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Essentially F1 car brakes are the same as on your road car, they are discs clamped hydraulically by calipers which squeeze brake pads onto the rotating disc surface. The driver pushes the brake pedal which forces a piston in and pushes brake fluid down the brake pipes to the caliper where the larger surface area of the pistons there creates a hydraulic leverage effect whereby a large movement by the driver is converted to a small but powerful movement in the brake calipers. The main difference with F1 brakes is the materials used for the friction material and calipers. The discs and pads are made of carbon reinforced carbon which can cope with massive temperatures without fading and produce huge amounts of friction to slow the car down. The pistons in the caliper are made from titanium because its strong and resists heat well as well as having low heat conduction properties that stop the heat boiling the brake fluid. Modern F1 cars use 4 or 6 piston calipers at the front, the discs are suprisingly small at 278mm diameter, which is smaller than many road cars. This is not suprising though when you consider they are made from cheaper materials and have to stop 4 or 5 times the weight, albeit from slower speeds less frequently. Interestingly F1 brakes take some time to bite after the pedal is pressed. This is because the carbon needs to heat up before it displays good friction properties. This takes 1/10th of a second where the driver feels little retardation while the brakes heat up, once they do its like hitting a wall as the brakes reach 1000's degrees and stop the 500kg cars with 4g or more of deceleration.

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