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Welcome back to Peloton PhD, a column in which physics PhD Dan Seaton uses science to explain the hows and whys of bike racing. In this instalment Dan looks at cornering, why we lean into corners, and how it can go wrong.
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.
The Spring Classics. My favorite part of the road season. From Strade Bianche’s iconic gravel roads to the bergs of Flanders’ to the impossible cobbles of Paris-Roubaix, I love the dynamic racing and suspense of the classics like no other road races. Winning one of these races requires the perfect marriage of tactics, endurance, power, and technical prowess, and rarely can you be sure of the winner until mere moments before they cross the line.
In previous columns about the physics of cycling we talked about what it takes to win one of these races and, in fact, we’ve already seen riders successfully use tactics that we described before. Zdenek Stybar rode a late attack to an impressive victory at Omloop Het Nieuwsblad in February, for example. Unfortunately, as often as riders leverage physics to their advantage, others suffer for it: they crash, they bonk after too much effort, and like Wout van Aert at Paris-Roubaix, sometimes they just can’t catch a break at all.
Avoiding disaster is as much a part of winning a classic as choosing the right race strategy. The twitchy, narrow roads on which these races play out are trouble waiting to happen. They’re muddy and slippery in wet conditions, dusty and unpredictable in dry weather. Any careless turn — or just a bit of bad luck — can cost a rider a shot at victory.
In honor of these unlucky few, let’s look today at how we steer our bikes through a turn and why those muddy springtime roads are so fraught for cyclists.
Why do we lean?
Anybody who has ridden a bike knows you have to lean to turn. In fact, you do this intuitively, without even thinking. But why do you do it? Superficially, you might think that leaning into a turn would only make it more likely you’ll crash, but, in fact, it’s the opposite. If you tried to turn without leaning at all, you’d be sure to crash. Why is this?
There are a few ways to think about it, but it boils down to the fact that for a bike to turn (to turn right, say) something has to push it to the right. Think back to your high school physics class: Newton’s first law says that unless a force acts on an object, it’ll just keep doing whatever it was doing. If you are riding along in a straight line and no forces act on you, you’ll just keep going straight at the same speed. To turn right, something has to push you right.
It’s logical that if you turn the handlebars to the right the front wheel will start to roll to the right and the bike will have to diverge from its straight path. So where does the force come from to move the bike in the direction of the turn? Friction between the tires and the road.
Think about it: if somebody starts pushing your tires to one side and you do nothing about it, you and the rest of your bike will act like a lever. The bike will start to rotate around its center of gravity. As the tire moves right, your upper body will rotate to the left and you’ll tip over (assuming you make no corrective action).
How do you prevent this? You need to apply an equal torque to the top of your body to counter this tendency to rotate away from the direction of the turn. And where does this force come from? On a bike, there are very few options for generating forces, but there’s one force (we talked about this one last year too) that’s all around you: gravity. By leaning, you can use gravity to your advantage.
When you lean into a turn, gravity applies a force to your body — towards the ground on the inside of the turn. As you lean to the right and the ground pushes your wheels to the right, gravity also pulls your upper body down and, because you are leaning, to the right. This creates a counter-torque on your upper body, fighting its natural tendency to rotate to the left.
When you lean at just the right angle, you achieve equilibrium. The road pushes you to the right, your leaning body pulls you to the right, and you rip a perfect turn.
When good turns go bad
As it turns out, bikes are essentially self-balancing, so even if you try to turn right without a lean, you probably won’t fall. Instead, the rotation of your body to the right will induce a lean — and a turn — to the left. This is what we mean when we talk about counter-steering. You turn the bars the opposite direction of where you want to go, which sets up a lean in the other direction that takes you where you do want to go.
So what happens when a good turn goes bad? To explain this we have to invoke two more laws of physics. The first is Newton’s second law, which tells us how the force you apply to an object is proportional to the object’s acceleration (F=ma; force equals mass times acceleration). The faster you enter a turn, the more rapidly you have to accelerate in the direction you want to turn (to avoid running off the road before you get through the turn).
So Newton’s second law tells us that the faster you progress through a turn, the more force is required to move you through the turn. And remember, that force has to come from somewhere — in this case, it’s the road pushing on the tires.
Newton’s third law, meanwhile, tells us that every force has an equal and opposite partner pushing back against it. The road pushes your bike to the right, your tires push back against the road in the opposite direction. The friction force between the tires and the road is surprisingly strong — plenty strong to push you through a hard, fast turn most of the time. But if you hit a slick spot or even just enter the turn a little too fast, there won’t be enough friction to keep your wheels in the turn. The outward force on your tires will cause them to start to slide to the left, out of the turn.
In this case gravity stops being your friend. The lean that counter-balanced you will start to work against you. As your wheels slide out your body will start to rotate, the wheels going left, and your head going to the right. Without any force to counteract it anymore, gravity will pull you to the ground and you’ll crash.
Wout van Aert’s costly fall on his way to Roubaix on Sunday was a textbook example. He leans hard into a right turn on what appears to be a very smooth road. Although he had just taken a new bike, odds are both the road and his tires were dusty from the race, perhaps inhibiting the normally tight connection — friction — between the road and tire rubber that should keep him latched into the turn. Without sufficient friction, the outward force on his tires cannot be balanced and they begin to slide outwards.
Once a slide begins, the friction force generally decreases even more, and the fall accelerates, unrecoverable. (Though, credit to the three-time cyclocross world champ — he made a valiant effort to save it.)
Putting it all together
So how can we harness physics to turn better? And is there anything we can do to avoid this kind of mishap? Well, for one thing, physics tells us a lean and its partner turn are deeply coupled: just as a sharper turn will induce a harder lean, a harder lean will induce a more rapid turn. By learning how to effectively counter-steer — that is, how to rotate the bars against the turn you want to make to initiate a lean — you can learn to corner more rapidly.
However, you have to remember, the harder you lean, the greater the force between tires and road required to push you through the turn, and the greater the risk of a fall. Here, physics tells us the most important thing is to make sure you maximize the force of friction holding your wheel in the turn.
The maximum friction force you can sustain, it turns out, is proportional to the force with which gravity pulls your wheel to the road. Some of this you can’t control, but there’s one aspect you can. It’s important to keep your weight evenly distributed between the two wheels of the bike. If you sit back and unweight the front wheel, the maximum friction force that can be maintained by that wheel will decrease, and you’ll be more likely to slip. Video of van Aert’s crash suggests this might be what happened to him: the front wheel started to slide first, taking the rest of the bike with it.
It actually turns out that the dynamics of bicycle balance, stability, and steering are much more complicated than this broad look, which really captures only the most basic properties of bicycle steering. It’s only very recently that physicists and engineers started to put together a complete enough picture to really understand how and why bicycle steering works.
So stay tuned. We’ll try to dig deeper into the deep weirdness of bike stability in a future column.
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 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.