especially in cars that don’t have ABS. But if you focus too much on braking, you may inadvertently also do the following.

Slow the car too much
Separate braking from turning
Get to throttle later
Cause understeer as you fight your way out of the corner

Examine Leon’s traces and see if you can find these symptoms.

Hold more entry speed

So if over-braking isn’t the answer to going faster, surely it must be holding more entry speed. Let’s take a look at what that looks like. Load up Michael Smith67 (1:46.328).

Look at vertical line in the picture. This is positioned just after the apex of T5. The speed graph shows that this is his point of minimum speed. I call this the nadir of the corner. Note where Alex’s nadir is: earlier. Michael is trying to go fast by holding as much speed as possible. Unfortunately, this means he’s still fighting the steering wheel at the apex. Meanwhile, Alex’s wheel is nearly straight and as a consequence he’s on the gas much earlier than Michael.

Practice makes perfect… not

Now let’s take a look at Hiroshi Ueda (1:42.509). Hiroshi is faster than most of the drivers we’ve been looking at. That’s understandable because he’s been an iRacing subscriber for 7 years and has over 1500 races under his virtual harnesses. The fact that he’s 2.5 seconds behind Alex suggests that he still has fundamental misunderstandings of how to drive a car.

If you look at his brake pressure you’ll see that it isn’t too bad. He gets to maximum pressure quickly and it then tapers off. It’s not as tidy as Alex, but it doesn’t look like the source of the 2.5 seconds. Now look at the throttle trace. Hiroshi is late to the throttle in nearly every corner. Why? Because he’s trying to keep too much speed. He’s fighting understeer as he works to keep the car on track. Meanwhile, Alex is completely unwound and at full throttle. Why is Hiroshi still driving like this after 7 years and 1500 races? Because there’s more to training than the number of hours. You have to train the right way. Going back through the archives at iSpeed I looked at some laps of his from 2 years ago. He’s faster now, but not in the right way. Hiroshi has been perfecting a low yaw early apex style of driving.

Summary

If you’re a slow driver and you want to drop your lap times, you can improve them in a number of ways. Pedal-mashing a high power car is one way. Holding more speed in a low power car is another way. Practicing either of these techniques will lead to good lap times but not great ones. Sadly, this is where most drivers end up: perfecting dead-end solutions. There is better way, and it’s a heck of a lot more work.

The 8 stages of driver development

Novices seek power. Intermediates seek grip. Experts seek balance.

— Ian Korf

Yes, I just quoted myself. Well, if a blog is anything, it’s self-serving. Let’s talk in more detail about the typical progression from driving the engine to driving the suspension. But not without first taking a detour into tennis.

The following photo comes from a blog on Learning the Different Types of Serve. People who know tennis will laugh at this photo pretty quickly. Not only are the players in the receiving court in the wrong position, but the guy has absolutely no idea how to hold a racquet. This is as bad as the Thrashin’ poster a few weeks ago with the dude’s wrist guards on backwards.

Serving is a complex motion that takes a long time to learn how to hit properly. In the beginning, players use a forehand grip (like the photo above), swing in a circular arc from head to toe, and possibly use a wrist snap in an effort to get more power. At the end of the stroke, their racquet is pointed at the ground. If they follow through, they are in danger of hitting their shins. Examine the next photograph, which shows the follow through of a proper serve. What do you notice?

The racquet is in front of the body, nowhere near the shins. The elbow is nearly as high as the shoulder. A proper tennis serve starts by holding the racquet in a backhand grip. The racquet is swung up and out, not circularly down. The follow through sees the arm pronating as it extends. That might look like a wrist snap, but it’s a rotation at the elbow. The palm ends up facing away from the body, not down at the ground. It’s a complicated motion that feels unnatural to novice players.

Track driving also features some unnatural feelings in the beginning. But over time they start to feel ok, then good, then just how it’s done. Let’s talk about the typical stages a driver goes through. Well, in my experience anyway. It’s not always the same order, and there are probably some other steps along the way and afterward. I’d be interested in hearing opinions on that.

Stage 1: Speed Focused

People who don’t know shit about track driving are generally concerned with the performance of the engine. When random people hear you drive a car on a race track, what’s the first thing they ask you? “How fast do you go?” Driving fast in a straight line is sort of thrilling for a little while, and many of the novice students I see come and go with that in mind. Part of the interest in going fast is to experience the awesome engineering in sports cars today. Well, there’s even more to appreciate in how well they do the twisty bits.

Stage 2: Exit Focused

In the next stage, drivers know the racing line, but they take the phrase in slow out fast a little too seriously. They slow down to a crawl, tip-toe through the corner, and floor it at the exit. They think that because they went in slow and out fast that they cornered correctly. These drivers may exhibit heel-toe shifting, because they want to be in the correct gear, since they’re still concerned with maximizing power. But the technique is often lacking and they press the clutch in way too early and let the revs fall. It’s also typical at this stage to drive a mostly circular arc through the corner. This leaves the car mid track at the exit and then the driver steers out to the apron because their coach told them they were supposed to use the whole track. Most of the drivers I work with in the Hooked on Driving Novice group are at this stage.

Stage 3: Brake Focused

As drivers become more confident, they stop coasting into braking zones and learn to threshold brake. These drivers exhibit a point-n-shoot driving style where they drive hard all the way to the braking point, hit the brakes hard, corner mildly, and then hit the throttle hard. It’s a fun time blasting your car in and out of corners, even if you don’t do it optimally. And high performance cars can get around a track pretty quickly like this. Lots of HPDE regulars settle into this style of driving. When their lap time stagnate, they buy a faster car. Too bad, because they would improve more by learning how to drive a momentum line with a slower car.

Stage 4: Hooligan

Some, but not all drivers, go through a hooligan phase where they have become enamored with burning rubber. Let’s face it, drifting looks cool and feels amazing. Although it’s not the fastest way around the track, it’s fun and requires some skill with the throttle pedal. What the hooligans misunderstand is that rotation in the corner isn’t supposed to be initiated with the throttle. I don’t get to see many hooligans as students. I had one, who broke the mold a bit as she was a 60 year-old lady. While she smoked the hell out of her tires in the figure 8 drill, she was clumsy and slow on track.

Stage 5: Grip Focused

The next phase is characterized by mid-corner tire squeal. Grip junkies can drive a car pretty damn hard. They aren’t necessarily consistent, especially at setting their corner entry speed. But their fast laps are truly fast. These drivers tend to open up their steering in the second half of the corner to maximize their traction. Some may be very good at countersteering. Although rare, I like working with these students because they are confident in their car control skills, just not refined. Sometimes it takes just a few words to get them changing their driving style for the better. I think a lot of HPDE coaches are at this stage.

Stage 6: Entry Focused

Trail-braking is such an essential skill that I teach it very early. As in the first day. Hard on, soft off keeps the car settled. But advanced trail-braking is a really different skill whose goal is to optimize the corner entry by (a) setting the ideal speed (b) setting the ideal angle.

Every corner has an optimal speed. If you enter too fast or too slow, the exit will be ruined in one way or another. So one of the primary goals of the advanced driver is arriving at the nadir (the point of lowest speed) at precisely the correct speed. Trail-braking helps you sense your speed because the self-centering torque of the steering wheel gives you critical tactile feedback.

Every corner also has an optimal angle, and it’s farther down the track than most people expect. Getting the car rotated early requires oversteer and therefore requires countersteering. But just because you’re countersteering doesn’t mean you’re cornering properly. Hooligans can be pretty good at countersteering but they do it under acceleration. Trail-braking requires countersteering while braking.

Stage 7: Balance Focused

The next stage of development sees drivers trying to optimize traction everywhere on track. Everything is a compromise and identifying the optimal inputs is a continual experiment as the car, track, and environment change. Balanced-focused drivers are concerned with making every transition, be it speed, direction, or gear, as smooth as possible. So they are tuned into their suspension to optimize their contact patches. They drive the capabilities of the car, they don’t ask the car to drive to their ability.

Why is smooth so important? In mathematical terms, it’s because tire load is sub-linear with grip. In seat-of-the-pants terms, you can’t get back traction you lost. Paradoxically, some very smooth drivers don’t look smooth from the cockpit. Don’t watch their hands, watch the attitude of the vehicle. Is the suspension quiet or is it rocking?

Stage 8: Unfocused

Some drivers are so damn good that they don’t even think about driving. Their minds are capable of completely independent thought while driving a car at the limit. If they’re technically-minded, they’re analyzing the behavior of the car to improve it later. If they’re competition-minded they’re figuring out the strengths and weaknesses of the drivers around them. If they’re assholes, they’re messing with their opponents’ heads. (That was Ravenclaw, Gryffindor, and Slytherin by the way. Hufflepuff is still in the pits helping some poor dude fix a throttle cable).

Rev-thrashin: part 1 of 2

Check out this awesome 1980s movie poster.

I weep every time I see this poster, partly because I grew up in the 80s, a time of particularly embarrassing fashion. But now I also weep because I just learned that Pamela Gidley recently died. She’s probably most famous for “Twin Peaks: Fire Walk With Me” but I’ll always remember her as Cherry 2000. However, the real reason I’m bringing this ~~poster~~ poseur to your attention is that the wrist guards are on backwards. Wearing them like that would do more harm than good. Obviously nobody at the photo shoot had any idea about skateboarding. Why am I talking about skateboarding. Oh, I don’t know…

Whether you call it rev-matching, blip shifting, or heel-toe-shifting, this technique is often categorized as an advanced skill. I agree, but not because it’s difficult to do, but because it doesn’t have much effect on lap times. It only becomes really important when you’re searching for tenths of a second and not whole seconds. That said, driving enthusiasts love to display their rev-matching skill on the street or track. Like the Thrashin’ movie poster, sometimes they do it so wrong that it looks like wrist guards on backwards.

Let’s look at an idealized corner depicted as a rainbow of colors.

Red – Threshold braking zone. All brake no steering.
Orange – Initial trail-braking zone. Ideally, this zone is really small.
Yellow – Trail-braking zone. The car is rotating as the mixture of brake plus steering puts more weight/grip on the front of the car.
Green – Nadir. This is the point where the right foot is moving from brake to gas, and the point of minimum speed. Ideally, this zone is really small, but some corners do benefit from a little coasting.
Blue – Throttle zone. The position and angle of the car are controlled by a mixture of steering and throttle.
Violet – Straight. All throttle no steering.

At what point along this path should you downshift? Your perspective may be different from reality, so if you have some video of yourself driving, observe your shift points. Ask yourself “what are the consequences to the driveline and handling of the car?” Tune in next week for some discussion.

P.S. The image above is from my upcoming book, “In Slow Out Fast (and other lies of the race track)”. This long-awaited sequel (by me, not you) to “You Suck at Racing: a crash course for the novice driver” focuses on the intermediate driver. Due out this Summer and available from Amazon.

Dropping 20 seconds in a day

Last week the student I was coaching at Thunderhill dropped 20 seconds off his personal best in one day. I thought it would be fun to investigate how that happened from the perspective of the coach and the student. The statements in blue are from the student.

The student had some previous autocross experience and had been to a Thunderhill track day once before. So he wasn’t a complete novice. The car was more commuter than track weapon. It was quite comfy with heated seats, adjustable bolsters, and nearly silent exhaust. Here’s his description.

2009 E90 328i 6 speed manual with sport package. No modifications except stainless steel brake lines installed by previous owner. Street brake pads and PSS tires (the tires help me to drop 5 seconds). I replaced engine mounts before 2nd track day. (use OEM mounts).

At the start of the day, I asked him what he felt he was good at and what he needed work on. He said his driving line was pretty good but that he should shift to 4th gear sometimes. As it turns out with rookies, perspectives can be misaligned. His driving line wasn’t very good and there was nothing wrong with not using 4th gear. We kept up with the fastest cars in our group using 3rd gear only. But we’re getting ahead of ourselves here…

Once we got in the car and took a few laps, I could see that, in fact, he does not shift. There are two places on the track where one can downshift to 2nd and three or four where one could get to 4th gear. I made no attempt to fix this. Driving is difficult enough without shifting. I wish all my students would drive 3rd gear only. Less power in corners means you have to learn to drive a momentum line. And less speed on the straights is less wear on the car. I’d also much rather top out at 90 mph than 120 mph in a car I’m not driving. Another thing that didn’t need fixing was his hand positions. He anchored them at 9 and 3 and I never saw them come off. Excellent. I did remind him a few times to relax his grip a little. Thankfully, the most important thing, situational awareness, also needed no fixing. He knew where the cars were around him at all times.

So what did need fixing?

Braking was early, excessive, and abrupt
Lack of confidence in grip
Driving line was circular

The first thing we worked on was trail-braking. What? Isn’t that an advanced driving skill? What am I doing teaching this first? What about the line? FUCK THE LINE. The most important thing you can learn about track driving is how to apply the brake. Hard on, soft off. No, we didn’t work on rotating the car with the brakes. We simply changed the brake pattern from hard on, snap off, to hard on, soft off. This is how one creates smoothness on corner entry, and it’s the foundation for rotating the car with trail-braking (later).

The next thing we worked on was speed sensing. The reason he was braking so hard was that he had no idea how fast one could go into the corner. Self-preservation instincts aren’t bad you know. They keep you safe. But they can also get in your way. One reason to get coaching is to lean on the coach’s experience to increase your limits. He just needed someone to let him know it was safe. The drill we did may seem unusual. I told him he wasn’t allowed to use the brakes at all. He had to plan the corner far enough in advance so that he arrived there with the right speed. Without the brake pedal getting in the way, he drove the entries much faster. With each corner he gained confidence and was eventually going into T2 (a long carousel) at high speed with just a lift, letting his tires scrub off the excess speed.

Lots of people unknowingly drive a circular arc. How can you tell? If the wheel stays at the same position throughout the corner, it’s circular. Some corners can be done that way, but most benefit from a late apex line where the radius of the first half of the corner is much tighter than the second half. And by the way, the halfway point isn’t the apex. The apex is in the second half of the corner. I call the halfway point the nadir. Ross Bentley calls it the EOB (end of braking). In any case, the point where you start to increase the radius is before the apex.

We spent most of the day working on corner entries. As a result, my student’s entry and mid-corner speeds were so much higher than the others in the group that we kept up or passed many faster cars (M2, M3, M4, 911, Lambo) despite not shifting gears. Nobody went faster in T2 despite having stickier tires and aero. And I guaranty our T8 speed was 10 mph faster than anyone else. After the event I emailed the student to find out how he dropped 20 seconds. Blue text is him. Red text is additional editorial comments.

Q: What was the most challenging thing? Physically became tired after 6 sessions. All that sensory input is exhausting. But you get used to it and driving becomes less taxing.

Q: What was the scariest thing? Saw someone rolled his car on track. This was in the last session of the day. Wisely, my student said he wanted to have a less intense final session.

Q: Was there an ‘aha’ moment or was it very gradual? I think it was very gradual for me. Ian is a good instructor who can explain things clearly. Communication is a 2-way street, and not every student-coach pairing is ideal. We were both mathematically inclined, so we communicated like engineers.

Q: Where do you feel you made the most improvements? On to throttle earlier and understeering out of turns. To get on throttle earlier is not so simple. He had to change his whole approach to cornering to make that happen. his use of understeering isn’t quite right. What he’s doing is adding throttle at the traction limit. This means the radius of the turn increases to compensate. It’s a very mild form of understeer.

Q: What would you tell someone who was going to the track for the first or second time? You may not need to drive a powerful car on to the track at the beginning. A well maintained car can give you as much fun as a Lambo or M3.

Here are a few things that I learned from Ian:

No braking approach. At second run session, Ian asked me to run a lap without braking.or minimum braking. It helps me a lot but how? I don’t know how to describe it.
My line late apex, early apex, circle arc line. It turned out that some of my lines are just pure circle arc line. My steering input stays same through out my turn.
Gas out approach/understeering. I finally realized that how to use throttle to exit a turn. I will try to use this approach at my next autocross event. I alway thought that understeering is NO good until my 2nd track day.
Learn road/surface condition. It applies to rally racing a lot. At T3, T5, T9, pay attentions to elevation change and bank angle.

Here are a few turn-specific notes he made, some of which are pretty perceptive.

During my first track day, I wasn’t sure how fast I could enter T1. To be on safe side, I always braked too early during my first track day. I thought my line was fine but during my second track day, I have learned that my line was actually a smooth circle instead of late apex. At the very last session of my second track day, I began to realize that I could accelerate a lot earlier or during my T1 entry point. In this way, with lots of throttle, my 328i could naturally move to right side of the T1 exit. (using natural understeering)
T2 is relatively straightforward. I became more comfortable at higher speed to go around T2 at my second track day. In the afternoon session, I started to appreciate the power out approach to exit the turn. Again, using natural understeering of the car. From the entry point to the half of the turn, I gradually added more throttle to almost full throttle. I feel that my newly installed pilot super sport tires have more grip than my old RE050 run flat tires. That is another reason I could run faster at T2 at 65mph(2nd track day) vs 47mph(1st track day).
At my second track day, I started to realize that there is a slight up ramp at the entry of T3. So my get off brake point is at the crest of the ramp right before entry of T3. My entry line is too tight to the right. I could have move to the left in one car width to have a diagonal entry point. This line seems to be better. Compared to my first track day, my speed at turn 3 is 56mph vs 50mph(1st track day)
At 2nd track day, my car has gained more speed at T5. My initial braking point was at the top of the hill which makes my car slide a bit. At faster speed, Ian got scared and told me to brake early during uphill ramp and turn in earlier. It makes more sense because braking at uphill gives more traction to turn in.
At my second track day afternoon session, I felt more comfortable to brake late at T9. I think we could use the uphill ramp to slow down the car and turn in without losing traction. After the crest, it seems that other more powerful cars can accelerate towards T10 a lot faster than my 328i. This is one of the two places at Thunderhill east that powerful cars can make more difference in my opinion. The other one is the straight finish line.
At T10, I tried to trail braking. I used to brake late and turn in. After discussion with Ian, it seems that I could initiate the turn earlier and carry more speed. However, there were couple of times that my car became too close to the track edge during T10 exiting.
T14-15 seems to be my worst corner. I feel that I could carry more speed at T14. At the end of 2nd track day, I could accelerate earlier before T15. This helps me to reach higher speed at finish line. At my first track day, I slowed down too much. I had to accelerate my car from lower speed at straight line.

Oh yeah, about that car that rolled. It was a brand-new (2018) BMW. The driver had purchased HPDE insurance for the day. Yes, it sucks to wreck a car, but it would suck a lot more if you didn’t have insurance. If you’re taking an expensive car to the track, please get HPDE insurance. It costs about the same as a track day. Driver was fine btw.

Backing up the corner

When you first start driving on track, the most common phrase you hear is in slow out fast. That’s generally a good idea for safety and lap times. Some drivers think they can go faster by holding more speed, but if they have to lift at the exit, it’s an overall loss. Another misconception is that one can reduce lap times by braking harder and later. This is only true for the novice who has no confidence in braking.

When people talk about advanced driving techniques, the most common topics are heel-toe shifting, trail-braking, and left-foot braking. All of these are physical things one does. All can improve lap times. They are considered advanced because they take some physical coordination and practice to apply. Doing them badly can get you into trouble. But the upside is lower lap times and a greater feel for the car. Myself, I trail-brake almost every corner and heel-toe shift every time. I don’t left-foot brake because I haven’t practiced it enough.

What about advanced techniques on the mental side? That’s the topic today. I want to talk about backing up the corner. You may have heard that phrase before and wondered what that was about. It means getting the braking, turning, shifting, and throttling done earlier in the corner. This technique is especially important for low powered FWD cars like mine.

There are two things to consider when backing up the corner, the mental discipline to do it, and the physical ability to execute it. Let’s talk about the mental side first. You must first recognize the nadir of the corner. As far as I know, that’s a term I made up. If every corner has an apex (top) it should also have a nadir (bottom).

The nadir of a corner is the point of lowest speed.

Where exactly is the lowest speed in the corner? Usually at the place where your cornering G-forces are highest. If you think back to your traction circle, the traction of your tires can be used for braking, cornering, accelerating, or some mixture. So max cornering is not under braking or accelerating, but strict cornering. If you’re trail-braking into a corner, which you should be doing most of the time, the maximum cornering should be at the time you’re taking your foot off the brake and moving it to the throttle (assuming you right-foot brake). If you want to back up the corner, you need to move the nadir earlier on the racing line.

That seems simple enough, right? Just do everything a little earlier. Well, it’s not that easy. If you want to be on the typical racing line, you’ll need to get the car pointed straight earlier. Simply braking and turning earlier will see you hitting an early apex and running out of track at the exit. You have to rotate the car early in the corner without losing speed. That means you have to slide the rear of the car out, countersteer to keep it on line, and add throttle before you’re fully straight.

Let’s take a look at what that looks like in telemetry. You’ll probably want to click on this image to see it full size as it’s pretty large. The track is Laguna Seca. The panels are speed, RPM, throttle, and time going top to bottom.

Point 1 is turn 1. The blue driver has shifted to 4th gear here. That’s why there is a 4 in the RPM panel. The time panel (bottom) shows there isn’t much difference switching to 4th briefly vs. banging off the rev limiter. When I saw this, I drove in 4th for my second stint as it’s nicer to the engine.

Point 2 is turn 2. The two drivers have very different approaches to this. The red driver does a double apex while the blue does a single. As you can see from the time graph, the double apex loses a bit of time and then makes up for it. Double vs single apex isn’t really the conversation today. Instead, I want to focus on the three 90° corners that follow. As you can see from the time panel, the red car gains a lot of time here.

Looking at the speed graph (top panel) it looks like the red line is shifted left compared to the blue line. This is especially apparent at points A-D. This isn’t a GPS alignment issue. It’s the red driver backing up the corners. Unfortunately, I don’t have a brake sensor on the CAN bus, but one can infer that the red driver must be off the brakes much sooner than the blue. He doesn’t necessarily get to full throttle sooner than the blue driver, and in some cases later, but he’s applying the throttle sooner. The points marked W indicate wheel spin in the RPM graph. The red driver is clearly trying to maximize throttle and steering because he’s at the limit of both (sadly, the car has an open differential).

How important is backing up the corner? Like other advanced techniques, it’s something that can drop lap times when done properly and a bit hazardous when not. It’s fun to work on. Like other advanced techniques, I suggest working it out on a simulator rather than a track session, and never on the street.

Bad driving tip #5: always drive the school line

In 1971, Alan Johnson published “Driving in Competition”. In that seminal work, he codified the three types of corners: Type I (leading onto a straight, Type II (after a straight), and Type III (connects other turns). The usual HPDE instruction focuses on the Type I corner. Here’s a charming picture from his book that uses Matchbox cars instead of an illustration.

The thing I find most interesting is point 3, which he calls the “balancing point”. Ross Bentley calls this the “end-of-braking”. In my book, I call it the “nadir” because if every corner has a top (apex) then every corner should have a bottom (nadir). Regardless of the terminology, this is the slowest point in the corner, and it occurs before the apex (point 4). Also note that it is described as the transition from braking to accelerating. The term trail-braking probably hadn’t been in use in 1971, but the fact that brakes are released during the corner entry means that trail-braking was part of Alan Johnson’s cornering technique, and probably many other drivers of the time. Mark Donohue is given a lot of credit for talking about brake release, but “The Unfair Advantage” was published 3 years later in 1974. I would guess that drivers were trail-braking from the beginning, because it’s the fast way through a corner.

In the HPDE world, students are taught the geometry of the Type I corner but not how to trail-brake, which is considered and advanced skill. I don’t want to get into teaching philosophy or this post will stray even further from the original intent. Let me just say that I completely disagree. So, back to the typical HPDE corner: start at the outside of the track, brake in a straight line, turn in to a late apex, track out to the outside. Oh, and if a faster car comes along, stay on the line and let them work around you. That may be fine for HPDE days, but robotically following this advice on a race track is folly. Here’s a trio of videos that will hopefully send that message home.

To be clear, these drivers aren’t at fault for the incident. They didn’t do the hitting, they got hit. But let’s say that the result is that the car is done for the weekend. It was supposed to be a weekend of racing with friends and it turned into a weekend of frustration and repair bills. You know what would have been better than following the line? Realizing that when you set up on the outside of the track, the shit-for-brains behind you sees that as an invitation to dive-bomb you.

Chalk Talk: the nadir

When coaches talk about driving techniques in the classroom, the conversation generally begins with the racing line. This is broken down into 3 component parts: turn in, apex, and track out. I find that students really latch onto the apex as the most important part of the corner. It might be the most obvious part of a corner, especially when coaches stick an orange cone on the track, but the apex is not the most important point. The apex impression apparently stays with them a long time, because even advanced drivers have a tendency to focus on the first part of a corner and have no idea what the second half of a corner is supposed to feel like. That’s the subject of this Chalk Talk.

A constant radius corner is not driven with a constant radius!

One way to think about a simple 90° corner is that it has 2 parts: a small radius in the beginning and a large radius at the end. The only way to get from a small radius to a large radius is to UNWIND THE WHEEL. That is, if you’re in a right turn, you have to steer back to the left when you want to increase your speed. When should this happen? No, it’s not the apex.

In the diagram below, the green arrows labeled “1” and “2” have different radii. Curve 2 has a radius about twice as large. The break between the arrows is called the nadir of the corner. It is the point of lowest speed on the racing line. It’s the point where you transfer from brake to throttle and the point at which you start unwinding the wheel. It is the most important part of the corner. Unfortunately, it’s not so easily labeled because you can’t stick a cone on it. Yeah, racing is hard.

The red line traces a constant radius. Lots of advanced drivers are actually on this line even if they disguise it. They corner at constant speed and then add throttle after the apex. They may even obediently steer out to the edge of the track in the belief that they are on the racing line… they are not. The racing line isn’t just where the car goes, but also how the car goes.