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The science of bicycles

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by Chris Woodford. Last updated: February 13, 2017.

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?

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

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).

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.

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 6–9kg (14–20lb) for a lightweight racing bike or 11–20kg (25–45lb) for a mountain bike or tourer, which is a fraction of your own weight.

Better efficiency means you can further on the same amount of fuel, which is another great advantage of bikes, although a little hard to quantify. According to the classic Bicycling Science book by David Gordon Wilson et al: "A racing bicyclist at 32km/h (20mph) could travel more than 574 kilometers per liter (1,350 miles per US gallon) if there were a liquid food with the energy content of gasoline." Whichever way you look at it, bikes are pretty amazing!

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?

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).

Two recumbent bicycles side by side in a race.

Photo: Bicycles work so well with the human body because they harness power from our large and very powerful leg muscles. Recumbent bicycles (ones you ride lying down) might look ultra-modern and a bit weird, but they date back at least 100 years. They're faster than conventional bicycles because their riders adopt a much more aerodynamic, tube-like posture that minimizes drag. Since the pedals are higher off the ground, the cranks can be longer, so you get more leverage, your muscles can make high power for longer, and do so more efficiently. Photo by Robin Hillyer-Miles courtesy of US Navy.

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

Chart: Slow mountain bikes waste most energy through rolling resistance; faster racing bikes waste more through air resistance.

How a bicycle frame works

Assuming an adult weights 60–80kg (130–180lb), 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

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.

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.

How bicycle wheels work

Physics of a wheel and axle: a simple machine

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.

If you've read our article on how wheels work, 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 50cm (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 70cm or 27.5 inches in diameter).

The wheels ultimately support your entire weight, but in a very interesting way. If the wheels were solid, they'd be squashed down (compressed) as you sat on the seat, and pushing back up to support you. However, the wheels of most bikes are actually formed of a strong hub, a thin rim, and about 24 highly tensioned spokes. Bicycles have spoked wheels, rather than solid metal wheels, to make them both strong and lightweight, and to reduce drag (some riders use flat "bladed" spokes or ones with an oval shape, instead of traditional rounded ones, in an attempt to cut drag even more).

It's not just the number of spokes that's important but the way they're connected between the rim and its hub. Like the strands of a spider's web, or the dangling ropes of a suspension bridge, a bike wheel is in tension—the spokes are pulled tight. Since the spokes criss-cross from the rim to the opposite side of the hub, the wheel isn't as flat and flimsy as it appears, but actually an amazingly strong, three-dimensional structure. When you sit on a bike, your weight pushes down on the hubs, which stretch some of the spokes a bit more and others a bit less. If you weigh 60kg (130lb), there's about 30kg (130lb) pushing down on each wheel (not including the bicycle's own weight), and the spokes are what stops the wheels from buckling.

Close-up of a bicycle wheel and its spokes, showing that it's a rigid three-dimensional structure

Photo: Despite appearances, a bicycle wheel is neither flat nor weak. The hub is much wider than the tire, the spokes are in tension, and they criss-cross, joining the hub at a tangent. All this makes a rigid three-dimensional structure that can resist twisting, buckling, and bending. Photo by David Danals courtesy of US Navy.

Since each wheel has a couple of dozen spokes, you might think each spoke has to support only a fraction of the total weight—maybe as little as 1–2kg (2.2–4.4lb), if there are 30 spokes, which it can do easily. In reality, the spokes bear the weight unevenly: the few spokes that are near the vertical bear much more load than the others. (There's still quite a bit of debate among bike scientists about how the load is actually borne, and whether it's better to think of a bike hanging from the spokes at the top or pushing down on the ones at the bottom.) As the wheel rotates, other spokes move closer to the vertical and begin to take more share of the strain. The load on each spoke rises and falls dramatically during each rotation of the wheel so, eventually, after many thousands of cycles of repeated stress and strain, during which each spoke stretches and relaxes in rapid alternation, one of the spokes (or its connection to the wheel or hub) is likely to fail through metal fatigue. That instantly and dramatically increases the load on the remaining spokes, making them more likely to fail too, and causing a kind of "domino" effect that makes the wheel buckle.

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.

Bicycle gears photographed from behind

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

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). Although some bikes now have disc brakes (similar to the ones cars use), with separate brake discs attached to the wheels, many still use traditional caliper brakes. 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.

A closeup of bicycle brake blocks

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

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.

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.

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, 8 August 2007. Or, for a simpler overview, check out How to Keep a Riderless Bike From Crashing by Jon Cartwright, Science, April 2011, which summarizes related research by Andy Ruina of Cornell University and his colleagues.

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