. Railroad construction. Theory and practice . Fig. 147. radius r of the connecting curve from F to Sj Fig. 147, and itslength or central angle. In the triangle CSF CS + CF:CS-CF:: tan i{CFS + CSF): tan h(CFS - CSF); 284 RAILROAD CONSTRUCTION, § 273. / , but -ACFS + CSF) =90-i(/^; and, since the triangle O^SF isisosceles, ^(CFS-CSF) =hF; .-. 2R + d:d-g::coth(:-cot JF:tan J^; ••• -i-i^- ■ • • From the triangle CO^F we may derive r — ig:R + ig::sm ^-sin (F + ip);sin (p (109) r-i9 = (R + ig); (110) sin(i^+9^) Also FS=2(r-ig)smi{F + (P) (Ill) 273. Connecting curve from a curved track to t
. Railroad construction. Theory and practice . Fig. 147. radius r of the connecting curve from F to Sj Fig. 147, and itslength or central angle. In the triangle CSF CS + CF:CS-CF:: tan i{CFS + CSF): tan h(CFS - CSF); 284 RAILROAD CONSTRUCTION, § 273. / , but -ACFS + CSF) =90-i(/^; and, since the triangle O^SF isisosceles, ^(CFS-CSF) =hF; .-. 2R + d:d-g::coth(:-cot JF:tan J^; ••• -i-i^- ■ • • From the triangle CO^F we may derive r — ig:R + ig::sm ^-sin (F + ip);sin (p (109) r-i9 = (R + ig); (110) sin(i^+9^) Also FS=2(r-ig)smi{F + (P) (Ill) 273. Connecting curve from a curved track to the INSIDE^. Fig. 148. As above, it may readily be deduced from the triangle CFS (seeFig. 148) that (2R-d): (c^-gr):: cot J^: tan ^F, and finally that 2n(d--g)2R-d (112) tan ^d)Similarly we may derive (as in Eq. 110) ir-lg)^iR-l,)^^^^ (113) §273. SWITCHES AND CROSSINGS. 28i Also FS=2(r-ig) sin i(F-cl^) (114) Two other cases are possible, (a) r may increase until itbecomes infinite (see Fig. 149),then F = (lf. 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. (b) (p may begreater than F. As before(see Fig. 150) 2R-d:d-g::cot J^itanji^; tan J 9^ 2n(d gl 2R-d
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