[The reason] Chain stress

It is common knowledge among riders that decreasing sprocket/driver size increases the stress on your chain. However most people think this due to the wrong reason, and can often misunderstand just how much the stress increases with each drop. From what I have read most riders are under the opinion that the stress increase is due to the same force over less links, this is only a small part of the problem. The real reason lies in physics and moments as will no be explain. For the examples I will be using the common ratio’s 36t-13t and 25t-9t which have radii of 6.9cm and 4.8cm respectively along side the 17.5cm crank arm length. For simplicity you can think of these examples in situ (i.e. these are stress levels when bike is still, either with front wheel against a wall or your brakes pulled in sharp).
The situation taken into consideration for these examples will be thus:



The full weight of the rider acting vertically down on the pedal will have a certain force. Let’s take 80kg for our example weight. 80kg acting vertically down under the force of gravity would have a force of 784.8N [80xacceleration due to gravity (9.81m/s2) = Force in Newtons (784.8N)].
This in turn will have a moment. The moment of a force is it’s turning effect (more commonly known as torque) and is equal to the force X the perpendicular distance from the pivot in meters (Nm). The moment in this scenario is (0.175m X 784.8N) 137Nm.
Now that we know the torque executed on the system by the rider we can work backwards to find out the effective stress on the sprockets (knowing that the system is not moving we can say that the torque of the sprocket must be 137Nm in the opposite direction). Let us take the 36 tooth first:

0.069m x F must equal 137, so 137 ÷ 0.069 = F = 1990N

This is the same as hanging 202Kg weight from your chain.

Now the 25 tooth:

0.048m X F = 137 so there for using same method as above F is 2861N or 291Kg weight hanging.

You can see that there is a difference of around 850N or 90Kg, and this is in situ. Say your where doing a 180 tap pivot out, there could be as much as 3 times your body weight acting on the pedal, multiplying all the other figures and very soon the differences can become very large. If you work it out using 240Kg on the pedal the difference turns out to be a difference of around 270Kg. And in other situation it could be more again. The 25 tooth in the case of 240Kg acting (3 times average body weight) on the pedals has 5971N acting on the chain. Most chains would average out at being able to cope with a ton (roughly 10,000N) before they snap, so nearly 6000N can do cause so serious stretching over time. As a warning don’t go smaller than you need to, in my opinion 28-10 is nice enough to keep your sprocket out of harms way, if you go smaller the only reason I can see is weight, which is miniscule.

All question welcome, and I apologise if that was slightly hard to follow.

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