. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 154. both figures The relative position of the frogs Fj and F2 maybe determined as follows, the solution being applicable to bothFigs. 153 and 154: /fOi^2 = 180°-(90°-i^i) -(90° + i^2) =^1--^2. Then GF,=2(R + id-^g)smi(F,-F2) (124) Since F2 comes out any angle, its value will not be in generalthat of an even frog number, and it will therefore need to bemade to order. §275. SWITCHES AND CROSSINGS. 315 (b) Continuing the switch-rail curves until they meet as areversed curve
. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 154. both figures The relative position of the frogs Fj and F2 maybe determined as follows, the solution being applicable to bothFigs. 153 and 154: /fOi^2 = 180°-(90°-i^i) -(90° + i^2) =^1--^2. Then GF,=2(R + id-^g)smi(F,-F2) (124) Since F2 comes out any angle, its value will not be in generalthat of an even frog number, and it will therefore need to bemade to order. §275. SWITCHES AND CROSSINGS. 315 (b) Continuing the switch-rail curves until they meet as areversed curve. In this case Fi and F2 may be chosen at pleasure(within limitations), and they will of course be of regular sizesand equal or unequal as desired. F^ and F2 being known, d^and 62 are computed by Eq. 95 and 91. In the triangle 00^2(see Fig. 155) 2(S-OO2)(S-OO0vers^= (002)(00i) in which S = i(00, + OO2 + Ofii); but 00,=R + id-r,, 002=R-id+r2y /. S = i(^R-h2r2)=R+r2;S-002 = R-\-r2-R-{-id-r2 = id;S-OOi=R + r2-R-^d + ri=r^-]-r2-id;. vers0 = Fig. ) {R-id + r2XR + id-ri) - nr^r, • ,00i . .R + ^sm (/fyr-~=sin ip ^ J; OA^=^+OA^; NF2-=2{R-\d-\-\g) sin ^{^j;-6,-62), (125) (126) (127)(128) 316 RAILROAD CONSTRUCTION. § 275. Although the above method introduces a reversed curve, yetit uses up less track than the first method and permits the use ofordinary frogs rather than those having some special angle whichmust be made to order. But the above solution impUes the useof circular lead rails. We may compute dimensions and laytrack between F^ and F^ on this basis and then change theswitch rails as desired. Strictly, r^ and r^ should be computedby Eq. 92 and 96, but for an easy main-line curve the approxi-mate rule is sufficiently accurate. Problem.—Required the dimensions of a crossover on a4° 30 curve when the distance between track centers is 13 frog for the outer main track (F^ in Fig. 155) is No. 9;F^ is No. 7. Then 22=; R^y for the out
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