Railway Curve Maximum Speed
Calculate the maximum allowable speed on a railway curve, V = √(127·R·(h_a + I) ÷ B), from the curve radius R (m), the applied cant h_a (mm), the allowable cant deficiency I (mm) and the gauge B (mm). It is the inverse of curve design: given an existing curve (radius and cant) and the permitted deficiency, it finds the maximum speed trains can run safely and comfortably. Speed is limited because above it the cant deficiency would exceed the allowable — passengers would feel excessive lateral force and wheel-rail wear and risk would rise. This is fundamental in railway operation: it defines each section's maximum speeds (line speed profile) and travel time. Raising speed on existing curves needs more cant (limited), more allowed deficiency (tilting trains) or, ultimately, larger-radius regrading — an expensive work. Enter the radius, applied cant, allowable deficiency and gauge.
Resultado
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Velocidade máxima em curva ferroviária
A velocidade máxima admissível em uma curva ferroviária é V = √(127·R·(h_a + I) ÷ B), a partir do raio R, da superelevação aplicada na via h_a, da insuficiência de superelevação admissível I e da bitola B. É a operação inversa do dimensionamento da curva: dada uma curva já existente (com seu raio e sua superelevação construída) e o limite de insuficiência que se permite, determina-se a velocidade máxima com que os trens podem percorrê-la com segurança e conforto. A velocidade é limitada porque, acima dela, a insuficiência de superelevação ultrapassaria o admissível — os passageiros sentiriam força lateral excessiva, e o desgaste roda-trilho e o risco de descarrilamento aumentariam. Este cálculo é fundamental na operação ferroviária: define as velocidades máximas autorizadas (VMA) de cada trecho, que compõem o perfil de velocidades da linha e, somadas, determinam o tempo de viagem e a capacidade. Aumentar a velocidade em curvas existentes não é trivial: só é possível elevando a superelevação (que tem teto), permitindo maior insuficiência (com trens pendulares, que inclinam a caixa) ou, em última instância, refazendo a geometria com raios maiores — uma obra cara e demorada. Por isso o traçado original de uma ferrovia define, em grande parte e por décadas, as velocidades que ela jamais poderá superar sem grandes investimentos. Informe o raio, a superelevação aplicada, a insuficiência admissível e a bitola.
Related Tools
Railway Cant (Superelevation)
Calculate the theoretical equilibrium cant (superelevation) of a railway curve, h = (B·V²) ÷ (127·R), from the dynamic gauge B (mm, distance between rail centers, ~1500 mm on standard gauge), the speed V (km/h) and the curve radius R (m). Cant is the raising of the outer rail above the inner one in curves, tilting the track inward — so the train's weight component helps provide centripetal force, balancing the centrifugal acceleration felt by passengers and reducing wheel-rail lateral wear. Equilibrium cant fully cancels the unbalanced lateral acceleration for a given speed; in practice a lower cant is adopted, since trains run at varied speeds on the same curve, and construction limits (~150-160 mm) apply for comfort and overturning safety of stopped trains. The difference between equilibrium and applied cant is the cant deficiency (or excess). Enter the gauge, speed and curve radius.
Railway Minimum Curve Radius
Calculate the minimum railway curve radius for a design speed, R = (B·V²) ÷ (127·(h_max + I_max)), from the gauge B (mm), speed V (km/h), maximum allowable cant h_max (mm) and maximum allowable cant deficiency I_max (mm). The minimum radius is set by combining the two comfort/safety limits available to 'absorb' lateral acceleration at the desired speed: the maximum buildable cant (limited by overturning risk of slow/stopped trains) and the maximum deficiency allowed to passengers. The larger these limits, the smaller the radius for a given speed — but both have normative caps. This is central to railway alignment: it defines how sharp a curve can be without speed reduction. Sharper curves require slowing down, penalizing travel time and line capacity — so high-speed railways need huge radii (kilometers). Enter the gauge, speed, maximum cant and maximum deficiency.
Cant Deficiency
Calculate the cant deficiency of a railway curve, I = (B·V²)/(127·R) − h_a, the difference between the theoretical equilibrium cant (for speed V, radius R, gauge B) and the cant actually applied to the track h_a (mm). Deficiency is the share of lateral acceleration NOT compensated by the applied cant — the residual centrifugal acceleration felt by passengers and transmitted laterally to the outer rail. Since a curve has fixed cant but is run at different speeds (slow freight, fast express), it is impossible to balance all: fast trains run with deficiency (outward force), slow ones with excess. Codes limit allowable deficiency (typically 100-150 mm for conventional trains, more for tilting trains) for comfort, safety and wear. Deficiency lets trains run above the curve's equilibrium speed within safe limits. Enter the gauge, speed, radius and applied cant.
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.