It’s raining lies: part 3

Are we finally going to end the “It’s raining lies” series? Yes, yes we are.

Screamer vs. Big Bang

Before we begin, let’s take a brief tour through a seemingly unrelated topic in the motorcycle world: big bang vs. screamer engines. A big bang engine is one where all the pistons fire at the same time (or very close together). A screamer engine spaces out the ignition pulses as much as possible. From an engineering standpoint, it shouldn’t matter much, but the screamer is a little more powerful because it vibrates less. However, from the rider’s perspective, the firing order makes a big difference. Bikes with screamer engines tend to send their riders off the high side. How the heck does piston firing order affect the rider?

In a big bang configuration, the tire gets a big kick in the ass every 720 degrees of rotation. But it also gets a long rest period before the next kick. In a screamer, the tire is getting kicked every 180 degrees (assuming a 4 cylinder motor). Apparently the downtime in the big bang configuration gives the rider more time to sense the level of grip and adjust accordingly. In a word, the big bang gives compliance.

Softer Suspension

Before getting to the objective stuff, let’s be subjective and talk about how driving in the rain makes us feel.

  • How does a car feel on a wet track? Unpredictable.
  • What are we afraid of? Crashing the car.
  • How does that make you drive? With a large margin for error.

It’s fine if you don’t want to admit it, but I will. Racing in the rain scares me a little. The tires don’t make the same sound. The steering wheel doesn’t have the same tug. The throttle pedal feels like an on/off switch. When things go wrong, it seems they go wrong suddenly and without warning. That said, I actually really like driving in the rain. The extra stress makes it extra fun.

The reason why we soften the suspension in the rain is to slow down weight transfer. A car with a stiff suspension is sort of like a bike with screamer engine. It is theoretically the faster configuration. Stiff suspension leads to less weight transfer which leads to more grip. Lap times should be lower with stiffer suspensions. This is true regardless of the wetness of the track. However, there is also the human element to consider. The weight transfer in a car with stiff suspension is much more abrupt than a car with soft suspension. A human driver needs time to make adjustments to grip, and a suspension that is too stiff does not give the driver enough time to sense and react to changes in traction. So what are the physics underlying this phenomenon?

Basics of Friction

The coefficient of friction (CoF, or µ), is a ratio of the downward force of gravity divided by the frictional force. In the old days it was thought that you couldn’t get more than 1G of frictional force, and that the CoF was limited to 1.0 (this was due to blindly following Coulomb’s Law, which doesn’t really apply to viscoelastic compounds like rubber). Racing tires can generate over 1.0G, and much more with downforce.

Tire grip comes from the interaction of the rubber with the road. These interactions occur at a variety of scales from invisible molecules to stuff the size of tires themselves.

There are two separate properties that account for tire friction: adhesion and hysteresis.

  • Adhesion – Microscopic contacts between the tire and surface. This is also called mechanical keying.
  • Hysteresis – Macroscopic contacts that deform the rubber. The energy used to deform the rubber creates grip.

Adhesion and hysteresis sometimes compete with each other. As a tire gets hotter, it increases its adhesive properties but loses hysteresis. Adhesion likes a smooth surface while hysteresis likes a rough surface. The optimal operating temperature of a tire is therefore a complex function that depends on the properties of the rubber and both the microscopic and macroscopic texture of the surface.

To simplify matters, one usually talks about the optimal friction and relates this as the CoF. The CoF of a steel plate doesn’t change, so it’s a convenient simplification to think of the CoF as a single value. But the CoF of rubber actually changes and therefore can take a variety of values depending on the situation.

Load is sub-linear

It is well known that friction increases with load. But the grip of tires with respect to load is sub-linear. That is, if you increase the load on a tire by 2-fold, it gives less than 2-fold more grip. As a result, all things being equal, a lighter car will have higher corner speeds than a heavier car. One reason for this may be that there are physical limits to hysteresis. Colloquially, once a tire has been sufficiently mashed into a surface, it can’t be mashed any further.

Optimal slip

Whenever a tire is asked to do anything other than roll freely, it will have some slip. We’re not talking about slip angle here. Imagine braking instead. There is a continuum from freely rolling to fully locked. At 0% slip, the tire has a CoF of nearly zero (there is some rolling resistance). At 100% slip the tire is locked into some amount of grip, but that grip isn’t optimal. The peak friction occurs at a relatively mild amount of slip.

Speed affects grip

A tire that is moving across a surface a high speed cannot press into the surface as well as it can at low speed. This means that tires have less grip at higher speeds.

The optimal slip ratio also changes with speed. The faster you go, the lower the optimal slip ratio. We often think of the CoF as a fixed value, but it isn’t. Given that you have less grip and a lower optimal slip ratio, it’s not just self-preservation that should make you drive more reservedly at high speed.

Water affects grip

Water affects grip by getting between the tire and both the microtexture and macrotexture. It can therefore reduce adhesion and hysteresis. Grooves or other kinds of texture in both tire and surface can help evacuate water.

The amount of water on the surface is really critical. If the water film is thin, slick tires grip better than grooved tires. But if there is too much water to be evacuated by the macrotexture, the grip of a slick tire becomes terrible.

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Hydroplaning

Under certain conditions, a tire may hydroplane. In the figure below, the dashed line represents a constant CoF while the solid line represents a variable CoF. The actual stopping distances are given in the inset, which match the variable CoF. The take-home message here is that the grip of wet tires depends on speed. Presumably that’s because of hydroplaning.

Summary

Water interferes with microtexture and macrotexture. It can also cause hydroplaning. As a result, the coefficient of friction of a wet tire is anything but constant. A dry tire is easy to drive because it has a very broad band of traction in which the CoF doesn’t change much. You can over-drive the hell out of it and it will still perform okay. This is not true of a wet tire, whose CoF depends on the amount of water, the grooves in the tire, and the speed of the tire. Push a wet tire too far and suddenly, you’re spinning.

The reason why one softens the suspension in the rain is because the coefficient of friction of a wet tire is variable and volatile. By slowing down weight transfer, we give the driver time to adapt to an unpredictable CoF.

Let’s finish off this series of posts with a few key points about driving in the rain.

  • The reason why traction loss feels sudden in the rain is because it actually is. So be careful out there.
  • You may not notice much difference in braking in wet vs. dry but it is substantial.
  • Be extra careful at higher speeds where hysteresis and hydroplaning effects seek to rob you of traction.
  • When applying throttle, make sure you do so gradually because once a tire starts spinning, the loss of traction is catastrophic.
  • Grip in corners is pretty good as long as you don’t upset the traction with too much throttle, too much brake, or jerky inputs.
  • The more water there is, the bigger the tire grooves need to be. If you don’t have grooved tires, pump them up so they have a crowned profile. If you do have grooves, decrease tire pressure.
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It’s raining lies: part 2

Where Were We Anyway?

If you recall, three weeks ago I did the following:

  • Called Ross Bentley a liar
  • Committed career suicide (see above)
  • Claimed that wet tires have 9/10 braking grip, 3/4 cornering grip, and 1/4 accelerating grip
  • Showed telemetry traces that support said claims
  • Calculated the G-forces in a Car and Driver tire test and found that braking loses much more grip than cornering
  • Lied that I would resolve the mystery the following week

In my defense, the series is called “it’s raining lies”. So let’s get back to our watery tale and see how this story resolves.

The Braking Mystery

Why do I feel like the car brakes equally well in the wet and dry when the data shows dry grip is so much better? I believe this is pretty simple. When the track is dry, we aren’t braking as hard as we could. Thinking back a couple weeks, let’s be Paul Gerrard and see if we can get to the root cause. It’s certainly not physics holding us back. Do we fear excessive Gs? Not exactly, what we fear is flat-spotting a tire. Our team races on a small budget and tires are the largest expense. Flat-spotting a tire is a huge no-no. Everyone on the team is acutely aware of that. Because we are afraid of destroying tires, we don’t brake as hard as we could.

If the car had ABS, we would probably brake harder in general because ABS prevents flat-spotting. Braking is so much easier with ABS: just mash the pedal and let the computer take over. Surely the Car and Driver tests were done with an ABS-equipped car. It makes the testing procedure much more repeatable if you minimize the human element. And why not use ABS? ABS systems probably brake better than you do. Nannies in cars are getting better and better. For most drivers, having various nannies on is faster and safer than driving fully analog.

Have you ever noticed that WWII fighter planes have wings that slope up and modern fighter jets have wings that are straight out or even slope down?

A dihedral wing, one where the wing tips are higher than roots, is inherently stable. But an anhedral wing is not. Build a paper airplane with an anhedral wing and it will flip over and fly as a dihedral. It’s very difficult to fly a plane with an anhedral wing angle. Human pilots can’t do it. There isn’t enough compliance. They need a fly by wire system that makes hundreds of tiny adjustments per second to keep the plane flying level. So why have anhedral wings? Because the inherent instability makes the plane want to turn, making it more agile. Could cars be tuned the same way, so twitchy that no human could drive one without nannies? Surely. The evolution of performance driving will someday see computers outperforming humans at every level of the sport. When that happens we’ll become even better drivers as we learn from computers whose AI can explore the parameter space more deeply than we can.

Let’s return from my crystal ball and recap: we under-brake in the dry because we are afraid of flat-spotting our tires. I’m happy to make this compromise for 3 reasons.

  1. A flat-spotted tire is a waste of money
  2. A tire that fails on track could cause a crash
  3. Time spent fixing things in the pits is time not lapping

Brake Bias

When tuning a car for driving in the rain, one parameter that is often changed is the brake bias. Since there is less overall weight transfer on a wet track, there’s less weight on the front wheels. With more weight on the rears, more braking is possible out back. In my old E30, I installed a manually operated prop valve. To adjust the bias, you lift the hood and twist a dial. Real race cars put the bias adjuster in the cockpit so the driver can make changes mid-race. Until you’ve tried an adjustable prop valve, you probably haven’t experienced how much it changes the handling of your car on corner entries. If you don’t trail-brake, you won’t notice much at all, but if you do, it’s basically an oversteer tuning dial. Want more oversteer? Add more rear brake. It’s really that simple. If you don’t have a prop valve, you can still tune your brake bias with different pad compounds, but the resolution is much lower.

The main problem with adjustable bias is forgetting to dial it back when the track dries. This can lead to disaster. The rears will lock up first, causing the back of the car to wander when braking in a straight line. This can even happen on a wet track if the brakes are horribly out of proportion. Early ABS systems were kind of crappy and just kept the rears from locking up. If you’ve got such a system and the ABS computer is defeated or the fuse is blown, the bias is dangerously out of whack. Watch below as the fast POV is destroyed by a slow BMW that loses control while braking in a straight line.

How did the BMW team not realize their brakes were so horrible? Probably because they usually brake very gently. The rain moved the lock-up G-force threshold lower and the driver found himself in unfamiliar territory. How do you mitigate this? That’s a very good question. On the one hand, you can tune the brakes appropriately with a prop valve, pad compounds, or ABS. That fixes the problem with the car. But there’s another problem, which is how to fix the driver. Should the car be good enough that the driver doesn’t matter? Or is it the responsibility of a driver to work around problems with the vehicle. Probably a little of both don’t you think?

So how do you get practice driving a car with horrible brake bias? How do you get experience with locked up rear tires? If you want to train yourself for disasters, you have to put yourself in disastrous situations… without wrecking other peoples’ property, your car, or your body. The answer, which you can guess if follow this blog, is simulation. Not every car has adjustable bias even in a sim. Find one that does and then experiment with brake bias. Once you experience how useful and fun it is to tune your corner entry oversteer, you may want to install a prop valve in your race car. It takes all of 30 minutes and costs less than $100.

There’s still more to come in the “it’s raining lies” series. We still haven’t discussed why you soften the suspension in the rain. Check back next week for the resolution (or possibly more lies).

Pineview Run, Optimum Drive, and S.Drives

Emergency. We interrupt our series in progress for an important and timely message on performance driving. This guest post comes from my twin brother Mario. Incidentally, if you have content you want to contribute to YSAR, I’d love to post it.

This last Sunday, Pineview Run held its first annual Pineview Challenge Cup, a time trial “race” of sorts. After an initial practice and qualifying session, you got three runs. Each run consisted of a warm up lap, and three timed laps. Trophies and $500 membership vouchers awarded for fastest times and most consistent laps.

For sure my 1.6 Miata on 195 S.Drives were not in contention for fastest laps. Here’s me lining up behind a McLaren 570. There were other fast cars: a Viper, Lotus Exige, M3, 911, etc., and all of them were on wider and stickier tires.

You’ll notice the RumbleStrip lap timer in the photo. Both of us absolutely love this thing. It’s the single best car thing I’ve ever purchased.

So I wasn’t going to be fastest, but I thought I had a shot at putting in the most consistent laps. Until a funny thing happened: I started driving better and better. I’ve been listening to the audio book Optimum Drive, and through some coincidence I had a moment of what the author calls driving greatness. Or what others have called being “in the zone”. In my terms, I started driving the Miata like a go-kart.

And that’s a good thing because I’m decent in a go-kart. Maybe it’s the lower speeds or simpler interface, but I can “zero steer” a kart and eke out more performance than most. In fact, after trouncing too many friends, Ian had a standing offer to pay for anyone’s track time if they beat me. He didn’t lose any money, but I also never translated that kart skill to car driving.

At least not until the Pineview Challenge Cup. Something clicked and I kept getting faster and faster. I enjoyed this so much that I stopped trying to put in consistent laps, and just explored the space, going faster, with less effort, lap after lap.

The less effort part was interesting. On corner entry I’d let off the throttle to shift the weight forward, turn the wheel slightly to tip the nose in, scrub off speed with the sides of my tires, and let the chassis come around on its own. Then I’d get on the gas and spin the rears to finish turning the back around. In all, I did very little steering with the wheel, and most of it with weight balance and throttle control. Some of you reading this might be good at that already, but I’d only done that in karts.

In three short sessions I knocked almost 3 seconds off my time, which is pretty incredible. To put this in perspective, the first time Ian and I went to Pineview, my best time was a 1:27 flat and Ian did a 26.5. I only did 5 laps total that day, but I thought I was doing OK. However, this time I put down an early 24.5, and in the last session I saw a 23.0 in disbelief. But my final lap was a 1:21.7! The kart nirvana I’d experienced finally made its way into my driving game. Man that was fun.

Now I’ve gone on talking about go-karts and Pineview at the same time, and I’ll never do that again. Anyone who says Pineview Run is a big go-kart track is just plain wrong. I’ve been on big go-kart tracks, like Dixon, Wenatchee, Stockton, etc, and Pineview simply isn’t one. There’s a lot of elevation and I think anything but a shifter kart would chuff annoyingly up the hills.  

Neither is Pineview a short race track. I raced Thompson last year, and did a HPDE at Waterford Hills this year, and while they have similar lap times to Pineview Run, they are meant for racing, with long straights and not many compromise corners. Comparatively, those tracks are tame. Boring, even.

Pineview Run run is a workout. It’s a rollercoaster. It’s a training and skills track. A test track. Pineview Run is also a great equalizer. The top cars on this day were a very modified BRZ and a M3, both driven extremely well. But there were a lot of fast cars, all of them so different, it really came down to the driver.

Well, ahem, unless you’re in a stock-ish Miata on 195 Yokohama S.Drives. At 300 treadwear and 10/32″ tread, they aren’t designed for the track. However, they are perfectly matched to my Miata’s 106 whp, and while I would have gone faster on stickier rubber, I wouldn’t have had as much fun. I ordered the S.Drives online at Walmart, and with free shipping and mounting, I was out the door for $200 for all four tires. Hard to beat that on a smiles-per-dollar ratio.

One final word about Pineview Run that Ian didn’t mention in his initial review, which is that it’s not just a car track. Pineview Run is also a shooting, hunting, ATV, snowmobile, horseback riding, and family-oriented outdoor country club. I’d never heard of a country club without a golf course or tennis court, but there you have it. And while I’m not into horses (yet), the rest of it was designed for people exactly like me. It’s an hour drive away on scenic back roads. Of course I joined.

We now return you to our previously scheduled programming (check back next week where we pick up the “It’s raining lies” series).

Book Review: Optimum Drive

Emergency, we interrupt the “It’s raining lies” series for an important service announcement. I just read a really great book.

Amazon had suggested this book to me several times. I was initially turned off by the cover, which looks like it came from a Tron movie poster. The title, : “Optimum Drive: The Road Map to Driving Greatness”, sounds a bit too much like an advertisement. Looking beyond the cover, we get to these summary sentences.

  • Optimum Drive is the complete step-by-step guide to maximizing human performance in any endeavor you choose to conquer
  • Optimum Drive is a motivational book that uses top level race car driving as a metaphor for peak performance.

Is this or is this not a book on driving? If it’s a book on driving, I’m interested. Self-help? Not so much. That said, “The Inner Game of Tennis”, by Timmothy Gallwey, has become a must-read in performance psychology. On the surface, it sounds like Optimum is trying to be the auto racing equivalent. The Inner Game is fantastic book, but I don’t recall there was that much Tennis. It’s not going to teach how to hit a topspin second serve, for example, which is the most crucial stroke in the game.

So let’s turn a few pages to see what’s inside Optimum Drive. I love audiobooks. I listen to them while working out, doing chores around the house, working on the racecars, and commuting. I even had this crazy idea of doing a Lemons theme with the Yaris (it has a complete sound system) where racers listen to an audiobook while driving and then give a quick synopsis while the next driver was getting in. Anyway, I didn’t actually turn any pages of Optimum Drive, but rather listened to it. As audiobooks go, it’s not very long: 3.5 hours. At first I didn’t love the narrator, but he grew on me and by the end I thought he was a great match for the content.

So is Optimum Drive another Inner Game? Yes and no. Yes, it is another performance psychology book that talks about flow psychology. That’s the modern term for getting in the zone. But overlap isn’t necessarily a bad thing. Even if the content was largely the same, it’s often very useful to have domain-specific books because the examples are more relevant. I see this all the time when teaching Biology students how to program. It’s much harder to learn fundamental principles of computer science when the exercises are things you don’t care about. But let’s be clear here, Optimum Drive is more than just a flow psychology book, it’s a damn good driving book. It teaches you the topspin second serve of driving. Will it transcend autosport and become as important as The Inner Game? I suppose it could, but tennis is more approachable. Anyone can pick up a tennis racquet but not everyone gets to drive a racecar. Should you get it? Absolutely. Here’s the brief 5-star review I wrote on Amazon.

I have a pretty large library of racing books. I’ve even written one of my own called “You Suck at Racing: a crash course for the novice driver”. I’d be flattered if you picked up my book but this book is better than mine. Read it, unlearn your bad habits and start from the root cause. This applies to all things, but very much so to driving where there’s so much misinformation and years of coping mechanisms.

Let’s look at one very specific example of the author’s way of thinking. Suppose you’re coaching a driver who is looking no farther down the track than the hood of his car. Saying “eyes up” or “look farther down the track” doesn’t really help the driver. The problem isn’t where his vision is. It’s that he is so concerned with what the car is doing this instant that he can’t plan for the future. The root cause is that he doesn’t have the car control skills to let his subconscious drive. The fix in this specific case is to slow down so the driver has more time. In order to solve problems, you need to get to the root of the problem. If you don’t, you’ll just lay some coping mechanisms on top that will prevent you from actually improving. And then later when you want to get better, you’ll have to break down these walls, which is a waste of time and will see you getting worse before getting better.

There are similarities between Paul Gerrard’s Optimum Drive and Carroll Smiths Drive to Win. They both have a bluntly honest writing style. However Gerrard would never say “other sports beckon”. He feels like anyone can attain greatness. Personally, I don’t need to be great and I have no aspirations of racing professionally. As a hobby racer, I don’t need to be an A+ driver. I tell my son that the best grade to get is A-. Above that you have diminishing returns that prevent you from learning more stuff. Why get an A+ in one class when with the same effort you can get an A- in two? Anyway, the parts of Optimum Drive that are out of my direct interests were still really fun to listen to. It’s great hearing what it’s like in the pro ranks even though I’ll never be there.

So what is the topspin second serve of driving? He calls it zerosteer. The driver who turns less wins. How can you get around a racetrack using less steering than the other guy? By driving with the correct amount of yaw. You can’t ask your front tires to do all the work because racing really comes down to tire management. Yes, you can progress up the tennis ladder hitting flat serves. But if your second serve is a patty cake, it puts a lot of stress on your return game. So you focus on your ground strokes because you like them more and they win you more games. That’s basically where B level tennis ends. Once in the A group, you have to win your serve and pressure your opponent’s.

Fucking tennis digressions… back to driving. Until you have the confidence to let your muscle memory drive a sliding car, you will enter corners too slow and with too little yaw. The entry determines everything about a corner. Unfortunately, most drivers have coping mechanisms between themselves and driving with enough yaw. Getting the car to step out a little isn’t something you do with the throttle. That’s too late. It has to be under braking. Zerosteer starts with trail-braking. I’ve talked a lot about trail-braking on this blog. I believe it’s the single most important skill in racing. It’s so nice to have that opinion validated.

Gerrard also talks about how to set up a car. Every tuning adjustment is a compromise. Making a car faster in one corner may make it slower in another. The job of the driver is to enjoy the corners where the car is set up perfectly and to earn his paycheck where it’s not. The setup used for qualifying is not the same as racing. In qualifying and time trials you are looking for the fastest single lap. But racing requires the driver to make constant changes throughout the race, and it’s the average lap time that matters more than the best. The word he uses to describe this is compliance. A setup that makes a car mathematically ideal may not work in practice because there is too little compliance for the human operator to work with. The struggle between engineers and drivers is finding the proper compliance.

If I have one criticism of Optimum Drive it’s that Gerrard only briefly talks about the importance of simulation training. At the very end he mentions that the top drivers spend more time in simulation than in real cars. Skid pads are his favorite tool for beginners. I also love them. But a sim rig is a lot more convenient, and in my experience it’s 90% as good as the real thing. If you have a chance to get on a skid pad, do it! Whatever your training plan is, you have to put in the hours. This is what he calls process. One reason I don’t like autocross is that there isn’t enough time spent driving. It can be a great reward for training, but it’s not training unless you can do it for hours upon hours. Musicians practice scales endlessly. Why should driving be any different? What you do on the street has almost zero overlap with what you do on track, so street hours don’t count. There are no shortcuts in the process. You have to put in the hours. Sometimes it may feel like Hell. You know what the trick is when going through Hell? Don’t stop, keep going.

After posting this, the author contacted me and told me that the ‘Tron’ car on the cover was his actual car, which took 2nd place at Pike’s Peak in the unlimited class. It’s unfortunately illegal to run anywhere else. I find it both humorous and humbling that I have written a review of his book and that he has talked to me about his car. More on the car: 7000 lbs of downforce at 12,000 ft, 5G cornering and braking, and 1.8G accelerating in 4th gear. The reason it looks like a spaceship is because it actually is one.

It’s raining lies: part 1

This week I attended a Ross Bentley webinar titled “The Art and Science of Racing in the Rain”. He runs webinars several times per year with a cost somewhere in the $50-100 range. Is it worth it? Yes, I think it is. If you’re serious about racing and improving your lap times, $59 is one of the cheaper expenditures you’ll have. Looking back, I’ve attended a bunch of his webinars: Speed Secrets, Tires, Drive Faster, Reading Your Car, Chalk Talk, and now Rain. That may be all of them. I’ll be the first to admit it, I’m a huge Ross Bentley admirer. But I’m also here to tell you he lies. OK, so that’s maybe too strong a statement. It would be more accurate to say his theory is sometimes incorrect. But this is YSAR and we write provocative shit here, so yeah, Ross Bentley is a goddamn liar.

Before some other Ross Bentley fanboi punches me in the face, let me explain (yes, I said other and I’m a little worried about hitting myself in the face as I write this). I don’t dispute Ross’ advice on driving in the rain. I’m going to do exactly what he says. What exactly did he say? Well, you have attend the webinar for that. I’m not about to pirate his content. But I will reference the parts that need critique.

In the rain, soften the suspension to decrease weight transfer.

— Ross Bentley

Softening the suspension does not decrease weight transfer. The more the vehicle pitches to the side, the more weight is transferred because the center of gravity moves more. One of the attendees wrote the equation for that in the chat box and it stopped all chat for a while. Nobody wrote “Ross, you’re full of shit” because we all respect Ross too much. But let’s be clear, softer means more weight transfer, not less. It is true that in the rain there is less weight transfer compared to dry, but that’s because the corner speeds are lower, not because the suspension is softer. So why, I ask you, should one ever soften the suspension? You’ll have to wait for that answer…

In the rain, lateral grip is affected more than longitudinal grip.

— Ross Bentley

This is not my experience. I find that braking works nearly as well in the wet as the dry. I use pretty much the same braking markers. Now it’s true that my straight speed is slightly lower in the rain, and pick up a later apex, but the grip is still darn good. Don’t take my word for it, or anyone’s word for it. Look at the data. In the image below, the blue line is dry and the black line is wet. The downward slope of the lines in the braking zones are nearly identical. The longitudinal G-forces in the 2nd panel show that peak Gs are similar, as you would expect.

Have you ever stepped on the throttle a little too eagerly in the rain? The car spins around without giving any warning. The grip under braking and accelerating are totally different in the rain. Note that this is from my experience driving high performance street tires not F1 racing tires. Since I’ll bet that you’re racing on tires sort of like mine, I think the difference between braking and accelerating grip is a very important distinction. My experience with corner grip is that it’s not as bad as you might think. The graph above backs that up. If I was going to put some subjective numbers on comparative grip levels in wet vs dry, I’d say braking has 9/10 grip, cornering is 3/4, and accelerating is 1/4. Although Ross didn’t put such numbers on these, he ranks them as braking > accelerating > cornering. So who is right? Turns out we’re both wrong.

Back in 2012, Car and Driver did a really nice comparison of 9 performance tires. For example, on the Bridgestone tire, the skid pad grip was 0.89G in the dry and 0.83G in the wet. That doesn’t sound like a very large change in grip level. They also reported 50-0 mph braking distance as 80 feet dry and 101 feet wet. Putting those distances in terms of Gs, that’s 1.04G dry and 0.83 wet. There are actually two lies we need to debunk here. The first one is that cornering grip is more adversely affected than braking. It isn’t. In terms of Gs, 0.06 is smaller than 0.21 by a metric shitload. To put this in terms that you might appreciate more, you can go 75.7 mph around a 200 ft radius circle at 0.89G. At 0.95G (plus 0.06) you get 78.2 mph. Racers would throw loved ones under a us for a 2.5 mph corner speed advantage. At 1.2G (plus 0.21) speed is 87.9 mph. I don’t think I have the macabre imagination required to describe what a racer would do to get a 12 mph advantage.

WHAT THE FUCK IS GOING ON HERE? This doesn’t mesh at all with my driving experience, the data above, or Ross’ instruction. Corner grip is less affected than braking? It’s true. It’s right there in the numbers. So why do we feel like it is less? And why do the telemetry traces tell a different story? Sorry, but you’ll have to check back next week for those answers.

What’s the other lie? It concerns the friction circle. The way the friction circle is explained, your tires have a certain amount of grip and you can divvy that up between lateral and longitudinal axes. So you could go 50/50 or 90/10 or 100/0. But it’s not symmetric, and therefore not a circle. Tires actually have more grip under braking than cornering. In the example above, 1.04G braking and 0.89 cornering. Circle shmircle. What’s one more drop in a bucket of lies?

Check back if you want to see how this mystery resolves…

Power, grip, and aero in theory

Six months ago I did some simulator tests where I used Assetto Corsa to answer questions about the relative contributions of power, grip, and drag. I wanted to follow that up a little with something a bit more rigorous. So I took my driving inconsistencies out of the equation and had the AI drive the car. I did a bunch of experiments on a lazy Sunday using the original rFactor. That was fun and informative, but I’m not reporting on that today because I decided to write a program that simulates a car driving around a track. Why? Well, honestly it’s because I wanted to implement the various equations myself. Most of the math is pretty easy in isolation. Equations for acceleration, lift, drag, etc. aren’t too complicated. Putting them together sometimes is though. For example, as you increase speed, you increase drag. So acceleration gets worse the faster you go.

The Model

Track

The track is modeled as a series of alternating straights and corners. The simplest description would look something like this.

S:2000
C:200:60

This means a 2000 foot straight followed by a 200 foot radius corner with a 60 degree arc. You can chain together any number of straights and corners to create whatever track you like. The sections don’t actually need to connect in a closed shape. I decided to use Thunderhill as that’s one of the most popular tracks in the region. I used Google satellite images and scale bar to rough out the track. It comes out as 2.94 miles, which is pretty close to the actual length. Note that my track model doesn’t take into account elevation or camber (yet).

Corners

Under the assumption that the driving line is circular, corner speed depends only on the radius of the corner and the grip of the tires. This is made a little complicated by aero modifications that increase grip and speed by adding downforce, but only a little. Because the corner speed is constant, it’s trivial to determine how much time was spent in the corner.

Straights

Straights are somewhat complex to model because the vehicle increases speed for some time, and then brakes to arrive at the correct speed for the next corner. This calculation depends on initial speed, engine power, gearing, aerodynamic drag, frontal area, and grip of the tires. A simple way of thinking about it is that the total time is the sum of the accelerating time plus the decelerating time. The way I solve it is by binary searching the transition from throttle to brake. At some number of seconds the distance covered and the final speed will be correct: it’s just a matter of making refined guesses.

Vehicle

Since Miata Is Always The Answer, I decided to do experiments with a virtual Miata. People sometimes say “the answer is always Miata” but that would spell out TAIAM, which doesn’t mean shit. Let’s give some parameters on the typical Miata that we will vary to see how the lap times change.

  • 2300 lbs with all fluids including the driver. We’ll strip some weight out of this to see what happens. We’ll also add a little.
  • 100 HP. My model assumes an engine of constant output. I don’t take into account the torque curve or gearing yet. It’s best to imagine “100” as a placeholder for both torque and horsepower, and the value of 100 is not a very healthy example of the breed.
  • 0.40 Coefficient of Drag. A hardtop Miata with windows down has a drag of something like 0.4. But topless it’s worse, and you could always add theme and make it terrible. For reference, a Prius is below 0.3 but it would be hard to get a Miata that low. However, a Prius has a larger frontal area.
  • 0.0 Coefficient of Lift. I abstract the various aero components into a single item rather than wing, splitter, diffuser, etc. A wing can be flat surface made from plywood with a CoL of 0.75  or something wing-shaped with a CoL of 1.0-1.6. The default value is 0.0 but a base Miata probably has some lift.
  • 0.0 sq-ft wing area. I’m not sure how to convert the various aero surfaces into wing area, but 0-12 feet in 4 foot increments seem like a reasonable range. The default value is 0.0.

Results

Power

It’s probably no surprise that more power reduces lap times. This is especially true if you have an anemic engine. Adding 20 HP sees lap times dropping by 3.08 sec. Another 20 HP is 2.57 sec. While there are diminishing returns, there are significant benefits to 200 HP and beyond. What’s amazing about engines is that you can realistically have them vary over a huge range. A turbo or supercharged Miata can make 300 HP. It might not make a good endurance racer at that point. However one of the most successful Lemons cars is the turbocharged Miata from Eyesore racing. In a race situation, high HP is doubly useful because it’s much easier and safer to pass under acceleration than braking or cornering.

Grip

The more corners a track has, the more grip becomes the key factor in performance. On a circular track, grip would be the only factor (assuming you have enough power to drive a given speed). Even a small change in grip can make a large difference in lap time. For example, a change from 1.00g to 1.05g drops lap time by 2.77 seconds. If you look at the telemetry of different drivers in the same car, you’ll see some people can extract more grip than others, and I think this is largely why some drivers are a couple seconds faster than others. In this model, an all season tire is about 0.90 grip. Summer tires 0.95, 200TW 1.0, Semi-slicks 1.1, Slicks 1.2. While these figures may not be correct, it’s the relative difference that’s important. If you want to win, get the grippiest tire allowed by the rules. The UTQG rating is only a rough indicator of the grip. In the crowded 200 treadwear class, I’ll bet there’s more than 0.05g of variation, especially when you consider differences in rim widths and tire pressures.

Aero

There are two components to aerodynamics, drag and lift (three if you count aesthetics). Drag has a relatively mild effect on lap times. Slipstreaming the heck out of it won’t see more than 1 second improvement. Similarly, ruining your CoD to a tune of 0.5 won’t see you slower by more than 1 second. Of course, every second counts, but this is the least useful area to tune. However, cosmetically, not much says racecar more than a wing.

Because lift affects grip, and grip is incredibly important, an aero package that increases downforce has a reasonable effect on lap time. Simply adding a wing could see your lap times dropping by 1.3 seconds (this is the Ideal 4 column below). There is some drag associated with wings, however, and on a track that is more straight than corner, a wing may do more harm than good. Note that a splitter can both decrease drag and increase downforce, so not all downforce increases drag. While you won’t see huge improvements in lap time from aero, it’s a one-time cost, unlike tires, and a well made aero package could see you dropping 1-2 seconds.

Weight

Removing 100 lbs will see lap times dropping by only about 0.6 sec. Weight reduction appears to have a relatively minor effect because it varies over such a restricted range. It’s a lot easier to improve your power:weight ratio by adding horsepower than removing pounds. So weight reduction might not seem like it’s worth doing, but it is. Out in the real world, the relationship between load and grip is sub-linear, so dropping weight is better than the model shows. There are also gains to be had in component longevity and fuel economy. The simple weight loss associated with angle grinders is relatively cheap, but when you start replacing structural parts with lightened versions it gets costly.

Some example builds

Let’s close this out with some example builds and lap times. Note that for a variety of reasons, the absolute lap times aren’t exactly as you would see at the track, but they aren’t very far off. It’s more important to think of the relative differences.

  • First day at the track – untuned engine (120 HP), all season tires (0.90g), open top (0.45 CoD, no downforce), and a coach in the right seat (2500 lbs) = 2:33.20
  • Solo – as above, but with Summer tires (0.95g) and no passenger (2300 lbs) = 2:28:91 (4.29 sec faster than above)
  • Sport build – engine is mildly tuned (130 HP), 200 TW tires (1.0g), hard top (0.40) and enough weight reduction to offset the top = 2:24.25 (4.66 sec faster than above)
  • Budget enduro – 100 lbs of weight reduction (2200), an additional 5 hp (135), DIY splitter and wing (0.35 CoD, 0.75 CoL, 8 sq-ft area) = 2:21.14 (3.11 sec faster than above)
  • TT build – as above, but using stickier, wider tires (1.05g) and professionally designed aero (CoL 1.3) = 2:17.36 (3.78 sec faster than above). Now I’m sure you’re wondering if it’s the tires or aero. It’s mostly tires (2:18.44 vs 2:20.09).
  • Eyesore – a famous Lemons car with a ghetto-charged motor that was dyno’d at 197 hp. It’s light (2200), has 200TW tires (1.0g), and theme for aero (0.45) = 2:17.29.

At some point I need to put this theory through some real life testing. I honestly can’t imagine anything more fun than going to a track day with 4 sets of tires, removable aero, and some ballast. It would be a long, hard day of work, but what a day. It costs $2200 to rent Thunderhill West for a 2-car test day. In the off-season, they sometimes cut that in half. I just need to find another car to share the session with and a crew to help out with the pit 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).