Second reply to this: I think your ratios are wrong. The leverage ratio is not the ratio of the axle-caliper vs caliper-rim distance, because if the radius of the rim is 12" and you have a 6" DIAMETER rotor, your ratio is only 3:1 (3 being the rim, 1 being the caliper). However, it should be 4:1.
Braking ratios in relation to the rim involve the radius of the braking surface divided by the radius of the WHEEL (including tyre). The rim is roughly 11" radius from the axle, whereas the tyre is 13" from the axle (on a 26" wheel). Using your force X etc:
- The force required by a rim brake to provide X braking force at the tyre is the inverse of 11/13 "X", which is 13/11 "X"
- The force required by an 8" rotor to provide X braking force at the tyre is the inverse of 4/13 "x", which is 13/4 "x".
- The force required by a 6" disc rotor to provide X braking force at the tyre is the inverse of 3/13 "x", which is 13/3 "x"
Let X = 1, for the sake of simplicity:
13/11 x = 1.18
13/4 x = 3.25
13/3 x = 4.33