. Railroad construction. Theory and practice . -fcosF -=2gn-f 2/n. (82) (83) Since r—^g = {L—f sec F) cot F, andr^y = (L—f cos F) cosec F,r=iL(cot i^ +cosec F) —J/ sec F cot F — iJ cos F cosec F -^-»(w-)- r=Ln-if cot iF =Ln -fn. Then from (83)r=2gn^—2fn . (84) 264. Effect of straight point-rails. The point switches,now so generally used, have straight switch-rails. This requires ^ § 265. SWITCHES AND CROSSINGS. 275 an angle in the alignment rather than turning off by a tangentialcurve. The angle is, however, very small (between 1° and 2°),and the disadvantages of this angle are small compared
. Railroad construction. Theory and practice . -fcosF -=2gn-f 2/n. (82) (83) Since r—^g = {L—f sec F) cot F, andr^y = (L—f cos F) cosec F,r=iL(cot i^ +cosec F) —J/ sec F cot F — iJ cos F cosec F -^-»(w-)- r=Ln-if cot iF =Ln -fn. Then from (83)r=2gn^—2fn . (84) 264. Effect of straight point-rails. The point switches,now so generally used, have straight switch-rails. This requires ^ § 265. SWITCHES AND CROSSINGS. 275 an angle in the alignment rather than turning off by a tangentialcurve. The angle is, however, very small (between 1° and 2°),and the disadvantages of this angle are small compared withthe very great advantages of the -a 2 sin i(i^ + a) sin h{F-a)g—k = 77T* * • • * COS a — cos i^ BF^L= FM cos i(F f a) + DN = {g- k) cot KF + a) + Z)i\r. (85) (86) I 265. Combined effect of straight frog-rails and straight point-rails. It becomes necessary in this case to find a curve whichshall be tangent to both the point-rail and the frog-rail. Thecurve therefore begins at M, its tangent making an angle of a(usually 1° 50) with the main rail, and runs to H. The central 276 RAILROAD CONSTRUCTION. 260 angle of the curve is therefore (F — a). The angle of the chordHM with the main rails is therefore HM== g—f sin F—k ^ r+ig== smi(F + a) HM 2sini(F-a) g—f sin F—k 2 sin i(F + a) sin i(F-a) g—f sin F — k^ cos a —COS F ST=2r sin i(F-a). BF=L=HM cos i(F + a) +/ cos F+DN = (g-f sin F-k) cot K^ + a) +/ cos F+DN. (87)(88) (89) i It may be more simple, if (r + ^g) has already been computed,to write L =2(r + ig) sin i(^-a) cos i(F-\-a) +/ cos F+DN= (r + ig)(sin F-sin a)-{-f cos F+DN (90) .- /I MN=fc. F
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