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Effect of downforce on weight transfer during braking


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#1 New Britain

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Posted 06 August 2018 - 18:59

Apologies if the answer to this is obvious, but I am trying to get a sense of whether weight transfer under braking is affected by how much downforce a car has.

 

For context, we are experimenting with carbon-carbon brake discs on a non-downforce car. Under heavy or sustained braking, the fronts are overheating, the rears doing almost nothing. Putting to one side the question of cooling, I am wondering whether part of the reason is that the weight transfer under braking is causing the front contact patches to expand, which enables the front brakes to do more more, which causes the front contact patches to expand further, which puts more demand on the front brakes, etc.

 

In general, carbon-carbon discs are used only on cars with very low centres of gravity, high downforce and stiff suspensions. I gather that the stiffness of the suspension does not affect weight transfer; CoG obviously does affect it. As the car decelerates, I would guess that the downforce generated would diminish at approximately the same rate front and rear, and therefore a car with balanced downforce will not experience weight transfer under braking at a substantially different rate from what would happen with the same car but without downforce. Is that correct?

 

Also, does anyone here have a general idea of how much weight transfer there is in a Formula One car under heavy braking?

 

Thank you for reading this. Any thoughts would be appreciated.

 

 

 



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#2 Joe Bosworth

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Posted 07 August 2018 - 05:06

Thought 1.  You are providing so little real information that no really sensible response is possible.

 

Thought 2.  There is nothing in common between an F1 car braking with down force at perhaps 5G and what you are doing with max retardation of something between .9G and 1.4G depending on the tires that you are using on a non-down force car.

 

Thought 3.  Front tire patch shape/change is immaterial to the degree of problems that you talk about.

 

Thought 4.  Construct a force diagram of your vehicle to understand the change in weight balance under breaking.

 

Regards

 

:confused:



#3 New Britain

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Posted 07 August 2018 - 10:00

Thought 1.  You are providing so little real information that no really sensible response is possible.

 

Thought 2.  There is nothing in common between an F1 car braking with down force at perhaps 5G and what you are doing with max retardation of something between .9G and 1.4G depending on the tires that you are using on a non-down force car.

 

Thought 3.  Front tire patch shape/change is immaterial to the degree of problems that you talk about.

 

Thought 4.  Construct a force diagram of your vehicle to understand the change in weight balance under breaking.

 

Regards

 

:confused:

Thank you for replying, Joe.

 

My thinking has been, "Racing cars designed to use carbon-carbon discs normally are able to cope with the risk of overheating front brakes, despite the enormous forces being put through them. Is that only because they are properly cooled, or are there other contributing factors, such as relatively little weight transfer?"



#4 gruntguru

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Posted 07 August 2018 - 22:53

Also, does anyone here have a general idea of how much weight transfer there is in a Formula One car under heavy braking?

 

Thank you for reading this. Any thoughts would be appreciated.

Assuming mass = 750, wheelbase = 3500, CGH = 200 and braking decel = 5g, the weight transfer comes to 214kg.

 

"Absolute" weight transfer increases in proportion to deceleration and therefore downforce.

As a percentage of normal force, the aero effect on normal force depends on grip. e.g.

For u=1, the percentage weight transfer doesn't change with DF.

For u<1, % WT decreases with DF.

For u>1, % WT increases with DF.



#5 New Britain

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Posted 08 August 2018 - 06:55

Assuming mass = 750, wheelbase = 3500, CGH = 200 and braking decel = 5g, the weight transfer comes to 214kg.

 

"Absolute" weight transfer increases in proportion to deceleration and therefore downforce.

As a percentage of normal force, the aero effect on normal force depends on grip. e.g.

For u=1, the percentage weight transfer doesn't change with DF.

For u<1, % WT decreases with DF.

For u>1, % WT increases with DF.

Ah, okay. so the effect of downforce on weight transfer is only indirect, in that more downforce will generate more braking decel.

If, alternatively, the vehicle had no downforce but instead had the world's stickiest tyres, enabling braking decel also of 5g, that would produce the same weight transfer.

 

Thank you - very helpful.



#6 NotAPineapple

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Posted 10 August 2018 - 21:01

Your temperature imbalance is either due to a too front biased brake balance or incorrectly sized discs. Its related to load transfer yes but more correctly its the total wheel vertical load that determines the braking energy (and therefore heating energy) which is passed through the brakes. Total wheel load is made up of static weight distribution, aero lift and load transfer.

To understand if the issue is brake balance or disc sizing its pretty straight forward. Move the brake balance rearward until you start getting stability issues and come back one step. This setup prioritises braking performance at the expense of turn in but it will serve to help you understand the temperature issue. If you still have a temp imbalance in this condition then your discs (and probably also calipers) are likely the wrong size. Either that or you have a bad stability problem in thw chassis which forces you to run a lot of front bias.

Have you calculated the brake force distribution with your current rotor and caliper setup? Do you know what % the front axle is contributing to the total braking force?

#7 New Britain

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Posted 12 August 2018 - 11:33

Your temperature imbalance is either due to a too front biased brake balance or incorrectly sized discs. Its related to load transfer yes but more correctly its the total wheel vertical load that determines the braking energy (and therefore heating energy) which is passed through the brakes. Total wheel load is made up of static weight distribution, aero lift and load transfer.

To understand if the issue is brake balance or disc sizing its pretty straight forward. Move the brake balance rearward until you start getting stability issues and come back one step. This setup prioritises braking performance at the expense of turn in but it will serve to help you understand the temperature issue. If you still have a temp imbalance in this condition then your discs (and probably also calipers) are likely the wrong size. Either that or you have a bad stability problem in thw chassis which forces you to run a lot of front bias.

Have you calculated the brake force distribution with your current rotor and caliper setup? Do you know what % the front axle is contributing to the total braking force?

Interesting that you say this, and thank you for your comments.

 

The car originally had smaller (iron) discs at the rear than at the front. There was no balance issue.

 

When I went to carbon-carbon, the consultant whom I was using (his brakes won a Formula One race earlier this year, so he should know what he's doing), recommended the same size discs front and rear. This may have been influenced by the fact that most calipers for carbon-carbon brakes seem to be designed to use the same size discs F-R. I am using AP calipers (CP6077/6078) that are designed to be used as a set, with the rears having smaller pistons but the same size discs F-R.

 

When we looked at brake balance, the problem was that when the discs were cooler there was too much braking at the rear. I could live with that in the dry, but was not interested in having to live with it in the wet. Hence we took the balance forward until it was right for when they were cooler, but, as I wrote above, under heavy braking the fronts were getting too hot and the rears ended up doing nothing.

 

In my car, I believe that under maximum braking the load on the front (road) tyres increases by about 39%, and the F-R weight ratio goes from 41-59 to 57-43, that sort of thing. According to AP, the calipers that I am using are designed for GT cars. I would think that on a GT car the load transfer to the front (slick) tyres and the change in weight ratio would be at least that much if not more.

 

If so, would that imply that having the same size discs but different caliper pistons is not the problem? Perhaps the problem is insufficient cooling of the fronts?

 

Cheers.



#8 NotAPineapple

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Posted 12 August 2018 - 14:27

Brake component sizing is almost exclusively driven by thermal factors - so if you are paying a consultant to advise on the brake system, this temperature issue is his problem.

What class are you racing in? Do you have a bit of a strange weight distribution that might be skewing things?

Also, what's the reasoning behind targeting a good balance when the discs are cold? Are you running short races that do not heat them up properly?

This could also be a large part of the issue as carbon brakes are setup to run at their operating temperature and have pretty unreasonable characteristics if you are outside of it.

#9 New Britain

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Posted 12 August 2018 - 14:40

Brake component sizing is almost exclusively driven by thermal factors - so if you are paying a consultant to advise on the brake system, this temperature issue is his problem.

What class are you racing in? Do you have a bit of a strange weight distribution that might be skewing things?

Also, what's the reasoning behind targeting a good balance when the discs are cold? Are you running short races that do not heat them up properly?

This could also be a large part of the issue as carbon brakes are setup to run at their operating temperature and have pretty unreasonable characteristics if you are outside of it.

This is a road car, no track use (the problem of CoF of carbon-carbon when cold is completely sorted.) Because the car is for road use only, it is unlikely that there will ever be a real-world situation when I am using the brakes enough that the fronts will overheat.

 

The overheating issue arose only when testing repeated 120-0 stops on an airfield. However I would like to cover all scenarios. Although unlikely, it is conceivable that I could be descending an Alpine road on a hot day and need to use the brakes repeatedly. This is why I am trying to resolve the issue.



#10 NotAPineapple

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Posted 12 August 2018 - 15:19

The fact that it's a road car is an important bit of info.

 

So if I understand correct, the baseline setup with cold discs had too much braking on the rear. How did you detect that? Did you feel instabilities in braking? Or was this a braking force calculation?



#11 New Britain

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Posted 12 August 2018 - 18:08

The fact that it's a road car is an important bit of info.

 

So if I understand correct, the baseline setup with cold discs had too much braking on the rear. How did you detect that? Did you feel instabilities in braking? Or was this a braking force calculation?

Thank you for continuing this dialogue with me - I appreciate it. :up:

 

When cold, the rears were locking under hard braking at low-medium speeds. We moved the bias forward to the point where the rears were no longer locking, and then the system was fine for normal road use.

 

However, when we then tested under repeated high-speed stops, the fronts were overheating (as in, the front discs had glowing red rings, and caliper temp strips (with a range, IIRC, of 149-260°C) indicated above the max at the front and below the min at the rear).



#12 NotAPineapple

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Posted 12 August 2018 - 18:56

Ok, that's all pretty clear. If the rears were locking before the fronts then it's pretty clear the bias was too far back.

Do you have a maximum allowed temperature on discs and calipers from the manufacturer? I don't think red glowing rings are necessarily a bad thing on sport car carbon discs. But the fact that the fronts are glowing and the rears are showing out of range low means there is a thermal management problem in limit braking.

 

I remember a big sports car OEM had overheating problems on their front carbon-carbon discs some time back and they fixed the issue with a redesign of the brake cooling. What kind of cooling setup do you have? Do you have two ducts running to the inside of the disc (radially) and to the calipers? If not this will be the first step to try.

 

I'd suggest putting some thermal paint on the discs if you get a chance to repeat the test. Would be interesting to see how much the rear discs are being worked.



#13 New Britain

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Posted 12 August 2018 - 19:29

Ok, that's all pretty clear. If the rears were locking before the fronts then it's pretty clear the bias was too far back.

Do you have a maximum allowed temperature on discs and calipers from the manufacturer? I don't think red glowing rings are necessarily a bad thing on sport car carbon discs. But the fact that the fronts are glowing and the rears are showing out of range low means there is a thermal management problem in limit braking.

 

I remember a big sports car OEM had overheating problems on their front carbon-carbon discs some time back and they fixed the issue with a redesign of the brake cooling. What kind of cooling setup do you have? Do you have two ducts running to the inside of the disc (radially) and to the calipers? If not this will be the first step to try.

 

I'd suggest putting some thermal paint on the discs if you get a chance to repeat the test. Would be interesting to see how much the rear discs are being worked.

I think the OEM supplier you have in mind supplied Porsche in about 2002-'03-ish. They were the first to use carbon-ceramic discs, in the 996 Turbo. As I say, however, those were carbon-ceramic discs. After a lot of work by two or three different OEMs, and at least two more generations of carbon-ceramic technology, they got the system to work.  I am certain, however, that no OEM has ever offered carbon-carbon on a road car. The only reason that I am able to do so is that the consultant with whom I have been working has a proprietary technique for dealing with the low CoF problem at low temperatures.

My understanding is that you don't want discs "red" hot for an extended period, as the heat can melt the caliper seals. In a racing car that's not so bad, because the seals will be replaced after the race, but in a road car one would not want that.

Above a certain temperature, a carbon-carbon disc will oxidise (as in, the solid will turn into a gas), and that is obviously not so good either!

 

Yes, I think you're right that we need to address the cooling effectiveness. We've got 3" hose going to the inside of the front discs, but we should probably have that split off and part of the flow redirected to the calipers.

 

I'll try the thermal paint as well.

 

Cheers.



#14 Joe Bosworth

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Posted 13 August 2018 - 04:37

You mention fronts as over heating in your first post.

 

How are you defining over heating?

 

Are you losing your front brakes?

 

How heavy and what kind of vehicle?

 

Use of a thermal temperature gun on fronts and rears immediately on stopping can provide some insights.

 

Different temperature thermal paint is a start but also check temps of calipers as well.

 

All of this can help define the problem and therefor the solution.



#15 New Britain

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Posted 13 August 2018 - 19:21

Joe,

 

Under repeated heavy braking, the front discs had glowing red rings on them. The temperature on the front calipers exceeded the range of the temp strips, whilst the temperature on the rear calipers did not even register on the strips.



#16 Joe Bosworth

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Posted 14 August 2018 - 14:11

Brit

 

In posts #2 and #14 I have been trying to pull some technical facts as what your conceived problem really is.  Others have chimed in with suggestions as fixes but to date you only come back to red glowing disks being a problem. 

 

Carbon carbon brakes are rated up to the 1400 C to 2000 C range depending on the supplier.

 

The red spectrum only starts to be seen at about 700 C and starts to blend into the yellow spectrums above 1000 C.  In the absence of some real temperature readings from you I simply don't understand what your front brake problem is.

 

You seem to have a bigger problem with your back brakes not coming to temperature but you fail to say why/how you alter bias which should be  almost infinitely adjustable.

 

You even fail to advise what use your brakes are being put to and it may well be that at your level of technical knowledge you really should be using cast iron rotors and good quality conventional pads.  Remember that cold/cool carbon brakes are pretty terrible for most road use applications.



#17 New Britain

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Posted 14 August 2018 - 19:56

Joe,

 

I have spoken with the chap who is assisting me in the project. As I mentioned above, he produces finished discs for F1 teams (at least four teams that I know of in recent seasons). I may have made mistakes in transcribing what he told me, but I doubt that he made mistakes in what he said. According to him:

- Carbon fibre begins to oxidise at 600ºC.

- Although in F1 the discs can register temps up to about 1200°, that is the transient temp measured at the surface, not what he calls the bulk temp, which is not normally above 750º.

- Between braking incidents, the system should be designed so that the bulk temp drops to 350° or less.

- A portion of a disc will begin to glow red at 500-550º, orange at 1100°, white at 1300º.

Therefore if the disc is becoming red, and its temperature is much above the minimum at which it will begin to glow red, you are starting to oxidise some of the carbon fibres. On a racing car on which you will be changing discs and pads after every event, that is not normally a problem, but you would not want to have that problem on a road car. It would be rare to have it on a road car with carbon-carbon discs and pads, but not impossible, as I noted above.

 

You are correct about the insufficient CoF normally experienced with carbon-carbon discs when cool, but that is not a problem with the proprietary system that I am using. Required brake pedal pressure when cool is indistinguishable from iron discs.

 

Brake bias is adjusted with a threaded bar behind the pedal.

 

The intended use is "normal" road driving, but I just want to make the system as robust and usable as possible, and the one area that we have yet to get sorted is this ramping-up of front temps (v rear temps) under repeated heavy demand.

 

 

 

 

 

 



#18 gruntguru

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Posted 15 August 2018 - 22:43

If the bias is correctly set and the front brakes are getting too hot, you need bigger front discs and/or more cooling. Likewise if the rears are not getting hot enough, you need smaller discs.



#19 Joe Bosworth

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Posted 16 August 2018 - 09:11

Grunt is absolutely correct.

 

You seem to have a problem setting the bias as you describe elsewhere.  Let's try to get some science and facts into the problem.  For as little as about $50 you can buy a small hand held remote temperature reading device.  Use the reader on your front and rear disks as you gently re-bias frlnt to rear.  I don't have a feel for your mechanism but on most of my past race cars I was able to find a change in 1/2 to i1 turn increments.  Start that small and work up if small changes don't see your rear brake temps go up and fronts go down.

 

Since you seem to be working with a road car you don't want to be seen and caught being a hoon.  Start out with using near full throttle in near a top gear and holding a constant speed with the brake peddle.A little trial and error will get you times and pressures that work for your testing regime.  If your disks are close to correct you will shortly give you sensible temps.  If they are as Grunt suggests then you need to re-think disk choice.

 

Once you are getting close in temperatures in the "static" tests as above then a it is time to fine tune in weight transfer mode but that should be easy once you get a feel for the results of the static tests.  Have no fear of red showing on the surface of your disks.  It takes a long time for the interior of the disks getting to anything like really hot enough to deteriorate even based on the temperatures that you seems to quote.

 

If you want further help please publish the test data you gather from above.

 

Regards

 

PS:  I really can't understand why you are choosing to use carbon/carbon on the road.  I can only remember once in my life where I ran out of brakes on the road and that was while taking a vacation in eastern W Virginia and western Maryland in a SS Chev wagon packed with four kids, wife and suit cases for all and I chose to take advantage of 2nd and 3rd class roads..  My no. one son also races a historic Corvette within rules that require iron disks,  He runs at the front end of the pack and advises that he gets 20 minutes of hard racing before heat sink sets in and the brakes get hot enough to lose effectiveness.



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#20 Lee Nicolle

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Posted 16 August 2018 - 09:12

Carbon rotors for a street car is a total waste of money. Even an exotic one. And down force will make 3/5 of stuff all difference. Even on a rally car that do really dive under brakes and squat under go.

IF you have that much discrepancy you have a cylinder sizing issue. Front brake temps will always be higher, though the rear should be at least 3/4 of the front. This on a race track. Road cars generally do most of their braking on the front, even with nanny brakes. With a very effective LSD or a spool you can put more brake on the rear. But both are impractical for normal driving. 



#21 New Britain

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Posted 16 August 2018 - 10:04

If the bias is correctly set and the front brakes are getting too hot, you need bigger front discs and/or more cooling. Likewise if the rears are not getting hot enough, you need smaller discs.

Thanks. I'm going to try improving the cooling first. If that doesn't work, I'll try to locate calipers that will work with smaller rear discs.



#22 New Britain

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Posted 16 August 2018 - 10:15

Grunt is absolutely correct.

 

You seem to have a problem setting the bias as you describe elsewhere.  Let's try to get some science and facts into the problem.  For as little as about $50 you can buy a small hand held remote temperature reading device.  Use the reader on your front and rear disks as you gently re-bias frlnt to rear.  I don't have a feel for your mechanism but on most of my past race cars I was able to find a change in 1/2 to i1 turn increments.  Start that small and work up if small changes don't see your rear brake temps go up and fronts go down.

 

Since you seem to be working with a road car you don't want to be seen and caught being a hoon.  Start out with using near full throttle in near a top gear and holding a constant speed with the brake peddle.A little trial and error will get you times and pressures that work for your testing regime.  If your disks are close to correct you will shortly give you sensible temps.  If they are as Grunt suggests then you need to re-think disk choice.

 

Once you are getting close in temperatures in the "static" tests as above then a it is time to fine tune in weight transfer mode but that should be easy once you get a feel for the results of the static tests.  Have no fear of red showing on the surface of your disks.  It takes a long time for the interior of the disks getting to anything like really hot enough to deteriorate even based on the temperatures that you seems to quote.

 

If you want further help please publish the test data you gather from above.

 

Regards

 

PS:  I really can't understand why you are choosing to use carbon/carbon on the road.  I can only remember once in my life where I ran out of brakes on the road and that was while taking a vacation in eastern W Virginia and western Maryland in a SS Chev wagon packed with four kids, wife and suit cases for all and I chose to take advantage of 2nd and 3rd class roads..  My no. one son also races a historic Corvette within rules that require iron disks,  He runs at the front end of the pack and advises that he gets 20 minutes of hard racing before heat sink sets in and the brakes get hot enough to lose effectiveness.

 

I fully appreciate that nobody needs carbon-carbon (or carbon-ceramic, for that matter) discs on a road car. Years ago when he came to F1 from CART, where he had always used iron discs, Alex Zanardi tried to persuade Williams to let him use iron rather than carbon-carbon on their racing car. After back-to-back testing, Williams concluded that there was no meaningful difference between the two in braking performance, but the difference in unsprung rotating weight was of course meaningful for other reasons, and they required Zanardi to adapt.

 

That's what is motivating me: a savings of roughly 7kg/corner. No, I don't need it, but for some people, especially those of us on this forum, our road cars are more than just transportation. We love to drive and we love to make our cars better than they "need" to be.

 

Cheers.



#23 New Britain

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Posted 16 August 2018 - 10:24

Carbon rotors for a street car is a total waste of money. Even an exotic one. And down force will make 3/5 of stuff all difference. Even on a rally car that do really dive under brakes and squat under go.

IF you have that much discrepancy you have a cylinder sizing issue. Front brake temps will always be higher, though the rear should be at least 3/4 of the front. This on a race track. Road cars generally do most of their braking on the front, even with nanny brakes. With a very effective LSD or a spool you can put more brake on the rear. But both are impractical for normal driving. 

Lee,

 

As I wrote in my previous reply, I'm just trying to improve the car. Whether doing that is a "total waste of money" would depend on an individual's priorities. There is no accounting for different people's tastes!  ;)



#24 gruntguru

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Posted 16 August 2018 - 22:27

Thanks. I'm going to try improving the cooling first. If that doesn't work, I'll try to locate calipers that will work with smaller rear discs.

Start by getting more air onto the caliper. The disc temp doesn't sound that bad.



#25 New Britain

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Posted 17 August 2018 - 00:21

Start by getting more air onto the caliper. The disc temp doesn't sound that bad.

That is the plan.

 

Thanks!



#26 kikiturbo2

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Posted 17 August 2018 - 02:51

I will throw one more problem in the mix... Your carbon carbon brake coefficient of friction is very temperature sensitive. Chances are, due to natural front bias of brakes, that your front brakes are getting up to temp, while rears arent. This will lead to  fronts and rear operating on two different points in the Cof vs temp graph when hot, and on the same, or very siimilar point when cold. This, in other words, means that your brake balance will change by a large margin during driving and during braking, depending on severity of use...



#27 NotAPineapple

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Posted 17 August 2018 - 18:08

Anyway, I ran a few numbers on the query on the original post and I have seen that with aero producing race cars your optimum brake balance will shift due to the aero effects but not enough to justify running the same discs front and rear.

 

Basically if your downforce balance is more rearward than your mass distribution then the optimum brake distribution will be more rearwards at high speed. You could be tempted to say this tendency explains why your consultant recommended the same disc sizing front and rear but the movement of the optimum brake distribution is only around 5%. That's a lot for braking performance but not so much in terms of thermal loading. Dissipated energy is always more biased to the front so there is no reason why the thermal mass on the rear should be similar to the front.

 

GT race cars usually always have rear discs which are 15-30mm smaller in diameter and 2-3mm thinner than the fronts. That goes for steel and ceramic brakes. If you assume your road car has no lift then applying a racecar disc sizing will result in you having rears which are too big thermally.

 

Where did you balance bar finish after you found a good balance which didn't lock the rears? Was is almost to the front extreme or is there still margin? Have you got larger master cylinders on the rear?



#28 gruntguru

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Posted 17 August 2018 - 22:40

. . . .You are correct about the insufficient CoF normally experienced with carbon-carbon discs when cool, but that is not a problem with the proprietary system that I am using. Required brake pedal pressure when cool is indistinguishable from iron discs. . . . 

 

 

I will throw one more problem in the mix... Your carbon carbon brake coefficient of friction is very temperature sensitive. Chances are, due to natural front bias of brakes, that your front brakes are getting up to temp, while rears arent. This will lead to  fronts and rear operating on two different points in the Cof vs temp graph when hot, and on the same, or very siimilar point when cold. This, in other words, means that your brake balance will change by a large margin during driving and during braking, depending on severity of use...



#29 New Britain

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Posted 18 August 2018 - 09:57

I will throw one more problem in the mix... Your carbon carbon brake coefficient of friction is very temperature sensitive. Chances are, due to natural front bias of brakes, that your front brakes are getting up to temp, while rears arent. This will lead to  fronts and rear operating on two different points in the Cof vs temp graph when hot, and on the same, or very siimilar point when cold. This, in other words, means that your brake balance will change by a large margin during driving and during braking, depending on severity of use...

Yes, I was thinking the same thing, but the F-R load transfer on my car, as a %, seems actually to be less than on the cars for which carbon-carbon brakes were designed. I think that brings us back to the problem being insufficient cooling at the front.



#30 New Britain

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Posted 18 August 2018 - 10:23

Anyway, I ran a few numbers on the query on the original post and I have seen that with aero producing race cars your optimum brake balance will shift due to the aero effects but not enough to justify running the same discs front and rear.

 

Basically if your downforce balance is more rearward than your mass distribution then the optimum brake distribution will be more rearwards at high speed. You could be tempted to say this tendency explains why your consultant recommended the same disc sizing front and rear but the movement of the optimum brake distribution is only around 5%. That's a lot for braking performance but not so much in terms of thermal loading. Dissipated energy is always more biased to the front so there is no reason why the thermal mass on the rear should be similar to the front.

 

GT race cars usually always have rear discs which are 15-30mm smaller in diameter and 2-3mm thinner than the fronts. That goes for steel and ceramic brakes. If you assume your road car has no lift then applying a racecar disc sizing will result in you having rears which are too big thermally.

 

Where did you balance bar finish after you found a good balance which didn't lock the rears? Was is almost to the front extreme or is there still margin? Have you got larger master cylinders on the rear?

The thing is, the AP calipers are for racing (with either iron or carbon discs), and they are designed for the same size discs front and rear. AP don't even make a related caliper for a different size disc. Their only allowance for different braking forces front and rear is that they come in two different piston sizes.