Braking Energy
Calculate the energy dissipated in braking, E = ½·m·(v₁² − v₂²), from the mass m (kg), the initial velocity v₁ and the final velocity v₂ (m/s). When a vehicle or machine brakes, its KINETIC energy is converted — by brake friction — into HEAT. The dissipated energy is the kinetic-energy change: braking to a stop (v₂ = 0) dissipates all the initial kinetic energy; partial braking, the difference. This heat must be ABSORBED and DISSIPATED by the brake without overheating beyond the limit (above which the friction material loses effectiveness — fading — and may even burn or glaze). That is why brakes for heavy vehicles, long descents (mountain trucks) and severe duty need large thermal capacity (big, vented discs, or auxiliary brakes like engine braking and retarders, dissipating energy by other means without overloading the service brakes). Braking energy grows with the SQUARE of velocity: braking from 100 km/h dissipates FOUR times more energy than from 50 km/h — so high-speed braking is so much more demanding. This is the basis of brake thermal design and overheating checks in repeated or prolonged braking. Enter the mass and the initial and final velocities.
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Braking energy
The energy dissipated in a braking event is E = ½·m·(v₁² − v₂²), from the mass m, the initial speed v₁ and the final speed v₂. When a vehicle or machine brakes, its kinetic energy is converted — by friction in the brake — into heat. The energy dissipated is the change in kinetic energy: braking to a full stop (v₂ = 0) burns off the whole of the initial kinetic energy; braking partially burns off the difference. That heat has to be absorbed and shed by the brake without pushing it past its limit (beyond which the friction material loses effectiveness — fading — and can even glaze over or catch fire). This is why brakes on heavy vehicles, on long descents (trucks on mountain grades) and in severe-duty applications need a large thermal capacity: big vented discs, or auxiliary brakes such as the engine brake and the retarder, which dump the energy by other routes. Braking energy grows with the square of speed: stopping from 100 km/h dissipates four times the energy of stopping from 50 km/h — which is why high-speed stops are so much more demanding. This calculation is the basis for the thermal sizing of brakes and for checking overheating under repeated or prolonged braking. Enter the mass and the initial and final speeds.
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Brake Temperature Rise
Estimate a brake's temperature rise from one braking, ΔT = E ÷ (m·c), from the braking dissipated energy E (J), the mass of the heat-absorbing component m (kg, the disc or drum) and the material specific heat c (J/(kg·°C), ~460 for steel, ~900 for aluminum). When a brake dissipates a braking's kinetic energy (converting it to heat), this heat is initially ABSORBED by the disc or drum mass, raising its temperature. This formula estimates that rise assuming ALL the heat goes into the component mass, with no loss to the environment (a conservative assumption, valid for a quick, isolated braking — in prolonged braking, part of the heat is dissipated by convection and radiation simultaneously). The temperature rise is critical because friction materials have a thermal limit: above a certain temperature (300-500°C for organic materials, more for metallic/ceramic), friction drops sharply (the FADING phenomenon, which has caused many mountain-descent accidents), the material degrades, and the disc can warp or crack from thermal shock. So severe-duty brakes use large discs (more mass, more heat-absorbing capacity), vented (more dissipation) and high-melting-point materials. This calculation is the heart of brake THERMAL design. Enter the dissipated energy, the mass and the specific heat.
Brake Power Dissipated
Calculate the power dissipated by a brake under torque, P = T·(2π·n/60), from the braking torque T (N·m) and the rotation n (rpm). Dissipated power is the rate at which the brake converts mechanical energy to heat — the product of braking torque and angular velocity. It differs from total braking ENERGY: energy is the total heat generated (joules), while power is the INTENSITY of that heat generation (watts), and it determines the brake's steady-state temperature. A brake dissipating much energy but slowly (low power) heats little; one dissipating the same energy fast (high power) heats much more. Dissipated power is critical in brakes working CONTINUOUSLY or repetitively: retention brakes on long descents, industrial equipment brakes (hoists, cranes, conveyors holding load), and dynamometers (which measure engine power precisely by dissipating it in a brake). There, the steady-state dissipated power sets the COOLING capacity needed (ventilation, water cooling) to keep temperature stable. Equating dissipated power to cooling capacity gives the equilibrium temperature. Enter the braking torque and the rotation.
Kinetic Energy Calculator
Compute kinetic energy KE = ½ m v² from mass (kg) and velocity (m/s). Result in joules.
Rotational Braking Time
Calculate the time to brake (stop) a rotating system, t = (I·ω) ÷ T, from the moment of inertia I (kg·m²), the initial angular velocity ω (rad/s) and the braking torque T (N·m). When a brake applies a constant torque to a spinning system (a shaft, flywheel, machine rotor), it DECELERATES it to a stop. By Newton's second law for rotation (T = I·α, with α the angular deceleration), the stopping time is the initial angular momentum (I·ω) divided by the braking torque. This matters in several situations: EMERGENCY STOPPING of machines (safety codes require dangerous parts to stop within a maximum time after brake actuation — the shorter, the safer), sizing motor and shaft brakes, and clutches (the engagement time, where the clutch 'synchronizes' two shafts' speeds, follows the same physics). Systems with large moment of inertia (heavy flywheels, big rotors) take longer to stop with a given torque — so high-inertia machines need powerful brakes or more stopping time. The braking time, with the dissipated energy and power, completes a braking analysis. Enter the moment of inertia, the angular velocity and the braking torque.
Zeldovich Number
Computes the Zeldovich number of a flame, β = E_a·(T_b − T_u) ÷ (R·T_b²), the activation energy made dimensionless by the temperature rise across the flame front. It measures how sensitive the reaction rate is to a small temperature change: a high β (typically 8 to 12 for hydrocarbons) means the reaction is concentrated in a very thin layer near the flame temperature, which justifies the large-activation-energy assumption of asymptotic flame theory and the extinction and cellular-instability criteria. The universal gas constant R = 8.314 J/(mol·K) is adopted, with activation energy in J/mol and temperatures in kelvin. Enter the activation energy, the burned gas temperature and the unburned gas temperature.
Kinetic Energy (J)
Calculates kinetic energy in joules given mass in kg and velocity in m/s via 0.5·m·v².
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.