SWITCHES.

291. The object of the switch is to adjust a single line of rails to two or more pairs, so that any two lines may be made continuous. The form in general use consists of two rails, as at a b, a b, fig. 144, moving upon a and a as centres. Here the tangent point of the turnout curve is at c. The data given for the switch are the length of switch rail and the motion at the toe (c) (which determine the direction of the starting tangent) and the radius of curvature of the turnout curve. The required elements are, the angle of frog at b and the distance from a to the point of the frog.

Fig. 144.

The following formula and table are by Josiah Hunt, Esq., (at present chief engineer of the Hannibal and St. Joseph Railroad, Mo.). The formula was first published in Appleton’s Mechanics’ Magazine, vol. 1, p. 575.

D = 2(g – s) × cot. S × cot. F
cot. S + cot. F.

Where S = angle of switch.

F = angle of frog.

s = the movement.

g = the gauge.

Example.—How far from the toe of the switch is the point of the frog, the gauge being 4′ 8½″, the rail twenty feet long, and moving five inches; the frog being six feet long, six inches wide across the head, and three inches at the mouth?

We have

D = 2(4.708 – .417) × 240/5 + 72/(6 + 3)
240/5 + 72/(6 + 3)

or, D = 8.582 × 48 × 8
48 + 8 = 58.85 feet.

In laying the rails, the distance from the point to the end of the frog (towards the switch) is to be taken from the above.

Table showing the distance between the frog and switch, gauge 4′ 8½″, movement of switch-rail five inches. Frog six inches across head, and three inches at mouth. Main track being straight.

Length of frog.	LENGTH OF SWITCH RAIL.
Length of frog.	12	14	16	18	20	22
3	29.1	29.7	30.1	30.4	30.7	30.9
3½	33.3	34.0	34.5	35.0	35.3	35.6
4	37.3	38.2	38.8	39.4	39.8	40.2
4½	41.1	42.2	43.0	43.7	44.3	44.7
5	44.8	46.1	47.1	47.9	48.5	49.1
5½	48.3	49.8	51.0	51.9	52.7	53.2
6	51.7	53.4	54.8	55.9	56.8	57.6
6½	55.0	56.9	58.5	59.8	60.8	61.7
7	58.1	60.3	62.1	63.4	64.7	65.7
7½	61.2	63.6	65.6	67.2	68.5	69.6

292. When the switch rail is short, the angle between the main line and the switch rail, when switched, is considerable; and causes quite a shock to the passing engine. The switch shown in fig. 145 remedies the evil, makes the machinery compact, and the calculation simple. The tangent point of the turnout curve is at n n (the usual heel). In place of adjusting the single to the double line of rails, the double is adjusted to the single line. The data given are the gauge and radius of curve; and as before, the elements required the frog angle and distance from switch to frog point.

Fig. 145.

Now

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.

Fig. 146.

Example.—Let the radius of outer rail be five hundred feet, and the gauge five feet. We have, then, the distance

(A.) D = √500² – 495² = 72 feet, very nearly.

Also, Sin E C D = Sin 90 log D
log R,

(B.) or Sin 90 log 72
log 500 = 8° 17′,

and the length of switch

(C.) √500² – 499.65² = 18¾ feet nearly.

Five hundred feet is, therefore, about the longest radius for which such switches should be used.

SIDINGS AND CROSSINGS.

Crossings occur where two tracks cross, and consist of four frogs, with the corresponding guard rails, as in fig. 147.

Fig. 147.