. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . track where it becomes parallel to the main track (FS in or 147). Call d the distance between track centers. Theangle KOiS = F (see Fig. 146). Call r the radius of the con-necting curve. Then d—g —K sin/ fr-k) = vers FFQ = (r-ig) sin F+K cos/ (81)(82) In these equations (and in several that follow) K is the distancefrom the theoretical point of the frog to the heel. The length,for each standard frog, is found in Table III, Part B. 350 RAILROAD CONSTRUCTION. § 309. r 309
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . track where it becomes parallel to the main track (FS in or 147). Call d the distance between track centers. Theangle KOiS = F (see Fig. 146). Call r the radius of the con-necting curve. Then d—g —K sin/ fr-k) = vers FFQ = (r-ig) sin F+K cos/ (81)(82) In these equations (and in several that follow) K is the distancefrom the theoretical point of the frog to the heel. The length,for each standard frog, is found in Table III, Part B. 350 RAILROAD CONSTRUCTION. § 309. r 309. Connecting curve ^from a curved track to the the main track is curved, the required quantities are theradius of the connecting curve from K to S, Fig. 147, and itslength or central angle. The accm-acy of all these computations on switches and frogsin cm-ved main track is vitiated by the fact that the frog-railsare straight. The design might be mathematically more perfectif the main track curve were transformed into two curves oneither side of the frog which had centers separated as far as the. Fig. 147. length of the frog, but this would introduce a very great andneedless complication and is never done. The more simple solu-tion is to consider that the frog-rail is a chord of the originalcurve, which (a) narrows the track gauge by an amount equal tothe middle ordinate of that chord and which (6) is not tangentto the curve at either end. For all-ordinary curvature neitherof these theoretical defects is vitally objectionable or even appre-ciable. In Fig. 147 KC is practically perpendicular to one frog-rail and KOi is exactly perpendicular to the other , thegle CKOi equals the frog angle F. While thefollowing calculations are amply precise for practical purposes,the discrepancy from strict mathematical accuracy should benoted and properly the triangle CSK CS+CK:CS-CK::tsiJi i(CKS+CSK):tsin i{CKS-CSK); but i{CKS+CSK) =90-^4^; and, si
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