Science Questions

Why can I cycle faster than the fastest runner?

Sat, 28th Apr 2012

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Trevor Barton asked:

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


Dave -   There are various different things which could be limiting how fast you can move.  There are various mechanical reasons, like you might not actually be able to move your muscles quickly enough or if you're pulling a very heavy weight, itís limited by the amount of force you can apply on the weight.  I think in this case itís limited by the amount of power you can put out.  Elite athletes are going to be able to put a lot more power out than you are, but you're using a method of transport which is much more efficient.  Bikes have been optimised over the course of 150 years to be incredibly efficient.  You use very, very little energy to keep going along.  In fact you need hardly any energy to keep them going along, itís just to accelerate them and to overcome air resistance, as thereís no friction there.  So, with a very relatively small amount of power, you can be going very, very fast.  

Whereas when running, you've got to move these great big legs around all the time and you actually kind of reach a limit to how fast you can move the legs backwards and forwards.  You've got to accelerate and decelerate every time you take a step.

Chris -   You're basically accelerating a bag of water weighing at least 60, if not 100 kilos which you're elevating and dropping and decelerating with every step, arenít you?  So, you're basically having to keep lifting this very heavy bag up and down, and itís not an efficient way to move.

Dave -   And also, you've got your legs, at 10 or 15 kilos each, which you're accelerating backwards and forwards.  So all of that takes a huge amount of effort whereas on a bike, all you've got to do is just push this off along through a very efficient mechanical train.

Diana -   Perhaps one of the reasons why humans are so good at doing long distances for a long time is because they've only got two legs whereas four-legged animals like horses, although they can go faster, they canít go as fast for as long as humans can because they've got four things to lift up.


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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. Cheese2001, Thu, 8th Mar 2012

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. Geezer, Thu, 8th Mar 2012

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.  Cheese2001, Thu, 8th Mar 2012

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. Geezer, Thu, 8th Mar 2012

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.

CliffordK, Fri, 9th Mar 2012

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.

Geezer, Fri, 9th Mar 2012

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. jpetruccelli, Fri, 9th Mar 2012

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.
Cheese2001, Fri, 9th Mar 2012

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.

On the gearing issue, when I was eleven I came off a bicycle over the handlebar at high speed while going down a hill when an idiot ran out onto the road in front of me. While flying through the air and rotating, I had a view of the road behind me, upsidedown, and then I watched the roofs of houses to either side rotating round as I looked up towards the sky, and then the idea occurred to me that I might be able to land on my feet, because the world was heading towards being the right way up again. Then I could see the road ahead again and it looked possible - the timing of the rotation was perfect and the only problem was that I was possibly travelling twice as fast as I had ever run before. Somehow, I made it - the forces were high on the first couple of impacts, but I had enough strength to absorb them and just managed to move my legs fast enough to stay upright for sufficient steps to avoid falling over forwards. I heard the bicycle hit the ground behind me and moved slightly to the side to avoid being collected by it, though it actually stopped a long way short of where I was and had in reality been no threat. The main difficulty was with the gearing - moving your legs forwards isn't in itself the hard bit, but the speed they have to move backwards is, and it then takes more effort to overcome that momentum to get your legs moving forwards again. David Cooper, Sat, 10th Mar 2012

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. Geezer, Sat, 10th Mar 2012

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.) jpetruccelli, Sat, 10th Mar 2012

It has to be more than just gearing...

As I mentioned above, the Olympic Speed Skaters hit 30 MPH, 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. CliffordK, Sat, 10th Mar 2012

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.

Bored chemist, Sat, 10th Mar 2012

Energy !!


Transformation of energy must be 'it'.. yor_on, Sat, 10th Mar 2012

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.

Phractality, Sat, 10th Mar 2012

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, Sat, 10th Mar 2012

Er, bollocks! Geezer, Sun, 11th Mar 2012

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. Phractality, Sun, 11th Mar 2012

Yeah, yeah yeah.

If you wave your arms any faster, your bike is liable to turn into an aeroplane. Geezer, Sun, 11th Mar 2012

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" Bored chemist, Sun, 11th Mar 2012

Yeah, yeah yeah.

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

Er, bollocks!
jpetruccelli, Sun, 11th Mar 2012

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.
trials bike vids to choose from.]
Phractality, Sun, 11th Mar 2012

Well, obviously, if you can make square gears, square wheels should be a breeze : ) Geezer, Sun, 11th Mar 2012

Bluedy 'eck! It can't be Groundhog Day already? Geezer, Wed, 2nd May 2012

Well, here's a compact version of the answer for those who've come to the party late. If you're on a bicycle, you can take a complete rest while still moving at speed, but if you try doing that while running you'll have a nasty crash into the tarmac. Runners have to work hard even to run slowly, whereas cyclists don't.

That's probably also why far more people drop dead while out jogging than do when cycling - you have to stop moving to have a proper rest if you're out for a run, but there's a psychological pressure on you to keep running no matter what, so you slow down rather than stopping and you fail to recover as quickly as you could, and may even continue to do the damage that will take you out. The cyclist has it easy - (s)he can keep going at a respectable speed while reducing the energy output to just a few percent.

So, you're comparing two very different activities - one involves high power all the time, while the other allows you to do a little work to get up to the same speed as the runner and then to coast along. Think about running downhill and you can see that the runner still has to work hard while the cyclist has no work to do at all. On steep uphills, the runner eventually gains an advantage, but it has to be steep. David Cooper, Wed, 2nd May 2012

"High power all the time" - Power is really instantaneous energy consumption, so presumably you mean high energy all the time.

The energy consumed can do two things. It can do useful work (moving you from A to B) or it can be dissipated into the environment in the form of heat. The efficiency of the "machine" is the ratio of the useful work to the total energy consumed.

We can't really alter the efficiency of the human body, but the bicycle clearly improved the efficiency of the overall machine (if you allow that the two cases are examples of "machines").

The only way you can improve the efficiency of a machine is by reducing friction. Geezer, Wed, 2nd May 2012

I was going to add that "a bike only improves efficiency by reducing friction which allows us to muck around with gearing ratios", but there is a bug in the forum software that won't let me turn off bold once I have turned it on :) Geezer, Wed, 2nd May 2012

I know you all had this discussion two years ago, but it came up near the top of my Google search.

Someone mentioned the upward force exerted when running. I think that's the most important issue. When you're running, you need to apply a force to the ground that propels you forward and upward (so I guess you apply a force backward and downward). On a bike, this happens where the wheels contact the ground, but the upward/downward force is taken care of by the rigidity of the bike frame and wheel, and so almost all of the energy you put into the pedal goes to propelling you forward. On the other hand, since running on a treadmill is not much easier than actually running, the propulsive part of running must not use a lot of energy, and so maybe it really is a matter of gearing.

By the way, if you remove the aerodynamic drag of riding a bike, you can go really fast. Bikes with fairings can do 70mph+, I believe, and bikes drafting a car can do 120mph. hiseri, Mon, 11th Nov 2013

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