The Bicycle: A Marvel of Physics and Engineering

Oh, how I love riding my bicycle! It has gotten me all over Chicago, all along the lakefront from the far south side to the north suburbs, through the college neighborhoods and the ethnic neighborhoods, residential ones and industrial ones, and through downtown. My bicycle has enabled me to explore parts of the city I never pass through or only stop in for specific reasons, with direct exposure to the sights, sounds, and smells of each local community.

I also love my bicycle as the beautiful machine it is: Its 24 speeds, its straight lines, its deep, black color. I bought it as a gift to myself after my last one was stolen while I was taking a final exam (talk about adding insult to injury). I love how efficient it is. For the amount of energy I put into it, I get most of it back in the form of forward motion. In fact, in the right conditions, bicycles are over 98% efficient! Cars on the other hand, don’t even come close: they’re only 20-40% efficient. Think about all that extra weight you’re pulling every time you accelerate. Recall the last time you burned your finger touching a running car engine. Where did that heat come from? It’s all the energy your car didn’t use to get you where you needed to go, but rather wasted.

As I ride along Monroe Harbor, swiftly cruising down the Lakefront Trail, speeding past the traffic stuck on Lake Shore Drive, I think about how each car requires an external source of fuel (gasoline), and how each driver is not only transporting themselves, but also a couple of tons of metal. I also have to turn my head away from the street as each car spews putrid, toxic gases into the air. Meanwhile, I rejoice in the fact that my bicycle doesn’t consume fossil fuels and it doesn’t have to waste energy sitting in traffic. The fuel for my bicycle comes from the food I eat.

bicycle physics
The rear axle of a fixie bicycle.

As I mentioned, I have a 24-speed bike. But if you’re looking to buy a bike for yourself, you have a lot more options. For instance, a lot of urban riders are buying fixed gear or “fixie” bikes these days. On these bikes, the chain wraps around a sprocket fixed to the pedals and a sprocket that is fixed to the back wheel. Because the sprockets are fixed to the pedals and the wheel, respectively, the wheels and the pedals always revolve together. This is a simple and easy-to-manage design, but it also causes problems when you want to coast: You simply can’t. If you try to stop pedaling while you’re going downhill, your wheels will stop too. On a fixie, a revolving pedal always revolves with the wheel, and vice versa, no exception.

bicycle physics
The rear axle of a single speed bike.

To solve this problem, most bicycles, such as the standard single-speed bike, have something fixed to the back wheel called a “freewheel.” A freewheel, as opposed to a fixed sprocket, allows you to stop pedaling, and even pedal backward, while your bike coasts forward.

When you’re pedaling forward with a single-speed bike, it acts much like a fixed-gear bicycle, in that pedaling will cause the wheel to revolve at a fixed speed compared to your pedals. But while a fixed gear acts like a wrench, a freewheel works like a ratchet: when you stop pedaling or pedal backwards, the pedal on a single-speed bike disengages from the sprocket and the sprocket continues to revolve by its own momentum. We’re coasting now!!

The video shows how this works. The first half of the video shows what happens when you coast or pedal backward, while the second half of the video shows what happens when you pedal forward.

Some cyclists prefer a fixed-gear bicycle because of its simplicity. But personally, I would choose a single-speed bike any day. If I did happen to find a hill in Chicago (it does happen sometimes!!), I’d much rather keep my feet on the pedals as I ride down it, rather than awkwardly raise my legs to get them out of the way or ride those pedals like a madman, trying to keep up with the momentum of the bike.

For me, a single speed isn’t even enough. I’m happy that a bike with a freewheel can coast, but when I’m pedaling forward, I want more flexibility. On a single-speed bike, as I said previously, the mechanics of pedaling forward work the same way as on a fixie. It’s pretty simple: the amount I revolve my pedals and the distance I travel will always be in a consistent ratio. On solid ground with no wind, this means that the amount of force I apply to the pedals will decide how fast I will go: the more force I apply, the faster the pedals revolve, and the faster the bike will go. But on hills and rough terrain, we run into problems. Whether it’s gravity pulling me down as a ride up an incline or it’s mud holding me back in a wet field of grass, for example, I’ll struggle more than usual to move forward. It is going to take more of my energy to overcome these forces and keep my bike moving at the speed I want to go.

bicycle physics

To circumvent this challenge, I opted to purchase a multi-speed bike, with three sprockets of successively smaller size fixed to the pedals, and eight sprockets in a similar arrangement fixed to the back wheel. On any given gear, like on any other type of bike, one full turn of the pedal makes the front sprocket revolve all the way around. That means if this sprocket has 53 teeth, for instance, one full revolution of the pedal will cause the bike chain to advance 53 spots. Meanwhile, the sprocket on the rear wheel is smaller (it might have 14 teeth or so), which means that when the chain advances 53 spots, the rear sprocket has to revolve more than once to advance as many spots. It will make one full revolution for 14, another to get to 28, a third to reach 42, and part of another to reach 53, matching a full revolution of the front sprocket. Notice how, in the video below, the smaller (rear) sprocket is revolving faster than the larger (front) sprocket. This is because the smaller sprocket has to revolve more to keep up with the chain that is being guided by the large sprocket.

The difference between the sizes of the front and rear sprockets is called the “gear ratio” and it affects how far I go each time I revolve the pedals. The smaller the rear sprocket is (on higher gears), the fewer teeth it has, which means it will revolve more times per full revolution of the pedals, and the bike will move farther. And this means that by changing the size of my sprocket, I can change how much force I need to apply to the pedal to make my bike move. In fact, if I revolve the pedals once while I’m riding on a smaller sprocket, causing the wheels to revolve a lot more per revolution of the pedal, the amount of energy I’ll need to put into pedaling will be spread out across more revolutions. This means I’ll have less energy to put into each individual revolution, and pedaling will feel a lot harder.

Conversely, If I’m on a lower gear, where my chain wraps around a larger sprocket, all the energy I put into the pedals will translate into less motion, which means that the energy I put into pedaling is more concentrated over a shorter distance, which makes pedaling feel much easier.

Riding in high gear, with a small sprocket, is really great when I’m going down hills, when my momentum is doing most of the work and my daredevil side wants to add a bit more speed on top. But going up hills, this could be torture for the calves.

As I mentioned previously, gravity is working against me when I’m going up a hill. In this case, I will want to switch to a lower gear. I won’t get to the top as fast (because I’ll be covering less distance per pedal stroke), but at least I won’t have to push as hard on the pedals to move forward, which means I’ll be able to tolerate the ride!

What Else Impacts Your Riding Efficiency?

External factors such as wind resistance and gravity aren’t the only things that affect the amount of force you have to put into your riding to get where you want to go at a certain speed. A lot of it depends on you and the bike you’re riding. When it comes to internal factors that affect your efficiency, enemy number one is rolling resistance.

Rolling resistance is the dragging force you feel when your bike tires are underinflated or when you’re riding on soft ground. When your bike wheel is rolling along the ground, the part that touches the ground deforms, using up energy and causing your bike to lose momentum. Besides underinflated tires and riding on soft ground, a heavy bicycle frame and your own weight all increase rolling resistance on a bicycle, meaning you have to work harder to travel at the same speed.

Weight also puts more pressure on the joints in your bicycle, causing more internal friction that takes energy away from your forward motion. In addition, weight also affects acceleration – have you noticed that it’s harder to get a full shopping cart going from a complete stop than an empty one? That’s because it takes more energy to change the speed of something if it is heavier. The same goes for your bicycle.

Serious cyclists try to stay skinny and ride lightweight bicycles with well-greased joints and thinner, well-inflated tires to reduce rolling resistance and internal friction as much as possible.

Optimizing a bicycle to minimize the effects of rolling resistance, internal friction, and wind resistance can run you thousands of dollars, so unless you are a competitive cyclist, you’ll do just fine keeping your chain greased and your tires properly inflated.

The Joy of Cycling

Cycling is considered the most efficient form of transportation — even more efficient than walking! It’s also great exercise (coasting down hills doesn’t count), and great for the environment. If you have a choice between driving and bicycling, leave the car in the garage and take your bicycle machine out for a spin. It might feel like more work, but your body and your planet will ultimately thank you for it.


  • Ben Marcus is a public relations specialist at CG Life and a co-editor-in-chief of Science Unsealed. He received his Ph.D. in neuroscience from the University of Chicago.