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Most people can ride 10 km on their bike. However, running 10 km is a lot harder to do. Why?

According to the law of conservation of energy, bicycling should be more intensive because you have to move a higher mass, requiring more kinetic energy to reach a certain speed. But the opposite is true.

So, to fulfill this law, running must generate more heat. Why does it?

Some things I can think of as (partial) answers:

  • You use more muscles to run.
  • While running, you have more friction with the ground; continuously pouncing it dissipates energy to it.
  • While you move your body at a slow speed, you need to move your arms and legs alternately at higher and lower speeds.
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Simplistically speaking, cycling puts more energy, including your own vertical movement, into horizontal movement, while running has that irritating waste of pushing energy into the ground vertically –  RhysW Apr 15 '13 at 13:03
also important to note, your question assumes a flat surface. One can run further up an incline from a standing start than someone who cycles up the same incline from a standing start –  RhysW Apr 15 '13 at 13:08
Don't forget the mechanical advantage a bicycle's drivetrain offers. –  Dean Brundage Apr 15 '13 at 14:00
It is a common misconception that energy is required to keep mass moving. There is not such law of physics. There is an opposite law, which says that mass keeps it velocity unless you (de)accelerate it with force (and energy). It is friction which dissipiates energy and bycicle may only add to it. Otherwise, there is a much stronger question: why do you get tired when keep heavy weight in your hands? According to the laws of physics, table does not loose any energy when you put the weight on it (despite another misconception). –  Val Apr 15 '13 at 20:32
@Val That's an interesting comparison in fact. Is there a question/article about that? –  Steven Roose Apr 15 '13 at 20:48

10 Answers 10

up vote 53 down vote accepted

One word: inertia. When you're riding a bike on a level gradient you just need to give it a push to get going, then you can coast for quite a while before friction and air resistance slow you down. The human body doesn't have wheels that can store kinetic energy, so while running you have to give a good kick to get going, and then another kick to keep going on the next step, and so on. When hills are involved the difference is even more pronounced, since we run downhill the same way we do on the level, by continually pushing ourselves forward; whereas on a bicycle you can take advantage of the slope and just coast down it.

I suspect that raising and lowering your centre of mass isn't as inefficient as the other answers have suggested. This is because your legs are springy, so at least to some extent you're just converting energy back and forth between gravitational potential and the spring force in your legs. Humans are possibly the most efficient long-distance runners in the animal kingdom. There is a school of thought that says the reason we are bipeds is that we evolved as endurance hunters, chasing our prey until it collapsed from exhaustion rather than trying to outrun it over short distances. Whether that's true or not, we probably wouldn't do all that bouncing up and down if there wasn't a good reason for it.

You might ask why, if using wheels is so much more efficient, didn't we evolve that instead? I don't know, but it seems no animal has been able to evolve wheeled locomotion.

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No animal ever evolved wheel locomotion because there was never an environment where wheeled movement would be beneficial. Nature lacks a specific important aspect that benefits wheeled movement. Roads / flat surfaces. –  RhysW Apr 15 '13 at 13:02
I know that there are several theories on why wheeled locomotion hasn't evolved. My money's on a combination of the "incomplete form" argument @Gugg mentioned, together with the difficulty in connecting up blood vessels, nerves etc. around a continuously rotating joint. (I think the "lack of roads" argument isn't a great one, because wheels have their uses offroad as well.) –  Nathaniel Apr 15 '13 at 13:57
VSauce on YouTube has a great video on why there are no animals that have wheels. –  Virtlink Apr 15 '13 at 15:28
Rubbish, there are tribes which traditionally hunt by outrunning animals on the plains and it's a battle of endurance. The beast collapses from exhaustion. –  wim Apr 15 '13 at 16:40
@Cleonis - you should do a little more research on this. Most other animals are much better sprinters, but it is definitely true that humans are one of the best long-distance running animals, and there's a lot of research to suggest that being bipedal helps with this. There's also no evidence that species before Homo Sapiens had tools more advanced than sharp sticks, such as the snares and nets you mentioned. The popular theory is exactly as Nathaniel suggested, that we evolved as persistence hunters. –  Joe K Apr 15 '13 at 17:27

Many of us have ridden bicycles at some time in our lives. and in fact this mode of transportation has become markedly more popular recently as a result of the energy shortage. Each morning at my own university, Duke, people can be seen riding machines with masses of $10$ to $20$ kilograms and struggling to reach one of the campus entrances at the top of a long, steep hill. As in many other aspects of animal locomotion, there is a paradox here. Why should people encumber themselves with such heavy apparatus, particularly while going uphill? Ask a rider this question, and the response is usually: "It's easier than walking" or "It's faster than walking." But why should it be?

A number of incorrect explanations are offered: "A bicycle has gears." Shifting gears allows the rider to vary the speed at which the feet move; but even if the foot speeds of a cyclist and a pedestrian are matched, the cyclist still goes farther and in less time on a given amount of energy than the pedestrian. "Your weight is supported by the seat." But if you pedal standing up, biking still is faster and less costly of energy than going on foot. "Your center of gravity doesn't go up and down." But it does if you pedal standing up. Why, then, is bicycling easier than walking or running?


We can now appreciate why bicycle riders are willing to propel the extra weight of a bicycle, even when going uphill. The cost of transport on a bicycle is low because active muscles are not stretched while pedaling, and mean muscle efficiency is about $.25$, nearly its maximum value. The wheels stabilize the rider's center of mass. Even if the rider accelerates the center of mass vertically by pedaling while standing up, active muscles need not be stretched. When the center of mass falls, the cranks, sprockets, chain, and rear wheel constitute a system of levers that transposes the vertical motion to a horizontal one by supplying a perpendicular force. Thus, humans can use external machinery to move along a level surface with the same muscular efficiencies that swimming and flying animals achieve naturally.

The Energetic Cost of Moving About: Walking and running are extremely inefficient forms of locomotion. Much greater efficiency is achieved by birds, fish—and bicyclists. V. A. Tucker, American Scientist, Vol. 63, No. 4 (July-August 1975), pp. 413-419

*Of course, most of the article is where I put "[...]". It's quite a good, fun read. There's even some kind of Galilean experiment with dropping pigeons and rats from heights.

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  • Bicycles make better use of inertia/momentum. As Nathaniel said, one push and you can coast for quite a while. That's just not possible while running.

  • Running wastes energy moving up and down. In addition to moving forward, running requires a substantial upward push to get your body airborne, giving you time to bring your other foot forward. You then cushion and spring forward and upward again. While bicycling does have an up-and-down component to the pedaling, because the bike doesn't leave the ground, the energy you use in pedaling is converted much more efficiently to forward motion.

  • Bicycling can translate weight to propulsion. While most serious bicyclists will tell you that pedaling is about spinning, not stepping, any 10-year-old can tell you that going butt-in-the-air and transferring your weight from left to right gets you going pretty quickly.

  • Pedaling with toe clips makes use of the entire leg motion. When your feet are locked to the pedals, it isn't just the pushing-down portion of the pedal stroke that is used; lifting your foot, pulling it forward, pushing down and pushing backward all keep tension on that chain and so add power to the stroke. When running, fully half of your foot's cycle is wasted energy from a forward-motion perspective.

  • Bicycling gives you mechanical advantage. Even with a single-gear bike, the motion of your foot is magnified when translated to the wheel. On a multi-speed bike, the ratio of the top gear is pretty high indeed. This allows two things; first, your effort is magnified, and second, your tempo slows, which reduces the amount of energy wasted moving the weight of your legs around.

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The last three points of this answer make no sense when speaking about energy-efficiency... –  Steven Roose Apr 15 '13 at 18:57
Are you kidding? All three of them have a profound effect on energy-efficiency of bicycling versus running. You can bicycle as fast as jogging (at least) just by straightening your leg and shifting your weight to one foot, using that weight to push the pedal down, then shifting your weight to the other leg. The "entire leg motion" point specifically states how it's more efficient than a running stride, and the mechanical-advantage point says when the motion does more work, the percent of energy spent moving the weight of your own legs versus pushing you forward is lower (aka more efficient). –  KeithS Apr 15 '13 at 19:10
Agree with Steven Roose. High gears only waste –  Kaz Apr 15 '13 at 23:00
Steven Roose is right: the last three points are no good in this context, where we're concerned with the overall energy requirement. Cycling sitting down, without toe clips, in a low gear takes less energy than walking: therefore, standing up, toe clips, and high gears can't be the explanation. –  Gareth Rees Aug 19 '13 at 15:50
  • Running requires intense muscle contractions with a low duty cycle, whereas cycling uses long, smooth contractions. If you work at running, you can easily get to the point where it is no longer an aerobic challenge, yet still tough: you hardly have to breathe, yet the legs struggle with lactic acid buildup.

  • Running wastes a lot more energy on compensating motions: the runner has to move her torso and arms to compensate the kicking motion of the legs. The leg motion is not symmetric in running: the forward kick of the recovering leg is faster than the backward movement of the drive leg, and so the arm on the same side as the recovering leg has to swing backward to compensate its motion. Compensation on a bike is mostly limited to a side-to-side rocking during a hard effort.

  • The runner basically flies through the air, but periodically comes down and touches the ground with one foot, and then exerts a force in order to get back up into the air. However, this is not done by an efficient, elastic bounce. The landing energy is dissipated, rather than stored and reused. In fact, the runner must exert energy in order to absorb the landing, and then exert more energy to get back into the air. The runner thus wastes considerable energy to stay in the air.

  • Depending on the nature of the footstrike, the runner may counter-productively be exerting energy which retards (brake) his forward motion, and then has to exert more energy to recover momentum.

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A lot of the answers here go into movement of your center of gravity etc. I think it's a lot simpler than that.

When you are cycling your vertical movement on the pedals is translated into horizontal movement of the wheels, coupled with inertia a small amount of energy can go a long way.

Whereas whilst running you are putting energy into moving horizontally, to get places, as well as vertically to reduce friction with the floor. However all the vertical movement is fighting gravity, and wasted as your vertical movement gets you no closer to your destination

This answer assumes that the distance is over a flat surface. As soon as you throw a three dimensional aspect on it then the system turns on its head.

For horizontal movement the bike is best as its wheels are designed to reduce friction, unlike feet.

However as soon as you come to an incline the lack of friction will cause the bike to roll backwards unless constant energy is put in to the system, whereas the increased friction one has from running allows anyone to stop and stay put.

As soon as you get to an incline from a standing start, running is much more efficient than cycling.

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To expand on Nicks answer, when you run, you sort of jump a little bit so that you raise your center of mass, which costs you energy equal to

$$\Delta E = m g \Delta h$$

Now when you lower your center of mass, the energy is dissipated as the vertical acceleration gained by going down is not increasing your horizontal speed.

This is definitely one of the causes.

Also, one can think about dissipated power, which might give us more insight. For example we have the following identity:

$$ P = \cfrac{\operatorname{d} W}{\operatorname{d} t} = \vec{F} \cdot \cfrac{\operatorname{d} \vec{x}}{\operatorname{d} t} = \vec{F} \cdot \vec{v}$$

Also, let's assume, that power losses in both cases are similar and that the input power is the same in both cases (we use similar muscles in both cases after all).

Now we have the velocity very different in both cases, and we could probably also agree, that there is much more force produced if we run as we can speed up to our maximum speed very quickly. So far everything agrees with the formulae.

Now we can easily convince ourselves, that even if the efficiency is similar in both cases, the loss of energy in running would be greater because we do it for longer for the same distance travelled.

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It's down to the biological inefficiency of maintaining the mechanical constraint of one foot stationary wrt the floor, with the rest of the body moving.

Let's suppose a skater on ice and another on rollers use approximately the same amount of energy to get to say 5 km/s. Both possess a different, but efficient compared to walking, mechanism that maintains that velocity, while satisfying any mechanical constraints. For the one on rollers, the point of contact between the ground and a roller must be stationary. For walking, the foot in contact with the ground must be stationary, and the biological mechanism for this introduces far greater biological losses.

However, there are far more efficient modes of biological transport such as hopping as in the case of Kangaroos, which uses half the energy of a marathon runner. Kinetic energy is converted into potential energy in the tendons while the mechanical constraint is maintained, with most converted back into kinetic energy upon leaving the gound.

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A quick guess would be that for running you are lifting your centre of mass with every step while with cycling your centre of mass has a constant height. Therefore you are only doing work against air resistance/friction in the bike mechanics. While running you are also working against gravity.

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You're working against gravity in a wasteful way: not like an elastic bouncy ball which stores energy and comes back to almost the same height, but more like a sack of rice. –  Kaz Apr 15 '13 at 22:45

We use muscles instead of wheels.

Using muscles involves friction inside your muscles, muscles act as both dampers and spring, but also as an actionner (like an engine). It uses many cells to do it.

The "isn't there any species which can rotate their limbs infinitely" question has already been asked.

From an evolutionary standpoint, you have to keep in mind that in biology, "parts" are always connected, so that the flow of blood and nerve can never be interrupted. In electricity, it's also a problem to make signals or a current flow between two rotating parts.

Biology is very flexible in its "design" (or whatever you call it), but keep in mind that live being are made of cells, even the bones or the horns and nails !

Maybe a viable way to evolve wheels, would be to dip them in some fluid that keep them alive inside the body, and when the animal wants to roll, he get it out and pushes himself to use inertia.

But don't ask me about rotational locomotion, that would be really hard to achieve/evolve for a live being.

Don't forget evolution works very much differently compared to man's inventions.

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The difference is in the underlying mechanism which transforms the chemical energy into kinetic energy of the vehicle or body. The answer is that the bicycle mechanism (due to having wheels etc..) is able to transform this energy better.

A classic analog is the lever or a pulley. One can use a lever or a pulley to lift a weight which would be very difficult (or even impossible) to lift with bare hands.

So to maintain same average speed with a bicycle one needs to use less chemical energy (than running) and as a result produce less heat.

"Give me a place to stand and I can move the earth"

                                            -- Archimedes on the principe of the lever (allegedly)

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