Factor of adhesion
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In railroad engineering, the factor of adhesion of a locomotive is the weight on the driving wheels divided by the starting tractive effort. The corollary of the above is that as a locomotive's available tractive effort increases, so must the weight on the driven axles increase for adequate rail adhesion. For most locomotives, the tractive effort of a locomotive can be guessed well just by knowing the number of driven wheels and the maximum axle load for which it was designed.
Diesel and electric locomotives
A common rule is that for a steam locomotive a good factor of adhesion equals or exceeds 4, but not by too much. A locomotive with a factor of adhesion below 4 will have a tendency to wheelslip, especially on starting, and will require careful operating and lots of sand in slippery conditions. A factor of adhesion greater than 4 is simply excess weight or insufficient power. The number 4 physically corresponds to the inverse of the coefficient of static friction for steel on steel.
The pulses can, to some extent, be smoothed in a steam locomotive by fitting 3 cylinders (with cranks at 120 degrees) or 4 cylinders (with cranks at 135 degrees). A 4-cylinder engine with cranks at 180 degrees will deliver similar pulses to a 2-cylinder engine. Alternatively, a geared steam locomotive can deliver a smooth torque similar to that of a diesel or electric locomotive.
The civil engineer of a railway sets the maximum load that can be placed on any one axle. Leading and trailing axles are used to carry loco weight that cannot be placed on the driven wheels because of vehicle limitations - such as position of cylinders and firebox. All available weight is placed on the driven axles, which have to be of sufficient number so as not to exceed the civil engineer's limit. Leading or trailing axles are provided to ensure the weight distribution of the loco is even - with typically all driven axles having the same load and using the smallest number of trailing axles possible to take surplus weight and distribute it evenly amongst them - again limited to the civil engineer's axle load limit.
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