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.
you suck at racing 
One of the things that I like about auto racing is that there’s an objective measurement of your skill. Or at least there is in sim racing, where, due to lack of income, I do most of my racing. Outside of racing, in this world, there’s a lot of poseurs and people who find success or credibility not because of what they can do, but because of who they know and how they network. I enjoy competitive hobbies that you cannot fake.
Still, I find people get insanely defensive when you point out that their slow times are due to their lack of skill. That they need to not only practice, but practice in a way that’s effective and makes sense. In sim racing, there’s always excuses: “if i had a direct-drive wheel I’d be faster”, “my computer is too old”, “I need a VR headset” etc. Meanwhile people on decade old Logitech wheels with 15″ CRT monitors are blowing their doors off. I had a guy this weekend who was 15(!) seconds off pace and wanted advice on trail braking. Buddy, you have far bigger issues than trail braking if you’re that slow.
Somehow there’s a culture where calling out journalists like the ones in the video is taboo. I’m sure if you did so, not only would they be extremely offended, but their fans would rush to their defense. The journalist would probably feel ashamed for being called out, when he should feel guilty for billing himself as an authority when he’s no better than a novice.
Anyways I had an experience where I (gently) explained to someone that they lacked fundamental driving skills and needed to work on them first and he blew up. I have this quote written on a sticky note on my desk: “The ego exists to protect the status quo”. It reminds me that the mental work of change and improvement will always be met with internal resistance. Other people, when you disrupt the status quo by going against the story they tell themselves, get angry and lash out. I was surprised but I shouldn’t have been.
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100% agreed! Sim racing puts everyone on equal footing and you can find out if people know how to drive. Most don’t. If you look at the RSR Live Timing site, it tells you what hardware the various people are using. A quick perusal of MX-5 cup car at Lagnua Sec shows that over half of the drivers in the top 20 are using a cheap Logitec wheel. You can find G25, G27, G29, G920, and even Driving Force GT among the fastest drivers. The other popular wheels are the Thrustmaster T500/T300 and Fanatec Clubsport. There’s no need for a direct drive wheel, VR, 3 monitors, or shifter.
I’ve definitely seen how fans rush to protect their heroes. I don’t know where that instinct comes from. Ego is a strange thing. In “Optimum Drive”, Paul Gerrard talks about how important the truth is. The way forward starts with honesty, not protecting your ego. “The truth will set you free. But first it will piss you off” — Gloria Steinam (and others).
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But… the euler spiral defines the ideal path of the car, not the ideal path of the steering wheel. It also only defines the corner entry more then the exit which depends more on the power of the car. Finally, grip on differing corner lines, corner camber etc would all change the “ideal” line away from a perfect euler spiral. So yeah, the practice doesn’t always perfectly match the theory but steering wheel input doesn’t seem a valid way to demonstrate it or the degree to which it differs.
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Good points attentive reader! Beikmann says this in his article when introducing the Euler line: “This corresponds to changing your steering wheel angle at a constant rate, say 20 degrees per hundred feet”. This is the steering input I have diagrammed. But he also talks about trail-braking during the entry and more vaguely about tracking out. These might not make the input constant. He never really says exactly what the steering wheel is doing and whether or not there are steering corrections. I may have interpreted him incorrectly, but I went with what I had. Overall, I think you’re correct: the Euler path is describing the arc not the steering input. Now I’m wondering if Beikmann’s model uses steering input or not. We need to know what the driver is doing, not just the car. Excellent comment btw, thanks for the correction.
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This response is really late in coming, but I just saw this while searching for better spiral transitions between different segments of the racing line.
The model I’ve been using is very simplistic, and does not explicitly include steering angle. It assumes that you can jump from any point on the car’s performance envelope to another instantly. Obviously your car can’t go from max braking to max cornering instantly (my new Cayman T is willing to move between conditions quickly though). Instead, I am working on limiting the transition rates myself, based on my track data.
So the reference to a linearly changing steer angle was just to give the reader an idea of what they would be doing with the wheel. The Euler spiral makes the curvature (1/r) change linearly. But the curvature is only linear vs. steering angle for smaller angles and becomes very nonlinear as your near the cornering limit.
On corner exit, a logarithmic spiral is superior, because it keeps the car on its “sweet spot” where the throttle is floored, and any remaining traction is used for cornering. (I’ve written on this since.)
I’ve been looking at my own data, and I’ve noticed I trail-brake into corners while increasing the lateral acceleration at about 1/2 G’s per second – about 2 second from no cornering to max cornering. My simulations with the Euler spiral, however, have ended up with 2 G’s/sec or more. The Euler spiral is meant to provide a linear change in lateral G’s only while going a constant speed, like a train transitioning into a curve. It provides good talking points for racing, but isn’t nearly ideal.
So my next step is to find or create a transition spiral that “drives” like I do. Remember that I’ve been developing this model to improve my driving, and it’s meant more to make me understand why we are told to do things like trail-braking, why they work, and how to implement it in my driving. There, I’ve been successful. I am way faster than I used to be, partly because I can envision how to implement the advice I get. Of course, I have a ways to go!
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OMG you replied. I love your material. Keep up the good work, and try not to get offended by any snarkiness here.
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