Theory vs. Practice (and chemistry?)

I just took part in a PhD qualifying exam in Chemistry. No, I’m not a chemist, but the student’s project was in metabolomics and they wanted someone on the exam with a more -omic perspective. One of the exam questions was about the van Deemter equation. This equation is used to describe the resolving power of a chromatographic column. Let’s put this into a simpler context you may have seen before. If you haven’t seen this, it’s easy enough to replicate at home.

The ink inside pens isn’t generally a single chemical, but a mixture of chemicals. If you want to see those individual chemicals, you can separate them with chromotagraphy. Get some high quality paper, like a coffee filter. Next, grab some pens and make a spot on the botton of the paper. In the picture below, the pen colors appear to be Black, Brown, Red, Green, Blue, and Orange (these were written in pencil because that won’t bleed in the next step). Place the bottom edge of the paper in liquid. As the liquid moves up the paper, the pigments will separate based on how much they “like” the liquid (faster) vs. how much they “like” the paper (slower). Some pigments will travel up the paper very quickly, while others will stay at the bottom. For the liquid part of this experiment, you can use water, alcohol, WD-40, or whatever you happen to have lying around. Depending on the liquid (actually called solvent), you will see different separations. Some pigments are soluble in water but not isopropanol and vice-versa.

If you did this experiment in school, the next part would be trying to determine the relative mobilities of the various pigments. That’s not what we’re doing today. Instead, we are interested in the shape of those pigment blobs. Notice how some pigments stay together better than others? It’s a lot easier to figure out where one pigment begins and the other one ends if the blob is small. In other words, our ability to resolve compounds depends on the size of the blob. This is where the van Deemter equation comes in. The resolving power, H depends on 3 different factors:

1. A, the molecular path through the paper. There is no straight path, and how much the pigment molecules deflect around the molecules of the paper matters.
2. B, the rate of diffusion along the length of the paper. If there is a lot of diffusion, the pigment molecules will be moving forward and backward while they are carried by the solvent. Note that the B term is divided by u, which is the speed of the solvent.
3. C, the mass transfer term, which corresponds to pigment molecules moving sideways across the paper because they have affinity for the paper. Note that this term also has sovent speed (u), but this time it is in the numerator rather than the denominator.

Optimal Separation

In chromotagraphy, the resolving power depends on a variety of factors, one of which is the speed of the solvent. Higher speed is good to counteract diffusion. But lower speed is also good because it allows more time for the pigment to interact with both solvent and paper. If you were designing an experiment, what would you choose as the optimal speed of the solvent? This is the blue line above, which combines the A (purple), B (yellow) and C(light blue) terms. The knee-jerk response is the value that minimizes H, or about 30 mL/min in the graph above. In theory, that value provides the best separation. However, this is not the value used in practice.

Every experiment involves some imperfections. As a result, on any particular day, dialing in 30 mL/min might not be ideal. Perhaps there’s an obstruction in the line that results in 20 mL/min or perhaps the pressure is high resulting in 40 mL/min. There are a lot of things that happen in the real world that makes practice different from theory. Because of this, experimentalists set their flow rates higher than the theoretical maximum. If they find the flow is off a little, it’s better to be on the right side of the maximum than the left. On the left side, if you’re off by a little, the performance drops way down.

What does this have to do with driving?

Wait, you’re still reading? Okay, I had better relate this to driving. The curve above looks a heck of a lot like the slip angle curve turned upside-down. In theory, you want to drive the slip angle that maximizes grip. That’s the peak of the curve. In practice, you want to drive to the right. That is, it’s better to overdrive your tires than underdrive them. FOR PEAK GRIP. Let’s be clear about one thing here, if your goal is optimal speed, then you care about optimal grip. If you care about other things, like tire wear or crashing your car, this isn’t necessarily the correct answer.

Driving on the right side of the slip angle curve takes courage, training, and more training. One reason I tell people to drive on all-season tires is that the slip angle curve is broader. When training, make the exercises easier. When learning to swim, you don’t throw novices into an ocean with giant waves. That will give them a lungfull of water and a fear of swimming that will last a long time. You put novices in the shallow end and give them things to hang onto. The same is true of driving. If you want to learn how to control a sliding car, don’t use R-comps on track. You’ll be surprised when they lose grip, you’ll spin and that will develop a fear of driving the limit. Instead, drive your car on slippery surfaces at low speed in a controlled environment (e.g. skid pad, simulation) to develop confidence in controlling a sliding car.

You suck at training

Type 1 suckage: “I use R-comps because I want to train on what I’ll be driving on”. This is most drivers. Almost every track day enthusiast drives on 200TW or less. I think they do this because they prioritize lap time over learning. A lot of HPDE regulars (including instructors) never learn to drive on the right side of the curve and their solution to getting faster is buying a faster car.

Type 2 suckage: “I drive in such a way that I never slip”. If you’re sim racing, you can drive just under the limit, watch half of your competitors crash out, and take 3rd place on the podium every time. This attitude isn’t improving your skill though. If you get into a situation where you need to control a sliding car, (e.g. off track, in rain, on dirt), you’ll wish you had driven more on the right side of the curve.

Type 3 suckage: “I always drive on the right side of the curve”. If you want to be an excellent driver, you have to also practice driving the left side of the curve. There are times (e.g. endurance racing) where wear-n-tear are more important than lap times. If you don’t practice the left side, you can’t optimize the left side.