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.
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Insuficiência de superelevação
A insuficiência de superelevação é I = (B·V²)/(127·R) − h_a, a diferença entre a superelevação teórica de equilíbrio (para a velocidade V, o raio R e a bitola B) e a superelevação efetivamente aplicada na via h_a. Ela representa a parcela da aceleração lateral que não é compensada pela superelevação construída — ou seja, a aceleração centrífuga residual que os passageiros sentem (empurrando-os para o lado de fora da curva) e que se transmite lateralmente ao trilho externo. O motivo de a insuficiência existir é fundamental: uma curva tem superelevação fixa, mas é percorrida por trens a velocidades diferentes. É impossível equilibrar todos ao mesmo tempo — os trens mais rápidos que a velocidade de equilíbrio circulam com insuficiência (sentem força para fora), e os mais lentos, com excesso (força para dentro). As normas limitam a insuficiência admissível, tipicamente 100 a 150 mm para trens convencionais (e mais para os trens pendulares, que inclinam a caixa para compensar e assim podem correr mais rápido nas curvas), por razões de conforto dos passageiros, segurança contra descarrilamento e desgaste roda-trilho. A insuficiência é justamente o que permite operar trens acima da velocidade de equilíbrio de uma curva, dentro de limites seguros — é o 'crédito' de velocidade que a engenharia concede. Informe a bitola, a velocidade, o raio e a superelevação aplicada.
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 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.
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.
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.