sport brakes HELP

[instructorbill]

I don't understand.

I've done the math.

My setup

Volvo 240 brakes with vented e21 fronts

VW rear front disk with VW/AUDI rear Calipers with ebrake

according to my math, I should be using a 1/2 inch (12mm) front master and a 1 inch (25mm) rear master using a dual master setup

What is everybody else with this setup (or similar) running?

[peteinjp]

Wish I could help. I need to do the math for my setup- where did you find that info?

[instructorbill]

Mind you, I had to "wing it" on my weight distribution and actual weight and center of gravity height, but even if my estimations were wrong, would I have a smaller master in front than in the rear? my calculations were with a 5.5:1 pedal ratio, pad friction co- at .4 and a pedal effort of 80lbf

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

2. Static weight on the rear axle

3. Maximum deceleration rate expected (typically between 1.0 to 1.5g for sedan or sports cars, unitless)

4. Center of gravity height (go online to learn methods of determining using corner weight scales)

5. Wheelbase

6. Tire rolling diameter (you can use the tire diameter)

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)

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)

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)

10. Pedal ratio (as discussed previously)

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.

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

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

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

15. The Dynamic Rear Axle Weight during a maximum –G stop is = the Static Rear Weight – ΔW

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

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

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

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)

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.

Individual Pushrods

Center Pivot

Adjuster bar

Clevises

If we subsequently determine that we need to change the bias, we will turn the adjuster bar screw causing the center pivot to move closer to one of the master cylinders. The master cylinder that is now closer to the center 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 caliper output force.

The next step is to calculate the front and rear circuit master cylinder sizes:

22. Master cylinder size of the front circuit = two times the square root of the result of taking master cylinder input force and dividing it by the front circuit pressure and dividing also by π, or 3.142

23. Master cylinder size of the rear circuit = two times the square root of the result of taking master cylinder input force and dividing it by the rear circuit pressure and dividing also by π, or 3.142

From these calculations you can do some what-if scenarios. For example, it is possible to calculate what the maximum indicated gage 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 and master cylinder size is as recommended (6.2:1 and 0.750 inch [19 mm]) and assuming the driver can leg bench press 600 lbs (300 on one leg), then 2100 psi would be the maximum gage pressure if no effort was lost due to any system compliance like the deflection of the pedal box mount or lack of caliper 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.

[peteinjp]

Stoptech- good info there for sure. I need to do this for my front/rear set-up to check size the calipers for the front to match up closely to the rear vette setup. I have e21 rotors up front as well. Are your rear calipers single piston? What is the bore and rotor size?

What info did you put in for the weight and how did you estimate it? I bet someone here on the board has some hard numbers there- then you could just estimate the difference with the m20.

[instructorbill]

Stoptech- good info there for sure. I need to do this for my front/rear set-up to check size the calipers for the front to match up closely to the rear vette setup. I have e21 rotors up front as well. Are your rear calipers single piston? What is the bore and rotor size?

What info did you put in for the weight and how did you estimate it? I bet someone here on the board has some hard numbers there- then you could just estimate the difference with the m20.

38mm bore -- single piston-floating caliper

9.5 inch outside diameter rear rotor

Took curb weight from link below for a 1600 at 2028, added 200lbs for me and my junk, fuel 10 gallons at 6.2lbs for 62lbs and an M20 differential of 65 lbs for a total of 2355lbs

http://www.marsmann.com/2002tii/colors_files/2002brochure.pdf

weight distribution 55 front 45 rear (with the battery all the way at the rear of the trunk this should be possible.)

Stole the cg height from a stock 320i at 22.32 inches (seemed like a good idea at the time), but it might be between 20 to 21 inches for all I know.

[peteinjp]

Just out of curiosity- is the rear rotor vented?

[TobyB]

Holy power, Bill-

I just called Tilton, and used their recommendation.

For tii front calipers with Sentra rears (not much different dimensionally

than the VW, I think) they had me with a 1" rear and 5/8" front.

It makes for a very firm pedal with a 6:1 ratio (stock's about 4.5:1, I think)

So yeah, your numbers seem good to me, intuitively...

BTW, Tilton just shoots for a 70% front, 30% rear bias- and

since my balance bar is within a few mm of center, I'd say they were

just about right on! So if you end up with that same 70:30 balance,

I'd think that'd be a good first approximation.

HTH,

t

Oh, BTW, how's your pedal box doing?

t

[instructorbill]

The short answer-- it aint done yet.

I've got the remote bracket fairly well sorted for the clutch, I will however have to remove the pedals to weld up the tab on the bottom of the clutch pedal to mimmick what is on the brake pedal. Additionally, I've still got much work to replicate the "transmission" linkage that is higher in the brake linkage that redirects to the booster.

I might just scrap that and go to a direct actuation of the clutch master from the pedal rod. It'll put the clutch master at a funky angle, but what do I care? It's just a matter of fabbing a mounting plate on the box that is roughly perpendicular to the average throw of the clutch actuating rod.

Since the clutch is close to the inner fender well, I don't think this will hurt my space requirements.