Train Movement Resistance (Davis)
Calculate a train's specific movement resistance by the Davis equation, R = A + B·V + C·V², from coefficient A (rolling resistance and mechanical friction, speed-independent), B (resistance proportional to speed, from flange friction and oscillations), C (aerodynamic resistance, proportional to speed squared) and the speed V (km/h). The Davis equation, from the 1920s and still standard in railway engineering, describes the total resistance to motion the locomotive must overcome on straight, level track, per unit weight (N/t or kgf/t). At low speed the constant and linear terms (friction) dominate; at high speed the quadratic aerodynamic term dominates, decisive for high-speed trains (hence their careful streamlining). Davis resistance, plus grade (gravity) and curve resistances, sets the required tractive effort, energy consumption and locomotive traction capacity. It is the basis of traction calculation and train performance. Enter coefficients A, B and C and the speed.
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Resistência ao movimento de trem (Davis)
A resistência específica ao movimento de um trem é dada pela clássica equação de Davis, R = A + B·V + C·V², a partir de três coeficientes e da velocidade V. O coeficiente A representa a resistência ao rolamento e os atritos mecânicos (mancais, contato roda-trilho), independente da velocidade; o coeficiente B, a resistência proporcional à velocidade, ligada aos atritos de flange (o friso da roda contra o trilho) e às oscilações da composição; e o coeficiente C, a resistência aerodinâmica, que cresce com o quadrado da velocidade. A equação de Davis, formulada por W. J. Davis Jr. na década de 1920 e ainda hoje o padrão da engenharia ferroviária, descreve a resistência total ao avanço que a locomotiva precisa vencer em via reta e nivelada, expressa por unidade de peso (N/t ou kgf/t). O comportamento é revelador: a baixas velocidades, dominam os termos constante e linear (os atritos mecânicos); a altas velocidades, o termo quadrático aerodinâmico passa a dominar e cresce explosivamente — é por isso que os trens de alta velocidade têm aquele perfil aerodinâmico tão cuidadosamente projetado, com narizes longos e carenagens, pois acima de ~250 km/h a maior parte da energia vai para vencer o ar. A resistência de Davis, somada às resistências de rampa (gravidade) e de curva (atrito extra nas curvas), define o esforço trator necessário, o consumo de energia e a capacidade de tração exigida da locomotiva. É a base de todo cálculo de tração e de desempenho de uma composição ferroviária — desde o dimensionamento da locomotiva até a previsão de tempos de viagem e de consumo de combustível. Informe os coeficientes A, B e C e a velocidade.
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Calculate a locomotive's maximum tractive effort limited by adhesion, F = μ·W, from the wheel-rail adhesion coefficient μ (typically 0.25-0.35 dry, less with rain, ice or leaves) and the adhesive weight W (N, the locomotive weight on powered axles). Tractive effort is the force the locomotive applies to pull the train, with two limits: power (engine) and adhesion (wheel-rail friction). At low speed and starting, ADHESION limits — however powerful the engine, if the demanded force exceeds μ·W, the wheels spin, losing traction and wearing wheels and rails. So locomotives concentrate weight on powered axles (adhesive weight) and use anti-slip systems and sand application to boost friction. The steel-on-steel railway contact has very low rolling resistance (the train's great energy advantage) but precisely therefore limited adhesion — the fundamental paradox of rail traction. This defines the maximum train a locomotive can start and pull on a grade. Enter the adhesion coefficient and the adhesive weight.
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