. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . F,F, = (R + ig) sin F,-(R-ig) sinF,; \ (130) Hi^, = (i^-i^)(sini^,-sini^i). f • 279. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii Ri and R2 areknown; also the angle M. rj, rg, rg, and r^ are therefore knownby adding or subtracting ^(7, but the lines are so indicated forbrevity. Call the angle ikfCjCz = (7i, the angle MC2Ci = C2, and the line CiC2=c. and Theni((7i + (72)=90°-iilf tan i(Ci-C2) =cot ^M^ -Ri R2-\-Ri Ci and C2 then b
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . F,F, = (R + ig) sin F,-(R-ig) sinF,; \ (130) Hi^, = (i^-i^)(sini^,-sini^i). f • 279. Two curved tracks. The four frogs are unequal, andthe angle of each must be computed. The radii Ri and R2 areknown; also the angle M. rj, rg, rg, and r^ are therefore knownby adding or subtracting ^(7, but the lines are so indicated forbrevity. Call the angle ikfCjCz = (7i, the angle MC2Ci = C2, and the line CiC2=c. and Theni((7i + (72)=90°-iilf tan i(Ci-C2) =cot ^M^ -Ri R2-\-Ri Ci and C2 then become known andC = C iC 2 ^=-n/2~ sin C (131) (132) 279. SWITCHES AND CROSSINGS. 323 In the triangle FiC^Ci, call Kc+n + rJ =5i; S2 = i(c + r2+r^\. V K / ^ V !| / \ \\ \ \ ll \ ri /\ h / S3 = f:(c4-ri+r3)Table XXX, Similarly Fig. 159.; and s^ = i(c-\-r2+r2). Then, by formula 29, yersi^,=^^--^-^^^^-^-\^ versi^,^^^--^-^^^--^-\ vers F^ = ^^ ^-^^-^ -, vers i^4 =sin 2(g,-r.)(6-, -r^) (7iC2i^,=sini^,^ . (133) sin (7iC2F2=sin i^2~; /. F^C^F^^CS^^F^-CfiJ^.,, (134) sin i<iCi(72=sin jPj—; sini^2CA=sini^2-, .-. F,C,F2=F,C,C,-F,Cfi2) .... (135)from which the chords F^F2 and i^2^4 are readily computed. 324 RAILROAD CONSTRUCTION, § 279. F1F2 and 7^2^4 ^^^ 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 = 3°) when the angle of their tan-gents at the point of intersection =62*^ 28 (the angle M inFig. 159). Solution i^i = ; 2^2 = ;n =-^2 + 1^ = + = ;^2 =-R,-i^ = = ;rg =J?i + i^ = + = ;r^ =J?i-i^ = = Eq. 131. log
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