TheSamba.com :: View topic

Sun Mar 07, 2010 1:29 am

When you increase the bore of the master cylinder you decrease the available pressure applied at the calipers or wheel cylinders.

Hopefully we can clear up some of the myths and perpetuation of falsehoods.

P=F/A Where P=Pressure. F=Force applied multiplied by the distance from the centerline of the master cylinder to the pedal. A=Surface Area of the Master cylinder piston that is applying the pressure to the fluid.

The Master cylinder piston is a circle that pushes against the fluid. The area of a circle is the Square of it's Radius multiplied by pi.

Lets break this down. D=Diameter, R=Radius A=Area

D=17 mm R=8.5 mm A=227 sq. mm or 0.352 sq. in

D=19 mm R=9.5 mm A=283.5 sq. mm or 0.439 sq. in

D=23 mm R=11.5 mm A=415.5 sq. mm or 0.644 sq. in

As an example, if the Driver exerts 20lbs of force on a pedal 5" from the centerline of the fulcrum/Master cylinder bore we arrive at 100lbs of pressure to the MC. Pivot is one inch below the centerline and the pedal is 5 inches above. This provides the 5to1 ratio I used.

Therefore when we divide the Force by Area we arrive at: D=Diameter, C=F/A, P=Pressure.

D=17mm C=100 lbs/0.352 sq. in P=284 psi

D=19mm C=100 lbs/0.439 sq. in P=228 psi

D=23mm C=100 lbs/0.644 sq. in P=155 psi

Therefore to increase pressure we must reduce the bore of the master cylinder. There is of course the rule of diminishing returns wherein the stroke of the master cylinder can come into play.

However at the far end we have the Calipers or Wheel cylinders. This brings us a new equation to consider.

F=P/AWhere again P=Pressure. F=Force applied multiplied by the distance from the centerline of the master cylinder to the pedal. A=Surface Area of the Master cylinder piston that is applying the pressure to the fluid.

This is where you must determine the force applied to the brake pads based on the piston size of your caliper or wheel cylinder. Just for giggles lets see how this works out with three different piston sizes. We'll use 38mm, 42mm, and 48mm. CP=Caliper piston size, A=Area of piston MC=Master cylinder bore, F=Force applied to the brake pads.

CP=38mm A=1.75sq.in MC=17mm F=497lbs MC=19mm F=399lbs MC=23mm 271lbs

CP=42mm A=2.15sq.in MC=17mm F=611lbs MC=19mm F=490lbs MC=23mm F=333lbs

CP=48mm A=2.80sq.in MC=17mm F=795lbs MC=19mm F=638lbs MC=23mm F=435lbs

As you can see increasing the piston size on the Caliper end increases the force applied to the pads.

These are just two factors which should be considered when changing your car to disk brakes. This of course does not go into the swept area of the disc nor the effective area of the pad. If you do not plan carefully you can end up with brakes that lock your wheels at the lightest tap or that will not stop you at all.

There is no knee jerk response to this. These are your brakes people. You can screw this up and kill yourself or worse someone else. Talk to whomever you are buying these parts from and ask the questions. Do the math yourself and decide where you want or need to be. Do not assume just because you see a "kit" offered the seller took any of this into consideration. ASK them for the numbers. It's your damn money and they need to prove themselves worthy of your business.

If you wish to read a little more on the subject there are two worthy items here.

http://www.tpub.com/content/engine/14105/css/14105_22.htm

http://www.tpub.com/content/engine/14105/css/14105_23.htm

Sun Mar 07, 2010 12:32 pm

While I agree that your math may show one thing, I have to say I disagree with the idea that a larger bore master cylinder degrades braking performance.
My example for this, although not VW, is a real life example of hydraulic braking performance problems, and factory fixes. In my fleet of trucks that I maintain at work there are several mid 90's Ford F series pickups ranging from F150's to F350's. They all employ the same braking system (booster, master cylinder, calipers and wheel cylinders) with the expection of the size of the rotors/pads and drums/shoes. The 250's and 350's have slightly larger diameter rotors/drums to accomodate the higher payload capacity of the trucks. The calipers are interchangeable between all of the trucks (we only keep one of each side in stock for all the trucks).
On all of the trucks we have had the problem of lack of braking action, requiring all of the operators to have to exert more than normal pressure on the pedal to get the vehicle to stop, most would not lock up the wheels with stomping of the pedal. After many hours of troubleshooting and research we discovered that the direct replacement part number for the master cylinder we had been using, had been superceded by the factory at a later date with an updated master cylinder. They increased the size of the bore 1/8". We ordered the updated part number and installed the new master cylinder on one of the trucks to test the difference as we were at a loss as to the answer to our problem (the trucks normally operate at about 3/4 payload capacity all the time so the brake components are being worked hard compared to an empty pickup). With no other changes, the increased bore master cylinder solved our braking troubles on all of our fleet of f-series trucks. The pedal requires much less effort to slow the vehicle, and when stomped in a panic style manuever would lock the wheels up completely.

Your example does not take into consideration how much force is actually required to lock a wheel up at considerable speed. Most braking systems operate at the 1000psi+ range which according to your calculations can't be possible with any master cylinder bore sizes you listed. You also need to take into consideration the ratio of the master cylinder to the slave cylinders/caliper pistons for the hydraulic multiplication factor. In my braking system (very rough size estimates) the caliper pistons are twice the size of the master cylinder bore giving approximately 2x force multiplication (100 lbs input=200lbs output).
Another factor to consider is amount of free movement in the pistons before they start acting on the braking components. A properly adjusted and working braking system will have almost no piston free play before the pads and shoes start engaging their respective braking surfaces. With minimal free play, the hydraulic system will start building pressure early (remember no resistance=no pressure) which will equate to a higher pressure available (full stroke worth of pressure capability) versus a system not adjusted correctly, taking pedal travel to move the piston distance in turn not building pressure (lets say half the pressure capability of that piston).
My point is you have to look at the brake system as a whole. You cannot say that increasing the cylinder bore will do x change to system, without knowing the condition/sizing/requirements of the rest of the braking system to figure into the equation. Everything is dependent on everything else.
I personally believe that increasing master cylinder bore will increase braking ability because you are getting more fluid flow vs stroke, therefore minimizing the lost stroke on piston movement on the business end of the system. You will essentially begin building pressure quicker, therefore increasing the amount of pressure available, simply because you have more stroke to work with.

Sun Mar 07, 2010 2:30 pm

I have to side with Bobby on this one.

If the larger MC cured all the braking problems of your Ford fleet, you had a volume problem, not a pressure problem. In other words, the rear wheel cylinders weren't extending all the way to reach the drums with the original MC, or something like that.

If everything was working properly and you increase the MC bore, you will have to push a lot harder on the pedal to get the same braking as with the smaller MC.

Sun Mar 07, 2010 2:50 pm

Sorry but you had a volume issue not pressure which I briefly covered in my post. You also must understand I used a vague 5 to 1 ratio for the pressure to simplify the math. The brake pedal arm is obviously longer than 5 inches. Are the brakes in these truck vacuum or servo assisted? That would explain a lot.

I just found a nice calculator for those not wanting to do the math.

http://www.markwilliams.com/calculators.aspx

I hate to argue but the science I presented is sound and proven. This is not what I believe this is fact. The previous two links I provided laid it out in detailed yet simple terms.

Sun Mar 07, 2010 3:06 pm

Bruce wrote: I have to side with Bobby on this one.

If the larger MC cured all the braking problems of your Ford fleet, you had a volume problem, not a pressure problem. In other words, the rear wheel cylinders weren't extending all the way to reach the drums with the original MC, or something like that.

If everything was working properly and you increase the MC bore, you will have to push a lot harder on the pedal to get the same braking as with the smaller MC.

Yes and no. I fully agree that if the larger master cylinder solved the problem...its generally a volume issue. This same problem happens commonly when people move from drums to discs and are not careful on what caliper they choose. They end of going to something with much larger caliper bore volume and its a feed issue.

But....even though Bobby's calculations are correct...the usage is not quite correct. Yes...P= F/A or Pressure = force divided by unit area.
The issue is whether we are speaking of the force generator or the actuator that pressure is being used against.

So just for grins here is the use of Bobby's formula....if you have 20 lbs of force applied to a MC piston of 1" diameter you get 20/1= 20 psi. So...20 pounds of force with a 2"MC bore gets you 20/2= 10 psi. But bear in mind that the wheel cylinder or caliper bore did not change size
Going back to the actual calculated use:

F2 is the force created by the caliper or WC
F1 is the force applied to the MC piston
A1 is MC piston face area
A2 is WC piston face area

F2=F1 (A2/A1)

so lets say in the original bore: A2= 2" and A1= 1" F1= 20 lbs and F2=?

F2= 20 (2"/1") = F2=40 psi will be generated from this combination

So lets increase bore size: A2=2" (unchanged) A1= 2" (new) F1= 20 lbs (same) and F2=?

F2= 20 (2"/2") = F2=20 psi.

Though this would appear to bear you out...that the larger bore does decrease output...except that we know it actually increases volume.

The original uses of this formula were for the original hydraulic press (Bramah Press). It was about the small piston lifting the large piston...a prescribed distance at the given output and load pressure.

But since this is a dead end system...with no appreciable stroke gap on the actuating cylinder.....the 2" master cylinder piston in this case will need to move only half the distance at the same psi of applied leverage to generate the same output force as the 1" cylinder because it is moving twice the volume in half the space.

If we were trying to simply get the 1" piston to move (lift) a dead weight in a cylinder.....it would indeed produce more lifting force than a 2" piston face....but that is not what we are doing.

This is about confined volume. These are not exactly the same as a normal hydraulic cylinder in which volume supplies power and expansion. In this case it is strictly pressure rise by volume. I can't even remember the true correct calculations.
Remember also...that the correctly used larger cylinder...also has a longer stroke and a change in leverage point for the pedal.

I went to a bus 22mm cylinder on my 412 and the pressure change went from 800+ at the regulator to about 1050 psi...with everything else unchanged. Because of the longer stroke and volume capability...I changed teh pivot point to take advantage of that longer stroke.....so as the piston travels....I eventually surpass the force supplied by the 19mm cylinder without any appreciable change in leverage.

Again...I'm way out of practice to quote all of teh caluclations that make this a different application than just a hydraulic cylinder. It does gp to show that you must be very careful when calculating brake changes. Ray

Sun Mar 07, 2010 3:35 pm

Sorry volume does not equal pressure. Please show me the math that explains or proves your premise. Volume only comes into play when we are discussing travel.

To simplify this even further if you place a 5lb cone shaped object with a 5 sq.in base on a solid surface what is the psi? If you then invert this 5lb cone to a 1sq.in tip what is the psi now?

Sun Mar 07, 2010 5:52 pm

When speaking about brakes you do have to consider both volume and pressures.

I have to digress on one point, but on the flip side stand my ground when the equation is changed a bit.

Disc brakes require much less volume than drums, however they require more pressure to produce the same braking effort. In this situation going with a larger bore master cylinder and not changing pedal ratio will in fact reduce braking performance. This is the part I will admit I erred on and I digress to. Disc brakes WILL perform better with a SMALLER bore master cylinder.

Drum brakes however require quite a bit of volume to operate, but provide better braking at lower pressures. The increased volume of the larger master cylinder can be beneficial in this case, where less pedal travel is required to start the drum braking effort. Drum brakes CAN perform well with a LARGER bore master cylinder.

The point I was trying to make earlier is this:
With a smaller master cylinder bore, you have to move the piston in the bore quite a ways before the brakes actually begin to engage (a quarter of pedal travel lets say, leaving 3/4 pedal travel left to actually produce pressure), this is where the volume part of the equation comes into play. A system with all drum brakes is obviously going to be more effected by this than all discs.
When moving to a larger bore master cylinder, the braking effect begins with much less pedal travel (lets say 1/8 of the pedal travel, leaving 7/8 pedal travel to produce pressure) therefore offering the driver much more hydraulic fluid to work with (when volume stops:pressure builds, its the laws of hydraulics) when the pucker factor shoots through the roof.

Quote from Hot Rod magazine:
Generally speaking, if the master cylinder bore is too large, the driver will feel a very hard pedal feel with minimal pedal travel, and will have a difficult time generating the necessary pressure to effectively operate the brake system. If the master cylinder bore size is too small, the driver will be able to generate a lot of pressure, but the pedal may have an excessively long stroke or a very spongy feel. And if the bore size is way too small, the pedal or master cylinder may bottom out before enough volume is pumped to operate the calipers. The best advice would be to consult with the manufacturer of the brake system you will be using and work with them to pick the right size for your application.

So yes, in a situation where there is no physical movement of the working end of the hydraulic system, a smaller bore will provide more pressure immediately. When the movement on the working end is figured into the equation, the balance is moved a little closer to even because you essentially start building pressure sooner with more volume. If you can move the input piston farther, with more fluid being displaced by it, the potential to make pressure is greater.

I see your side Bobby, and am in no way implying that someone should just go around swapping brake parts with stuff that 'fits just fine' because someone told them so without any education on how hydraulics work. The person doing the modifications needs to understand what needs to happen, and what will happen, and design their system to work as a whole.
Increasing master cylinder bore size without changing pedal ratio, especially on an all disc brake setup, is just asking for trouble.
Hydraulics, while very helpful, are a very serious matter that should not be taken lightly.

Sun Mar 07, 2010 5:59 pm

Bruce wrote: If the larger MC cured all the braking problems of your Ford fleet, you had a volume problem, not a pressure problem. In other words, the rear wheel cylinders weren't extending all the way to reach the drums with the original MC, or something like that.

.

You very well could be right on that one. We had exhausted all other options and this was the only one that worked. I may try to get ahold of some technical drawings of the two and see exactly how different the two are from each other.

Viande wrote: You also must understand I used a vague 5 to 1 ratio for the pressure to simplify the math. The brake pedal arm is obviously longer than 5 inches.

I understand you were simply throwing out an easy to compute number set.

Viande wrote: Are the brakes in these truck vacuum or servo assisted? That would explain a lot.

Yes, all vacuum assisted. Pedal travel decreased significantly in all cases but as you mentioned we could be doing more 'work' with the vacuum assist than we feel with our foot.

By the way Bobby, got those seals a while ago. I'm very pleased with how they feel, haven't tried to stick any glass in yet but I'm positive there won't be any fitment issues. Thanks again!

Sun Mar 07, 2010 6:25 pm

[quote="raygreenwood"] Bruce wrote:

So just for grins here is the use of Bobby's formula....if you have 20 lbs of force applied to a MC piston of 1" diameter you get 20/1= 20 psi. So...20 pounds of force with a 2"MC bore gets you 20/2= 10 psi. But bear in mind that the wheel cylinder or caliper bore did not change size
Going back to the actual calculated use:

Ray

Sorry, that's wrong. Pressure is a function of area not dia. So, 20lbs on 1"dia = 20/(0.25*pi*1*1) ~25.5psi.

When you go to a 2" dia MC, the PSI drops by a factor of 4 = 6.4psi.

So, pressure chg is proportion to the square of the dia change.

Sun Mar 07, 2010 6:56 pm

Basic hydraulic issue....increasing the diameter of the master cylinder piston allows more flow at the same pedal force but less pressure...

Hydraulics 101

flow X resistance = pressure

an increase in flow,as with moparfreaks ford fleet master cylinder upgrade allowed adequate flow to reach the wheel cylinders for them to work efficiently.That doesnt always cure the issue,in some cases a smaller master cylinder will raise pressure to an adequately supplied wheel cylinder, reducing pedal effort...my question for this whole exercise...properly maintained drum style stock brakes perform well once the operator applies the correct pressure...the only gain with disc brakes is a slight reduction in application time....and if your needing that,you'll most likely wreck your ride anyway.

Sun Mar 07, 2010 7:06 pm

Viande wrote: Sorry volume does not equal pressure. Please show me the math that explains or proves your premise. Volume only comes into play when we are discussing travel.

To simplify this even further if you place a 5lb cone shaped object with a 5 sq.in base on a solid surface what is the psi? If you then invert this 5lb cone to a 1sq.in tip what is the psi now?

Volume against restriction creates pressure....always. How do you think your fuel pumps work? EFI pumps put out "0" head pressure...only volume with a backstop of check valve. The regulator is teh restriction that creates pressure.

Same in a brake master. They create wirtually "0" pressure....without the restriction of the wheel cylinder or caliper. The piston moves fluid ahead of it against a very small movement amount of the caliper or WC piston. Yet it takes and amazingly long stroke of brake mater to move a piston effectively .020". This is volume movement. Since the liquid is uncompressale....its simply filling the space volume presents the diameer of the piston....and that .020". All else after that is locked up solid. All extra volume results in a ride in force. Having twice the master cylinder piston face volume...results in the larger volume movement faster. Once that caliper or WC volume is filled to the locking point.....the rest is nothing but force rise.
Remember...basic hydraulic calculations are not just about force in the slave cylinder...they are based on movement. Ray

Sun Mar 07, 2010 7:06 pm

johnnypan wrote: Basic hydraulic issue....increasing the diameter of the master cylinder piston allows more flow at the same pedal force but less pressure...

Hydraulics 101

flow X resistance = pressure

an increase in flow,as with moparfreaks ford fleet master cylinder upgrade allowed adequate flow to reach the wheel cylinders for them to work efficiently.That doesnt always cure the issue,in some cases a smaller master cylinder will raise pressure to an adequately supplied wheel cylinder, reducing pedal effort...my question for this whole exercise...properly maintained drum style stock brakes perform well once the operator applies the correct pressure...the only gain with disc brakes is a slight reduction in application time....and if your needing that,you'll most likely wreck your ride anyway.

Good way of putting it Johnnypan.

I hope it did not come across as trying to discount Viande's information provided. He is absolutely right that if you change just one thing in your braking system, without regard to anything else, you are asking for trouble. The braking system is just that, a SYSTEM. Everything needs to work with everything else. Plain and simple.

Sun Mar 07, 2010 7:11 pm

[quote="bnam"] raygreenwood wrote: Bruce wrote:

So just for grins here is the use of Bobby's formula....if you have 20 lbs of force applied to a MC piston of 1" diameter you get 20/1= 20 psi. So...20 pounds of force with a 2"MC bore gets you 20/2= 10 psi. But bear in mind that the wheel cylinder or caliper bore did not change size
Going back to the actual calculated use:

Ray

Sorry, that's wrong. Pressure is a function of area not dia. So, 20lbs on 1"dia = 20/(0.25*pi*1*1) ~25.5psi.

When you go to a 2" dia MC, the PSI drops by a factor of 4 = 6.4psi.

So, pressure chg is proportion to the square of the dia change.

Uh yes...Iknow. You realize of course that I was using basic measurements for an example....not trying to be anal. The basic numbers represent the same function. A larger piston "diamter" has a larger area no matter what term we use. And no matter what the pressur drop...the volume rise is double in that equation. In a closed system with a piston that moves in a barely perceptable distance...that equates to a faster pressure rise....and Johnnypan....pointed that out perfectly. nThere is a differnt set of calculations for flow....which is the point everyone is missing here. Ray

Sun Mar 07, 2010 7:13 pm

johnnypan wrote: Basic hydraulic issue....increasing the diameter of the master cylinder piston allows more flow at the same pedal force but less pressure...

Hydraulics 101

flow X resistance = pressure

an increase in flow,as with moparfreaks ford fleet master cylinder upgrade allowed adequate flow to reach the wheel cylinders for them to work efficiently.That doesnt always cure the issue,in some cases a smaller master cylinder will raise pressure to an adequately supplied wheel cylinder, reducing pedal effort...my question for this whole exercise...properly maintained drum style stock brakes perform well once the operator applies the correct pressure...the only gain with disc brakes is a slight reduction in application time....and if your needing that,you'll most likely wreck your ride anyway.

Exactly....well put. There is more than one concept at work here. Ray

Sun Mar 07, 2010 7:14 pm

raygreenwood wrote: There is a differnt set of calculations for flow....which is the point everyone is missing here. Ray

THAT is what I was trying to spit out. Thanks for filling the gap Ray. Flow has to be taken into consideration unless the system is just capped (deadheaded as we heavy equipment technicians call it) because there is absolutely movement before there is pressure. That is the point I was trying to make. The more movement (or flow) you have, the more potential for pressure you have.

If you can try to force 1 cup of fluid into a passage that is blocked, you have x pressure potential (say you are acting on a very long progressive spring)
If you double the fluid capacity (flow) then you potentially can double the pressure potential to 2x (you can move that progressive spring twice the distance even though the resistance has increased)
BUT this is all proportional to the input force applied.

Sun Mar 07, 2010 8:18 pm

Stay tuned...next week we will tackle hydrostatics and review how applying pressure and flow to a variable speed hydraulic motor correctly can achieve increases in motor speed without a subsequent loss of motor torque...bring your calculators, a pop quiz immediately follows.

Sun Mar 07, 2010 8:24 pm

Okay, Johnnypan was correct when he stated that...

Quote: Basic hydraulic issue....increasing the diameter of the master cylinder piston allows more flow at the same pedal force but less pressure...

Yet you are asserting that increasing the area of the MC piston will increase available pressure? Volume only enters the equation here to provide adequate fluid to close the gap between the caliper/WC piston and the pads/disk.

Pascal proved all this around 1640.

Pascal was also the first to prove by experiment that the shape and volume of a container in no way alters pressure.

This pressure of 10 psi acts on all parts of the fluid container, including the bottom of the output piston. The upward force on the output piston is 200 pounds (10 pounds of pressure on each square inch). In this case, the original force has been multiplied tenfold while using the same pressure in the fluid as before. In any system with these dimensions, the ratio of output force to input force is always ten to one, regardless of the applied force. For example, if the applied force of the input piston is 50 pounds, the pressure in the system will be 25 psi. This will support a resistant force of 500 pounds on the output piston. The system works the same in reverse. If we change the applied force and place a 200-pound force on the output piston (fig. 2-11), making it the input piston, the output force on the input piston will be one-tenth the input force, or 20 pounds. (Sometimes such results are desired.) Therefore, if two pistons are used in a fluid power system, the force acting on each piston is directly proportional to its area, and the magnitude of each force is the product of the pressure and the area of each piston.

Sun Mar 07, 2010 8:42 pm

Viande wrote: Okay, Johnnypan was correct when he stated that...

Quote: Basic hydraulic issue....increasing the diameter of the master cylinder piston allows more flow at the same pedal force but less pressure...

Yet you are asserting that increasing the area of the MC piston will increase available pressure? Volume only enters the equation here to provide adequate fluid to close the gap between the caliper/WC piston and the pads/disk.

Pascal proved all this around 1640.

Pascal was also the first to prove by experiment that the shape and volume of a container in no way alters pressure.

This pressure of 10 psi acts on all parts of the fluid container, including the bottom of the output piston. The upward force on the output piston is 200 pounds (10 pounds of pressure on each square inch). In this case, the original force has been multiplied tenfold while using the same pressure in the fluid as before. In any system with these dimensions, the ratio of output force to input force is always ten to one, regardless of the applied force. For example, if the applied force of the input piston is 50 pounds, the pressure in the system will be 25 psi. This will support a resistant force of 500 pounds on the output piston. The system works the same in reverse. If we change the applied force and place a 200-pound force on the output piston (fig. 2-11), making it the input piston, the output force on the input piston will be one-tenth the input force, or 20 pounds. (Sometimes such results are desired.) Therefore, if two pistons are used in a fluid power system, the force acting on each piston is directly proportional to its area, and the magnitude of each force is the product of the pressure and the area of each piston.

No,my assertion is that flow will increase with a larger piston moving the same stroke as a smaller piston.The larger piston requires more input force to create the same pressure than the smaller piston does,but with an accompanying increase in flow.

Flow X pressure = speed force is applied

If you increase the pedal effort with the bigger master cylinder you will get a faster acting brake than the small master cylinder,,,the small cylinder requires less force to create the pressure required but also puts out less flow,slowing the effect on the wheel cylinder.This is where matching the master cylinder to the wheel cylinders is critical,so that speed of application and pressure of application are balanced to provide the fastest acting efficient brake.

Sun Mar 07, 2010 9:38 pm

johnnypan wrote: Stay tuned...next week we will tackle hydrostatics and review how applying pressure and flow to a variable speed hydraulic motor correctly can achieve increases in motor speed without a subsequent loss of motor torque...bring your calculators, a pop quiz immediately follows.

AWW MAN!
I'm having a hard enough time with these damn integrals in my Calculus II class to deal with any more math!
My poor graphing calculator had to work for about 20 minutes on one problem because I needed an approximate answer, not a factored answer all because I was too lazy to freehand it :oops:

Sun Mar 07, 2010 10:25 pm

When i was a child we did all our arithmetic on one of these....did our math too and half our spelling.