[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.