Force in a chain?

[02gf74]

To simplify matters, assume the 16 rear cog is twice the diameter of the 8 cog ).
Therefore, to exert the same rotational force on tyre/ ground contact point requires half the force at the chain/sprocket point because the lever for the 16 t cog is twice as long as the 8t cog.

...... and so on

ok, so you explained how gears work - that is fine. but when you are pedalling at your maximum, the stress on the chain is the same - if you are in the 8 cog you are going slower than if you were in the 16 cog because as you have explained, it needs more effort for the higher gear.

so the gear at the back does not affect the stress in the chain.

 

[WD Pro]

It would be interesting to start a poll – When did you break your chain ? including options with a combination of - big chain wheel / small chain wheel / on road / off road / low cadence / high cadence etc

Go on, someone set it up - theory class is over, let's have a look at the reality ...

WD

 

[suburbanreuben]

To simplify matters, assume the 16 rear cog is twice the diameter of the 8 cog ).
Therefore, to exert the same rotational force on tyre/ ground contact point requires half the force at the chain/sprocket point because the lever for the 16 t cog is twice as long as the 8t cog.

...... and so on

ok, so you explained how gears work - that is fine. but when you are pedalling at your maximum, the stress on the chain is the same - if you are in the 8 cog you are going slower than if you were in the 16 cog because as you have explained, it needs more effort for the higher gear.

so the gear at the back does not affect the stress in the chain.

And as I've already explained, more effort = greater power = greater force being transmitted through the components. The force in the chain is tension. Higher force = higher tension= greater stress on the chain.

But yes, under maximum effort conditions, the tension in the chain would be the same. You wouldn't, though, be able to exert maximum power in a low gear unless tyou're climbing a steeper hill.
In the example I gave, everything apart from the cog size was equal.

 

[gtRTSdh]

The maths is quite simple;

Looking at the situation when maimum torque is applied and there is sufficient traction. With drive side crank being loaded with the force of the riders weight/strength at the horizontal position (maximum leverage), ignoring the small (vertical) difference in angle of the chain when on size different sprockets at the rear.

Chain force = riders weight x [ crank length (mm) / chainring radius (mm) ]

100Kg rider 24T granny ring, 44T big ring.

So 100Kg x [175mm/45mm ( radius of 24T chainring)] = 388.8 Kgs
So 100Kg x [175mm/90mm ( radius of 44T chainring)] = 194.4 Kgs

In reality what breaks chains is the tension when the chain is not straight, so often biggest chainring to mid cassette will be the failure point.

There is also the point to consider that in the easiest gear, because the gear is so easy to pedal the rider does not have time to achieve full muscle strain, which is why it you can pedal with more force at lower cadences.

Which in turn moves on to cadence, and the fact that using the slow cadence/greater force tires your muscles much more quickly than 'spinning' using anaerobic reactions in your muscles (without oxygen), which is why spinning at greater cadence is commonly accepted as the most efficient movement possible over a longer period, due to the fact the lower muscle loads are aerobic reactions (with oxygen) and can be sustained by breathing, which is quiite helpful!

Have I bored you yet?

 

[JamesM]

If the ratio's are the same, the load at the rear wheel is the same and the force applied to the cranks is the same. A gear set with smaller cogs (say 32:16) would generate more chain tension than a gear set with larger cogs (say 48:24) for the same outcome.

The tension in the chain in these examples wiould be the same...

I respectfully disagree. But feel free to explain why!!!

To simplify matters, assume the 16 rear cog is twice the diameter of the 8 cog (it isn't, but humour me).
Therefore, to exert the same rotational force on tyre/ ground contact point requires half the force at the chain/sprocket point because the lever for the 16 t cog is twice as long as the 8t cog.
Still with me?
If the force at the 8t cog is twice that at the 16tcog, then the force in the chain ,must also be twice as strong with the smaller cog,

 

[suburbanreuben]

If the ratio's are the same, the load at the rear wheel is the same and the force applied to the cranks is the same. A gear set with smaller cogs (say 32:16) would generate more chain tension than a gear set with larger cogs (say 48:24) for the same outcome.

The tension in the chain in these examples wiould be the same...

I respectfully disagree. But feel free to explain why!!!

To simplify matters, assume the 16 rear cog is twice the diameter of the 8 cog (it isn't, but humour me).
Therefore, to exert the same rotational force on tyre/ ground contact point requires half the force at the chain/sprocket point because the lever for the 16 t cog is twice as long as the 8t cog.
Still with me?
If the force at the 8t cog is twice that at the 16tcog, then the force in the chain ,must also be twice as strong with the smaller cog,

Because the gear ratio is the same in both cases.

 

[02gf74]

If the ratio's are the same, the load at the rear wheel is the same and the force applied to the cranks is the same. A gear set with smaller cogs (say 32:16) would generate more chain tension than a gear set with larger cogs (say 48:24) for the same outcome.

The tension in the chain in these examples wiould be the same...

I respectfully disagree. But feel free to explain why!!!

I go back to the example where the rear wheel is bolted to the ground so it cannot turn.

You climb on the bike and give it your max effort. The amount of force you apply on the pedal is the same no matter what gears you select.

The tension in the chain will be highest when the chain in on the smallest front chain wheel.

The chain can be on any rear sprcoket - that does not affect chain tension - all it does it stop you from moving.

The praticalities of when a chain actually does break in the real world is a different question altogehter and stuff like chain line, how you pedal etc affect it.

 

[suburbanreuben]

Yeah, but who bolts their wheel to the ground?
For the sake of (a Saturday nite) argument, maximum force is applied at that point when you're honking on the pedals up a steep hill, and you simply cannot turn the pedals anymore, and you fall over sideways. At that point the force applied , and transmitted by the chain , is the same.
Whoever said it was anything else is talking out of their arse!
This month I'm mainly riding singlespeed , so I know what I'm talking about!

 

[JamesM]

If the ratio's are the same, the load at the rear wheel is the same and the force applied to the cranks is the same. A gear set with smaller cogs (say 32:16) would generate more chain tension than a gear set with larger cogs (say 48:24) for the same outcome.

The tension in the chain in these examples wiould be the same...

I respectfully disagree. But feel free to explain why!!!

To simplify matters, assume the 16 rear cog is twice the diameter of the 8 cog (it isn't, but humour me).
Therefore, to exert the same rotational force on tyre/ ground contact point requires half the force at the chain/sprocket point because the lever for the 16 t cog is twice as long as the 8t cog.
Still with me?
If the force at the 8t cog is twice that at the 16tcog, then the force in the chain ,must also be twice as strong with the smaller cog,

Because the gear ratio is the same in both cases.

Torque applied at the cranks is the same (controlled input). Rotataional force at the wheel is the same (resulting output) for both cases beacuse the ratio is the same. But, with the 32 front chainring more force is being applied to the chain becaue the effective lever is longer than with the 44 tooth. The extra force from the 32 however is needed to generate the same rotaional force at the rear wheel because (as you explained previously) the 16 is a shorter lever than the 24. The 24 requires less force, being a longer lever, to generate the same rotational force at the rear wheel. Which just as well because for the same torque applied at the crank the 44 won't generate as much force. So more chain tension in the example with the smaller gearset for the same input and the same resulting output beacuse the ratio's are the same. Discounting frictional losses of course . There I've gone full circle!!!

 

[doctor-bond]

I suspect the problem here is that no one is reading any of the responses before posting. Anyway here goes ...

In the real world of riding bikes, chains break when the most force is being applied through them.

A chain is more likely to break when:

1. the rider is giving his maximum effort (big push on the crank, weight forward, pull on the bars, etc.)
2. The chain feels that effort. Be the chain.

Now, think about the circumstances in which the chain feels the rider's effort:
1. Going down a steep hill in a low gear (for example, with a small front ring): the chain isn't able to feel much of that effort. All it does is easily transmit effort into forward motion. That chain doesn't even break a sweat.
2. Going up a steep hill in a high gear (like when using a large front ring): the chain now feels all the weight of the rider and his steed and has to take all of the rider's force and try to turn the back wheel despite the strain. Now that chain -- if it is anything like the shimano one that snapped on my singlespeed on a 1:4 hill -- will feel the effort.

So.... in theoretical situations, with all inputs being equal, the most tension you can transmit to a chain is when employing a small front ring. The OP and others have proved this 10 times over.

AND ...

In practice, the most force is usually transmitted to chains when fat riders try to pedal up hills on single speeds with large front rings and small rear ones.


Having said all that, maybe we should consider the torsion equivalence of the rear cluster -- especially in relation to the tensile density of freewheel pawls and the specific gravity of modern tyre rubber compounds ..... oh and what about gravel liquefaction due to vertical sheer stress?