The New York Rapid-transit Subway

Proceedings.] PARSONS ON NEW YORK RAPID-TRANSIT SUBWAY. 33 is based on the theory that the curvature increases directly as the distance from the point of transition, from zero at the tangent to the curvature of the circular curve where it connects therewith. Although there are several methods of laying out spiral curves, this one was preferred for the following reasons :— The curvature increases directly as the distance. The calculations are simple. The method may be used for a long easy transition-curve or a short sharp one; or between two parts of a compound curve, to provide a gradual change from one to the other. It may be laid off by off-sets or by deflection. It lends itself to field-work, as the instruments may be set up on an intermediate point and work continued. The sharpest curve on the subway is the one at the City Hall loop, which has a radius of 147'5 feet. There is a station on the outside of this curve, and all trains approaching it have to move very slowly, regardless of the curve. The sharpest curve where trains are likely to proceed rapidly is one at the south end of the Grand Central station, where there is a deflection of 90°. In order to reduce the taking of very expensive property this curve was laid out with a short radius. It begins at the end of the platforms with a radius on the centre-line of 250 feet. After proceeding for a short distance with this curvature, the transition-curve begins with a con- stantly increasing radius to the point of tangency in Park Avenue. The sharpest curve between stations on the express lines is that passing from 42nd Street into Broadway, the radius of which is 458 feet. This curve necessitates the slowing-down of trains to a speed not exceeding 25 miles per hour. Superelevation was adapted separately to each curve on the line according to the speed that the trains would be scheduled to make on such curves, taking into account, if necessary, the reduction of speed due to the curvature. Superelevation was computed by the following formula :—• Elevation in inches——— (Velocity in miles per hour)2 Radius in feet Wherever possible, the superelevation is divided between the two rails, the inside rail being lowered and the outside rail raised, each by one-half of the elevation to be attained. The maximum elevation permitted is 63 inches, corresponding with a speed of about 30 miles per hour on a curve whose radius is 525 feet. On sharper curves the speed is reduced to correspond with this elevation. The standard minimum clearance from the side of the car to the side of the, column [the INST. C.E. VOL. CLXXIII.] D