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.
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Raio mínimo de curva ferroviária
O raio mínimo de uma curva ferroviária para uma velocidade de projeto é R = (B·V²) ÷ (127·(h_max + I_max)), a partir da bitola B, da velocidade V, da superelevação máxima admissível h_max e da insuficiência de superelevação máxima admissível I_max. O raio mínimo é determinado pela combinação dos dois limites de que a engenharia dispõe para 'absorver' a aceleração lateral na velocidade desejada: a superelevação máxima que se pode construir na via (limitada pelo risco de tombamento de trens lentos ou parados e pela geometria) e a insuficiência máxima que se permite os passageiros sentir. Quanto maiores esses dois tetos, menor pode ser o raio para uma dada velocidade — mas ambos têm limites normativos. Este cálculo é central no traçado geométrico de ferrovias: define o quão fechada uma curva pode ser sem obrigar a reduzir a velocidade. Curvas mais fechadas que o raio mínimo exigem redução de velocidade, o que penaliza o tempo de viagem e a capacidade da linha. É por isso que as ferrovias de alta velocidade exigem raios enormes — de vários quilômetros —, traçados que evitam curvas fechadas mesmo ao custo de grandes obras (túneis e viadutos) para manter o trem veloz. O raio mínimo é o parâmetro que conecta a velocidade desejada à geometria possível. Informe a bitola, a velocidade, a superelevação máxima e a insuficiência máxima.
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.
Railcar Axle Load
Calculate a rail vehicle's axle load, P_axle = total weight ÷ number of axles, from the gross weight of the wagon or locomotive (N, tare plus load) and the number of axles. Axle load is the most important parameter for track design: it is the force each axle transmits to the track (and, per wheel, to each rail), governing stresses in the rail, sleepers, ballast and subgrade. Railways are classified by their axle-load capacity: heavy-haul railways (such as ore lines) run at 30-40 tonnes per axle and need heavy rail, concrete sleepers and reinforced ballast; passenger and light-freight lines run lower loads. Exceeding the allowable axle load causes accelerated fatigue, permanent deformation and failures — so rolling-stock and track-class compatibility is strictly controlled. Axle load also limits maximum train weight and thus transport productivity. Enter the total weight and the number of axles.
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.