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I'm building a recumbent trike and have reason to have the rear cassette offset from the cranks.

At the same time, the chain is very long, so the offset is compensated. It looks like the chain will be running about 3.25 degrees when the chain is on the smallest cog.

I tried to compare this with normal bike chain angles, but have a hard time finding information about chainline in terms of angles. Usually, chainline is specified in mm from the center of the bike, and there is no specific range of chain angles which is considered bad, usually there is just a vague rule of thumb not to ride cross-chained.

On a road bike with a 41cm long chainstay and 40mm wide cassette, we can use trig to calculate a max chain angle of about 2.7 degrees, if the front chainwheel is centered on the cassette. If the front chainwheel is offset 5mm from the center of the cassette, such as a cross-chain situation, then maybe chain angle is as much as 3.5 degrees. But these are approximate calculations.

Does anyone know any actual data on what chain angle is ok, except for vague warnings about cross-chaining, which depends on the bike geometry anyway?

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    Changed you post title to better reflect your question. Chainline is the distance between the center of the bike and the plane the chain nominally sits on – Argenti Apparatus Mar 25 at 22:08
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Rear cogs on a 9-speed are about 4.5mm apart, center to center. A typical chainstay length is a hair over 400mm. The arctangent of 4.5/400 is about 0.65 degrees. At such a shallow angle you can simply multiply 0.65 times the number of cogs you're spanning to come up with the angle that is spanned when you shift that number of cogs. In other words, shifting from cog 1 to cog 9 would span 8 cogs and produce about a 0.65 x 8 = 5.2 degree change in chain angle.

Front cogs are probably a little bit farther apart, but not much.

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There is a paper on bicycle chain efficiency from John Hopkins that discusses this issue along with others. Basically, cross-chaining being "bad" is a myth with relatively modern chains and cassettes. As long as the angle is shallow enough to prevent the chain catching on the next cassette cog, I think you should be just fine. Even back in the bad old days of 5 speed freewheels, thick roller chains and 42/52 cranks, cross chaining being "bad" was more bike shop myth than reality. I rode cross chain back then and I do now when it suits me.

John Hopkins Bike Efficiency Article

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