Sizing a master cylinder is dependent on many factors.
Who knew the brake pedal could be so complicated?
It’s just a simple bit of steel – right?
I’ve also been working on the handbrake.
I’ve been working on various parts of the brake system….
I checked out the Sierra handbrake and found it was a little too tall; ideally I wanted something at least 2 inches more compact. The answer came in the Peugeot 206 Xsi. I used the version with the chrome button. They are very common and cost barely more than a pint of beer. They are much more common than Sierra items, with plenty in the scrap-yards, so I think you’d struggle to find a better handbrake lever for the job.
It sits slightly off centre, which when down, gives the driver plenty of elbow room whilst driving. I tilted the mounting bracket slightly forward, allowing the lever to lay parallel with the top of the tunnel.
I did want to keep the whole braking system from the Cosworth Scorpio, but annoyingly, the master cylinder and servo fouled the engine. I therefore chose to use a master cylinder from the Land Rover Series 3 LWB and removed the servo. I was wondering whether it was as simple as just removing the servo……. read on
A while back I went a bought a similar 1″ (25.4) sized master cylinder to that of the Cosworth Scorpio I used as a donor. The Land Rover item (part No. 90577520) had a horizontal reservoir which was an advantage. They might be from old cars but they are from cars that have an enthusiastic club scene with a good spares network.
The braking system is a complex arrangement and simply changing one component may completely upset the whole set-up. Pedal ratio, plus bore sizes of the master cylinder, calliper pistons and wheel cylinders are all very critical to maintaining the correct system pressure, and safe braking performance. Weight distribution, tyre size and suspension can all have an effect. Therefore, I decided to do some research. I knew I wasn’t going to get the set-up bang on first time, but at least I wanted to get close. I had read a number of forum pages where builders of Locost type cars complained of the rear locking up under heavy braking and didn’t want the same.
At this stage, I decided to research the whole subject and some maths…………
Luckily, for those out there not wanting to do so many sums….
I found this excel spreadsheet on the web.
But you can follow the maths below….
It’s a shame I found it after I had finished 🙁
Calculating the Master cylinder size
As mentioned before there are numerous factors that have an effect on master cylinder size, so lets work through them one by one.
Master Cylinder size is very important and selecting the right one can be tricky.
Brake Pedal Ratio
The proportions of the brake pedal are important whether you are using manual or servo assisted power brakes. With power brakes, if the ratio is too high, the brakes will be highly sensitive to the lightest of touch and if it is too low, the force required on the pedal may be more than the pedal travel can supply. With manual brakes, too high a ratio isn’t so much of a problem, although some drivers feel reasonable force inspires confidence.
As I’m not fitting a servo, the extra force would have to be supplied by the driver. This would require a different pedal ratio or a longer brake pedal. A longer brake pedal would have a longer throw making pedal operation slow and awkward. If the pedal ratio is less than required, then either the master diameter(if fitted) will need reducing or the brake calliper piston size increased. Often a combination of all 3 are used to compensate for the loss in assisting force.
As the pedal ratio gets closer to 1:1, the pedal travel drops. The higher the mechanical advantage of the pedal, the greater the braking force generated but at the cost of an additional pedal travel, it’s a delicate balancing act.
Typically on a street car, effort is at or below 40lbs (18kg). In high performance vehicles and race cars the level is kept below 120lbs (54kg), with 80lbs (36kg)considered ideal for race applications.
On a servo assisted vehicle, if servo assistance fails, you still want to be able to stop the car, therefore maximum braking effort should be 80lbs (36kg).
Servo / Power assisted brakes
3.4:1 → 4.0:1 pedal ratio (4.0:1 is the maximum for sports cars)
Non Servo / Manual Brakes
5.5:1 → 7.0:1 (6.2:1 being recommended)
Calculating the Brake Pedal Ratio
A = Distance from pivot point to middle of push / pull point
B = Distance from pivot to point of push on master cylinder
P = Pivot point
F = Force or push supplied by driver
Divide the length from the pivot point to the push rod (B) into the length from the pivot point to the centre of the foot pad (A).
Haynes Roadster Brake Pedal Ratio Example:
For a Haynes Roadster the set-up matches Figure 4.
(B) Length from pivot point to push rod = 31mm
(A) Length from pivot point to centre of foot pad = 202.5mm
202.5 ÷ 31 = 6.5
Pedal ratio = 6.5:1
Nb. You can see that the standard Haynes Roadster is not designed to have a Servo.
Standard Ford Sierra Brake Pedal Ratio Example:
For a Ford Sierra the set-up matches Figure 1
(B) Length from pivot point to push rod = 61mm
(A) Length from pivot point to centre of foot pad = 275mm
275 ÷ 61 = 4.5
Pedal ratio = 4.5:1
NB. Pedal pressure may appear very soft for a sports car. For my car, I have removed the servo and changed distance B to 44mm (6.2:1).
In general, if you have a pedal ratio of approximately 6.2:1 then it is likely that a 3/4 inch (0.750 inch or 19 mm) master cylinder will be close to the right size when combined with a front 4-piston calliper with piston sizes of 38mm and 42mm and a tire with a 24.4 inch outer diameter (such as a commonly used tire size 245/40R17). It is possible to calculate the master cylinder sizes with relative precision, but you will need the following data, in either metric or English units:
- Static weight on the front axle
- Static weight on the rear axle
- Maximum deceleration rate expected (typically between 1.0 to 1.5g for sedan or sports cars, unit-less)
- Centre of gravity height
- Tire rolling diameter (you can use the tire diameter)
- Brake calliper piston sizes front and rear, converted to total piston area (piston area = diameter of each piston squared, then divided by 4, then multiplied by π, or 3.142)
- Effective radius of the brakes front and rear, or the lever over which the pads apply their clamping force (approximately ½ of the rotor diameter minus ½ of the pad height, or the average of the inner and outer diameter of the swept portion of the brake rotor, will be relatively close)
- Pad friction coefficient, front and rear (if you do not know, assume it is 0.5 for race friction and 0.4 for street friction, also unit-less)
- Pedal ratio (as discussed previously)
- Target driver foot effort at maximum brake output. For racing use this should be around 80 lbs. We are actually speaking of force here so we should use the correct convention and call it pound-force written as lbf. One lb by definition is equal to one lbf in the earth’s gravitational field of one G. One lbf also equals 4.448 newtons (N) and 0.454 kgf. The same convention of mass versus mass in a gravitational field applies between kg and kgf. The reason for making this point will be made clear later in the context of driver leg input effort.
In all cases the result of the calculations below will need to be tested since the vehicle behaviour under braking is also affected by suspension design and set up, tire pressures, shock set up and spring used.
Vehicle Mass (M)
To begin the calculation we need to estimate the weight transfer under a maximum deceleration or –G stopping force scenario. Start by adding the Static Front and Rear Weight (1 and 2 above):
Vehicle Mass (or total weight) M = Static Front + Rear Weight
A Haynes Roadster typically has a 55% Front to Rear Weight Bias and weighs 600 → 700Kg
Vehicle Mass (or total weight) M = 849lbs(385Kg) + 694lbs(315Kg) = 1543lbs(700Kg)
Weight Transfer (ΔW)
To calculate weight transferred (ΔW), multiply M by the maximum deceleration rate (3 above) multiplied by Centre of gravity height (4 above) divided by Wheelbase (5 above):
ΔW = M * γ(rate of deceleration in negative Gs) * Height of Centre of Gravity(C.O.G).
Street Car = -1.0 G
Race Car = -1.5G
A Haynes Roadster Centre of Gravity sits at about waste height approx 18″, and typically pull -1.2G in braking. The wheelbase can vary, but I’ve used 92″.
ΔW = 1543 * 1.0 *18 = 301.89
Dynamic Axle Weight During a Maximum G stop
ΔW is then added to the static front weight and subtracted from the static rear weight for the purpose of estimating the dynamic axle loading conditions:
The Dynamic Front Axle Weight during a maximum –G stop is = Static Front Weight + ΔW
The Dynamic Rear Axle Weight during a maximum –G stop is = the Static Rear Weight – ΔW
For A Haynes Roadster:
The Dynamic Front Axle Weight during a maximum –G stop is = 849lbs + 301.89lbs = 1150.89
The Dynamic Rear Axle Weight during a maximum –G stop is = 694lbs – 301.89lbs= 392.11
Next, we need to calculate the maximum individual front and rear torque requirement by dividing the dynamic weight in half and multiplied by half the rolling diameter of the tire (6 above) and multiplied by Maximum Deceleration Rate (3 above):
Torque front (Tfront) (units are either lb-ft or N-m) = (Dynamic front axle weight in either pounds or newtons / 2) * (Tire Rolling Diameter front in feet or meters / 2) * Maximum deceleration rate
Torque rear (Trear) (units are either lb-ft or N-m) = (Dynamic rear axle weight in either lbs or newtons / 2) * (Tire Rolling Diameter rear in feet or meters / 2) * Maximum deceleration rate
For A Haynes Roadster with 205/50/15 tyres:
Torque front (Tfront) = (1150.89/ 2) * (23.07 / 2) * 1.2 = 6638.01
Torque rear (Trear) = (392.11/ 2) * (23.07 / 2) * 1.2 = 2261.57
Calculating Calliper Piston Area in Square Inches
Π(3.1416) x (radius of the piston)2 x (number of pistons on axle)
Ford Scorpio / Sierra Piston Area Example:
|Number of Pistons||1||1|
|Piston Area (sq./in)||4.37||1.58|
Radius of a 2.36″ piston = 1.18″
3.1416 x (1.18 x 1.18) x 2 = 4.37 sq./inches
Willowed Dynalite (120-6814) Piston Area Example:
|Number of Pistons||4|
|Piston Area (sq./in)||4.81|
Radius of a 1.75″ piston = 0.875″
3.1416 x (0.875 x 0.875) x 8 = 9.62 sq./inches
Effective Rotor Radius
Rfront = (Front Brake Rotor or Brake Disc Diameter / 2) – (Front Pad Height / 2)
Rrear = (Rear Brake Rotor or Brake Disc Diameter / 2) – (Rear Pad Height / 2)
For Haynes Roadster:
Rfront = (10.24″ / 2) – (1.45″ / 2) = 4.4
Rrear = (9.92″ / 2) – (1.3″ / 2) = 4.47
Calliper Torque Output
The torque output of the front and rear brake system will have to equal these values for a stopping event at maximum deceleration.
The torque output for the front brakes can be expressed as follows:
Pfront = Tfront / Apfront, total Area of pistons for one half of front calliper or in the case of a slider calliper design the total area of pistons of front calliper * Rfront, the effective radius for the front brakes (8 above) * μ, the pad friction coefficient (9 above) * 2 (for two sides to the rotor and pad interfaces) * Pf, the circuit pressure
Now we want to change the equation to solve for the front circuit pressure:
Front circuit pressure Pfront(in N/mm2 or psi) = Tfront / (Apfront * Rfront * μfront * 2)
Rear circuit pressure Prear(in N/mm2 or psi) = Trear / (Aprear * Rrear * μrear * 2)
For Haynes Roadster:
Front circuit pressure Pfront(psi) = 6638.01/ 4.37 * 4.4 * 0.4 * 2 = 431.59
Rear circuit pressure Prear(psi) = 2261.57 / (1.58 * 4.47 * 0.4 * 2 = 414.47
With the circuit pressure requirement known one can solve for the pedal ratio and master cylinder size. U.S. Federal and E.C. regulations for automobile and light truck braking performance establish requirements for maximum effort by a driver in the case that the brake assist fails. In some cases the assisted effort is too low and the unassisted effort might be close to what a race driver would want. Typically on a street car effort is at or below 40 lbs (~178 N or 18 kgf). In high performance vehicles and race cars we try to keep the leg force required below 120 lbs (~534 N or 54 kgf). Eighty lbs (~356 N or 36 kgf) is ideal for most race applications.
Master Cylinder Input Force
It is important not to confuse the input force from the drivers foot and the Master Cylinder Input Force. The force supplied by the driver is multiplied by the pedal ratio to achieve the force present at the master cylinder.
To determine master cylinder push-rod input force:
Master cylinder push-rod input force = Driver foot input force / 2, since this force will be distributed to two master cylinders and presuming for calculation purposes that the pedal bias adjuster will be centred * pedal ratio
Haynes Roadster Example:
(6.5 x 40) / 2 = 130
40 pounds of driver input force with a 6.5:1 pedal ratio results in 130 lbs of input pedal force to the master cylinder.
Selecting the correct master cylinder is important and its requirements are linked to pedal ratio. The recommended pedal ratios are based on 150 pounds maximum force on the lever to attain the maximum rated pressure for the master cylinder.
Driver Input force recommendations:
- 40lbs for Street,
- 80lbs for Race,
- 120lbs for Max human effort (under reproducible stressful conditions)
Where 2 master cylinders are present you could subsequently change the bias, by turning the adjuster bar screw causing the centre pivot to move closer to one of the master cylinders. 130 lbs of master cylinder input force act on each master cylinder push-rod with the bar centred. The master cylinder that is now closer to the centre pivot will experience an increase in input force equal to a decrease in the opposite master cylinder input force. This change in the ratio of input force will cause a change in the ratio of circuit pressures and therefore a change in the ratio of wheel end calliper output force.
When setting up the master cylinder pushrod, remember that the pedal needs around 10mm of travel before the master cylinder piston moves at all. Otherwise, without the slack it is easy the the pads to drag on the discs causing the bakes to bind. Also, even the slightest of pedal pressure could cause brake bind. You therefore need a slight gap between the push-rod and the master cylinder piston (equvalent to 10mm of pedal travel).
Master Cylinder Size
The next step is to calculate the front and rear circuit master cylinder sizes:
Master cylinder size of the front circuit = 2 * √ Master Cylinder Push Rod Force / (Pfront * π)
Master cylinder size of the rear circuit = 2 * √ Master Cylinder Push Rod Force / (Prear * π)
Haynes Roadster Example:
Master cylinder size of the front circuit = 2 * √ 130 / (431.59 * 3.142) = 0.51″
Master cylinder size of the rear circuit = 2 * √ 130 / (414.47 * 3.142) = 0.52″
Ideally, these two values should be as close together as possible, especially if using a dual master cylinder on an adjustable dual set-up. You can see from this example, the size of the front brakes could be slightly improved.
From these calculations you can do some what-if scenarios. For example, it is possible to calculate what the maximum indicated gauge pressure should be for either circuit. Of course, the answer will depend on your leg strength, the pedal ratio, and the master cylinder size:
Assuming that the pedal ratio, the master cylinder size is as recommended and assuming the driver can leg bench press 600 lbs (300 on one leg), then 2485 psi would be the maximum gauge pressure if no effort was lost due to any system compliance like the deflection of the pedal box mount or lack of calliper stiffness. In practice the maximum leg force possible is only around 120 lbs, which results in only 840 psi of circuit pressure. Even then, while most drivers are able to exert this much leg force without difficulty in the garage, it would be very hard to sustain this level for even a short race length.
Calculating Master Cylinder Line Pressure
Pressure = (Leg force on the pedal) x (Pedal Ratio)
(Master Cylinder Piston Area)
Haynes Roadster Master Cylinder Line Pressure Example:
Calculate the line pressure of a 1″ bore master cylinder using a 6.5 ratio pedal.
Leg Force (Effort) = 120 lbs.
Pedal Ratio = 6.5:1
Square Inches of Area (1″ Bore Master Cylinder) = .785
120 x 6.5 ÷ .785 = 994 psi
|Master-Cylinder Size vs. Piston Area|
|Normal Bore Size||Diameter In.||Area Sq. In.|
|Listed are diameters of popular mass-produced master cylinders and their areas.|
I spotted there are many factors that have a big effect on the master cylinder sizing, for instance changing the height of the centre of gravity, the target stopping G force, pedal ratio and just about anything to do with braking components. With the values I chose, my 1″ master cylinder turned out pretty close, but it turned out to be a much more sensitive setup, then I had imagined. This explains why many drivers decide to fit dual master cylinder pedal box set-ups. If I had room, I’d jump at fitting one. I thoroughly recommend you play with the excel spreadsheet above.
Get as much info on the following you can:
- all brake components
- brake pedal dimensions
- tyre sizes
- corner weights
- stopping distances of similar vehicles with similar tyres and suspension (for target de-acceleration G)
Put these figures into the spreadsheet and keep swapping values back and forth until you can get those master cylinder front and rear values as close to each other as possible. In this case, front and rear master cylinders ended up quite close, but it’s a sensitive set-up and you can easily understand how some people suffer from one end locking up long before the other.
Once, I worked through the maths, I could understand the frustrations the race guys go through. With one turn of a shock absorber, they almost need to start from scratch with brake biacing. Happily for me, the values I randomly chose, gave good results for the master cylinder I had bought months before.
It also goes to show that when the Haynes books went to print, someone had beaten me to the maths.
Common Brake Problems
1. Spongy Pedal
- Air – Bleed from the furthest bleed screw from the master cylinder and work in . Bleed screws up
- Calliper brackets not square to rotor causing calliper deflection
- Rubber brake lines deflecting
- Brake fluid too hot
- Pedal ratio too high
- Silicone brake fluid – highly compressible
2. Low Pedal – Have to pump the pedal to get it hard
- Master cylinder too low causing fluid drain back to reservoir – install 2 lb. Residual pressure valve or move reservoir higher than callipers
- Warped rotor causing piston knock back
- Excessive rotor run-out causing piston knock back
- Excessive piston retraction – install square seals
3. Low Pedal – Won’t Pump Up
- Bad calliper seals, leaking
- Leak in hydraulic system
- Balance bar too far off centre
- Badly worn pads
4. Pedal Hard – Car Won’t Stop
- Master cylinder too large, too much volume
- Pedal ratio too small – Insufficient pressure on master cylinder
- Glazed rotors
- Glazed pads