g = gauge of road.
R = radius of curve.
E = elevation of outer rail in feet and decimals.
g and R are the only fixed quantities in the formula; and the average weight and speed of a car must be assumed.
Examination of the formula shows how important it is that all trains should run at such a velocity as to demand the same elevation of rail. The absolute elevation must be arranged to meet the requirement of the fastest trains; and other trains must conform, even at a disadvantage.
Note.—The subject of the mechanics of traversing railroad curves, is yet quite in the dark. The action of the train, as caused by its own momentum, is tangential; while the action of the engine tends to pull the cars against the inner rail, being opposed to the first motion. This might require a reduction of the elevation given by the formula when the engine is exerting a strong tractive power, but when running without steam the full elevation is needed, (see chapter III.)
Fig. 149.
In laying and maintaining the rails to the proper elevation, a clinometer attached to a rail gauge, as in fig. 149, answers a good end: the small arc being graduated according to the different elevations required by curves of different radii. Thus the index of the level being placed at 2°, when the rails are fitted to A and B, the elevation is correct for a 2° curve; or for a curve of 2,865 feet radius.
The difference in gauge of one foot makes a difference in the elevation of but 0.009 feet, or about ⅒ of an inch.