Bleeding brakes

[Fozzy48]

Ok guys, I'm here again. I've made a new brake pipe up and fitted it. My RS2000 has cosworth calipers on the back with cosworth handbrake cable. My good lady wife sat in the car and pumped the brakes for me as I bled away working from the furthest away from the master cylinder. Although the brakes work, the pedal is going right to the bottom, although if I pump it a bit it comes to about a quarter of the way up but then goes back to the bottom. The handbrake works ok. It seems to me that the pistons arn't self asjusting up and staying open. So what have I done wrong and is there a procedure to getting the pistons to self adjust. 

Cheers

Fozzy

[DT36]

If your pistons are stuck out, then you would eventually still build up pressure by adding fluid to fill this space. Do you have any rubber brake hoses on your system that you can Clamp off? 

If so, then this might help to isolate where you are getting your pressure loss. 

[Fozzy48]

9 minutes ago, dt36 said:

If your pistons are stuck out, then you would eventually still build up pressure by adding fluid to fill this space. Do you have any rubber brake hoses on your system that you can Clamp off? 

If so, then this might help to isolate where you are getting your pressure loss. 

I have since rebled the system as there was a very slight leak on the T piece on top of the diff housing, that is now ok and its bled better. I took the OS rear wheel off to look at the piston. It was out behind the the pads so that to me looks like it's adjusted out as it should. As for the NS rear,  I don't know as I'd had enough by this time and went home. Was just chatting to a mate and he thinks that as it's all new it will have to bed in, pads onto discs etc.

I'll have another look in the next day or 2 as I've got to make a new handbrake rod from the lever bottom. 

Cheers.

Fozzy

[katana]

Just out of interest are you using the Original RS 2 master cylinder or is there a bias pedal box fitted? If the former that's the reason for the long pedal - no amount of bleeding will cure it!

[Fozzy48]

1 hour ago, katana said:

Just out of interest are you using the Original RS 2 master cylinder or is there a bias pedal box fitted? If the former that's the reason for the long pedal - no amount of bleeding will cure it!

That's interesting mate, yes I am using the original master cylinder. 

So why is this. ?

I have considered putting a bias box on and may have in the future.

Will the set up I have at the moment pass it's test.?

Thanks bud.

Fozzy

 

[DT36]

The surface area of the pistons in the disc calipers is now greater than what you had in the original wheel cylinders.  Therefore, the displacement of fluid from your master cylinder is still the same, but that displacement now needs to deliver more volume of fluid. 

... or something like that 

[Fozzy48]

10 minutes ago, dt36 said:

The surface area of the pistons in the disc calipers is now greater than what you had in the original wheel cylinders.  Therefore, the displacement of fluid from your master cylinder is still the same, but that displacement now needs to deliver more volume of fluid. 

... or something like that 

Cheers buddy. Well it looks like I'm going down the road to buying a bias pedal box. One bloody job leads to another. 

Fozzy

[DT36]

2 minutes ago, Fozzy48 said:

Cheers buddy. Well it looks like I'm going down the road to buying a bias pedal box. One bloody job leads to another. 

Fozzy

You'll still achieve good pressure at the pads. Just means you got to push a bit harder on the whoowers. 

Maybe hang fire for now and see how it feels when all set up. 

[Fozzy48]

I was running it without servo help for a while when the servo went knackered and didnt find it too bad. I need to get it tested first and then we're moving to lincs, so the pedal box will have to wait anyway mate. If I can get it through test as is, then I'll be happy.

Cheers. 

Fozzy

[colr6]

Just a quick read for you Ian to sort your brake problem out, let me know when you've worked it out.

• Home » 
• Knowledge Center » 
• Brakes » 
• Master Cylinder Math

MASTER CYLINDER MATH

Going faster creates a need for stopping faster. Efficient braking is based on choosing the right components and matching the proper combinations will result in a brake system that works in conjunction with the specifics of your car, track and driver style. It is highly recommended that you work with your brake company engineer to assist you in building the right combination to tailor a system for your application. Since pad compound, rotors, calipers and master cylinders all work together in relation to car weight, speed and track characteristics, it makes sense to think of your brake system as a package. Each brake component relates to the other braking variables and an individual change may necessitate the need to reanalyze your entire brake system in your effort to achieve a balanced clamping force on your car. 

We contacted long time brake expert Carl Bush from Wilwood engineering to help our readers understand the brake system. While I encourage you to consult your brake company engineer to build the right braking system, I also encourage you to learn how the parts interrelate. With your own knowledge base, education will allow you to better communicate your needs resulting in the best brake system possible.

• Billet Clamp on Reservoir Mount

  A Billet Clamp On Reservoir Mount allows you to mount your brake fluid reservoir at a high point resulting in improved brake bleeding. Remote mounting keeps unwanted heat away from your brake fluid. 

• Q: How do you pick the proper master cylinder?

   

  Carl Bush: 
  Master cylinders are an integral component in the brake system. They are responsible for sending the correct amount of pressure and balance to the brake calipers. But it must be remembered that they are only one component in a system, and do not function alone. Brake requirements for different types of race cars will vary by component and element. But all systems do carry a common thread. They must allow the driver to stop the car with comfortable leg effort while contributing to the overall handling and performance of the car. 

• Q: How do master cylinders work?

   

  Carl Bush: 
  A master cylinder is used to convert force from the brake pedal into the hydraulic pressure that operates the brake calipers. The amount of pressure generated is a function of the force being applied, divided by the master cylinder bore area. A 1” master cylinder has a bore area of .785” inches squared. For every hundred pounds of force applied to the master cylinder piston by the pedal pushrod or balance bar, that master cylinder will generate pressure equal to 100 divided by .785 or 127.4 PSI. By calculating the area in inches squared (bore x bore x .785”) for any master cylinder size, you can calculate how much pressure change would be affected by a bore size change. 

  A 7/8” bore master cylinder has a bore area of .6” inches squared. If we apply that same 100 pounds of force to the 7/8” master cylinder, using the formula 100 divided by .6, that same 100 pounds of force from the pedal will generate 166.7 PSI. A decrease in master cylinder bore area produced a proportionate increase in line pressure. This line pressure management becomes a key factor in setting brake balance. 

• Master Cylinder bore size

  Master Cylinder bore size is the element that affects pressure

• Math Explained

  Carl explains that a 1” Master Cylinder has a bore area of .785” squared. To get to this number you use the formula for Area which is: Area = 3.14 (Pi) multiplied by the radius squared. So you calculate the radius of 1” bore which is simply half of the diameter which equals .5” (half an inch). The result is that a 1” master cylinder has a radius of half an inch. You then multiply your radius which is a half an inch (.5) by itself so .5” X .5” = .25” or a quarter of an inch. .Multiply .25 X 3.14 (pi) and you arrive at Carl’s .785” area number. Basically, I just repeated what Carl said in an effort to make the math more simple and I bet the barrage of numbers made the calculation more intimidating and confusing? It’s ok – we will get to a simple way to look at the master cylinder math and going through the steps will make the process easier to understand.

  Another way to explain Carl’s math uses a 7/8” master cylinder as the example. We will do the calculation and show our work to reinforce the math for calculating bore area.

  Bore = 7/8” 
  7 divided by 8 gets us the decimal equivalent = .875”
  The Radius is .875” divided by 2 = .4375”
  .4375” Multiplied by .4375” (Squared) = .1914” 
  .1914” Multiplied by (Pi) 3.14” = .6” - which is the answer Carl explained above.

  With the progression towards understanding the math we can do take the steps the easy way. Use Carl’s magic formula of Bore X Bore X .785” (.785 is the magic number that simplifies the above equations as it simply pre-calculates the squared business relating to Pi in advance). So a 7/8” bore is .875” X .875” X .785” = .6” Bore Area. It turns out you can use the number .785” and multiply it by ANY Bore X Bore as the reusable number of.785” is a derivative of Pi and it is a repeatable math number that can be used with any and all bore sizes. So, the complicated math shown relating to Master Cylinder Bore Area can be simplified. Now we have taken another step towards understanding.

  Bore X Bore X .785” - you can always use .785” in the equation.

  Let’s check with the Easy 1, 2, 3 method:

  For an example 7/8” Bore master cylinder the Bore Area math is:

  • Step 1 – Convert the fraction Bore to a decimal by dividing the bottom number in the fraction into the top number.
    • 7 divided by 8 = .875”. 7/8” is the bore marked on the outside of the master cylinder and .875” is the decimal bore equivalent of 7/8”
  • Step 2 – Multiply the bore diameter (our example is .875”) by itself which is the same as bore squared.
    • .875” X .875” = .766”
  • Step 3 – Multiply the bore squared result from step 2 (.766) by the reusable number (always .785 with every master cylinder size – you can count on .785 to work every time with every master cylinder size).
    • .875” X .875” = .766
    • .766 X .785” = .6
    • .6 is the Bore Area for a 7/8” Master Cylinder!
  • The EASY 1, 2, 3 Bore Area calculation is right here!

  Our example was for a 7/8” master cylinder. Now you can use the bore size on your car and substitute your actual numbers to come up with your Bore Area, front and rear, by following the 1,2,3 calculation above. Now that we have our Bore area numbers of .6 for a 7/8” master cylinder and .785” for a 1” master cylinder what do we do next? Carl states that a smaller master cylinder bore creates more pressure with an equal amount of force. A 1” master cylinder creates 127.4 PSI as compared to a 7/8” master cylinder which is 166.7 PSI based on your foot making 100 pounds of force at the master cylinder. It is important to consider that the smaller cylinder makes more pressure but the smaller bore will move less fluid. More travel will be needed to make up for the reduction in fluid moved by a 7/8” master cylinder as compared to the larger 1”. Carl explains further in the next section.

• Caliper Mount

  Utilizing a bolt on caliper mount ensures that your calipers are square to the rotor improving pad wear and braking efficiency.

• How do fluid volume and leverage come into play?

   

  Carl Bush:
  While a change in master cylinder bore size affects a pressure change, it also changes the amount of pedal travel realized to add the additional stroke needed to displace enough fluid to move the caliper pistons. This volume ratio plays an important role in the clamping capability of the caliper, and leverage that the driver has to generate that clamping force. The ratio between the caliper and master cylinder is a function of the net effective caliper piston bore area divided by the bore area of the master cylinder. To compare these ratios and do the calculation, you must start with the total piston area of the pistons in one side of one caliper.

  A front brake set using four piston calipers with 1.75” diameters will have a net bore area of 4.8” inches squared as each 1.75” diameter piston has an individual bore area of 2.4” inches squared.

  Jeff’s Easy Math works for caliper piston bores too – 1.75” X 1.75” = 3.06” X Reusable Number .785” = 2.40” X 2 Pistons = Carl’s Net Bore Area of 4.8”

  Carl Bush - Continued

  By running the formula, the leverage ratio between a 7/8” bore master cylinder and the 1.75” four piston caliper will be equal to:

  Effective Caliper Piston Area (4.8) / Master Cylinder Bore Area (7/8 which is .6) =
  4.8 / .6 = 8 for an 8:1 ratio

  The driver leverage is then determined by multiplying the Pedal Ratio x the Caliper Piston Bore to Master Cylinder ratio. (Note from Jeff: “The pedal ratio is marked on your pedal assembly when you buy it or use the Pedal Ratio Drawing shown”)

  Carl's Example

  Pedal Ratio (6:1) x (Piston Bore (4.8) / Master Cylinder Ratio (.6) results in (8) = Driver Leverage (48:1) 
  6 x (4.8 / .6) = 48:1

  You can substitute any number of piston bore combinations with master cylinder sizes with any pedal ratio to determine the driver’s actual brake leverage.

  For fun Carl has given you the answer to the test with this chart.

   

  Common Caliper Piston Size Diameter / Area

  Diameter, Inches	1.12	1.25	1.38	1.62	1.75	1.88	2.00	2.38	2.75	2.94
  Area / Piston, Inches	0.99	1.23	1.48	2.07	2.40	2.76	3.14	4.45	5.94	6.78

   

  Common Master Cylinder Bore Sizes / Area

  Diameter, Inches	0.62	0.75	0.81	0.88	1.00	1.12
  Area / Piston, Inches Sq.	0.31	0.44	0.52	0.60	0.79	0.99

   

  By changing to a 7:1 ratio pedal (from the 6:1 shown in Carl’s Example), the driver would then realize a final ratio of 56:1 with the same caliper and master cylinder (Jeff’s math 7 x (4.8 / .6) = 56:1). Consequently, a 5:1 pedal would only give the driver a 30:1 ratio (Jeff’s math 5 x (4.8 / .6) = 30:1). If we compare the front leverage ratio to the rear leverage ratio on any given car, this tells us the front to rear static bias capability of the car.

   

  

  A = Distance from pivot point to middle of push / pull point

  B = Distance from pivot to point of push on master cylinder

  P = Pivot point

  F = Force or push

  Pedal Ratio is determined by dividing length "A" by length "B". The amount of force at "F" determines the force to the master cylinders

• Now that we know the math, can you explain a common set up for our readers?

   

  Carl Bush:
  A common set up that could be found on a weekly show short track asphalt car is to use the example above with 1.75” piston calipers on the front with a 7/8” bore master cylinder, and a pair of 1.38” piston calipers on the rear with a 1” master cylinder. A 6:1 floor mount pedal ratio is also common. We have already determined that the 1.75 pistons with a 7/8” master cylinder and a 6:1 pedal will give the driver an overall brake leverage of 48:1 on the front. If we use the same formulas with the 1 3/8” piston calipers and 1” master cylinder on the rear, that produces a total driver’s rear leverage ratio of 22.75:1. When we compare the 48:1 ratio in the front, to the 22.75:1 ratio in the rear, we see that the car will be baselined with a front to rear static leverage bias of 67.8%, as long as the balance bar is centered and equal force is being applied to both master cylinders. You can substitute any combination of parts and their sizes to determine the exact influence they will have on the baseline static bias ratio.

• Four piston calipersFour piston calipers can usually be found with piston sizes from 1.125" to 1.875". The area of two pistons on one side of the caliper determine the calipers influence on clamping capability.
• How do we use pressure to determine brake bias?

   

  Carl Bush:
  Although racing with a perfectly centered balance bar is the ideal goal, it seldom happens in reality. Besides, one of the advantages in using an adjustable balance bar is having the ability to adjust that leverage to optimize handling and driver comfort on track. Trying to measure the post-race leverage split at the balance bar is difficult and unrealistic. However, using pressure gauges to measure pressure differentials s at any given balance bar setting is relatively simple. The brake gauges will show the actual pressure split in the car based on the balance bar adjustments made by the driver. Those pressures can then be multiplied by the effective caliper piston bore areas to calculate the last on-track static bias settings.

  Going back to our (common setup) example, if we apply 50 pounds of leg force against a 6:1 pedal, we will generate 300 total pounds of force against the balance bar. If the balance bar is perfectly centered, it will distribute that force equally to each master cylinder. With each master cylinder receiving an equal force amount of 150 pounds, the 7/8” master cylinder should produce 250 PSI (Jeff’s math: 250 PSI comes from 150 divided by .6 which is the 7/8” master cylinder math result) while the rear 1” master cylinder produces 192 PSI (Jeff’s math: 192 PSI comes from 150 divided by .785 which is the 1” master cylinder math result). In practical use of gauges, you can use any level of effort and pressure for your comparisons. The end result will be the same.

  When the front pressure of 250 PSI from the 7/8” master cylinder is multiplied by the 4.8” inches of caliper bore area of the front 1.75” piston front calipers, we get a front clamping force of 1200. On the rear, we will have 192 PSI x 2.97” caliper area or 570 pounds of rear caliper clamping force. When comparing the these front to rear clamping force total in the same way you would compare wheel weights for balance, we would see that this car has a total of 1770 pounds of caliper clamping force at these line pressures with 1200 pounds or 67.8 % on the front. It’s that same static bias ratio that was measured using the overall driver leverage ratios.

  Now, if every car and driver had the same braking requirements and pedal feel preferences, we would never need to adjust anything. But, every car and every driver are unique and adjustments will get made.

  The ratio examples that have been used here are very common in many short track asphalt cars. But your car, for a wide variety of reasons, may have quite different requirements. As a racer or crew chief, you can use these formulas to map the existing brake setup on your own race car, and then make calculated decisions when the desired handling or driver feel isn’t being delivered. The inability to reach the desired bias or driver’s feel of the pedal is the indication you will need to evaluate your component selection and consider possible alternatives. By using the formulas in these examples, you can accurately calculate what affects a component change will make to your existing baseline, and record those final ratios in your records to use for future adjustments and set up for any given track type or conditions.

• Metric CaliperCalipers such as this metric replacement only have one piston on one side. The calculation of their clamping capability still uses the same formula.
• ClosingAs you can see, using the experience of you brake manufacturer is very valuable. Still, when you breakdown the math it is not all that hard. By understanding the pressures, bore areas and ratios you can improve your understanding of the brake system. A thorough understanding will help you to make improvements to an existing car or transfer learned knowledge to a new car. Be taking the time to understand the basic math behind the braking system you can calculate and record winning brake set ups. Slowing down to do the math will help you to go fast.

Go Forward – Move Ahead 
Jeff Butcher 
Courtesy of JOES Racing Products 
3/1/11

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[colr6]

As DT 36 said it's something like that, well above is just THAT !!......lol

[Fozzy48]

I won't quote the thread bud, as it's taken up enough of this page as it is. I've started to read it and will keep coming back to it everyday for the next fortnight. 

Cheers bud.

Fozzy

[johnnyspencer]

I always bleed from the closest first.

[Fozzy48]

2 hours ago, johnnyspencer said:

I always bleed from the closest first.

Really?, not as far as I know mate. I've not bled brakes since I had an escort in the 80s-90s and I always bled from the furthest away, same as central heating radiators. I'm happy to be proven wrong.

Anyway, a bit of an update. Got speaking to a mate of mine who put a rover V8 into an escort in the mid to late 90s. He put a 2.8I capri axle on it and bought a disc conversion kit. He's just told me that the recommendation was to uprate the master cylinder to a landrover one which he did, as they have a bigger piston so can push more volume behind the caliper pistons. His brake pedal was at the top from the off and had no trouble, so looks like the way forwards. 

Cheers.

Fozzy

[katana]

Bleed furthest first is correct.

The Landy's have choice of 0.75", 1.0" and 1.125" bore cylinders and indeed will pass more fluid per stroke but the pressure at the pistons will be lower compared to std!

So, as its a single common system, the reduced pressure may not lock the rear's but could give less braking at the front which isn't what you want. Not sure what the std cyl bore is on the Escort but I believe it's 0.75".

[Fozzy48]

It will have been 86-91 landy master cylinder he used, but he's at work ATM so waiting for him to confirm. 

How can the pressure behind the pistons be less than std with more pressure ability from the master cylinder.?

It's a dual braking system. 

I can fully understand how uprating the cylinder size works. It makes common sense to me that if you increase the amount off fluid behind something then you need to uprate the pressure ability to push it.

Cheers.

Fozzy

[DT36]

It can be a minefield, Fozzy.

Pressure and flow are not the same. Think about a doris being about 9st in weight. If she stood on your chest in her slippers, it would probably be bearable. 

However, if she puts her stilettos on and stands on your chest, then it's gonna feck in hurt ?  The same weight is now being exerted through a much smaller cross sectional area. So, the pressure coming through the heel is much greater, even though the same weight is (9st) is stood on you. 

Hopefully this makes sense? Oh, and picture her in a nice red set too... ?

[Fozzy48]

23 minutes ago, dt36 said:

It can be a minefield, Fozzy.

Pressure and flow are not the same. Think about a doris being about 9st in weight. If she stood on your chest in her slippers, it would probably be bearable. 

However, if she puts her stilettos on and stands on your chest, then it's gonna feck in hurt ?  The same weight is now being exerted through a much smaller cross sectional area. So, the pressure coming through the heel is much greater, even though the same weight is (9st) is stood on you. 

Hopefully this makes sense? Oh, and picture her in a nice red set too... ?

So what you are saying is that as it is at the moment i am creating more pressure with a smaller diameter cylinder.?

I have to say I'm still not convinced bud.

What about if a weedy little shite tries to push a great big bloke against a wall for a knee trembler.  He can't do it cos he ain't got the power. But if the big guy tries to push the weedy little shite up against the wall for a knee trembler then he's in deep shite. 

Red little number, mmmm. 

Cheers.

Fozzy

[DT36]

In hydraulic terms it's called a Force Multiplier. 

Probably the best thing to do is to leave it as is. See how it fares on the brake tester during the MOT. 

As for the 2 blokes getting pally in the ally, I think we're going down the realms of power to weight ratio ???

[Fozzy48]

44 minutes ago, dt36 said:

In hydraulic terms it's called a Force Multiplier. 

Probably the best thing to do is to leave it as is. See how it fares on the brake tester during the MOT. 

As for the 2 blokes getting pally in the ally, I think we're going down the realms of power to weight ratio ???

Well my mate at local garage says as long as pedal doesn't bottom out and it brakes as it should then that's what matter.

Cheers mate.

Fozzy

[mk2dk]

Hi Fozzy.

I've had the same problem.  Try to loosen the tension on the handbrake cable until the small arms on both calibers are fully returned, against their stop screws. Then drive the car and use the brakepedal several times to help the piston adjustment against the pads. After that re-adjust the handbrake cable. Solved my problem.

mk2dk

[Fozzy48]

2 hours ago, mk2dk said:

Hi Fozzy.

I've had the same problem.  Try to loosen the tension on the handbrake cable until the small arms on both calibers are fully returned, against their stop screws. Then drive the car and use the brakepedal several times to help the piston adjustment against the pads. After that re-adjust the handbrake cable. Solved my problem.

mk2dk

Hi mate, you have brought up a valid point that I need to do. On initial testing the handbrake was a bit too kean. I was going to take some of the tension off it but the rod from the handbrake to the cable broke. So at the moment I've ordered a new rod which will be here this next week and then I can have another go a setting it up. 

Cheers bud. 

Fozzy

[johnnyspencer]

17 hours ago, Fozzy48 said:

Really?, not as far as I know mate. I've not bled brakes since I had an escort in the 80s-90s and I always bled from the furthest away, same as central heating radiators. I'm happy to be proven wrong.

Anyway, a bit of an update. Got speaking to a mate of mine who put a rover V8 into an escort in the mid to late 90s. He put a 2.8I capri axle on it and bought a disc conversion kit. He's just told me that the recommendation was to uprate the master cylinder to a landrover one which he did, as they have a bigger piston so can push more volume behind the caliper pistons. His brake pedal was at the top from the off and had no trouble, so looks like the way forwards. 

Cheers.

Fozzy

no your right, sorry I was pi**ed!

[Fozzy48]

3 minutes ago, johnnyspencer said:

no your right, sorry I was pi**ed!

No problem buddy. 

ATB

Fozzy