Author: Alexander aka dll (madtuning.ru; live4race.ru)

Source

This article will help you:

1) Understand how the braking system works

2) Accurately identify what you don't like about your brakes

3) Communicate intelligently during discussions on brake systems

4) Decide which upgrades work for you to achieve your goals

5) Choose the right components and understand how they will work together

6) Maintain axle balance

What does a braking system consist of?

1) Pedal assembly, this is a lever that increases the effort created by the foot (Pedal ratio).

2) Master brake cylinder (Master Cylinder)

3) Brake lines

4) Valves, to maintain balance. The braking system may have the following valves between the master cylinder and calipers: Residual pressure valve, proportioning valve, combination valve, or load-sensing valve.

5) Brake calipers

6) Brake pads

7) Brake rotors

-=So let's start with the basics (physics)=-

Braking force

This is a torque created by the effective radius of the brake rotor, the clamping force of the brake pads and the coefficient of friction between the pad and the rotor. This is the force with which the wheel together with the tire slows down. The main components that affect braking force are how tightly the pads are pressed together and how far from the center of the hub this force is applied. Thus, the larger the size of the brake rotor, the farther the clamping force is applied from the center of the wheel and thereby we increase braking force (lever effect). This is also like when you need to unscrew a rusted bolt, the longer the wrench (lever) the easier it is.

Recommended braking force is calculated with the following formula:

TSr = SSF x (tire rolling radius)

the coefficient of traction between the tire and the road is quite difficult to calculate, it can be from 0.1 on ice to 1.4 on a dry racing track with slicks. If you do not know it, use it as equal to 1.

Remember, weight transfer must be taken into account because during braking the rear end becomes unloaded and the front is loaded.

Front:

SSFf = μ*WSp / 2

WSp = Wm*((1-CgF/ML)+(μ*CgR/ML))

Rear:

SSFr = μ*WSr / 2

WSr = Wm — WSp

Where

TSr — recommended braking force (kg)

SSF — tire traction force (kg)

SSFf — front tire traction force (kg)

SSFr — rear tire traction force (kg)

μ — coefficient of friction between the tire and road surface (use 1)

WSp — vertical force acting on both front tires (kg)

WSr — vertical force acting on both rear tires (kg)

Wm — weight of the car (kg)

CgF — distance from the front axle to the center of gravity of the car (cm)

KB — wheelbase (cm)

Yts — distance from the ground to the center of gravity of the vehicle (cm)

After careful calculations, we will be able to understand how powerful our brakes need to be and what factors influence this force:

— Is not dependent on speed

— Can change depending on tire quality, road surface quality, weather conditions

— Depends on wheel size (as you think, do all those who install huge wheels or huge brakes ever calculate them together in any way? =)

— Dependent on the weight of the car, ground clearance and wheelbase, indeed, the lighter and lower the vehicle is, the less weight transfer affects braking.

Compression force

The force with which the caliper presses brake pads to the disk is measured in kilograms. This force is created by multiplying the pressure in the brake system by the area of the pistons (caliper without bracket), or 2*on the area of the pistons (caliper with bracket). It is measured in kg/cm^2. To increase compression force, you either need to change the system pressure or increase piston size. Changing the pad composition (friction coefficient) does not affect the compression force.

Calculated by the following formula:

CS = Pp*Dg

Where

CS — Compression Force (kg)

Pp — Pressure created by the Master Cylinder (kg/cm^2)

Dg — Effective piston area (for caliper with bracket this is 2*the piston area)

So now we can calculate how much braking force our brakes produce:

STp = CS * µL * Re

Where

STp — Produced Braking Force (kg)

CS — Compression Force (kg)

µL — Coefficient of friction between the pad and disk

Re — Effective radius of the brake rotor (from hub center to pad center)

Friction coefficient

This is an indicator of the strength of friction between the brake disc and the pad. The higher the coefficient, the greater the force of friction. For stock pads, this coefficient varies from 0.3 to 0.4. For racing pads from 0.5 to 0.6. 'Hard' pads have a low friction coefficient but wear less. On the other hand, 'soft' pads have a high friction coefficient and wear out faster. Most pads have a dependency of the friction coefficient on temperature; therefore, racing pads need to be heated up while regular pads would lose their properties at such temperatures.

Heat Capacity

I hope that it's no secret for anyone that brakes stop a car by converting kinetic energy into heat. Therefore, the heavier the vehicle and the faster you drive, the more heat it must dissipate in order not to overheat fluid, discs, and burn out pads. The ability of rotors to dissipate heat depends on their weight and how well they are cooled.

Kinetic Energy formula for a moving car:

K = (Vm * Sm^2) / 2

Where

K — Kinetic energy (J)

Vm — Vehicle weight (kg)

Sm — Car speed (m/s)

Nothing new here, we clearly understand that brake choice depends on the weight of your car and/or how fast you drive. And from driving courses (for those who did not buy a license=), you should remember that doubling your speed quadruples your braking distance. This is exactly what kinetic energy does.

Temperature increase formula during braking:

Tp = ((Kd - Kp) / (417 * Vd)) + Tw

Where

Tp — Temperature after braking (°C)

Kd — Kinetic energy before braking (J)

Kp — Kinetic energy after braking (J)

Vd — Total weight of brake discs (kg)

Ty — Brake Disc Temperature Before Braking (C)

Let's take my car as an example, braking before T2 in Myachkovo =)

Car weight — 1220kg

Disc weight — 33.5kg (front 12kg, rear 4.75kg)

Speed on the straight — 177km/h (49.17m/s)

Speed before T2 — 70km/h (19.44m/s)

Brake disc temperature before braking — 25C

Kd = (1220*49,17^2) / 2 = 1474826 J

Kp = (1220*19,44^2) / 2 = 230669 J

Tp = ((1474826-230669) / (417*33.5)) + 25 = 114 C

So after such braking, the temperature of the discs will be around 114 degrees. Let's compare with your results? =) For simplicity, you can just say the weight of the car and the weight of all brake discs)

And so, let’s pause on physics for a moment and move to more theoretical aspects.

There are three things that brakes need to do to stop a car:

1) Press brake pads against the disc strongly enough

2) Produce sufficient braking force to lock wheels on any surface

3) Have adequate mass and cooling of discs to dissipate heat generated by kinetic energy.

All these together should provide excellent feedback.

Pedal assembly

As we have already discussed, to brake the driver must simultaneously move fluid and create pressure. The master cylinder moves the fluid to create sufficient clamping force on the pads.

You activate the brakes with the pedal, which also acts as a lever that amplifies the pressing force. This effect is called 'pedal ratio'.

We usually press the brake pedal with a force from 22 to 45 kg to actively decelerate.

For example, on racing cars without power assist this effort is around 35kg, for cars with power assist it's about 22kg. 45kg would be too much, the pedal would be very stiff.

Pedal ratio can be calculated by dividing the distance from where the pedal is attached to the point of force application over the distance from the attachment point to the pushrod going to the master cylinder.

As we see, the higher this ratio, the more force is transmitted to the master cylinder. But one thing needs to be remembered: increasing the ratio also increases the pedal travel.

For cars with power assist this ratio is usually around 4-4.5. For cars without power assist from 6 to 7.

Therefore, removing a booster with a stock pedal is not a correct option =)

Hydraulics

As I have already written, to press brake pads against the disc it’s necessary to move fluid and create pressure in the system. This all is managed by the laws of hydraulics (Pascal's law).

The ideal scenario would be achieving sufficient clamping force with minimal pedal travel.

Force applied to the master cylinder creates pressure in the system. Pressure is a force applied to the master cylinder piston divided by its cylinder area. Therefore, the smaller the surface area of the cylinder, the higher the pressure.

Pressure in the system = Sp / Ap

Where

Sp — Force applied to the master cylinder piston (kg)

Ap — Area of the master cylinder piston (cm^2)

I'll give an example with my stock master cylinder (cylinder 0.875″) at a force of 500kg

Pressure in the system = 500 / 3.87 = 129 kg/cm^2

And for the master cylinder (cylinder 1″)

Pressure in the system = 500 / 4.91 = 101 kg/cm^2

From this we can see that the higher the pressure, the stronger brake pads press against the disc, meaning more braking force. But it doesn't mean that if we want powerful brakes we should install a small master cylinder. Here another factor comes into play — movement. Since fluid is incompressible, any movement of the master cylinder leads to movement of pistons in calipers. This movement in hydraulics is called displacement and is calculated as multiplication of piston travel by its area. Measured in cm^3

Displacement = Ap * Dp

Where

Pp — Piston area (cm^2)

Dp — Master cylinder piston movement (cm)

Let's recalculate it for my car's stock GTMC (0.875) and with a 3 cm stroke

Displacement = 3.87 * 3 = 11.61 cm^3

And for the same GTMC (cylinder 1″) but with a 3 cm stroke

Displacement = 4.91 * 3 = 14.73 cm^3

Here we see an opposite situation, the smaller the cylinder area, the less displaced volume there is at the same pedal stroke (meaning more pedal travel).

Now let's move on to analyzing the system as a whole, it's known that the braking system is closed and therefore pressure is transmitted throughout the system in equal values. In addition, besides the GTMC, there are calipers with pistons (for calculations, the total area of all pistons is used)

This means that the pressure created by the GTMC drives all the pistons in the system. Since the piston area in the caliper is larger than that of the GTMC, then according to the laws of hydraulics, the force delivered by the caliper increases significantly.

The greater this leverage factor, the less force needs to be applied to the pedal (and more pedal travel) to achieve the same result.

To calculate the amplification factor, you can use the formula

Sz = (Sp * Ps) / Pg

Where

Sz — Force exerted by caliper (kg)

Sp — Force applied to GTMC piston (kg)

P_s — Effective area of pistons (for a caliper with a bracket, this is twice the area of the pistons)

Pg — Area of the GTMC piston (cm^2)

For example, I'm taking my car again (cylinder 0.875″) =)

Sz = (500 * 10.17 * 4) / 3.87 = 5255.8 kg

And for the GTMC (cylinder 1″)

Sz = (500 * 10.17 * 4) / 4.91 = 4142.6 kg

From this it follows that with a constant force on the GTMC, we can increase the compression force by either increasing the caliper piston area or reducing the GTMC piston area.

But it's not that simple. Don't forget about another factor — movement. Unfortunately, playing around with cylinder areas changes pedal travel. For example, reducing the GTMC reduces the amount of displaced fluid — you have to work harder on the pedal to compensate for this (pressure will not begin to rise until the pad presses against the disc). This is also true when increasing caliper piston area (with one GTMC).

Let's calculate the piston travel:

Xp = (Dp * Pg) / Ps

Where

Xp — Caliper piston travel (cm)

Dp — GTMC piston movement (cm)

Pg — Area of the GTMC piston (cm^2)

Ps — Effective area of pistons (for a caliper with a bracket, this is twice the area of the pistons) (cm^2)

And how can we be without an example? =) My stock car (cylinder 0.875″), GTMC stroke 3 cm:

Xp = (3 * 3.87) / 40.68 = 0.29 cm

And for the cylinder (1″)

Xp = (3 * 4.91) / 40.68 = 0.36 cm

From this we see that if you don't want to change pedal travel, then when changing caliper area (installing huge brakes), remember about the GTMC as well. And vice versa.

GTMC

This is the heart of the entire braking system. It's activated by pressing on the brake pedal, initially the piston moves fluid through the system until the pads make contact with the rotor, then since the system becomes closed, pressure starts to rise creating a braking force. From this it follows that the harder you press on the pedal, the higher the braking force.

The main parameters of GTMC are the piston diameter and its travel. Usually encountered GTMCs have diameters from 0.625″ to 1.5″ and stroke from 2.5 cm to 3.81 cm. Matching both these parameters with recommended values for your car ensures good performance. It's worth remembering that at one pedal effort, a small GTMC will give higher pressure but can displace less fluid. Also, the larger the GTMC travel, the more it can displace fluid, but this also means more pedal travel is required. The best result can be achieved by calculating a compromise between pedal travel and pressure for your car.

Pressure regulators

— Pressure Relief Valve (RPV)

pressure relief valves

Needed to maintain the specified pressure in the system (for disc brakes 0.14 kg/cm^2, for drum brakes 0.70 kg/cm^2)

There are a couple of reasons to use such valves

1) Only for drum brakes so that the return spring does not pull the pads too far from the drum, creating an extra pedal travel during subsequent braking.

2) For disc brake systems where the master cylinder is below the caliper level (some race cars and hot rods). Without this valve, fluid would drain back into the master cylinder making the pedal soft and again increasing its travel.

If you are replacing drum brakes with discs — be sure to remove such valves from the system

— Proportioning Valve (Hold-off)

Proportioning Valve

Since there is a return spring on rear drum brakes, as described above, drums require more travel for the pad to reach the drum than self-adjusting disc brakes where the pad is always close to the rotor. The dosing valve (installed in the front circuit) prevents pressure buildup in the front brake circuit until it reaches a set value in the rear (usually 5-10 kg/cm^2) so that the drum pads can get closer to the drum.

If you are replacing drum brakes with discs — be sure to remove such valves from the system

— Pressure Distribution Valve (PBV)

Pressure Distribution Valve

As we mentioned above, during braking the weight of the car shifts forward. Since brake force must distribute proportionally to the load weight (where there is more weight, there is more brake force), a front-to-rear brake balance needs to be maintained. For example, during hard braking up to 85% of the weight goes to the front of the vehicle. On correctly adjusted systems, both front and rear brakes are nearly simultaneous engaged. It is usually installed between the master cylinder and the rear circuit to reduce pressure in the rear circuit at the initial moments of braking. Note that pressure in the rear circuit may not always be lower than in the front due to this valve, you change the rate of pressure increase. In the front brakes, when pressing on the brake, it is created faster than in the rear.

Stock valves are non-adjustable but there are racing versions with which you can adjust the brake balance on a modified braking system.

PBV

PBV + tee for the front circuit

Pressure increase in the rear circuit depending on the position of the adjustable valve

If you install an adjustable valve, don't forget to remove the stock one!

— Combined Valves

Combined Valve

Used on most stock cars with disc-drum systems. Combines proportioning and pressure distribution valves.

Brake pads

It all depends on quality and material here. This is where you should not skimp. On good branded pads, the coefficient of friction is always indicated! It is denoted by two letters. The first letter indicates the cold pad friction coefficient, the second hot.

For example DS2500 FF

C = up to 0.15.

D= 0.15 to 0.25.

E= 0.25 to 0.35.

F= 0.35 to 0.45.

G= 0.45 to 0.55,

H= more than 0.55.

For example

Ferodo DS2500 — FF

Hawk HPS — FF

Hawk HP+ — GG

Some stock pads might be FE, meaning they will brake worse when hot compared to cold.

————————————————————————

So. I talked about many nuances in the braking system. So how do you actually create a proper braking system from scratch?

Let's go step by step

1) Try to use brake discs of necessary size for dissipating kinetic energy of your car (after braking from max speed to 0, temperature should not exceed 540 C).

If you plan to run hard, when calculating the radiated heat use a brake disk temperature before braking equal to 260 C.

2) Choose the sturdiest, strongest caliper (so that deformation during disc compression is minimal). Use a caliper with the maximum possible piston effective area.

3) Calculate the recommended braking force

4) Calculate the recommended maximum pressure in the brake system

Rd = TCr / (µL * Pp * Re)

Where

Rd — Recommended pressure created by the master cylinder (kg/cm^2)

TCr — Recommended braking force (kg)

µL — Coefficient of friction between pad and disk

Pp — Effective piston area (for a caliper with brackets this is 2*the piston area)

Re — Effective radius of the brake disc (from hub center to pad center)

5) Estimate how sensitive a pedal you want. For sports use, for example, you can take 35 kg for active braking.

6) Choose whether you want brakes with or without an assist unit.

An assist unit is needed, for example, if you don't have the possibility to achieve sufficient pedal travel and required force with chosen components, or if you cannot install a pedal with high leverage. Or your car is VERY heavy.

7) Determine the pedal ratio, size of the master cylinder, and (if installed) vacuum booster boost factor.

We know what pressure needs to be created and how sensitive you want the pedal to be. We have three components (or two) by which this pressure can be created. Perhaps some components you do not wish to change in your car, such as the brake pedal. So its value can be left fixed and played with other components.

— Pedal ratio

Can range from 3 to 7. When choosing take into account several factors, is there enough space for installation, will not the pedal hit the floor at full travel of the master cylinder. And don't forget that the higher the ratio, the more travel and mushiness of the pedal.

— Calculate the force with which the pedal shaft presses on the master cylinder

For example, you would like to achieve maximum braking force when pressing down on the pedal with 35 kg. And your pedal ratio is 4.5. So the force applied to the master cylinder will be 35*4.5 = 157.5 kg. If you are using a booster, it also needs to be multiplied by the boost factor.

— Choosing the correct size of the master cylinder

Now knowing the recommended pressure and the force applied by the pedal shaft we can calculate the size of the master cylinder

Pp = Sp / Rd

Where

Pp — Area of the master cylinder piston (cm^2)

Sp — Force applied to the master cylinder piston (kg)

Rd — Recommended pressure created by the master cylinder (kg/cm^2)

Suppose we need a pressure of 65 kg/cm^2, and we can apply force on the master cylinder with 157.5 kg

Pp = 157.5 / 65 = 2.45 cm^2

Let's convert this into typical master cylinder inch designations

Diameter of the master cylinder in (in) = (2 * (square root of 2.45/3.14)) / 2.54 = 0.695 in

It turns out we need a cylinder of size 11/16 = 0.687 inches. One of the smallest. Don't forget to check if it can push enough fluid.

If not, you will have to increase the size of the master cylinder, which means you'll need a larger force applied to the master cylinder piston to create sufficient pressure. If you don’t change the pedal ratio — the only solution would be to install an assist unit.

8) Check the amount of displaced fluid for chosen components. Make sure that pedal travel is enough to produce compression force.

9) Calculate the braking force created with components which you've selected and compare it to recommended

Voila! =) now, if you managed all this, you know how to build your brake system or what to change in it!

I hope this article will be very useful, and I would be happy to answer any of your questions and help with calculations if you can provide me with the initial data:

- Brake assist ratio

- Pedal ratio

- Master cylinder diameter

-Front piston diameter + (number and type of caliper)

-Rear piston diameter + (number and type of caliper)

-Pedal force

-Vehicle weight

-Tire-road friction coefficient

-Distance from front axle to vehicle center of gravity

-Wheelbase

-Clearance height (distance from ground to vehicle center of gravity)

-Lining and disc friction coefficient

-Efficient radius of the brake disk (from hub center to pad center) front

-Efficient radius of the brake disk (from hub center to pad center) rear

-Rolling radius of tire (overall wheel diameter/2)

-Travel of brake caliper

In general, with my car, the force applied to the pedal sufficient for wheel lockup is only 15kg =) While a typical setup for race cars is 35kg and more =)