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

Rad.² – Rad. less gauge² = distance²,

or R² – R – g² = D²,

and D = √R² – (R – g)².

The angle of frog is also

Sin angle of frog = Sin 90 log D
log R.

The length of this switch rail depends upon the radius of curvature. The distance between the two rails at S must be enough to admit the wheel flange, that is, at least two inches.

Let A B, fig. 146, be the straight rail; E D the curved one. Draw G H parallel with and two inches distant from the inner edge of A B. No point of the curved rail must fall within G H; whence E is the turning-point, and E D the length, found as follows.

Let R equal the radius of curve to outside of outer rail; d equal two inches plus width of rail, or i e, and D equal D E.

Then

D = √R² – (R – d)².