. 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 . book. In Fig. 14both notations are given, the A. R. E. A. notations beinggiven in parentheses. Both notations are also shown inFig. 36, which illustrates a transition curve or spiral. Itshould be .noted that some of the notations coincide for someof the elements. 51. Elements of a curve. Considering the line as runningfrom A toward B, the beginning of the curve, at A, is calledthe point of curve (PC). The other end o
. 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 . book. In Fig. 14both notations are given, the A. R. E. A. notations beinggiven in parentheses. Both notations are also shown inFig. 36, which illustrates a transition curve or spiral. Itshould be .noted that some of the notations coincide for someof the elements. 51. Elements of a curve. Considering the line as runningfrom A toward B, the beginning of the curve, at A, is calledthe point of curve (PC). The other end of the curve, at B, iscalled the point of tangency (PT). The intersection of thetangents is called the vertex (V). The angle made by the m TIAILKOAD CONSTRUCTION. 52. t-angents at V, which equals the angle made by the radii to%\iQ extremities of the curve, is called the central angle (A). AVand BY, thp two equal tangents from the vertex to the PCand . T, are called the tange I distances (T). The chordAB is pallefi the long hard (LC). The intercept BG fromthe middle of the long chord to the middle of the aye is calledthe middle (M). That part of the secant GV from. Fig. 14. the middle of the arc to the vertex is called the external distance{E). From the figure it is very easy to derive the followingfrequently used relations: r^i^tanfA (4), LC = 222siniA (5) M=i2versiA. {&), • E = R exsec ^A . (7)^ 52. Relation between T, E, and A^ Join A and G in Fig. 14. The angle VAG = lA, since it is measured by one half of the. .1arc AG between the secant and tangent. A€O = 90°-iA. § 53. ALINEMENT. 61 AV :VG::sm AOV : sin VAG;sin AGV-Bva. AGO ^cos lA; T : E :: cos jA : sin |A; T=E cot lA (8) I r Ths sapae relation may be obtained hy dividing Eq. 4 by Eq, 7, since tan a-^exsec a = cot |a. ji 53. Elements of a 1° curve. From Eqs. 1 to Sit is seen thatthe elements of a curve vary directly as 72. It is also seen tobe very nearly true that R varies inversely as D. If the ele-ments
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