Brake maths check...

[HRG]

Can someone check my maths and assumptions please, particularly the bit about ratios.

I'm trying to calculate some mechanical braking ratios. Basically I've upgraded my front brakes to larger four pots and I want to check the rear upgrade I'm planning is sane. I'm using the same rear caliper just mounting it further from the hub with larger discs. I'm not doing any hydraulic calcs as the cylinders are the same and I don't have any values for them anyway.

To calculate original braking force:

AxB/C

Where:
A is the area of the brake piston
B is the distance to the centre of the piston
C is the distance from the ground to the centre of the hub (I've measured with the weight of the car on the tyres)



So, my very vague maths (with working out as I'm pants at it!) is below

Original front piston diameter 58.5mm
Original distance to ctr of caliper 109mm
original ground to ctr of wheel 290mm

Area of piston = (pi r2) x2 ((58.5mm /2)2 * 3.142) *2) = 5320.664

To calculate original braking force:

AxB/C

A) 5320.664
B) 109mm
C) 290mm

Original front braking force = 1999.835

Current front piston diameter(s) 40 mm & 32mm
Current distance to ctr of caliper 116mm
Current distance to ctr of wheel 290mm

Large piston (pi r2) x2 ((40mm /2)2 * 3.142) *2) = 5026.52
Small piston (pi r2) x2 ((32mm /2)2 * 3.142) *2) = 1608.48

A) 6635
B) 116
C) 290mm

Current front braking force = 2654


Original rear piston dia 40mm
Original distance to ctr of caliper 119mm
Original ground to ctr of wheel 315mm

A) Area of piston (pi r2) x2 ((40mm /2)2 * 3.142) *2) = 2513.274
B) Distance to ctr of caliper 119mm
C) Distance to ctr of wheel 315mm

Original rear braking force = 949.459


Therefore the original ratio was 949.459 to 1999 or approx 2.1054:1 front bias
I believe my current ratio is 949.459 to 2654 or 2.79527:1 front bias


Proposed Rear with 300 mm disc:


A) Area of piston (pi r2) x2 ((40mm /2)2 * 3.142) *2) = 2513.274
B) Distance to ctr of caliper 130mm
C) Distance to ctr of wheel 315mm

Proposed rear braking force = 1037.11

Which I believe will give a 2.559:1 front bias.




Am I right??

[HRG]

That's what I thought

[HRG]

rejn said:

HRG said:

Am I right??

um no - I don't think so (but I'm not an expert) - too many variables not included within your calcs - including size and efficiency of both pad and disk, etc.

Also, I can't believe that the height from the ground is that vital - otherwise wouldn't car manufacturers put the calipers at the bottom of the disk, not the middle?

As I say, I'm not an expert, but just a reasonable mathematician.

HTH,
Richard.

[edited to say - oops, just re-read what you said, and it's height of hub you mention - I still don't think that's vital, but obviously makes mounting point of calipers irrelevant]

Edited by rejn on Thursday 9th October 13:54

C is what resists AxB if I understand my lever theory, which is all this is? I know there's loads of other factors which will influence overall stopping distances, however they are all remaining constant for the purposes of this.

[HRG]

GreenV8S said:

OJ said:

GreenV8S said:

OJ said:

Oh and to add, if you're that worried about it, just fit a brake bias valve. Job's a goodun.

Sorry to contradict again but no, no it isn't. You need to set the static and dynamic brake balance and a bias valve will not do both.

Can you clarify that for me?

The theoretically ideal brake balance requires a curved relationship between front and rear braking, corresponding to the weight transfer that occurs under braking. The goal is to produce a brake system that is reasonable close to that ideal curve under all conditions from light to very hard braking.

At low levels of braking the weight transfer is negligible and the balance is determined purely by the hydralic/mechanical leverages through the system. This is termed the static brake balance. You can tweak this by changing caliper sizes, moving calipers towards/away from the hub, with twin m/c setups you can alter the m/c sizes or use a balance bar to vary the mechanical relationship between the two m/cs.

As the amount of braking is increased the linear relationship defined by the leverages needs to be modified to produce a curve. Usually this is done very crudely by putting a regulator valve in the rear circuit that allows the rear brakes to see full line pressure up to a certain limit (1:1) and then restricts the rear flow above that limit (1:3 is typical). If you plot the front versus rear line pressures you get a line with a kink in it. As long as this kinked line stays fairly close to the theoretically ideal curve, the brakes will be more or less balanced OK. To achieve that you need to set the mechanical leverages up to give the right distribution under light braking, and then use a bias valve to introduce the 3:1 kink at the right point.

Edited by GreenV8S on Thursday 9th October 14:49

I believe you are very familiar with the AxB/C theory as it came from The Bible

Rear caliper is the same, I'm just relocating it further from the centreline of the hub.

According to my (possibly very suspect) maths

The original ratio when it left the factory was 949.459 to 1999 or approx 2.1054:1 front bias
I believe my current ratio with four pots is 949.459 to 2654 or 2.79527:1 front bias

If I upgrade the rear it will give a 2.559:1 front bias.

It's a Griff, so I don't really want to restore the original bias...