lucid:
For ALL CSiC thermal conductivities I have seen and all rotor thicknesses I have examined, for a given stop, due to the material properties, the CSiC system will indeed be hotter. And you can't argue that at some point hotter is closer to fading. This is more so from their low weight than their thermal conductivity. You just can not find a conductivity that will change this basic physics. There are no CSiC rotors that are three times the thickness nor three times the area of a traditional system to provide the equivalent thermal mass. The reason that high temperatures are the ultimate evil is that the pads will eventually simply give out, fade is first, accompanied or followed by excessive outgassing, material transfer, delamination, melting, ignition, etc.
We could settle this debate pretty well if we had the "magic" friction-temperature curve for a typical CSiC rotor and pad combination but for the life of me I can not find one. I actually expect that information is fairly proprietary. I have seen some fade data for CSiC systems, but not in this useful form and they were so far from fade (i.e. at such low temperartures) it was not really very interesting. A typical temperature-friction plot for a variety of Pagid brake pads is shown below. As you can see the lesser ones fade around 400 °C and the more high performance ones not until about 650 °C (note the C and F reversal/typo in the plot...). Since I figured you had seen on of these plots previously I did not feel the need to post it, but it sounds like you haven't, so here it is. You can see here, as I have been referring to, the "knee point" in each curve and it represents the onset of fade. Lastly on this point these are definitely not the highest performance/highest temperature pads available. Turner Motorsports sells a pad that can cope with over 760 °C!
Now here is a kicker: As far as I can tell, CSiC rotor brake systems actually do use standard issue pads, albeit standard "ceramic" pads with added ceramic for both wear and high temperature capability. Of course such pads are available for non CSiC rotors as well!
Pads are the more critical factor here, much more critical than the rotors.
You keep talking about how this can be made heavier or this can be thicker or this can be engineered, etc., etc.
That is not what this discussion is about. It is simply about is a CSiC braking system more fade resistant (with the clarification you have added that we should discuss a high end version of each system - do note that that would imply an alloy steel rotor not a cast iron one...)?
But we are not talking about what CAN be done, we are restricted here to what IS available now, today. Agree or disagree?
I never denied any fundamental equations of heat transfer and yes I have studied the subject thank you very much. Although typically my interest was a notch or two above the basics of heat transfer - more on the statistical mechanics side of things - the first principles from which thermodynamics comes.
The equation I provided is a darn good approximation, based on sound principles and real world experience. The other effects are truly secondary as I pointed out. Think about it this way: just at the end of a very hard but very intense and rapid braking event, when everything begins at ambient temperatures, where is the vehicles kinetic energy? It has to go somewhere and very little is lost to the structures other than the rotor (and pad) and very little has had time to dissipate by convective cooling. The rotor may still have a thermal gradient and indeed in a CSiC rotor it will probably have a higher gradient than in a very conductive iron/steel rotor which will reach a uniform temperature quite quickly (this is certainly a factor in saying the equation ignores 2nd order effects, of which non uniform temperatures is one indeed). Then when you combine multiple stops you certainly get some convective cooling and conduction which provides the temperature rise of other components (caliper, pistons, fluid, hub, rim, etc) accompanied by the temperature fall of the rotor. Indeed all of this is exactly as per some of the equations you mentioned.
But once you slam on the stoppers again the temperature rise is, to first order, governed by the equation I provided. I know it is fairly accurate not only as it is from first principles, but because I have actually tested it. It works, plain and simple. If you can provide another simple expression that provides the temperature gain of a rotor under a given braking scenario please do so. It is a matter of drastically different time scales, energy production can be extremely rapid but both conduction and dissipation are much slower due to a poor path (by design - we can't have brake fluid at the temperature of the disc!) and basic material properties respectively. Again the other equations you mention would be used to rigorously prove this for a typical, real world brake system. But this is why the parameters and equations you mentioned are not critical to the question of fade. It is quite simply - more simple than that for an actual real world system.
Now we all know that a particular pad may operate better at a higher temperature than another, but you also keep sticking to this rather absurd idea that you always want a hotter rotor so it will cool faster. This is pretty nonsensical. Its just like saying that if the goal is to empty a container you should keep filling it so you can empty more from it. Hotter is fine, as long as your typical operating temperature is far enough away from the knee for some margin.
I read the "...Tribological" paper as well. It was the source for my comments above about the importance of conductivity in the design of CSiC rotors.
BUT conductivity is important to prevent thermal stress from making a rotor fail - NOT TO PREVENT IT FROM FADING. These are fundamentally different concerns.
Until we have the magic temperature-friction curve for a typical high end CSiC pad-rotor combination we can not really settle this debate. If we can find such data we may have the answer for one particular system but even then not an answer in general. Lastly if we did have the data, I would simply go right back to the conservation of energy equation and see which system would reach its fade temperature first. What would you do with the temperature-friction curve?
My beliefs/suspicions/educated guesses/calculations support the following:
1. Some high end racing brake systems based on a steel rotor and very high temperature pads will show better fade resistance than a typical CSiC rotor based system. The reason being is the simple fact that a CSiC systems rotors are so lightweight they will get to their fade temperature sooner under an identical total/cumulative energy input.
2. Most CSiC systems (being that they are intrinsically very high end) will show improved fade resistance to a mid range/sports brake system such as say our very own E92 M3 braking system.
The primary weak link in a system like ours is NOT the rotor material but first pad material, followed by sufficient brake cooling.
3. The advantages of a CSiC rotor based braking system are, in order of most benefit to least benefit:
a. Weight reduction
b. Longevity
c. Fade resistance (which comes more from the pad choice rather than the rotor material).
P.S. Eagle: This is not a thread jack. We are right on topic on carbon ceramic rotors and this forum tends to get pretty techie/nerdy (especially when lucid and I are involved...). If you don't like it you don't have to read.