# B Bicycles: Question about Energy Conservation

#### Djf321

I just have a basic physics question about bicycles that has been confusing me. Consider three situations. In the first situation a person, of mass m, is running down a street at constant velocity v1. In this case the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv12. In the second situation the same person is riding a standard simple single-gear bicycle down the same street going at constant velocity v2, where of course v2>v1. So again the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv22. Finally, the third situation involves the same person now riding the Aerovelo, a super-fast recumbent bicycle that can go 89 mph, down the same street at constant velocity v3 (v3>v2>v1). Now the energy stored in this same person's body, in the form of biochemical energy, is being converted into a much greater value of translational kinetic energy of their body ½mv32.

There are two parts that I am confused about. For one, how can it be that bicycles allow for so much more biochemical energy stored in the body to be transferred to translational kinetic energy in comparison to running? I would have naively imagined that the amount of biochemical energy released would be entirely dependent on the speed with which you moved your limbs, and yet you don't necessarily move your limbs more when biking. And second, why is it that when riding a standard bicycle, where you are going much faster than running, the bicycle riding makes you less tired than running even though you can be going faster? And in the extreme case compare the Aerovelo to running. I would have thought that how quickly you became tired would be dependent on how quickly and how much biochemical energy gets converted into translational kinetic energy of your body. And yet you clearly become tired more quickly running than biking even though less translational kinetic energy is being produced when running.

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#### PeroK

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I just have a basic physics question about bicycles that has been confusing me. Consider three situations. In the first situation a person, of mass m, is running down a street at constant velocity v1. In this case the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv12. In the second situation the same person is riding a standard simple single-gear bicycle down the same street going at constant velocity v2, where of course v2>v1. So again the person is converting energy stored in their body into translational kinetic energy of their moving body ½mv22. Finally, the third situation involves the same person now riding the Aerovelo, a super-fast recumbent bicycle that can go 89 mph, down the same street at constant velocity v3 (v3>v2>v1). Now the energy stored in this same person's body, in the form of biochemical energy, is being converted into a much greater value of translational kinetic energy of their body ½mv32.

There are two parts that I am confused about. For one, how can it be that bicycles allow for so much more biochemical energy stored in the body to be transferred to translational kinetic energy in comparison to running? I would have naively imagined that the amount of biochemical energy released would be entirely dependent on the speed with which you moved your limbs, and yet you don't necessarily move your limbs more when biking. And second, why is it that when riding a standard bicycle, where you are going much faster than running, the bicycle riding makes you less tired than running even though you can be going faster? And in the extreme case compare the Aerovelo to running. I would have thought that how quickly you became tired would be dependent on how quickly and how much biochemical energy gets converted into translational kinetic energy of your body. And yet you clearly become tired more quickly running than biking even though less translational kinetic energy is being produced when running.
It takes no energy to move at constant velocity. All the energy in the cases you mention is used to overcome resistance to motion of one form or another.

You need energy initially, of course, to reach your cruising speed.

Running is very inefficient biomechanically. Bicycles and any wheeled vehicles are much more efficient.

#### anorlunda

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It seems that your question is not about physics but bio-mechanical efficiency. Consider this.

I can lift a weight with my arm, but my finger is too weak to lift it at all. Attempting to lift it with my finger results in zero bio-mechanical efficiency. Chemical work expended, but zero useful work done. It even takes nonzero chemical energy to think about moving the weight. The point is that you really can't apply ordinary physical mechanics to bio processes.

#### jrmichler

Some things to include in your thoughts:
1) Air resistance is proportional to speed squared times frontal area times coefficient of drag. The Aerovelo has low frontal area and very low coefficient of drag.
2) The runner lifts him/herself up every step. That takes work.
3) The runner's legs move back and forth every step. That takes work.
4) Bicycles need additional work to climb an upgrade.
5) Bicycles have rolling resistance.

The $\frac 1 2 mv^2$ translational kinetic energy does not include any of the above. But all of the above need to be included to understand why bicycles are faster than running.

I tried to run directly into a 45 MPH headwind once. The key word here is "tried".

#### Delta2

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I think the main reason that bicycles are more efficient in converting body energy to speed (kinetic energy) is that they have wheels!. Our legs just cant function as wheels when we are running, a lot of energy is lost in bending our knees e.t.c when we are running with legs, and this energy is not converted into kinetic energy of our body. On the contrary when we are using bicycles most of the energy that comes out from our bodies goes into kinetic energy of the wheels and the bicycle.

#### A.T.

Running is very inefficient biomechanically. Bicycles and any wheeled vehicles are much more efficient.
This very much depends on the terrain. There is a reason why bicycles, a relatively simple machine, became really popular relatively late, when enough smooth hard surface was available to ride on.

#### PeroK

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This very much depends on the terrain. There is a reason why bicycles, a relatively simple machine, became really popular relatively late, when enough smooth hard surface was available to ride on.
That begs the question why the Romans, Greeks or any ancient civilisation never invented the humble bicycle, despite the engineering marvels they did achieve.

#### A.T.

That begs the question why the Romans, Greeks or any ancient civilisation never invented the humble bicycle, despite the engineering marvels they did achieve.
Riding a simple bicycle on cobblestone, sand or mud is no fun. Especially in hilly areas. I think the improvement of roads was one factor that made bicycles popular. But other advancement in technology were also needed to make it light, durable and efficient enough.

#### PeroK

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Riding a simple bicycle on cobblestone, sand or mud is no fun. Especially in hilly areas. I think the improvement of roads was one factor that made bicycles popular. But other advancement in technology were also needed to make it light, durable and efficient enough.
The bicycle became popular before proper paved roads. Its effect was transformational in rural areas in Britain in the early 20th century. Even on country roads a journey to a nearby village could be made much faster than on foot.

Ironically, of course, one significant development in recent years has been the mountain bike, where riders seek out rugged terrain.

#### Torbert

Roll and unshod wooden wheel and a rubber tired wheel down an unpaved incline.
How much faster and further does the rubber tired wheel go compared to the solid wheel?
This efficiency difference may have delayed bicycles until the technology reached rubber tires on the wheels.
The visuals were so compelling measurements were not taken, my youthful self was easily convinced.

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