. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . spikes,it becomes necessary to cut the flange of the guard-rail. Thelength of the rail should be 16 feet 6 inches, the middle portionbeing straight for a length of 3 feet 6 inches, and the ends, eachbeing 6 feet 6 inches long, curved out so that the side of therail head at each end is 4 inches from the main rail head, whenthe flange-way at the center is If inches. See Fig. 136a MATHEMATICAL DESIGN OF STVITCHES. In all of the following demonstrations regarding switches,turnouts,
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . spikes,it becomes necessary to cut the flange of the guard-rail. Thelength of the rail should be 16 feet 6 inches, the middle portionbeing straight for a length of 3 feet 6 inches, and the ends, eachbeing 6 feet 6 inches long, curved out so that the side of therail head at each end is 4 inches from the main rail head, whenthe flange-way at the center is If inches. See Fig. 136a MATHEMATICAL DESIGN OF STVITCHES. In all of the following demonstrations regarding switches,turnouts, and crossovers, the lines are assumed to represent thegauge-lines—, the lines of the inside of the head of the Design with circular lead-rails. The simplest method is to consider that the lead-railscurv^e out from the main track-rails by arcs of circles which aretangent to the main rails andwhich extend to the frog-point simple curve frpm D to F isof such radius that (r + ig) vers F=g, in which i^ = the frog angle,g=gauge, L=the lead (BF),and r=the radius of the center ofthe Fig. 137. r-hig = vers F (74) Also,Also, BF^BD==cotiF, BD=g; BF=L. .-. L=g cot iF (75) L = (r + ig)smF; ..... (76) QT=2rsmiF. ........ (77) These formulae involve the angle F. As shown in Table III,the angles (F) are always odd quantities, and their trigonometricfunctions are somewhat troublesome to obtain closely with 298 RAILROAD CONSTRUCTION. § 262. ordinary tables. The formul?? may be simplified by substitut-ing the frog-number n, from the relation that n = | cot ^F,Since r — ig=L cot F and r-{-ig=L cosec F, then r = JL (cot F + cosec F) = ig ^ot §i^(cot i^^-cosec F) = hg cot^ Ji^, since (cot a + cosec a) =cot Ja = 2gn , , . (78) Also, L = 2gn, (79) from which r=nXL. . , (80) These extremely simple relations may obviate altogether thenecessity for tables, since they involve only the frog-number andthe gauge. On account of the great simphcity of these rules,they
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