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

The summit tangent must be horizontal.

The curve at springing must inclose the ellipse.

The radius of summit must not be greater than the span.

The number of arches composing the curve must not be less than three, nor more than eleven; and must be uneven. Perronet’s fine bridge of Neuilly, over the Seine at Paris, has eleven centres. In spans of sixty feet and under, it is unnecessary to use more than five centres.

Fig. 119.

251. The three centred curve is described as follows, fig. 119:—

Let A B represent the span, and c D the rise, with c as a centre and c A as radius, describe the quadrant A F E; make the angle A C F 60°. Parallel to F E draw D G, and parallel to F C draw G K. H is the centre, and A G the arc of the springing curve; also GD is the arc, and K the centre of the summit curve.

THE FIVE CENTRED CURVE.

252. The common construction of the five centred curve leaves the radii of the extreme curves to be assumed. The following method fixes all of the dimensions when the span and rise are given:—