Brake maths check...
Discussion
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??
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 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
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
Forget braking force at the ground its irrelevant.
The actual braking 'force' depends purely on the friction coefficient of the pads and the pressure being applied to it. You wont be able to get the friction coefficient of the pads (its highly dynamic anyway), therefore the only thing you need to worry about is brake pressure.
Therefore, I think all you need to worry about is any change in hydraulic areas, as this will significantly change the proportion of force from front to rear. I.e. If you have a much bigger slave cylinder area at the front, the braking pressure will be lower and the bias will shift rearwards (check this as i'm a little rusty on my hydraulic principles!). Many people who put big brakes on their cars complain of squishy pedal feel, as the master cylinder is still the same size.
You increase the size of the brake to increase the contact area and thus reduce brake temperatures. This means you can fit 'softer' pads to increase the friction coefficient if you want, or increase brake endurance with the same pad material. You increase the number of pistons to allow for even braking pressure over larger pad area, again reducing temperatures.
Bigger brakes don't automatically mean 'more force'. A car with standard stoppers can stop just as quickly as one with massive brakes if they have the same pad material and braking pressure applied, the difference is the big braked car will be able to do it more than once.
If you were being fussy then you could take into account the change in braking torque by the increase in brake diameter, but realistically there's no need.
The actual braking 'force' depends purely on the friction coefficient of the pads and the pressure being applied to it. You wont be able to get the friction coefficient of the pads (its highly dynamic anyway), therefore the only thing you need to worry about is brake pressure.
Therefore, I think all you need to worry about is any change in hydraulic areas, as this will significantly change the proportion of force from front to rear. I.e. If you have a much bigger slave cylinder area at the front, the braking pressure will be lower and the bias will shift rearwards (check this as i'm a little rusty on my hydraulic principles!). Many people who put big brakes on their cars complain of squishy pedal feel, as the master cylinder is still the same size.
You increase the size of the brake to increase the contact area and thus reduce brake temperatures. This means you can fit 'softer' pads to increase the friction coefficient if you want, or increase brake endurance with the same pad material. You increase the number of pistons to allow for even braking pressure over larger pad area, again reducing temperatures.
Bigger brakes don't automatically mean 'more force'. A car with standard stoppers can stop just as quickly as one with massive brakes if they have the same pad material and braking pressure applied, the difference is the big braked car will be able to do it more than once.
If you were being fussy then you could take into account the change in braking torque by the increase in brake diameter, but realistically there's no need.
OJ said:
Forget braking force at the ground its irrelevant.
No, it's critical. Everything else is just a means to work that out.Haven't bothered to check the arithmetic, but can you confirm you're keeping the same basic caliper type (not changing from floating to fixed or anything like that)? If you have changed the overall leverage of the front brakes then you will be working at a different line pressure which means that the brake bias valve is probably now wrong. How wrong, and whether this is a problem, will depend on how far you're changing from standard. There's quite a bit of tolerance in the brake balance and it doesn't need to be perfect to three decimal places, but was the balance more or less right originally before you did any upgrades? If so that's a sign that you should be aiming to restore the original balance.
GreenV8S said:
OJ said:
Forget braking force at the ground its irrelevant.
No, it's critical. Everything else is just a means to work that out.GreenV8S said:
There's quite a bit of tolerance in the brake balance and it doesn't need to be perfect to three decimal places, but was the balance more or less right originally before you did any upgrades? If so that's a sign that you should be aiming to restore the original balance.
How can one tell if brake bias is too much towards the front?What are the symptoms?
(Just curious, as I go through front pads on track, but never rears...making me think my balance could be something daft like 90F:10R.)
Get Karter said:
GreenV8S said:
There's quite a bit of tolerance in the brake balance and it doesn't need to be perfect to three decimal places, but was the balance more or less right originally before you did any upgrades? If so that's a sign that you should be aiming to restore the original balance.
How can one tell if brake bias is too much towards the front?What are the symptoms?
(Just curious, as I go through front pads on track, but never rears...making me think my balance could be something daft like 90F:10R.)
Only start worrying if
A) You start getting brake fade or
B) You lock either the front or rear wheels very easily. Ideally you want the front and rears to lock at almost the same time, although in reality this is difficult to achieve. A slight variation on this balance can be used to alter the balance of the car on corner entry.
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.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
So basically, I should have stopped at the end of my first post 
But surely at light pressures its only really a road driving brake and pedal feel issue though, rather than one of actual balance, and that the relatively light forces involved you'd have to make some pretty big changes to make an appreciable difference?
I would have thought for safety purposes only the top end of the pressure spectrum really matters? I suppose you could argue that if you really stamp on the brakes then you'd be more likely to lock the front wheels if the static bias was towards the front
But surely at light pressures its only really a road driving brake and pedal feel issue though, rather than one of actual balance, and that the relatively light forces involved you'd have to make some pretty big changes to make an appreciable difference?
I would have thought for safety purposes only the top end of the pressure spectrum really matters? I suppose you could argue that if you really stamp on the brakes then you'd be more likely to lock the front wheels if the static bias was towards the front
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