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.
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Brake temperature rise
The temperature rise of a brake during a single stop is ΔT = E ÷ (m·c), from the energy dissipated in braking E, the mass of the component that absorbs the heat m (the disc or drum) and the specific heat of the material c (~460 for steel, ~900 for aluminium). When a brake dissipates the kinetic energy of a stop (turning it into heat), that heat is first absorbed by the mass of the disc or drum, raising its temperature. This formula estimates that rise assuming all of the heat goes into the mass of the component, with no losses to the surroundings — a conservative assumption, valid for a short, isolated stop; in prolonged braking, part of the heat is carried away by convection and radiation at the same time. The temperature rise is critical, since friction materials have a thermal limit: above a certain temperature (300-500°C for organic materials, higher for metallic and ceramic ones), friction drops sharply (the phenomenon known as fading, which has caused many accidents on long mountain descents), the material degrades, and the disc can warp or crack from thermal shock. That is why severe-duty brakes use large discs (more mass, more capacity to absorb heat), vented rotors (better dissipation) and materials with a high melting point. This calculation is the heart of the thermal sizing of a brake. Enter the dissipated energy, the mass and the specific heat.
Related Tools
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.
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.
Temperature-Humidity Index (THI) for Cattle
Calculates the temperature-humidity index (THI) used to gauge heat stress in cattle, in the metric form of the 1971 NRC formula, from air temperature and relative humidity. Below 72 the animal is comfortable; 72 to 78 is alert, 79 to 88 is danger and above 88 is emergency. Enter temperature and relative humidity.
Disc Clutch Torque
Calculate the torque transmissible by a disc clutch (or brake), T = μ·F·N·r_m, from the friction coefficient μ, the axial clamping force F (N), the number of friction surfaces N and the mean friction radius r_m (m). A disc clutch transmits torque between two shafts by FRICTION between surfaces pressed together: an axial force F clamps the discs, and the friction at that interface, acting at the mean radius, generates the torque. The number of friction surfaces N multiplies the capacity — a single disc clutch has N=1 (one face) or N=2 (disc between two faces); MULTI-PLATE clutches (motorcycles, automatic transmissions) stack several discs with high N, transmitting large torque in compact space. The same principle applies to disc and clutch BRAKES: the braking (or transmitting) torque is μ·F·N·r_m. This is central in clutch and brake design: it sets the actuation force (pedal, spring, hydraulic actuator) needed to transmit/brake a given torque, and the area and number of discs. The design torque includes a service factor (1.2-3) over the nominal, to cover peaks and wear. Enter the friction coefficient, axial force, number of surfaces and mean radius.
Junction Temperature
Calculate the junction temperature of a power semiconductor, T_j = T_a + P × R_th, from the ambient temperature T_a, the dissipated power P and the total junction-to-ambient thermal resistance R_th (°C/W). The result, in °C, is the device's internal temperature (silicon junction), which must not exceed the manufacturer's limit (typically 150 °C) on pain of failure. The thermal resistance adds the junction-to-case, case-to-heatsink and heatsink-to-ambient stages. Lowering R_th (larger heatsink, ventilation, thermal paste) lowers the junction temperature. It is the central calculation of power electronics thermal design. Enter the ambient temperature, the dissipated power and the thermal resistance.
Growing Degree Days (GDD)
Compute the growing degree days (GDD), GDD = (Tmax + Tmin)/2 − Tbase, the daily thermal accumulation above the base temperature below which the plant does not grow. Since crop development is driven by temperature, summing degree days predicts phenological stages — flowering, maturity, harvest — more accurately than the calendar. Also used for pests and insects. Enter the day's maximum and minimum temperatures and the crop base temperature.
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