Quote:
Originally Posted by makemdan
Maybe being simplistic here but wouldn't the new range be the original + the difference between the radii of the 2 sprockets?
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Not quite! Don't forget the chain isn't parallel to the swinging arm (nor to an imaginary line drawn between the sprocket centres). It makes a shallow angle by being closer at the gearbox end and farther away at the rear wheel. The chain clearance is measured half-way between the two.
Because you're only changing the rear sprocket, then, yes, the chain link on the very bottom of the new, larger, rear sprocket will be farther from the swinging arm by R2-R1 (where R1 is the radius of the 39T sprocket and R2 the radius of the 42T).
But, by contrast, a chain link at the bottom of the gearbox sprocket will be exactly the same distance from the swinging arm, whichever size rear sprocket you have.
Consequently, if you think of the chain as being the base of a triangle between the gearbox sprocket (A), rear axle (B) and bottom of rear sprocket (C), you've increased the length of side BC and increased the angle between sides AB and AC.
So the clearance difference will be at its maximum (R2-R1) at point C and zero at point A. As you measure the clearance working from C to A, the difference will gradually reduce until it is zero at point A.
As the chain clearance is measured half-way between front and rear sprocket, the increased clearance will also be someway between zero and R2-R1 (but not half-way between!).