377. Of the mechanical details of car building it is not necessary here to speak; but of those matters which fit a car for special duty, and depend upon particular characteristics of any road, such as the gauge, something must be said.
The trend of the wheel tire, as remarked in Chapter XIII., is not turned cylindrical, but conical. A perfectly straight road would of course require no cone upon the wheels; the object of the latter being to vary the wheel diameter when upon curves. The general practice is to give a certain standard cone to all wheels, for all gauges. This is quite wrong, as will be seen by the following formula, which is from “Pambour on the Locomotive Engine.”
Let _m m′_, fig. 156, represent the outer rail, and _n n′_ the inner one. The circumferences upon the same axles must evidently vary as the length of these curves, which are included between the same radii.
Let _D_, be the diameter of the first wheel, and _d_, that of the second; and we shall have,
Expressing the radius of curvature by _r_, and the half gauge by _e_, the above proportion may be expressed by
(_mm′_)/(_nn′_) = (_r_ + _e_)/(_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.
Let the radius of curvature be 1,000 feet. The gauge of the road, 6 feet. The wheel diameter, 4 feet.
(2_ed_)/(_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.