. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . tical defects is vitally objectionable or even appre-ciable. In Fig. 147 KC is practically perpendiculat to one frog-rail and KOi is exactly perpendicular to the other , the angle CKOi equals the frog angle i^.. While thefollowing calculations are amply precise for practical purposes,the discrepancy from strict mathematical accuracy should benoted and properly valued,in the triangle CSK CS+CK:CS-CK
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . tical defects is vitally objectionable or even appre-ciable. In Fig. 147 KC is practically perpendiculat to one frog-rail and KOi is exactly perpendicular to the other , the angle CKOi equals the frog angle i^.. While thefollowing calculations are amply precise for practical purposes,the discrepancy from strict mathematical accuracy should benoted and properly valued,in the triangle CSK CS+CK:CS-CK ::tan i(CKS+CSK):tan i{CKS-CSK); but ^{CKS-\-CSK) =^90-^xf^; and, since the triangle OiSK isisosceles, ^iCKS-CSK)^iF, 310. SWITCHES AND CKOSSINGS. 351 .*. 2R+d-j-K sin F : d-g-K sin F::cot ^^|/ : tan ^F ^F : tan^^;2n(d-g-K sin F) .*. tan 1^ = 2R+d+K sin F (83) From the triangle COiK we may derive r-^g : i?+i^+ii: sin i^::sin ^ : sin {F-\-ip); sin \p Also r-hg = iR-\-h+K sin F)-. ^^ , . sin {F+\l/) KS = 2(r-ig)sinUF-\-rP). . (84) (85) 310. Connecting curve from a curved track to the INSIDE. As above, it may readily be deduced from the triangle CKS (seeFig. 148) that. Fig. 148. CK+CS : CK-CS:: tan UCSK+CKS) : tan UCSK-CKS);(2R-d-KsinF) : (d-g-K sin F:: cot ^^ : tan fF; 2n(d-g-K sin F) tan h\I/ = - 2R-d-KsinF * From triangle COiK, OiK : Cii:::sin ^ : sin (F-^p);(r-^g) : {R-\g-K sin F) ::sin ^ : sin (F-^); sin \p (86) (^-k) = (^-i9-XsinF) sin {F~\l/) (87) 352Also BAILKOAD CONSTRUCTION. KS = 2ir-ig)sm^{F-rl^). §310. (88) c :5
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