A Cantilever Brake Design Discussion

Prelude

During a discussion of how to improve the braking power for someone whose brakes were inadequate, someone suggested going to Shimano V-brakes.

Kristan Roberge posted the following response:

Or hell, just buy some long-arm regular cantilevers.

To which Clyde Soles countered:

Kristan, you must have small feet or skinny ankles. Many folks have clearance problems with cantis and low straddle cables. This fact seems to be ignored in most of the discussions advocating this setup. I agree it works fine...as long as your not bloodied by the end of a ride.

Clyde's counter-response led me to the following relatively high-level (i.e. without any equations) discussion of cantilever design issues.

The Discussion

The problem isn't with the low straddle cable; you can put the straddle as low as you want with exactly the same heel clearance -- just shorten the straddle cable.

The problem with doing this is that as the straddle cable is shortened you get a faster change in the angle of the straddle to the canti arm as the straddle is pulled. That causes faster leverage rate changes through the cable pull, and since it's hard to get acute angles between them the leverage rate is usually a falling rate. Shorter straddles are, therefore, bad news.

To solve this problem without spreading the canti arms out (hurting clearance) you can lengthen the arms. This allows you to keep the arms closer to parallel without having to shorten the straddle wire. Rather than hurting heel clearance, therefore, longer canti arms tend to improve it.

Shimano Cantilever

Now, if the canti arms are long enough, you can improve heel clearance at the same time that you increase the angle of the arms with respect to each other: put a bend in the arms such that the arm is parallel to the wheel down near the pad, but angles outward near the straddle. If the bend is high enough you have plenty of heel clearance without sacrificing straddle length. This design should be familiar: it's Shimano's canti design.

Another option is to make the canti arms long enough that the straddle wire clears the tire when run straight across. If this is done it's no longer necessary to pull the arms indirectly through the straddle; instead, you can pull both of them directly using the brake cable as the straddle. When this is done the length of the straddle doesn't affect the leverage rate at all, only the angle

Shimano V-Brakes

between the arms does, and that doesn't change much. Peak power occurs when the arms are perfectly parallel, which is great because that's also the position where you get the best heel clearance. This design should also be familiar: it's the design of Shimano's V-brake.

The downside of longer arms is that the pads move less for a given amount of cable pull, and herein we find the reason why it is that none of the rim brake designs vary much in peak performance.

The mechanical advantage of the system as a whole is the ratio of brake lever motion to brake pad motion. This is the case regardless of whether the braking system uses hydraulics or cables or straddle cables or direct pull or anything else.

Increasing the power for the system necessarily means that the brake levers must move farther for a given travel of the brake pads. We can increase the power only as much as we can increase the lever motion or tighten the tolerances between the pads and the rim.

Unfortunately you can only increase the brake lever motion to the extent that you can grasp it; any more and the brake is useless. For all practical purposes brake lever motion is already optimized.

The only tunable, therefore, is to minimize required pad motion. Unfortunately even the earliest rim braking systems pushed the acceptable tolerances; we cannot effectively shrink them. To deal with this situation nonlinear mechanical systems are utilized which provide less power early in the brake lever stroke, allowing the pads cover the distance to the rim with little lever movement, and which increase the power later in the stroke while the pads are already against the rim. This is the technique used in Shimano's ServoWave levers.

Because of practical limits in how much you can move the brake lever and how close you can set the pads to the rim, there is an upper-bound on the total power possible using any of the rim braking systems, and an analysis of each shows that all of them are pushing that limit. There are, therefore, no practical differences in the different braking systems in terms of peak power, no matter how many magazine writers say otherwise.

jim frost
jimf@world.std.com
http://world.std.com/~jimf