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A bicycle in the desert

The science of bicycles

by Chris Woodford. Last updated: June 18, 2014.

If you had to pick the greatest machine of all time, what would you say? If we were talking about machines that helped spread knowledge and educate people, you'd probably opt for the printing press. If we meant inventions that let people farm the land and feed their families, you might plump for the plow or the tractor. If you think transportation is really important, you could go for the car engine, the steam engine, or the airplane jet engine. But for its sheer simplicity, I think I would pick the bicycle. It's a perfect example of how pure, scientific ideas can be harnessed in a very practical piece of technology. Let's take a look at the science of cycles—and just what makes them so great!

Photo: The bicycle—a brilliantly simple form of transportation, wherever in the world you happen to be. Something like 130 million new bicycles are produced, worldwide, each year and over 90 percent of them are now manufactured in China. Photo by Roger S. Duncan courtesy of US Navy.

What's so good about bicycles?

What's so good is that they get you places quickly without gobbling up fossil fuels like gasoline, diesel, and coal or creating pollution. They do that because they very efficiently convert the power our bodies produce into kinetic energy (energy of movement). In fact, as you can see from the chart opposite, they're the most efficient transportation machines humans have developed so far. Harnessing the power from your muscles in an amazingly effective way, a bicycle can convert around 90 percent of the energy you supply at the pedals into kinetic energy that powers you along. Compare that to a car engine, which converts only about a quarter of the energy in the gasoline into useful power—and makes all kinds of pollution in the process.

Chart comparing the efficiency of bicycles with car, diesel, and steam engines, gas turbines, electric motors, and other common machines

Look at it this way: If you drive a car, you're dragging a lump of metal that probably weighs 10–20 times as much as you do wherever you go (a typical compact car weighs well over 1000kg or 2000lb). What a waste of energy! Go by bike and the metal you have to move around with you is more like 6–9 kg (14–20) pounds for a lightweight racing bike or 11–20kg (25–45) pounds for a mountain bike or tourer, which is a fraction of your own weight.

Chart: Efficiencies of everyday machines compared (rough, guideline figures expressed as percentages). With the exception of the bicycle, newer technologies (such as diesel engines) are generally more efficient than older technologies (such as steam engines).

Where does your energy go?

We've described a bicycle as a "machine" and, in scientific terms, that's exactly what it is: a device that can magnify force (making it easier to go uphill) or speed. It's also a machine in the sense that it converts energy from one form (whatever you had to eat) into another (the kinetic energy your body and bicycle have as they speed along). Now you've probably heard of a law of physics called the conservation of energy, which says that you can't create energy out of thin air or make it vanish without trace: all you can do is convert it from one from to another. So where does the energy you use in cycling actually go? It scientific terms, we say it goes into "doing work"— but what does that mean in practice?

Chart comparing the air resistance and rolling resistance energy losses in mountain and racing bikes

Cycling can sometimes feel like hard work, especially if you're going uphill. In the science of cycling, "hard work" means that you sometimes have to use quite a lot of force to pedal any distance. If you're going uphill, you need to work against the force of gravity. If you're going fast, you're working against the force of air resistance (drag) pushing against your body. Sometimes there are bumps in the road you have to ride over; that takes more force and uses energy too (bumps reduce your kinetic energy by reducing your speed).

But whether you're going uphill or downhill, fast or slow, on a smooth road or a bumpy one, there's another kind of work you always have to do simply to make your wheels go around. When a wheel rests on the ground, supporting a load such as a rider on a bike, the tire wrapped around it is squashed up in some places and bulging out in others. As you cycle along, different parts of the tire squash and bulge in turn and the rubber they're made from is pulled and pushed in all directions. Repeatedly squashing a tire in this way is a bit like kneading bread: it takes energy—and that energy is what we know as rolling resistance. The more load you put on the tire (the heavier you are or the more you're carrying), the higher the rolling resistance.

For a racing bike traveling fast, about 80 percent of the work the cyclist does will go in overcoming air resistance, while the remainder will be used to battle rolling resistance; for a mountain biker going much more slowly over rough terrain, 80 percent of their energy goes in rolling resistance and only 20 percent is lost to drag.

Chart: Mountain bikes waste most energy through rolling resistance; racing bikes waste more through air resistance.

How a bicycle frame works

Assuming an adult weights 60–80 kg (130–180 lb), the frame of a bicycle has to be fairly tough if it's not going to snap or buckle the moment the rider climbs on board. Ordinary bicycles have frames made from strong, inexpensive, tubular steel (literally, hollow steel tubes containing nothing but air) or lighter alloys based on steel or aluminum. Racing bicycles are more likely to be made from carbon-fiber composites, which are more expensive but stronger, lighter, and rustproof.

A mountain bike frame

You might think that a bike frame made out of aluminum tubing would be much weaker than one made from steel—but only if the tubes are similar in dimensions. In practice, every bike needs to be strong enough to support the rider's weight and the loads it's likely to experience during different kinds of handling. So an aluminum bike would use tubing with a larger diameter and/or thicker walls than a bike made from steel tubing.

The frame doesn't simply support you: its triangular shape (often two triangles joined together to make a diamond) is carefully designed to distribute your weight. Although the saddle is positioned much nearer to the back wheel, you lean forward to hold the handlebars. The angled bars in the frame are designed to share your weight more or less evenly between the front and back wheels. If you think about it, that's really important. If all your weight acted over the back wheel, and you tried to pedal uphill, you'd tip backwards; similarly, if there were too much weight on the front wheel, you'd go head over heels every time you went downhill!

Frames aren't designed to be 100 percent rigid: that would make for a much less comfortable ride. Virtually all bike frames flex and bend a little so they absorb some of the shocks of riding, though other factors (like the saddle and tires) have much more effect on ride comfort. It's also worth remembering that the human body is itself a remarkably efficient suspension system; riding a mountain bike along a rough trail, you'll very quickly become aware of how your arms can work as shock absorbers! Indeed, it can be quite instructive to view the body as an extension (or complement) of the bike's basic frame, balanced on top of it.

Photo: The bicycle's inverted A-frame is an incredibly strong structure that helps to distribute your weight between the front and back wheels. It helps to lean forward or even stand up when you're going uphill so you can apply maximum force to the pedals and keep your balance.

How bicycle wheels work

Physics of a wheel and axle: a simple machine

If you've read our article on tools and machines, you'll know that a wheel and the axle it turns around is an example of what scientists call a simple machine: it will multiply force or speed depending on how you turn it. Bicycle wheels are typically over 50 cm (20 inches) in diameter, which is taller than most car wheels. The taller the wheels, the more they multiply your speed when you turn them at the axle. That's why racing bicycles have the tallest wheels (typically about 70 cm or 27.5 inches in diameter).

Photo: Like a car wheel, a bicycle wheel is a speed multiplier. The pedals and gears turn the axle at the center. The axle turns only a short distance, but the leverage of the wheel means the outer rim turns much further in the same time. That's how a wheel helps you go faster.

The wheels ultimately support your entire weight. So if you weigh 60 kg (130 lb), there's about 30 kg (130 lb) pushing down on each wheel (not including the bicycle's own weight). The spokes are what stops the wheels from buckling. Since each wheel has around 30–40 spokes, each spoke has to support only a fraction of the total weight—in this case, less than 1kg (2.2 lb), which it can do easily. Bicycles have spoked wheels, rather than solid metal wheels, to make them both strong and lightweight. Spokes also reduce the air resistance on the front wheel when you're cornering. Read more in our article on how wheels work.

Bicycle gears photographed from behind

How bicycle gears work

A typical bicycle has anything from three to thirty different gears—wheels with teeth, linked by the chain, which make the machine faster (going along the straight) or easier to pedal (going uphill). Bigger wheels also help you go faster on the straight, but they're a big drawback when it comes to hills. That's one of the reasons why mountain bikes and BMX bikes have smaller wheels than racing bicycles. It's not just the gears on a bicycle that help to magnify your pedaling power when you go uphill: the pedals are fastened to the main gear wheel by a pair of cranks: two short levers that also magnify the force you can exert with your legs. Read more in our main article on gears.

Photo: A gear is a pair of wheels with teeth that interlock to increase power or speed. In a bicycle, the pair of gears is not driven directly but linked by a chain. At one end, the chain is permanently looped around the main gear wheel (between the pedals). At its other end, it shifts between a series of bigger or smaller toothed wheels when you change gear.

How bicycle brakes work

A closeup of bicycle brake blocks

No matter how fast you go, there comes a time when you need to stop. Brakes on a bicycle work using friction (the rubbing force between two things that slide past one another while they're touching). When you press the brake levers, a pair of rubber shoes clamps onto the metal inner surface of the front and back wheels. As the brake shoes rub tightly against the wheels, they turn your kinetic energy (the energy you have because you're going along) into heat—which has the effect of slowing you down. There's more about this in our main article on brakes.

Photo: The rubber shoes of this bicycle's brakes clamp the metal rim of the wheel to slow you down. As you lose speed, you lose energy. Where does the energy go? It turns into heat: the brake blocks can get incredibly hot!

How bicycle tires work

Friction is also working to your advantage between the rubber tires and the road you ride on: it gives you grip that makes your bike easier to control, especially on wet days.

Like car tires, bicycle tires are not made of solid rubber: they have an inner tube filled with compressed (squeezed) air. That means they're lighter and more springy, which gives you a much more comfortable ride. Pneumatic tires, as they're known, were patented in 1888 by Scottish inventor John Boyd Dunlop.

Different kinds of bicycles have different kinds of tires. Racing bicycles have narrow, smooth tires designed for maximum speed (though their "thin" profile gives them higher rolling resistance), while mountain bicycles have fatter, more robust tires with deeper treads, more rubber in contact with the road, and better grip (though being wider they create more air resistance).

Why clothing matters

Friction is a great thing in brakes and tires—but it's less welcome in another form: as air resistance that slows you down. The faster you go, the more drag becomes a problem. At high speeds, racing a bicycle can feel like swimming through water: you can really feel the air pushing against you and (as we've already seen) you use around 80 percent of your energy overcoming drag. Now a bicycle is pretty thin and streamlined, but a cyclist's body is much fatter and wider. In practice, a cyclist's body creates twice as much drag as their bicycle. That's why cyclists wear tight neoprene clothing and pointed helmets to streamline themselves and minimize energy losses.

Narrow handlebars on a racing bicycle

You might not have noticed, but the handlebars of a bicycle are levers too: longer handlebars provide leverage that makes it easier to swivel the front wheel. But the wider you space your arms, the more air resistance you create. That's why racing bicycles have two sets of handlebars to help the cyclist adopt the best, most streamlined position. There are conventional, outer handlebars for steering and inner ones for holding onto on the straight. Using these inner handlebars forces the cyclist's arms into a much tighter, more streamlined position. Most cyclists now wear helmets, both for safety reasons and improved aerodynamics.

Photo: Racing bicycles have two sets of handlebars. Inner handlebars let riders reduce air resistance by keeping their elbows closer together. Photo by Ben A. Gonzales courtesy of US Navy.

Bicycles are physics in action

Let's briefly summarize with a simple diagram that shows all these different bits of cycle science in action:

A summary of the science at work in a bicycle

Why is it so hard to fall off a bicycle?

Cycle route sign showing crashed bicycle with buckled wheel

People often say that it's virtually impossible to fall off a bicycle because its spinning wheels make it behave like a gyroscope—but, unfortunately, it's not quite that simple!

Scientists have been puzzling over what makes bicycles balance since they were invented, back in the 19th century. In 2007, a group of engineers and mathematicians led by Nottingham University's J.P. Meijaard announced they'd finally cracked the mystery with a set of incredibly complex mathematical equations that explain how a bicycle behaves—and it turns out that gyroscopes are only part of the story.

According to these scientists, who used 25 separate "parameters" or "variables" to describe every aspect of a bicycle's motion, there's no single reason for a bicycle's balance and stability. As they say:

"A simple explanation does not seem possible because the lean and steer are coupled by a combination of several effects including gyroscopic precession, lateral ground-reaction forces at the front wheel ground contact point trailing behind the steering axis, gravity and inertial reactions from the front assembly having center-of-mass off of the steer axis, and from effects associated with the moment of inertia matrix of the front assembly"

Or, in simple terms, it's partly to do with gyroscopic effects, partly to do with how the mass is distributed on the front wheel, and partly to do with how forces act on the front wheel as it spins. At least, I think that's what they said!

If you're feeling brave and your maths is top notch, you can read more in: 'Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review' by J. P. Meijaard, J. M. Papadopoulos, A. Ruina, and A. L. Schwab. Proceedings of the Royal Society, 2007. Or, for a simpler overview, check out this short video, Physics of the Riderless Bike, from Science Friday.

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Text copyright © Chris Woodford 2007, 2012. All rights reserved. Full copyright notice and terms of use.

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Woodford, Chris. (2007) Bicycles. Retrieved from http://www.explainthatstuff.com/bicycles.html. [Accessed (Insert date here)]

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