BMW Performance Accesories - carbon ceramic brakes coming?

[swamp2]

OK lets get to specifics. Lets look at the 2004 Porsche GT3 with and without PCCB. Perhaps not the most recent example, but a good one in which a high end brake system is fitted in both configurations. The car was available with both a cast iron rotor (perhaps alloy steel, but we will simply assume cast iron) or the PCCB system with carbon ceramic (CSiC) rotor. A key finding here is that at the OEM brake pads were either Pagid directly or used Pagid compounds and the RS19 compound was supplied for both systems. This compound, according to the chart I supplied earlier, fades at approximately 500 °C. The CSiC rotors were supplied by SGL Group so I used their specific material properties. Perhaps the properties listed presently are not the ones from 2004. I actually expect they are not, but the properties today are likely improved so again this small assumption errs on the side of giving the benefit to the PCCB system.

I am going to continue to use the conservation of energy principal but will demonstrate that the materials relative conductivity favors my conclusion even stronger. If a rotor had an extremely high conductivity it would exhibit nearly isothermal conditions in any shape and under any thermal loads. Since the conductivity of CSiC as used for PCCB system is lower than the cast iron it means that the temperature difference across a given path from the surface where heat is generated to cooler areas such as the center of the disc (laterally or radially) or the exposed surface of an internal cooling fin will always be LARGER with the CSiC rotor. Basically the CSiC rotor stores more surface heat longer creating larger peak temperatures than the cast iron system.

The snapshot of a spreadsheet (at the end of the post) I made shows clearly that this rotor will always experience a larger increase in average temperature for any given stop independent of its beginning temperature distribution. Yes the friction surface of both rotors immediately after braking will be hotter than their respective spatially averaged values, but again the CSiC rotor will have AN EVEN larger difference between its cooler and warmer spots due to its lower conductivity.

Now assuming there is no brake cooling (which certainly is not true in the initial braking portion from this very high speed) a single stop from 165 mph to zero will produce and average rotor temperature and hence pad temperature that exceeds the brake pads fade temperature limit with the CSiC system. However, the cast iron system remains well under its limit. The difference between the two is over a whopping 300 °F. And I would make an educated guess (again supported by the conductivity point) that this is not only the difference between their average temperature but also a lower limit between their peak temperatures. The difference is plenty large enough to make up for other approximations in the method. No cooling is not a terrible assumption either as brake heat generation rates drastically exceed both the lumped capacity and forced convective (through the internal fins/flow) cooling rates. If you still do not like the assumption of no cooling, simply consider a rapid succession of stops from 70 mph ->0 where the cooling rates are truly negligible in comparison with the heat generation rate. Each one will cause a larger temperature increase in the CSiC rotor.

Lastly even if compatible with and fitted with the Pagid RS15 pads with a fade temperature of 650 °C the CSiC system would still reach this temperature BEFORE a traditional system with the RS19 compound.

The conclusion here is simply that he CSiC brake system in the 2004 Porsche GT3 is more prone to fade than the conventional brake system offered in the car. This is due primarily to the reduced mass of the rotors and a pad choice that does not offer an increased fade knee point to deal with the naturally higher rotor peak and operating temperatures. I was able to find "experimental" evidence of this phenomena as well (at least on the 2002 GT2 with PCCB vs 2001 TT with conventional. This story about a very frustrated PCCB owner who clearly highlights his problems with brake fade at Watkins Glen. Link to post here. Or direct quote,

In October of 2002 I took the car to Watkins Glen for a Driver�s Education event. I brought the GT2 and our 2001 Twin Turbo and I was looking forward to testing it out. While going around the track I noticed that with the GT2 there was a slight brake fade on a couple of the turns. Because the weather was cold I thought perhaps the brakes had not warmed up enough. After being sure that the brakes were hot I was going down the back strait, hit my brakes hard for the chicane turn, and actually shot past the turn and into a cone because the brakes did not work � there was significant brake fade. (The cone put some scratches on the car and it cost me $800 to refinish it). Before I left the Glen I wanted to try the same thing again, as a carefully planned test, and again I went straight past the chicane turn because the brakes failed again (however, I anticipated the failure and didn�t hit any cones this time).

The rest of the post is even more damning of the technology in terms of wear and insuitability of "alternate" Porsche recommended brake pads.

Note Porsche seems to be well aware of this fundamental limitation as the current GT3 has substantially larger rotors when you get the PCCB option 15" vs. 13.8" (I believe they have been doing this for some years now) They simply need more thermal mass and a larger rotor makes up some of that ground. As well I'd bet they do not use the same pads and the PCCB pad will have a higher knee temperature.

[Radiation Joe]

As much as my voyeuristic tendencies are keeping me reading this, I think I need to recommend that you two get a room.

[swamp2]

Originally Posted by Radiation Joe

As much as my voyeuristic tendencies are keeping me reading this, I think I need to recommend that you two get a room.

Ha, very funny, I knew there would be at least one other person nerdy enough to follow this. Cheers.

[lucid]

Hey Swamp, thanks for the comparison. I'll respond to your post(s), just busy. At a first glance, 2 clarification questions:

1. Why is the iron rotor volume less than the CC rotor volume given they seem to have the same thickness? (this will actually strengthen your argument if it is a simple data entry error). If this is not an error, does it have to do with the vent geometry?

2. Why did you pick c=800 J/kgK for the CC rotor? Were you able to verif that was the spec for the GT3 back in 2004? I assume you went with the data on the SGL website (I don't know how up to date that is). However, their 2006 SAE presentation is referencing 1350 J/kgK, and 2005 Krenkel paper is stating 1200 J/kgK for the Brembo rotors.

[lucid]

Originally Posted by Radiation Joe

As much as my voyeuristic tendencies are keeping me reading this, I think I need to recommend that you two get a room.

RJ, since you seem to have something to do with radiation, you should model the heat transfer out of the rotor via thermal radiation to the environment on this one! Probably around 0.001% of PowerIn.

Swamp and I had a few email exchanges as things as we weren't approaching the dialog the right way, and sorted things out. It'll be constructive from now on.

[swamp2]

Originally Posted by lucid

Hey Swamp, thanks for the comparison. I'll respond to your post(s), just busy. At a first glance, 2 clarification questions:

1. Why is the iron rotor volume less than the CC rotor volume given they seem to have the same thickness? (this will actually strengthen your argument if it is a simple data entry error). If this is not an error, does it have to do with the vent geometry?

2. Why did you pick c=800 J/kgK for the CC rotor? Were you able to verif that was the spec for the P-car back in 2004? I assume you went with the data on the SGL website (I don't know how up to date that is). However, their 2006 SAE presentation is referencing 1350 J/kgK, and 2005 Krenkel paper is stating 1200 J/kgK for the Brembo rotors.

Good questions.

1. Yup, typo and vents, great guesses. When looking at rotors I wanted to properly model the volume due to the vents. My approximation, which I think is very good is to consider the annular friction surface part to be three sections, two outer ones solid and an inner one, all of equal thickness. For the inner one I figured it had 1/2 the material removed for vents. This places a 5/6 factor in the volume equation which was then missing for the CSiC case. It raised the 534 temperature figure significantly to a whopping 637.

However, the quoted weight savings spec from Porsche of 18 kg for all four rotors is the way I backsolved for the rotor ID. taking the above into account changes the ID and again worsens the case for the CSiC. A revision is included below that fixes both issues.

2. Again I used numbers from SGL website for current SGL materials. SGL was and is the supplier for Porsche. If their specific heats are better now than then this again would only show worse performance for the PCCB set up back in 2004. A value as high at 1350 would bring the temp way down to 386, just a hair higher than the iron.

[lucid]

Originally Posted by swamp2

Another reason this is so is because the peak temperature is maintained for a relatively short amount of time as the rotor itself and pad both equilibrate. So sure if you want a very precise calculation of whether the fad temperature is exceeded by even the slightest amount for even a short period of time, indeed you will need to worry about conduction.

Keep in mind the power input into the pad is really a pulse, and not a step input. Also, keep in mind that it is clear that the researchers worried about the low conduction of CC rotors and had to manipulate the material in order to increase its conduction, possibly at the at the expense of strength. If conduction was such a non-issue, why did they bother?

Originally Posted by swamp2

Sorry but I have to call diversion on this as well. We are not talking about a future improved design, we are talking about currently available systems and none of the ones I have seen have a 37% greater volume compared to a similar high end iron/steel set up.

Swamp, buddy, I would appreciate it if you wouldn't call it a diversion every time I frame the conceptual problem differently than you do. We have been through this several times now. We clearly are approaching the issue from different angles. You are interested in comparing what is out there today. That is a valid viewpoint. I am interested in where this technology will go in about 5-7 years, which is also a valid viewpoint. The CC material clearly has highly attractive, and IMO, superior, qualities. This will really turn into an optimization problem between mass, volume, and specific heat capacity more than anything else. For me, those are the 3 key design parameters, and you can be sure that developers will be exploring different combinations.

Originally Posted by swamp2

I am specifically questioning the quotations you have provided, not the full context of all work, public or confidential that a particular source has conducted. Whether or not the conclusions are light on science, I still firmly believe that such statements which attempt to universally rank the performance of a material against another for a specific capability such as fade resistance are woefully imprecise and inadequate. As we both surely can agree it is a system question and even more so, system by system. Science, not marketing...

That is why I took the SGL claims on the advantages of the CC systems with a grain of salt, and turned to/referenced the literature. Yes, there can be biases there as well, but those people just don't publish stuff without having solid rationale, especially if they are well respected.

You are saying general claims were made in the article, and I am saying that that is most likely due to the fact that I quoted from an abstract. Regardless, I think the same criticism can apply to your statements on the fade issue as well, which have been somewhat broad. You clearly have a "constant volume" and "system must currently exist" criteria for instance when comparing these systems, and that wasn't clear to me until we started this exchange.

Originally Posted by swamp2

I certainly saw it that way and I think anyone reading would agree. I never said I was an expert in CSiC nor CC brake technology. Nor did I make any comparisons between myself and any experts in the field. However, I certainly have done enough work to find that conservation of energy is a darn good approximation and have enough insight to know it will work reasonably well for bikes, cars, motorcycles, wheelbarrows or whatever.

OK. I was too harsh there. Sorry about that. But keep in mind that there are material specific issues here. For instance the conductivity of CC materials is not uniform in 3-axis. And, people with expertise on CC materials who are specifically evaluating them for friction systems must possess much better knowledge about where they are going in the future than either one of us.

Originally Posted by swamp2

The simple ratio of (mass1 x specific heat1)/(mass2 x specific heat2) will be a great factor to determine the ratio of peak OR average rotor temperature increases for any combination of unsteady braking conditions (again given identical scrubbed energies and identical cooling).

You realize which material will come on top with if you allow them to weigh the same (they don't even have to weigh them same--I've been saying this all along).

Originally Posted by swamp2

Further on that I would scrap the idea of requiring the systems to weigh the same. Occupying the same volume is a much more fair comparison as each system would need to fit a given wheel/hub/suspension set up and fixing the rotor overall diameter and choosing and existing caliper is the most fair way to evaluate the rotor material change alone.

I think it is perfectly fair to increase the volume of the CC rotor within reason--as long as that doesn't require wheel or suspension modifications. It is fair to say that increasing rotor volume might/would require caliper and/or pad redesign since that is a part of the braking system.

Originally Posted by swamp2

You still have not suggested a simple formula and procedure to get a first order accurate calculation of which rotor will reach its pad specific fade temperature first.

OK. You actually made me remember the relevant material and setup the governing differential equation. This is in 1D. I believe it is a reasonable approximation of what is going on. We can discuss the details if you'd like over email, but I am really short of time and need to post less on this thread.

Please feel free to check the math and let me know. And also feel free to solve the resulting governing equation based on the initial and boundary conditions. I am not doing that. It's been 15 years since I solved one of these suckers, and it would take time for me to remember all that. However, I suspect that the temperature response can be obtained via the seperation of variables method. Better yet, a computational model would be great as you suggested!

I agree that convection during braking is not a significant factor. I think at exreme conditions and at high speeds (such as braking with an seriously overheated system), it could be ~5% of the Power into the system. In more realistic conditions, such as when you are breaking from 165mph and reach 100mph, that could be around 2.5% at that point. That's based on some very simple estimations though.

P.S. I will respond to your GT3 post when I get a chance...

Cheers man!

[watrob]

Man, I have to learn to read Egyptian!

[swamp2]

Originally Posted by lucid

Keep in mind the power input into the pad is really a pulse, and not a step input. Also, keep in mind that it is clear that the researchers worried about the low conduction of CC rotors and had to manipulate the material in order to increase its conduction, possibly at the at the expense of strength. If conduction was such a non-issue, why did they bother?

I'd disagree on this as well. The power input into both the pad and rotor is much more like a step function than a delta funciton. However, the power varies with vehicle speed as well. So for any short duration of an entire braking process it is roughly a constant. Again conduction is an issue in rotor design but is not an issue in a back of the envelope/first order estimate of temperatures nor fade.

Originally Posted by lucid

Swamp, buddy, I would appreciate it if you wouldn't call it a diversion every time I frame the conceptual problem differently than you do. We have been through this several times now. We clearly are approaching the issue from different angles. You are interested in comparing what is out there today. That is a valid viewpoint. I am interested in where this technology will go in about 5-7 years, which is also a valid viewpoint. The CC material clearly has highly attractive, and IMO, superior, qualities. This will really turn into an optimization problem between mass, volume, and specific heat capacity more than anything else. For me, those are the 3 key design parameters, and you can be sure that developers will be exploring different combinations.

This has been part of the essense of our lack of communication on this issue. You asked me to establish the CSiC rotors do not provide improved fade resistance. You never asked me to show that CSiC with some future improved properties and a future improved design (less weight savings...) in a future improved system could not improve fade resistance.

Originally Posted by lucid

You are saying general claims were made in the article, and I am saying that that is most likely due to the fact that I quoted from an abstract. Regardless, I think the same criticism can apply to your statements on the fade issue as well, which have been somewhat broad. You clearly have a "constant volume" and "system must currently exist" criteria for instance when comparing these systems, and that wasn't clear to me until we started this exchange.

I have been pretty clear on this point. We even got the point of agreeing we would compare two existing high end systems and that was my point all along and what I finally provided in the post about the 2004 GT2.

Originally Posted by lucid

OK. I was too harsh there. Sorry about that. But keep in mind that there are material specific issues here. For instance the conductivity of CC materials is not uniform in 3-axis. And, people with expertise on CC materials who are specifically evaluating them for friction systems must possess much better knowledge about where they are going in the future than either one of us.

You realize which material will come on top with if you allow them to weigh the same (they don't even have to weigh them same--I've been saying this all along).

I think it is perfectly fair to increase the volume of the CC rotor within reason--as long as that doesn't require wheel or suspension modifications. It is fair to say that increasing rotor volume might/would require caliper and/or pad redesign since that is a part of the braking system.

I never for a split second would claim that the material does not have great POTENTIAL. It has a lot going for it - obviously - that is whey you can buy rotors of it today. But also there is a bit too much hype. Equal weight is a clear victory for CSiC. In the GT2 case it would mean somewhere between the equivalent existing diameter and 4" thick (yes 4"!) or a rotor OD/ID of 35"/32", i.e. equal mass simply is not going to happen. And who would want it to? The massive lowering of unsprung mass with these babies is (....again) their largest benefit.

Originally Posted by lucid

OK. You actually made me remember the relevant material and setup the governing differential equation. This is in 1D. I believe it is a reasonable approximation of what is going on. We can discuss the details if you'd like over email, but I am really short of time and need to post less on this thread.

Please feel free to check the math and let me know. And also feel free to solve the resulting governing equation based on the initial and boundary conditions. I am not doing that. It's been 15 years since I solved one of these suckers, and it would take time for me to remember all that. However, I suspect that the temperature response can be obtained via the seperation of variables method. Better yet, a computational model would be great as you suggested!

Basic equation is not correct for this case. Fouriers heat equation is only for the case with no transient heat generation. We need to solve the full diffusion equation with a time dependent heat generation term (because brake power varies with speed!). Here the futility becomes obvious. If we can't get a reasonable answer with conservation of energy then we would need "the full monty"; we would need to work in three dimensions, we would also need to add the finite brake pad and the time dependent heat generation. Here there clearly will be no closed form solution and hence you can not really use such a method to answer our fundamental question! That was my point as well about a PRACTICAL method to evaluate materials and systems.

Finite elements are the absolute natural answer.

[lucid]

Originally Posted by swamp2

I'd disagree on this as well. The power input into both the pad and rotor is much more like a step function than a delta funciton. However, the power varies with vehicle speed as well. So for any short duration of an entire braking process it is roughly a constant.

Power input into the pad is definitely more like a step function, however, the rotor spins and the contact surface is constantly changing. So if you focus on a specific area of the surface as big as the pad surface, power input to the rotor through that surface is more like a pulse. There will of course be diffusion to the region under that surface from the other parts of the rotor, but that should be relatively lower compared to the diffusion through the contact area.

Originally Posted by swamp2

I have been pretty clear on this point. We even got the point of agreeing we would compare two existing high end systems and that was my point all along and what I finally provided in the post about the 2004 GT2.

That car is 5 model years old. You said that they upgraded its rotors to 15" and shipped it with matching pads.

How about the ZR1? I know it has 15.5" Brembo rotors up front, but I couldn't find any data on thickness or volume.

Originally Posted by swamp2

I never for a split second would claim that the material does not have great POTENTIAL. It has a lot going for it - obviously - that is whey you can buy rotors of it today. But also there is a bit too much hype. Equal weight is a clear victory for CSiC. In the GT2 case it would mean somewhere between the equivalent existing diameter and 4" thick (yes 4"!) or a rotor OD/ID of 35"/32", i.e. equal mass simply is not going to happen. And who would want it to? The massive lowering of unsprung mass with these babies is (....again) their largest benefit.

How did you arrive at 4" for the same mass? Clearly, the c values are higher in the products that are shipped today. At least for the Brembos. The SGL data seems less certain. Their website says c=800, and their SAE presentations says c=1350. I am not sure how to intepret that.

And, again--I've repeated this several times--they don't even have to weigh the same for the thermal performance of the CC rotor to be superior. According to the specs for the CSiC materials that are being used in the rotors TODAY, you need increase the CC rotor volume/mass by just 37% for the mass x specific heat capacity ratios to be equal. Anything beyond that hands the advantage over to the CC rotors.

Originally Posted by swamp2

Basic equation is not correct for this case. Fouriers heat equation is only for the case with no transient heat generation. We need to solve the full diffusion equation with a time dependent heat generation term (because brake power varies with speed!). Here the futility becomes obvious. If we can't get a reasonable answer with conservation of energy then we would need "the full monty"; we would need to work in three dimensions, we would also need to add the finite brake pad and the time dependent heat generation. Here there clearly will be no closed form solution and hence you can not really use such a method to answer our fundamental question! That was my point as well about a PRACTICAL method to evaluate materials and systems.

Finite elements are the absolute natural answer.

The 1D solution by no means yields a comprehensive solution. Clearly, the 3D equation would be much more descriptive. I used the 1D equation to illustrate how one would go about determining the temperature of a specific point in the rotor at a specific time, and not necessarily as THE model. One can do a sensitivity analysis around the relevance of the k value at different rotor thicknesses and Power inputs. My guess is that the k value can be a significant factor in certain ranges, and once it is above a certain value for a given thickness and power input range, it won't matter. Clearly there is a major problem if k=0, and no problem whatsoever if k is infinite. The only piece of data we have is that the early CSiC compositions were problematic for braking applications due to low k values, which therefore, had to be increased. Yes, if you want to model non-steady Power input, you would need to solve the full diffusion equation, but at that level, there is no point in trying to arrive at an analytical solution to the problem, and it makes much more sense to turn to a computational environment.

The point is that the lump sum thermal model will not yield that level of detail, which might very well be necessary to understand the fade performance of a braking system. The lump sum model would most likely have not predicted the surface temperature/fade issues in the early CSiC compositions that are referenced for instance.

I'd be happy to work on a computational model with you on this one.

[swamp2]

Originally Posted by lucid

That car is 5 model years old. You said that they upgraded its rotors to 15" and shipped it with matching pads.

I did not choose it because it is old. I chose it because I could find all of the necessary data. I agree the the latest Porsche systems are likely much better.

Originally Posted by lucid

How about the ZR1? I know it has 15.5" Brembo rotors up front, but I couldn't find any data on thickness or volume.

I heard the ZR1 uses rotors straight off the Enzo.

Originally Posted by lucid

How did you arrive at 4" for the same mass? Clearly, the c values are higher in the products that are shipped today. At least for the Brembos. The SGL data seems less certain. Their website says c=800, and their SAE presentations says c=1350. I am not sure how to intepret that.

And, again--I've repeated this several times--they don't even have to weigh the same for the thermal performance of the CC rotor to be superior. According to the specs for the CSiC materials that are being used in the rotors TODAY, you need increase the CC rotor volume/mass by just 37% for the mass x specific heat capacity ratios to be equal. Anything beyond that hands the advantage over to the CC rotors.

Not the best estimate. That was for equivalent mass, not equivalent thermal mass. For equivalent thermal mass with the lower c you would need 2.5 thickness or a 22/19 diameter (or something in between). For the improved c you need a modest 1.5 thickness or a 15/12 diameter. Funny how the latter looks to be right about where things have gone, 15" OD and perhaps a bit thicker than "normal"!

Originally Posted by lucid

I'd be happy to work on a computational model with you on this one.

That would be fun. We still need some concrete material (pad and rotor data) to make the models truly meaningful. We'll also need conductivity as a tensor (ugh). My thoughts were just a transient thermal analysis leaving all thermal expansion and stress effects out of the model. As well I would assume a non-rotating system with a annular patch power input, initially constant then later allowing it to ramp down with vehicle speed. I'd like to have an estimate of this difference between peak and spatially averaged temperature results and a model can do that. It would also test conservation of energy. My company was recently acquired by ANSYS so I will have access to a great deal of best in class tools in the structural, thermal and fluid domains (ANSYS bought Fluent (CFD) a while back as well). Cheers.

[lucid]

Originally Posted by swamp2

I heard the ZR1 uses rotors straight off the Enzo.

The ZR1 seems to be using the Enzo rotors, which are 380x34mm, in the rear wheels only. In the front, the ZR1 has 394mm rotors. I couldn't find thickness info though.

Originally Posted by swamp2

Not the best estimate. That was for equivalent mass, not equivalent thermal mass. For equivalent thermal mass with the lower c you would need 2.5 thickness or a 22/19 diameter (or something in between). For the improved c you need a modest 1.5 thickness or a 15/12 diameter. Funny how the latter looks to be right about where things have gone, 15" OD and perhaps a bit thicker than "normal"!

Nope. That was not for equivalent mass. It was for equivalent heat capacity, which I assume is what you mean by "thermal mass". If we simply choose an equivalent heat capacity spec (4000 J/K seems to be a reasonable number although it doesn't matter what we pick as long as we use the same number for each case) and do the arithmetic on what it takes to provide that heat capacity based on the specs published for the different materials, we get what you see below:



As you can see, if one uses the currently available commercial Brembo CSiC rotor, one needs just 33% more volume to obtain the same thermal mass as an iron system. If the CSiC rotor referenced in the SGL SAE presentation exists, the difference is only 13%!

Now, back to your GT3 iron vs. CSiC rotor comparison. Let's shelve the relevance of conductivity and the temperature distribution, and use the lump sum thermal model you've been using. Let's also shelve where CSiC technology is going in the near-mid future, and look at what is available today for high-end production cars. I did a survey of rotor sizes in high-end performance cars, and the following are the largest rotor sizes I could find that are available today:

Iron: Maserati MC12; 380x34 mm
CSiC: F430 Scuderia; 398x36 mm (Brembo)

It turns out your assumption about the air gap being 1/3 of the total thickness and the total vent space resulting in 1/6 reduction in volume does not hold up. I went through the Brembo catalog for racing rotors and the air gap is more like 1/2 of the total thickness, and the reduction due to vents is more like 33% for a rotor of similar size 380x35 mm (see attachement for pdf page). This makes sense if you look at some pictures of the M3 rotors. Anyway, not that this should affect the iron vs CSiC comparison unless they have drastically different vent geometries, which I doubt is the case. (The carbon racing rotors do have a drastically different vent geometry though--they seem to have less vent spacing. Check them out on the Brembo website).

Anyway, using the 33% vent volume factor, I came up with a comparison. I stuck the largest available rotors of each kind in the F430 Scuderia. It obviously wouldn't have been fair to use the MC12 chassis as that is heavier than the Scuderia. If the Scuderia can accommodate the larger CSiC rotors, it can accommodate MC12's iron rotors as well, so this is an appropriate comparison. Here are the results:



The first thing to notice is that the two systems have comparable heat capacity--just above 4000 J/K--so the temperature increases experienced by the two systems should be comparable as well (again, we are not considering conductivity).

I am assuming that the pads can deliver peak CoF close to the respective peak operational temperatures of the two systems, and we have already agreed that that is not bad assumption. If we just run a 260kph to 50kph brake event with cold rotors, neither system will fade of course. Let's assume that we run the car through some tight parts of the track and seriously heat up the rotors without giving them a chance to cool down (we also agree that one can charge a rotor much faster than one can discharge it). Say they go up to 600C. Then let's say we accelerate to 265 kph and brake down to 50kph. Let's assume to rotors cooled down from 600C to 450C before the beginning of the braking event.

As expected, the lump sum thermal model predicts a similar temperature rise for each system, which puts the temperature toward the end of the braking event slightly over 700C for both systems. Now, the catch is that this is well below the operational limits of the CSiC system, whereas the operational limit for the iron system has been exceeded.

Also, note that the CSiC rotor is still 5.3 kg lighter. It is possible to make it thicker for even higher thermal mass and lower temperatures while maintaining a weight advantage.

[swamp2]

Just a couple of comments.

-The 1/6th correction factor was again a rough 1st order approximation that I got from taking one quick look at one rotor picture and another one in a vertical cross section to see the vanes. The vanes in typical cast iron systems are clearly different than the ones in the pdf you posted and for them my 1/6th approximation is better. As you note is does not affect the comparison if both rotors are roughly the same which is very likely. I did not choose this number to bias either system. I did so because I knew the OD, a rough ID and weight differences. This value seemed to work fine based on my quick examination and the quoted weight differences.

-My figures above stand of how much thickness or diameter you would need with the 800 J/kgK material in comparison to the 13.8" OD iron Porsche rotors. An equivalent sized rotor of this material is at a SIGNIFICANT thermal disadvantage hence the much larger sizes required.

-In terms of the comparison of the larger CSiC rotor to the smaller iron one the results are obviously skewed in the direction favoring the CSiC. The advantage here is from the larger rotor more than from the material! Also, I would say the figures are close enough that conductivity may just start to to be the deciding factor. We know the CSiC materials have a lower thermal conductivity so they will exhibit a larger core to surface delta T than iron. We need an estimate of the difference in peak surface vs. core temperature for two different values of conductivity (again FEM would be good to get a reasonable estimate of this).

-I also found some data that says in general grey cast iron, despite the type or alloy, looses considerable strength above 500 °C (and looses it rapidly with increasing temperature, source here: http://www.sae.org/events/bce/tutorial-ihm.pdf ). What this means is that yout Tinitial is likely way too high and in practice would be almost impossible to obtain on any real iron braking system under any conditions except the most deliberate fade inducing ones. A more reasonable value would be 500 as a max allowable.

-All of our analyses point to a larger peak and operating temperature for the CSiC rotor system. Hence having a T initial that is equal for both, given an equivalent near term braking history, is quite a poor assumption. I made that one too in my analysis, but I was considering a braking event beginning with brakes at the temperature of the environment.

-Nonetheless, assuming all of your other numbers are correct (didn't check them in detail), and again ignoring conductivity, it does under these circumstance show a slight advantage for the CSiC system. Of course, as you mentioned, it also ASSUMES you have an appropriately matched pad (which they didn't back them).

I think both of our analyses together shows the important conclusion. CSiC systems are not hands down better. If you run an oversize system with the absolute latest greatest CSiC material and a carefully matched pad, you may just barely outperform a cast iron system from a thermal perspective. But you will clearly out perform it on the weight side which is very important in other regards. More or less my point all along! Finally when you factor in cost, I would say you are actually taking a step backwards.

[lucid]

Originally Posted by swamp2

-The 1/6th correction factor was again a rough 1st order approximation that I got from taking one quick look at one rotor picture and another one in a vertical cross section to see the vanes. The vanes in typical cast iron systems are clearly different than the ones in the pdf you posted and for them my 1/6th approximation is better.

Actually, I quoted the most conservative gap volume ratio. The Brembo catalog has about 60 cast iron rotors of different sizes and vent geometries. I punched in the data for 5 more starting from the closer sizes, and the gap ratio varied from 35-56%. I tried uploading the catolog but the website doesn't let me.
Then I checked the stoptech website here:

http://www.stoptech.com/products/img...rDataSheet.pdf

I punched in the numbers for the 4 rotors to the right of the chart, and the gap ratio ranged from 35-40%. Just look at the ratio of the air gap to the overall thickness. It's almost always around 1/2 (same for the Brembo rotors).

You must be looking at an unusual rotor, or my calculations have an error, or your estimate is off.

Originally Posted by swamp2

-My figures above stand of how much thickness or diameter you would need with the 800 J/kgK material in comparison to the 13.8" OD iron Porsche rotors.

I don't understand how you end up with 2.5 times the thickness when the required volume increase for equavilant heat capacity is 84% for the SGL rotor with 800 J/kgK, or with 1.5 times the thickness when the required volume increase for equavilant heat capacity is 13% for the SGL rotor with 1350 J/kgK.

For c=800 J/kgK, punch in 0.085 for thickness into the last spreadsheet you posted and check the c X m row, and you should end up with m X c of ~4700 J/K, which is significatly higher than the cast iron spec.

One of us has an error in the calculations.

Originally Posted by swamp2

-In terms of the comparison of the larger CSiC rotor to the smaller iron one the results are obviously skewed in the direction favoring the CSiC. The advantage here is from the larger rotor more than from the material!

Of course it is because of the larger rotor. But the point is that the larger rotor still weighs less! You get the same total heat capacity at a lower mass. If you want to design for increased total heat capacity for better braking performance, you just need to increase the volume more, and the system would still weigh less up to a point. What can that be attributed to if not the material?

Any increase in volume is NOT really a penalty as long as:

1. There is no interference between the brake system and the wheel and suspension.
2. The resulting mass of the CSiC brake system is still lower than the iron system.

Originally Posted by swamp2

Also, I would say the figures are close enough that conductivity may just start to to be the deciding factor. We know the CSiC materials have a lower thermal conductivity so they will exhibit a larger core to surface delta T than iron. We need an estimate of the difference in peak surface vs. core temperature for two different values of conductivity (again FEM would be good to get a reasonable estimate of this).

I agree with this point. My take is that the conductivity of CSiC rotors will be further improved in the near-mid future. That's why I quoted the c and k ranges for both material in my initial post on this.

Originally Posted by swamp2

[INDENT]-I also found some data that says in general grey cast iron, despite the type or alloy, looses considerable strength above 500 °C (and looses it rapidly with increasing temperature, source here: http://www.sae.org/events/bce/tutorial-ihm.pdf ). What this means is that yout Tinitial is likely way too high and in practice would be almost impossible to obtain on any real iron braking system under any conditions except the most deliberate fade inducing ones. A more reasonable value would be 500 as a max allowable.

Yes, I mentioned that cast iron goes through a phase transition from a BCC to FCC crystal structure at around those temperatures. It loses tensile strength and becomes ductile. I believe recrystalization is complete around 912C, and begins earlier. The SGL website is quoting 700C as the max operational temperature.

Anyway, if we take 500C as the max operational temperature, then the situation is clearly even worse for the Scuderia with the cast iron rotors in the comparison even if you pull the initial T down as the Scuderia with CSiC rotors will keep on performing.

Originally Posted by swamp2

-All of our analyses point to a larger peak and operating temperature for the CSiC rotor system. Hence having a T initial that is equal for both, given an equivalent near term braking history, is quite a poor assumption.

Nope. The two Scuderia's in my analysis with the largest CSiC and iron rotors currently sold operate with very similar temperature rises.

Originally Posted by swamp2

Of course, as you mentioned, it also ASSUMES you have an appropriately matched pad (which they didn't back them).

I read the ZR1 pads cost $6000. They can't be asking for that much for good old pads that have been around.

Originally Posted by swamp2

I think both of our analyses together shows the important conclusion. CSiC systems are not hands down better. If you run an oversize system with the absolute latest greatest CSiC material and a carefully matched pad, you may just barely outperform a cast iron system from a thermal perspective.

Yes, this currently seems to the case.

Originally Posted by swamp2

But you will clearly out perform it on the weight side which is very important in other regards. More or less my point all along!

Well, weight is linearly related to total heat capacity. So, you'll optimize for one or the other. By increasing the volume even further, you can easily create a CSiC system that will significantly outperform an iron system if you want.

Now, maybe the real question is this: is there a need for higher total heat capacity than what can already be achieved with a cast iron 380x35mm rotor? If there is, for whom? I surely do not have that need on the street or the track.

Originally Posted by swamp2

Finally when you factor in cost, I would say you are actually taking a step backwards.

I don't have a need to spend $30k on a brake system either, but we'll see where this all goes in 10 years in terms of pricing.

[swamp2]

Originally Posted by lucid

I don't understand how you end up with 2.5 times the thickness when the required volume increase for equavilant heat capacity is 84% for the SGL rotor with 800 J/kgK, or with 1.5 times the thickness when the required volume increase for equavilant heat capacity is 13% for the SGL rotor with 1350 J/kgK.

Ahhh, no... 2.5" thick as compared to 1.34", not 2.5 times as thick (with my 1/6th correction factor)! I thought that would be clear with the other numbers I was quoting like 22/19 (which were without units but obviously in inches). Also using your 66% volume correction (1/3 rd reduction) I can not get a reasonable ID and 18kg weight savings for the GT2 system. I think 5/6th is better for that particular rotor (likely wider vanes in the angular direction meaning less air *******.

Of course I agree just by a visual examination that 66% is a better estimate for many systems.

Originally Posted by lucid

Anyway, if we take 500C as the max operational temperature, then the situation is clearly even worse for the Scuderia with the cast iron rotors in the comparison even if you pull the initial T down as the Scuderia with CSiC rotors will keep on performing.

Nope. The two Scuderia's in my analysis with the largest CSiC and iron rotors currently sold operate with very similar temperature rises.

....

Now, maybe the real question is this: is there a need for higher total heat capacity than what can already be achieved with a cast iron 380x35mm rotor? If there is, for whom? I surely do not have that need on the street or the track.

You are following my reasoning. My point was both that 450 C initial temp is unrealistic because we know the rotor in your example is more than adequate to be almost fade proof in a Scuderia. It seems you chose that value quite arbitrarily to exceed the working temp range/limit of cast iron. As well, the CSiC system still shows a higher single stop delta T, combine that with the lower conductivity and you will definitely have a significantly higher T initial for that rotor. I agree with your point, you can find a CSiC system that will outperform a cast iron one - there is no doubt there. It is just this analysis is quite a bit on the optimisitic side in favor of the CSiC. My analysis was quite unbiased and used two real systems available on a real car

Overall I think we are both just about on the same page, which is encouraging. Cheers.

[lucid]

Originally Posted by swamp2

Ahhh, no... 2.5" thick as compared to 1.34", not 2.5 times as thick (with my 1/6th correction factor)!

OK. I didn't see the units (") after the 2.5 and you have mentioned 4" before (but that was for equvialant mass), so I misread this. It makes sense now.

Originally Posted by swamp2

You are following my reasoning.

Not really.

I still maintain that CSiC can offer better thermal performance than cast iron rotors. It's just that most people don't need it.

Originally Posted by swamp2

My point was both that 450 C initial temp is unrealistic because we know the rotor in your example is more than adequate to be almost fade proof in a Scuderia. It seems you chose that value quite arbitrarily to exceed the working temp range/limit of cast iron.

Well, pick an initial T of 250C then, which is totally reasonable so we don't need to argue about T_initial. The Scuderia with the iron rotor still ends up >500C.

Originally Posted by swamp2

As well, the CSiC system still shows a higher single stop delta T, combine that with the lower conductivity and you will definitely have a significantly higher T initial for that rotor.

By 13C. You consider that to be significant? It can become significant with the conductivity consideration though.

Originally Posted by swamp2

I agree with your point, you can find a CSiC system that will outperform a cast iron one - there is no doubt there. It is just this analysis is quite a bit on the optimisitic side in favor of the CSiC.

Well, I stuck the best brake systems--from a thermal performance point of view--that come on production cars TODAY that I am aware of on the same car for the comparison. I don't see how that favors one system or the other. (I didn't even consider what will be possible 4-5 years from now).

Originally Posted by swamp2

My analysis was quite unbiased and used two real systems available on a real car

I am not accusing you of deliberately manipulating the situation and I understand why you chose the 2003 GT3, but that doesn't mean that setup isn't already obsolete, and to a great extent, irrelevant.

If you run the same analysis for the 2008 GT3 with 380mm PCCB and iron rotors (they were still at 350mm in 2008) and use c=1200 J/kgK for the PCCB rotors, which we know is on the street today, the results will favor PCCB by 35C. My guess is that the c=1350 J/kgK spec in the SGL presentation was a response to the Brembo specs. Meaning, SGL is most likely currently shipping rotors to Porsche with c=1350 J/kgK--if SGL is still the Porsche vendor--which would give the 2008 GT3 with PCCB an 87C advantage according to the lump sum thermal model.

However, I agree that most people would not benefit from the thermal performance of a CSiC system. They don't need it. I've been saying that all along.

Originally Posted by swamp2

Overall I think we are both just about on the same page, which is encouraging. Cheers.

Definitely more agreement than before.

[swamp2]

Originally Posted by lucid

Not really.

Well, almost... At least we are back to smilies...

Originally Posted by lucid

I still maintain that CSiC can offer better thermal performance than cast iron rotors. It's just that most people don't need it.

I agree but I'll push it even further. No one needs them given the quality of current cast iron systems unless they are either a) racing competitively or b) weight obsessed.

Originally Posted by lucid

Well, pick an initial T of 250C then, which is totally reasonable so we don't need to argue about T_initial. The Scuderia with the iron rotor still ends up >500C.

But here is the point: If this particular iron system was at 250C, I would bet this particular CSiC system would be at at least 300C given an identical history. A very crude guess but probably not terrible either. As well showing a Scud reaching a fade temperature (or critical rotor strength temp) with these monster iron front rotors at these speeds shows a clear problem in the model.

Originally Posted by lucid

By 13C. You consider that to be significant? It can become significant with the conductivity consideration though.

This effect is additive! Not perfectly, but it is additive, brake event after brake event.

Originally Posted by lucid

Well, I stuck the best brake systems--from a thermal performance point of view--that come on production cars TODAY that I am aware of on the same car for the comparison. I don't see how that favors one system or the other. (I didn't even consider what will be possible 4-5 years from now).

Your basic choice of rotors or a car doesn't show the favoritism. Again it is the T initial and moreso the equality of the T initial. Any model that shows the Scud fading these iron fron rotors has a problem.

Originally Posted by lucid

I am not accusing you of deliberately manipulating the situation and I understand why you chose the 2003 GT3, but that doesn't mean that setup isn't already obsolete, and to a great extent, irrelevant.

Fair and accepted, both points.

Originally Posted by lucid

If you run the same analysis for the 2008 GT3 with 380mm PCCB and iron rotors (they were still at 350mm in 2008) and use c=1200 J/kgK for the PCCB rotors, which we know is on the street today, the results will favor PCCB by 35C.

And to me this is hard to believe. They simply got greedy on the weight and down played thermal mass in designing their systems, hence the weak/weaker initial systems. Our work shows you really need a larger rotor to win on both mass AND thermal even with todays best materials.

Originally Posted by lucid

Definitely more agreement than before.

Yes, finally, cheers!

We probably need to wind this one down. Not that anyone other than Rad. Joe is reading but we have each made our points and pretty much agree.

[lucid]

Originally Posted by swamp2

We probably need to wind this one down. Not that anyone other than Rad. Joe is reading but we have each made our points and pretty much agree.

OK man. Let's shelve this one. Good points made overall. It's been a good discussion...

[rzm3]

Alright engineers, can you guys now write an Executive Summary for the mangers?

[Sticky]

Originally Posted by watrob

Man, I have to learn to read Egyptian!

Hahahahahah!

[swamp2]

Originally Posted by rldzhao

Alright engineers, can you guys now write an Executive Summary for the mangers?

Lucid and I might actually resort to blows if we had to do this... (sarcasm...)

If you followed this mess this long but don't quite get all of the details I think you truly deserve an executive summary. Maybe we can put one together that we agree on and is concise and to the point.

[rzm3]

Originally Posted by swamp2

Lucid and I might actually resort to blows if we had to do this... (sarcasm...)

If you followed this mess this long but don't quite get all of the details I think you truly deserve an executive summary. Maybe we can put one together that we agree on and is concise and to the point.

Yes please. Findings, conclusions, disagreements, and recommendations for further investigations.