. Railroad construction. Theory and practice . Fig. 152. If the frogs are unequal, we will have (see Fig. 152)r2 vers d+ri vers d=d; d \ vers 6 = (118) (119)(120) (121) also the distance along the track B2N = (r,+r,) sin d (122) Problem, A crossover is to be placed between two parallelstraight tracks, 12 2 between centers, usiag a No. 8 and a No. 9 288 RAILROAD CONSTRUCTION. §274. frog, and with a reversed curve between the frogs. Requiredthe total distance between switch-points (the distance ^2^ i^^Fig. 152). Solution. If straight point rails and straight frog rails areused, the radii, r^ and
. Railroad construction. Theory and practice . Fig. 152. If the frogs are unequal, we will have (see Fig. 152)r2 vers d+ri vers d=d; d \ vers 6 = (118) (119)(120) (121) also the distance along the track B2N = (r,+r,) sin d (122) Problem, A crossover is to be placed between two parallelstraight tracks, 12 2 between centers, usiag a No. 8 and a No. 9 288 RAILROAD CONSTRUCTION. §274. frog, and with a reversed curve between the frogs. Requiredthe total distance between switch-points (the distance ^2^ i^^Fig. 152). Solution. If straight point rails and straight frog rails areused, the radii, r^ and rg, taken from the middle section of TableIII, are and vers 6 = —;— ci = 122 =, log = log (r,+r2) = 3^08245log vers ^ = Eq. 122. ri = = ,+-2= Eq. 122. e = s° 08 06 log(ri+r2) = sin ^ = = The length of the curve from B., = lOO{d~d) =100(8° 08 06--8° 250 = The length of the other curve is 100(8° 08 06 -^. Fig. 153. 10° 52) = As a check, + = , which isslightly in excess of , as it should be. §275. SWITCHES AND CROSSINGS. 289 275. Crossover between two parallel curved tracks, (a) Usinga straight connecting curve. This solution has limitations. Ifone frog (F^) is chosen, F2 becomes determined, being a functionof F^. If F^ is less than some limit, depending on the width (d)between the parallel tracks, this solution becomes Fig. 153 assume F^ as known. Then F^H=g see F^. In thetriangle HOF2 we have sin HFfi: sin F^HO ;sin F^HO = cos F,; HF^O = 90° + Fn;,\ sin HF20=cos \-id-ig-g sec F^; F20=R-hd-\-ig; ^ ^ R-hid — hq — q sec F. cos F.^cos F. ^—^V-^, R-id + ig (123) Knowing F2, 6^ is determinable from Eq. 91. Fig. 153 showsthe case where 62 is greater than F2. Fig. 154 shows the casewhere it is less. The demonstration of Eq. 123 is applicable to
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