. Railroad construction. Theory and practice . Fig. 154. htjih. figtifes The relative position of the frogs F^ and F2 maybe determined as follows, the solution being applicable to 153 and 154: Then Gi^i=2(i^ + J^-k)sinKi^i~i^2) (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. 290 RAILROAD CONSTRUCTION. §275. (b) Continuing the switch-rail curves until they meet as areversed curve. In this case F^ and F2 may be chosen at pleasure(within limitations), and they will of course be of regular si
. Railroad construction. Theory and practice . Fig. 154. htjih. figtifes The relative position of the frogs F^ and F2 maybe determined as follows, the solution being applicable to 153 and 154: Then Gi^i=2(i^ + J^-k)sinKi^i~i^2) (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. 290 RAILROAD CONSTRUCTION. §275. (b) Continuing the switch-rail curves until they meet as areversed curve. In this case F^ 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 Fg being known, 0^and 62 are computed by Eq. 95 and 91. In the triangle 00^2(see Fig. 155) 2{S-002){S-00,)vers ^ (002)(00i) in which S = ^{00^ + OO2 + Ofli)) but 00i=i^ + ic?-ri, 002=R-hd-r2, .-. S = h{2R-\-2r2)=R+r2]S-002=R + r2-R + id-r2 = id;S-00^=R + r2-R-id + r^=r,-hr2-id;. Fig. 155. ^^^^^~ {R-hd^r2){R-\-hd-r,) m 00A =sm ^^^^=sm <p ^^^^^ ; . 020J) = (p-\-Ofi20] NF2 = 2{R-^d + lg) sin ^{^-6^-62), sm (125) (126) (127)(128) § 275. SWITCHES AND CROSSINGS. 291 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 wliichmust be made to order. Problem. Required the dimensions of a crossover on a 4° 30curve when the distance between track centers is 13 feet. TheI frog for the outer main track {F^ in Fig. 155) is No. 9; F2 is No. 7^ = ; R^, for the inner main track, =; D^==4° 29; ^2 = ; Z)2=4°31; ri=radius for {d,-\-D,y curve =radius for (8° 25 + 4° 29) curve =; r^ =radius for {d^-D^Ycurve =radius for (14° 27-4° 31) curve = (See §§ 267-268.) Eq. 125. rf=13; log= ri+r2-ic?=; log = 72-^d + r2= ; log = ; co-log = i2 + id-ri= ; log =
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