|Figuring Out Pedal Ratio and Master Cylinder Bore Size -|
One area hot rodders, racers and custom car (and truck) builders tend to ignore is the brake master cylinder and, in particular, the actual brake pedal ratio. After all, it doesn’t make the car one bit quicker or faster, and if the thing eventually stops, why worry? Perhaps you should.
The critical component in the braking equation is the pedal ratio. In operation, the brake pedal acts as a lever to increase the force the driver applies to the master cylinder. In turn, the master cylinder forces fluid to the disc brake caliper pistons or drum brake wheel cylinders. If you examine a brake pedal, you'll see the pivot point (where the pedal swivels) and the mounting point for the master cylinder pushrod are usually different. By varying the length of the pedal, and/or the distance between the pushrod mount and the pivot, you can change how much force (from your leg) is required to energize the master cylinder. This is the "mechanical advantage" or pedal ratio. This formula will help you figure it out: Input Force x Pedal Ratio ÷ Brake Piston Area = PSI.
Mathematical babble? The arithmetic simply equates to the amount of force exerted by your leg times the pedal ratio divided by the area of the brake piston(s). FYI, the typical adult male can exert roughly 300 pounds of force (maximum) with one leg—and that’s a bunch. Something in the order of 1/3 or 1/2 that figure is obviously more comfortable, even in a hardcore racecar.
The average manual (non-power boosted) master cylinder requires somewhere between 600-1,000 PSI to be totally effective. Somehow, 100-150 pounds of leg force has to be translated into 600-1,200 PSI. The way it's accomplished is by way of pedal ratio. While changing the overall length of the pedal is possible, it's often easier and far more practical to shorten the distance between the pivot point and the master cylinder pushrod mount location. That's precisely how many racecar chassis shops modify brake pedals.
Brake Line Pressure
Brake line pressure is a different thing than the force you apply to the pedal. Force acts in one direction and is addressed in pounds. Pressure acts in all directions against surrounding surfaces and is addressed in pounds per square inch or PSI. "Levers" (brake pedals) can be used to change the force. Inside the hydraulic system, the surface area of the piston is what is affected by pressure. Decreasing the bore size of the master cylinder increases the pressure it can build. Pistons in master cylinders are specified by bore size. But there's a hitch: The area of a circle (or bore) is Pi–R-Squared. The area of the piston surface increases or decreases as the square of the bore size or diameter. For example, the area of a common 1-1/8-inch master cylinder is approximately 0.994-inch. The area of an equally common 1.00-inch bore master cylinder is approximately 0.785-inch. Switching from the larger master cylinder to the smaller version will increase the line pressure approximately 26.5% assuming that pedal ratio hasn't changed.
As the pedal force or the pedal ratio (or both) is increased, the stroke of the master cylinder is shortened (brake line pressure is unaffected). When the size of the master cylinder piston increases, the output pressure of the master cylinder decreases. A smaller master cylinder piston will exert more line pressure with the same amount of force (pedal ratio) than a master cylinder piston with a larger piston area. There's another catch: Since the brake line fluid pressure is working against the surface of the wheel cylinder (or disc brake piston), increasing the area of the cylinder will increase brake torque.