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Updated Formulae 

The following equations were taken from the winning solar car and outlines what is required for our braking system

Deceleration at wheel lock up is

a = f(N/2)

a = acceleration

N = normal force on front or back of car

f = coefficient of friction on road and tire (0.8)

Normal force on the front and rear of the car is

Nf = [(CGf)W + 20(Fb)]/100

Nr = [(CGr)W - 20(Fb)]/100

Nf = normal force on front of car

Nr = Normal force on rear of car

CGf = % along wheelbase center of gravity is (example if front and rear wheels are 150cm away and cg is 90cm away from rear, CGf = 60)

CGr = % along wheelbase center of gravity is (if 90 cm away from rear, CGr = 40)

Fb = mass of car multiplied by deceleration

W = car weight (kg)

Torque of the brake when locking up occurs is given to be 

T = (f)(N)r/2

T = torque

r = tire radius (m)

Friction Force required on braking pad is

F = T/2R

F = friction force

R = radius from centre of wheel to point where brake pad contacts brake disc

Normal force required on brake pad 

n = F/0.2

n = normal force on brake pad

0.2 = coefficient of friction of brake pad on steel brake disc (safe estimate)

The pressure required from the master cylinder than is 

P = 4N/[pi(d^2)]

P = pressure in cylinder

d = diameter of piston in brake caliper

Lastly the force required in compressing the master cylinder is

Fp = P(pi/4)D^2

Fp = force compressing master cylinder (reasonable to expect 446N)

D = master cylinder diameter

For more details on how these equations were derived, or what each variable, refer to the Winning Solar Car Pg 241 - 253