. Elements of railroad track and construction . Fig. 101. AD = BC = G cosec F (79) If the gauges are equal, A D =B C =A B =D C, butif the gauge of the other track is G, then from the tri-angle A B G, AB = DC = G cosec F (80) 161. Computing the Crossing-frogs for a Straightand a Curved Track.—It is necessary to know theangle between the tangent tothe center line of the curveand the center line of thestraight track, and the gauges,Gi and G, of the tracks, sincetrue curved crossings are verylikely to be used on yard orshop industrial tracks. InFig. 102, let Oe = R, anda h and c eh he the centerli
. Elements of railroad track and construction . Fig. 101. AD = BC = G cosec F (79) If the gauges are equal, A D =B C =A B =D C, butif the gauge of the other track is G, then from the tri-angle A B G, AB = DC = G cosec F (80) 161. Computing the Crossing-frogs for a Straightand a Curved Track.—It is necessary to know theangle between the tangent tothe center line of the curveand the center line of thestraight track, and the gauges,Gi and G, of the tracks, sincetrue curved crossings are verylikely to be used on yard orshop industrial tracks. InFig. 102, let Oe = R, anda h and c eh he the centerlines of the tracks, intersecting at e, and the angle a ef. Fig. 102. I PRACTICAL TURNOUTS. 167 =0 be measured in the field, then it is required tofind the frog-angles F, Fi, F2; and F3 at A, Ai, A2;and A3 respectively. Draw 0 e and 0 A, and project eto B and A to C on a line parallel to the straight trackIn the triangle A 0 C, the angle 0 A C =F, and A C =0 A cos 0 A C = (R +J Gi) cos F; in the triangle e 0 B,the angle 0 e B =, and but eB = Oe cos 0 = R cos 0,AC = Be + |G, substituting, we have (R + ^Gi) cos F = R COS 0 + f G, COSF = ^Z:7.^. ^ (81) R COS 0 + ^GR+IGi To find Fi at Ai, in Fig. 102, draw 0 Ai and projectAi to D, then in the triangle Ai 0 D, AiD = (R + iGi) cos Fi, butAiD = Be - |G;equating the values of Ai D, (R + §Gi) cos Fi = R cos <A - §G,R cos <^ — ^G Similarly it can be shown that „ R cos — |Gcos F2 = and cos F3 = (82) R — 2G1R cos 0 + iG R-^G, (83) (84) 168 RAILROAD TRACK AND CONSTRUCTION. To find the chord distance between frogs, in , draw the Une AAi, and a hne from 0 to themiddl
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