How hard can 4 cones in a row be to master?

At the most recent ADSI high-performance driving school day on June 22, they treated us to a simple yet very effective (and humbling) exercise: drive through four cones laid out in a straight line 60 feet apart as fast as you can. Sounds easy, right?

We sat down and calculated our theoretical max speed (vmax) first. The big thing that determines your max speed is the radius of the curve you are driving and the grip of your tires. If you could drive perfectly close to the cones and your car is 5.5 feet wide and the cone is another foot wide, the center of your driving line begins 2.75 feet away from the center line. Then let's assume that you'll arc from the mid-point of a set of cones to the next mid-point. This gives you a radius for your arc of 138.5 feet. If your car can achieve 0.95G (mine should be close to that), you get a vmax of 44.3mph.

Here is our theoretical case:

So we drove the course, trying to bump our speeds up slowly while being measured by a radar gun to know our speeds on entry, midway, and exit. It was tough to maintain a constant speed. And tough not to hit cones as you went faster. And even harder to be smooth. But we slowly started to beat our theoretical vmax speeds. But how? I was perplexed on the exact details and knew I had some math ahead of me. And boy am I rusty when it comes to geometry and let's not even talk about calculus... But I had to know how and why.

If you did 100 cones in a row, I'd bet that you'd get really consistent with this drill and could rhythmically bang out a nice, even line at the vmax easily. Not being robots or Schumachers, we all made some mistakes in our short four cone drill. Sometimes we went in too hot and had to scrub some speed with hard turns and some sliding. Sometimes we went too slow and could turn in a bit earlier and make up time. We certainly didn't use brakes at all. So why could we exceed vmax at times without spinning? It appears to come down to the fact that the arc really can change a bit even in such a short course. And the effects are not small. Let's look at a case where you turn in really quickly - like right after the first cone, then round the second cone, and then aim for just the far side of the third cone. You are effectively making the arc as shallow and as long as it could be between the first and third cones. If we do that, the radius of the arc goes up. And not by just a little.

The radius goes up to a whopping 448.6 feet! And the vmax for an arc that size is 79.7mph! So if you could perfectly "cheat" one set of cones, you could run at 80mph instead of the paltry 44mph that should be the top speed.

In reality, about 47 or 48mph was the best I could manage at any given point. Real-world considerations like acceleration times and inability to fully cheat any section should be fairly obvious. But this also shows how sacrificing corner entry speeds on the corner right before a straight to get a better exit speed pays big dividends. I got it intuitively after a while. But now the math is making it that much more clear. And maybe its more clear to you too now?

It got really intense when the instructors put a row of cones as "walls" 7 feet away from the slalom cones on each side. Then the pressure was on. We had to drive the slalom but inside these new "walls". Speeds tumbled as we all summoned our courage and nascent skills. It was a humbling and fun experience. As I get older, not being able to be good at things is often far more interesting than things I'm good at.

I hope you enjoyed this trip into "driving geek land" again. I've got a few more goodies soon hopefully, having stumbled across an amazing resource called the "Physics of Racing". Hopefully all this theory goes through my brain and into my body...

Hope you're enjoying summer and I hope to see you all sliding sideways soon!

1 response
Almost made me want to come back to the States, but not quite. Enjoying cacio e pepe here in Roma much more!