understanding hydraulics
(corrected version)

Hydraulics are basically liquid gears. Work at one end is transferred to the other. The relative sizes of the hydraulic cylinders at each end will affect how much movement or power is available at the output, just as gear sizes will affect the same in a geartrain.

A master cylinder is used to apply pressure to the hydraulic system. At the other end, this pressure will push out a slave cylinder. The relative areas of the cylinders will determine the “gear ratio” of the system. Since the hydraulic fluid in the system cannot be compressed then we can ignore it from a functional viewpoint. Multiple pistons, as found in many brake calipers, can be considered as one large piston with an area that is the sum of all the smaller ones.

Let’s picture a braking system at the moment. There is a master cylinder activated by the brake pedal. The slave cylinders are the pistons in the calipers. A large master cylinder will move more fluid for a certain amount of travel, and will therefore generate more pressure after moving the same distance as a smaller master. However, it will also require more force to be moved so you’ll have to push harder on the pedal.

The same thing happens at the other end. Larger pistons can exert more pressure on the brake pads with the same pressure in the line, but they will require more fluid to do so. A system with relatively large master cylinders and small caliper piston sizes will have a nice firm pedal, but will require more leg strength to get the same amount of braking. A smaller master cylinder and/or larger piston sizes will make the brake pedal softer but require less effort.

Let’s look at some numbers. Let’s say we have a car with a master cylinder of 0.625”. This gives us 0.307 in2 of surface area. In order to generate 500 psi of hydraulic pressure, we’ll have to apply 153 lbs of force on the piston. If the master cylinder is changed for one that is 0.875”, we will have a surface area of 0.601 in2. Then we will have to apply 300 lbs of force for that same hydraulic pressure. This means we have to push almost twice as hard – but the pedal will only move half as far.

At the other end, let’s say we have a four-piston caliper. Each bore is 1.5”. Each piston has an area of 1.77 in2. A little quirk is that when calculating the forces used in braking, we only take into account the pistons on one side of the caliper. This means that we'll treat this four-piston caliper as equivalent to one with a single 3.53 in2 piston. Our 500 psi of hydraulic pressure will be converted into 1767 pounds of force on the pads. Not bad! Increasing the size of the pistons in the calipers to 1.625” will give us 2074 pounds of force on the pads, but will increase pedal travel.

In the end, what matters is the relative size of the two ends. Our 0.625” master cylinder and 1.5” four-piston caliper have a relative area ratio of 23:1 – the caliper will provide 11.5 times as much force as applied on the master (remember, we only get to count half the pistons here), but the master will have to move 23 times further. To move the pistons and thus the pads by 0.010”, the piston in the master cylinder will have to move 0.230”. If our master cylinder is feeding two calipers as it usually is, then it will have to move 0.460" as there will be twice as much fluid to move. When calculating volumes, all the pistons have to be taken into account. A caliper with opposing pistons will only require half as much movement (and thus volume) as a sliding caliper with pistons on only one side so again, one large piston on one side is equivalent to a pair of opposing pistons with half the area each.

To make things more difficult, there’s also a mechanical ratio in the pedal itself. A 6:1 pedal ratio will have the pedal moving six times as far as the piston. This decreases the amount of force needed but again, increases the travel. Looking at our previous 23:1 travel ratio, this now changes to 138:1. 0.010” of pad travel for a pair of calipers will require 2.76 ” of pedal travel, but 50 pounds of force on the pedal will provide 3450 pounds of force on the pads thanks to a force ratio that is 69:1.

In general, most drivers prefer a hard pedal that requires a strong push. It’s confidence-inspiring – but if it’s too heavy, the driver may not be able to generate enough braking force! It all sounds complex, but in reality only a few of the variables are ones that will realistically be changed.

Power assist can change these equations drastically, giving a firm pedal without high effort. On a light homebuilt car, this can also make the brakes very sensitive and difficult to modulate.