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This question is cross-posted from Bicycles.SE, but it is really one for those that know a bit about physics.

Why does the back tyre of a bicycle wear out quicker than the front tyre?

I have my uneducated suspicions but I would appreciate an educated answer.

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Cross-posted from bicycles.stackexchange.com/q/4568 –  Qmechanic Jun 21 '13 at 18:06

5 Answers 5

Certainly my experience when cycling has been broadly the same. Supposing we're cycling at a constant speed on a flat surface, there are, at the lowest level of thinking about this problem, four forces acting: (1) wind resistance, mostly horizontal and to the rear, but with smaller components acting on the wheel spokes that I will discuss in a moment; (2) gravity, vertical and downwards; (3) A force acting at the front tyre (about which more in a moment); (3) a force acting at the rear tyre (again, more in a moment).

The vertical force of gravity is balanced by the upward vertical forces acting at the tyres. The vertical forces acting through the front and rear tyres will be different depending on the mass distribution of the rider and of the bike components, but the vertical component of the force will not contribute as much to wear as will the horizontal component of the force.

The horizontal forces at the tyres are the most interesting for this Question. Both tyres are at rest relative to the ground in the region of contact with the ground. There is frictional resistance to any attempt to make the tyres not be at rest relative to the ground wherever they are in contact. Tyre resistance starts and stops when the vertical motion of the tyre material takes it in and out of contact with the ground.

There is a frictional force that acts backwards on the front wheel that is sufficient to balance the air and axle resistance of the front wheel. I think this can best be thought of in terms of torque. The wheel is rotating at a constant speed, which is resisted by friction in the axle and by wind resistance, both of which act against the direction of rotation of the wheel. The force (properly, the torque) acting in the region of contact of the wheel with the ground has to act to keep the wheel rotating, which means that the force has to act backwards.

There is a forward force acting at the rear wheel, that balances the backward forces of wind resistance and at the front wheel. The upper part of the chain is under more tension than the lower part of the chain (because there is more force acting on one pedal than on the other), which acts as a torque on the rear wheel that is much more than enough to balance the air and axle resistance acting on the rear wheel. In the absence of frictional resistance provided by the tyre at the ground (and transmitted by the spokes, but I'm not going into how that could be said in more detail), the rear wheel would accelerate to much higher speed (turning the bike upside down shows how fast the rear wheel turns with only a little arm strength if there is only wind and axle resistance). The frictional resistance at the rear wheel therefore acts to keep the rear wheel from rotating too fast, so it acts in the forward direction.

Because the frictional resistance at the rear wheel balances both the frictional resistance at the front wheel and the wind resistance, the frictional resistance at the rear wheel is strictly larger in amplitude than the frictional resistance at the front wheel unless the bicycle is not moving, so there must always be greater wear of the rear tyre.

Finally, when we accelerate, the details of the above description don't change. When we brake, the resistance of the brake materials on the wheel rim have to be included. Not going over the handlebars dictates that we should use the front brakes more judicially than we use the rear brakes, but there is another Question of whether the front or the rear brakes wear more quickly that I suspect is more personal. One might as a matter of habit never use the front brakes. The recent fad for fixed wheel bikes must result in more wear on the rear tyre, although this will only be significant if traffic forces many stops and starts.

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On most bicycles, your center of gravity is not halfway between the front and back wheel - it is closer to the back wheel (image source: http://www.esquire.com/cm/esquire/images/d1/bike-080210-lg.jpg).

enter image description here

This means that the back wheel carries more of the weight. Now assuming that you inflate the tires with the same pressure, this means that the contact area (area touching the ground at one time) of the back wheel is larger - because to support a weight $W$ with a tire with pressure $P$ you need area $A = \frac{W}{P}$.

Now when you consider a tire as a cylinder, then the "flat bit" that represents the contact area is the chord of a circle - and if you were to follow a point on the surface of the tire from the moment it touches the ground until the moment it is released, you would see that it will have to slide first forward, then backward. As the flat spot gets bigger, this sliding rapidly gets worse - it goes roughly as the square of the chord length.

This means that a tire with more weight on it, but inflated to the same pressure, will have more wear.

Next, you have the fact that you apply the pedaling power through the back wheel - this will obviously add some more friction. I think that braking represents a relatively small fraction of the forces on the tire (unless you are into mountain biking, perhaps) - and even there, the tire that is more heavily weighted is likely to bear the majority of the friction (although the weight shifts forward during braking - which would tend to even things out).

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Unless the cyclist is leaning forward most of the weight is on the back tire. Therefore it has more contact with the road and when you turn there is more lateral force on the back. You do more braking whith the back so you don’t go head first. And finally you are applying your entire forward force on it so that contributes to more wear.

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Sorry but there are a couple of incorrect assertions and even more spelling mistakes in this, hence a -1 I'm afraid. –  qftme Jun 30 '11 at 9:48
    
In a date: "To wait or not to wait?" –  Georg Jun 30 '11 at 10:27
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@qftme do spelling mistakes make a case for voting down? –  bubble Jun 30 '11 at 12:49
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If I could down vote I would. I mostly brake with the front brakes - the rear brakes are not even close to being as effective. Amateur/beginner cyclists use the rear brake more because of the incorrect admonishment that if they pull hard on the front brake they will flip over the handlebars. –  Tim Jun 30 '11 at 19:30
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There is an element of truth to the front braking is dangerous claims. For a rigid bicycle, what matters stability wise if the riders center of gravity, and the vector force (gravity plus decelleration). If that force vector, drawn from the center of gravity, projects below the wheels axle, the system is stable, if not it is unstable. Using the back brake only, braking force will go to zero, as that force vector reaches the front axle (because there in no pressure on the back tire then). With the front brake, it is up to the rider to keep the braking force within stability limits. –  Omega Centauri Jul 1 '11 at 16:06

The simplest way of describing it is that all of the accelerating force is applied through the rear tyre

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Except braking and turning, maybe? –  Nick Jun 21 '13 at 17:54
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Even if you excluded all acceleration and just looked at a rider coasting the back tire wears faster due to uneven load distribution. –  Brandon Enright Oct 30 at 18:24

When braking, most of your weight is going to be on the front tire (due to your forward momentum). This is why the front brake is so much more effective than the rear brake. That also means that, if you use the rear brake, you are pretty likely to skid (which only rarely happens on the front tire), because the weight on it is reduced. I imagine that rear-wheel skidding, which should not occur very often with proper (front-wheel) braking, likely contributes to rear tires wearing out faster. (In my opinion, the rear brake is only really useful when the roads are slick and as an emergency back-up brake.)

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protected by Qmechanic Jun 21 '13 at 18:03

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