# Math quiz

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LOL, I will not know if your right or wrong. I am trying to determine if or what percent  the gearing would become longer by switching front sprockets from a 12 to a 13. I know it will move everything higher, but I think, mathmathicly speaking, that it will make the gears seemingly longer, to a small percent, maybe 5%, I don't know, but there should be a way to calculate it

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You'll have approximately an 8% taller final drive ratio. 13 / 12 = 1.083333. I initially thought the rear sprocket would have an effect but t I was wrong. For example use a 50 tooth rear sprocket 50 / 12 = 4.166666. 50 / 13 =  3.84615. Find the change of those ratios (4.166666 / 3.84615) and it's 1.083333. Use a different rear sprocket size - say 75 teeth (hypothetical) and we get 75 / 13 = 5.76923. 75 / 12 = 6.25. Still approximately an 8% change (6.25 / 5.76923). Clay

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Handy online sprocket calculator: http://www.sprocketcalculator.com/

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I have created a calculator just so you can know exactly what speeds you will go in every gear.

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Interesting input, but what I am looking for is how it will make the gears feel longer, just by a very little amount, likely not even enough to feel it.  EDIT, I think the answer is in WildAlaskan's post, if I can interpret it.

Edited by 1gr8bldr

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The first post answered it: 8%. I don't know where he went from there. (50/12)/(50/13)=13/12 is not exactly news.

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I have pencils,  so I don't use tables as a rule.   The exception was when I was racing certain types of events where you changed gearing as the track changed etc I started using tables to remove one thought process for the day after tricking myself doing the simple math in my head.

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9 hours ago, Wild Alaskan said:

I have created a calculator just so you can know exactly what speeds you will go in every gear.

I didn't look long enough or try,  can you plug in different numbers for the internal ratios?

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1 hour ago, ossagp said:

I didn't look long enough or try,  can you plug in different numbers for the internal ratios?

yes, it will even calculate how steep of a hill you can pull at peak torque if you fill out those values

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4 hours ago, 1gr8bldr said:

Interesting input, but what I am looking for is how it will make the gears feel longer, just by a very little amount, likely not even enough to feel it.  EDIT, I think the answer is in WildAlaskan's post, if I can interpret it.

yep put manufacturer data in the red boxes, your front and rear sprocket in the final drive, add the min and max rpm and you will get a graph with every gear min max speeds

The default data is for a ninja ex500

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3 hours ago, mikea 2 said:

The first post answered it: 8%. I don't know where he went from there. (50/12)/(50/13)=13/12 is not exactly news.

I wonder... 8% higher, sounds right, but 8% longer gear usable range???? It seems it would be a percent of this percent, LOL

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I have been thinking, would the gears get a longer more usable gear range even if it were only a small percent???? We know 1st gear does, do the others?

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the ratio of velocity to RPM is linear, all gearings have zero velocity at zero RPM, the spread at peak RPM is adjusted by gearing. The minimum usefull RPM goes up with gearing as IC engines in these applications make peak torque high in the RPM range.

So in fifth gear you may in theory be able to go anywhere from say 8-50 mph from 1300- 10000 RPM but you will have horrible acceleration for the first quarter of the rpm range and would have been going much faster by using lower gears and running them until the end of the range where the torque the engine produces drops off far enough that the torque advantage the lower gear has is no longer an advantage.

Same concept applies to how changing sprockets applies to firstgear, you get more velocity range, but you lost torque throughout, which means the engine will need to be at a higher rpm to make the same torque at the wheel as it would have with lower gearing (loss of low end), which means you always need to be going faster

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22 hours ago, Wild Alaskan said:

yes, it will even calculate how steep of a hill you can pull at peak torque if you fill out those values

We used to have a program to do it for large trucks and other pieces of equipment.  Handy keeper.

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On 4/25/2017 at 11:13 PM, nuity5 said:

You'll have approximately an 8% taller final drive ratio. 13 / 12 = 1.083333. I initially thought the rear sprocket would have an effect but t I was wrong. For example use a 50 tooth rear sprocket 50 / 12 = 4.166666. 50 / 13 =  3.84615. Find the change of those ratios (4.166666 / 3.84615) and it's 1.083333. Use a different rear sprocket size - say 75 teeth (hypothetical) and we get 75 / 13 = 5.76923. 75 / 12 = 6.25. Still approximately an 8% change (6.25 / 5.76923). Clay

If you are going from 12:13 it is 8.3% change.

Going from 13:12 is 7.7% change.

If you go from 1 to 2 it is 100% change.

If you go from 2 to 1 it is a 50% change

So it seems whatever you are starting with goes in the denominator. OK, I am better now..LOL

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Is it possible to over-think an issue?  I sometimes use a chart if, for example I changed by one tooth on the countershaft and it was too big of a change, then I'd find that actual ratio and go from there. I would tell me by the numbers, what ratio would a 2 or 3 tooth change on the rear give me.  I can't see the need to analyze any deeper when you can't change individual gears (ratios). Beyond that - seat of the pants.  IT AINT A Hewland!

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Reason for my math quiz, My KTM seems to have short gears. My other bike has long gear ranges. I am going to switch from a 12 tooth front to a 13 to make 1st more usable..... and I though, hmmmm, it may make the gears feel ever so slightly longer

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20 hours ago, motoxvet said:

Is it possible to over-think an issue?  I sometimes use a chart if, for example I changed by one tooth on the countershaft and it was too big of a change, then I'd find that actual ratio and go from there. I would tell me by the numbers, what ratio would a 2 or 3 tooth change on the rear give me.  I can't see the need to analyze any deeper when you can't change individual gears (ratios). Beyond that - seat of the pants.  IT AINT A Hewland!

But it is a math quiz... It is impossable to overthink a math quiz.  There is a correct answer and understanding how it is acheived is part of the fun.  Sure, in this app, it is seat of the pants, but there are real world ratio problems where knowing this is essential to avoid trial and error during design stage.

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31 minutes ago, wielywilly-g said:

But it is a math quiz... It is impossable to overthink a math quiz.  There is a correct answer and understanding how it is acheived is part of the fun.  Sure, in this app, it is seat of the pants, but there are real world ratio problems where knowing this is essential to avoid trial and error during design stage.

Is this considered "recreational mathematics"?.  Yes, it's a real thing.  The thing is, I didn't study for the quiz so I'm just trying to bluff my way thru it.  How am I doing?

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