Brakes

Brakes convert kinetic energy into heat by friction. Learn disc, drum, band and block brakes, braking torque, energy and temperature rise, self-energising action, friction materials, and vehicle braking distances.

Stopping safely is as important as moving. Brakes on cars, trains, cranes, elevators and wind turbines absorb huge amounts of energy in seconds — a car stopping from 100 km/h dissipates about half a megajoule.

Design balances torque capacity, heat dissipation, wear, fade and controllability.

An analogy

Rubbing your hands together to warm them: friction turns motion into heat. A brake does this deliberately and on a large scale.

Brake types

Disc brakes (calliper squeezes pads on a rotor — cars, bikes), drum brakes (shoes press outward inside a drum — rear axles, trucks), band brakes (a band tightens around a drum — winches), block brakes (railways), and electromagnetic/eddy-current retarders.

Energy and heat

All kinetic energy becomes heat in the brake. Temperature rise per stop depends on disc mass and specific heat; repeated stops (mountain descents) need cooling — ventilated discs, larger rotors. Overheating causes fade (μ drops) and fluid boiling.

Self-energising action

In drum and band brakes friction can help apply the shoe (leading shoe), multiplying torque — but making it sensitive to μ variations. Disc brakes are not self-energising, so they're more consistent.

Vehicle braking systems

Weight transfer during braking loads the front axle, so front brakes do 60–70 % of the work. Anti-lock braking (ABS) keeps tyres near peak slip; brake-by-wire and regenerative braking in EVs blend friction and motor braking. Friction materials (organic, semi-metallic, ceramic, carbon–carbon) trade μ, wear, noise and temperature capability.

Formulas

• Disc brake torque: T = μ · F · r_eff · n_faces
• Energy to stop: E = ½ m v² (+ ½ I ω²)
• Temperature rise (single stop): ΔT = E / (m_disc · c)
• Band brake: T₁/T₂ = e^{μθ}, T_b = (T₁ − T₂) r
• Stopping distance: s = v²/(2a), a ≤ μ_tyre g

Worked example: Disc brake torque

Given: μ = 0.4, clamp force 10 kN; r_eff = 0.12 m, two pad faces

Find: Braking torque.

• T = 0.4 × 10 000 × 0.12 × 2 = 960 N·m

Answer: 960 N·m

Worked example: Temperature rise

Given: 1500 kg car from 100 km/h; 4 discs × 8 kg, c = 460 J/kg·K (all energy to discs)

Find: Energy and mean temperature rise.

• E = ½ × 1500 × 27.8² = 579 kJ
• ΔT = 579 000/(32 × 460) = 39 K

Answer: ≈ 579 kJ, ≈ 39 K per stop (front discs get more)

Common mistakes

• Wrong: Sizing brakes for one stop only. — Right: Check repeated stops and long descents for fade and temperature.
• Wrong: Forgetting rotating inertia. — Right: Add ½Iω² of wheels, motors and drivetrain.

Applications

• Automotive & rail: Disc brakes with ABS; rail disc/tread brakes plus regenerative braking.
• Cranes & elevators: Spring-applied, electrically released fail-safe brakes.
• Wind turbines: Rotor and yaw brakes for parking and emergency stops.

Key takeaways

• Brake torque = μ F r_eff n.
• E = ½mv² — speed squared.
• Heat capacity and cooling prevent fade.
• Front axle does most braking work.

Going further

• Regenerative braking: EV motors act as generators, recovering 10–30 % of energy in urban driving.
• Thermal modelling: Transient FEM predicts rotor hot spots, cracking and judder.
• Carbon–ceramic discs: Light, fade-resistant rotors for performance cars and aircraft.