The purpose of this article is to discuss several misunderstood, and poorly defined concepts that relate to bicycle brakes. Even if you are not into the equations, you should still be able to follow this discussion without difficulty. The goal is to describe the following concepts in quantitative terms as they relate to bicycle road calipers:

 

1. Power

2. Modulation

 

Brakes exert a normal force, Fn, onto a brake rim. In turn, the brake pad applies a tangential force to the rim, Ft. The tangential force, Ft, is what stops the bike. If u is the coefficient of friction of a brake pad, then

 

Ft = u*Fn                                             (1)

 

This equation says that as u goes up, the braking force goes up. Increasing u is why trials riders will apply tar to their rims. The problem with high u brake pads is that they are sticky and tend not to hold up well.

 

Increasing the leverage is one way to increase Ft. Let d1 be the vertical distance from the brake pivot to the brake shoe, let d2 be the horizontal distance form the pivot to the force Fc exerted by the Bowden Wire. Substituting in equation (1), then the leverage is:

 

Ft = (d2/d1)*Fc*u                               (2)

Of course, as you squeeze the brake harder by increasing Fc, then Ft goes up and the brake stops harder. If d2 increases and d1 decreases, the brake leverage goes up and the brake stops harder under the same hand squeezing effort. This ratio, d2/d1, is why dual pivot brakes have more leverage. With dual pivot brakes the pivot is moved to the side to increase d2. The pivot is also moved downward to decrease d1.

 

 The great Archemedes once declared, "If I had a lever big enough I could move the world." Likewise, if I had a brake with long enough arms, I could make a bicycle brake that would stop a double-decker bus. One problem with increasing leverage is that the brake arms become unreasonably long. This makes the brake heavier, less aero, and causes chatter. Long brake arms can also cause squealing or howling because of longer arms have lower frequency harmonics, but this is more of a problem with cantilever brakes than caliper brakes. In general, high leverage brakes exert large amounts of tangential force with minimal hand force. This is what is meant when a brake is called “grabby”. While the “grabby” term is often used in a derogatory way to describe disc brakes, it is synonymous with brakes that have high “braking power”.

 

 

Real brakes are not actually levers, they are springs! Though you cannot see it because the deflection is usually small, when brakes are actuated the arms flex. Assuming that the spring constant for the brake is Ks, and dx is the distance that the brake arm deflect under being actuated, using hooks law we have:

 


 

 Fc = Ks*dx                                         (3)

 

And equation 2 actually becomes

 

 

 

 

 

 

 

Ft = (d2/d1)*u*Ks*dx                         (4)

 

 

 

 

Equation 4 tells us that if both sides remain equal, as Ks goes up, dx goes down. In other words, as the brakes become stiffer springs, the distance traveled by the brake lever becomes less. This is what “modulation” is all about. Stiff brakes have very little lever travel under harder braking. Brakes with too little modulation do not provide enough position feedback. Imagine if the brake lever did not move and that it was perfectly rigid. The harder you push, the faster you slow down. Not being able to feel the lever move would diminish your sense for how hard you are braking.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alternatively, the brakes could be designed to flex like limp noodles. While flexible brakes work well under light braking, they have good modulation. However, too much modulation means that the brake lever bottoms out against the handle bar or grip. In that case, your brakes lack “braking power”. Achemedese should have said “if I had a lever big enough and stiff enough . . .”.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Modulation requires an understanding of deflection. Computer models using finite element analysis provide not only a way to analyze stress, but also a way to understand stiffness. Computer models allow for designs that have just the right combination of modulation and leverage.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

If leverage plays such a central role for braking power you would think that everyone would make high leverage brakes. The problem with high leverage is that the brake shoes travel a shorter distance. This in turn results in too much modulation because the brake flexing becomes magnified. Even if the brake is made stiffer, the rim, brake shoes, brake lever, cables, cable housings, and frame mounts all have deflections. Rim brakes do have an upper limit on braking power. Fortunately, that limit is plenty for most situations.

 

The greatest problem with high leverage is that the brake pads must ride closer to the rim when the brakes are not in use. This makes it much more likely that the pad will rub the rims when the brakes are not being used. Out-of-true rims cause rubbing, but even if the rims are trued routinely, lightweight parts such as the wheel, frame, or skewers tend to flex.

  

 

All brakes are (or should be) designed with the aformentioned considerations in mind.

 

Of course, a bad design can compromise on everything. You should stay away from brakes that have the following bad design practices:

 

  1. Uses of lots of moving parts, this is generally true for all machine design
  2. High friction bearing pivots
  3. Loose pivots with lots of play, brake play eats travel and you gain nothing
  4. Highly non-linear motion, this limits travel.

 

Lever Position