Factor of adhesion

In railroad engineering, the factor of adhesion of a locomotive is the weight on the driving wheels divided by the starting tractive effort. This is an important statistic, because obviously extra power is pointless if there's not enough traction to put it to useful work. 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 driving and lots of sand in slippery conditions. A greater factor of adhesion 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.

Diesel and electric locomotives can work with a much lower factor of adhesion than a reciprocating steam locomotive because their power is applied smoothly, unlike the latter's pulsed power delivery. 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 corollary of the above is that as a locomotive's available tractive effort increases, so must its weight for adequate adhesion. This explains why steam locomotive designers were never that interested in saving weight. Since a steam locomotive must have leading and trailing wheels for stability if it intends to travel at any speed, and these wheels must have some weight on them for good tracking, the steam locomotive's weight increases further.

As weight on the driving wheels increases, the number of driven axles must also increase; maximum axle load is limited by the railroad's civil engineer, since bridges and other structures are built to take only a certain loading. Thus, the tractive effort of a locomotive can be guessed well just by knowing the number of driven wheels and the maximum axle load it was designed for.