andrew_s wrote: ↑19 Oct 2016, 10:45pm
adding one tooth moves the rear axle forwards by approximately 1/8 inch.
An extra tooth increases the chainring (or sprocket) circumference by 1/2", but only half the circumference is in contact with the chain, so that part increases by 1/4". To get that back with a fixed length of chain requires that you move the axle 1/8", recovering that much in each of the top and bottom chain runs.
It's not exact because the top and bottom chain runs aren't parallel to the chainstay and the angle changes with chainring size changes, but it won't make any significant difference for normal gears and a couple of teeth
^^ Not necessarily immediately obvious but still the case. I hope I’ve got my head around this now.
Typically the chainwheel is circa twice as big as the rear sprocket and the uneven tooth numbers don’t seem to be common, changing the tooth number at the front (by two teeth) changes the overall gear ratio by about 5% (2/40=0.05) and moves the axle 1/4” (1/2”/2=1/4”). Sprockets might be available in both even and uneven numbers of teeth, changing the tooth number at the rear (by one tooth) changes the overall gear ratio by about 5% (1/20=0.05) and moves the axle 1/8” ((1/2”/2)/2).
If you want to ‘sort of’ retain the overall rations the 2 teeth more at the front needs 1 tooth more at the rear and 2 teeth less at the front needs 1 tooth less at the rear.
To move the rear axle backwards by 1/8” add two links to the chain, add two teeth to the front and add 1 tooth to the back
((2 - (2/2) - (1/2))*1/2”)/2 = 1/8”
To move the rear wheel forwards by 1/8” remove two links from the chain, remove two teeth from the front and remove 1 tooth from the back.
If you need to move the axle further then double up on the changes above or accept a circa 5% change in ratio.
2 teeth added to or removed from the chainwheel will move the rear wheel by 1/4”……. (((2/2)*1/2”)/2) = 1/4”
1 tooth added to or removed from the sprocket will move the rear wheel by 1/8” ……….(((1/2)*1/2”)/2) = 1/8”
Adding or removing two links from the chain will move the wheel by 1/2” ……………………((2*1/2”)/2) = 1/2”
If the above isn’t quite right then someone will, no doubt, please correct it.
I was considering using a half link on a chain but apparently, from reading a few threads here, they ‘aren’t ideal’. Has anyone got experience that suggests that they’re worth considering?