The science of riding a bike

By David Klein

David Klein is a science storyteller based in Wellington, who has a love of science, entertaining, and bikes.

Featured in Capital #39
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When I hop on my bike, I don’t really think about it – I just turn the pedals and eventually end up where I need to go.

Recently though, I’ve been thinking a lot about the intersection of cycling and science. 

First it’s worth simply considering the quiet miracle that is the bike. You and two wheels gliding along, using what has been called the most efficient means of transport. A whole string of engineering masterpieces have evolved to create the bike you’re riding – bearings, chains, levers, and so on. Sometimes it seems so effortless and natural that you can forget about the bike (I like to do this, just imagining myself floating along). But let’s think about the close partnership between you and the bike.

It’s a closed system. There’s no mysterious fuel in the engine, or mechanics in the train. Just you – your body and legs – working in concert with your steed to get you where you want. And it’s food that powers the system. Through a series of complex processes, your body breaks down all the food you eat, separating out the fats, sugars, carbohydrates and proteins. These components are then assimilated into your cells, giving you the energy to keep cycling. It’s rather nice to reflect as you eat your packed lunch and drink your water that you’re powering the trip, while lightening your load.

And it can be quite a load – food, water, and sacks and clothes and camping equipment. I have a Surly “Big Dummy,” which is a long tail cargo bike. It can carry up to 100kg (in theory!), but in turn weighs quite a bit to support all that. I’ve often felt like a tortoise, making my way slowly up a hill, with my “house” on the back.

Pedaling yourself and all your gear up a hill obviously requires energy input – first to get things moving (the first law of motion! An object at rest will stay that way unless a force acts upon it), and then to overcome the force of gravity. The work you put into raising yourself and the bike up a hill gets turned into gravitational potential energy. It can be a real struggle creaking up to the top (Wellington is an ideal training ground), but all that stored energy has a wonderful flip-side. Your gravitational potential is turned into kinetic energy, and a fully loaded bike can really move! With only friction, the wind and traffic conditions to slow you down, you can cover a lot of ground. Once you’re flying down that hill, you have momentum. You are mass in motion, and momentum is that mass times velocity. With a fully loaded bike, all the mass will keep you traveling for some time.

Hills are fascinating, but it can be good to take your mind off the upward grind. I often find myself thinking about instantaneous rates of change – cast your mind back to high school calculus for this one. Between any two points on a curve (or say, a hill), we can find the average slope or tangent. We can bring these points closer together, finding a more accurate tangent – but what if we want to know the slope at a single point? For that, we need differential calculus. At any centimetre along a hill, we could stop and calculate the slope. In practice, nearing the top of a hill, I do try to spot the point at which the slope finally becomes zero, flattens out, and the hill “stops.”

Hills, gravity, hours of cycling – how come you don’t just fall over sometimes? One of the reasons lies in the wheels. As they turn, the angular momentum of their spin is conserved. The wheels “want” to stay in the plane in which they’re traveling, which means that your bike does a good job of staying upright all by itself. 

Like so many things, cycling is a whole string of little miracles. Of course, you don’t need to know any of this to enjoy the ride. The big question is, where do you want to cycle today? 


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