# The Naked Scientists Forum

### Author Topic: Why can I cycle faster than the fastest runner runs?  (Read 14072 times)

#### thedoc

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##### Why can I cycle faster than the fastest runner runs?
« on: 01/05/2012 17:29:58 »
Hiya - congratulations on your podcasts.

Here's a question for you:
Wikipedia tells me that the men's 1 mile running record is held by Hicham El Guerrouj at 3 mins 43.13 secs. This, according to my maths, equates to 16.03 mph. Needless to say El Guerrouj is an elite athlete!

I go cycling on my (not very expensive) bike most weekends. I usually cover about 20 miles on a ride and my average speed is never less than 16 mph.

I am not an elite althlete - in fact I'm almost 50, weigh 100 kg and have a BMI which puts me well into the obese range.

Why am I able to move at the same speed as an elite athlete, for 15 times longer - especially when you consider that the bike adds 10% to my overall weight plus lots of friction from the moving parts?

Keep up the good work
Best wishes
Trevor Barton

Visit the webpage for the podcast in which this question is answered.

« Last Edit: 01/05/2012 17:29:58 by _system »

#### Cheese2001

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #1 on: 08/03/2012 15:00:07 »
It's all about the gearing ratios!  The governing equation here is:

Vt = r * w   (The tangential velocity is equal to the radius times the angular velocity)

As you push your feet on the pedals, it spins the front sprocket with the chain leading to the back sprocket.  The angular velocity you impart to the pedals, is the same angular velocity you impart to the sprocket.  That becomes an tangential (linear) velocity the chain moves back to the rear sprocket.  The chain imparts an angular velocity on the rear sprocket that is the  same angular velocity of the rear tire.  The edge of the rear tire moves quickly along the ground thanks to the advantage of the largest radius on the bicycle!

So, without going through and carrying the subscripts through a bunch of equations, the power stroke on a bicycle is normally the down-going leg.  It's a relatively short motion, but through the gearing, rotates a portion of the circumference of the rear tire determined by the ratio of the radii of the chain sprockets and radius of the rear tire.

Back to running, no gearing to be had, so the only velocity the athlete can achieve is out of his own legs.  A bicyclist can get a higher velocity than what his or her legs can generate thanks to the gearing.
« Last Edit: 08/03/2012 15:03:17 by Cheese2001 »

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #2 on: 08/03/2012 17:54:03 »
It's really more to do with friction than gearing. You don't need a bicyle. All you need to do is reduce the friction between your feet and the ground in the direction that you want to travel, and you can do that by strapping a pair of roller blades or ice skates on to your feet.

#### Cheese2001

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #3 on: 08/03/2012 22:20:16 »
But the question was about a bike!  Not what different ways how he move faster than an elite athlete!

Totally agree with your observation though.  The reduced friction decreases his or her deceleration.

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #4 on: 08/03/2012 23:42:47 »
Well, yes : )  But the main reason a cyclist can travel so fast is also because of the lack of friction. You can coast quite a long way on a bicycle without any exertion at all. Unless you are falling off a cliff, it's pretty difficult to coast for any distance without some sort of anti-friction means.

Once you've eliminated a lot of the friction you can use gears to match your speed to your muscles' ability to do do work, or, you can do something similar on skates by applying a lateral force to produce forward acceleration.

#### CliffordK

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #5 on: 09/03/2012 05:31:46 »
I generally don't grease the outside of my tires.
A little friction is good.

Perhaps part of the answer is that the bicycle provides vertical support to the rider.

With each step, the runner has to exert a certain amount of force and effort to counteract gravity.  The bicycle, on the other hand, uses the wheels to efficiently counteract gravity.  There are situations such as going up a steep hill where the runner and the cyclist are on much more even performance terms.

Also, gearing, as mentioned.  With running, to a large extent, the longer the legs, the better.

Perhaps Geezer is onto something with friction though.
The Olympic Skaters are going about 50 kph, 30 mph, which is quite a respectable speed, with no extra gearing.
http://en.wikipedia.org/wiki/List_of_speed_skating_records

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #6 on: 09/03/2012 07:30:52 »
Yup! It's all about friction, and the efficiency of the machine.

A cyclist travels much faster faster than a runner, even though both are consuming energy at the same rate. So we know the cyclist is doing a lot more work than the runner. So where did the runner's energy go? The only place it could go - heat, due to friction. The cyclist is much more efficient because his bicycle reduced friction.

That's really all that wheels do, but they seem to do a pretty good job, particularly when they are supported by rollers of some sort.

#### JP

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #7 on: 09/03/2012 15:14:09 »
Not to disagree too much with my esteemed colleague, Geezer, but the answer to the top speed question is essentially one of gearing, as Cheese said.  In both cases, friction comes into play, since it describes how your body interacts with the ground and how you provide a forward force, but top speed really comes down to how much horizontal linear velocity you can produce in the point (tire or foot) that's in contact with the ground.

In plainer terms, imagine you're moving your legs as fast as possible.  This obviously places a limit on how fast you can run and you can do little to change your maximum running speed without making your legs move faster (this is why professional runners train to increase their leg turnover speed.)  Now imagine you're on a bike and moving your legs as fast as possible.  You can always change the gearing ratio to go faster, even if your leg speed is maxed out.

The technical reason is that to accelerate at all, you're pushing off against static friction, but to push off against static friction, the point in contact with the ground doing the pushing has to move with a higher speed backwards than you are moving forwards.  If not, then you can't gain any acceleration.  When your legs are moving at top speed, the bike is designed so that the contact point with the ground has a higher horizontal velocity than your foot would if you're running at top speed.

#### Cheese2001

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #8 on: 09/03/2012 23:48:57 »
I ran a few numbers to actually see how this works out.  I know I can comfortably riding a stationary bike at 80 RPM for 30 minutes.  I made some measurements on my actual bike and found (rounded to the nearest cm):

Radius of the front sprocket:  10 cm
Radius of the rear sprocket:  3 cm
Radius of the rear tire:  37 cm

Given the RPM and the radius of the front sprocket, the chain moves along the sprocket at 0.84 m/s.  The chain moves at the same speed along the rear sprocket at the same speed, but induces a rotational speed of almost 28 rad / sec (or about 270 RPM).  At the wheel tread, this gives me a very respectable 10 m/s (or 23 mph) of forward travel.

In this case, the gearing gave me more than 3 turns out of the rear wheel for every turn on the pedals.  That speed is due to the gearing, not the friction.

The friction between the ground and the motive surface (tire or shoe) provides the forward moving force, right?  I'm assuming the coefficient of friction between a shoe and pavement is very close in value to the coefficient of friction between rubber and pavement.  If that's true, and I do not have an appropriate table of coefficients available to me, the body plus the bike should make more friction than the body alone.
« Last Edit: 10/03/2012 00:42:53 by Cheese2001 »

#### David Cooper

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #9 on: 10/03/2012 00:58:29 »
Clearly the gearing is the most important factor when it comes to reaching the top speed, although air resistance is also an issue - a cyclist can get into an aerodynamic tuck and reduce drag a fair bit. If you're comparing a cyclist with a runner at 16mph though, the cyclist has an easier time of things primarily because the runner is wasting a lot of energy jumping up and down. Other species have better springs in their legs which enable them to run as fast as a cyclist by not losing so much energy on each jump, the best example being the kangaroo - almost all the energy it puts into each jump is recovered for reuse when it lands, whereas we turn a lot of it into heat.

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #10 on: 10/03/2012 02:32:17 »
Far be it from me to argue with one so learned as you JP, but I think you have your cause and effect front to back.

Gearing is useful on a bicycle for maximizing speed, but only because the bicycle's wheels have eliminated most of the friction necessary for propulsion. In fact, the first bicycles didn't have any gears at all. The rider used his feet on the road for propulsion.

A sprinter can accelerate very rapidly, and actually achieve quite a high top speed. The problem is that a sprinter cannot maintain that speed for any length of time because of the considerable power output required. A cyclist can maintain the speed because his power output is only a fraction of the sprinter's output.

Same thing when running down a hill. A cyclist might expend no energy at all while coasting down a hill on his frictionless wheels while a runner will have to keep using a considerable amount of energy on the same hill.  And, as I mentioned already, you only need to eliminate friction with a pair of inline skates to travel at high speed for great distances - no gears are required.

The friction I am referring to is not the friction between the runner's shoes or the bicycle's tires and the road surface.  It's the lack of friction created by the rolling bearings in the wheels that allow the mass of the cyclist and his bicycle to retain their combined momentum. I suspect a sprinter can out-accelerate a cyclist for quite a distance, but he can't maintain the speed because it takes continuous power consumption to maintain it.

However, I think there is something more fundamental about how the bicycle works that we could all be overlooking. I think the pedal mechanism automatically conserves the momentum of the cyclists legs, whereas the momentum of the runner's legs is not conserved at all, and, because of that, the runner has to expend a much greater amount of energy. I'm a bit hazy on all of the details because running is a pretty complicated business, but I think the argument is at least partially valid.

It's like any other machine. You have to figure out where all the energy is really going to properly understand it.

#### JP

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #11 on: 10/03/2012 03:13:22 »
Ok, ok.  It involves more than just leg turnover speed/gearing ratio.  There are really two separate questions here: highest possible speed and maintaining a high speed.  The maximal speed you can achieve for short instants has to do with leg turnover speed/gearing ratio.  Maintaining that speed for a long time has to do with both gearing ratio, friction, and the ability of a bike to make efficient use of the human body's energy for propulsion (running has to provide a constant upward force with each stride as well as forward propulsion, and you also have to engage your core muscles a lot to keep your upper body in the right place.)

#### CliffordK

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #12 on: 10/03/2012 10:33:28 »
It has to be more than just gearing...

As I mentioned above, the [url-http://en.wikipedia.org/wiki/List_of_speed_skating_records]Olympic Speed Skaters hit 30 MPH[/url], with no "gearing"
I'd be hard pressed to hit 30 MPH on my bike for 10K.

What the speed skaters have that runners don't have is that each push with the legs moves them forward more than an ordinary stride length, so perhaps it is in a sense like gearing, without the gears.

#### Bored chemist

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #13 on: 10/03/2012 12:27:27 »
An indirect answer to this is that you can't really ride a bike up stairs and your blood vessels would get horribly tangled if your feet had wheels.

Wheels make transport much more efficient, but only if there's a reasonably flat surface for them to run on. Legs do a much better job on uneven ground and they also get round the problem of connecting wheels to a body.

#### yor_on

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #14 on: 10/03/2012 16:00:03 »
Energy !!

:)

Transformation of energy must be 'it'..

#### Phractality

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #15 on: 10/03/2012 17:17:19 »
Running stores kinetic energy in the springiness of muscles and sinews. When a muscle is stretched against its own resistance, a small amount of energy can be stored and recovered when the muscle contracts. Running faster exceeds the ability of muscles and sinews to store kinetic energy, so a greater fraction of it is turned to heat. At maximum speed, most of your effort goes into generating heat in the muscles. Only a small fraction goes into stirring up the air around you. Running downhill converts gravitational potential energy into heat in the muscles.

A moving mass on wheels, rolling on a smooth surface, is a much more efficient mechanism for storing kinetic energy. Each stroke of the pedals puts more kinetic energy into storage. The quantity of kinetic energy that can be stored that way is limited by air drag, slope and gearing. At maximum speed, most of your effort goes into stirring up the air; only a small fraction goes into generating heat in the muscles.  Coasting downhill converts gravitational potential energy into turbulence in the air. Rolling friction is negligible if the surface is smooth and the tires fully inflated.

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #16 on: 10/03/2012 22:19:48 »

What the speed skaters have that runners don't have is that each push with the legs moves them forward more than an ordinary stride length, so perhaps it is in a sense like gearing, without the gears.

There is something akin to a gear involved.

The lack of friction between the skates and the ice in the forward direction maintains most of the skaters momentum with a very small loss, mostly due to windage. The skater exerts a considerable force normal to his direction on the ice. Because the skates produce large lateral friction, the lateral force is translated into a much smaller forward force that acts for a long interval, but the lateral distance the skate moves in that time is only really obvious when the skater is accelerating.

You only have to use a pair of inline skates for about 30 minutes to realize you are using a set of muscles that barely get exercised while running or walking.

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #17 on: 11/03/2012 01:14:52 »

An indirect answer to this is that you can't really ride a bike up stairs

Er, bollocks!

#### Phractality

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #18 on: 11/03/2012 01:35:04 »

An indirect answer to this is that you can't really ride a bike up stairs

Er, bollocks!

More to the point: Climbing stairs on mountain bike.
With some fancy gearing, you could make stair climbing easier, but the gears would have to match the spacing of the stairs.

Combining those special gears with odd-shaped wheels could make for a smoother ride. Square-wheeled bike.
« Last Edit: 11/03/2012 01:37:22 by Phractality »

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #19 on: 11/03/2012 04:55:43 »
Ok, ok.  It involves more than just leg turnover speed/gearing ratio.  There are really two separate questions here: highest possible speed and maintaining a high speed.  The maximal speed you can achieve for short instants has to do with leg turnover speed/gearing ratio.  Maintaining that speed for a long time has to do with both gearing ratio, friction, and the ability of a bike to make efficient use of the human body's energy for propulsion (running has to provide a constant upward force with each stride as well as forward propulsion, and you also have to engage your core muscles a lot to keep your upper body in the right place.)

Yeah, yeah yeah.

If you wave your arms any faster, your bike is liable to turn into an aeroplane.

#### Bored chemist

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #20 on: 11/03/2012 10:27:29 »

An indirect answer to this is that you can't really ride a bike up stairs

Er, bollocks!

A fascinating video featuring a more or less total lack of bicycles and stairs.

Though I accept that I was, perhaps a little lazy in saying "up stairs", when I should have said "across rough terrain that's not particularly designed for people to travel over"
« Last Edit: 11/03/2012 10:29:48 by Bored chemist »

#### JP

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #21 on: 11/03/2012 12:38:07 »
Ok, ok.  It involves more than just leg turnover speed/gearing ratio.  There are really two separate questions here: highest possible speed and maintaining a high speed.  The maximal speed you can achieve for short instants has to do with leg turnover speed/gearing ratio.  Maintaining that speed for a long time has to do with both gearing ratio, friction, and the ability of a bike to make efficient use of the human body's energy for propulsion (running has to provide a constant upward force with each stride as well as forward propulsion, and you also have to engage your core muscles a lot to keep your upper body in the right place.)

Yeah, yeah yeah.

If you wave your arms any faster, your bike is liable to turn into an aeroplane.

Er, bollocks!

#### Phractality

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #22 on: 11/03/2012 17:39:11 »
Ok, ok.  It involves more than just leg turnover speed/gearing ratio.  There are really two separate questions here: highest possible speed and maintaining a high speed.  The maximal speed you can achieve for short instants has to do with leg turnover speed/gearing ratio.  Maintaining that speed for a long time has to do with both gearing ratio, friction, and the ability of a bike to make efficient use of the human body's energy for propulsion (running has to provide a constant upward force with each stride as well as forward propulsion, and you also have to engage your core muscles a lot to keep your upper body in the right place.)

Yeah, yeah yeah.

If you wave your arms any faster, your bike is liable to turn into an aeroplane.

Er, bollocks!

What's with all these totally irrelevant video links?
Trials bicycling video. Many trials bikes look like regular mountain bikes until you examine the gears. The one in this video can be pedaled backwards. Some trials bikes have small wheels, like maybe 16" instead of the usual 26" for mountain bikes.
[Having trouble getting the right video to play. It might be a copyright problem, but there are plenty of decent trials bike vids to choose from.]
« Last Edit: 11/03/2012 18:03:47 by Phractality »

#### Geezer

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##### Re: Why can I cycle faster than the fastest runner?
« Reply #23 on: 11/03/2012 20:07:49 »

A fascinating video featuring a more or less total lack of bicycles and stairs.

Well, obviously, if you can make square gears, square wheels should be a breeze : )

#### thedoc

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##### Why can I cycle faster than the fastest runner runs?
« Reply #24 on: 01/05/2012 19:07:08 »
Hiya - congratulations on your podcasts.

Here's a question for you:
Wikipedia tells me that the men's 1 mile running record is held by Hicham El Guerrouj at 3 mins 43.13 secs. This, according to my maths, equates to 16.03 mph. Needless to say El Guerrouj is an elite athlete!

I go cycling on my (not very expensive) bike most weekends. I usually cover about 20 miles on a ride and my average speed is never less than 16 mph.

I am not an elite althlete - in fact I'm almost 50, weigh 100 kg and have a BMI which puts me well into the obese range.

Why am I able to move at the same speed as an elite athlete, for 15 times longer - especially when you consider that the bike adds 10% to my overall weight plus lots of friction from the moving parts?

Keep up the good work
Best wishes
Trevor Barton

Visit the webpage for the podcast in which this question is answered.