The performance distribution is not a bell curve

In the recent post about my new car (BMW 318ti), I showed a graph of qualifying times for the BMW Compact Cup and said it looks just like every other race distribution. So let’s look at some other distributions.

Here are some virtual lap times from iRacing (Laguna Seca, MX-5 Cup).

And these come from Assetto Corsa (Brands Hatch Indy, NA Miata).

Isn’t it kind of amazing how similar they are? Real or virtual racing, performance is similarly distributed. In the real world there is car-to-car variation, but not in the virtual world. And in some series, like the iRacing one shown above, the cars have fixed setups, so EVERYTHING is identical, except for the driver. People vary a lot in their performance. But is the shape of that performance curve the same in other activities? How about we look at the finishing times at the Boston Marathon.

What the hell? It’s the same shape. Are all performance distributions the same? Forget racing, here’s the score on Exam #1 in my Winter 2019 MCB182 Genomics/Bioinformatics course at UC Davis (I’m a professor by profession if you didn’t know). The graph is in the opposite direction, but once again, it has the same shape. About 10% of the students perform really well and another 10% perform poorly, but the middle is not a bell curve, as many would want you to expect. It’s highly asymmetric.

No matter how much I try as a teacher, some people always do poorly in my class. They may have complications in their lives or some other mitigating factor. It’s okay. Not everyone shines at the same time or place. The long tail represents a lot of people who aren’t really in the game. Give them time and they may come around. On the other hand, they may not. Not everyone has to excel at racing, marathons, or academics. Let’s agree not to make fun of people who aren’t at their best.

Next, let’s talk about the people on the other end of the spectrum. Even at the elite levels of some activity, there are people who stand out above the rest. It’s kind of amazing that such talents exist. Performance at such a high level requires natural ability, a commitment to training, and usually a strong support structure around the performer.

To me, the most interesting region is the middle. Everyone eventually runs into a wall where their performance reaches a plateau. For many people, that wall is near the same place. Why do some people get beyond this and others do not? If you know it’s possible to do a marathon in 2.5 hours, why are so many people stuck at 3? Well, I’m pretty sure that I couldn’t do a 3 hour marathon if I trained for it my entire life. Is that kind of statement also true of virtual activities? While it is possible to do a 1:40 lap at Laguna Seca, are some people never going to get there no matter how much they try? And is that true of 1:41, 1:42, and other arbitrary thresholds? How much of our current limit represents a hard limit and how much is a soft limit that could be lifted with more coaching, training, practice, or support?

Tuning myth: change one thing at a time

I have a love/hate relationship with the Mythbusters. It’s mostly love because they ask interesting questions and have a philosophy that “failure is always an option”. The hate part is that their experimental design is more based on “will this be entertaining?” rather than “does this answer the question?”. I actually taught a course at UC Davis where we examined Mythbusters episodes and discussed what went right and wrong. We even did our own experiment: “does hot sauce increase your body temperature?”.

One of the common car culture myths is that when tuning your car, you should change only one thing at a time. I’m going to give a very simple example of why that isn’t necessarily a good idea, and I’m going to do that using my own research as an example. Get ready for some bioinformatics-flavored genome science. If you’re too lazy or time-constrained to read the whole blog, here’s the short version: you can’t predict how different parts interact, so optimizing one thing at a time isn’t optimal. Now that you know the end of the story, let me tell the beginning and middle.

A little molecular genetics for car enthusiasts

Proteins are the building blocks of your body. They are both the structure (chassis) as well as the moving parts (pistons, connecting rods). Proteins are not the fluids (oil, gasoline, air) though. Those parts we call metabolites. For our purposes, the blueprints for building each protein are contained in genes, and the sum total of all of the genes are in a book we call the genome. Over the last 20 years or so, we have gotten very good at sequencing genomes. That is to say, we can print out the instruction set for lots of different organisms. We aren’t so good at determining what those instructions mean because it’s hard to determine where the genes are in a bunch of letters.

GCTACTTTCTATACTTTTGCGTAAATACTATAGTTTTTCTATAAAACACCCATTAAAATTATTTTTATAAAATGATTTTTCCAATAAAAATAAAATGCGCAAAATGATTCTTTTCCAGAATCCTATATGCGCCTTTAAAATCTCTCGGATTACTGTAGTTTCAAAGAAATTATCCTTTATATTTTTAATTTTAAATTTTTTCCTGAATGTCAAATATTAGGGGAAAAATTATAATAATATGTGCTTTATTCATATGAGTGTAGAATTAGTGAAAAAGAAAAAAAACATGTATGGACTGTAAAATTGGAATTTTAGCGAGAAAATAAAAATAATATGCAGAAAAAATTAAAATTTTCAGGAAAAAAGTCAGTAAAGCCATCAAAAACTACTCGATTTTGAAGGAAATCAGCAAGAAAAATTAGAAAAAAGTATTTTTAAGTTGGAAAACCCCTGCTTGAATTTGTACACTAAATTGGGCATAAAAGCGTACAAATTCGCAAAAACCGGTAAAAATCTGGGGATCGTGATGGATGGAGTGTTTTGTGAAAAAATGCAGCGAAAAATTGAGTAGACAATTTCAAAAATGTCGATTTTTGAAATTTGTGACGAAAAAATTGAACAAAAACTGTTTTTTTTTGGAATTTTCAACAAGAAGTTTTATAAATTTTTTTGTTTAAAATTTTGAATATTATATGAGTTTGGTTTCACTTAACAGAACAATTCGAACAAAAGTATTCTAGAAAGGAAATGTGCGCTCCAGCACACTATTTGCCCGTGGAGCGCACTTGTGTGCACGAACG

The sequence above is 800 letters randomly selected from a favorite genome. What do they mean? Does this paragraph correspond to a gene or something else? Deciphering such passages in the various books of life is literally my day job. It’s a pretty sweet gig if you’re into solving puzzles. So let’s imagine briefly that each protein is like a group of sentences. In order to find the genes, we just need to break the genome into sentences. So let’s do that in the following passage.

Nid oes gennyf fawr o bleser gydag ysgrifennu un math o farddoniaeth heblaw caneuon bychain o’r fath hyn. Fy mhlant fy hun ydyw’r Caniadau. Dymuniad fy nghalon a balchder fy mynwes ydyw eu dwyn i fyny yn blant da. Wrth adael i rai ddawnsio mewn plentynrwydd, ac i’r lleill chwerthin ac ysmalio, caiff nifer o honynt gadw carwriaeth ac eraill ganu hen alawon eu brodir. Caiff bechgyn weithio yn y graig, a bugeilio ar y mynydd, a phan fydd dolefiad corn y gâd yn galw, fe’u cyfeiriaf i faes y frwydr i amddiffyn eu cartref, ac i farw’n ddewr tros Ryddid eu mamwlad. Yn nesaf at ofni Duw ac anrhydeddu y brenin, cant garu eu gwlad a meddwl yn dda am eu hiaith a’u cenedl.

I have absolutely no idea what this says because it’s written in Welsh. However, I can tell where the sentences are because I can recognize some punctuation (capital letters, periods, commas). But genomes don’t have punctuation. So now try breaking this up into sentences when you don’t know the language or punctuation.

SYTLAWDYNLLONROIHUNIWFRONGLWYFEDIGONDMEINICERFOFARMORTRWCHAGUDDIENTLWCHPENDEFIGWRTHFEDDDANGYSGODYWENGRINDAUBLENTYNOEDDYNWYLOMEWNINGAHIRAETHARYPRIDDLLEROEDDEUMAMYNHUNCERFODYDDAUMEWNNEWYNMAWRARLAWRROEDDDARNOFARAEDRYCHENTARNOWEITHIAUNSYNERHYNNIWNAENTEIFWYTAFYANWYLBLANTGWNEWCHDDWEYDIMIPAMRYCHCHWIMEWNCYFYNGDERACYNGWASTRAFFURBWYDEIC

Let’s further complicate matters by imagining that the instructions for each protein are often interrupted by several advertisements, much as you would see in a magazine (weirdly, much of our genome sequence appears to be junk, like advertisements, and not useful content). In order to read the article, you have to remove the advertisements. We call the advertisements introns and the act of removing them splicing.

Modeling splicing

In order to splice out the advertisements (introns) to read the article (protein) we must first recognize what the signals look like. In real life, advertisements are usually less than a page, and there is usually a bounding rectangle as well as changes in background or font. That is, we can discern an advertisement by its surrounding context. Genomes don’t have such features, so we use the patterns of letters themselves to provide context. Splice sites have two sides called donor and acceptor. For the experiment today, we are going to look at just one side: the splice acceptor.

The consensus splice acceptor sequence is TTTTCAG. That is to say that this is the most likely sequence of letters. But not all splice acceptors have the same sequence. Sometimes they are ATTACAG, for example. The last two letters, AG, are almost always AG, but the other letters can change quite a bit. A very simplistic model of splicing would be that every AG is a splice acceptor site. But those occur about once every 16 letters while advertisements occur every 100-200 letters. So how do we recognize splice acceptor sites? By looking at the sequences to the left and right. These provide context, much in the same way that a change in fonts or dialect provides context of change.

Here’s a diagram depicting a simple model of a splice acceptor site that we will use for our experiments. On the left is an advertisement (intron). This contains a dictionary of all the common words found in advertisements. On the right is part of a protein-coding sentence (exon). It contains a dictionary of all the common words found in articles (proteins). Importantly, the frequency of words in the two dictionaries are different. For example, the word sale occurs many times in advertisements, but rarely in the article. In the middle is a sequence that ends in AG, which represents the various splice acceptors we have seen before (changes in font/dialect/background/whatever).

Experiment

In order to think of this experiment in car terms, we are going to imagine the model above as a car. The intron represents the front suspension, the exon is the rear suspension, and the AG box is a combination of tire and pressure. We can make changes to any of these components and see how performance changes.

The first thing we are going to do is make a sweep over tire pressures using our favorite two tires. Here, let’s imagine the Y-axis is grip or some similar approximation of optimality. Both tires appear to like 27 lbs.

Now let’s make some changes to the suspension. We can go with soft or hard springs up front.

Front Soft (rear soft) 0.905
Front Hard (rear soft) 0.720

Soft is clearly better than hard. If we are allowed to change only one thing at a time, we can change the rear springs to hard to see if that’s better.

Front Soft, Rear Soft 0.905 (as seen before)
Front Soft, Rear Hard 0.891

If we change only 1 thing at a time, we max out performance at 0.905 using tire 1 at 27 lbs and soft-soft suspension. However, it’s only one more test to examine hard on both sides.

Front Hard, Rear Hard 0.938

So hard-hard is better than soft-soft, and we can’t know that unless we try all combinations. Since there are only 2 sets of springs, this isn’t a big deal. But what if we use all combinations of tire compounds, tire pressures, and springs? Is there a combination better than tire 1, 27 lbs, and hard-hard?

Yes. It turns out that tire 2, 29 lbs, and hard-hard results in 0.942 performance. If we are allowed to optimize one thing at a time, we end up with 0.905 performance, but if we try all combinations, we end up with 0.942. We did have to test 64 combinations to arrive at that result however. Most car testing scenarios can not schedule enough time to do 64 different tests. And with the conditions changing throughout the day, even if one could do 64 tests, the results may be polluted by external conditions.

Given how difficult it is to find optimality, how does one approach the problem? For me, personally, I have cars that don’t have a lot one can tune. I’m pretty much limited to changing tire compounds and pressures. Tuning means driving around a car’s problems more than fixing them. But that’s because I suck at racing. Hopefully your tuning program is better than mine. And hopefully it means testing combinations of parameters rather than greedy/serial optimization.

Conclusions

Tuning is difficult because there are many parameters that may interact in ways that are difficult to predict. While testing all combinations of parameters is the only way to be sure, it may be impractical or impossible to do this in the real world. Tune as well as your time and wallet permit and drive around what you can’t.

Notes

The experiment above was conducted using hidden Markov models, a popular architecture to model biological sequence signals. Tire pressure is actually the length of the splice acceptor signal from 2-9 nt (rather than 22-29 psi). Tire 1 vs 2 is a change in emission context from 0 to 1. Soft vs. hard suspension is a change from 0 to 1 in emission context for the intron and exon states. The data source was the first 1% of each chromosome in Caenorhabditis elegans.

Winning B Class: part 2, black flags

Last week I talked about why driving in Enduro style may be our best chance to win class B. By consciously driving 1% off pace we increase fuel economy by 13%, which may save one pit stop, resulting in a 5-6 lap advantage. Driving slower also reduces the chance of getting a black flag, which I parenthetically stated would ruin our race. Which begs the question “what exactly is the cost of a black flag?” We had better answer that. By ‘we’ I mean me and brother Mario.

The Slowest Driver

Early in our racing career, our team went through what most teams go through, which is learning how to drive fast. We eventually learned how fast you can drive in a race, which is an entirely a different thing. We also had to learn about pit strategy, conserving wear items, flat spotting tires, acceptable risk, going off track, hitting other cars, mechanical damage, and of course black flags.

Different race organizations feel differently about throwing black flags. 24 Hours of Lemons is very liberal with them, they’ll throw a black flag for putting wheels off track, for any contact, for passing under yellow (there are always yellows), for driving like a dick, for behaving like a dick, for exceeding paddock speeds, and anything else they feel warrants it. Consequently, Lemons racing is quite safe, because they sit down the idiots and give them a time out, or give them some ridiculous task that takes forever.

On the other end of the spectrum, ChampCar is more loose about “racing incidents” and generally doesn’t care about putting wheels in the dirt or minor contact. We brought the ChampCar judges video footage of an EC car (EC stands for Exception Class, meaning the car doesn’t fit into the competition rules and is just out there for fun) that barges into us mid-corner and almost takes us out. The officials really didn’t care. But I guess that goes both ways because we’ve never received a black flag in ChampCar, either.

But to get back to Lemons, in our first race and we were driving a MR2 with a wooden boat wrapped around it. You could bottom out the suspension by leaning on it, and it was making maybe 90 hp, but that wasn’t why we didn’t place well, it’s because we got hammered with black flags. After too many infractions (mostly passing under yellow, but also going four off), Judge Phil gave us our sentence: write out “you can’t win a race in one corner but you can lose one” 100 times. On both sides of the car. Right-handed on the right side and left-handed on the left side. That may not have been the actual phrase, but it was something like that.

In our next race, some of us were still collecting black flags, most of which were a result of driving too close to the limit. And by that I mean not just the limits of the track or adhesion, but physical and mental limits as well. In order to demonstrate how much this affects lap time, we did some work in a spreadsheet.

A typical 2 hour stint is less than 120 minutes because nearly every stint has some FCY (full course yellow) time. So let’s say that a stint has 100 minutes of spirited driving. At a 2 minute pace, a driver can complete 50 laps during this time. How many laps can be completed if one also picks up a black flag? Some black flags are only a few minutes and some are quite long if there are other cars also being attended to. At some tracks the race stewards are outside the timing loop so you lose whatever lap you were on. 8 minutes sounds like a good average.

The cost of a black flag is therefore 4 laps and the black flagged driver can complete only 46 laps. You know who else completes 46 laps? The driver way off pace lapping at 2:10. Getting a single black flag will turn the fastest driver into the slowest driver. Once getting a black flag, there’s no way to drive fast enough to make up for the transgression. That would mean driving a 1:50 pace or faster. That might not be physically possible, and if you’re getting black flags at a 2:00 pace, you’ll pick up a dozen more driving at 1:50. The second black flag will set your actual pace to 2:23.

How hard should you drive?

Regardless of how skilled you are, the more you push yourself, the greater your risk. To examine this, let’s look at the Assetto Corsa world records at the RSR LiveTiming site. As I’ve done in some previous posts, I’ll use Brands Hatch Indy and the NA Miata as the source. The top driver, Marius Golombeck, has somehow manged a blistering 59.757 lap time. That’s almost 1 second faster than I’ve done (1:00.653). He’s logged 181 laps to achieve this. And in doing so, he’s had the equivalent of 113 black flags (invalid laps from going off course). So even aliens can’t manage to stay on track when they’re driving 10/10ths. And this is just a time trial without any traffic.

So if you shouldn’t drive 10/10ths, what is acceptable? I can lap all day with zero risk of self-inflicted harm (there’s never zero risk with other people on track) when I’m 1-2% off pace. Hey, that’s like the Enduro pace from last week. Not only can it cut 1 pit stop (gaining 5-6 laps), it also reduces the chance of getting a black flag (costing 4 laps). You don’t lose much by waiting for a safe time to pass a slow car, giving extra space to less experienced drivers, pointing by a train of faster cars, or staying off the curbs and grass. Not doing those things could cost you the whole race if you pick up a black flag and find yourself making repairs.

In a typical amateur endurance race, drivers may have different capabilities. Everyone needs to cut their own 1-2%. The benchmark can’t be the fast driver. I recall a race at Willow Springs where my comfortable pace was 5 seconds ahead of a teammate who drove over his limit, crashed the car, and ended our race. Egos and red mist sometimes win over reason. To combat this, clever teams have put the driver’s cell phone in a bag on the front bumper or set a fastest lap anti-bounty (fastest driver pays $100 for bragging rights). We haven’t done these things yet, but we talk about it.

Mario’s Advice

Here’s what I do: Drive at a pace where I have total situational awareness and a huge margin for other drivers fucking up; Follow drivers that are a bit slower than I am, for as many laps as they let me; Point-by everyone who’s on my bumper; Be kind to the car; Exit the car after my 2-hour stint feeling refreshed – not tired, not energized, not angry, not pumped, not frustrated, but refreshed and ready to get back in.

Ian’s Advice

Have a mindset that the race is safer and more fun for everyone (not just you) because of the way you drive. Race with people, not against them, and for fucks sake, don’t have a competition within the team. Drive 70% of the time at 7/10ths, and when you need to step it up a notch, go to 8/10ths not 8/8ths.

Stopwatch or it didn’t fucking happen

Probably like many of you, I sometimes watch car reviews on YouTube. I wish there was some way of determining ahead of time if the people reviewing the car were experts or poseurs. Here’s what one journalist says as he drives the Civic Si.

Chuck it into a corner like so… yeah, and you can feel that diff working up front, you can feel it pulling the car through the corner.

Now let your imagination fill in the scene… the driver approaches a tight corner at high speed… he brakes and throws the car in… the rear drifts around as the front tires dig the car out of the slide…

OK, time to click the link…

How embarrassing. The only thing he chucks into the corner is his credibility. He can feel the diff working… without any wheel spin? You fucking P-O-S-E-U-R. Apparently the 50k+ subscribers are tuning in for their sparkling personalities or handsome visages, because it’s certainly not the driving.

What about those reviews where the journalist gets out of the car for the track test? Hey Randy Pobst, can you take over? Pretty please. Drive the goddam car yourself. It’s literally part of your job description. Of course I understand why they do it. Professionals are more consistent. But the journalists should also post their lap times. If they’re 5 seconds off, I want to know that. It speaks to their credibility. Stopwatch or it didn’t fucking happen.

On the Physics of Racing

One of the first things I read on racing is a collection of articles called “The Physics of Racing” by Brian Beckman. This made a big impression on me because the author takes a very mathematical view of racing. That’s something I could sink my teeth into because I had more experience with math than performance driving. Then I got to the part where he went to a racing school at Sebring. He was more experienced than the novice racers but he was also older. All the students drove identical Panoz cars. He found that his old-fashioned straight-line braking left him 65 feet (about 0.5 seconds) behind the more modern students who were trail-braking. Then he drops this bomb.

A record time around the course in the Panoz school cars is 2 min 28 seconds. The students were doing 2:40 to 2:45. I believe I uncorked a 2:36 somewhere along the way, but my typical lap was 2:40 and the quicker guys pulled about 65 feet on me at the start-finish every lap, which I reckoned before to be worth half a second

I don’t want to know why he thinks he’s 0.5 seconds slower than a bunch of rookie racers. I want to know why his typical lap was 12 seconds off! Clearly there’s a more important lesson here than a little trail-braking. If the lap record is a 2:28, a 2:36 isn’t uncorking anything other than a bottle of shit. That said, he posted his lap times, and for that he should be commended. It puts things into perspective. He’s a guy who understands the theory of racing but has some trouble putting it into practice. That’s okay. Lots of people are in the same boat. Like me, or maybe you.

YSAR in 2019

As this is my first post of 2019, I thought I would say a few words on the future direction of YSAR. There are a lot of people who offer insight on performance driving. Most of them know their shit better than me. I’m not Ross Bentley or Peter Krause. So why tune into YSAR? I guess because you like your driving content with an eclectic mix of math, simulation, video, science, irreverence, and irrelevance. YSAR used to focus on crashes, but I think it has evolved into some kind of mental pit stop for the improving driver.

As we look forward to 2019, I’m eager to find out where this performance driving journey will take us. Frankly, I’m as much a passenger as a driver in this endeavor. Before we start, let’s agree to chuck the poseur bullshit into the corner. There’s no room for artifice where we’re going. There is room for incompetence though. Let’s find out where those 8-12 seconds went and fix that shit. Oh, and there’s also room for a metric ass-ton of swearing. This is you suck at racing, after all. The shit has, and always will be, fucking real. Or in more gentlemanly terms, I will always be honest with you. Whether it’s modeling vehicle dynamics, debunking driving myths, reviewing the latest gizmo, or recounting my latest driving adventure, I will present stuff as factually as possible. I give zero fucks about impressing professionals or companies, and won’t alter my content in an effort to impress or appease them.

Am I just going to ramble on this week or is there going to be any actual driving content? Okay, okay, let’s call bullshit on someone with more racing credentials than me.

The Euler Line

Do you subscribe to Speed Secrets Weekly? It’s a weekly newsletter delivered to your inbox. If not, you might consider it. Every Tuesday there’s new content from Ross Bentley and usually a guest writer. Professional drivers, engineers, and coaches contribute regularly. And also amateurs like me. I’ve written two articles for him in the past and just a few days ago I started a new 2-part article on why spinning is an important part of driver development. I won’t regurgitate those posts here but instead urge you to subscribe to SSW. It’s only $15 per year and makes every Tuesday just a little better.

One of the recent posts that got my attention was written by Randy Beikmann. It’s a theoretical post about the ideal driving line that compares the circular arc to an Euler spiral (pronounced “oiler”). Probably every book since Piero Taruffi’s 1958 classic, “The Technique of Motor Racing”, introduces the racing line as a circular arc. Nobody actually drives this arc. It’s used (1) to demonstrate the largest possible radius through a corner and (2) as a point of comparison to the typical late apex racing line. Here’s an awesome picture of the ideal line from that book.

One unrealistic thing about the circular arc is that one goes from straight wheels to turned wheels instantaneously. The author suggests that instead of turning the wheel suddenly, you should turn the wheel at a constant rate. Steer it in gradually, steer it out gradually. The path through the corner is not circular. It follows an arc called an Euler spiral, which is more gradual at the entrance and exit. The author goes one step further and shows through a Mathematica simulation that driving on the Euler arc is faster than a circular arc. In the diagram below, you can see the flatness of the blue line. That’s the constant speed of a circular arc. The Euler line has a lower minimum corner speed but makes up for it by getting to throttle sooner.

I greatly admire the elegance of the Euler spiral model, but it left me wondering “does anyone actually steer like this?” We can answer that pretty clearly by comparing theoretical and actual steering traces. TL;DR nobody drives the Euler line.

The black line below represents the steering angle of the Euler line: constant winding in followed by constant winding out. It’s shaped like a capital A. In reality, there are steering corrections. An idealized representation is shown by the green line, which looks like a capital M. The steering wheel is turned in a little, but then the back of the car rotates around (often from trail-braking). A steering correction (steering the opposite direction and back) puts the car back on line, and then the steering wheel is unwound towards the exit.

Here are some traces driven by the Assetto Corsa AI. Steering angle is the 3rd panel. As you can see, it doesn’t look like the letter A expected from an Euler line. The top of the peak is flattened and there’s often a spike in the middle representing the steering correction. At around 4000 feet the trace looks like the letter W, not V.

How about real drivers? Here are the “alien” steering traces I showed in part 5 of the Ghosting the Aliens series of posts. Where are the isosceles triangles? The steering wheel is rarely turned at a constant rate, and sometimes very quickly.

Here is me driving in simulation with 3 very different setups (blue understeer, red oversteer, green neutral). The middle panel is the steering angle. The understeer setup is the most similar to the Euler line, but it’s hardly symmetrical and there’s a steering correction late in the corner.

In theory, there’s no difference between theory and practice. In practice, there is.

So if nobody drives an Euler line, why is Randy Beikman wasting time writing and talking about it. It’s because it’s not a waste of time. It’s important to understand the theory behind racing. It’s even more important to understand where the practice differs from that theory. In the end, we want the theory to catch up to the practice. When that happens, we can take our speed beyond our current understanding. It takes time to model these things correctly. While less than perfect, I admire the work by Beikmann and his Euler model. Beautiful things can have flaws.

Ghosting the Aliens: part 2, braking bad

The end of the 2018 YSAR Author Contest is just 1 week away… click the Contest link at the top of the page if you want to win some cool prizes.

Last week we discovered we can get telemetry software and data for free from iSpeed. We’re going to be using these for a few weeks to examine exactly what separates the fast from the slow. At the end of the post last week, we loaded up the fast laps from Alex Czerny and Bastian Stirl for the iRacing Global MX-5 Cup at Laguna Seca (Season 3 Week 4). The reason we are focusing on the Global MX-5 Cup is that the series uses a fixed setup. So you’re not allowed to change suspension settings, tire pressures, fuel load, or anything else. This will let us focus on the difference among drivers rather than setups.

Braking backwards

Let’s load up Alex and Bastian again and talk about one of the most common problems of inexperienced drivers: braking backwards. If you don’t remember how to load laps into iSpeed, look back at the post from last week. The proper way to brake is hard on, soft off. You should get to maximum brake pressure very quickly and then modulate it from there. Many rookies like Bastian brake gradually at first, realize they need to brake more, and build brake force as they slow. When they’re done, they snap their foot off the pedal. Releasing the brake quickly causes the suspension to rock, unsettling the car. It’s the opposite of smooth. Why then is it okay to hit the brakes hard initially? Because at the start of the braking zone you’re going in a straight line. At the end, you’re turning and need the car as quiet as possible to maximize traction.

The highlighted region in the image below shows how completely different Alex and Bastian apply and release the brake.

In slow, out fast

Let’s replace Bastian with Roy Johansson’s 1:48.367. I’m sure you’ve heard the phrase “in slow out fast” before. Your instructor told you to drive that way because he wanted to survive the day, not because he wanted you to be fast. While it is true that you need to slow down to enter a corner, if you put too much emphasis on the slow you’ll end up with terrible mid-corner speed that you can never recover from. Roy brakes hard for every corner whether he needs to or not. And in a lot of places, he doesn’t need to brake at all. This is what I see from a lot of HPDE drivers. When they do get to throttle, they can go very quickly to 100% because they’re going so damn slow. It’s easy to be full throttle at the kink (or whatever) if you brake unnecessarily hard and kill your speed.

Hard on, hard off

Now let’s load Thiabault Nicolas’ 1:43.918 into Lap 2.

This lap is a good deal faster than the previous ones. This is the typical braking pattern of the intermediate driver. Notice how the brake traces all look like rectangles. The driver is no longer scared to use the brake pedal, but they don’t have any finesse. The brake pressure trace shows that the brake is either 100% on or 100% off. A high horsepower car can get around a track pretty quickly by mashing one pedal or the other, but it’s by no means optimal and no way to drive a momentum car like the MX-5.

Another problem with snapping off the brake is that the weight quickly transfers to the rear. With less weight on the front wheels, the car has less grip to turn. And this is happening at corner entry right when you need that grip the most. People who complain about understeer should examine how they release the brake. The two are highly related.

Soft on, soft off

The opposite of hard on, hard off above is of course soft on, soft off. Load up the fastest lap by Mark Turek (1:44.412) to see what that looks like.

The brake traces here look like isosceles triangles. Although Mark trails Thiabault by a half second, I think he’s actually driving much better. He’s easier on the car and his brake modulation is a critical step in improving his driving skill.

Fixing problems

So how do we go about correcting these braking problems exhibited here? By practicing the fundamentals correctly.

Hard on
Soft off

Check your telemetry trace. Do you get to maximum brake pressure instantaneously? At the end of the braking zone, does the brake pressure taper off? If the answer to either of these question is no, you need to practice until the answers are both yes. This is a fundamental skill in the way that hitting a tennis serve out of a backhand grip is fundamental skill. If you keep serving out of a forehand grip, you’re perfecting a high risk flat serve that will see your opponents feasting on your weak 2nd serves. If you ever want to get out of the intermediate ranks, you have to hit top spin serves. And if you ever want to become an advanced driver, you have to learn how to use the brake pedal.

It is amazing how many drivers, even at the Formula One Level, think that the brakes are for slowing the car down. — Mario Andretti

In case this isn’t crystal clear, he’s saying that brakes are for turning the car.

Heraclitus Redux

The YSAR author contest deadline is looming. Fame, fantastic prizes, learning by doing. Click the contest link above for more information.

Out of every one hundred men, ten shouldn’t even be there, eighty are just targets, nine are the real fighters, and we are lucky to have them, for they make the battle. Ah, but the one, one is a warrior, and he will bring the others back. — Heraclitus

Below is some Time Attack data from iRacing. The car is the MX-5 and the track is Laguna Seca. 281 drivers have taken part in this particular challenge. That’s actually a small number compared to the number of people who race weekly in the MX-5 series (the last race week at Laguna Seca saw 3,148 drivers). Time Attack isn’t as popular as racing right now because it’s part of a beta UI (and maybe other reasons). But the data for fast laps is easier to mine from TA than races so that’s where the histogram comes from.

Following Heraclitus, the top 10% are the real fighters. This corresponds roughly to the 1:39-1:41 segment (actually only half of the 1:41s). The bottom 10%, who shouldn’t even be here, are lapping at 1:50 and above. Only the top 3 drivers are his warriors. If you’re looking at these lap times and comparing them to your own iRacing lap times, make sure that you’re using the exact same weather conditions (78°, late afternoon, partly cloudy, 55% humidity, wind 2 mph N) and setup (baseline, just like in the MX-5 rookie series with fixed setup). Otherwise you may conclude you’re slower or faster than you really are.

In the world of racing, we don’t call the best drivers warriors, we call them aliens. In 2009, Colin Edwards used that term to describe Rossi, Lorenzo, Stoner, and Pedrosa, the 4 riders with a strangle hold on MotoGP. Since then, the term has spread well beyond MotoGP and it’s one of the more common accolades in virtual racing. As long as we’re labeling driver skill, let’s put labels on various levels of driving because Heraclitus’ targets isn’t a very descriptive term for the 80% of the drivers in the middle.

Alien: top 1% of drivers, the benchmark
Expert: top 5% of drivers, around 1% slower than aliens
Advanced: top 10% of drivers, around 2% slower than aliens
High Intermediate: top 50% of drivers, 4-5% slower than aliens
Low Intermediate: top 75% of drivers, 7-10% slower than aliens
Novice: bottom 25% of drivers

So how does one become an alien? Not being one, I can only say so much. My best time under these time attack conditions is 1:40.3. While I’ve been an iRacing member for 5 years, I haven’t used it much for the last 3 years. So I’m actually pretty pleased that I was able to pull out a 1:40.3 after a few sessions back from a long hiatus. I know I lack the precision and consistency to be an alien. I might be able to get there one day, but it would be a lot of hard work and I’m not sure that takes priority in my life. More importantly, I generally understand how to drive a car fast. But what about those people who have been on iRacing for 10 years and still haven’t figured out why they are 3 seconds off pace? What are they doing wrong? How can they fix it? These are two very different questions, and something we will be exploring in detail via telemetry analysis as we finish out 2018 (and we’ll continue in 2019 as well).

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.

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.

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.

A flat-spotted tire is a waste of money
A tire that fails on track could cause a crash
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).

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.