This is my personal scratch sheet for figuring out my Brake System.
For Reference I am using the Stoptech White Papers:
http://www.stoptech.com/tech_info/PedalSetup-DualMaster-Guide.pdf
REAR 996 caliper:
Pistons size: 28/30
FRONT 996 caliper:
Pistons size: 38/44
Brake Pedal Design and SelectionFirst, let’s define the term pedal ratio. The pedal ratio is the overall pedal length or distance from the pedal pivot called the fulcrum to center of the pad your foot will push against (L1+L2) divided by the distance from to the fulcrum to the master cylinder push rod attachment point (L1).FulcrumMaster Cylinder Pushrod AttachmentExperience has shown that a pedal ratio of 6.2:1 is recommended (with 5.5:1 being the recommended minimum) to replace most of the brake force assist that was provided originally by the vacuum assist and the original equipment pedal ratio of 3.5 to 4.0:1. This means that you cannot usually reuse the original equipment pedal to build a pedal arrangement with dual master cylinders because the stock pedal is simply not long enough and often the fulcrum is too low to the floor to provide enough room to make the brake pedal longer.Shortening the distance from the fulcrum to the pushrod would have the same effect, but is a difficult task best left to an expert fabricator. Without this extra mechanical advantage, you would have to use a smaller master cylinder than may be available or you are at least setting yourself up for a difficult time in picking other system components to make up for the missing mechanical advantage. There are many well-designed and manufactured pedal arrangements with dual master cylinders available from race component suppliers. If you still choose to fabricate your own assembly then take care to design and build a sound pedal.
Master Cylinder Selection
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 caliper 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:
1. Static weight on the front axle
Using the Vorshlag Car Weights +100 F&R: 1498 lbs
2. Static weight on the rear axle
1210 lbs
3. Maximum deceleration rate expected (typically between 1.0 to 1.5g for sedan or sports cars, unitless)
1.5g
4. Center of gravity height (go online to learn methods of determining using corner weight scales)
30″ = 762 mm
5. Wheelbase
106.3″
6. Tire rolling diameter (you can use the tire diameter)
24.4″ = 245/40R17 = 619.76 mm
7. Brake caliper 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)
36mm/40mm Front Pistons 28mm/30mm Rear Pistons
REAR 996 caliper:
Pistons size: 28mm/30mm
((((28+28+30+30)^2)/4)x π) = 10568.30876
FRONT 996 caliper:
Pistons size: 38mm/44mm
((((38+38+44+44)^2)/4)x π)
(164)^2=26896
26896/4 = 6724
6724 x π = 21124.05116
8. 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)
Front 345mm
172.5mm – 65.9mm = 106.6
Rear 328mm
164mm – 65mm = 99mm
9. 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 unitless)
0.4
10. Pedal ratio (as discussed previously)
1.0
11. 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.
60 lbf
In all cases the result of the calculations below will need to be tested since the vehicle behavior under braking is also affected by suspension design and set up, tire pressures, shock set up and spring used.
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):
12. Vehicle Mass (or total weight) = M = Static Front + Rear Weight
2780 lbs
To calculate weight transferred (ΔW), multiply M by the maximum deceleration rate (3 above) multiplied by Center of gravity height (4 above) divided by Wheelbase (5 above):
13. ΔW = M * γ (rate of deceleration in negative Gs) * Ht of C.G. / Wheel base
(2780 * 1.5*30)/106″=1180.1886
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:
14. The Dynamic Front Axle Weight during a maximum –G stop is = Static Front Weight + ΔW
1498+1180.1886=2678.1886
15. The Dynamic Rear Axle Weight during a maximum –G stop is = the Static Rear Weight – ΔW
1210-1180.1886=30.1886
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):
16. 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
(2678.1886/2)*12.2=16336.95046*1.5 = 24505.42569
17. 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
(30.1886/2)*12.2=184.15046*1.5 = 276.2256916
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:
18. Tfront = Apfront, total Area of pistons for one half of front caliper or in the case of a slider caliper design the total area of pistons of front caliper (7 above) * 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
10562.02558*106*.4*2*60=53739586.15104
Now we want to change the equation to solve for the front circuit pressure:
19. Front circuit pressure = Pfront (in N/mm2 or psi) = Tfront (from immediately above) / Apfront / Rfront / μfront / 2 (don’t forget the 2)
60
Similarly we can solve for the rear by substituting the data that is different for the rear:
20. Rear circuit pressure = Prear (in N/mm2 or psi) = Trear (from immediately above) / Aprear / Rrear / μrear (rear specific, if different) / 2 (don’t forget the 2)
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. We provide the kgf unit of mass conversion at one G so that readers used to using metric units can make a comparison of the data being presented to one half of their body mass being the force they experience on each of their feet while standing due to gravity.
To determine master cylinder pushrod input force:
21. Master cylinder pushrod 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 centered * pedal ratio
For example, 40 pounds of driver input force with a 6.2:1 pedal ratio results in 250 lbs of input pedal force to the adjuster bar and 125 lbs of master cylinder input force acting on each master cylinder pushrod with the bar centered.
