Author Topic: Gear ratios and the RPMs that love them  (Read 1680 times)

Bartlioni

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Gear ratios and the RPMs that love them
« on: September 13, 2014, 11:53:32 am »
This may not be the right place to post this, but WTF.  Our brother's post on wide-bandwidth gear ratios got me thinking a lot about how changing out my front sprockets from 14 - 15 (stock) - 16 tooth affects fuel efficiency.  I can't bring myself to spend major smucks on a new gear set, but it isn't hard to change out front sprockets.  So I'm going to stay with the sprocket approach and tailor my scoot for a particular ride.  But looking into it further, I learned that the Duke has nearly identical fuel efficiency as the Enduro R even though it comes out of the stable with a 16/40 sprocket combination. And then last week I met up with a dude that owns a Duke, and I asked him some questions about shift points.  It turns out that my experience with the 16-tooth needing to down-shift at ~52mph as apposed to 42mph with the 15-tooth on my 690e was pretty-much right on.  He says that particular shift point is ~55mph on his duke.  Note that both bikes use the same primary gear ratio.  Just the sprockets are different.  But it looks like fuel efficiency is at least somewhat if not largely independent of a given RPM the engine is running at.  Engine wear is obviously highly dependent on RPM, but apparently fuel efficiency isn't.  But my current theory goes like this:

14-tooth front - For hauling most royal butt on all terrain that isn't paved.  (mega power wheelies in 1-4th gear I think.)
15-tooth front - A good general purpose compromise.  (power wheelies 1-3 comfortably)
16-tooth front - For hauling most royal butt on pavement, gravel, and well-defined trails (still got power wheelies in second.  Maybe third.  Haven't tried it)

So what do you guys think?  The real question I'm pondering over is if there's any difference between (say) adding a tooth on the front versus removing three teeth from the back sprocket.  I don't think there is but I've been wrong before.
- Bartlioni

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Rusty Shovel

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Re: Gear ratios and the RPMs that love them
« Reply #1 on: September 14, 2014, 06:48:47 pm »
The real question I'm pondering over is if there's any difference between (say) adding a tooth on the front versus removing three teeth from the back sprocket.  I don't think there is but I've been wrong before.

Hey Bartlioni,

Changing the front sprocket on my DR650 was the best thing I ever did for the poor wheezing monster.  It still wasn't a hotrod, but going down a tooth sure made tight trails easier.  That said, the only possible downside of going down a tooth on the front is that, if you use the wrong front sprocket/rear sprocket/chain length combo, you could wear out your chain very quickly.  GearingCommander. com calls this a "same tooth-same link situation:

As explained on gearingcommander.com:

'Same tooth - same link' situation
This happens when the number of links of the chain divided by the number of teeth on a sprocket is a round number. Let's assume you have a chain with 60 links, a front sprocket with 10 teeth and a rear sprocket with 20 teeth.
(F = 10, R =20 L = 60) Not a very realistic situation but easier for the example.

The number of Links divided by teeth on Front = L / F  = 60 /10 = 6
This means that after six rotations of the front sprocket, the chain made exactly 1 rotation and the first tooth on the front sprocket hits the exact same link of the chain.

Same goes for the rear: L/R= 60/20=3. So every 3 rotations of the rear sprocket, the chain made 1 complete rotation and the teeth are exactly in the same position again.
So when this chain rotates once, both front and rear sprockets are in the same position and hit the same link all the time. This is not good.

It would be better if the chain had un uneven number of links, say 61. Since this is not very likely (chains almost always have an even number of links), lets take a chain with 62 links. The calculation now are:

Front: L/F = 62/10 = 6.2
Rear:  L/R = 62/20 = 3.1

This means that after 1 rotation of the chain, the front made 6.2 and the rear 3.1 rotations. This means other teeth hit the same link in the chain ! That is better !

Now how long (how many rotations of the chain) does it take this time for the teeth to hit the same link again? We then have to find the out how many links will have to pass before the division results in an even number. That is the case when we have the LCD of these numbers, the Least Common Multiple. This can be calculated using the GCD, the Greatest Common Denominator. The GCD for 62 and 10 is 2, that is the greatest number both can be dived by which results in an even number.
Now the LCD = the multiple of 62 and 10 divided by the GCD:  (62 * 10)/2 =  310.
this means after 310 links, the front sprocket is in the exact same position again.
310 links means 310 / 62 =  5 rotations of the chain. So when having a china with 62 links instead of 60 links, results in less wear because now only every 5 rotations of the chain, the same tooth is hit.

So what would be the optimum number of chain rotations then ? That would be when we have a maximum number of links needed for the same position. So the division LCD = (#1 * #2) / GCD should be maximum. That is the case when GCD = 1 cause the result would then be (#1 * #2) / 1 = #1 * #2.
So when the GCD is 1 we reached our goal. This happens when one of the number is uneven. Lets say we take an 11 sprocket instead of a 10 sprocket, Rear =20 and Links = 60. This results in a GCD of 1 and the number of links needed is: (11 * 60) / 1 = 660 links. This means the chain has to rotate 660/60 =  11 times before the same tooth hits the same link again. This is the optimum !


Take a look at the gearing commander website; they have an awesome tool that does all the math for you.  I punched in the numbers and it looks like the 14/45 combo is okay, but the 16/45 combo may result in more wear than you're willing to accept.  [EDIT: ***Whoops! I had that wrong: Both combos are okay, in fact the 16/45 appears to be slightly superior in terms of potential wear.]

I would like to hear from folks who've taken the plunge.

I think I'm gonna get a 14 tooth and pop it on for dedicated off-road days, but stick with the 15 tooth for everyday use.
« Last Edit: September 16, 2014, 04:33:05 pm by Rusty Shovel »
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Bartlioni

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Re: Gear ratios and the RPMs that love them
« Reply #2 on: September 16, 2014, 04:42:25 pm »
I'm with you on the 15 for everyday use.  That's a really good site Rusty.  Thanks for pointing it out.  Rusty Shovel to the rescue.  I went to it and plugged in the data for the KTM 690e and here's what I came up with:  I hope I'm reading these results correctly.  Rusty knows this site better than I do so sing out if I'm wrong.

Same Tooth / Same link -

14t - 7
15t - 5
16t - 8

If I'm reading this data correctly this is saying that the 16t has minimum wear (bigger number) and the 15t has maximum wear (smallest number).  But this just represents rotations of the sprocket before the same link contacts the same tooth.  Apparently this is one of two wear indicators.  The second wear indicator from the gearcommander site is the number of times any tooth (on the front sprocket in this case) makes contact with any link on the chain over a mile traveled.   Here's the numbers for that:

14t - 2417 (any tooth touches any link per mile)
15t - 2256
16t - 2115

So if I'm reading this right, it says that the 16t has fewer contacts with the chain per mile which indicates lower wear.  The same tooth / same link number for the 15t indicates more wear than the 14T, but the 15t has fewer contacts per mile than the 14t, and ultimately I think this means less wear than the 14t.  But between the 16 and the 14, the percent difference is just slightly over 13%.  So the worst case would be that using a 14t sprocket would wear out your sprocket and chain 13% faster than it would for the 16t. 

But what does it all mean Basil?

To me this means I'd throw one of them little 14t puppies on and yell yeeee-haaaaw without giving it a second thought.  To hell with 13 lousy percent.  If that's the price for being able to climb fardrifter's 45 degree hills then so be it.  Front sprockets are cheap and chains aren't that expensive.  Lets rock!
- Bartlioni

 "Bwaaaaaaa.  Get that little Pointy-Head!"

Rusty Shovel

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Re: Gear ratios and the RPMs that love them
« Reply #3 on: September 18, 2014, 08:38:16 am »

To me this means I'd throw one of them little 14t puppies on and yell yeeee-haaaaw without giving it a second thought.  To hell with 13 lousy percent.  If that's the price for being able to climb fardrifter's 45 degree hills then so be it.  Front sprockets are cheap and chains aren't that expensive.  Lets rock!

Absolutely.  Also, since I'd be reserving my 14t sprocket for hairy off road rides, I'll run very little mileage with it.  It took me all day to run 195 miles during Uncle's Desert Challenge.  I'll probably only swap out the cog for "events".  For mixed trail riding, I'll stick with the 15.
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Bartlioni

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Re: Gear ratios and the RPMs that love them
« Reply #4 on: September 18, 2014, 08:41:29 pm »
What!?!?  Stop the presses dude.  That 14t will cost you 6.9% more wear than your 15t.  Best keep some fancy chain lube handy.  Bwaaaaaaaa.  Hayeeeell Yeeaaaah!  We in the chain lube zone ma'an. 

:)

- Bartlioni

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Rusty Shovel

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Re: Gear ratios and the RPMs that love them
« Reply #5 on: September 19, 2014, 08:09:00 am »
Best keep some fancy chain lube handy.  Bwaaaaaaaa.  Hayeeeell Yeeaaaah!  We in the chain lube zone ma'an. 

:)

Yeah!  It's about time I did a chain maintenance post.  Thanks.
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Re: Gear ratios and the RPMs that love them
« Reply #6 on: October 05, 2014, 08:09:20 am »
I went to Texas creek; I thought it would be easy - I was wrong.  Crazy rocky uphills, some section jumping on and bouncing off and up of cliff faces!  Okay, now I see the reason for the gear change.  My buddies Honda's 2nd gear was lower than my first gear!  I had to really go for it, and on the downhills he could use 1st gear to gear down while I had to hold the clutch in  (in case I needed a forward boost) and idle/bounce down the rocks - not easy!  A slightly lower ride height would have probably helped as well.  I can really see the case for the supermoto/dirt set-up.  The good news is that I made the entire ride.  I did lay it down about 5 times (in a 5 hour ride), but no more major damage than a bent mirror which I just bent back. :o

Bartlioni

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Re: Gear ratios and the RPMs that love them
« Reply #7 on: October 05, 2014, 05:48:47 pm »
Sounds like a job for a 14t on the front and maybe even some touratech foldy-uppy mirrors.  I love mine.
- Bartlioni

 "Bwaaaaaaa.  Get that little Pointy-Head!"