Brake Pedal Ratio and Line Pressure
Why doubling the master-cylinder bore quarters the pressure: Pascal's law end to end. mc_force = pedal x ratio x booster; line pressure = mc_force / (pi/4 x bore^2); clamp = line pressure x caliper area; brake torque = clamp x 2 x friction x rotor radius. A 50 lb pedal at 5:1 manual through a 7/8 in master makes 416 psi -> 1,663 lb clamp -> 5,987 in-lb per corner; swap to a 1.75 in master (double the bore) and the pressure drops to 104 psi, exactly a quarter, for the same leg -- the whole manual-vs-boosted trade. The 2 in the torque is both pad faces. A design aid; the pad friction, thermal state, and system compliance govern.
Formula and source
mc_force = pedal_force x ratio x booster; line_pressure = mc_force / (pi/4 x bore^2); clamp = line_pressure x caliper_area; brake_torque = clamp x 2 x friction x rotor_radius.
Hydraulic brake force chain (Pascal's law; SAE brake-system design practice), first-principles, by name; the actual pad friction, thermal state, and system compliance govern.
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