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# Technical FAQ: Deeply diving into graphs of rolling-resistance data

## An interesting back-and-forth discussion of rolling resistance data.

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Have a question for Lennard? Please email him at veloqna@comcast.net to be included in Technical FAQ.

For Monday’s Memorial Day, here is an interesting back-and-forth discussion of rolling resistance data and its analysis from quite a while ago. You may have to be interested in how many angels can dance on the head of a pin to follow it.
― Lennard

Dear Lennard,
Regarding your January 4 VeloNews posting with remarks from both Josh Poertner and Tom Anhalt- Whatever their real data shows, their “model” for describing what is happening is fatally flawed and does not explain the data. Under Tom Anhalt’s comments there is a link “the plot that illustrates the ‘breakpoint pressure’ concept” that links to a page on the Silca site:

After the first two graphs, which are plots of actual data, there is a collection of three graphs, where the third, “Theoretical rolling and impedance losses..” is supposed to be the sum of the first two, as indicated with a red plus sign. These are cartoons at best, and are very misleading; in fact just plain wrong. The sum of two smooth, that is, differentiable functions, is also a smooth function. Thus, the curves in the third graph cannot result from adding those in the first two. The sum of such functions would be U-shaped with no sharp breakpoint pressure. If they had actually defined example functions mathematically- for example, exponential decreasing and add linear increasing, and plotted, they would have seen this even with no knowledge of calculus. There is nothing wrong with cartoons or hand drawn plots for illustration. But it is clear they made up the sum graph based on what their data seemed to show. It really makes me question the veracity of their other claims, data collection methods, and analysis.

Mike

Dear Mike,
Here is what Silca’s Josh Poertner has to say in response:

“He’s absolutely, technically right about the smoothness of the resulting function if we were to add the functions and plot it in mathematica, or if we were to take an infinite number of measurements at impossibly small air pressure differences in field testing. However, just like wind tunnel testing, when you can only take a finite number of data points at relatively coarse intervals, you will always end up with a hard break point in your graph as we have here (also not to mention, you are pretty much guaranteed to miss the real break-point transition, which theoretically will be smooth). But of course, if we use smoothing functions on the graph, then they become even more misleading relative to the actual amount of data that is taken, so, same as with tunnel data, we choose to just plot the points and use straight line connection.

Because the resulting graphs from the field test data plot with this hard transition, it only makes sense in trying to explain the phenomenon to the average person to show it the same way. People already struggle to get these concepts, and, 10 years ago when this was first published, trying to even get folks to read these articles, much less understand the basic concept here, was pushing a rather large rock up a pretty steep hill. So, adding a sidebar explaining the limitations of the field study data collection and giving a dissertation on the mathematical behavior of adding these functions just seems like a further additional barrier for the average reader. Remember, we’re still trying to convince a large percentage of people that rolling resistance even matters in the first place. So, the entire goal here was to help people build a simple mental model that they could internalize and ideally share with others regarding the then-revolutionary discovery that higher pressure wasn’t always faster. To that end, I’d say we’ve been rather successful, even if we’ve pissed off a few math professors here and there!

I’ll also point out that there is no way that the impedance function is a straight line as we show it on these same graphs (honestly have never run enough of these far enough to know exactly what the function really is…). It certainly can’t be as indicated by the post-breakpoint data, but again, nobody reading these articles needs to know or care about that. Maybe it was our use of the “crayon” line font that got us a pass on that front!”

Josh

And the response from Mike:
Thanks for looking into this and for your response. Josh is still missing the point though, which was not that the real-world data would be smooth if you plotted enough points at “impossibly small air pressure differences”, but that the math used to explain the data is incorrect.

I am all for “simple mental models”- in fact these are often preferred, as long they convey the spirit of the underlying more rigorous analysis. But this is a mathematical argument. Since it is incorrect, I don’t see how it can add to understanding. Why not just eliminate it for now?

Mike

Like I said before, mathematically Mike is right, and I would be thrilled if he or another mathematician went and figured out what the math here really is. However, from a big picture perspective, I disagree that this is a math problem. This is an elevator-pitch/human-behavior-and-understanding problem. The question we were faced with 12 years ago when we discovered this was that now we’ve learned that our previous understanding of things is wrong.

Now we have a repeatable and robust data set of what is much better. How do we, in 30 seconds, explain it to somebody at a charity ride or an Ironman race in a way that they can quickly see the difference in the new model, then open their minds to changing their prior beliefs, and then nudge them into trying out the change we are suggesting? Similarly, how can we create a single image or mental model that is sticky enough that people can both remember it and also then accurately relay it to others, weeks or even months later, alongside the personal anecdote of their amazing experience of going fast while being comfortable at a tire pressure they never before would have considered? For the sake of our blog, event attendance, and public speaking, youtube channel, articles with Velonews, Bicycling, and even WorldTour pros, this isn’t really at all about math, it’s about convincing them to open their minds to choosing an optimum pressure over a maximum pressure.

From my spot in all of this, our job here was in discovering (along with Tom Anhalt) the phenomena, testing it across multiple disciplines and locations, validating it across numerous users (Tom Anhalt, Robert Chung, FLO, now hundreds more…), creating the massive data set from which we could do some curve fitting to begin estimating behavior, and then effectively spreading the word that the old model of decreasing drag with increasing pressure was clearly missing something. Of course, our new model is also still wrong, likely on multiple fronts, but it’s good enough to give us pretty darn accurate predictions, which, for the purpose of making riders faster and more comfortable, is all we really need.

Having said all that, our original, simplistic model remains alive, happily waiting to be updated and improved upon by whoever comes next. And when that happens, I’ll be thrilled to promote the heck out of whoever that is, while also keeping these old models living in the history as, “aww, look at how naive we were” pieces of historical art. Until then, this is the best anybody has come up with, and, quite frankly, these have probably done more to change conventional wisdom and public thinking on this topic than just about any graphic in the history of our sport. So, even being incomplete, or even just plain wrong in some mathematical sense, I think these graphics certainly continue to be useful in helping people change behavior in ways that result in a better experience.

Lennard Zinn (https://www.velonews.com/byline/lennard-zinn) , our longtime technical writer, joined VeloNews in 1987. He is also a custom frame builder (www.zinncycles.com) and purveyor of non-custom huge bikes (bikeclydesdale.com), a former U.S. national team rider, co-author of “The Haywire Heart,” and author of many bicycle books including “Zinn and the Art of Road Bike Maintenance,” “DVD, as well as “Zinn and the Art of Triathlon Bikes” and “Zinn’s Cycling Primer: Maintenance Tips and Skill Building for Cyclists.”
He holds a bachelor’s in physics from Colorado College.