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This is the second of what will be an occasional column in which we’ll try to use very simple science to try to explain not just how people win bike races, but why. If you’ve got questions about bicycling science, let us know in the comments section below, and we’ll try to tackle them in future editions.
Saturday’s epic Strade Bianche was packed with notable performances, but as a guy who covered cyclocross in Europe for a decade, it was ’cross world champion Wout Van Aert’s ride into third place that stood out for me. The 23-year-old Belgian managed to gut his way into the day’s decisive break, then rode to a third-place finish in his first attempt at the race.
To get there, he had to overcome an ugly moment on the Santa Caterina climb into Siena. Van Aert, cramping, simply could no longer turn the pedals, tumbling to the ground before grabbing his bike, running a few steps, re-mounting, and riding his way up the final stretch of the climb.
A lot went into Van Aert’s difficulties on the final climb: a slick road surface that required ultimate concentration and balance, five hours of riding in grueling conditions, and muscles that were literally seizing up. But still, I’m not just a guy who wrote about cyclocross for years, I’m also a physicist, and it got me thinking: Just how hard does a hill have to be to force a cyclocross world champion off his bike?
Van Aert posted his ride data to Strava, and it is a sight to behold. Five hours and 186 km worth of astounding efforts in the worst of conditions. And lucky for us, we can use it to get a handle on the effort spent on that final climb up to the finish at the Piazza Del Campo.
— Wout van Aert (@WoutvanAert) March 7, 2018
According to Strava data, the climb is 210m long with an average gradient of 15%, including a few pitches towards the end that angle upwards as much as 25%. Percent grade is a measure of how far upwards you travel over a certain distance, or the rise over run of a climb. On a 1% slope you would travel 1m upwards for every 100m you travel horizontally; on a 15% slope, you travel upwards 1.5 m for every 10m of road you pedal.
Anybody who rides in a place with hills knows a 15% grade is a viciously steep climb. On a 15% slope you will climb about 1000 ft (about 300m) over the course of just 1.25 miles (2.1km). But a 15% grade works out to an angle of just 8.5°, which is actually quite a shallow angle. So, you might find yourself asking how such a mild slope turns out to be so hard to climb on a bike.
We can use some basic physics to answer this question.
We’ll keep things simple by just looking at the a Wout’s average performance on the climb and the climb’s average gradient. We could look at what happened on the steepest part of the climb, where he was forced to dismount, but because of his bobble there’s a little gap in his data there, and besides, the math for his average performance is a little easier to understand.
If you took an introductory physics course in school, you probably learned to tackle questions like this in terms of forces — figuring out the force of gravity, then using trigonometry to calculate how hard gravity pulls you down the slope. But it turns out a simpler way to think about this, particularly for cyclists who are used to thinking about power, is to consider it energetically.
When you climb a hill, you have to do work to overcome the force of gravity pulling you down towards the center of the Earth. As you ascend, you expend energy with your muscles. This energy is effectively stored in your body as potential energy, and you get it back when you descend. Gravity pulls you down the hill; all that potential energy you stored on the way up gets converted into speed, or kinetic energy.
No matter how steep the slope you climb, the energy it costs you to climb depends on the same three factors. First is the pull of gravity, or gravitational acceleration, second is your mass, and third is the height to which you ascend. These three numbers, mass × gravity × height, give you the energy expenditure to overcome gravity and climb.
Of course, traveling at the same speed, you will rise faster on a steeper slope. So you have to spend more energy over the same amount of time to climb a steeper slope. Since energy expenditure over time is how we measure power, this is another way of saying the steeper the slope, the more power it takes to climb it.
This simple relationship allows us to calculate the average power Van Aert had to spend to climb the Santa Caterina — up until the point he fell, anyhow. Strava tells us this slope rises about 32 metres over its 210 m length. And it tells us he did the climb in about 1:13. (He toppled over right at the end of the Strava segment, so we’ll round down to an even 70 seconds to account for this and keep the numbers a little simpler to work with.)
According to his team website, Van Aert weighs 74kg (163 lbs). If we add in a bike around the UCI minimum of 6.8 kg, and a few extra kg for his clothes and whatever else he was carrying, we can estimate he had to haul about 83kg up to the top of the hill. Then we can use the formula above to calculate his energy expenditure and divide by the time it took to get the average power spent to fight gravity on the climb.
Turns out Van Aert averaged about 370 watts, just to fight gravity. In fact, Strava shows Van Aert spent more power on the climb than this, but this is a pretty accurate measure of the work he did just due to the slope. The rest of his effort was pumped into overcoming the slight wind resistance at the slow speed he was traveling, rolling resistance, and other mechanical inefficiencies.
For some perspective, we can use a very slightly modified version of the equation I wrote about last week to estimate what kind of headwind Van Aert would have to battle to expend the same power on a flat surface as he did on that climb. Traveling at Van Aert’s average of about 11kph, it turns out that headwind would be screaming at about 70 kilometres per hour (45mph). Ouch.
After you ride a bike enough you probably know most of this intuitively from experience: A 2% grade is not bad, an 8% grade is a solidly hard climb, and a 15% grade is extremely difficult. Still, it seems to defy logic that climbing a slope of just a few degrees turns out to be equal to doing battle with a tropical storm force wind.
I think the underlying physical logic is this: Gravity is a very strong force. You might not notice it most of the time, but it’s actually much stronger than most of the forces most of us experience in our daily lives. In free fall you accelerate at roughly the same rate as the fastest cars ever built, cars like the Porsche 918 Spyder. Those g’s you feel pushing you into your seat during takeoff on an airplane? Maybe they add up to 10 or 20% of gravity at most.
Because of this, you don’t need a big slope to generate big forces — and the power to overcome those forces adds up quickly. And on the steepest part of a climb with a 15% average gradient, in the rain, on a street paved with slippery, smooth stones, after 185km of racing, while both legs are cramping? Forget about it. It’s time to follow Wout’s example, hop off the bike and run.
— Kingston Wheelers CC (@kingstonwheeler) March 3, 2018
About the author
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 Ph.D. 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.