. Railroad construction. Theory and practice . Fig. 158. (130) F,F, = (R + hg) sin F, -{R- ^g) sin F, ;HF, = {R- l,g) (sin F, - sin F,). 279. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii R^ and R2 areknown; also<the angle M. r^, r^^ rj, and r4 are therefore knownby adding or subtracting \g, but the lines are so indicated forbrevity. Call the angle MC^C^^C^, the angle MC2C^ = C2, andthe line Cfi^^c. Then «Ci + C2)=90°-iMand tanKCi-C2)=cotp/Ci and C2 then become known and sm (7i R2z-_Ri R2-\-Ri (131) (132) 296 hailroad coNSTHtrcrioN. § 279. *
. Railroad construction. Theory and practice . Fig. 158. (130) F,F, = (R + hg) sin F, -{R- ^g) sin F, ;HF, = {R- l,g) (sin F, - sin F,). 279. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii R^ and R2 areknown; also<the angle M. r^, r^^ rj, and r4 are therefore knownby adding or subtracting \g, but the lines are so indicated forbrevity. Call the angle MC^C^^C^, the angle MC2C^ = C2, andthe line Cfi^^c. Then «Ci + C2)=90°-iMand tanKCi-C2)=cotp/Ci and C2 then become known and sm (7i R2z-_Ri R2-\-Ri (131) (132) 296 hailroad coNSTHtrcrioN. § 279. * In the triangle i^ACz, call iC^+rj+rJ =Si; S2 = i{c + r2+r^);. 4 Fig. 159. S3 = i(c + ri-\-r.^); and §4 = 4(^ + ^2+ ^3)- Then, by formula 29,Table XXX, 2(si-ri)(si-r4) vers jPi = r,r v i Similarly vers F2 = -^^ ^^^^ , ^2^ vers Fo = 2(-^3-n)(^^3-n) r,r 13 vers F, = 2(54-r2)(54-r3) rnV, (133) i sin CiCiF^ = sin i^^—; sinCA^2 = sini^2-;c F^C.,F^=Cfi,F^-Cfi^F.„ (134) sin i^iCCz=sin i^i-^; sin7^2<^iC2=sinF2-, I .-. F,C,F,=F,Cfi,-F,C,C^; (135) from which the chords F^F-^ and F^Fi are readih computed. M-^ I §279. SWITCHES AND CROSSINGS. 297 F1F2 and F2F^ are nearly equal. When the tracks are straightand the gauges equal, the quadrilateral is equilateral. PrGhlem. Required the frog angles and dimensions for a cross-ing of two curves (Z)i=4°; D2 = S°) when the angle of their tan-gents at the point of intersection =62° 28 (the angle AI inFig. 159). Solution Eq. 131. i^i = ; 7?2 = ;Ti =i?2 + Js^ = + = ; •^2 =i^,-ig = = ;r, =i^i + i9 = + = ;U =i?i-i^ = = lo
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