Dave,
Nice work on the calculations.
I think that for the deceleration calculation, you're using force = mass x acceleration where mass is in kg. So that should be F = 215 x 2.5 = 537N. However 5 secs feels like a very long time - (it's taking us less than that to do the whole length of the straight in front of the pits at Stretton) - so maybe 1.5-2.5sec?
Looks like you also needed to include the pad coefficient and number of pads in the clamping force calculation...
Plugging those back into your calculations:
Calculate deceleration force. I assumed an initial rate of 33mph and a terminal speed of 7mph, stopping over 2 seconds. This is 15m/sec to 3m/sec.
Therefore 12/2 = 6m/sec/sec. x 215 = 1290N.
The torque on the wheel...( I used 560mm for the wheel dia., 280 for half ).
T = F x Rad. T = 1290 x 0.28m = 361Nm.
Calculate clamping load on wheel. C = T/ eff rad of disc x coef of pad x no of pads
C = 361/(0.1*0.35*2) = 5157 N.
Calculate system pressure required P = C/ A ( slave piston area)
P = 5157/982 mm2. = 5,251,527Pa = 762psi
So, it would seem that more pressure would be helpful to bring your performance up to what you're hoping for.
However, I think there's a very important distinction between brake performance and brake reliability. If our brakes don't have great performance but do the same every time, then you can drive to suit that....but based on your description of what happened, what I think you experienced was a sudden change in your brakes' performance. Sudden unpredictable changes are dangerous.
There's been talk about brake fade and "pad gassing" (lots of debate about whether this is real), pad glazing and boiling fluid.
Assuming a 215kg cyclekart incl driver, stopping from 15m/s/s to 0.
Kinetic energy = 0.5 x mass x velocity squared
= 0.5 x 215 x (15*15)
=24,188 Joules
Taking a brake disc of say 0.5 kg (note the Gemini one weights about 1.5Kg so 0.5kg would be very light.)
The specific heat capacity of steel is about 420 J/kg.C. Assuming all the kinetic energy is lost as heat in the brakes, then the temperature rise in that one braking event would be
24,188 / (420 * 0.5) = 115 C
This assumes all the energy goes into the brake disc, and that no heat is lost from the surface of the disc or brake calliper. It also assumes that no heat goes into the brake hub or the rear axle.
But, what temperature does brake fade happen at? I've read and heard all sorts of temperatures, but the vast majority are around 600-700 C and higher. So to me it seems unlikely that the brakes would get up to those sorts of temperatures except for on the flimsiest of disc rotors, through a mechanical problem with the brakes, or the driver "riding" the brake pedal.
Boiling of brake fluid seems more likely than brake pad fade although normally, only a small proportion of the energy goes as heat into the calliper. Also, we'd expect the brake pedal to go soft.
So, for me the jury is still out. Any other thoughts?