Adhesion is the frictional resistance that prevents a locomotive's driving wheels from slipping on the rail. Available adhesion depends on the conditions of both the rail and the wheel. With a clean dry wheel running on a clean dry rail the "frictional coefficient" between them may be as high as 0.35 or 35%. The presence of oil and other contaminents may reduce it to near zero.
Frictional coefficient is the available frictional resistance ÷ adhesive weight on the driving wheels.
Adhesion Factor (the inverse of Friction Coefficient) = adhesive weight on the driving wheels ÷ available frictional resistance.
A clean dry wheel running on a clean dry rail may have an available coefficient of friction as high as 0.35 or 35%. This can drop to 0.25 in wet conditions, and very much lower if the rail is contaminated with lubricating substances such as ice, oil and leaves.
A locomotive must be designed so that its tractive effort is not so high that it "loses its feet" on starting. Equally importantly, its tractive effort should be limited so that it does not slip at speed. This latter becomes a much more important consideration for Second Generation Steam locomotives like the 5AT which maintain a relatively high tractive effort at high speed (see Tractive Effort page).
In the past, locomotives were commonly designed to operate with a minimum frictional coefficient of 0.20 (or 20%) on starting. Through careful specification of its sanding system, Wardale has been able to increase this to 25% for the 5AT. Furthermore he has undertaken detailed calculations to ensure that the available adhesion will be sufficient to avoid slipping even at the 5AT's maximum speed of 200 km/h (see FDC 1.4).
This and other aspect of locomotive adhesion are discussed in greater detail in the 5AT Features page of this website.
See also the Advanced Adhesion page of this website in the Principles of Modern Steam section.