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[Closed] Relationship between sproket sizes and efficiency

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I'm wondering what the relationship is between chainring/sprocket size and drivetrain efficiency. Does the below sound correct, or any different thoughts you have?

Let's say you're doing a TT at 300W and you've established with your current setup you'll be spending most of it in 50T/10T which results in a drivechain loss of 8 Watts. The tensioned chain links between the front and rear sprockets articulate through an angle of 43.2 degrees every time the chain moves forward by 1 link (7.2 degrees pulled onto the front chainring and 36 degrees pulled off the rear sprocket).

If you increase the size of all the chainrings by 20% to 60T/12T the final ratio is the same, cadence etc remains the same. The tensioned chain links between the front and rear sprockets articulate through an angle of 36 degrees every time the chain moves forward by 1 link (6 degrees moving onto the front chainring and 30 degrees moving off the rear sprocket), which is 20% less than the former 43.2 degrees.

So for this latter configuration, the chain is articulating through 20% less angle per link, the chain is moving faster also but this counteracted by correspondingly lower tension. Drivechain loss being proportional to this articulation angle is therefore 20% less, so reduced to 6.4W. So the 20% larger chainring saves 1.6W of drivechain loss (may be offset by increased weight and frontal area).


 
Posted : 20/10/2020 4:30 pm
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yes, in a nutshell small sprockets = tight chain angles = more loss from friction in the chain.


 
Posted : 20/10/2020 4:45 pm
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Time to find something like a 90T chainring to marry with something like an 18T sprocket in the middle of the cassette. 😆


 
Posted : 20/10/2020 4:51 pm
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I saw some Muc-Off video where they claimed to measure the difference in friction losses between individual chains and identify the lowest loss ones for Team Sky to use for key TTs etc.


 
Posted : 20/10/2020 4:54 pm
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But bigger rings and sprockets are heavier, how's that factor in?


 
Posted : 20/10/2020 5:00 pm
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But bigger rings and sprockets are heavier, how’s that factor in?

Don’t be coming in here with problems, we want solutions. 😂


 
Posted : 20/10/2020 5:05 pm
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And is there not more friction on larger sprockets from contact area with the sprocket itself?


 
Posted : 20/10/2020 5:08 pm
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But bigger rings and sprockets are heavier, how’s that factor in?

fairly minimally on a flat course with hardly any acceleration (as it is irrelevant when traveling horizontally at constant speed)


 
Posted : 20/10/2020 5:14 pm
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Don't care much about a bit of about Watts and weight, a longer chain and more sprocket and chain ring teeth last longer. Runs smoother I'd say too. But since I can't tell when my dynamo is on or off I'm also not that bothered solely by saving 2W on a chain. Still, good workings.. interesting.

I saw some Muc-Off video where they claimed to measure the difference in friction losses between individual chains and identify the lowest loss ones for Team Sky to use for key TTs etc.

The lengths you need to go to in making up marginal gains as masking agents ; )


 
Posted : 20/10/2020 5:17 pm
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But bigger rings and sprockets are heavier, how’s that factor in?

Never mind that, what about the increased frontal area of that massive chainring?
Won't someone please think of the precious, precious Aeroz!!! I thought that was the whole thing with TTers now, get the Aero optimised, contort yourself into a wheeled human cruise missile! Breathing, seeing straight not battering your biff on the nose of your saddle are all secondary to sliding through the air like a greased weasel...

Surely the lowest possible loss drivetrain is fixed, no horrible little mech pulleys for your chain to whip round, no possible risk of that freewheel wasting your precious watts by deflecting or indulging in friction betwixt pawls and ratchet ring, the straightest, least frictional chain-line possible...

And of course why not pay someone an exorbitant amount to dip your chain in some sort of MoS2 goop, then reserve that chain for special, high efficiency, occasions...


 
Posted : 20/10/2020 5:46 pm
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Belt drive for the win ?


 
Posted : 20/10/2020 6:59 pm
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I'm sure a proper engineer will be along to correct me, but I vaguely recall that the ideal minimum size for an efficient chain cog is 23 teeth.

For that to work on a bike, we would need to use much finer pitch chains. Shimano had a go at that quite a few years back with a 10mm pitch.


 
Posted : 20/10/2020 8:12 pm
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What's a 'chain cog' please?


 
Posted : 20/10/2020 9:11 pm
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@boblo a cog for a chain.


 
Posted : 20/10/2020 10:10 pm
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Aahhhh, thanks that clears it up 👍 🤔


 
Posted : 20/10/2020 10:15 pm
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This is why testers are regarded which such disdain by road racers.


 
Posted : 20/10/2020 10:17 pm
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fairly minimally on a flat course with hardly any acceleration (as it is irrelevant when traveling horizontally at constant speed)

Isn't there an angular momentum penalty for them though? Same as goes for heavier tyres and rims. You're constantly changing the direction in which a section of tyre/rim/chainrig/sprocket is going.

Might be called moment of inertia actually, cant quite remember words this early in the morning.


 
Posted : 21/10/2020 8:28 am
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Isn’t there an angular momentum penalty for them though?

No. Once they've been given angular momentum, they keep it, as long as you are pedalling at the same speed.

You’re constantly changing the direction in which a section of tyre/rim/chainrig/sprocket is going.

Yes, but for every section of tyre going one way there's another identical section on the other side of the hub going the other way that cancels it out. That's why you can spin balanced wheels for ages without adding any energy.


 
Posted : 21/10/2020 9:34 am
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For that to work on a bike, we would need to use much finer pitch chains.

If it's to do with the angle of bend of chain it's really the diameter of the chainring and rear cog. Going to a smaller pitch chain just means more teeth are required to have the same size cogs.

In addition (if we are going on this thought process) smaller links = more links = more plate friction, maybe?


 
Posted : 21/10/2020 9:48 am
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I ride a fixed gear (with perfect chainlink) on an 18 tooth rear cog so must have a pretty efficient drivetrain. Doesn't stop all those road bike riders on their 10t cogs passing me though...


 
Posted : 21/10/2020 9:54 am
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If it’s to do with the angle of bend of chain it’s really the diameter of the chainring and rear cog.

In relation to the chain pitch. A smaller chain pitch means that each link bends less. This means that it's purely about how many teeth there are on the sprocket.

For pros doing time trials, this might make the difference between winning and coming second, but most riders aren't putting out massive power in the smallest sprocket for extended periods. On an MTB, you are mostly in a large sprocket climbing a hill when you are consistently needing max power.

On top of that, even if going to a bigger chainring and sprocket saved 2% power, your increase in speed will be much less because aerodynamic drag increases as the cube of speed, and aero drag is the major factor. If we ignore rolling friction, a 2% increase in power would give a 0.7% increase in speed. Completely irrelevant except for serious time-trial competitors.


 
Posted : 21/10/2020 10:00 am
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Good point we will made.


 
Posted : 21/10/2020 11:41 am
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I spent a good 30 minutes gazing at my navel over this and still didn't have a clear answer to why I would worry.


 
Posted : 21/10/2020 11:54 am
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I spent a good 30 minutes gazing at my navel over this and still didn’t have a clear answer to why I would worry.

Because spending a month's salary on expensive gear to get a 1% improvement is much easier than dieting and training to lose 25 pounds of spare tyre round your gut. (I'm well acquainted with this, so trust me.)


 
Posted : 21/10/2020 12:25 pm
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This is interesting. It's more about friction on the pins rather than the plates. And doubling the size of the sprockets halves the chain tension but that only translates into about 0.5% efficiency improvement and the fact doubling size of sprockets is not really practical in terms of bike design....

https://www.newscientist.com/article/mg15721260-700-big-is-better-how-sprocket-scientists-have-given-cyclists-a-speed-boost/


 
Posted : 21/10/2020 1:06 pm
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If it’s to do with the angle of bend of chain it’s really the diameter of the chainring and rear cog. Going to a smaller pitch chain just means more teeth are required to have the same size cogs.

It doesn't really work like that, the links being pulled onto or off the cogs are tensioned and articulating and the angle they articulate through is proportional to the number of teeth, not the diameter. So there is some advantage in making the pitch smaller (Shimano did produce a system with 10mm chain pitch at one point) but that'd also have a smaller load rating, smaller bearing surfaces, etc.

I've found this FrictionFacts/Ceramicspeed report and my conclusion that the loss scales with chainring size maps very well with their findings (e.g. chart on page 14).

I suspect there are some additional factors for small cogs (e.g. less than 12T) not accounted for here, as when there are large angle/few teeth things don't mesh well/slide etc.

However, in general, the conclusion I am drawing is that this cog size thing is somewhat insignificant, albeit much more significant than things like jockey wheel size, other factors like chain misalignment are more significant.

To put this into context, for the last major TT I did I bought a bigger 56T chainring to replace the 53T chainring. This was an improvement but I still spent the tailwind half of the course in 12T sprocket and headwind half in 13T. I think I made a mistake, should have gone biggerer 60T chainring where I would have been using 13T/14T sprockets which would have a bit less wraparound loss but more significantly better chain alignment.


 
Posted : 21/10/2020 1:33 pm
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The application of friction is not linear. As you apply a force there is initial resistance to the two surfaces moving and sliding past each other. This force is very high initially until the movement starts. After that the force required to maintain slippage/movement is very low/negligable. This is the stick slip phenomenon. So I'm not sure the amount of friction in the system is linked to the angle of bend of each link...more the number of bends in a given time. Also there is another component to friction- that is force. This is where the gear diameter comes in. for a given power a larger diameter sprocket will generate less force in the chain and reduce friction.


 
Posted : 21/10/2020 2:15 pm
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The application of friction is not linear. As you apply a force there is initial resistance to the two surfaces moving and sliding past each other. This force is very high initially until the movement starts. After this the force required to maintain slippage/movement is very low/negligible. This is the stick-slip phenomenon. So I’m not sure the amount of friction in the system is linked to the angle of bend of each link… more the number of bends in a given time.

I doubt there is much difference between static and dynamic friction for a relatively well-oiled chain.

Also there is another component to friction- that is force. This is where the gear diameter comes in. for a given power a larger diameter sprocket will generate less force in the chain and reduce friction.

Sure, I agree with you here, I was on the wrong track with this articulation angle relationship. So the drivetrain efficiency improves with reduced chain tension. Increase the cog sizes by a percentile, the tension and friction is reduced by the same percentile. This also means than chain efficiency is better for smaller wheels 🙂

The 'cogging' effect that I relate to sprockets with small number of teeth is apparently called the polygonal effect, or chordal action. When driven by cog of a constant speed a chain actually has a speed variation caused by the offset between PCD and the engagement points, this speed variation decays exponentially with increasing number of cog teeth. This speed variation would create noise and inefficincy.

Ratio of speed change = (Vmax − Vmin) / Vmax = 1 − cos (180°/N). It seems this becomes non-trivial under 23T, and significant under 12T.

Excellent description here


 
Posted : 21/10/2020 7:35 pm

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