## Glossary of Breaking Terms

 This section with give you a brief description of all those strange words used in the braking industry.

# Brake Calculations

There are many books on brake systems but if you need to find a formula for something in particular, you never can. This page pulls them together with just a little explanation. They should work for any two axle vehicle but it’s YOUR RESPONSIBILITY to verify them. Use them at your risk…..

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VEHICLE DYNAMICS

Relative Centre of Gravity Height

Dynamic Axle Loads (Two Axle Vehicles Only)

The changes in axle loads during braking bears no relationship to which axles are braked. They only depend on the static laden conditions and the deceleration.

Note: The front axle load cannot be greater than the total vehicle mass. The rear axle load is the difference between the vehicle mass and the front axle load and cannot be negative. It can lift off the ground though. (Motorcyclists beware)!

STOPPING THE VEHICLE

Braking Force

The total braking force required can simply be calculated using Newton’s Second Law.

Wheel Lock

The braking force can only be generated if the wheel does not lock because the friction of a sliding wheel is much lower than a rotating one. The maximum braking force possible on any particular axle before wheel lock is given by:

Brake Torque

Having decided which wheels will need braking to generate sufficient braking force the torque requirements of each wheel need to be determined. For some legislation the distribution between front and rear brakes is laid down. This may be achieved by varying the brake size or more likely using a valve to reduce the actuation pressure.

FOUNDATION BRAKE

The effective radius (torque radius) of a brake disc is the centre of the brake pads by area.
For dry discs it is assumed to be:

For full circle brakes it is:

Note: the difference is because full circle brakes contact on the full face but caliper pads are not usually a quadrant but have square sides (Given the variability of friction the difference is not important in practice).

The clamping load is assumed to act on all friction surfaces equally. For dry disc brakes it doesn’t matter whether the brake is of the sliding type or opposed piston. Newton’s Third Law state every force has an equal and opposite reaction and a reaction force from a sliding caliper is the same as an opposed piston one.

Brake Factor

Ball ramp brakes have a self servoing effect rather like a drum brake. The brake factor multiplies the output torque.

Brake Sensitivity

High factor brakes become very sensitive to manufacturing tolerances and lining friction variations. A measure of sensitivity is the amount the brake factor varies for a change in lining friction. It can be calculated:

GENERATING BRAKING

System Pressure

Pressure is a function of the required clamp load and the piston area. Remember on an opposed piston disc brake it’s only the area on one side of the disc.

Servo Booster

Servo characteristics are defined graphically. The output will have at least two slopes but will also have a dead band at the bottom.

Pedal Force

The pedal ratio is calculated to the centre of the foot pad. The pedal return springs may make a significant contribution to the overall pedal force. Especially at full travel.

REAL LIFE DECELERATION & STOPPING DISTANCE

The deceleration used in calculations is a steady state one called MFDD (mean fully developed deceleration). It assumes the vehicle is either braking or not. In practice it takes a time for the system pressure to rise and the friction to build up. This is not the driver reaction time but the system reaction time. Where a calculation requires a stopping distance or an average stop deceleration then this delay must be taken into account. For calculations a linear build up over 0.6 second is used ie 0.3 second delay.

For testing the following graph show the requirements for 71/320/EEC and ECE R13.

BRAKE HEATING

Stop Energy

The energy dissipated in a stop is the sum of energy from three sources, kinetic, rotational and potential.

Kinetic Energy

Assuming the stop is from the test speed down to zero then the kinetic energy is given by:-

Rotational Energy

The rotational energy is the energy needed to slow rotating parts. It varies for different vehicles and which gear is selected however taking 3% of the kinetic energy is a reasonable assumption.

Potential Energy

The potential energy is the energy gained or lost by stopping on a hill.

Braking Power

Only when the brake is applied (but rotating) is energy being dissipated in the brake system. Some of the stop energy is dissipated in the tyre as wheel slip. Managing the ideal wheel slip is the ultimate goal of ABS development but here assume 8%. The energy to each brake depend on the number of brakes and the proportion of braking on each axle.

In order to calculate the power we need to know the brake on time:

The power is then given by:

This is the average power, the peak power at the onset of braking is double this.

Dry Disc Temperature Rise

These calculation are based on that given in the following reference:

Brake Design and Safety 2nd edition by Ruldolf Limpert

Single Stop Temperature Rise

In order to approximate the temperature rise of the disc an assumption as to where the energy is going has to be made. Initially most of the heating takes place in the disc, however this can then be rapidly cooled by surrounding components and the air stream. The calculation assumes 80% goes to the disc.

Heat flux into one side of the disc:

Single stop temperature rise is:

The temperature rise after repeated stopping can also be approximated, although so many variables exist it is suggested this is only used for basic optimisation work.

After a number of stops:

PARKING ON AN INCLINE

When parking on an incline the lower axle has a higher load than it does on the level.

The rear axle load is the difference between the vehicle mass and the front axle load.

Traction Force

If the braked wheel is very light on an incline then it is possible the tyre will slip before the brake. Hill hold is usually required with the vehicle facing both up and down the hill. The traction force required to park the vehicle is:

Where only one of the two axles is braked the limiting slope is:

LOSSES FROM CABLE OPERATED BRAKES

Cable losses are not inconsiderable and vary depending on the number and angle of bends. A typical cable supplier uses the following calculation to calculate cable efficiency:

HYDRAULIC BRAKES

Brake Fluid Volume Requirements

When an hydraulic brake is applied fluid is required to move through the pipes. If the fluid source is a master cylinder it has a finite capacity. The following components need fluid:-

Foundation Brake Requirements

Brake fluid is required to take up running clearance.

It is also needed to compensate for lack of stiffness of the brake housing. For a disc brake the following approximation can be used:

Pad compressibility varies between hot and cold conditions. Worst case figures are 2% cold and 5% hot at a pressure of 16MPa. The fluid required is given by:

Rubber Hose Expansion

The rubber hose expansion coefficient is usually taken as

Steel Pipe Expansion

Pipe expansion is very small and unlikely to be of interest however it should be noted that it is proportional to the cube of the diameter, so using bigger pipe than necessary on a system with a fixed fluid volume will cause longer travel for two reasons, the stiffness of the pipe and more importantly the additional fluid compression losses.

Master Cylinders Losses

Fluid losses in master cylinders increase with bore size and pressure. A reasonable assumption can be found by using the following:

Fluid Compression

Fluid compression varies with temperature and the type of fluid used.

The fluid needed to take account of compression is calculated:

It is usual to allow about 3% for trapped air in the circuits that can’t be removed by bleeding. This air is squashed totally flat during braking.

DYNAMOMETER INERTIA

When testing Brakes on a dynamometer it is important to calculate the inertia requirements.
Many brakes do not run at the same speed as the wheels so it is important to understand how the brake will be mounted on the rig.
Ignoring the inertia of the wheels the required dynamometer inertia is given by

• ## Basics of Cutting Brake

Cutting brakes are a system of levers, switches, or pedals that allow you to lock up individual brakes in order to stop one wheel and then use the other wheels to drive the vehicle, thus pivoting around that locked wheel. The result is a tremendously tight turning radius, and they can be implemented in a variety of ways.

One thing to be extremely careful with is using cutting brakes at high speeds and on the street, as it can have deadly consequences.

• ## Working Operation

On many tractors the brake is divided into two pedals, one for the left rear wheel and one for the right rear wheel. If you need to stop, you step on both pedals at once. But if you want to turn really sharp, you step on one pedal and turn the steering wheel, and the tractor will spin around the wheel that is locked up.

When you want to turn sharply in your 4×4, simply engage a cutting brake for one of the rear wheels and this will let the front axle pull you around the turn. This works very well in a vehicle that either has a selectable rear locker and/or a transfer case that allows you to engage the front axle only. If you have a full-time locker in the rear like a Detroit, you need to engage the front axle only, otherwise the rear tires will drive through the cutting brakes. If you have a rear selectable locker like an ARB, Ox, or E-locker that gives you an open differential when unlocked, you can unlock the rear locker but still engage four-wheel drive when you use one rear cutting brake. This will send the power to the three unlocked wheels and you will pivot around the locked one.

In some situations you can achieve an even tighter turning radius if you can unlock the rear locker, put your transfer case in front-wheel-drive only, and lock the cutting brake on the rear tire opposite of the direction you want to turn. This will allow the inside rear tire to actually turn backwards as you pivot around the outside rear tire while your front tires pull you around. However, this maneuver often requires that you be pointed up a hill, and you must let the front tires spin and actually lose traction so you can slide back around the locked tire.

Another option is to use cutting brakes as a cheap traction tool. Say you have a cutting brake at each rear wheel, but you do not have a locking differential. You could be driving up a hill and one rear and one front wheel start to spin until you stop moving forward. By applying the cutting brake to the spinning wheel, the open differential will send power to the other wheel, and if it has traction it will begin pulling you up the hill. This is sort of a poor man’s traction control.

Of course placement of the lever needs to be easy for the driver to reach. Many buggies have them mounted between the seats, between the driver’s legs, or between the driver seat and the sidebars.

Another cool trick we’ve seen is using a line lock (also known as a roll control or roll stop) such as this one. It can be plumbed right on the axle and is activated either electronically or by switching a valve. Simply step on the brake pedal to apply the brakes, flip a switch that activates a solenoid, or close the line-lock valve-depending on the design you’re using-and it holds the pressure in the wheel cylinder to lock the wheel.

We have also seen trail-rig builders taking tricks from the tractors by putting dual brake pedals in their rigs. This allows them to lock either the front axle or the rear axle. Locking both brakes on the axle still helps in doing tight turns with the front axle driving only (commonly referred to as a “front dig”), but not as well as locking each individual corner.