BMW M3 Forum (E90 E92)

BMW Garage BMW Meets Register Search Today's Posts Mark Forums Read


Go Back   M3Post - BMW M3 Forum > E90/E92 M3 Technical Topics > Suspension | Brakes | Chassis
 
GT Haus
Post Reply
 
Thread Tools Search this Thread
      06-02-2012, 11:35 AM   #1
r53s65e90
8300
 
r53s65e90's Avatar
 
Drives: r53 s65e90
Join Date: Mar 2009
Location: San Jose, CA

Posts: 529
iTrader: (0)

Brake balance calculations

I am looking for piston diameters for brakes in M3 applications. Rotor sizes are readily available. If you want to be super accurate the fitment templates have extra information, such as where the pad bites on the rotor e.t.c.

Brake torque T can be expressed as follows T=c*A*D. c= a constant for a given master cylinder and friction material (pads). A=total piston surface area on one side of the caliper. D=rotor diameter (or more accurately diameter of circle that the center of the clamping force on the disc, but rotor diameter should be enough for good estimates). A can be calculated given the piston diameters that seem to be nowhere available online. Only stop tech provides diameters.

Given the above simple formula brake bias front to back is calculated as follows: B=(Af*Df)/(Ab*Db) f=front b=back

Why these calculations are useful:

1) Stoptech says you can mix and match stock calipers with their calipers. This assumes that both the st60 and st40 front calipers do not alter (increase) brake torque. I don't want to assume in general if it is easy to calculate.

2) Brembo says nothing about mixing and matching so I want to figure out whether their caliper increases brake torque at the front so that it needs to be matched by a corresponding increase in the back. This is another simple calculation:

B=(Abr*Dbr)/(As*Ds) br=brembo s=stock (either back or front assuming same pad material)

If B>1 brembo calipers generate more torque = they will stop a wheels going 100 mph faster to the point where most braking force is applied to actually stopping the vehicle instead of decreasing the rotational energy of the wheel.

I searched before posting this as I am definitely not the only one to look for information like that. I will measure stock pistons next time I change into my track pads. Can anyone provide information about the stock and aftermarket pistons? (Vendors you should know this stuff. If you don't please could you measure some of the calipers you have lying around).

I will update the data below adding balance ratios as needed:

Piston diameters:
stock front= 60mm
stock back= 46mm
st40 355 front = p1: 44mm p2: 42mm
st40 355 back = p1: 34mm p2: 30mm
st60 380 front = p1: 36mm p2: 30mm p3:30mm
brembo 6 for 365 rotor =?
brembo 6 front for 380 rotor =?
brembo 4 back 380=?
brembo 4 back 350(?)=?
ap racing 6 front=?
ap racing 4 back=?
(... whatever else ...)

Please point out flaws in the write up above. Its all high school physics.

(All the above given same friction material front and back). Hence, stoptech can rightfully claim they provide a balanced upgrade no matter what you go with. All the balances above are within at least 2.5% of stock. Nice!

Last edited by r53s65e90; 06-10-2012 at 09:26 PM. Reason: update with actual stop tech piston sizes available on their website
r53s65e90 is offline   United_States
0
Reply With Quote
      06-02-2012, 01:58 PM   #2
JAJ
Captain
 
Drives: 2014 Shelby GT500
Join Date: Apr 2008
Location: Vancouver, BC

Posts: 924
iTrader: (4)

Quote:
Originally Posted by r53s65e90 View Post
I am looking for piston diameters for brakes in M3 applications. Rotor sizes are readily available. If you want to be super accurate the fitment templates have extra information, such as where the pad bites on the rotor e.t.c.

Brake torque T can be expressed as follows T=c*A*D. c= a constant for a given master cylinder and friction material (pads). A=total piston surface area on one side of the caliper. D=rotor diameter (or more accurately diameter of circle that the center of the clamping force on the disc, but rotor diameter should be enough for good estimates). A can be calculated given the piston diameters that seem to be nowhere available online. Only stop tech provides diameters, but I couldn't find which ones are used for the M3 applications.

Given the above simple formula brake bias front to back is calculated as follows: B=(Af*Df)/(Ab*Db) f=front b=back

Why these calculations are useful:

1) Stoptech says you can mix and match stock calipers with their calipers. This assumes that both the st60 and st40 front calipers do not alter (increase) brake torque. I don't want to assume in general if it is easy to calculate.

2) Brembo says nothing about mixing and matching so I want to figure out whether their caliper increases brake torque at the front so that it needs to be matched by a corresponding increase in the back. This is another simple calculation:

B=(Abr*Dbr)/(As*Ds) br=brembo s=stock (either back or front assuming same pad material)

If B>1 brembo calipers generate more torque = they will stop a wheels going 100 mph faster to the point where most braking force is applied to actually stopping the vehicle instead of decreasing the rotational energy of the wheel.

I searched before posting this as I am definitely not the only one to look for information like that. I will measure stock pistons next time I change into my track pads. Can anyone provide information about the stock and aftermarket pistons? (Vendors you should know this stuff. If you don't please could you measure some of the calipers you have lying around).

I will update the data below adding balance ratios as needed:

Piston diameters:
stock front=?
stock back=?
st40 355 front =?
st40 355 back =?
st60 380 front =?
brembo 6 for 365 rotor =?
brembo 6 front for 380 rotor =?
brembo 4 back 380=?
brembo 4 back 350(?)=?
ap racing 6 front=?
ap racing 4 back=?
(... whatever else ...)

Please point out flaws in the write up above. Its all high school physics.
Stock piston sizes are cast into the calipers.

As you say, the Stoptech ones are available from ST. Brembo doesn't say anything. AP Racing diameters are on the UK site in the assembly drawings.

I've done all these calculations and the various calipers I've evaluated are all within about 10% of each other. Basically, the auto industry has what looks like an industry standard for front and rear piston sizes, at least within a narrow range of total areas. Most BBK's match the stock sizes closely, usually slightly less piston area. Rotor sizes and swept diameters are also pretty standard, although the OEM rotors are usually deeper from rim to inside edge of the friction face.

Keep in mind that when you change pads, all your careful calculations go out the window because the mu of the new pads could be anywhere from half to double the mu of the pads you took off.
JAJ is offline  
0
Reply With Quote
      06-03-2012, 08:08 PM   #3
paradocs98
Major
 
paradocs98's Avatar
 
Drives: 2014 991 Carrera S
Join Date: May 2009
Location: NY

Posts: 1,342
iTrader: (0)

Since brake torque is a product of total piston area and rotor diameter, I would assume that going to a BBK would increase brake torque over the equivalent stock application. If StopTech says you can use their ST40 front caliper or their ST60 front caliper with the stock rears and brake bias is not affected, they must be varying the individual piston sizes of the ST40 4–piston setup vs. the ST60 6-piston setup to maintain the same overall piston area as the OEM SINGLE piston.

I know StopTech prides themselves on their "balanced brake upgrades," so varying piston sizes must be the answer. Otherwise, an ST40 front/OEM rear or ST60 front/OEM rear would have a different front-rear bias compared to my ST60 front/ST40 rear setup. Is it possible that with the ST60f/ST40r setup they actually allow higher brake torque at each axle over OEM, but front and rear torque is increased to the same degree, so the overall front-rear bias stays the same as OEM?

And what about the rotor diameter part of the equation? The 380mm rotors used with the ST60 front calipers are larger than OEM, so the brake torque should also be increased over OEM, unless they decrease the total piston area vs. OEM to compensate--3 StopTech pistons on one side of the rotor having LESS total area than a single OEM piston--but why would they do this? Are multiple pistons only for providing more uniform pressure/contact of the pads on the rotors vs. a single piston?

I'm probably just reiterating the original post, but I'm trying to work it through in my head...
paradocs98 is offline   United_States
0
Reply With Quote
      06-03-2012, 08:24 PM   #4
r53s65e90
8300
 
r53s65e90's Avatar
 
Drives: r53 s65e90
Join Date: Mar 2009
Location: San Jose, CA

Posts: 529
iTrader: (0)

Quote:
Originally Posted by JAJ View Post
Stock piston sizes are cast into the calipers.

As you say, the Stoptech ones are available from ST. Brembo doesn't say anything. AP Racing diameters are on the UK site in the assembly drawings.
Thanks for the pointers. I updated the 1st post with new numbers. Given the stock piston sizes (60mm front 46mm rear) and the data found on stoptech's web site, the piston sizes should be based on my calculations as follows:

st40 355 front = p1: 44mm p2: 42mm (44mm is max size for st40)
st40 355 back = p1: 34mm p2: 32mm
st60 380 front = p1: 36mm p2: 34mm p3:32mm (or 40 34 29 who knows?)

These sizes would allow mixing and matching stoptech and stock rotors with negligible change to brake balance.

Stock balance is: F/R = 1.74
Stoptech ST40 all around is: F/R = 1.69
Stoptech ST60/ST40 is: F/R = 1.70
Stoptech ST60/stock is: F/R = 1.78
Stoptech ST40/stock is: F/R = 1.77

(All the above given same friction material front and back). Hence, stoptech can rightfully claim they provide a balanced upgrade no matter what you go with. All the balances above are within at least 2.5% of stock. Nice!

Would be nice to figure out piston sizes for the other brands. I ran out of time while looking for piston sizes on APs website... Some other time maybe.

Quote:
Keep in mind that when you change pads, all your careful calculations go out the window because the mu of the new pads could be anywhere from half to double the mu of the pads you took off.
All the calculations I want to perform do not yield absolute values. So friction material does not factor as long as you use the same pads on both front and rear.

Last edited by r53s65e90; 06-03-2012 at 08:44 PM.
r53s65e90 is offline   United_States
0
Reply With Quote
      06-03-2012, 08:33 PM   #5
r53s65e90
8300
 
r53s65e90's Avatar
 
Drives: r53 s65e90
Join Date: Mar 2009
Location: San Jose, CA

Posts: 529
iTrader: (0)

Quote:
Originally Posted by paradocs98 View Post
I know StopTech prides themselves on their "balanced brake upgrades," so varying piston sizes must be the answer. Otherwise, an ST40 front/OEM rear or ST60 front/OEM rear would have a different front-rear bias compared to my ST60 front/ST40 rear setup. Is it possible that with the ST60f/ST40r setup they actually allow higher brake torque at each axle over OEM, but front and rear torque is increased to the same degree, so the overall front-rear bias stays the same as OEM?
What you are asking is possible. With the use of larger pistons you WILL increase brake torque. However, you will also increase pedal travel if you keep the same master cylinder as you will need to displace more fluid. Hence, there is a tradeoff here.

Quote:
And what about the rotor diameter part of the equation? The 380mm rotors used with the ST60 front calipers are larger than OEM, so the brake torque should also be increased over OEM, unless they decrease the total piston area vs. OEM to compensate--3 StopTech pistons on one side of the rotor having LESS total area than a single OEM piston--but why would they do this? Are multiple pistons only for providing more uniform pressure/contact of the pads on the rotors vs. a single piston?

I'm probably just reiterating the original post, but I'm trying to work it through in my head...
I updated my first post with piston sizes I think Stoptech would use to achieve whatever they advertise. I assumed that they would not go for higher brake torque vs stock given the same friction material. It is probably better to just use higher frictions pads to increase torque.
r53s65e90 is offline   United_States
0
Reply With Quote
      06-04-2012, 03:17 PM   #6
p0lar
New Member
 
p0lar's Avatar
 
Drives: 2004 BMW M3
Join Date: May 2012
Location: Midwest

Posts: 14
iTrader: (0)

Quote:
Originally Posted by r53s65e90 View Post
What you are asking is possible. With the use of larger pistons you WILL increase brake torque. However, you will also increase pedal travel if you keep the same master cylinder as you will need to displace more fluid. Hence, there is a tradeoff here.
This is absolutely correct.

Do you happen to know the width of the brake pads, front and rear?

I believe I came up with 65mm - based on that, I am getting a slightly higher bias of 1.77:1 for an OEM configuration based on those width estimates, though I am only basing those on the measured braking surface of the E9x rotors.

I built a massive spreadsheet containing a worksheet of front caliper/rotor combinations, and one of rear caliper/rotor combinations, then a cross between the two in another worksheet that gives any given bias for any given combination of F/R caliper/rotor combination.

This spreadsheet is for the E46 M3 and its variant packages, but should work just fine for anything you'd want to plug in if you have more numbers. It really is interesting to see how certain brake kit combinations could produce an astonishingly dangerous rear bias.
p0lar is offline   United_States
0
Reply With Quote
      06-04-2012, 08:51 PM   #7
RickyBobby
Lieutenant
 
RickyBobby's Avatar
 
Drives: M3
Join Date: Mar 2008
Location: NorCal

Posts: 462
iTrader: (1)

Your stoptech information is incorrect. I'm looking at my caliper right now and can confirm that the front st60 piston sizes are 36 36 30.

Last edited by RickyBobby; 06-09-2012 at 11:39 PM.
RickyBobby is offline  
0
Reply With Quote
      06-05-2012, 01:50 AM   #8
r53s65e90
8300
 
r53s65e90's Avatar
 
Drives: r53 s65e90
Join Date: Mar 2009
Location: San Jose, CA

Posts: 529
iTrader: (0)

Quote:
Originally Posted by p0lar View Post

Do you happen to know the width of the brake pads, front and rear?
Check these out:
Front http://www.pagidracing.com/brakes/8053.html
Rear: http://www.pagidracing.com/brakes/8021.html

They are links from: http://www.pagidracing.com/car.html

Quote:
I believe I came up with 65mm - based on that, I am getting a slightly higher bias of 1.77:1 for an OEM configuration based on those width estimates, though I am only basing those on the measured braking surface of the E9x rotors.
Your calculations are more accurate. I just used rotor diameter instead of the more accurate rotor diameter minus 60mm which takes into account where the piston applies force. If you do this you get 60*60*300/(46*46*290)=1.76. I was just interested in ballpark numbers to start with. Once I have the real piston sizes I can go fancy.

Quote:
I built a massive spreadsheet containing a worksheet of front caliper/rotor combinations, and one of rear caliper/rotor combinations, then a cross between the two in another worksheet that gives any given bias for any given combination of F/R caliper/rotor combination.

This spreadsheet is for the E46 M3 and its variant packages, but should work just fine for anything you'd want to plug in if you have more numbers. It really is interesting to see how certain brake kit combinations could produce an astonishingly dangerous rear bias.
This sounds nice. Can you share?

Last edited by r53s65e90; 06-05-2012 at 01:56 AM.
r53s65e90 is offline   United_States
0
Reply With Quote
      06-05-2012, 05:48 PM   #9
p0lar
New Member
 
p0lar's Avatar
 
Drives: 2004 BMW M3
Join Date: May 2012
Location: Midwest

Posts: 14
iTrader: (0)

Quote:
Originally Posted by r53s65e90 View Post
Can I check out any FMSI if I know the pagid reference number there?

Edit: I just looked, that gives the overall height of the backing plate, not necessarily the pad width. Getting real dimensions from FMSI specs seems like pulling teeth to me. It has taken a lot of first-hand intelligence to get specs from various pads to ensure that the swept area matches the rotor diameter - annulus when matching different caliper to rotor combinations. It also is a fundamental requirement when calculating the brake torque. The length of the pad is irrelevant, but the width is very much relevant and can change the bias significantly.


Quote:
Your calculations are more accurate. I just used rotor diameter instead of the more accurate rotor diameter minus 60mm which takes into account where the piston applies force. If you do this you get 60*60*300/(46*46*290)=1.76. I was just interested in ballpark numbers to start with. Once I have the real piston sizes I can go fancy.
Gotcha - I always attach units to calculations so I don't lose track of where I got them from, which is confusing enough as it is.


Quote:
This sounds nice. Can you share?
PM your eMail address.. I'll remove the riff-raff and shoot it over. It's rather comprehensive.. .. and not finished, but should still be an interesting read and help you with any calculations you're making. I'll promise you that, at least for the E46 M3, it'll be more comprehensive than anything else online!
p0lar is offline   United_States
0
Reply With Quote
      06-09-2012, 08:32 PM   #10
r53s65e90
8300
 
r53s65e90's Avatar
 
Drives: r53 s65e90
Join Date: Mar 2009
Location: San Jose, CA

Posts: 529
iTrader: (0)

Upated post 1 with information from here:
http://www.stoptech.com/Search/Produ...NA/BigBrakeKit
http://www.stoptech.com/Search/Produ...NA/BigBrakeKit
http://www.stoptech.com/Search/Produ...NA/BigBrakeKit
r53s65e90 is offline   United_States
0
Reply With Quote
      07-07-2012, 10:30 AM   #11
p0lar
New Member
 
p0lar's Avatar
 
Drives: 2004 BMW M3
Join Date: May 2012
Location: Midwest

Posts: 14
iTrader: (0)

I just wanted to supply an update about a thread I posted over at m3forum.net. Though the specs in parentheses are only correct for the E46 M3, the arithmetic and algebra should be consistent across the board. When contemplating master cylinder changes, the overall brake bias of a car is significantly different than what is usually reported, which is simply that of the front to rear caliper measurements, using a single average line pressure for front and rear, which all know to be patently false. That being said, if one stays within the confines of adjustment on the same car, ceteris paribus, only adjusting calipers, rotors and pads, it's OK to neglect line pressure as it's still a linear formula - it's the differential that matters most, either more or less forward than an OEM configuration.

Here is the direct link to the thread I started there, I'll try to keep it maintained/updated to the best of my ability.

If it's so desired, I can make both the F/R caliper/rotor/pad calculations AND overall including MC piston sizes if those are known for the E92 M3 and post them here.

BTW, not ALL BBK manufacturers post the piston diameters on the caliper, or the piston. I've got on the order of at least a dozen different Brembo calipers in my hands at this very moment, and I can easily count on one of those hands, unfortunately, how many actually cast the size of the piston into the caliper.

Totally off the topic: the best way to make the determination is to remove the pistons from one bank using a small fitting (10mmx1.0mm thread pitch adapted to a tire valve) and a bicycle pump. Using an air hose can be dangerous, not to mention the increased likelihood of damaging a ceramic-topped piston as it ejects from the cylinder bore at a ridiculously-high velocity (which directly translates to kinetic energy). Ask me how I know this, even when I covered the piston in question and took reasonable measures to ensure it wouldn't get damaged. NOW, I have a very specific "device" that covers one piston in its entirety, such that when it does "pop", it is pushed into a 1/2" rubber-foam lined cavity. Then, measure the piston -- SOMETIMES, in caliper/piston combinations that have been in service for quite some time, that they have a slight taper from front to rear. It's interesting to me, though I can't find rhyme or reason as to why that is the case. Either way, I'm always absolutely certain to mate the original pistons to their respective bores, even if I'm certain they're well within sufficient operating tolerance to behave correctly.

Ok, enough about that - I hope that post helps someone!
p0lar is offline   United_States
0
Reply With Quote
      07-08-2012, 01:34 AM   #12
Sleeper519
Captain
 
Sleeper519's Avatar
 
Drives: 08 E92 M3 DCT
Join Date: Nov 2009
Location: Atlanta, GA

Posts: 732
iTrader: (0)

Ok, alright, break it up all you engineering nerds!

This is a REAL car forum, so the answer to any and all questions on this board can be summed up as follows:

Needs a drop, tints, and add 20s.

__________________

2008 M3 Coupe / DCT // StopTech BBK 380/355 / Pagid RS29 / Motul / Apex Arc-8 / BFG R1S / Ground Control / MS filter / Performance spoiler / BPM tune // Road Atlanta 1:39.80 / VIR Full 2:10.87 / Barber 1:42.20
Sleeper519 is offline   United_States
0
Reply With Quote
Post Reply

Bookmarks

Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -5. The time now is 11:07 AM.




m3post
Powered by vBulletin® Version 3.7.0
Copyright ©2000 - 2014, Jelsoft Enterprises Ltd.
1Addicts.com, BIMMERPOST.com, E90Post.com, F30Post.com, M3Post.com, ZPost.com, 5Post.com, 6Post.com, 7Post.com, XBimmers.com logo and trademark are properties of BIMMERPOST