Check my math. I think it is 1 extra link for two teeth.
Assuming that the chain leaves the gear at the halfway point, which is close but not exact, you get:
Chain length old = 2*L + (2*pi*r1)/2 + (2*pi*r2)/2
Where L is the distance between sprockets r1 is the radius of the front sprocket and r2 is the radius of the second sprocket. (2*pi*r) is the circumference of the sprocket, but the chain only travels half of the sprocket so (2*pi*r).
So if you add two teeth, to the sprocket the circumference is 2*pi*r+2x. where x is a link length.
My new equation with the new rear sprocket, keeping the sprocket adjuster in place (the length between the sprockets is constant) is then
Chain Length new = 2*L + (2*pi*r1)/2 + (2*pi*r2 + 2x)/2
Which is
Chain Length New = 2*L + (2*pi*r1)/2 + (2*pi*r2) + 2x/2
So Chain length New minus chain length old is 2x/2 = x = the length of 1 link. ??
Or intuitively, you can think of one tooth being added to the right of the sprocket, where the chain is, and one tooth being added to the left of the sprocked where the chain ain't...so the chain only has to get one tooth longer...
???
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