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by Dan Seaton
October 3, 2018
Photography by Kristof Ramon
Welcome back to Peloton PhD, a column in which physics PhD Dan Seaton uses science to explain not just how people win bike races, but why. In this instalment Dan uses the elite men’s time trial at the recent Road World Championships to explain why it takes a special kind of rider to succeed in TTs on varied terrain.
Got a question about the science of cycling? Let us know in the comments section below, and we’ll try to tackle it in future editions.
In previous editions of this column we’ve talked about what a nightmare air resistance is for a chase group and how you can reach speeds where going even a handful of km/hr faster becomes a physical impossibility. We’ve also talked about how brutal gravity is and how even a grade of a few percent can be absolutely vicious to climb. If ever there was a great opportunity to see these lessons in the real world, the men’s individual time trial at last week’s Road Worlds was it.
The race, which combined a long, mostly flat run up to the steep and difficult Gnadenwald climb — with its average 9% grade for more than 3 km and a total climb of about 5 km — could only be won by a truly complete rider. In his winning ride, Rohan Dennis had to show off both of the skills we talked about before, battling air resistance for 30 km before battling gravity for the next 5 km.
As it turns out, a lot of riders can do one better than the other. Dennis — and the others who finished on the podium — did both.
As we’ve discussed previously, the power it takes to overcome air resistance increases as the cube of the velocity of the rider. So, the power you need to go faster increases eight times every time you double your speed. But the weight of the rider has essentially no bearing on this equation, so if you want to go fast on the flats it’s mainly a matter of how much power you produce.
On the other hand, when you climb, the power you need depends on the slope, your mass, and your speed. If two riders produce the same power, but one of them is lighter, the lighter one will climb faster every time. Here it’s not how much power you produce, but how much power per mass, or watts/kg. A good climber doesn’t necessarily pump out massive power numbers that would look impressive next to a world class sprinter, but rather they make a lot of power for their weight.
The plot below shows how this works. On the horizontal axis we have the power you are producing at any given time. On the vertical axis, the grade you are riding in percent. If you are climbing a shallow slope, almost all your power can go into overcoming air resistance, but as the slope increases, more and more of your power has to go into climbing, with the result that you will go slower overall.
The dividing line between the two shaded regions shows where, for a rider of average size and weight, the power to fight the slope and the power to find drag are equal, with various speeds indicated to show how fast you can go as a function of power.
At about 450 watts, on a slope a little below 3.5%, your power is equally divided between drag and the climb, and you’ll be able to ride about 35 km/hr in this situation. If the slope gets any steeper, you’ll find yourself in the white part of the graph, mostly battling gravity. If the slope slackens, you’ll be in the shaded part of the graph.
Riders who are good in both of these regions are often Grand Tour contenders — if they have the endurance for long climbs and grueling TTs over three weeks — or maybe hilly classics riders if they have less endurance but a more punchy style. Climbing specialists do well in the white. Breakaway specialists and pure sprinters will do better in the shaded area.
We can see exactly how this worked to favor certain well-rounded riders in the Worlds time trial and how it hurt others. Unfortunately, most of the top riders at Worlds didn’t publish their power data, but two riders who did — and who have very different skill sets — finished back-to-back in 28th and 29th. Let’s look at a couple of case studies I was able to put together from some Strava data.
Italian Alessandro de Marchi finished 28th. According to the official results, his first split, mostly on flat roads, was nothing to write home about. He covered the 16.6 km section in 19:46, only 46th best on that part of the course. His second split, which includes the climb, was 29:34, 13th best on that section. According to his team, de Marchi weighs just 66 kg (about 145 lbs), so he’s a pretty small guy.
Meanwhile, Britain’s Alex Dowsett was 29th. His first split was 15th best overall, at 18:53, but his second split was not so great — he was just 43rd overall at about 30:52. Dowsett is a much bigger rider, weighing around 75 kg (165 lbs), so perhaps it’s not so surprising his climb was not as strong. It’s also worth noting that Dowsett and de Marchi’s final splits, on the descent, were actually pretty close together, just a handful of seconds apart, so we’ll assume they basically neutralized each other there and focus on the first two parts of the race.
Here’s what’s really interesting: using Strava to estimate the pair’s respective power on the flat first 30 km and the steep part of the climb, I arrived at the following:
Dowsett put out more power on the flat than de Marchi, and it showed. (Dowsett is also probably a bit of a better time-trialist than de Marchi, but we’ll return to that in a moment.) The interesting thing is that he also put out more total power than de Marchi on the climb. But his power per kg was about 12% less than de Marchi, and indeed, he went slower.
It’s the exact principle we’ve been talking about: on the flats, pure power wins out. On a steep climb, all that matters is watts per kg.
In fact, my estimate shows Dowsett climbed about 14% slower than de Marchi. The fact his power per kg was about 12% less shows just how well this rule holds. If these numbers were wildly different, you’d have reason to suspect what I’m telling you isn’t true. The fact they are so similar confirms that what we’re talking about here works in the real world.
Dowsett looks like a rider who does best in the shaded part of our graph; de Marchi in the white part. But neither rider looks to be all that good on both sides of the line.
Before we conclude, here’s one more wrinkle for you: the rider who finished 10th overall, Denmark’s Martin Toft Madsen. Madsen’s first split was 12th overall at 18:45, and his second was ninth at 29:19. In fact, Strava reveals that his speed on the climb was a little slower than de Marchi, but that second split includes quite a bit of flat, so his advantage there boosts his result slightly.
Madsen put together a remarkably consistent race. He performed well in both the shaded region and in the white region of the graph, and it paid off. But what’s really surprising is what Strava’s power numbers show about his overall ride.
Madsen’s climb and his watts per kilogram numbers match pretty much the result we saw above. He number is about 6% less than de Marchi’s, and it turns out he went about 7% slower. No surprise there. What’s wild is that he actually produced the least overall power of any of our three riders, but he went by far the fastest on the flat section of the race.
This brings up another key concept. For most of this discussion I’ve swept the small variations between riders’ shapes and kits and bikes under the rug. Why? Because those variations are small compared to changes in power due to changes in speed. But that’s not entirely true: riders who are more aerodynamically efficient wring more value out of each watt on a flat stretch.
Like anybody, at a certain speed they will run into an insurmountable wall as the aerodynamic power demands increase, but that speed is a percent or two faster for them than for everybody else.
Just as you’d expect, sports scientists have a name for this concept. They call it watts/CdA, and just as watts/kg is a measure of your power output to weight (we could call it “climbing efficiency”), watts/CdA is a measure of your power to aerodynamic efficiency. CdA (drag area), refers to your drag coefficient × frontal area — the terms in the aerodynamic power equation that a rider can control. You use more aero materials in your bike and kit to reduce Cd, and you can adopt a more aero position to reduce A.
A rider like Madsen, who made a fairly serious hour record attempt this past summer and is a three-time Danish TT champion, is able to get into a very aerodynamically efficient position. As a result, his watts/CdA is higher than many others. This means he can maintain a slightly faster pace with less effort. He’s not a true mountain goat, but he’s light enough to climb efficiently. And being such a well-rounded rider, he was rewarded last week with a top-ten finish at Worlds.
So what’s the lesson? If you are a big, powerful rider, and want to have a better shot at winning races with varied terrain, your best chance is by dropping weight and improving your watts/kg score. We’ve seen a number of riders do this and reap benefits in big-time stage races — just think about Geraint Thomas.
On the other hand, if you’re a small person who can climb, but can’t make massive power numbers, all is not lost. You might not be able to improve your total power all that much, but you can get faster on the flats by improving your CdA — getting more aero — and wringing more out of the power you can produce.
And if you’re already pretty good at both? Well, good for you. Maybe there’s a yellow jersey or some rainbow stripes in your future.
Dan Seaton has been photographing and writing about cycling for the better part of a decade. He has been a contributor to VeloNews, Grit.cx, and CyclingTips. He also has a PhD in physics and, when he’s not writing about bikes, is a solar physicist at the University of Colorado. He lives with his family in Boulder, Colorado.