. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . (95) (96) Fig. 156. 317. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii Ri and R2are known; also the angle M. ri, r2, r^ and r^ are thereforeknown by adding or subtracting Jgr, but the lines are so in-dicated for brevity. Call the angle MCiC2 = Ci, the angleMC2Ci = C2y and the line CiC2^c. Theni(Ci+C2)=90°-W ^^ tani(Ci-C2)=cot|M|p^. . (97) R^-\-R] Ci and C2 then become known and C = C1C2 = R2~. ~ Sin Ci (98) §317. SWITCHES AND CR
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . (95) (96) Fig. 156. 317. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii Ri and R2are known; also the angle M. ri, r2, r^ and r^ are thereforeknown by adding or subtracting Jgr, but the lines are so in-dicated for brevity. Call the angle MCiC2 = Ci, the angleMC2Ci = C2y and the line CiC2^c. Theni(Ci+C2)=90°-W ^^ tani(Ci-C2)=cot|M|p^. . (97) R^-\-R] Ci and C2 then become known and C = C1C2 = R2~. ~ Sin Ci (98) §317. SWITCHES AND CROSSINGS. 363 In the triangle FiCid, call Kc+ri+r^) =si; Si = \{c+ri+rd;. Fig. 157. S3 = Kc+ri+r3); and S4 = Kc+r2+r3). Then, by formula 29,Table XIV, 2(si-ri)(si-r,) Similarly vers F^ ^ 14 vers F^ = -^-^—j^ , r->r 24 vers i^Q vers 2G^3-n)(g3-n) ^ ^2(g4-r2)(g4-r3) sinCiC2^,=sini^,^%- (99) sin C1C2F2 =sin i^g—;c &^C^=^•, (100) sin i^jCiCj =sinF2^,c /. F,C,F,=F,Cfi,-F,Cfi,) ..... (101)i from which the chords F^F^ and F^F^ are readily computed. ^ 364 RAILROAD CONSTRUCTION. §317, F1F2 and i^2^4 ^^^ nearly equal. When the tracks are straightand the gauges equal, the quadrilateral is equilateral. Problem. Required the frog angles and dimensions for a cross-ing of two curves (Z)i=4°; 2)2 = 8°) when the angle of their tan-gents at the point of intersection =62° 28 (the angle M inFig. 157). Solution Eq. 97. i?i = ; i^2 = ;Ti =J?2 + i9 = + = ;^2 =-R,-k = = ;^3 =i^i + isr = + = ;U =2^1-49^ = = log cot JM =,-R,=477A; log = 7^2 + ^^1=3342
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