. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . KAILROAD CONSTRUCTION. § 312. FiT sin Fi+g cos Fi = d-g; . (91) FiT=-r—^-g cot Fi. sin Fi The total distance along the track maybe derived as follows: DZ = DiFi+D2F2+F2Y ==DFi+D2F2+XY-XF2; XY=={d-g) cot Fi;XF2 = g^sin F^; DiZ =2DiFi + {d-g)cotFv 9 Fig. 151. sin Fi (92). 312. Crossover between two parallel curved tracks. Usinga straight connecting curve. This solution has limitations. If one frog (Fi) ischosen, F2 mus
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . KAILROAD CONSTRUCTION. § 312. FiT sin Fi+g cos Fi = d-g; . (91) FiT=-r—^-g cot Fi. sin Fi The total distance along the track maybe derived as follows: DZ = DiFi+D2F2+F2Y ==DFi+D2F2+XY-XF2; XY=={d-g) cot Fi;XF2 = g^sin F^; DiZ =2DiFi + {d-g)cotFv 9 Fig. 151. sin Fi (92). 312. Crossover between two parallel curved tracks. Usinga straight connecting curve. This solution has limitations. If one frog (Fi) ischosen, F2 must bedetermined, being afunction of Fi. IfFi is less than somelimit, depending onthe width (d) betweenthe parallel tracks,this solution becomesimpossible. In assume Fi asknown. Then KiN = g eec Fi. In the triangle NOK% wehave sin NK^O : sin K2NO ::N0 : K2O; sin ZaiVO = cos Fi; NK^O^dO^+Fi; ,. sin NK20 = cos F2. NO-H+hd-hg-KisinFi-gsecFi] KiO^R-^d+^g -i-Kz sin Fi] R+id—^g-Ki sin Fi-g sec Fi Fig. 152. /.COS Fi^Qos Fi- R-^d-{-^g-]-K2sinFi (93) § 312. SWITCHES AND CROSSINGS. 355 The solution of this equation involves the frog angle F2, which isthe angle sought, but there is little error in considering in thissolution that K2 sin F2 is numerically equal to Ki sin Fi andsolving accordingly. If the computed value of F2 is very differentfrom Fi, it would be more precise to recompute Eq. 93 by sub-stituting for Ki sin F2 the more exact q
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