Handbook of Railroad Construction; For the use of American engineers. / Containing the necessary rules, tables, and formulæ for the location, construction, equipment, and management of railroads, as built in the United States.

by George L. Vose

D
d = r + e
r – e,

and finally

D – d = 2eD
r + e.

This equation shows the difference in diameters that ought to exist between the inner and outer wheels, that the required effect, (no dragging of the outer and no slipping of the inner wheel,) is produced.

Example.
Let the radius of curvature be	1,000 feet.
The gauge of the road,	6 feet.
The wheel diameter,	4 feet.

And the formula becomes

2ed
r + e = 24
1003 = .024 feet,

or .288 inch on both wheels, or 0.144 inch for each wheel; which for four inches breadth, gives a curve of 1
28 of the width, or decimally, 0.144, and vulgarly, ⅐ of an inch. For a three feet wheel, the rule gives a cone of 0.11 inch.

Note.—Messrs Bush and Lobdel cone their wheels 0.08 inches in a four inch tire; or ¼ inch per foot. The formula above for a three feet wheel, and 4′ 8½″ gauge, gives a curve of 0.09 inches.

The wheel most used upon American roads is made of cast-iron, in one piece, and consists either of two side plates, connected by a hub and rim, or of a central plate ribbed on the sides. Messrs Whitney and Son, (Philadelphia,) pass all their wheels through an annealing process, which renders them much less liable to fracture from shocks and from cold than when the wheel is allowed to cool at once, when hot from the foundery.