. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 147. radius r of the connecting curve from F to S, Fig. 147, and itslength or central angle. In the triangle CSF CS + i(CFS-^CSF):tsin i(CFS -CSF); § 273. SWITCHES AND CROSSINGS. 309 but i(CFS-^CSF) =90-i(p; and, since the triangle O^SF isisosceles, i(CFS-CSF)=hF; .-. 2R-\-d:d-g::coti(p:tsiniF::cot JF:tan i<(f; ■■■ W-i^ <™ From the triangle CO^F we may derive r — hg:R-i-ig::sin (/f• sin (F-h(p); ^-*^ = (^-^i^)swf?) ^^ Also FS = 2(r-ig)smi(F-^(/;) (Ill
. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 147. radius r of the connecting curve from F to S, Fig. 147, and itslength or central angle. In the triangle CSF CS + i(CFS-^CSF):tsin i(CFS -CSF); § 273. SWITCHES AND CROSSINGS. 309 but i(CFS-^CSF) =90-i(p; and, since the triangle O^SF isisosceles, i(CFS-CSF)=hF; .-. 2R-\-d:d-g::coti(p:tsiniF::cot JF:tan i<(f; ■■■ W-i^ <™ From the triangle CO^F we may derive r — hg:R-i-ig::sin (/f• sin (F-h(p); ^-*^ = (^-^i^)swf?) ^^ Also FS = 2(r-ig)smi(F-^(/;) (Ill) 273. Connecting curve from a curved track to the INSIDE,. Fio. 148. As above, it may readily be deduced from the triangle CFS (seeFig. 148) that (2R-d):{d-g)::cot J^:tan JF, and finally that 2n(d-g) tan J^ = 2R-d Similarly we may derive (as in Eq. 110) (112) (113) 310 RAILROAD CONSTRUCTIOX. §273. Also FS = 2(r-ig)smi{F-<P) (114) Two other cases are possiblebecomes infinite (see Fig. 149),then F = (p. In such a casewe may write, by substitut-ing in Eq. 112, 2R-d = 4n\d-g), . (115) This equation shows the valueof R, which renders this casepossible with the given valuesof n, d, and g. (h) ^ may begreater than F. As before(see Fig. 150) 2R—d:d—g::cot iipitanhF;the same as Eq. 112, but T-¥hg = {R-h9) (a) r may increase until it
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