A reader (Phil) has kindly offered this summary of locomtive numbering:

The number on a locomotive refers to the locomotive’s wheel arrangement. If it is all numbers, the engine is a steam locomotive. The first number will be the number of wheels on the leading or “pilot” truck, if any (or 0 if it has none); the last number is the number of wheels on the trailing truck (again, 0 if it has none). The middle number or pair of numbers is the number of driving wheels, that is, the wheels actually powered by the action of the pistons; these are connected by side rods so they work together. Tender wheels are not counted unless they are actually driving wheels, which would be an unusual situation; tender “boosters” are not considered driving wheels.

If a “T” follows the numbers, then it is a “tank” engine, which has no tender.This is the “Whyte” system of classification. (In Europe, particularly France, axles are counted instead of wheels, but European models intended for sale in the U.S. will use the Whyte system.) A “2-8-0”, then, has a pilot truck with two wheels, eight driving wheels and no trailing truck. This type is called a “Consolidation” or occasionally a “Pershing” (this refers to certain groups of Consolidations that were shipped to France during World War I and later given to the French).

A 2-8-8-4 has a pilot truck of two wheels, two sets of eight driving wheels each, and a four-wheel trailig truck. This is a “Yellowstone,” an articulated engine.There are a few exceptions, notably geared locomotives and Beyer-Garratts, but I won’t get into that.

If instead of numbers there are letters, or both letters and numbers, the engine is either a diesel or an electric. The letters designate powered axles, so a typical EMD diesel with four powered axles in two trucks would be a B-B. Unpowered axles receive numbers, so an A1A truck means there are two powered axles separated by an unpowered axle.

The Fairbanks Morse passenger C-liner, for instance, had a B-A1A arrangement. (Don’t confuse this with sets of diesel cab units, which usually do not use hyphens between the letters). Designations like Bo-Bo or Co-Co are European, and are the same as B-B and C-C. Unpowered leading and trailing trucks are handled the same way, with the number of axles counted, as for instance 2-C+C-2.

Generally, the more driving wheels an engine has the more powerful it is, and for steam locomotives, the more wheels in the trailing truck, the larger the firebox.

There is no “best” wheel arrangement; the railroad’s own operating requirements determined that, and also wheel arrangements evolved over time. For much of the 19th century the 4-4-0 was so common that it was known variously as the “American” or “American Standard”, sometimes just “Standard” (also “Eight Wheeler”). It was a dual-service engine, hauling both passendgers and freight. Later the 4-6-0 (Ten Wheeler), 2-6-0 (Mogul) and 2-8-0 also saw much dual service. As fireboxes grew larger, the 2-8-2 (Mikado) was introduced: it became a standard freight engine all over the country. The 4-4-2 (Atlantic) and 4-6-2 (Pacific), usually equipped with large driving wheels, were common passenger engines, especially the latter. Engines with four-wheel trailing trucks, to support still larger fireboxes, the 2-8-4 (Berkshire), 4-6-4 (Hudson) and 4-8-4 (Northern and other names) were introduced shortly before diesels and were again fast, dual-purpose engines.

The articulated types (2-6-6-2, 2-8-8-2, etc.) hauled long, heavy freight trains for the most part, though some also were used in passenger service: Southern Pacific 4-8-8-2 cab-forwards, for instance, were dual-service.

Engines with ten or twelve driving wheels were generally used for freight. Except in the earliest years (before the Civil War), engines without either pilot or trailing trucks were switchers.

There are numerous introductory books on railroads and model railroading that go into more detail on these matters.

If you are modeling a particular railroad, be aware that not every type was used by a railroad. The Kansas City Southern, for instance, had many Consolidations but no Mikados.For your own modeling, if your layout is small, with tighter curves, pick smaller engines with fewer driving wheels (shorter wheelbases, you see) to avoid excessive overhang and even derailments.I hope this has been of some help.