The math (I think):
Approximate Chain Freedom Length = (cog-radius * sin(engagement-angle):
(An approximation that does not actually measure the arc length, but half the side length of an inscribed polygon with sides numbering 360/engagement-angle/2. So really all the chain freedom lengths will be slightly longer, but the ratios should be similar enough for comparison's sake. (Edit: and I found an arc length formula, and it's within a couple tenths of a mm for circles this size, so basically negligible))
Using a ~35mm diameter 21t Eagle cog:
20 degrees of engagement (18 POE) would give about 6.2 mm of maximum chain freedom, ~3.1mm average
5 degrees of engagement (72 POE) would give about 1.6 mm of maximum chain freedom, ~0.8mm average
With a locked wheel.
Smaller cogs give a smaller difference, larger cogs give larger diffs. For example, a 200mm 50t Eagle gives averages of 17mm for 20 degrees and 4.4mm for 5 degrees. 20mm 10t gives 1.6mm for 20deg and 0.45 for 5 degs.
Looks like a late model Enduro has about 30mm chain growth at bottom out, about 10mm at sag, pretty linear. Takes just 30mm of suspension movement to make 6mm of chain growth and thus always catch up to a hub with 20 degrees engagement and a locked wheel on a 21t cog. That's only 15mm of wheel travel to catch up on average with a 20 degree hub, ~6mm for a 5 degree hub. If a (15 - 6 =) 9mm bump (~3mm if you're hauling ass in the 12t or 10t cog) is going to wreck you... maybe got more problems than a number in a hub.
Note: I'm not saying it can't be felt in descending, I'm saying it's maybe not as important as some might think.
March 15, 2023, 1:30 p.m. - Justin White
The math (I think): Approximate Chain Freedom Length = (cog-radius * sin(engagement-angle): (An approximation that does not actually measure the arc length, but half the side length of an inscribed polygon with sides numbering 360/engagement-angle/2. So really all the chain freedom lengths will be slightly longer, but the ratios should be similar enough for comparison's sake. (Edit: and I found an arc length formula, and it's within a couple tenths of a mm for circles this size, so basically negligible)) Using a ~35mm diameter 21t Eagle cog: 20 degrees of engagement (18 POE) would give about 6.2 mm of maximum chain freedom, ~3.1mm average 5 degrees of engagement (72 POE) would give about 1.6 mm of maximum chain freedom, ~0.8mm average With a locked wheel. Smaller cogs give a smaller difference, larger cogs give larger diffs. For example, a 200mm 50t Eagle gives averages of 17mm for 20 degrees and 4.4mm for 5 degrees. 20mm 10t gives 1.6mm for 20deg and 0.45 for 5 degs. Looks like a late model Enduro has about 30mm chain growth at bottom out, about 10mm at sag, pretty linear. Takes just 30mm of suspension movement to make 6mm of chain growth and thus always catch up to a hub with 20 degrees engagement and a locked wheel on a 21t cog. That's only 15mm of wheel travel to catch up on average with a 20 degree hub, ~6mm for a 5 degree hub. If a (15 - 6 =) 9mm bump (~3mm if you're hauling ass in the 12t or 10t cog) is going to wreck you... maybe got more problems than a number in a hub. Note: I'm not saying it can't be felt in descending, I'm saying it's maybe not as important as some might think.