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Cuneiformist
The Imperfectionist

USA
4955 Posts

Posted - 12/29/2022 :  06:18:48  Show Profile Send Cuneiformist a Private Message  Reply with Quote
Hello all,

It's been a thousand years since I've been here. I hope everyone is well.

I have a math question that a friend and I came up with about 30 years ago that's been sitting in my brain and I'd love to solve. However, I lack the math skills to solve it, so perhaps some SFN person here can help.

(I came here because in my real world interactions, I don't know a lot of math-inclined people, but I recall this space having a number of them-- they may not visit anymore, but perhaps others here are similarly talented.)

The question on the surface is simple: I am asking for the length of a bike chain-- that is, the chain that goes around the pedals to the back wheel. Assume that this is a one-speed bicycle-- there are no gears.

The measurements are arbitrary, but suppose that the diameter of the front chain wheel (or whatever it's called) is six inches. And suppose the back chain wheel (again, I don't know the actual terminology) is two inches. And suppose that the distance between the center of the front chain wheel and the back chain wheel is 30 inches.

On the surface, this is just some simple geometry and one could work this out to figure the length of the chain. However, because the two chain wheels are different diameters it seems to me-- and I think I can visualize this-- that the chain will not cover (as it were) each chain wheel in the same way.

That is, the chain will not cover the smaller back chain wheel at 50% and it will cover the front chain wheel at more than 50%, and that is the issue. I do not know how to calculate that.

This is all just a dumb thought problem and perhaps I'm mistaken, but I'd love for someone to enlighten me as to a solution.

Dave W.
Info Junkie

USA
26020 Posts

Posted - 01/03/2023 :  07:55:40   [Permalink]  Show Profile  Visit Dave W.'s Homepage Send Dave W. a Private Message  Reply with Quote
Hey, Cune! Nice to see you back!

Ricky was our math PhD.

I think you're asking for the belt length between two pulleys, since bike chain only comes in discrete lengths. You can only change the length of a chain by adding or removing links, after all, you can't add a quarter link. Plus, bikes tend to be tolerant of having a little slack in the chain (and 10-speeds have an extra idler sprocket to remove any slack).

- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too.
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ThorGoLucky
Snuggle Wolf

USA
1475 Posts

Posted - 01/19/2023 :  15:11:39   [Permalink]  Show Profile  Visit ThorGoLucky's Homepage Send ThorGoLucky a Private Message  Reply with Quote
Cuneiformist, I hear that chatGPT is good at answering math problems. A friend is using it to help him hone his skills for substitute teaching.
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Kil
Evil Skeptic

USA
13474 Posts

Posted - 01/20/2023 :  21:55:26   [Permalink]  Show Profile  Visit Kil's Homepage  Send Kil an AOL message  Send Kil a Yahoo! Message Send Kil a Private Message  Reply with Quote
Machi4velli, who is Ryan White on FB, has a Ph.D. in Math. Boron10 or Tim Householder on FB is a math and physics teacher too.

Uncertainty may make you uncomfortable. Certainty makes you ridiculous.

Why not question something for a change?

Genetic Literacy Project
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Dr. Mabuse
Septic Fiend

Sweden
9682 Posts

Posted - 01/22/2023 :  13:18:23   [Permalink]  Show Profile  Send Dr. Mabuse an ICQ Message Send Dr. Mabuse a Private Message  Reply with Quote
Cuneiformist! Nice to see you write again. It was just around Christmas, I think, I was thinking "long time since..."

Dr. Mabuse - "When the going gets tough, the tough get Duct-tape..."
Dr. Mabuse whisper.mp3

"Equivocation is not just a job, for a creationist it's a way of life..." Dr. Mabuse

Support American Troops in Iraq:
Send them unarmed civilians for target practice..
Collateralmurder.
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