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#1235219 - 05/17/12 11:49 PM Disc brakes: All the math that you never wanted to know
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Some folks liked the numbers that came up in the brake thread. I've thrown the most common stuff out in the open. Now, an engineer would be kicking and screaming about this stuff but it's good enough to get an idea what's going on.
I'll try to keep it simple for those who don't care much for math. These calculations build on one another. It's kind of a step by step thing.

Get a pencil, some paper, and a simple calculator. I use the calculator included in Windows.
Click your start button > All Programs > Accessories > Calculator.

It will be helpful if you write down what the numbers mean. Instead of 7 try writing "pedal ratio = 7" so you will remember what each of the numbers mean.

For this example I will use a common brake setup. Nothing exotic here. 11.75" Cordoba rotors, 2.75" slider calipers, manual 15/16" master cylinder, and a typical brake pedal.
Measure the stuff on your car. Don't use my measurements.


PEDAL RATIO

Before you start with crazy math, go find your brake pedal ratio. Measure from the middle of the pedal pivot to the middle of the pad on the brake pedal. Now measure from the middle of the pivot to the middle of the master cylinder push rod pin.

Divide the total length by the push rod distance. That is your pedal ratio.
14" pedal? 2" to the MC pin? Ratio is 14/2 = 7.
7:1 pedal ratio. Write that down. You will need it later.


AREA OF A CIRCLE (PISTON)

The very first thing you need to do is remember how to find the area of a circle. Your circle can be the master cylinder piston or the brake caliper piston.
It's pretty easy.

Pi R squared

Yes, the pies mom made were round but in physics Pi R squared.

Pi = 3.14 (number goes on forever but this is good enough)
R = radius of the circle (half the width of the piston)
squared = radius times the same radius.

Have a 2.75" piston? The radius is 1.375" (half of 2.75).
So, 3.14 times 1.375 times 1.375
The area of the piston is 5.93". Feel free to call it 5.9 inches.

Wanna cheat? Click here: http://www.calculateme.com/cArea/AreaOfCircle.htm

A note for people with multi-piston calipers: Only count the pistons on ONE side. Don't worry about why. Just count one side. It's the correct thing to do. Your numbers will be accurate and your headache will be smaller. Be sure to measure all the pistons on that side. They may be different sizes. Find the area of each piston on that one side. Once you do that, add the numbers together for a total area. Use that number for your caliper piston measurements.

Most master cylinders for our old cars are measured with fractions. Not good with fractions? Grab your calculator. Divide 1 by 16. Now you know 1/16 of an inch is .0625".
A 15/16 master cylinder is 15 times .0625 or .9375 of an inch. Plug that in to the above formula and the area of the master cylinder piston is .6902 square inches.


MASTER CYLINDER PRESSURE

Want to find the pressure made at the master cylinder?
You need the pedal ratio, the size of the master cylinder, and figure out how hard you want to push on the pedal.
I'm working with a MANUAL master cylinder. Throw a booster (vacuum or hydro) in the equation and you're on your own.

Multiply the pressure you push on the pedal times your pedal ratio. Divide your answer by the surface area of the master cylinder piston.
Using the numbers above, the pedal ratio was 7:1 and the master cylinder was .6902". Let's stomp on the pedal with 100 lbs of push.
100 times 7 equals 700. Divide that by .6902. You get 1014 pounds of force.


EFFECTIVE RADIUS OF A ROTOR

To work with the actual braking ability you really need to find what is called the effective radius of your brake rotor. To do that you need to know the caliper piston diameter (only the biggest one for calipers with more than one piston) and the diameter of your rotor.
Effective radius is the total diameter of the brake rotor plus that same diameter AFTER you subtract the diameter of the piston. Then, divide by 4.
Use a "big" Mopar 11.75" rotor and the 2.75" caliper we used above.
11.75" minus the 2.75" piston is 9 inches.
So, 11.75" plus 9" is 20.75".
Divide by 4 and you get a 5.18" effective radius.


BRAKE TORQUE

Now we're ready to find out what stomping on the pedal does for us.
To find the actual brake torque (stopping force of the brakes) we need the master cylinder pressure, the caliper area, and the effective radius.
Multiply the line pressure by the caliper area.
Take that number and multiply by the effective radius.
The result is your brake torque.
Since we were measuring in inches we need to divide by 12 to make it ft/lbs.
Our line pressure was 1014.
The caliper area was 5.9.
The effective radius was 5.18.
1014 * 5.9 * 5.18 = 30989 in/lbs
30989 in/lbs divided by 12 = 2582 ft/lbs.
Guess what? That's only one side of the rotor. The calipers press on both sides of each rotor so double that number.
You can have 5164 ft/lbs of braking on each front wheel with 100 pounds of pedal effort.
That's serious stuff! Think your tires can handle it?


BRAKE PEDAL MOVEMENT VS BRAKE PAD MOVEMENT

To find out how far your brake pads actually move when you push your brake pedal you need the pedal ratio, the master cylinder area and the caliper piston area. We're going to assume you've already taken up all the slack in the pedal and push rod.
Divide your master cylinder area by the caliper piston area.
Divide that number by the pedal ratio.
Divide that number by the 4 front brake pads (2 pads on the left and 2 pads on the right).

.6902" master cylinder divided by the 5.9" caliper piston area gives you .1169".
.1169" Divided by the pedal ratio of 7 gives you .0167".
Dividing by 4 front brake pads gives you a total of .0041" of movement.

So, every time you move that brake pedal one inch the brake pads each move 4.1 thousandths of an inch.
Brake pads are generally a couple thousandths of an inch off the rotor so they can't move far. If they did your pedal would fall to the floor.



Clear as mud?

That's enough math for tonight. It's late and I probably bumbled some of that info already.

Have a question or an issue? Ask away. I'll answer after I get some sleep.

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#1235220 - 05/17/12 11:56 PM Re: Brakes: All the math that you never wanted to know [Re: feets]
Frankenduster Offline
Moparts proctologist

Registered: 02/15/10
Posts: 14684
Loc: Granite Bay CA
THIS should get a sticky!
Thanks Feetsie!

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#1235221 - 05/18/12 12:01 AM Re: Brakes: All the math that you never wanted to know [Re: Frankenduster]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Thanks.

Let's hope it's all correct. I think it is but my mind is mush after a long day at work.

I'm gonna hit the sack and see if those numbers still make sense in the morning.
I didn't bother with coefficients of friction and some other engineering blah blah blah stuff so I'm sure others will chew it pieces. What do I know? I'm just a parts guy.


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#1235222 - 05/18/12 05:51 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
BigBlockMopar Offline
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Registered: 01/22/03
Posts: 3121
Loc: The Netherlands
Good write-up.


Quote:

Have a question or an issue? Ask away.



Since you asked... Where's the start button?



Attachments
7210944-StartButton.jpg (163 downloads)

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#1235223 - 05/18/12 06:23 AM Re: Disc brakes: All the math that you never wanted to know [Re: BigBlockMopar]
70Cuda383 Offline


Registered: 10/07/03
Posts: 21330
Loc: Marysville, O-H-I-O
WHo uses paper and pencil anymore?

build yourself an excel spreadsheet that does all that calculations for you, so that all you have to enter is the master cylinder bore, Caliper piston(s) bore, and the pedal ratio.
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#1235224 - 05/18/12 06:24 AM Re: Disc brakes: All the math that you never wanted to know [Re: BigBlockMopar]
70Cuda383 Offline


Registered: 10/07/03
Posts: 21330
Loc: Marysville, O-H-I-O
Quote:

Good write-up.


Quote:

Have a question or an issue? Ask away.



Since you asked... Where's the start button?






Oooh, I was gonna say, click on the little black circle icon at the bottom that looks like a tachometer with a red needle, it's called "dashboard" but...you don't have that on your desktop!
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#1235225 - 05/18/12 06:28 AM Re: Disc brakes: All the math that you never wanted to know [Re: BigBlockMopar]
DGS Offline
mopar

Registered: 07/08/05
Posts: 451
Loc: Graz, Austria
Very nice!

but maybe you should mention that this is for manual brakes only! Power brakes have a brake linkage between the pedal and the booster which effectively lowers the pedal ratio and shortens pedal travel! This means that 100lbs of brake force at the pedal results in only 300-400 lbs at the booster (vs. 700 lbs at the MC with manual brakes). The booster then adds a certain amount of force to that number (depends on booster size and if it's a single or a dual diaphragm)! Now the available brake power is greater than with manual brakes which allows you to use a bigger bore MC and pedal effort is lower than with a manual car.

The formula to calculate booster assist is:

diaphragm area (in square inches) times vacuum (in hg) times 1/2

example for a single 10" booster (radius is 5"):
5*5 * Pi (3.14) = 78.5
78.5 * 18hg vacuum = 1413
1413 * 0.5 = 706.6 lbs assist with a 10" single diaphragm booster

with a dual diaphragm area you just have to double the diaphragm area. e.g. dual 8" = 4" * 4" * Pi (3.14) * 2 = 100.48 square inch total diaphragm area = just 25% more than a single 10"!

IMPORTANT: This is for a booster with 100% efficiency - normally boosters work with about 80-85% efficiency. Just multiply the number you get by 0.8 to get a more realistic number!


Edited by DGS (05/18/12 06:52 AM)

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#1235226 - 05/18/12 06:29 AM Re: Disc brakes: All the math that you never wanted to know [Re: 70Cuda383]
70Cuda383 Offline


Registered: 10/07/03
Posts: 21330
Loc: Marysville, O-H-I-O
question kevin. on a dual sided caliper, such as my 4-piston Brembos from Viper or your 8-piston Brembos from Merc, you ignore one side of pistons because of how they push against each other and cancels out some of that line pressure.

Does that mean your brake torque calculation where you double it for the other pad, should not be doubled? or do you still double that number because you already accounted for the "loss" of piston force from the opposing pistons?


And what about the coefficient of friction between the pad/rotor? should that be accounted for somewhere?


---or is that some of the details that you said an engineer would throw a fit over?


while I'm on that subject, don't forget to subtract loss of line pressure from rubber brake lines deforming under pressure


Edited by 70Cuda383 (05/18/12 06:32 AM)
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#1235227 - 05/18/12 08:07 AM Re: Disc brakes: All the math that you never wanted to know [Re: 70Cuda383]
DARTH V8Я Offline
Oh No!! I just had a moron attack!

Registered: 11/01/11
Posts: 2154
Loc: Its a TRAP!
also need to take into account fluid expansion when the brakes get hot
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#1235228 - 05/18/12 08:10 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Uhcoog1 Offline
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Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Great post, Feets!

I just learned all of the math and found a few excel spreadsheets. There is a good excel probably 3/4 of the way down or so. It allows you to determine weight transfer at a specified G force stop, etc. I don't like his power brake calculations, though.

http://www.pirate4x4.com/tech/billavista/Brakes/

A couple things I learned along the way:
My duster has a 6.5:1 manual pedal ratio. When adding the power linkage, it drops to 3.5:1.
A dual master cylinder (side by side masters) split the input force, a tandem master does not.

I still have questions about halving the total piston volume in a fixed caliper, though. The above excel doubles the piston volume in a sliding caliper instead.
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#1235229 - 05/18/12 08:21 AM Re: Disc brakes: All the math that you never wanted to know [Re: DARTH V8Я]
DynoDave Offline
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Registered: 01/20/03
Posts: 2995
Loc: MICHIGAN
Thanks feets. This is super!

And yes, this should be in the tech archive.
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#1235230 - 05/18/12 08:29 AM Re: Disc brakes: All the math that you never wanted to know [Re: DynoDave]
moparx Offline
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Registered: 09/03/03
Posts: 7812
Loc: north of coder
feets, i liked the pedal movement vs pad movement. i'v never seen that equasion before... THANKS !

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#1235231 - 05/18/12 08:51 AM Re: Disc brakes: All the math that you never wanted to know [Re: DynoDave]
runinonmt Offline
mopar

Registered: 05/19/05
Posts: 416
Loc: Franklin Co. Illinois
Quote:

Thanks feets. This is super!

And yes, this should be in the tech archive.





Ron
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#1235232 - 05/18/12 10:18 AM Re: Disc brakes: All the math that you never wanted to know [Re: DGS]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

but maybe you should mention that this is for manual brakes only!





Look under the part where I discussed master cylinder pressure. I clearly stated this was for MANUAL BRAKES ONLY. If you use a vacuum or hydro booster you are on your own.

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#1235233 - 05/18/12 10:48 AM Re: Disc brakes: All the math that you never wanted to know [Re: 70Cuda383]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

question kevin. on a dual sided caliper, such as my 4-piston Brembos from Viper or your 8-piston Brembos from Merc, you ignore one side of pistons because of how they push against each other and cancels out some of that line pressure.




The pistons are the same size left and right. That means you have to divide the measurements by two. When you finish the equation you have to add the numbers together to get a total. You just did extra work and cancelled it out in the end.

Quote:

Does that mean your brake torque calculation where you double it for the other pad, should not be doubled? or do you still double that number because you already accounted for the "loss" of piston force from the opposing pistons?




The torque calculation solves for rotor force. The brakes grab both sides of the rotor with the same force due to that whole equal and opposite reaction thing. Since you have drag on both sides it adds together.

Quote:


And what about the coefficient of friction between the pad/rotor? should that be accounted for somewhere?
---or is that some of the details that you said an engineer would throw a fit over?





You are correct. The coefficient of friction divides the brake torque. In the sample above we had the magic brake pads with a coefficient of 1.
This is indeed where engineers begin frothing at the mouth. Brake fluid compresses. Different fluids compress at different rates as temperature changes and water content increases. Rubber brake hoses stretch. Steel brake lines stretch. All kinds of other things come into play.

If you want to get technical, everything I listed is "useless" to a Formula 1 team. Pedal pivot friction, play between the mechanical bits, minute amounts of air trapped in the lines, and all kinds of other stuff changes the numbers.

I was going to build an Excel spreadsheet that would allow people to enter their measurements and get the answers but I have nowhere to host it.

This was meant to be a quick and dirty way to run the calculations.
It sure is dirty but there was nothing quick about it.

Hopefully it will help a few people get a rough idea of what's going on in the brake system.

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#1235234 - 05/18/12 12:20 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Uhcoog1 Offline
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Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:



I was going to build an Excel spreadsheet that would allow people to enter their measurements and get the answers but I have nowhere to host





I'll host. PM sent
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#1235235 - 05/18/12 12:32 PM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Thanks!

I'll put something together.

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#1235236 - 05/18/12 02:30 PM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
MuuMuu101 Offline
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Quote:

Quote:



I was going to build an Excel spreadsheet that would allow people to enter their measurements and get the answers but I have nowhere to host





I'll host. PM sent




I want a copy of that program!
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#1235237 - 05/18/12 02:45 PM Re: Disc brakes: All the math that you never wanted to know [Re: MuuMuu101]
hooziewhatsit Online   content
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Registered: 10/05/07
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Loc: State of Jefferson
I can host it too, if need be.

Now I need to calculate how far my pistons move vs. pedal movement. Also need to get a pressure gauge so I can see if my booster is actually doing anything or not
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#1235238 - 05/18/12 09:14 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Excel file is available for download here:

http://www.3gduster.com/brakes.html

Enjoy!
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#1235239 - 05/18/12 10:44 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
68440fish Offline
member

Registered: 10/31/04
Posts: 151
Loc: Plano, TX
Quote:

where engineers begin frothing at the mouth




Mechanical advantage of the lever at the pedal, area ratio from the master to the caliper, lump capacitance of the fluid system / materials, torque on the wheel from the braking force, coefficient of friction at the pad rotor interface dependent on: brake pad material(s) - rotor material - rotor surface condition - pad surface condition - temperature - humidity, reaction torque from the tire road interface, coefficient of friction at the tire interface as a function of the slip ratio.. nooooo... let it goooo...


OK Kevin, I think I am OK now...

---------------------
Michael
AS in Automotive Technology (1990)
ASE Certified Master Tech (1991)
BS in Mechanical Engineering (1997)
MS in Mechanical Engineering w/ a concentration on Dynamic Systems and Controls (2005)

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#1235240 - 05/18/12 10:47 PM Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish]
68440fish Offline
member

Registered: 10/31/04
Posts: 151
Loc: Plano, TX
Anyone want to see the bond graph representation of a torque converter?

Oh... never mind...
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#1235241 - 05/18/12 11:37 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
68440fish Offline
member

Registered: 10/31/04
Posts: 151
Loc: Plano, TX
Quote:

Dividing by 4 brake pads gives you a total of .0041" of movement.




Kevin - this is where modeling the system gets really "fun". Not picking on you or anything, this is the good stuff. All the numbers and ratios and everything you are tossing out there all assume a steady state A/B type ratio. Those numbers are what comes into play when the brake pads are in contact with the rotors and we are slowing down. What is really cool - and may be one of the more important things is what happens before that. The actual travel you have before the pad - or shoe - engages is going to be different front to rear. So you actually have several different states each with a different model. #1 - foot on pedal, no pads touching yet; #2 - first set of pads engage; #3 second set of pads engage. Before contact the pistons in the rear are moving at a different speed than the ones in the front. If we assume the force to get the piston / pads moving is about the same, the front pistons have more leverage and thus less reflected force back into the system. This means you would get considerably more movement on the front and they will engage first, then, as they meet more resistance at the pad rotor interface the slack in the rear would be taken up. Interesting - be nice to go out and slowly press the pedal with someone turning each wheel to see if this is indeed what happens. The only way around this would be separate master cylinders and a balance bar, you could then tune it to your liking.

I feel like a nerd... forgot how much I like this stuff.
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#1235242 - 05/19/12 12:05 AM Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish]
autoxcuda Offline
Too Many Posts

Registered: 01/20/03
Posts: 25339
Loc: So Cal
Quote:

Interesting - be nice to go out and slowly press the pedal with someone turning each wheel to see if this is indeed what happens. The only way around this would be separate master cylinders and a balance bar, you could then tune it to your liking.
...




On of the advantages to dual masters with balance bar setup. We've done that very test on our circle track cars. We've caught cars with rears that grab first or at the same time.
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#1235243 - 05/19/12 01:05 AM Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Michael, I am aware of most of the stuff you listed but didn't want to get into that stuff. It would make the post totally useless for most folks.

Also, when I was referring to the movement of the 4 brake pads, I meant the front brakes. The rear brakes were not addressed in the post. I didn't want to go there due to the different proportioning valves in use.


Again, I believe the stuff I dumped out there will be good enough to get someone in the general ball park.
Obviously, the brake torque calculation shows a perfect scenario where the real world will see the number cut by as much as 65% with the use of poor quality brake pads.

Sometimes it's just fun to fiddle around with numbers.

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#1235244 - 05/19/12 08:54 AM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
DynoDave Offline
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Registered: 01/20/03
Posts: 2995
Loc: MICHIGAN
Quote:

Excel file is available for download here:

http://www.3gduster.com/brakes.html

Enjoy!




When I suggested in the other thread that it would be nice if this was all in an excel spreadsheet, I didn't think anyone would actually do it! I was thinking of trying to do it myself, but it would have taken a week, and I still would not have gotten it right.

Thanks to both of you for all the time you have put into this. This sheet has been downloaded, saved, and backed up for future reference.
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#1235245 - 05/19/12 09:11 AM Re: Disc brakes: All the math that you never wanted to know [Re: DynoDave]
Supercuda Offline
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Registered: 09/04/07
Posts: 12397
Loc: West Texas
one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C
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#1235246 - 05/19/12 09:58 AM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
68440fish Offline
member

Registered: 10/31/04
Posts: 151
Loc: Plano, TX
Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Less leverage is less stroke at the pedal. Stroke at the master is determined by the system downstream.
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#1235247 - 05/19/12 11:00 AM Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish]
Supercuda Offline
I Live Here

Registered: 09/04/07
Posts: 12397
Loc: West Texas
Quote:

Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Less leverage is less stroke at the pedal. Stroke at the master is determined by the system downstream.




Stroke at the pedal is irrelevant. Stroke at the M/C is, Frankenduster had an issue with his manual all disc setup I am thinking is volume out the M/C related. The problem cured up with him swapping to power (less leverage at the pedal, more stroke at the M/C, same MC).

In a lever situation, which this is, stroke and leverage are directly related.
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#1235248 - 05/19/12 04:23 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

one bit of math missing here.

relationship of piston stroke in the M/C versus pedal ratio.

Someone here thinks less leverage is less stroke at the M/C




Look at the chart again.

The third input requested is pedal ratio. 7 in the example.
The sixth (and last) input requested is how far you moved the pedal. 5 inches in this example.

The third output listed is "the master cylinder moved this far". .7143" in this example.

There's your stroke by pedal ratio.


You referenced FD's power booster conversion. I specifically stated that the math in these examples was for a manual brake system only and that if you used a booster you were on your own.

If you want to get into pedal effort by master cylinder size, start punching numbers.
Put in a 1" master with 100 lbs pedal effort and see what the brake torque is.
Put in a 1-1/8" master with 100 lbs pedal effort and see what the brake torque is.
Start putting higher numbers in the pedal effort until you get back to the same brake torque.

Going from the example's 15/16" master cylinder to a 1-1/8" master cylinder shows that the pedal effort increases from 100 lbs to 144 lbs to get the same brake torque. A 44% increase in pedal effort is not going to make for a happy driver.

Go back and play with the numbers and see what the spreadsheet will do for you. It's kinda fun.

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#1235249 - 05/19/12 05:40 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Supercuda Offline
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Registered: 09/04/07
Posts: 12397
Loc: West Texas
I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.
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#1235250 - 05/19/12 05:54 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
68440fish Offline
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Registered: 10/31/04
Posts: 151
Loc: Plano, TX
Quote:

I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.




Steve - what does the power booster have to do with the volume output from the master? The only time that is going to make any difference is if he ran out of pedal before the brakes were fully applied. In that case, he could have also cured the issue by going to a larger diameter bore on the master. So, was the root issue too much pedal travel?
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#1235251 - 05/19/12 06:18 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

I understand all that, but it' not as obvious as it might need to be for some.

Anyway, one other thing to consider when using your formulas is the capacity of the m/c and the needs of the calipers. Not enough volume out of the M/C and the calipers will not do the job, which is what I think FD had for a problem.




Again, go back and play with the numbers. You can see how far the calipers move with different size master cylinders as well as the pedal force required to generate enough brake torque.

It won't magically tell you everything you want to know. Playing with it and reading all of the results will help you understand what is going on.

Again, it's not the final word in brake info. Instead, it will get you in the ball park assuming you read and understand the info presented.

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#1235252 - 05/19/12 06:22 PM Re: Disc brakes: All the math that you never wanted to know [Re: 68440fish]
DoctorDiff Offline
master

Registered: 01/20/03
Posts: 7791
Loc: Polson, MT
A 15/16" bore master cylinder should have ample volume in this case, because the caliper pistons only move a fraction of an inch.
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#1235253 - 05/19/12 09:35 PM Re: Disc brakes: All the math that you never wanted to know [Re: DoctorDiff]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
I think we bore that out in the math.




The 15/16" master worked fine once he put the booster back in.

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#1235254 - 05/19/12 09:50 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Hmm, only 408lbs from the master cylinder. I sure hope the booster is actually doing its thing

I ordered the pressure gauge and adapters today to make sure
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#1235255 - 05/19/12 09:53 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Perhaps you could build some sort of electric brake controller that will vary the brake pressure based on speed, traffic conditions, and the presence of radar emissions directed at the vehicle.


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#1235256 - 05/19/12 09:56 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Frankenduster Offline
Moparts proctologist

Registered: 02/15/10
Posts: 14684
Loc: Granite Bay CA
Quote:

I think we bore that out in the math.




The 15/16" master worked fine once he put the booster back in.




The manual 15/16" master cylinder wasn't likely to blame, since I also had trouble with the other two manual units that I tried. The 15/16" unit I have on the car NOW with the power booster is an iron unit spec'd for a 75 Dart with power brakes.

Something wierd was happening and I still don't know what is to blame.

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#1235257 - 05/19/12 10:14 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Quote:

Perhaps you could build some sort of electric brake controller that will vary the brake pressure based on speed, traffic conditions, and the presence of radar emissions directed at the vehicle.




No more of this ABS stutter-stop stuff. Just lower the pressure in the event of wheel lockup. And/or change the rear pressure based on road speed and current load (for trucks). Should work great!
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#1235258 - 05/19/12 10:17 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
Supercuda Offline
I Live Here

Registered: 09/04/07
Posts: 12397
Loc: West Texas
When you decrease the pedal ratio, you increase the stroke in the M/C. Power brakes systems use less pedal ratio, therefor more stroke at the MC for a given pedal travel.

Same bore M/C going from manual to power sends out more volume for a given pedal travel.

That's what is different.
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#1235259 - 05/19/12 10:23 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Quote:

When you decrease the pedal ratio, you increase the stroke in the M/C. Power brakes systems use less pedal ratio, therefor more stroke at the MC for a given pedal travel.

Same bore M/C going from manual to power sends out more volume for a given pedal travel.

That's what is different.




But wouldn't that be true only if the brake pedal was also swapped to the corresponding 'correct' ratio?

ie, just throwing a booster behind a MC won't necessarily change the stroke, or will it? It should build more pressure, which I guess would necessitate a little longer stroke, assuming you haven't bottomed out the MC.

Another question: Do manual master cylinders have more travel built in to them than power MCs do? (assuming the same diameter bore)?
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#1235260 - 05/19/12 10:37 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

When you decrease the pedal ratio, you increase the stroke in the M/C. Power brakes systems use less pedal ratio, therefor more stroke at the MC for a given pedal travel.






Please explain to me how the mechanical ratio of the pedal is modified when you install a booster with no other changes.
A brake booster is a straight through design. It simply uses vacuum to help push the pedal and reduce your leg effort.



Where are the levers and other gizmos to change the mechanical advantage?


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#1235261 - 05/19/12 10:40 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:


Another question: Do manual master cylinders have more travel built in to them than power MCs do? (assuming the same diameter bore)?




To my knowledge, the only difference is the provision for a push rod retainer in the manual master cylinder.
I have installed power brake master cylinders on non-power setups.

If you try this you MUST make sure it is not possible for the brake push rod to fall out. That's why it's not recommended. It would suck to have the rod fall out and prevent you from hitting the brakes at a rather critical moment.

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#1235262 - 05/19/12 10:49 PM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
Frankenduster Offline
Moparts proctologist

Registered: 02/15/10
Posts: 14684
Loc: Granite Bay CA
Quote:

When you decrease the pedal ratio, you increase the stroke in the M/C. Power brakes systems use less pedal ratio, therefor more stroke at the MC for a given pedal travel.
Same bore M/C going from manual to power sends out more volume for a given pedal travel.
That's what is different.




I thought that the travel of the piston in the master cylinders was about the same. I might be operating on a "fuzzy memory" here, but when I bench bled the master cylinder, I bottomed out the piston. When I put the master cylinder in the car, it appeared that the with the brake pushrod in the M/C, it bottomed out only a fraction deeper than the brake pedals travel. I'm certain that you don't want the pedal to stop 2 inches off of the floor because the M/C ran out of stroke.

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#1235263 - 05/19/12 10:57 PM Re: Disc brakes: All the math that you never wanted to know [Re: Frankenduster]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Some disc/drum masters don't have enough stroke for rear disc brakes. If the pedal it's a rock solid stopping point deep in the stroke you may want to check that out.
I know it's theoretically possible but I haven't experienced it myself.

The hot rod has a D150 manual disc/drum 1-1/8" unit pushing fluid to the AMG disc brakes.

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#1235264 - 05/19/12 11:37 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
RichV Offline
top fuel

Registered: 01/20/03
Posts: 1671
Loc: Seattle WA
Quote:



EFFECTIVE RADIUS OF A ROTOR

To work with the actual braking ability you really need to find what is called the effective radius of your brake rotor. To do that you need to know the caliper piston diameter (only the biggest one for calipers with more than one piston) and the diameter of your rotor.
Effective radius is the total diameter of the brake rotor plus that same diameter AFTER you subtract the diameter of the piston. Then, divide by 4.
Use a "big" Mopar 11.75" rotor and the 2.75" caliper we used above.
11.75" minus the 2.75" piston is 9 inches.
So, 11.75" plus 9" is 20.75".
Divide by 4 and you get a 5.18" effective radius.





Effective radius of the rotor is unrelated to the piston diameter. It is the center of contact for for the brake pad to the rotor. Typical undergrad engineering calculation put it outboard of the center, but the taper wear of pads typically moves back inboard. So the center of contact is good compromise.

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#1235265 - 05/20/12 06:27 AM Re: Disc brakes: All the math that you never wanted to know [Re: RichV]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

Effective radius of the rotor is unrelated to the piston diameter. It is the center of contact for for the brake pad to the rotor. Typical undergrad engineering calculation put it outboard of the center, but the taper wear of pads typically moves back inboard. So the center of contact is good compromise.




What this calculation does is average the diameter of the rotor and the diameter of the rotor minus the piston diameter. Doing that finds you the center of the piston. That is going to be pretty close to the center of the pad.

Now, I'm NOT going to measure every stinkin pad in the world and spoon feed you the information.
If you want to use the calculation, go for it.
If you want to gather all the info from each individual setup and present it to the person requesting it in a 24 hour 7 day format then be my guest.

Again, put down the engineering texts and reread the part where I said these were good enough to get the average guy in the ball park without requiring a high level of math or engineering degree.

Now, are you frothing at the mouth or trying to accomplish something else?

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#1235266 - 05/20/12 08:17 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Supercuda Offline
I Live Here

Registered: 09/04/07
Posts: 12397
Loc: West Texas
You can tell the A body guys.

The A body power setup uses an offset crank assembly to lessen the pedal ratio

You can see it in this link

http://www.ebay.com/itm/1967-MOPAR-MOPAR...R-/290681535604
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#1235267 - 05/20/12 08:38 AM Re: Disc brakes: All the math that you never wanted to know [Re: Supercuda]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

You can tell the A body guys.

The A body power setup uses an offset crank assembly to lessen the pedal ratio

You can see it in this link

http://www.ebay.com/itm/1967-MOPAR-MOPAR...R-/290681535604




Interesting.
It looks like it uses the crank mechanism to raise the booster for more clearance for valve covers. The 273 used a mechanical cam and I imagine things get a little tight under those hoods.

Have you done the math to calculate the actual mechanical advantage of this setup? It would require measuring the complete assembly including the pedal.

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#1235268 - 05/20/12 08:39 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Supercuda Offline
I Live Here

Registered: 09/04/07
Posts: 12397
Loc: West Texas
Sorry, I do not own any power brake A bodies, I think my last one was in 1984. Since then they have all been manual brake setups. I am not a fan of power brakes in A bodies.
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#1235269 - 05/20/12 08:45 AM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:


My duster has a 6.5:1 manual pedal ratio. When adding the power linkage, it drops to 3.5:1.





The 73+ had 15/16 master cylinders with power brakes.

I have an excel calculating booster help if anyone wants to see it.
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-'02 Dodge Viper Ex-World Challenge racecar
-'73 Duster, 6.1 based 392 hilborn hemi, tko600, full floater rear 9", Hellwig custom bars, viper brakes, built for road course

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#1235270 - 05/20/12 02:07 PM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Quote:

The 73+ had 15/16 master cylinders with power brakes.

I have an excel calculating booster help if anyone wants to see it.



Is it any different than the one at Pirate4x4 that just adds a multiplier to the pressure output?

Heck, send it to my username at hotmail.com.
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#1235271 - 05/22/12 09:50 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
dusted72 Offline
member

Registered: 02/09/12
Posts: 29
Loc: Iraq
Feets you have just saved me weeks of headaches. I have been attempting to figure all this out with very little luck on where to start. I am planning a big brake swap on my Ram and have figured some stuff out but I really was wanting to get the specifics behind it all. I had been talking to Tom (70cuda383) on another board and he told me to come over here and check out your posts. Boy was he right. Thanks.

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#1235272 - 05/22/12 09:55 PM Re: Disc brakes: All the math that you never wanted to know [Re: dusted72]
feets Offline
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Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Thanks, but remember this stuff will only get out in the ballpark. There are lots of other things that go into real brake system equations. Some of it has been discussed in this thread.

Feel free to use this as a basic guide. If you're saving your pennies to build something when you rotate home there's enough time to run lots of numbers.

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#1235273 - 05/24/12 11:15 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Here's a file that compares manual to power brakes.

It looks like it takes the surface area of the booster and current vacuum to calculate the additional pressure provided.

Then it has two lines for each manual and power so you can compare different sized MCs. I think the table on the right is different foot pressures. For power it then adds the pressure provided by the booster (I think it's looking at the 9").

Although I think it needs to take into account pedal ratio somewhere in there

As always, use this at your own risk

edit: cleaned up file available a few posts down


Edited by hooziewhatsit (05/24/12 11:10 PM)
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#1235274 - 05/24/12 03:05 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:

Here's a file that compares manual to power brakes.

www.ma-uav.com/Manual_v_Vacuum_Brake_Pressures.xls

It looks like it takes the surface area of the booster and current vacuum to calculate the additional pressure provided.

Then it has two lines for each manual and power so you can compare different sized MCs. I think the table on the right is different foot pressures. For power it then adds the pressure provided by the booster (I think it's looking at the 9").

Although I think it needs to take into account pedal ratio somewhere in there

As always, use this at your own risk




This is my file, so I'll answer some questions on it. I'll clean it up and host a better version on my website later.

The pedal ratio is accounted for- but isn't in an obvious place for you to toggle. That is calculating off a fixed 9" single booster. The numbers at the top of the table are foot force in pounds.

I didn't realize hooziewhatsit was going to host this for download when I emailed it to him. I'll make it more user friendly tonight and make that version available for download.
_________________________
-'02 Dodge Viper Ex-World Challenge racecar
-'73 Duster, 6.1 based 392 hilborn hemi, tko600, full floater rear 9", Hellwig custom bars, viper brakes, built for road course

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#1235275 - 05/24/12 07:06 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
dusted72 Offline
member

Registered: 02/09/12
Posts: 29
Loc: Iraq
Ok so after reading through this whole thread I am still a little confused as to what the actual equations are used for. I know how to get the answers but why? Am I using those to get the figures for the stock setup compared to proposed setup? I am just unsure. In particular the purpose of the area of a circle and effective radius of a rotor? I did the math for both stock and proposed. What does it mean if the stock are of a circle is 6.78inches and the propsed is 7.06inches? Same with the Effective radius? Stock is 5.07 and proposed is 6.23. I just don't know. Also are there any braking books out there that are a must read? I am in Kuwait right now and will be returning back to the states within the next 2 weeks so if there are any recommended readings out there please share.

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#1235276 - 05/24/12 07:31 PM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:

Quote:

Here's a file that compares manual to power brakes.

www.ma-uav.com/Manual_v_Vacuum_Brake_Pressures.xls

It looks like it takes the surface area of the booster and current vacuum to calculate the additional pressure provided.

Then it has two lines for each manual and power so you can compare different sized MCs. I think the table on the right is different foot pressures. For power it then adds the pressure provided by the booster (I think it's looking at the 9").

Although I think it needs to take into account pedal ratio somewhere in there

As always, use this at your own risk




This is my file, so I'll answer some questions on it. I'll clean it up and host a better version on my website later.

The pedal ratio is accounted for- but isn't in an obvious place for you to toggle. That is calculating off a fixed 9" single booster. The numbers at the top of the table are foot force in pounds.

I didn't realize hooziewhatsit was going to host this for download when I emailed it to him. I'll make it more user friendly tonight and make that version available for download.




User friendly version posted here:
http://www.3gduster.com/brakes.html

Manual vs Vacuum

The equation isn't going to be correct down low, given it just adds the full vacuum force to the manual force you're pushing. It's a useful equation to get an idea for the upper end.
_________________________
-'02 Dodge Viper Ex-World Challenge racecar
-'73 Duster, 6.1 based 392 hilborn hemi, tko600, full floater rear 9", Hellwig custom bars, viper brakes, built for road course

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#1235277 - 05/24/12 07:55 PM Re: Disc brakes: All the math that you never wanted to know [Re: dusted72]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:

Ok so after reading through this whole thread I am still a little confused as to what the actual equations are used for. I know how to get the answers but why? Am I using those to get the figures for the stock setup compared to proposed setup? I am just unsure. In particular the purpose of the area of a circle and effective radius of a rotor? I did the math for both stock and proposed. What does it mean if the stock are of a circle is 6.78inches and the propsed is 7.06inches? Same with the Effective radius? Stock is 5.07 and proposed is 6.23. I just don't know. Also are there any braking books out there that are a must read? I am in Kuwait right now and will be returning back to the states within the next 2 weeks so if there are any recommended readings out there please share.




Go here, read it all, and use the excel:
http://www.pirate4x4.com/tech/billavista/Brakes/

The purpose of the math is to determine how much braking force you need and what balance you need. The usable brake torque is determined how much grip your tires have with the road surface (coefficient of friction between tires and surface). You can calculate the force needed by the caliper, and the master cylinder needed to produce that force. The diameter of the rotor determines the leverage.

The brake bias needed changes through the 'curve'. Assuming a 54/46 (f/r) weight bias when static in my duster, a .1 G braking even will require very close to a 55/45 ideal bias. It will change, ending up at a 75/25 ideal bias at a 1.3 G braking event. You need to calculate weight transfer at different G braking events.

Does that help?
_________________________
-'02 Dodge Viper Ex-World Challenge racecar
-'73 Duster, 6.1 based 392 hilborn hemi, tko600, full floater rear 9", Hellwig custom bars, viper brakes, built for road course

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#1235278 - 05/24/12 11:09 PM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Quote:

I didn't realize hooziewhatsit was going to host this for download when I emailed it to him. I'll make it more user friendly tonight and make that version available for download.




oops. Sorry

The cleaned up file is pretty interesting through... it says I should have roughly 900psi. I just got my brake pressure gauge, so at some point when I get some time I'll have to verify that.

Thanks for the file
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#1235279 - 05/25/12 12:28 AM Re: Disc brakes: All the math that you never wanted to know [Re: dusted72]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Quote:

Ok so after reading through this whole thread I am still a little confused as to what the actual equations are used for. I know how to get the answers but why? Am I using those to get the figures for the stock setup compared to proposed setup? I am just unsure. In particular the purpose of the area of a circle and effective radius of a rotor? I did the math for both stock and proposed. What does it mean if the stock are of a circle is 6.78inches and the propsed is 7.06inches? Same with the Effective radius? Stock is 5.07 and proposed is 6.23. I just don't know. Also are there any braking books out there that are a must read? I am in Kuwait right now and will be returning back to the states within the next 2 weeks so if there are any recommended readings out there please share.





It's not too difficult to overcome a tire's friction with the ground. A basic brake package will do that.
When you get by going to larger brakes is the heat dissipation for repetitive stops. You also gain better feel over the brake function. In another thread I described it as tightening a bolt with a long wrench or a short one. You can break the bolt with either wrench but it's easier to feel the torque with the longer one. It's easier to feel and modulate the brakes with larger rotors.

The reason for the math is to make sure your stuff will work together. Will the master cylinder you're looking at work well with the calipers you have in mind? Will the pedal effort increase or decrease? Can you stop the car with one foot on the brakes or will it take both feet and your butt in the air to haul the car down?

In my case I copied an existing brake system. All my stuff is from a 2005 Mercedes S55. I didn't have to do anything except find an appropriate master cylinder.

The Pirate 4x4 site is great. I've been looking at it off and on for several years. It's got a lot of stuff that will work in many vehicles not just 4x4s.

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#1235280 - 05/27/12 04:43 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
hooziewhatsit Online   content
master

Registered: 10/05/07
Posts: 2551
Loc: State of Jefferson
Just hooked up my pressure gauge. Engine off I'm getting ~400psi at the front calipers. Engine on, I'm getting 700psi, and if I pump it half a dozen times, it'll go up to 900psi (with the pedal bottomed out (?)). This is actually very close to what the booster excel file predicted

This means my ok-ish braking is due to an issue/mismatch somewhere, and not just because they're 'ok'

Troubleshooting will have to wait for another day though
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#1235281 - 05/27/12 07:39 PM Re: Disc brakes: All the math that you never wanted to know [Re: hooziewhatsit]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
It sounds like you either have air in the system or the master cylinder is bad.

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#1235282 - 06/15/12 07:18 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
1964Polara Offline
enthusiast

Registered: 03/28/05
Posts: 276
Loc: Germany
GREAT THREAD!!!!

I have 64 B-Body with SSBC-A156 Disc Brakes and poor braking performance with a hard pedal feel.
Specs:
Rotor Diameter: 11,25
4 Pistons each 43 (mm I guess) = 1,69' x 2 = 2,39 for the calculator
Master Cylinder bore: 1 1/32 = 1,03'
Pedal Ratio not measured, taken 7' from the file

With the specs I have calculator shows torque 3100 and pad movement 0,0047. When I change to a 15/16 MC torque raises to 3824 but pad movement just 0,0039.

If I change the brake pedal move from 5 to 6 inches due to other stroke pad movement goes up to 0,0047.

So I might improve braking torque about 20% with a 15/16 Master Cylinder. I was thinking of buying a 1975/1976 A-Body master but they are all power units. Any other 15/16 Master recommendations?

Many thanx in advance

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#1235283 - 06/15/12 11:28 AM Re: Disc brakes: All the math that you never wanted to know [Re: 1964Polara]
Uhcoog1 Offline
super stock

Registered: 05/12/05
Posts: 717
Loc: Houston Tx
Quote:

GREAT THREAD!!!!

I have 64 B-Body with SSBC-A156 Disc Brakes and poor braking performance with a hard pedal feel.
Specs:
Rotor Diameter: 11,25
4 Pistons each 43 (mm I guess) = 1,69' x 2 = 2,39 for the calculator
Master Cylinder bore: 1 1/32 = 1,03'
Pedal Ratio not measured, taken 7' from the file

With the specs I have calculator shows torque 3100 and pad movement 0,0047. When I change to a 15/16 MC torque raises to 3824 but pad movement just 0,0039.

If I change the brake pedal move from 5 to 6 inches due to other stroke pad movement goes up to 0,0047.

So I might improve braking torque about 20% with a 15/16 Master Cylinder. I was thinking of buying a 1975/1976 A-Body master but they are all power units. Any other 15/16 Master recommendations?

Many thanx in advance




Dr Diff (Cass) is the only one I am aware of that sells a 15/16 manual master with the groove to keep the pushrod in place. He machines the groove in place himself. I just bought one, and it's sitting waiting to be installed.
_________________________
-'02 Dodge Viper Ex-World Challenge racecar
-'73 Duster, 6.1 based 392 hilborn hemi, tko600, full floater rear 9", Hellwig custom bars, viper brakes, built for road course

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#1235284 - 09/19/12 09:09 AM Re: Disc brakes: All the math that you never wanted to know [Re: Uhcoog1]
1964Polara Offline
enthusiast

Registered: 03/28/05
Posts: 276
Loc: Germany
To follow up this Thread...BTW best ever Thread on this board?

I've ordered the 15/16 MC from Dr.Diff and had it installed yesterday on my SSBS Setup and it improved a lot! Everything appeared what I was expecting. Longer pedal travel, softer pedal and much more braking force! After some testing brakes the pads where already starting to smell...I will change them asap...maybe even slotted rotors later.

By theory I got now 870 MC Pressure and 6213 brake Torque.
And if I want to further upgrade I still can hang up the MC pushrod and increase pedal ratio to 7:1 which will give my by theory more than 1000PSI & 7200 braking torque..

Great Thread! Thanx!!!

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#1235285 - 09/19/12 10:30 AM Re: Disc brakes: All the math that you never wanted to know [Re: 1964Polara]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
I'm glad you found it useful and were able to improve your brakes.

Remember the braking torque is not a true value. I added it to show what kind of difference in braking power you would have when changing parts.
Brake pads will not have a perfect friction value of 1 like the math shows. In the real world you'll be between .35 and .45 and the brake torque will drop to that percentage.
Still, it allows you to compare the changes in hydraulic forces assuming no change in brake pad compounds.

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#1972325 - 12/18/15 06:40 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
48Heap Offline
enthusiast

Registered: 02/14/05
Posts: 351
Loc: Spokane, WA
Originally Posted By feets
What this calculation does is average the diameter of the rotor and the diameter of the rotor minus the piston diameter. Doing that finds you the center of the piston. That is going to be pretty close to the center of the pad.


I know this is an old thread, but I kind of tripped over it just now and just have to ask a question.

The calculation of the effective radius of the rotor completely confused me. So I read through the thread and found this post explaining what the calculation is supposed to do.

My question is, if the calculation is supposed to average the diameter of the rotor and the diameter of the rotor minus the piston diameter, shouldn't the piston diameter be doubled? A larger diameter minus a smaller diameter doesn't return the inner diameter, it returns the diameter of the circle that would pass through the smaller circle. On the other hand, a larger diameter minus a smaller diameter divided by 2 would return the number I believe you are looking for.

Another way to calculate it is half the diameter of the rotor, minus half the diameter of the piston.

For example, a 11.75" rotor has a radius of 5.875", and if you laid a 2.75" piston on the edge of the rotor and came back in to the center of the piston 1.375", the radius from the center of the rotor to the center of the piston would be 4.5". The calculation as it stands returns 5.1875" which is only .6875" less than the radius of the rotor.

Am I missing something? Is that not what you are shooting for, the distance from the center of the caliper piston to the center of the rotor?

Not trying to start a fight, or nit pick anything, just trying to understand the math.


Attachments
Hot Rod Jan 82 Article.jpg

Description: High-Caliper Braking, HR Jan 82


_________________________
15 Chrysler 200S 3.6
15 Challenger R/T 6M STP
74 Duster 360 -> original 4 speed car

a.k.a. DionR

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#1990226 - 01/13/16 06:56 PM Re: Disc brakes: All the math that you never wanted to know [Re: 48Heap]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
Originally Posted By 48Heap
shouldn't the piston diameter be doubled?


Yeah, you're right. I guess I blew It on that one.

It's easiest to think radius of the rotor minus radius of the piston.

Looking back I guess I was hung up on the diameter since that had been used in other calculations.
Kinda funny that it only took a few years for someone to catch that.

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#2217370 - 12/19/16 09:16 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
goldduster318 Offline
pro stock

Registered: 01/19/03
Posts: 1400
Loc: Lake Orion, MI
I think this calculator might really be what we're looking for. Pretty interesting since you can figure out how much you need for a 1g stop, etc.

http://www.jakelatham.com/radical/info/brake_calculators.shtml
_________________________
'70 Duster 470hp 340/A-833/8 3/4 3.23 Sure-Grip

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#2222870 - 12/29/16 02:06 PM Re: Disc brakes: All the math that you never wanted to know [Re: goldduster318]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
That calculator is kinda neat but it's making the same assumptions mine does and then some.

Keep in mind that mine was designed to give a quick and dirty idea of the size master cylinder you need for specific calipers and rotors. The rest of it was done just for grins.


There are some serious calculators out there that go much deeper than mine or the one above but I seriously doubt many people here will have the information required to make them work correctly. I know I don't have that kind of info on any of my setups.

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#2298674 - 05/04/17 12:16 AM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
CBODY67 Offline
member

Registered: 03/20/17
Posts: 5
Loc: TX
When I started reading "the math", I was certain the pad/rotor friction coefficient would be "a value" as "a constant" of sorts. Which is fine for the calculations used.

On the edge of brake pad material is that pad's "birth certificate". Listing a code for the manufacturer, batch/date manufactured and/or other ID, AND the pad's coefficients when "cold" and "hot". Letters from "C" to "F", I believe. The letter code is two letters, first being "cold" and the second being "hot".

Question might be just how much difference there might be in these coefficient levels?

When vehicles started to be downsized in the 1980s, brake components got smaller, too, for the lighter cars. Pad dimensions were also decreased as metallic pad compositions became more common . . . less pad, more stopping power (brake torque). On many current "supercars", the rotors have grown to larger diameters and brake pads seem to have (again) become smaller in surface area.

Another "given" will be a constant surface finish of the rotor itself. A shiny smooth used surface might have less "bite" than a freshly cut and patterned or new (with factory in-broken-in contact surface) rotor.

The key curiosity is the difference between the pad co-efficient letters?

Thanks for all of the great information!
CBODY67
_________________________
66-CL42, 67-CE23, 70-DH43 Each under about 25K built. Numbers decrease with options and colors! How'd I manage that?

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#2318644 - 06/09/17 06:57 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
feets Offline
Senior Management

Registered: 01/20/03
Posts: 26740
Loc: Irving, TX
I haven't got a clue about the pad/rotor friction. There are too many variables to even play that game. That's why I used the magic value of 1. It shows the difference made when you change the other components.

That's what the thread was about. I concentrated on hydraulics and dimensions. You can use whatever pad and rotor material you like and the performance change will vary based upon the effectiveness of the mechanical system.

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#2319212 - 06/10/17 10:45 PM Re: Disc brakes: All the math that you never wanted to know [Re: feets]
Mattax Offline
super stock

Registered: 02/28/10
Posts: 938
Loc: Phila. Pa.
There's a thread discussing Brake Lining Edge Codes.

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