The α (alpha) Coefficient

The α (alpha) Coefficient of a locomotive is defined as

In other words, it gives a measure of the average forces applied to the locomotive’s machinery as compared to the maximum forces that it is designed to withstand.  It could therefore be said to be a measure of “mechanical efficiency”, being the amount of use that is made of the metal that goes into the machinery, or more vitally, it is a measure of “capital efficiency” being the amount of use that is made of the capital cost of the machine.

A machine with a low α-coefficient is one that is designed to withstand forces that are much larger than the average forces applied to it and which therefore makes low usage of its size, weight and/or capital investment.  For instance, diesel engines have to withstand very high compression ratios and therefore tend to have a very low α-coefficient.  Porta quotes a figure of 0.11 for a two-stroke marine diesel engine, noting that diesel manufacturers have learned to artificially boost their α-coefficients through the use of compressors or turbo-chargers.

Single (simple) expansion steam engines might have an α-coefficient of 0.2 when operating most efficiently at 20% cut-off. However Porta compares these figures with that of an “advanced” compound expansion steam engine operating at 50% cut-off whose α-coefficient may exceed 0.5.

Thus compound expansion engines, by virtue of their ability to operate efficiently at long cut-offs make much better use of their their cost and the mass of the steel that goes into making them. Or to put another way, they deliver more power per tonne of engine weight, which is another way of saying that they have a higher power-to-weight ratio.


Several pages of this website include text and diagrams copied from Porta’s “compounding” paper, including the pages covering condensation/wall effects, steam leakage, clearance volume, incomplete expansion and triangular losses.  More specific references to his theories on compound expansion can be found on the Compound Expansion page.

Sincere thanks to Adam Harris of Camden Miniature Steam, publishers of “Advanced Steam Locomotive Development – Three Technical Papers” for allowing the sections of the book to be published on this website.