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Old 05-22-2002, 05:44 PM   #1
Jon Bogert
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Question Wanna help me do some brake math?

The question for all you brake engineers is: what size master cylinders (F & R) would you recommend? Please support your answer with at least a little bit of math.

Here are the parameters:

Brake rotor diameter: 260mm F, 220mm R
Effective radius (to center of pad): 110mm F, 95mm R
Caliper type: 4 pot (2 per side) F, 2 pot (1 per side) R
Caliper piston area: 31.1cm^2 F, 15.6cm^2 R
Pedal ratio: 5.5:1
Vehicle weight: 1500lbs
Desired braking force ratio: 80% F, 20% R
No booster--all manual.

I think that's all you should need--let me know if I missed something.

Thanks!

Jon
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Old 05-22-2002, 06:33 PM   #2
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There is no front/rear. For master cylinder all you need to worry about is the caliper piston sizes and pedal ratio. The master cylinder (MC) is only there to provide volume for the calipers.


The brake bias comes from your prop valve and rotor/caliper sizing.


You can use the largest MC you can find, there is no such think as too big, just to small. The above are the minimum you will need to even be close to decent.

The larger the bore of the MC the less stroke you will need, but the softer the pedal will be. If you can live with not so good pedal feel then get a 26.99mm MC, which is what is used on most large trucks (Like Ford F-150).

Here is how to calculate mechanical advantage:

Area of MC * pedal ratio = M
Area of front piston= N

ME= M/N = larger is less effort


25.4mm (1 inch) MC gets you close to a 1:1 so for every 100lbs at the pedal you get a 100 pounds at the caliper.

Your racer only weighs 1500 pounds you don't need much.
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Old 05-22-2002, 06:50 PM   #3
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The pedal is setup for dual MCs. There is an adjustable bias bar, so no proportioning valve is needed. Here's a pic so you know what I'm dealing with:



I can have just about ANY master cylinder sizes I want with this arrangement. I'd prefer to size the rear MC appropriately so that I have adjustment room on either side.
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Old 05-22-2002, 08:44 PM   #4
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Well what I wrote above still holds. Just now your splitting the car in half.

Basically look at the rears separate from the fronts.

So you would look at the MC size for the fronts just by looking at the front pistons.

Same for the rears

The only thing that can be tuned is feel. You can go to a larger bore for a shorter pedal stroke or to a smaller bore with a longer stroke but firmer feel.


By the way all modern MC are TMC, tandem master cylinder, which is a dual MC in one casting. Of course this means both chambers need to be the same diameter.





It's hard to tell you exactly what size because I don't know your feel preferences. Personally for racing I would rather have a short stroke, low effort pedal (large bore/short stroke) for long distance racing and the firm, longer stroke for sprints( small bore/long stroke). Why? Because on long races my leg will cramp up!


Geez..that thing costs! You must be serious about your motorsports!


This can help you get close to "ideal"

Stopping Force = pedal force * brake pad coefficient of friction * mechanical force ratio * (1/radius of the tire) * brake rotor effective radius

stopping force = weight of car * longitudal coefficient of friction of tires

mechanical force ratio is what you are looking for.

This ratio should get you right to lock up.

Take that ratio and divide it by the pedal ratio.

This is the ratio of mastercylinder bore area and caliper piston bore area.

So say a 4:1 then for a 30cm^2 caliper piston you want a 7.5cm^2 MC or ~28mm bore MC.

For the fronts use the total mass of the car, for the rears use the weight just over that axle. This ensures you get max braking power without locking up the rear all the time.


PLEASE CHECK MY MATH...I have a headache right now.

Last edited by romanom; 05-22-2002 at 11:06 PM.
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Old 05-22-2002, 09:03 PM   #5
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You know this company selling you the assembly should be able to tell you the master cylinder sizing based on simple computer simulations
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Old 05-22-2002, 10:14 PM   #6
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Front - Rear Bias

personally I'd concentrate on the fronts since you only want 20% rear bais but here you go:

Front Force = weight front + total weight * tire friction * height of CG * (1/wheel base)

Rear Force is the same except substitute weight front with weight rear and change the + to a -

The ratio Front/Rear should be used to get the Front Braking Force and Rear Braking Force percentages.

I.E. For a Front/Rear = 3:1 then the use 75% of the Stopping Force for to get the diameter of the MC for the front calipers.

Last edited by romanom; 05-22-2002 at 11:07 PM.
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Old 05-22-2002, 11:08 PM   #7
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Jon,

Read my stuff carefully. I'm not feeling all the well and I've already found some mistakes/typos.

If something sounds odd ask.



Mike
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Old 05-22-2002, 11:24 PM   #8
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Summary of Equations:
(for ease and consistency try and use meters and kg)

1.
stopping force = weight of car * longitudal coefficient of friction of tires


2.
Stopping Force = pedal force * brake pad coefficient of friction * mechanical force ratio * (1/radius of the tire) * brake rotor effective radius

.....solve for mechanical force ratio


3.
Front Force = weight front + total weight * tire friction * height of CG * (1/wheel base)

4.
Rear Force = weight rear - total weight * tire friction * height of CG * (1/wheel base)


5.
% front = Front Force/Stopping Force


6.
% Rear = Rear Force/Stopping Force

7.
mechanical force ratio front = mechanical force ratio * %front
mechanical force ratio rear = mechanical force ratio * %rear


8.
Take that ratio and divide it by the pedal ratio.

This is the ratio of mastercylinder bore area and caliper piston bore area.

So say a 4:1 then for a 30cm^2 caliper piston you want a 7.5cm^2 MC or ~28mm bore MC.
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Old 05-22-2002, 11:40 PM   #9
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Wow, great stuff!

But, is equation 2 for the whole car? How do you account for different effective rotor diameters front and rear?
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Old 05-22-2002, 11:52 PM   #10
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Quote:
Originally posted by Jon Bogert
Wow, great stuff!

But, is equation 2 for the whole car? How do you account for different effective rotor diameters front and rear?
I hate you! Good question.

Yes it is for the whole car.

Use the fronts as this will have the most work to do.

Nothing is perfect, but this gives you a very good estimate.

For instance if you use larger rear tires then it's friction coefficient will be different, but it's small enough to ignore.

Also the weight of the car is total weight including any aero down force you produce at max velocity of the car and you and fuel and etc......


Just keep in mind that the MC does not effect the stopping distance, just the pedal effort and stroke.

Which means that once you get a bore diameter and then calculate the stroke from the volume requirement you can increase or decrease bore as long as you go in the other direction with stroke. Simply you can trade effort for stroke or visa versa.
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Old 05-23-2002, 12:08 AM   #11
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OK, so just using the fronts--as if the fronts are stopping 100% of the weight (which isn't far off), here's what I get:

Code:
Pedal pressure          100 lbs
Brake pad Cf            0.5	
Effective disc radius   0.36 feet
1/tire radius           1.07	

All up weight           1500	
Tire Cf                  1.2	
Stopping Force          1800	

Force ratio             93:1
Pedal ratio              6:1
Caliper to MC area      15.6 	
Caliper piston size     44.5mm
Caliper piston area     3111mm^2
x two calipers          6221mm^2	
MC area needed           399mm^2
MC diameter               23mm
So I should be fine with a standard 7/8" MC
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Old 05-23-2002, 04:35 AM   #12
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I knew that you were about to set up a new pedal assembly, is this for a Sub or for you rally car? We are also looking at this set up for our car let me know how you like the tilton assembly we are looking at that one and the AP assembly
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Old 05-23-2002, 09:09 AM   #13
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Quote:
Originally posted by Jon Bogert
OK, so just using the fronts--as if the fronts are stopping 100% of the weight (which isn't far off), here's what I get:

Code:
Pedal pressure          100 lbs
Brake pad Cf            0.5	
Effective disc radius   0.36 feet
1/tire radius           1.07	

All up weight           1500	
Tire Cf                  1.2	
Stopping Force          1800	

Force ratio             93:1
Pedal ratio              6:1
Caliper to MC area      15.6 	
Caliper piston size     44.5mm
Caliper piston area     3111mm^2
x two calipers          6221mm^2	
MC area needed           399mm^2
MC diameter               23mm
So I should be fine with a standard 7/8" MC
You did it right!

Now keep in mind that if you want less pedal force (lower effort) then you will need a larger bore MC.

Now imagine that a 23.88mm MC is a commom size on many smaller cars. Now with out a booster it's nearly impossible to stop those cars. The only reason you can get away with a 23 is that the car is so light.

Last edited by romanom; 05-23-2002 at 09:19 AM.
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Old 05-23-2002, 10:20 AM   #14
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The exact formulas you need can be found in Milliken and Milliken's "Race Car Vehicle Dynamics". It's expensive, but it's crammed full of usefull info, especially if you are doing a lot of re-engineering/redesigning. You can plug in all the info you have and not only can you calculate the bore diameter you want, you can also get a starting point for your bias bar offset.
You will also need to know front to rear weight transfer under braking, so you will need to know the CG height and the wheelbase.
What car are you building that only weighs 1500lbs?
Good luck
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Old 05-23-2002, 10:53 AM   #15
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I'm building a Fury:



There's a long thread in the Motorsports Forum with lots of details.

I'm not sure the Tilton floor mount pedals would work well with a rally car. I believe floor hinged pedals work best ergonomically when your butt is very close to the floor and your legs are relatively straight. For a production car, top hinged pedals are a better choice. I also looked at the AP pedals--they come with a gas pedal, too--but $1200 is a bit steep. The Tiltons are $225, or $360 complete with MCs and reservoirs.
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Old 05-23-2002, 10:59 AM   #16
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Mike just to clarify, I think you got something reversed:

A larger MC results in...
> less pedal travel
> a firmer pedal
> less hydraulic advantage

A smaller MC results in...
> more pedal travel
> a softer pedal
> more hydraulic advantage

Larger caliper piston area results in...
> more pedal travel
> a softer pedal
> more hydraulic advantage

Smaller caliper piston area results in...
> less pedal travel
> a firmer pedal
> less hydraulic advantage
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Old 05-23-2002, 12:37 PM   #17
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Quote:
Originally posted by Jon Bogert
Mike just to clarify, I think you got something reversed:

A larger MC results in...
> less pedal travel
> a firmer pedal
> less hydraulic advantage

A smaller MC results in...
> more pedal travel
> a softer pedal
> more hydraulic advantage

Larger caliper piston area results in...
> more pedal travel
> a softer pedal
> more hydraulic advantage

Smaller caliper piston area results in...
> less pedal travel
> a firmer pedal
> less hydraulic advantage
Say you have 2 tubes, one is 1 sq in the other 2 sq in. Tubes are filled with fluid with a piston inside. You apply 100 lbs to the piston.

The 1 sq in tubes will produce 100PSI at the other end while the 2 sq in tube will produce 50PSI at the other end. Which is all that's coming back at you. So your displacing the same volume but building less pressure with the larger MC which is why you feel less effort at the pedal.

It's similiar to flow through a tube, the larger the tube the less effort. Like an exhaust system, larger tubing and less back pressure.

So everything else you have is correct, but the effort part for the MC.

To put in non braking terms:

The larger the bore of a tube the less back pressure and the less hydraulic pressure at the other end. So with a larger bore you flow more, more easily, but get less force at the other end.


Unfortunately with many cars that have large volume requirements (to ensure full travel of the caliper piston) your sometimes forced to go with a large bore MC otherwise the pedal travel is just too long (imagine a MC in your SUV that's 80mm long, packaging and casting nightmare).
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Old 05-23-2002, 01:58 PM   #18
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Jon,

You probably already know this, but just in case.

Are you going to install a driver adjustable prop valve?

I recommend you do, they're driver adjustable by the driver while driving. There are the screw type and lever type. The screw type are "infinitily" adjustable through a range, while the lever type has a certain number (5-8) of presets. The advantage of the lever type is you just pull/push to a preset and you're done.

They're very nice because you can back out the rear braking as tires start to go and fuel mass drops.

You just install it in line on the brake tube. Takes some wierd routing, but it's quite easy.

The difference between this and a bias bar is a adjustable prop valve can actually change the overall braking force, not just shift the bias.

I belief Tilton makes both.

Here's an example:
http://www.racerpartswholesale.com/propvalv.htm


Mike

Last edited by romanom; 05-23-2002 at 03:11 PM.
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Old 05-23-2002, 06:41 PM   #19
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OK look at it this way...

If you use a larger MC, but change nothing else, the ratio of the MC area to the caliper piston area will increase. If it's 1:70 and you double the size (area) of the MC, it becomes 1:35. So to produce equivalent stopping force, you have to push twice as hard.

Take this example to its limits--with equal area MC area and caliper piston area--and you'd have to push pretty damn hard to generate that 1800lbs of force!
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Old 05-23-2002, 07:37 PM   #20
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Quote:
Originally posted by Jon Bogert
OK look at it this way...

If you use a larger MC, but change nothing else, the ratio of the MC area to the caliper piston area will increase. If it's 1:70 and you double the size (area) of the MC, it becomes 1:35. So to produce equivalent stopping force, you have to push twice as hard.

Take this example to its limits--with equal area MC area and caliper piston area--and you'd have to push pretty damn hard to generate that 1800lbs of force!
Yes your right.

I did get myself mixed up. In my own mind confused effort and feedback. Hey I am a little sick so I'm sure the beer had nothing to do with it.

Sorry I shouldn't have used the term effort. I forget that not everyone thinks the same way I do.


With a larger MC bore you will have less "feedback" Think of it in the same terms are air in the system, requires more effort to stop and gives a mushy pedal (of course air also increase travel).

I should have put it in terms of feedback. A larger bore MC gives you less feedback.

SUVS and full-size pickups are great examples. Even when their brake sizing at the corners is fine they still require a hefty push on the pedal, but the pedal feels like a bag of marshmellows because of the large bore MC they have to get the required volume.

In pedal feel there's:

Effort vs. Travel
Travel vs. deceleration
Effort vs. deceleration
Work vs. deceleration


I hang my head in shame!

Last edited by romanom; 05-23-2002 at 08:14 PM.
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Old 05-23-2002, 08:02 PM   #21
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Quote:
Originally posted by romanom

I hang my head in shame!

Well u shouldn't! *I* hang my head in shame, i have no idea what the hell you guys are talking about
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Old 06-11-2002, 02:31 PM   #22
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This is great stuff!

But I have a question. Does anyone make a larger MC that can bolt to the factory booster? If not what is the best solution for a street driven car with big brakes front and rear (ie 6-pots/f and 4 pots/r)?

Please help!!

-Kevin
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Old 06-11-2002, 02:43 PM   #23
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Quote:
what is the best solution for a street driven car with big brakes front and rear (ie 6-pots/f and 4 pots/r)?
With a street driven car you have the advantage of knowing the stock baseline specs. Start from there and calculate the % change in front and rear piston area vs. stock. Chances are it won't be that far off and you won't need to change a thing.
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Old 06-11-2002, 11:07 PM   #24
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Quote:
Originally posted by Jon Bogert

With a street driven car you have the advantage of knowing the stock baseline specs. Start from there and calculate the % change in front and rear piston area vs. stock. Chances are it won't be that far off and you won't need to change a thing.

Stock MC's from the factory area at least 20% "overstroked." This is to allow max pedal travel even with a circuit failure.

It's called "the MC over-travel"
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