Cones in theory

If you’ve read my book (linked at the right) you know I love quotes. Here’s one of my favorites that I find applies equally well to my day job (bioinformatics if you didn’t know) and my weekend hobby (racing of course).

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

I can’t tell you how many times I’ve come up with an optimal solution to some problem only to find out that it isn’t really optimal. Real life is unfortunately always more complex than a mathematical/computational model. We make models to simplify, but modeling isn’t simple. So let me tell you about the theoretical optimal path around a set of cones, fully aware that the model isn’t completely accurate. Here are the key points to the model.

  1. Corners are semi-circular and driven at constant speed
  2. Straights feature a throttle zone to get to maximum speed and a braking zone that reduces speed to exactly the corner speed
  3. It takes no time to switch from throttle to brake and vice-versa
  4. Tire grip is the same for accelerating, braking, and cornering
  5. Gearing and RPM are ignored

As models go, this one is pretty simple. The only complex part is figuring out exactly where to transition from throttle to brake so that the car enters the corner at the correct speed (which is the hard part of cornering in real life too). There’s probably an elegant solution to this problem, but I cheated and wrote a program to do find the switch point.

So let’s get to the theoretically optimal solutions. Question 1 from last week featured a Spec Miata going around a set of cones that are pretty close to each other. Should the path be oblong (A), circular (D), or some hybrid? First, we have to know a little about the performance of a Spec Miata. How much grip does it have and how quickly does it accelerate. Let’s say it has 1.1G of grip and 0.25G of acceleration. It will be accelerating on the straights at 0.25G but braking and cornering at 1.1G. Well, except path D which is cornering only.

Turns out the answer is A, the shortest path.


After investigating a variety of scenarios, the car and surface hardly ever matter, the answer is almost always A. Corvette? A. Rain? A. Snow? A. WRX? A. In almost every common situation, the answer is the shortest path. One situation where A is not optimal is when tire grip is really high, acceleration is really low, and the cones are farther apart. So if you find yourself competing in some weird cone-circling competition where you’re only allowed to use 4th gear, take path F or G and you’ll save a few hundredths of a second.


So is there any situation where circular paths (D and H) are optimal? Yes! If you don’t have brakes, your top speed is limited by the corner speed. So if you ever find yourself in a no-brakes competition, take a circular line.


GRX: Autocross report

My Generic Racecar Experiment, or GRX, is a 2007 Toyota Yaris. What makes it a racecar? Well honestly, I think any car can be a racecar. But in the case of the Yaris, it’s all the safety equipment (roll cage, harness, fire system, etc.). I’m planning on driving this in all manner of racing events like autocross, rallycross, hillclimb, endurance racing, sprint racing, and even stage rally. Today, I took the GRX to an autocross event because it’s something I’ve never tried.

The event took place in the parking lot at Sonoma raceway. Normally when I go to Sonoma, it’s to drive the racetrack, not the paddock. But when TrackMasters Racing hosts track days at Sonoma, they sometimes also host autocross events. I’ve seen people doing this and it looked like the course was big and you get a lot of runs. Sounds like fun, and for $75 it’s less expensive than a typical track day.

The day started at 6 am. Sonoma is about an hour from my house. The weather forecast was for rain, so I brought my longish raincoat and an umbrella. The car was packed the night before with a helmet, tool box, and some track tires. I had 205/50/15 Nitto NT-05s for the front and 195/65/14 Dunlop Star Specs for the rear.

At the driver’s meeting, the organizer told us the rules. Briefly, you work half the time and drive half the time. Working means replacing cones and waving a red flag if a car stops for any length of time. I was in the work first group. The schedule was 1.5 hours of working in the morning followed by two 1 hour shifts in the afternoon. So a total of 3.5 hours of working and 3.5 hours of driving.

Working an autocross event is pretty simple stuff. You wait for cars to mess up then replace cones. Each station has several people, so you end up doing a lot of talking. If you’re a car enthusiast and want to talk to other car enthusiasts about cars and driving, you can make a lot of new friends at an autocross event. If you like the actual driving, do something else. In the morning session, I spent 2 hours and 56 minutes waiting to drive and 4 minutes driving. In the afternoon session I was home, doing something more useful with my time.

I’ve never tried surfing. Years ago, I asked a surfer what surfing is like. He said it’s like swimming. In the spirit of that answer, I will summarize what autocross is like: spectating. There are brief moments of driving here and there, but the majority of the day is spent watching and talking.

Autocross is far more popular than track driving. I’m trying to figure out why that is. Certainly it’s more accessible. You can turn any parking lot into an autocross course with a few orange cones. And the cars don’t need nearly as much safety equipment. Those may be reasons enough, but I suspect that the real reason are social and cultural. For car enthusiasts, standing around talking about cars is not just part of the fun, but the best part. It can’t be the driving. There just isn’t enough of it.