Brake Hydraulics

Recall that the brake’s hydraulic system must supply movement and force. The movement must be enough to take up all slop, clearance, and deflection of parts as well as move the caliper pistons sufficiently to bring brake pads into firm contact with the rotors.  The force must be enough to create enough friction between pad and rotor to stop the trailer.

It is the piston of the master cylinder that provides both the movement and the force, and the brake fluid that transmits both to the calipers.
The goal is to have a system that provides maximum force with small movement – i.e. we want to be able to brake hard without excessive travel.
Force applied to the MC piston creates pressure in the brake fluid. The pressure is the force applied, DIVIDED by the area of the piston. Therefore, the smaller the master cylinder piston, the greater the pressure created.
Recalling that the pressure created is a direct factor in how much clamping force and therefore brake torque is developed, it may seem that for the most powerful brakes, we would want to use a small MC piston.
But, the trade-off is the other component required of the brake system – namely movement.  Because the fluid is incompressible, any movement in the MC piston translates into movement of the caliper pistons (excluding expansion of hoses and lines, which should be minimal in a properly working system).  This movement in a hydraulic system is known as displacement and is calculated as the area of the MC piston multiplied by its stroke. Displacement is a volume, measured in cubic inches. Therefore, the smaller the master cylinder piston, the less displacement created.
The trade-off between force and movement in selecting a MC piston size. The smaller the piston, the greater the pressure created but the less displacement produced (and therefore greater pedal travel required.)
So far, we have considered only the effect of the size of the MC piston, but of course in a brake system there are two pistons – the MC piston and the caliper piston (for calculations, the total area of all pistons in a multi-piston caliper act the same as a single piston of equivalent area in a single-piston caliper.)
There is, of course, a relationship between the pistons in the system that affects both force and movement.
Because the brake hydraulic system is a closed, sealed system, and brake fluid cannot be compressed, there is a law of hydraulics that we make use of to multiply force – that is, to apply more force at the calipers than the driver applies to the MC piston. It is quite simple, and quite possibly the most important concept in this is:
In a closed hydraulic system, pressure is equal over all surfaces of the containing system.
In our discussion of brake systems we will refer to the MC piston as the “input” piston and the caliper piston as the “output” piston.
The above law means that whatever pressure is created by the input piston is applied equally to the output piston. Because the output (caliper) piston is of much larger area than the input (MC) piston, this has the effect of multiplying force in the brake system.
The amount of force-multiplication thus achieved is known as the brake’s “Hydraulic Ratio” Hydraulic Ratio can be calculated or expressed a number of ways. It is the ratio of fluid displacement by the master cylinder to fluid displaced in the caliper pistons. It is also equal to the ratio of force applied to the MC piston to the force generated by the caliper pistons. The stiffer the caliper and the stiffer the pad, the higher the hydraulic ratio that can be employed.
For example, suppose we apply 100 lbs of force to a ½” diameter MC piston, we develop approx. 500 psi. This 500 psi acts evenly on all other surfaces in the system, including the caliper pistons. Suppose the caliper piston has a diameter of 3 inches. Multiplying our 500psi by the area of the caliper piston (~ 7 sq. in), we develop nearly 3500 pounds of clamping force at the brake pads.