Ben
I think calculating:
The front chainline for the outer and inner rings of the double and comparing them to
The rear chainline for the #5 sprocket (mid point of a 9s)
AND THEN calculating which sprocket lines up with the 2 rings will give the minimal wear combination.
Then assuming Outer to #1 sprocket is acceptable and Inner to #9 sprocket is acceptable,
determine how far you can go down on the Outer ring
& likewise how far UP you can go on the Inner ring) so chain wear is no greater than Outer to #1 or Inner to #9.
Shimano spec for Road front Chain Line (CL) is 43.5mm. I can’t find a crank spec for the Outer to Inner ring spacing, but my best measurement on a XD2 triple is 7mm from Outer to Middle ring.
Outer Ring CL = 43.5 + 3.5 = 47mm
Inner Ring CL = 43.5 – 3.5 = 40mm
Can’t find a Shimano spec for a rear CL with a 130mm OLD hub, but I calculated 42.5mm (for #5 Sprocket) using
130mm OLD
4mmm from DO to face of #1 sprocket
4.3mm sprocket spacing.
So Outer Ring is 4.5mm out from the #5 sprocket, or just about even with the #4 Sprocket. This places the # 1 Sprocket 12.9mm out from the Outer Ring (3 x 4.3mm), which is acceptable wear.
Outer to Sprocket #7 has the same 12.9mm distance, so Outer Ring & #7 has same wear as to #1 sprocket. Outer Ring to #8 or #9 sprockets has increased wear.
Inner Ring
Front CL is 40mm (43.4-3.5) which lines up about
REAR CL (#5) is 42.5mm so the Inner Ring is about in the middle of #5 and #6 Sprocket.
Rear CL on #9 Sprocket is 25.3mm (42.5 – 4x4.3, the 4 is spacing for5 to 6, 6 to 7, 7 to 8, 8 to 9).
So Inner to #9 distance is 14.7mm or about 4/10 ths of sprocket more than Outer to #1.
SO the Inner to #2 sprocket has the same 14.7mm distance, indicating Small to #2 has about same wear as Small to #9.
Hopes this helps, the math probably needs checked.
John Hawrylak
Woodstown NJ