brake bias math
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
brake bias math
Brake bias math and its effects on handling
Recently I have been toiling with the idea of ditching my 6th gen calipers that I upgraded to a few months ago for some J30/Q45 calipers which are 2 piston sliding (effectively 3 piston) compared to the 6th gen and 5/4th gen calipers which are all 1 piston sliding (effectively 2 piston). My reasons for upgrading from my stock 2000 maxima rotors and calipers were two fold: to obtain larger rotors and calipers up front which look a whole lot better underneath my 18” street wheels, and to obtain the use of significantly larger pads and rotors equaling proportionately less fade up front lessening the possibilities of rotor warping (a common issue which consistently plagues 5th gen owners due to the rotors being to small to effectively absorb and dissipate all the heat incurred in a track or autocross environment). Most 5th gen owners have remedied this by getting aftermarket higher quality slotted or cross-drilled rotors and aftermarket pads which resist fade better…more often than not, those 5th gen owners whom are warping their rotors consistently, are not taking some very simple preventative measures to avoid such a hassle ie. –
-Do not cool the brakes off rapidly with water, mud, etc if they are above normal temperatures.
-If you make a quick stop from highway speeds (for a stoplight for instance), do not stay on the brakes after you are stopped if you can help it. This is especially true for automatic transmissions. By holding pressure brakes, you are creating a "hot-spot" on the rotor which will lead to uneven cooling.
Now, brakes are an all too often overlooked performance upgrade for our maxima’s or any car which is destined to see the track/autocross at some time or another!
After researching exhaustingly on methods and options to upgrade our stock brakes to avoid such warping issues and to resist the fade of which I was destined to encounter at the local road courses I frequent, I found several big brake kits or “BBK’s” for short available for our cars at a premium price—mind you, all of these would have alleviated and nearly eliminated all possibilities of fade or warping at any level of aggressive performance driving, however, there is much more to braking performance than meets the eye and things can get quite complicated…basically the lesson I learned was simple—keeping factory brake bias when you upgrade your brakes is essential, unless you want a particular bias change for some reason such as you want to induce more oversteer or more understeer (which I am sure the latter should never be the desire of any self-respecting competitive maxima driver on here). So herein lies the problem, all of these fancy 18 thousand piston 20” rotor front big brake kits look great with their powder-coated calipers and recognizable names, but taking into account that more front bias would induce more understeer in our already difficult to rotate front heavy machines would hamper my performance at the track and especially so at autocross events. So dismissing the expensive overly large brake kits from the large companies, I went in search of an affordable brake upgrade which would serve all of my desires—less fade, cheap, and keeping the factory brake bias front to rear. I knew this daunting task was not going to solve itself or be easy, but I will let you make your own conclusions based on what your specific needs are and make your own informed decisions on what will work best for you depending on your type of performance driving/characteristics you would like your maxima to exhibit out on the local road coarse/autoX.
I have done some relatively simple brake bias math (all #’s were rounded to the nearest hundredth) using what was hopefully reliable info/data on the internet and FSM’s…and using the Hawk HPS pad as an example for each in terms of size/dimensions…
To obtain a rough idea of brake bias we need a few simple equations and basic arithmetic:
1. effective rotor diameter= rotor diameter - radial pad width
2. effective piston area= piston diameter^2 x how many pistons in caliper
3. brake torque= effective rotor diameter x effective piston area
4. front brake bias= front brake torque / (front brake torque + rear brake torque)
5. rear brake bias= 1.00 - front brake bias
for the sake of me not getting carpal tunnel syndrome, lets make this small legend effective from this point forth:
1. effective rotor diameter= ERD
2. effective piston area= EPA
3. brake torque= Bt
4. front brake bias= BBf
5. rear brake bias= BBr
First and foremost looking at stock 4th and 5th gen brakes for comparison purposes:
A. Stock 2000 maxima front brakes:
2.25” single piston sliding calipers (effectively 2 piston)
~11” rotor diameter
5.4” x 2.09” pad (11.286 sq in. rough estimation)
B. Stock 2000 maxima rear brakes:
1.52” single piston sliding calipers (effectively 2 piston)
10.94” rotor
4.15” x 1.69” pad (~7 sq in. pad)
C. Blehmco Z32 rear calipers w/Z32 fronts:
1.5” 2 piston fixed caliper with drum type e-brake
11.69” rotor
2.88” x 2.15” (6.192 sq in. pad)
D. Blehmco relocated 2000 maxima front calipers over 6th gen rotors:
2.25” single piston sliding calipers
12.6” rotor
5.4” x 2.09” pad
E. Jeff’s relocated 2000 maxima front calipers over 13” cobra rotors:
2.25” single piston sliding
13” rotor
5.4” x 2.09” pad
F. Full 6th gen calipers and rotors:
2.25” single piston sliding calipers
12.6” rotor
5.34” x 2.60” pad (13.884 sq in.)
G. Blehmco relocated J30/Q45 calipers over 6th gen rotors:
1.72” 2 piston sliding calipers (effectively 3 piston)
12.6” rotor
5.48” x 2.35” pad (12.878 sq in.)
H. Jeff’s relocated J30/Q45 calipers over 13” cobra rotors:
1.72” 2 piston sliding calipers
13” rotor
5.48” x 2.35” pad
I. Blehmco relocated Z32 front brake calipers over 6th gen rotors:
1.6” 4 piston fixed calipers
12.6” rotor
4.69” x 2.45” pad (11.49 sq in.)
J. Jeff’s relocated Z32 front brake calipers over 13” cobra rotors:
1.6” 4 piston fixed calipers
13” rotor
4.69” x 2.45” pad
A.
ERD= 8.91”
EPA= 10.125”
Bt= 90.214
BBf= 68%
BBr= 32%
B.
ERD= 9.25”
EPA= 4.62”
Bt= 42.735
BBf= 68%
BBr= 32%
C.
ERD= 9.54”
EPA= 4.5”
Bt= 42.93
BBf= ~70%
BBr= ~30%
D.
ERD= 10.51”
EPA= 10.125”
Bt= 106.414
BBf= 71%
BBr= 29%
E.
ERD= 10.91”
EPA= 10.125”
Bt= 110.46
BBf= 72%
BBr= 28%
F.
ERD= 10”
EPA= 10.125”
Bt= 101.25
BBf= 70%
BBr= 30%
G.
ERD= 10.25”
EPA= 8.8752”
Bt= 90.97
BBf= 68%
BBr= 32%
H.
ERD= 10.65”
EPA= 8.8752”
Bt= 94.52
BBf= 69%
BBr= 31%
I.
ERD= 10.15”
EPA= 10.24”
Bt= 103.936
BBf= 71%
BBr= 29%
J.
ERD= 10.55”
EPA= 10.24”
Bt= 108.032
BBf= 72%
BBr= 28%
*I don’t claim for all the math to be perfect as I received most of my data from external sources on other forums, most items were rounded which can affect accuracy and are just approximations to give you a general idea of bias trends based on different caliper/rotor setups…
So as you can see, upgrading to the Z32 4 piston fixed front calipers alone (while increasing clamping force and feel/ability to modulate would throw the front brake bias up roughly 3 or 4% compared to stock)…adding the Z32 rear upgrade also offered from Matt Blehm, would put it back to around stock bias, but at an added cost of another $1000 or so if you use all new stuff instead of sourcing rebuilt items; however, this setup would give you better and more balanced braking than all of those front only 6 piston aftermarket front kits for a good deal less. Nonetheless, looking at the data, I believe what will work best for me is the J30/Q45 2 piston sliding (effectively 3 piston) setup…which allows slightly more clamping force as well as more evenly distributed clamping force due to the extra inside fixed piston, more pad area than our stock pads for less fade on the track, and no clearance issues with wheels necessitating the need for spacers as the J30/Q45 pistons are located inboard and thus would fit any wheel our stock calipers fit. My only issue with the J30/Q45 and 6th gen calipers are there inherent lack of pad availability, Hawk only offers the HPS and not the HP+ compound…whereas our stock calipers and the Z32 calipers have a greater pad availability—the Z32 being the best of course.
There is an excellent article published by Stoptech regarding brake bias and proper caliper piston selection as well performance taking into account weight distribution of the car under heavy “dive” or braking conditions at the end of the article you can see a pic which illustrates that even they admit that their 4 wheel upgrade kits are considerably more balanced than a huge front or rear kit alone: http://www.stoptech.com/tech_info/wp...formance.shtml
You can also apply their weight distribution under heavy braking to our cars given that our cars are about 63 or 62% front weight biased from the factory, therefore more front bias braking is always more desirable in our cases, both for safety and best deceleration capability, however, in most cases, auto manufacturers instill more front bias than is necessary for stability reasons (which can hinder braking distances) as they do the same when they engineer in understeer for safety reasons, so let’s not make things worse by adding even more front bias, that is unless you have tons of weight in your front end and none in the rear, then in that case, your rears will lock too easily if they have too much brake torque applied to them, but I very much doubt the crowd I am preaching to right now would make their weight balance worse than it was from the factory!
Here is some random other data which you might find interesting (fixed piston calipers are traditionally lighter even if made from the same material:
240SX 300ZX TT Skyline GTR R34 Q45
Rotor Diameter: 10 inch 11 inch 11.6 inch 11 inch
Rotor Thickness: 18mm 30mm 32mm 28mm
Rotor Weight: 12.5 lbs 17.5 lbs 19 lbs 17.5 lbs
Caliper Type: 1-piston sliding 4-piston fixed 4-piston fixed 2-piston sliding
Caliper Weight: 9.5 lbs 6.5 lbs (alum), 10lbs (iron) 6.5 lbs 11 lbs
Recently I have been toiling with the idea of ditching my 6th gen calipers that I upgraded to a few months ago for some J30/Q45 calipers which are 2 piston sliding (effectively 3 piston) compared to the 6th gen and 5/4th gen calipers which are all 1 piston sliding (effectively 2 piston). My reasons for upgrading from my stock 2000 maxima rotors and calipers were two fold: to obtain larger rotors and calipers up front which look a whole lot better underneath my 18” street wheels, and to obtain the use of significantly larger pads and rotors equaling proportionately less fade up front lessening the possibilities of rotor warping (a common issue which consistently plagues 5th gen owners due to the rotors being to small to effectively absorb and dissipate all the heat incurred in a track or autocross environment). Most 5th gen owners have remedied this by getting aftermarket higher quality slotted or cross-drilled rotors and aftermarket pads which resist fade better…more often than not, those 5th gen owners whom are warping their rotors consistently, are not taking some very simple preventative measures to avoid such a hassle ie. –
-Do not cool the brakes off rapidly with water, mud, etc if they are above normal temperatures.
-If you make a quick stop from highway speeds (for a stoplight for instance), do not stay on the brakes after you are stopped if you can help it. This is especially true for automatic transmissions. By holding pressure brakes, you are creating a "hot-spot" on the rotor which will lead to uneven cooling.
Now, brakes are an all too often overlooked performance upgrade for our maxima’s or any car which is destined to see the track/autocross at some time or another!
After researching exhaustingly on methods and options to upgrade our stock brakes to avoid such warping issues and to resist the fade of which I was destined to encounter at the local road courses I frequent, I found several big brake kits or “BBK’s” for short available for our cars at a premium price—mind you, all of these would have alleviated and nearly eliminated all possibilities of fade or warping at any level of aggressive performance driving, however, there is much more to braking performance than meets the eye and things can get quite complicated…basically the lesson I learned was simple—keeping factory brake bias when you upgrade your brakes is essential, unless you want a particular bias change for some reason such as you want to induce more oversteer or more understeer (which I am sure the latter should never be the desire of any self-respecting competitive maxima driver on here). So herein lies the problem, all of these fancy 18 thousand piston 20” rotor front big brake kits look great with their powder-coated calipers and recognizable names, but taking into account that more front bias would induce more understeer in our already difficult to rotate front heavy machines would hamper my performance at the track and especially so at autocross events. So dismissing the expensive overly large brake kits from the large companies, I went in search of an affordable brake upgrade which would serve all of my desires—less fade, cheap, and keeping the factory brake bias front to rear. I knew this daunting task was not going to solve itself or be easy, but I will let you make your own conclusions based on what your specific needs are and make your own informed decisions on what will work best for you depending on your type of performance driving/characteristics you would like your maxima to exhibit out on the local road coarse/autoX.
I have done some relatively simple brake bias math (all #’s were rounded to the nearest hundredth) using what was hopefully reliable info/data on the internet and FSM’s…and using the Hawk HPS pad as an example for each in terms of size/dimensions…
To obtain a rough idea of brake bias we need a few simple equations and basic arithmetic:
1. effective rotor diameter= rotor diameter - radial pad width
2. effective piston area= piston diameter^2 x how many pistons in caliper
3. brake torque= effective rotor diameter x effective piston area
4. front brake bias= front brake torque / (front brake torque + rear brake torque)
5. rear brake bias= 1.00 - front brake bias
for the sake of me not getting carpal tunnel syndrome, lets make this small legend effective from this point forth:
1. effective rotor diameter= ERD
2. effective piston area= EPA
3. brake torque= Bt
4. front brake bias= BBf
5. rear brake bias= BBr
First and foremost looking at stock 4th and 5th gen brakes for comparison purposes:
A. Stock 2000 maxima front brakes:
2.25” single piston sliding calipers (effectively 2 piston)
~11” rotor diameter
5.4” x 2.09” pad (11.286 sq in. rough estimation)
B. Stock 2000 maxima rear brakes:
1.52” single piston sliding calipers (effectively 2 piston)
10.94” rotor
4.15” x 1.69” pad (~7 sq in. pad)
C. Blehmco Z32 rear calipers w/Z32 fronts:
1.5” 2 piston fixed caliper with drum type e-brake
11.69” rotor
2.88” x 2.15” (6.192 sq in. pad)
D. Blehmco relocated 2000 maxima front calipers over 6th gen rotors:
2.25” single piston sliding calipers
12.6” rotor
5.4” x 2.09” pad
E. Jeff’s relocated 2000 maxima front calipers over 13” cobra rotors:
2.25” single piston sliding
13” rotor
5.4” x 2.09” pad
F. Full 6th gen calipers and rotors:
2.25” single piston sliding calipers
12.6” rotor
5.34” x 2.60” pad (13.884 sq in.)
G. Blehmco relocated J30/Q45 calipers over 6th gen rotors:
1.72” 2 piston sliding calipers (effectively 3 piston)
12.6” rotor
5.48” x 2.35” pad (12.878 sq in.)
H. Jeff’s relocated J30/Q45 calipers over 13” cobra rotors:
1.72” 2 piston sliding calipers
13” rotor
5.48” x 2.35” pad
I. Blehmco relocated Z32 front brake calipers over 6th gen rotors:
1.6” 4 piston fixed calipers
12.6” rotor
4.69” x 2.45” pad (11.49 sq in.)
J. Jeff’s relocated Z32 front brake calipers over 13” cobra rotors:
1.6” 4 piston fixed calipers
13” rotor
4.69” x 2.45” pad
A.
ERD= 8.91”
EPA= 10.125”
Bt= 90.214
BBf= 68%
BBr= 32%
B.
ERD= 9.25”
EPA= 4.62”
Bt= 42.735
BBf= 68%
BBr= 32%
C.
ERD= 9.54”
EPA= 4.5”
Bt= 42.93
BBf= ~70%
BBr= ~30%
D.
ERD= 10.51”
EPA= 10.125”
Bt= 106.414
BBf= 71%
BBr= 29%
E.
ERD= 10.91”
EPA= 10.125”
Bt= 110.46
BBf= 72%
BBr= 28%
F.
ERD= 10”
EPA= 10.125”
Bt= 101.25
BBf= 70%
BBr= 30%
G.
ERD= 10.25”
EPA= 8.8752”
Bt= 90.97
BBf= 68%
BBr= 32%
H.
ERD= 10.65”
EPA= 8.8752”
Bt= 94.52
BBf= 69%
BBr= 31%
I.
ERD= 10.15”
EPA= 10.24”
Bt= 103.936
BBf= 71%
BBr= 29%
J.
ERD= 10.55”
EPA= 10.24”
Bt= 108.032
BBf= 72%
BBr= 28%
*I don’t claim for all the math to be perfect as I received most of my data from external sources on other forums, most items were rounded which can affect accuracy and are just approximations to give you a general idea of bias trends based on different caliper/rotor setups…
So as you can see, upgrading to the Z32 4 piston fixed front calipers alone (while increasing clamping force and feel/ability to modulate would throw the front brake bias up roughly 3 or 4% compared to stock)…adding the Z32 rear upgrade also offered from Matt Blehm, would put it back to around stock bias, but at an added cost of another $1000 or so if you use all new stuff instead of sourcing rebuilt items; however, this setup would give you better and more balanced braking than all of those front only 6 piston aftermarket front kits for a good deal less. Nonetheless, looking at the data, I believe what will work best for me is the J30/Q45 2 piston sliding (effectively 3 piston) setup…which allows slightly more clamping force as well as more evenly distributed clamping force due to the extra inside fixed piston, more pad area than our stock pads for less fade on the track, and no clearance issues with wheels necessitating the need for spacers as the J30/Q45 pistons are located inboard and thus would fit any wheel our stock calipers fit. My only issue with the J30/Q45 and 6th gen calipers are there inherent lack of pad availability, Hawk only offers the HPS and not the HP+ compound…whereas our stock calipers and the Z32 calipers have a greater pad availability—the Z32 being the best of course.
There is an excellent article published by Stoptech regarding brake bias and proper caliper piston selection as well performance taking into account weight distribution of the car under heavy “dive” or braking conditions at the end of the article you can see a pic which illustrates that even they admit that their 4 wheel upgrade kits are considerably more balanced than a huge front or rear kit alone: http://www.stoptech.com/tech_info/wp...formance.shtml
You can also apply their weight distribution under heavy braking to our cars given that our cars are about 63 or 62% front weight biased from the factory, therefore more front bias braking is always more desirable in our cases, both for safety and best deceleration capability, however, in most cases, auto manufacturers instill more front bias than is necessary for stability reasons (which can hinder braking distances) as they do the same when they engineer in understeer for safety reasons, so let’s not make things worse by adding even more front bias, that is unless you have tons of weight in your front end and none in the rear, then in that case, your rears will lock too easily if they have too much brake torque applied to them, but I very much doubt the crowd I am preaching to right now would make their weight balance worse than it was from the factory!
Here is some random other data which you might find interesting (fixed piston calipers are traditionally lighter even if made from the same material:
240SX 300ZX TT Skyline GTR R34 Q45
Rotor Diameter: 10 inch 11 inch 11.6 inch 11 inch
Rotor Thickness: 18mm 30mm 32mm 28mm
Rotor Weight: 12.5 lbs 17.5 lbs 19 lbs 17.5 lbs
Caliper Type: 1-piston sliding 4-piston fixed 4-piston fixed 2-piston sliding
Caliper Weight: 9.5 lbs 6.5 lbs (alum), 10lbs (iron) 6.5 lbs 11 lbs
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
also here is a some interesting info on brake bias and it's effects on handling:
Brake Bias and Performance
Why Brake Balance Matters
by Tom McCready and James Walker, Jr. of scR motorsports
Long, long ago in a magazine far, far away, a few renegade brake engineers rallied together to bring forward the following message:
“You can take this one to the bank. Regardless of your huge rotor diameter, brake pedal ratio, magic brake pad material, or number of pistons in your calipers, your maximum deceleration is limited every time by the tire to road interface. That is the point of this whole article. Your brakes do not stop your car. Your tires do stop the car. So while changes to different parts of the brake system may affect certain characteristics or traits of the system behavior, using stickier tires is ultimately the only sure-fire method of decreasing stopping distances.”
However, there’s more to the story. Yes the tires stop the car, but improper brake balance can make a complete mess out of even the best components.
There’s always a “but”, isn’t there?
In order to demonstrate the concept of proper brake balance, it is usually simpler to analyze a car’s handling characteristics and then apply those principles back to the braking system. (For some unknown reason, people seem to have a much better understanding of handling than they do of braking. Brake guys think that’s not fair, but we’ll try to use it to our advantage here.)
In theory what everyone is looking for is that all-too-elusive handling balance which makes the car corner as fast as it possibly can. Generally speaking, this is referred to as the ‘neutral’ car and takes the driver directly to victory circle following the race. Rarely do we ever hear of a winning driver explaining that the car was a handling nightmare.
Of course, no car is ever perfect, so we have ways of expressing how far from optimal the handling balance really is. When a car enters a corner and the front end skids off into oblivion, this is called understeer – the car is turning less than the driver intends. On the other hand, if the rear end breaks free and begins to lead the car through the corner this is called oversteer – now the car is turning more than the driver intends.
In both cases, when one end of the car breaks traction, or begins to slide, the driver can pretty much bet on the fact that he (or she) has found the maximum cornering speed for that particular corner. Yes, there are a million other factors at play which can govern the handling relationship, but the longer each end of the car can “hold on”, the higher the cornering speeds. Conversely, if one end or the other consistently breaks traction early in the cornering event, corner speeds will suffer dramatically.
Naturally, as speeds continue to increase something has to eventually give and slide; however, the very best suspensions do a great job of ensuring that both ends of the car break traction at relatively the same time. How far one end breaks traction in advance of the other is ultimately a function of driver preference (this is just one reason why there is no single “perfect” set-up), but if there are complaints of heavy understeer or terminal oversteer you can rest assured that one end of the car is three steps farther ahead than the other.
Umm…isn’t this an article about brakes?
So, now that we are all chassis tuning experts, let’s look at how this information can be used to understand our braking system. Grab a pop and a bag of chips and hang on.
Like the corner carvers, the brake guys are always looking to achieve maximum accelerations, but of course these accelerations are now really decelerations. Stopping distance is everything and every single foot counts. Remember: outbraking your opponent by just two feet every lap for a twenty lap sprint race can result in a three to four car length advantage at the checkered flag. Attention to detail matters.
As braking force is continuously increased, one end of the car must eventually break traction. If the front wheels lock up and turn into little piles of molten rubber first we say that the car is “front biased”, as the front tires are the limiting factor for deceleration. In the not-so-desirable situation where the rear tires are the first to lock we say that the car is “rear biased”, but the driver would probably have a few more choice adjectives to add. In either case, however, one end of the car has given up before the other, limiting the ultimate deceleration capability of the car.
Just like the car that pushes its way through corners all day long, a car which is heavily front biased will be slow and frustrating, but relatively easy and benign to drive. On the other hand, like the oversteer monster that people are afraid to even drive around the paddock, a car which is severely rear biased will be a scary, twitchy ride resulting in a bad case of the white-knuckle syndrome. Envision an imaginary co-pilot yanking up on the park brake handle in the middle of every corner, and you begin to get the idea. While a rush to drive at speed, it will be horribly slow on the stopwatch.
The car with perfectly balanced brake bias will, however, be the last one to hit the brakes going down the back straight. By distributing the braking forces so that all four tires are simultaneously generating their maximum deceleration, stopping distance will be minimized and our hero will quickly find his way to victory lane. Just like neutral handling, balanced brake bias is our ticket to lower lap times.
All that said, once the braking system has achieved its perfect balance, it is still up to the tires to generate the braking forces. It’s still the tires that are stopping the car, but a poorly designed braking system can lengthen stopping distances significantly, expensive sticky tires or not.
So why is brake biasing necessary?
The maximum braking force that a particular tire can generate is theoretically equal to the coefficient of friction of the tire-road interface multiplied by the amount of weight being supported by that corner of the car. For example, a tire supporting 500 pounds of vehicle weight with a peak tire-road coefficient of 0.8 (a typical street tire value) could generate, in theory, 400 pounds of braking force. Throw on a good race tire with a peak coefficient of 1.5, and the maximum rises to 750 pounds of braking force. More braking force means higher deceleration, so we again see the mathematical benefits of a sticky race tire.
On the other hand, if our race tire was now only supporting 300 pounds, the maximum force would drop from 750 pounds of braking force to 450 pounds of braking force – a reduction of 40%.
Since the amount of braking force generated by the tire is directionally proportional to the torque generated by the calipers, pads, and rotors, one could also say that reducing the weight on the tire reduces the maximum brake torque sustainable by that corner before lock-up occurs. In the example above, if an assumed 700 ft-lb. of brake torque is required to lock up a wheel supporting 500 pounds, then only 420 ft-lb. (a 40% reduction) would be required to lock up a wheel supporting 300 pounds of vehicle weight.
At first glance, one could surmise that in order to achieve perfect brake bias you could just:
1. Weigh the four corners of the car
2. Design the front and rear brake components to deliver torque in the same ratio as the front-to-rear weight distribution
3. Win races
In other words, for a rear-wheel-drive race car with 50/50 front/rear weight distribution it would appear that the front and rear brakes would need to generate the same amount of torque. At the same time, it would look like a production-based front-wheel-drive car with a 60/40 front/rear weight distribution would need front brakes with 50% more output (torque capability) than the rears because of the extra weight being supported by the nose of the car.
Like most things in life though, calculating brake bias is not as simple as it may appear at first glance. Designing a braking system to these static conditions would neglect the second most important factor in the brake bias equation – the effect of dynamic weight transfer during braking.
During braking, weight is transferred from the rear axle to the front axle. As in cornering where weight is transferred from the inside tires to the outside tires, we can feel this effect on our bodies as we are thrown against the seat belts. Consequently, we now need to add several more arrows to our illustration, but the most important factor is that our CG now has an deceleration acting on it.
Because the deceleration force acts at the CG of the vehicle, and because the CG of the vehicle is located somewhere above the ground, weight will transfer from the rear axle to the front axle in direct proportion to the rate of deceleration. In so many words, this is the effect of weight transfer under braking in living color.
At this point, the brake system we so carefully designed to stop the vehicle with a 50/50 weight distribution is going to apply too much force to the rear brakes, causing them to lock before we’re getting as much work as we could out of the front brakes. Consequently, our hero is going to get that white-knuckled ride we talked about earlier because he creates more tire slip in the rear than the front, and it’s going to take longer for him to stop because the front tires are not applying as much force as they could be.
So what influences brake bias?
If we look at the equations we have developed, we see that all of the following factors will affect the weight on an axle for any given moment in time:
· Weight distribution of the vehicle at rest
· CG height – the higher it is, the more weight gets transferred during a stop
· Wheelbase – the shorter it is, the more weight gets transferred during a stop
We also know from fundamental brake design that the following factors will affect how much brake torque is developed at each corner of the vehicle, and how much of that torque is transferred to the tire contact patch and reacted against the ground:
· Rotor effective diameter
· Caliper piston diameter
· Lining friction coefficients
· Tire traction coefficient properties
It is the combination of these two functions – braking force at the tire versus weight on that tire – that determine our braking bias. Changing the CG height, wheelbase, or deceleration level will dictate a different force distribution, or bias, requirement for our brake system. Conversely, changing the effectiveness of the front brake components without changing the rear brake effectiveness can also cause our brake bias to change. The following table summarizes how common modifications will swing bias all over the map.
Factors that will increase front bias Factors that will increase rear bias
Increased front rotor diameter Increased rear rotor diameter
Increased front brake pad coefficient of friction Increased rear brake pad coefficient of friction
Increased front caliper piston diameter(s) Increased rear caliper piston diameter(s)
Decreased rear rotor diameter Decreased front rotor diameter
Decreased rear brake pad coefficient of friction Decreased front brake pad coefficient of friction
Decreased rear caliper piston diameter(s) Decreased front caliper piston diameter(s)
Lower center of gravity Higher center of gravity
More weight on rear axle Less weight on rear axle
Less weight on front axle More weight on front axle
Less sticky tires (lower deceleration limit) More sticky tires (higher deceleration limit)
Perfectly balanced, in theory
While we can do calculations to determine what the optimum front-to-rear brake bias should be under all conditions, the difficult part is creating a brake system that can actually keep up with all of this. Our hero racer has it a little easier than those of us building cars for the real world. If he knows what his maximum deceleration capability is due to the tires he’s using, he can tune his brake system for that specific deceleration level. The good part is, if he tunes his vehicle for this 1.5g decel condition, because of the way weight transfer works, his car will be more front-biased in lower traction conditions, such as rain.
Back to the “fishbone diagram” mentioned earlier. Figure 3 shows front and rear axle weight versus deceleration of the vehicle. Now let’s look at it now as a percentage of the total vehicle weight. We can add on top of this chart the front-to-rear balance of the brake system. For example, if we use the exact same brake components at the front and rear axles of the car, they will each perform 50% of the braking, and the chart will look like Figure 4.
Evaluating this chart, we see that the vehicle will always be rear-biased. That is, the rear brakes will always be applying more force at the tire contact patch than the weight of the rear axle can sustain. This vehicle will always lock the rear brakes before the front. Not so good.
Most cars, however, have brakes at the rear that are smaller than the front. There are a lot of reasons for doing this, and one of them is to help provide the correct brake bias. Also, most cars have a proportioning valve which limits the amount of brake pressure seen at the rear calipers. If we look at the same chart with a more realistic braking system (one that takes into account these effects) it might look like the chart in Figure 5.
Perfect brake bias is obtained when the front-to-rear balance of the brake system exactly matches the front-to-rear weight balance of the vehicle. Looking at our typical brake system chart, we see how difficult this is to do. However, if we’re trying to optimize a brake system for a particular deceleration level, it becomes much easier. We can tune the system so that the two lines cross (or come close to it) at the deceleration level the vehicle will be operating at most often. This is easy for a non-aero racing vehicle which typically operates at one fixed deceleration level. For a street car, this is almost impossible to achieve, because a car driven on the street doesn’t always operate at one deceleration level (if yours does, you probably don’t get too many repeat passengers!).
And here’s a free tip – effects of poor brake bias on the street not only include sub-optimal stopping distances, but also include sub-optimal brake pad life. If a car is too heavily front-biased in the deceleration range it typically operates in, it will wear front pads more quickly due to the fact that the rear brakes aren’t doing as much of the stopping work as they could be. However, the rear brake pads will probably last forever…
Perfectly balanced, in practice
Brake bias can be measured in several ways. One method – the way the auto manufacturers do it – is to actually mount wheels on the vehicle that are equipped with strain gages, so that the actual torque at each wheel can be measured throughout a stopping event. Analysis of the vehicle deceleration data combined with the measured torque values and knowledge of the vehicle parameters mentioned above (wheelbase, CG height, weight on each axle at rest) allow us to calculate brake bias for that particular event. This is the most precise method of measuring brake bias. However, there are simpler and cheaper methods that can be just as effective.
We know where most auto manufacturers tune brake bias – they like our cars to be front-biased in all conditions achievable by the tires offered on the vehicle. This helps to insure vehicle stability under braking by the mass public. If we measure stopping distance of the vehicle as delivered from the showroom floor, we have a good benchmark for a vehicle with a 5% to 10% front brake bias.
Now, if we make changes to the car that can effect brake bias and re-measure stopping distance, we can tell immediately if we have taken a step in the wrong direction. For example, it is not uncommon to install more aggressive front brake pads (which will make the car even more front biased) and see stopping distances go up 5% or more. Dedicated race pads can result in even longer stopping distances.
The most dramatic front-bias impacts are usually brought about by “big brake kits” which are not properly matched to the intended vehicle. Any time that a bigger front rotor is installed, there is a simultaneous need to decrease the effective clamping force of the caliper (installing smaller pistons is the easiest method) to offset the increased torque created by larger rotor effective radius. The objective is to maintain a constant amount of brake corner output (torque) for a given brake line pressure as Figure 6 illustrates. Unfortunately, too many upgrades do not take this factor into account, and those poor cars end up with both bigger rotors and larger pistons which serve to drastically shift the bias even more forward. While rock-solid stable under braking, stopping distances will go up dramatically.
The flip side can be seen by making changes to increase the amount of rear bias. Because the auto manufacturers leave a little bit of wiggle room in their designs, it is usually possible to make small changes to increase rear bias and end up with shorter stopping distances than stock. Keep in mind, however, that there is only so much of this wiggle room to play with. After a point, increased rear bias will make the car unstable under hard braking and will consequently drive the stopping distances through the roof.
The moral of the story
So, what have we learned? Every car has a “sweet spot” for brake bias which will generate the shortest stopping distances possible. Typically, the auto manufacturers design their cars to be 5% to 10% more front-biased than optimum for maximum deceleration, but they provide enhanced brake stability in return. Not a bad trade-off for the public at large, and not necessarily a bad place for a race car in the heat of battle either.
In summary, your tires certainly still stop the car, but if your bias is out in left field you might not be able to use everything they have to offer. Your braking system is just that – a system – and keeping an eye on brake bias effects during modification will go a long, long way toward bringing home the checkered flag. Of course, selecting the proper kit from a manufacturer who has already done the hard part for you can make the trip to victory lane that much easier…
Why Brake Balance Matters
by Tom McCready and James Walker, Jr. of scR motorsports
Long, long ago in a magazine far, far away, a few renegade brake engineers rallied together to bring forward the following message:
“You can take this one to the bank. Regardless of your huge rotor diameter, brake pedal ratio, magic brake pad material, or number of pistons in your calipers, your maximum deceleration is limited every time by the tire to road interface. That is the point of this whole article. Your brakes do not stop your car. Your tires do stop the car. So while changes to different parts of the brake system may affect certain characteristics or traits of the system behavior, using stickier tires is ultimately the only sure-fire method of decreasing stopping distances.”
However, there’s more to the story. Yes the tires stop the car, but improper brake balance can make a complete mess out of even the best components.
There’s always a “but”, isn’t there?
In order to demonstrate the concept of proper brake balance, it is usually simpler to analyze a car’s handling characteristics and then apply those principles back to the braking system. (For some unknown reason, people seem to have a much better understanding of handling than they do of braking. Brake guys think that’s not fair, but we’ll try to use it to our advantage here.)
In theory what everyone is looking for is that all-too-elusive handling balance which makes the car corner as fast as it possibly can. Generally speaking, this is referred to as the ‘neutral’ car and takes the driver directly to victory circle following the race. Rarely do we ever hear of a winning driver explaining that the car was a handling nightmare.
Of course, no car is ever perfect, so we have ways of expressing how far from optimal the handling balance really is. When a car enters a corner and the front end skids off into oblivion, this is called understeer – the car is turning less than the driver intends. On the other hand, if the rear end breaks free and begins to lead the car through the corner this is called oversteer – now the car is turning more than the driver intends.
In both cases, when one end of the car breaks traction, or begins to slide, the driver can pretty much bet on the fact that he (or she) has found the maximum cornering speed for that particular corner. Yes, there are a million other factors at play which can govern the handling relationship, but the longer each end of the car can “hold on”, the higher the cornering speeds. Conversely, if one end or the other consistently breaks traction early in the cornering event, corner speeds will suffer dramatically.
Naturally, as speeds continue to increase something has to eventually give and slide; however, the very best suspensions do a great job of ensuring that both ends of the car break traction at relatively the same time. How far one end breaks traction in advance of the other is ultimately a function of driver preference (this is just one reason why there is no single “perfect” set-up), but if there are complaints of heavy understeer or terminal oversteer you can rest assured that one end of the car is three steps farther ahead than the other.
Umm…isn’t this an article about brakes?
So, now that we are all chassis tuning experts, let’s look at how this information can be used to understand our braking system. Grab a pop and a bag of chips and hang on.
Like the corner carvers, the brake guys are always looking to achieve maximum accelerations, but of course these accelerations are now really decelerations. Stopping distance is everything and every single foot counts. Remember: outbraking your opponent by just two feet every lap for a twenty lap sprint race can result in a three to four car length advantage at the checkered flag. Attention to detail matters.
As braking force is continuously increased, one end of the car must eventually break traction. If the front wheels lock up and turn into little piles of molten rubber first we say that the car is “front biased”, as the front tires are the limiting factor for deceleration. In the not-so-desirable situation where the rear tires are the first to lock we say that the car is “rear biased”, but the driver would probably have a few more choice adjectives to add. In either case, however, one end of the car has given up before the other, limiting the ultimate deceleration capability of the car.
Just like the car that pushes its way through corners all day long, a car which is heavily front biased will be slow and frustrating, but relatively easy and benign to drive. On the other hand, like the oversteer monster that people are afraid to even drive around the paddock, a car which is severely rear biased will be a scary, twitchy ride resulting in a bad case of the white-knuckle syndrome. Envision an imaginary co-pilot yanking up on the park brake handle in the middle of every corner, and you begin to get the idea. While a rush to drive at speed, it will be horribly slow on the stopwatch.
The car with perfectly balanced brake bias will, however, be the last one to hit the brakes going down the back straight. By distributing the braking forces so that all four tires are simultaneously generating their maximum deceleration, stopping distance will be minimized and our hero will quickly find his way to victory lane. Just like neutral handling, balanced brake bias is our ticket to lower lap times.
All that said, once the braking system has achieved its perfect balance, it is still up to the tires to generate the braking forces. It’s still the tires that are stopping the car, but a poorly designed braking system can lengthen stopping distances significantly, expensive sticky tires or not.
So why is brake biasing necessary?
The maximum braking force that a particular tire can generate is theoretically equal to the coefficient of friction of the tire-road interface multiplied by the amount of weight being supported by that corner of the car. For example, a tire supporting 500 pounds of vehicle weight with a peak tire-road coefficient of 0.8 (a typical street tire value) could generate, in theory, 400 pounds of braking force. Throw on a good race tire with a peak coefficient of 1.5, and the maximum rises to 750 pounds of braking force. More braking force means higher deceleration, so we again see the mathematical benefits of a sticky race tire.
On the other hand, if our race tire was now only supporting 300 pounds, the maximum force would drop from 750 pounds of braking force to 450 pounds of braking force – a reduction of 40%.
Since the amount of braking force generated by the tire is directionally proportional to the torque generated by the calipers, pads, and rotors, one could also say that reducing the weight on the tire reduces the maximum brake torque sustainable by that corner before lock-up occurs. In the example above, if an assumed 700 ft-lb. of brake torque is required to lock up a wheel supporting 500 pounds, then only 420 ft-lb. (a 40% reduction) would be required to lock up a wheel supporting 300 pounds of vehicle weight.
At first glance, one could surmise that in order to achieve perfect brake bias you could just:
1. Weigh the four corners of the car
2. Design the front and rear brake components to deliver torque in the same ratio as the front-to-rear weight distribution
3. Win races
In other words, for a rear-wheel-drive race car with 50/50 front/rear weight distribution it would appear that the front and rear brakes would need to generate the same amount of torque. At the same time, it would look like a production-based front-wheel-drive car with a 60/40 front/rear weight distribution would need front brakes with 50% more output (torque capability) than the rears because of the extra weight being supported by the nose of the car.
Like most things in life though, calculating brake bias is not as simple as it may appear at first glance. Designing a braking system to these static conditions would neglect the second most important factor in the brake bias equation – the effect of dynamic weight transfer during braking.
During braking, weight is transferred from the rear axle to the front axle. As in cornering where weight is transferred from the inside tires to the outside tires, we can feel this effect on our bodies as we are thrown against the seat belts. Consequently, we now need to add several more arrows to our illustration, but the most important factor is that our CG now has an deceleration acting on it.
Because the deceleration force acts at the CG of the vehicle, and because the CG of the vehicle is located somewhere above the ground, weight will transfer from the rear axle to the front axle in direct proportion to the rate of deceleration. In so many words, this is the effect of weight transfer under braking in living color.
At this point, the brake system we so carefully designed to stop the vehicle with a 50/50 weight distribution is going to apply too much force to the rear brakes, causing them to lock before we’re getting as much work as we could out of the front brakes. Consequently, our hero is going to get that white-knuckled ride we talked about earlier because he creates more tire slip in the rear than the front, and it’s going to take longer for him to stop because the front tires are not applying as much force as they could be.
So what influences brake bias?
If we look at the equations we have developed, we see that all of the following factors will affect the weight on an axle for any given moment in time:
· Weight distribution of the vehicle at rest
· CG height – the higher it is, the more weight gets transferred during a stop
· Wheelbase – the shorter it is, the more weight gets transferred during a stop
We also know from fundamental brake design that the following factors will affect how much brake torque is developed at each corner of the vehicle, and how much of that torque is transferred to the tire contact patch and reacted against the ground:
· Rotor effective diameter
· Caliper piston diameter
· Lining friction coefficients
· Tire traction coefficient properties
It is the combination of these two functions – braking force at the tire versus weight on that tire – that determine our braking bias. Changing the CG height, wheelbase, or deceleration level will dictate a different force distribution, or bias, requirement for our brake system. Conversely, changing the effectiveness of the front brake components without changing the rear brake effectiveness can also cause our brake bias to change. The following table summarizes how common modifications will swing bias all over the map.
Factors that will increase front bias Factors that will increase rear bias
Increased front rotor diameter Increased rear rotor diameter
Increased front brake pad coefficient of friction Increased rear brake pad coefficient of friction
Increased front caliper piston diameter(s) Increased rear caliper piston diameter(s)
Decreased rear rotor diameter Decreased front rotor diameter
Decreased rear brake pad coefficient of friction Decreased front brake pad coefficient of friction
Decreased rear caliper piston diameter(s) Decreased front caliper piston diameter(s)
Lower center of gravity Higher center of gravity
More weight on rear axle Less weight on rear axle
Less weight on front axle More weight on front axle
Less sticky tires (lower deceleration limit) More sticky tires (higher deceleration limit)
Perfectly balanced, in theory
While we can do calculations to determine what the optimum front-to-rear brake bias should be under all conditions, the difficult part is creating a brake system that can actually keep up with all of this. Our hero racer has it a little easier than those of us building cars for the real world. If he knows what his maximum deceleration capability is due to the tires he’s using, he can tune his brake system for that specific deceleration level. The good part is, if he tunes his vehicle for this 1.5g decel condition, because of the way weight transfer works, his car will be more front-biased in lower traction conditions, such as rain.
Back to the “fishbone diagram” mentioned earlier. Figure 3 shows front and rear axle weight versus deceleration of the vehicle. Now let’s look at it now as a percentage of the total vehicle weight. We can add on top of this chart the front-to-rear balance of the brake system. For example, if we use the exact same brake components at the front and rear axles of the car, they will each perform 50% of the braking, and the chart will look like Figure 4.
Evaluating this chart, we see that the vehicle will always be rear-biased. That is, the rear brakes will always be applying more force at the tire contact patch than the weight of the rear axle can sustain. This vehicle will always lock the rear brakes before the front. Not so good.
Most cars, however, have brakes at the rear that are smaller than the front. There are a lot of reasons for doing this, and one of them is to help provide the correct brake bias. Also, most cars have a proportioning valve which limits the amount of brake pressure seen at the rear calipers. If we look at the same chart with a more realistic braking system (one that takes into account these effects) it might look like the chart in Figure 5.
Perfect brake bias is obtained when the front-to-rear balance of the brake system exactly matches the front-to-rear weight balance of the vehicle. Looking at our typical brake system chart, we see how difficult this is to do. However, if we’re trying to optimize a brake system for a particular deceleration level, it becomes much easier. We can tune the system so that the two lines cross (or come close to it) at the deceleration level the vehicle will be operating at most often. This is easy for a non-aero racing vehicle which typically operates at one fixed deceleration level. For a street car, this is almost impossible to achieve, because a car driven on the street doesn’t always operate at one deceleration level (if yours does, you probably don’t get too many repeat passengers!).
And here’s a free tip – effects of poor brake bias on the street not only include sub-optimal stopping distances, but also include sub-optimal brake pad life. If a car is too heavily front-biased in the deceleration range it typically operates in, it will wear front pads more quickly due to the fact that the rear brakes aren’t doing as much of the stopping work as they could be. However, the rear brake pads will probably last forever…
Perfectly balanced, in practice
Brake bias can be measured in several ways. One method – the way the auto manufacturers do it – is to actually mount wheels on the vehicle that are equipped with strain gages, so that the actual torque at each wheel can be measured throughout a stopping event. Analysis of the vehicle deceleration data combined with the measured torque values and knowledge of the vehicle parameters mentioned above (wheelbase, CG height, weight on each axle at rest) allow us to calculate brake bias for that particular event. This is the most precise method of measuring brake bias. However, there are simpler and cheaper methods that can be just as effective.
We know where most auto manufacturers tune brake bias – they like our cars to be front-biased in all conditions achievable by the tires offered on the vehicle. This helps to insure vehicle stability under braking by the mass public. If we measure stopping distance of the vehicle as delivered from the showroom floor, we have a good benchmark for a vehicle with a 5% to 10% front brake bias.
Now, if we make changes to the car that can effect brake bias and re-measure stopping distance, we can tell immediately if we have taken a step in the wrong direction. For example, it is not uncommon to install more aggressive front brake pads (which will make the car even more front biased) and see stopping distances go up 5% or more. Dedicated race pads can result in even longer stopping distances.
The most dramatic front-bias impacts are usually brought about by “big brake kits” which are not properly matched to the intended vehicle. Any time that a bigger front rotor is installed, there is a simultaneous need to decrease the effective clamping force of the caliper (installing smaller pistons is the easiest method) to offset the increased torque created by larger rotor effective radius. The objective is to maintain a constant amount of brake corner output (torque) for a given brake line pressure as Figure 6 illustrates. Unfortunately, too many upgrades do not take this factor into account, and those poor cars end up with both bigger rotors and larger pistons which serve to drastically shift the bias even more forward. While rock-solid stable under braking, stopping distances will go up dramatically.
The flip side can be seen by making changes to increase the amount of rear bias. Because the auto manufacturers leave a little bit of wiggle room in their designs, it is usually possible to make small changes to increase rear bias and end up with shorter stopping distances than stock. Keep in mind, however, that there is only so much of this wiggle room to play with. After a point, increased rear bias will make the car unstable under hard braking and will consequently drive the stopping distances through the roof.
The moral of the story
So, what have we learned? Every car has a “sweet spot” for brake bias which will generate the shortest stopping distances possible. Typically, the auto manufacturers design their cars to be 5% to 10% more front-biased than optimum for maximum deceleration, but they provide enhanced brake stability in return. Not a bad trade-off for the public at large, and not necessarily a bad place for a race car in the heat of battle either.
In summary, your tires certainly still stop the car, but if your bias is out in left field you might not be able to use everything they have to offer. Your braking system is just that – a system – and keeping an eye on brake bias effects during modification will go a long, long way toward bringing home the checkered flag. Of course, selecting the proper kit from a manufacturer who has already done the hard part for you can make the trip to victory lane that much easier…
Senior Member
Joined: Jul 2001
Posts: 1,341
From: state of confusion
There is quite a bit more, as there are several other factors that deserve consideration. CG height, tire diameter(s) and grip level(s), proportioning valve characteristics, pad coefficient(s) of friction, and pedal effort just to list a few of the things that can vary even with common brake and tire/wheel/suspension mods.
Having slightly more forward brake bias is not necessarily the wrong approach if you really can develop greater decelerations - the increased forward load transfer requires a little more front brake (and a little less rear) to take full advantage. Most commonly, this comes about due to the use of grippier tires. The downside? Somewhat more rapid front pad wear, as the front will now be more "overbraked" under normal driving conditions while the rear brakes are taking life even easier.
What would be really nice to know is the ABS logic, as this may place some unexpected limits on brake bias tuning.
Norm
Having slightly more forward brake bias is not necessarily the wrong approach if you really can develop greater decelerations - the increased forward load transfer requires a little more front brake (and a little less rear) to take full advantage. Most commonly, this comes about due to the use of grippier tires. The downside? Somewhat more rapid front pad wear, as the front will now be more "overbraked" under normal driving conditions while the rear brakes are taking life even easier.
What would be really nice to know is the ABS logic, as this may place some unexpected limits on brake bias tuning.
Norm
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
if you read the entire article it does mention that quite a bit more front bias is diserable but not more than we already have stock....! we already have more than adequate proportionment to the front stock...
and I also did address that with all things equal such as the same size and type of tire all the way around and pad compound/coeffecient of friction
accounting for abs logic wouldn't be as dynamic in it's change on our setup possibility as you would think if the abs system is truly very good, as then it would only be based on total grip possible at each corner under braking...in either case, on the track or autoX, abs condition braking is not desired and one should keep it just short of that zone "threshold braking", the level at which this would be is dependant on many conditions that were listed above...
what I wrote was simply to ascertain the relevant bias shifts accompanied by going with the respective different brake setups currently available for our cars if you keep all things front and rear the same such as tires and brake pads...the second part was an article written by Tom McCready and James Walker, Jr. of scR motorsports regarding proper brake bias setup/selection and it's effects on braking potential, characteristics, and handling...
and I also did address that with all things equal such as the same size and type of tire all the way around and pad compound/coeffecient of friction
accounting for abs logic wouldn't be as dynamic in it's change on our setup possibility as you would think if the abs system is truly very good, as then it would only be based on total grip possible at each corner under braking...in either case, on the track or autoX, abs condition braking is not desired and one should keep it just short of that zone "threshold braking", the level at which this would be is dependant on many conditions that were listed above...
what I wrote was simply to ascertain the relevant bias shifts accompanied by going with the respective different brake setups currently available for our cars if you keep all things front and rear the same such as tires and brake pads...the second part was an article written by Tom McCready and James Walker, Jr. of scR motorsports regarding proper brake bias setup/selection and it's effects on braking potential, characteristics, and handling...
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
I would need the caliper piston size and # of pistons...as well as the general brake pad dimensions...and rotor size of course
wilwood, so I am guessing 4 piston fixed...and anywhere from a 12.1-13.1" rotor?
wilwood, so I am guessing 4 piston fixed...and anywhere from a 12.1-13.1" rotor?
Senior Member
Joined: Jul 2001
Posts: 1,341
From: state of confusion
Originally Posted by michaelnyden
. . . if the abs system is truly very good, as then it would only be based on total grip possible at each corner under braking...
I'll go back through the first couple of chapters . . .
Norm
Can you please calculate the following for me?
Piston Diameters: 1.5in x 2 / 1.63in x 2 (4 total)
Piston Area: 49.5cm²
Rotor Diameter: 13in
Pad Radial Depth: 1.98in
Pad Length: 5.21in
Pad Area: 57.4cm²
Piston Diameters: 1.5in x 2 / 1.63in x 2 (4 total)
Piston Area: 49.5cm²
Rotor Diameter: 13in
Pad Radial Depth: 1.98in
Pad Length: 5.21in
Pad Area: 57.4cm²
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
effective rotor diameter=11.02"
effective piston area=9.8138" sq. in.
brake torque up front=108.148
brake bias front=71.6767296514517871463319260619155%
brake bias rear=28.3232703485482128536680739381%
so ~72% front (about 4% more front bias then stock)
28% rear...
now of course this is assuming you are running pads with the same friction coefficient up front as the rear, and the tires are the same size/type...if you are running much more hardcore pads up front, then the bias will shift even farther forward...
effective piston area=9.8138" sq. in.
brake torque up front=108.148
brake bias front=71.6767296514517871463319260619155%
brake bias rear=28.3232703485482128536680739381%
so ~72% front (about 4% more front bias then stock)
28% rear...
now of course this is assuming you are running pads with the same friction coefficient up front as the rear, and the tires are the same size/type...if you are running much more hardcore pads up front, then the bias will shift even farther forward...
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
Brake bias
Front braking power relative to rear braking power is significant for two somewhat contrary reasons. Under braking, a rolling tire has more traction than a sliding tire. If rear brakes lock first, the front brakes will have more grip and the vehicle will tend to spin. Thus, to enhance stability, the braking action is usually biased so the front brakes lock first. Over biasing in this manner diminishes the braking effectiveness.
Brakes can also be advantageously biased to emphasize instability. According to the traction circle theory, a tire can do only so much total work. If asked to accelerate or brake while turning, less traction is available for turning. Most of us are familiar with "driving with the throttle" in a turn. Similarly, by biasing braking more strongly at the rear and utilizing trailing brake into a corner, more turning traction is available at the front and less at the rear. Thus the vehicle rotates into a corner. Turn-in can be greatly aided by this technique. As can spinning!
Stopping Force Calculations
Equations:
(for ease and consistency try and use meters and kg)
NOTE: Equation 1 does not mean more weight you have more stopping force, it is just to calculate the stopping force required. As you can see in Equation 8, the larger the stopping force is the larger and more aggressive the brakes need to be.
1.
stopping force total = weight of car * longitudinal coefficient of friction of tires
2.
Front Force = (weight front + total weight) * tire friction * height of CG * (1/wheel base)
3.
Rear Force = (total weight - rear weight) * tire friction * height of CG * (1/wheel base)
4.
% front = Front Force/Stopping Force
5.
% Rear = Rear Force/Stopping Force
6.
Area of Master Cylinder * pedal ratio = M
Area of front or rear piston= N
Mechanical Force Ratio= M/N
7.
mechanical force ratio front = mechanical force ratio * %front
mechanical force ratio rear = mechanical force ratio * %rear
8.
Stopping Force = pedal force * brake pad coefficient of friction * mechanical force ratio * (1/radius of the tire) * brake rotor effective radius
.....solve for the parameter you need
Front braking power relative to rear braking power is significant for two somewhat contrary reasons. Under braking, a rolling tire has more traction than a sliding tire. If rear brakes lock first, the front brakes will have more grip and the vehicle will tend to spin. Thus, to enhance stability, the braking action is usually biased so the front brakes lock first. Over biasing in this manner diminishes the braking effectiveness.
Brakes can also be advantageously biased to emphasize instability. According to the traction circle theory, a tire can do only so much total work. If asked to accelerate or brake while turning, less traction is available for turning. Most of us are familiar with "driving with the throttle" in a turn. Similarly, by biasing braking more strongly at the rear and utilizing trailing brake into a corner, more turning traction is available at the front and less at the rear. Thus the vehicle rotates into a corner. Turn-in can be greatly aided by this technique. As can spinning!
Stopping Force Calculations
Equations:
(for ease and consistency try and use meters and kg)
NOTE: Equation 1 does not mean more weight you have more stopping force, it is just to calculate the stopping force required. As you can see in Equation 8, the larger the stopping force is the larger and more aggressive the brakes need to be.
1.
stopping force total = weight of car * longitudinal coefficient of friction of tires
2.
Front Force = (weight front + total weight) * tire friction * height of CG * (1/wheel base)
3.
Rear Force = (total weight - rear weight) * tire friction * height of CG * (1/wheel base)
4.
% front = Front Force/Stopping Force
5.
% Rear = Rear Force/Stopping Force
6.
Area of Master Cylinder * pedal ratio = M
Area of front or rear piston= N
Mechanical Force Ratio= M/N
7.
mechanical force ratio front = mechanical force ratio * %front
mechanical force ratio rear = mechanical force ratio * %rear
8.
Stopping Force = pedal force * brake pad coefficient of friction * mechanical force ratio * (1/radius of the tire) * brake rotor effective radius
.....solve for the parameter you need
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
for more info on brake systems look here:
http://www.scoobymods.com/forums/showthread.php?t=1122
http://www.scoobymods.com/forums/showthread.php?t=1122
Originally Posted by michaelnyden
I would need the caliper piston size and # of pistons...as well as the general brake pad dimensions...and rotor size of course
wilwood, so I am guessing 4 piston fixed...and anywhere from a 12.1-13.1" rotor?
wilwood, so I am guessing 4 piston fixed...and anywhere from a 12.1-13.1" rotor?
The rotor is 12.2"
I'll return with the rest of the info.
A lot of people do not understand that 60-0 stopping distance will be relatively the same even when you upgrade your brakes if you have the same kind of tires. What changes dramatically is the 60-0 stopping distance the second and third time around one after the other and so on. The upgraded brakes will have a stopping distance closer to the first time around.
-Larry
-Larry
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Joined: Jul 2001
Posts: 1,341
From: state of confusion
Originally Posted by Cheocwa
A lot of people do not understand that 60-0 stopping distance will be relatively the same even when you upgrade your brakes if you have the same kind of tires. What changes dramatically is the 60-0 stopping distance the second and third time around one after the other and so on. The upgraded brakes will have a stopping distance closer to the first time around.
-Larry
-Larry
Elsewhere, I've heard with pretty good authority that lateral grip is about an 0.7 power of vertical tire load. I'd expect that longitudinal grip would bear a generally similar relation to VTL (the exponent being something less than 1.0). I think the bottom line here is that slightly overbraking the rear axle may not be quite as evil as the all-linear-behavior brake balance math would suggest.
Norm
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Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
why would it suggest it being "evil" I am all for it, and if you really go in depth with the brake bias math and start factoring in items like coefficient of frictions, torque arm radii, rotational mass difference front to rear, and weight transfer in correllation with VTL as you are mentioning, I would agree with you, that most of the kits above are way to front biased...but I think our factory bias is well setup for safety and performance, although in competitive applications, it could use a tad more rear bias; however, if the choice between all the different brake options listed in my 1st post and keeping the bias as close to stock, I would try to keep it as close to stock instead of the common trend of all the other kits--throwing the bias far forward...
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Posts: 1,341
From: state of confusion
Simple example: let's say that the ideal ratio, linearly computed, for some particular car, loading, etc., is 70/30, which would represent the vertical tire load front:rear ratio. A 68/32 brake balance ratio suggests that rear lockup would occur first, with consequential loss of rear tracking stability near the limit (that's the potentially "evil" situation). But if the lightly loaded tires are capable of a relatively greater proportion of the braking than their proportion of the load, you might manage to find that the 70/30 load distribution was good for more like 67.5/32.5 brake force distribution (and theoretically, front lockup would occur first).
Norm
Norm
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
for those of you reading these articles/posts such as those by myself or norm's, and you simply can't picture it in your head, go to stoptech's site and under white papers, the article I posted way up top is on there with full picture illustration...which in the end just simply accepts that what norm is saying, is the idea of advanced brake bias setup and performance as a result...
Originally Posted by Norm Peterson
Elsewhere, I've heard with pretty good authority that lateral grip is about an 0.7 power of vertical tire load.
Norm
Norm
-Larry
Thread Starter
Joined: Feb 2003
Posts: 3,431
From: Los Angeles, CA
well let's not start considering braking while turning, then things get way too complicated very fast mathematically, but yes, more negative camber dialed in as a typical competitive driver should choose to, would comprimise the contact patch, however, under braking things get more interesting as even what tire pressures you are running will dictate when weight is loaded off the rear and on to the front, how much the tire "deforms" and essentially enlarges its contact patch accordingly...
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Posts: 1,341
From: state of confusion
That figure was only intended for use as a general correlation between the horizontal and vertical forces in order to demonstrate a rather specific point. Not as design gospel. Since it came directly from an individual who has been employed in the suspension business at the OE level for a number of years I have to think that it's pretty good information for its stated use. I'm sure that tire & suspension configurations can be put together that, overall, do not follow it all that closely. But in the absence of actual tire mfr research & development data (or the results of independent testing performed with equal thoroughness) I don't think we'll find anything better to work with. For data that's that expensive to develop, I'm not holding my breath.
Norm
Norm
Senior Member
Joined: Jul 2001
Posts: 1,341
From: state of confusion
Originally Posted by michaelnyden
. . . things get more interesting as even what tire pressures you are running will dictate when weight is loaded off the rear and on to the front, how much the tire "deforms" and essentially enlarges its contact patch accordingly...
Norm
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