Ok, you have three separate problems with the design.
1) the amount of energy produced by braking the kart
2) the conversion of that energy into a different form
3) disposing of that energy within the performance limits of the materials chosen.
If you look at one particular problem, the possibility of the hydraulic fluid boiling, there are a variey of answers.
The simplest, raise the boiling point of the fluid. Dot 5 instead of Dot 3.
The next simplest is to reduce the amount of heat. Two brake units instead of one (ie two rotors, two sets of calipers).
3, Stop the heat getting to the fluid. Put a heat insulator between the rotor and the caliper (you have to stop radiated heat as well as conducted heat)
4) Stop the heat. a) Use two brakes not one. b) use a different system to slow down, eg the pump. c) cooled brakes (see truck racing or the GP cars of the 50's for total loss water systems.)
5) Reduce the amount of heat transferred to the fluid. If you had a small hydraulic pump it could maintain enough flow in the system that you didn't have 'static' fluid in the caliper (think constant rail diesel). Consider energy loss when not braking.
Then you have the actual purpose of the pad/rotor interface.
What does it do? Convert the kinetic energy of motion into heat energy by friction.
What causes that conversion? Adherent and mechanical friction.
What degrades their performance?
One factor is that the pad material outgasses under heat and floats the pad off the surface, like aquaplaning.
How do you stop aquaplaning? Tread design, critical speed, depth of water, contact pressure (tyre pressure). What are their brake/gas counterparts.
There are many existing designs of kart brake. Grooved brakes wipe the gas film off the pad, drilled brakes release the pressure of the gas, vented brakes increase the cooling area and increase the heat mass of the brake, vented pump brakes use the fan effect to suck air through the centre and increase the cooling. Do they work? Could you increase the efficiency of a vented fan brake by machining the fan elements rather than casting them?
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