Adhesion Tractive Effort (Locomotive)
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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Adhesion tractive effort (locomotive)
The maximum tractive effort of a locomotive limited by adhesion is F = μ·W, from the wheel-rail adhesion coefficient μ (typically 0.25 to 0.35 in dry conditions, and far lower with rain, ice or leaves on the rail) and the adhesive weight W (the share of the locomotive weight carried by the powered axles). Tractive effort is the force with which the locomotive pulls the train, and it has two distinct ceilings: the power limit (from the engine) and the adhesion limit (from wheel-rail friction). At low speed and on starting, adhesion is what binds — however powerful the engine, if the force demanded exceeds μ·W the wheels slip: they spin uselessly, losing traction and wearing out both wheels and rail. That is why locomotives concentrate as much weight as possible over the powered axles (maximising the adhesive weight) and use electronic wheel-slip control plus sand dropped on the rail to raise friction on grades and at start-up. Here lies a fundamental and elegant paradox of the railway: the steel-on-steel contact between wheel and rail has extremely low rolling resistance (roughly a tenth of a tyre on asphalt), and it is precisely that low resistance that gives the train its enormous energy efficiency — but the very property that cuts rolling resistance also caps the adhesion available for pulling. Efficiency and traction pull in opposite directions. This calculation sets the heaviest train a locomotive can start and haul, especially on a grade, and it drives motive-power planning (how many locomotives per train). Enter the adhesion coefficient and the adhesive weight.
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