davidalone wrote:
The problem is that real world riding conditions are rarely consistent. gradients are rarely constant, your cornering line might not be the same, It will reach equillibrium assuming NO NEW INPUTS to the system. every time you brake you are adding new energy into the system.... so you have to recalculate based on that.
just throwing out some rough numbers.
Let's assume the carbon fiber wheel is heated up uniformly and area is about 0.3m square ( assume conductivity is slow enough that you only have the brake track at the temperature, conductivity is low enough to neglect heat loss to conduction. unrealistic, but we want to see heat loss from convection, the main source of cooling.)
heat transfer coeffecient of still air relative to bike would be around 30 W/m2K
heat transfer by convection :q= hA(T1-T2)
I dont have figures for temperature of brake tracks but I've heard the maximum can reach above 100 degrees celcius. lets take that as an extreme assumption. T2= ambient temperature, lets take a hot day at 30 degrees C: 30(0.3)(100-30)=10(70)=700
if you were at the start of the descent, your q would be even lower , becasue your brake tracks would be cooler.
KE of a 78kg rider+bike at 50kph: 9984J (approx)
KE of a 78kg rider+bike at 30kph: 2500J (approx)
assuming all KE is converted to heat by braking, it takes 2220J applied via braking to the rim . lets say you brake over a 10 second period, that is
748W of work applied to the rim. so you have an extra 48J of heat being applied to the rim per second.
the problem is q is constantly changing due to varying conditions of heat of the rim. and also varying speeds. so you would never have 'consistent conditions'.
Related to the above, here's a WKO4 chart that somebody posted recently to the WKO4 beta testers list. I don't know the exact details, but the cyclist in question is about 145 lbs and lives where there are short, steep-ish descents.
Heat-induced clincher blow-outs can happen to tandems ridden in the mountains, even with aluminum rims and good braking technique (no sane person would ride tubulars under such conditions, as the glue would readily melt). Because of this, people have marketed packets of heat-sensitive stickers that can be placed on your rims, so you have an idea of what sort of temperatures they reach. IIRC, the range went to over 200 deg C.