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Your feet may know the condition of your vehicle’s brakes and the quality of the brake pads before your brain puts it all together. Consider this. A running 4,000-pound vehicle requires the driver to depress the pedal and create friction at the wheels before it will stop. What happens between the pedal and the brake pads can determine how much pressure the driver needs to apply to stop the vehicle at a safe distance.
Engineers will look at the braking system as an equation. When the vehicle leaves the assembly line, the braking system is balanced on both sides of the equation because the variables are known. But if the vehicle has had its first set of brake pads replaced, the variables will change and the inputs may no longer match the outputs.
These changes can come from worn, defective or low quality brake pads.
The hydraulic brake system converts and amplifies force. It works on the simple principle that brake fluid is incompressible unless it is exposed to extremely high pressure and temperature. When pressure is generated at one end of the system, the same pressure comes out the other end.
In a hydraulic brake system, when the driver generates force by depressing the brake pedal, that force is amplified by the pedal, booster and master cylinder. The driver adjusts the pressure on the pedal to stop the vehicle between 20 and 120 pounds. Humans will use their senses to bring the vehicle to a safe stop.
Doing the Math
During stopping, the average driver generates a peak force of 70 pounds on the rubber pad at the end of the brake pedal. The brake pedal is nothing more than a mechanical lever that amplifies the driver’s force.
The pedal ratio is the overall pedal length or the distance from the pedal pivot point to the centre of the pedal pad, divided by the distance from the pivot point to the point where the pushrod is attached.
On some older vehicles a manual disc drum was used with a pedal ratio of 6.2:1. This meant that the 70 lbs applied by the driver was now amplified to an output force of 434 lbs (6.2 x 70 lbs). One problem was the rather long pedal travel due to the position of the pivot point and the connection of the master cylinder.
A booster will increase pedal force, in which case a lower mechanical pedal ratio can be used, as a lower ratio allows for shorter pedal travel and better adjustment. Most vacuum boosters have a mechanical pedal ratio of 3.2:1 to 4:1. The size of the booster diaphragm and the amount of vacuum produced by the engine will determine how much force can be generated. Most engines will produce about -8 psi of vacuum.
If the master cylinder has a 1″ bore, the surface area of the piston is 0.78 square inches. If you divide the surface area of the piston by the output force of 434 lbs, you will get 556 lbs (434 lbs divided by 0.78″) at the master cylinder port. That’s not bad for 70 pounds of manpower.
If the surface area of the piston is reduced, you will get more pressure. This is because the surface area of the piston has become smaller, but the output force of the pedal will remain the same. If you use a master cylinder with a 0.75 inch bore and a piston with a surface area of 0.44 square inches, you will get 986 pounds of pressure in the ports of the master cylinder (434 pounds divided by 0.44 inches). However, the pedal stroke will increase.
When you depress the brake pedal with 70 pounds of force, this causes 556 pounds per square inch of brake fluid to flow into the caliper. So, do you know how this pressure stops the car? If the caliper is a single piston floating design with a 2″ piston diameter (piston surface area = 2πR2), we simply multiply the surface area of the piston by 556 lbs. to get a clamping force of 3419 lbs. on both front calipers.
On one side of the equation is the clamping force and friction coefficient and on the other side is the braking torque. Whichever variable is added will change the torque that can be generated by the system.
Clamping force is used to create friction, which creates torque to stop the vehicle. This is where the “coefficient of friction” comes into play. The coefficient of friction is calculated by dividing the force required to slide an object across a surface by the weight of the object.
Essentially, engineers balance the coefficient of friction with the piston and master cylinder dimensions so that the vehicle gets the right stopping power and pedal feel. If you increase or decrease the coefficient of friction, you could upset that balance.
In our theory above we have ignored some realistic factors that affect the magnitude of the clamping force. The reality is that some pressure is lost as the brake hose expands, and not all of it reaches the interface between the brake pads and the rotor. However, most of the factors that can increase pedal force or pedal travel are not hydraulic but mechanical.
Even if all the pressure reaches the caliper piston, some of the force generated will be lost as the caliper flexes. In the case of a floating caliper design, the movement of the caliper on the slideway requires it to be placed in the centre of the rotor and additional fluid movement occurs. If the slides or pads get stuck, the clamping force is reduced, resulting in an uneven clamping force on the pads. This will reduce the footprint of the friction material on the rotor and the force required to generate sufficient braking power will increase.
The brake pads themselves will increase the force and travel of the pedal. If the backing plate is not stiff enough, it will bend. This affects the hydraulic components in two ways. Firstly, the backing plate of the brake pad is bent by the hydraulic forces. Secondly, when the brake pad bends, it changes the clamping force on the rotor. The edge of the brake pad may have a lower clamping load than the centre of the pad. This results in less braking torque being generated. However, friction at the interface between the brake pad and rotor can also lead to brake noise if it is not stable. If the brake pads are damaged by the friction material delaminating from the backing plate, the brake pads can generate less torque. This requires the driver to press the brake pedal harder.
In the braking equation, that is the human element behind the pedal that never changes. The driver can only apply so much force to the pedal and their mind can only react so quickly in an emergency. If the mind and foot are struggling with brake pad or hydraulic system problems, hopefully it will end up in your workshop before an accident occurs.