# Chainring use of teeth

At any instant how many teeth in a (not new) 52 chainring are actually doing the chain pulling when torque is being applied.

• Depends on 1) how not new the chain ring is and 2) the wear (i.e., stretch) of the current chain. Also it will not be a binary engaged/not engaged but the force experienced by each tooth will be slightly different so we would need criteria for what constitutes engaged/pulling. Jan 8, 2018 at 21:13
• i think this question is a bit vauge Jan 9, 2018 at 6:41
• Given that the calculations we've made depend on the rest of the drivetrain, you should update your question with more information. As it is, it's too broad for a definitive answer Jan 10, 2018 at 8:52
• I'm voting to close this question as off-topic because it's a question about physics, not cycling. Jan 10, 2018 at 10:18

Depends how well the chain and chainring mesh. Assuming perfect alignment, exactly half the teeth are engaged.

In the real world, the chain will be somewhat elongated. So your worst case is one single tooth is taking all the strain. At this point, wear is accelerated.

You should use "27 teeth" and "1 tooth" as inputs for your needs.

EDIT ChrisH calculates that assuming a 52 tooth chainring and an 11 tooth rear cog, there will be an 11 degree angle between the horizontal and the chain, on either side.

So 22 degrees over 180 gives 202 degrees of the chainring are touching the chain. 202/360 shows 56.1%of the chainring, which is 29.18 teeth, so 29 teeth in contact with the chain, highest possible value assuming a 400 mm chainstay length.

• Assuming the sprocket isn't the same size as the chainring it won't necessarily be 50% (even with a derailleur, which we don't know the OP has). Imagine a single-speed with small wheels (short chainstays increase the angles) and 52/11. You'll get well over 50% engagement Jan 9, 2018 at 16:51
• @ChrisH good point - Assuming a super short 400mm chainstay and an 11 tooth rear cog, what's the effective contact length on the 52 tooth chanstay? My maths isn't up to it, but I suspect it wouldn't be more than 7 degrees which one tooth.
– Criggie
Jan 9, 2018 at 19:15
• Following stem2.org/je/pulley.pdf I get just over 29 teeth engaged (11° where the chain arrives and the same again where it leaves). So close to your guess Jan 9, 2018 at 20:40
• Note that this assumes there's no derailleur: with one (especially a long-arm), the chain is likely to be in contact with less than half the ring. Jan 10, 2018 at 10:19