How to work out brake bias and torque

[n1smo200sx]

I shamelessly copied from anoither forum...

Since there's some discussion on various big brake upgrade kits, Erik asked me to do some calcs and make a post on what's important for brake systems.

First, some assumptions:
1) The F/R brake bias set by the manufacturer is ideal, or close to it (this may or may not be true, but it gives us a reasonable target to shoot for)

2) All pads have the same coefficient of friction

Now, some general info:

The #1 thing to remember about bigger brakes is that the main goal is NOT to stop your car quicker! If you can lock up your stock brakes, you won't see much, if any, improvement in stopping distances with larger brakes. Larger brakes are used for their heat capacity, in turn giving improved fade resistance.

Also, more pistons does not equal better braking! The main benefit of more pistons is the ability to use a larger pad, which will last longer and have more heat capacity. An exception is when you go to 8 pistons or more, which typically use two separate pads -- supposedly the pad edge 'bites' a little better than the rest of the pad.

Ok...so if you want to figure out what effects various brake setups will have on the brake

bias, the key is brake torque. How do you calculate brake torque? Easy:

Torque = Force x lever arm

Force in this case is the pressure in the brake line multiplied by piston area of the caliper and the coefficient of friction of the pads.

The lever arm is how far out on the rotor you apply the force. For these calculations, we use the center of the pad as the "effective" rotor radius. And then you compare between front and rear, or various different caliper/rotor combinations,etc.

A few things to note:
1) I already said earlier, we're assuming the coefficient is the same in all cases, so if we stick to just comparing different setups, then it doesn't matter (it's just a scale factor)

2) same with factors of pi, or 4 (from, say, using the diameter instead of the radius of the pistons to calculate area) -- as long as you're consistent in your calculations (i.e. as long as you're wrong consistently!), the results will still be valid. I'm going to leave out factors of pi and use the piston and rotor diameter instead of radius.

3) A sliding caliper has effectively TWICE the number of pistons as it actually has. So a single piston sliding caliper acts, in hydraulic terms, as if it were a 2-piston fixed caliper. The reason is because the piston presses directly on the inboard pad, but the caliper body itself acts as an "inverse" piston and pulls on the outboard pad via the pad frame (the part that arches over the top of the rotor). At any rate, there's a factor of
2 you have to remember if you want to compare sliding calipers to fixed calipers.

Ok...so lets throw some numbers out here.

Stock 240sx non-ABS front brakes (CL22VB):

- Single piston sliding caliper
- 54.0mm piston diameter
-252mm diameter rotor
-45mm wide pad ('width' is the radial dimension of the pad, following the terminology in the FSM)

effective rotor diameter: 252-45 = 207
effective piston area: 54^2 x 2 (<-sliding caliper) = 5832
"brake torque" = 1207224

Stock 240sx rear brakes (CL9H):

- Single piston sliding caliper
- 34mm piston diameter
- 258mm diameter rotor
- 40mm wide pad

Effective rotor diameter: 218
effective piston area: 34^2 x 2 = 2312
"brake torque" = 504016

front brake bias = 1207224 / (1207224 + 504016) = 70.5%
rear brake bias = 1 - front brake bias = 29.5%

So those are our baseline numbers.

To compare, let's see what happens if you put 300ZX brakes on the front of a 240sx...

300ZX front brakes (OPF25B)

- 4 piston fixed caliper
- 40.45mm piston diameter
-280mm diameter rotor
-50mm wide pad

effective rotor diameter: 230mm
effective piston area: 40.45^2 x 4 = 6545
"brake torque" = 1505350

front brake bias = 1505350 / (1505350 + 504016) = 75%
rear brake bias = 25%

Now if you put the 300ZX rear brakes on too, what happens?

300ZX rear brakes (OPZ11VB)

- 2-piston fixed caliper
- 38.1mm diameter piston
- 297mm diameter rotor
- 36.5mm wide pad

effective rotor diameter: 260.5mm
effective piston area: 38.1^2 x 2 = 2903
"brake torque" = 756231.5

front brake bias = 1505350 / (1505350 + 756231.5) = 66.5%
rear brake bias = 33.5%

Just for completeness, Q45 brakes (2-piston sliding, 43mm pistons, and 280mm diameter rotor) and stock rear brakes give 78.5% front brake bias.

I don't have piston sizes, etc, for the Altima/180sx brakes, unfortunately.

OK. So that gives us a range that we can work with -- 67% to 75% front brake bias. I'd be wary of using any less front brake bias than ~67% because that could cause the rears to lock before the fronts -- not good.

ARRIGHT, NOW...

Suppose you want something bigger

Let's do an example. For concreteness, let's assume that we're going to use 4-piston fixed calipers at each corner with equally-sized pistons in each caliper (but different front and rear), 323mm (12.72") front rotors, and 309.7mm (12.19") rear rotors (those are commonly available sizes from vendors such as Wilwood, Coleman, etc).

What piston sizes do we want in order that the front brake bias be, say, 70%?

Well, of course it's just the reverse of what we did up above.

front brake torque: FBT, rear brake torque: RBT

FBT / (FBT + RBT) = .7

One equation, two unknowns...how do we solve it? The astute reader will notice that the equation above is insensitive to multiplying both FBT and RBT by the same constant factor (say multiply everything by 1.5) -- this amounts to either scaling up the rotor size on each end by that factor, or scaling the piston areas on each end by that factor.

Let's constrain the piston areas so that the TOTAL piston area is the same as 300ZX front brakes + stock rear brakes (this is probably the limit where you'd get too mushy a pedal if the total piston area gets any bigger)

So we have:
front piston area + rear piston area = 6545 + 2312 = 8857

let's solve for the rear piston area and we'll use that to eliminate the rear brake bias term in the previous equation.

rear piston area = 8857 - front piston area

and remember our equation for brake torque is:

brake torque = effective piston area x effective radius

first let's rearrange the brake bias relation to solve for FBT:
FBT = 2.33 x RBT

plugging in for FBT and RBT (and assuming a 50mm pad width):
(front piston area x 273) = 2.33 x ( (8857 - front piston area) x 259.7)

front piston area = 6103

or, front piston diameter = 39.06mm (1.54")

now we can find the rear piston area = 8857 - 6103 = 2754

or, rear piston diameter = 26.24mm (1.033")

Of course, you can't get calipers with just whatever piston sizes you want, so you'll have to juggle available piston sizes, rotor sizes, etc, etc to determine what will work. For instance...the combination above won't work because the piston sizes are too small (nobody I know of makes a caliper with 1" pistons), for example. Conclusion: In this case, you either allow the overall piston area to increase, thus likely requiring the use of a bigger master cylinder for proper brake feel, or you can leave the rear brakes alone and recalculate for just a front big-brake upgrade that would give the proper brake bias.

[Vlade]

good writeup mike... Or copied that is

[Hennie Marais]

Very interesting, I bet 95% of people don't even calculate stuff like that.

I'm sticking with my stock brakes sizes. I'm only upgrading the disks to brembo's and fitting performance pads and overhauling the calipers. They work perfectly for me as is.

[Gary57]

Those calculations are only valid if the pressure in the brake lines are all the same, which they are not. The rears always (well most of the time, not sure about the sx) have a lower line pressure than the fronts, it is the function of the master cylinder and or slave cylinder (suppose some manufacturers dont do this).

[Vlade]

very valid what you say there... you'll notice in pro track cars they actually have 2 brake master cylinders 1 front 1 rear and both without a booster

[Gary57]

How does the sx master cylinder work?? Does it deliver different pressures to front and rear, would think it would?! On Ferarri's, Lamborghini's, most high end italian cars have adjustment screws on the master cylinders to deliver different brake bias depending on the driving conditions and style.

[veecee]

On Ferarri's, Lamborghini's, most high end italian cars

i'm so glad you didnt say alfa!!!

[Gary57]

i'm so glad you didnt say alfa!!!

Oh ja some Alfa's too.

[Hennie Marais]

There's a brake proportioning valve build into the master cylinder.

[Gary57]

Is this valve adjustable?? Anyone have a pic of one??

[Hennie Marais]

not from what I can remember, maybe if you disasemble it and mod it.

[Vlade]

IIRC there is some adjustment you can make to the booster the guys talk about it when you do a full Z32 conversion the stock master cylinder is a little small to cope, so one can adjust the booster to make it feel less mushy...

[Gary57]

Do you know how Vlade??

[Vlade]

not really from what I can remember they talk about a screw/nut or something at the back at the booster

[Gary57]

Must find that out cause the Z32 master cylinder are more scarce than the calipers.