. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . Bs^R vers J. \ R=R- Bs==Rvers Jrvers J (16) vers {A —a) Fig. 27. As^R sin J. As=Rsin J. .. AA^.As-As^Rsin J-R sin J. . (17) The above solutions are given to illustrate a large class ofproblems which are constantly arising. All of the ordinaryproblems can be solved by the application of elementary geome-try and trigonometry. 64. Limitations in location. It may be required to run acurve that shall join two given tangents and also pass through agiven point The point (P, ) is
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . Bs^R vers J. \ R=R- Bs==Rvers Jrvers J (16) vers {A —a) Fig. 27. As^R sin J. As=Rsin J. .. AA^.As-As^Rsin J-R sin J. . (17) The above solutions are given to illustrate a large class ofproblems which are constantly arising. All of the ordinaryproblems can be solved by the application of elementary geome-try and trigonometry. 64. Limitations in location. It may be required to run acurve that shall join two given tangents and also pass through agiven point The point (P, ) is assumed to be deter-mined by its distance (VP)from the vertex and by theangle AFP=/?. It is required to determinethe radius (R) and the tangent-distance (AV), J is known. PF(? = K180°-J)-/?=90°-(ii+/?).PP=2yPsinPFG=2yPcos(JJ+/?).. ... SP^VP$^,sm ^J Fig. 28. 74 RAILROAD CONSTRUCTION. § 65. AS = VSP X SP = VSP(SP+PP^ ^JvP^[vP^ + 2VPcos(iJ+^8)l\ sm JJ L sm iJ ^ ^ J VP I sin^/^ 2sin^cos(4J+./?)\sinn^ sm§J sin JJ AV=AS+SV yp . = -^[sin(ii+/?)+\/sin2/? + 2sin/?smJJcos(ii+^)]. (18) 2^=A7cot}J. In the special case in which P is on the median line OY,fi = 90—iJ, and (ii+/?)=90^ Eq. 18 then reduces to VP AF = -r^.(l +COS Ji) =VP cot iJ, sm JJ^ as might have been immediately derived from Eq. 8. In case the point P is given by the offset PK and by thedistance VK^ the triangle PKV may be readily solved, giving thedistance VP and the angle /?, and the remainder of the solutionwill be as above. 65. Determination of the curvature of existing track, (a) Usinga transit. Set up the transit at any point in the center of thetrack. Measure in eech direction 100 feet to points also in thecenter of the track. Sight on one point with the plates at 0°.Plunge the telescope and sight at the other point. The anglebetween the chords eq
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