Tour de France Physics

It’s Tour de France time. What goes best with long sporting events? Physics is the answer. Here are some summaries of older posts about physics and cycling.

In one of the stages of the Tirreno-Adriatic race in 2013, there was a 27 percent gradient. That’s pretty steep for a race. Many cyclist would just have to walk their bike up such an incline. But how steep is too steep? There are a few different reasons that a cyclist couldn’t make it up an incline.

• Limit due to human power. As a cyclist rides up an incline at a certain speed, it requires energy to move up the hill (work against gravity). Based on my estimations, a human with a 300 Watt output could go up a 20 percent gradient at 2 m/s.


• Limit due to center of mass. Of course you can’t ride up a vertical wall, a cyclist would flip backward. The key is that the center of mass of the human-bike system must stay in front of the rear wheel. Based on this, I estimate a cyclist leaning forward could conquer a 93% gradient (this is an incline of 43 degrees).


• Limit due to friction. What prevents the bike from sliding down the incline? Friction depends on the force the ground pushes on the bike (the normal force). At a steeper incline, this force and thus the frictional force decrease. With some estimations of the coefficient of friction, I get a maximum gradient of about 80 percent.

There is one more possible gradient limit – it’s in the homework questions below. Here are all the details from the original post.

What if you put your bike in a super aerodynamic shell with a lower profile? How fast could you go? Could you go 100 mph? If you assume a small enough cross sectional area and drag coefficient then yes. If you have a 1,000 watt human you could go 100 mph. 1,000 watts seems crazy – but it’s not too crazy for very short periods of time.

Here is the whole post with the details.

In 2010, Cancellara would have such awesome attacks that people wondered if he was cheating with a hidden motor in his bike. Does he cheat? No. There are no hidden motors. If you look at a video of one of his attacks, two things happen. First, Cancellara is going just a little bit faster than the pack. Second, he has a slightly higher acceleration. These two things together make his break away look more dramatic. Here are the details.

But what if you really did have a hidden battery in your bike? In this other post, I estimate that you could have a 1.6 kg hidden battery that would give you about 500 watts for 1.5 hours. That’s just an estimate.

What happens if you are riding a bike both into and against the wind? It turns out that the headwind hurts you much more than a tail wind benefits you. Why? Two reasons. If you make a round trip, you will have a lower speed (and longer time) going against the wind. Also, if the air drag is proportional to the relative air speed squared, a little increase in wind means a major increase in required power.

Here is the full post.

How do you learn to ride a bike? Training wheels is NOT the answer. They really don’t help. What does this have to do with the Tour de France? Well, don’t you think at some point these cyclists had to learn to ride a bike?

Why do training wheels not help? They don’t teach you the most important thing about riding a bike: if you are falling to the left, turn to the left. If training wheels don’t help, then what works? I recommend a push bike. With a push bike, a child just uses his/her feet to propel the bike forward. Here is an example.