. Railroad construction. Theory and practice . a. Bs = R vers A/. R=R Bs=Rvers A Fig. 22. As vers (A —a)RsinA. As=Rsin A (16) AA=As-As=R sin A-R sin A. (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. 34. 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
. Railroad construction. Theory and practice . a. Bs = R vers A/. R=R Bs=Rvers A Fig. 22. As vers (A —a)RsinA. As=Rsin A (16) AA=As-As=R sin A-R sin A. (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. 34. 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 AVP^/^. It is required to determinethe radius (R) and the tangentdistance (AV). A is known. PFG = K180°-J)-^=90o_(ij + /?). PP=2VP sin PVG =2FPcos(iJ+/?).PSV^^ SP = VP Fig. 23. sin ^A § 35. ALIGNMENT. 35 .4 ^ = VSP~X~SP = VSP{SP-^PP) \ sin J J [_ sm JJ ^- . /J _ sin^;9^ 2 sin /9 cos (jJ + S) ~ Xsin^i-/^ sin* J SlFx J J AV==AS + SV = i^JsinCiJ +^) +\/sin2^ + 2sin^5siniJcos(iJ +^9)]. (18)sin2-j R=AV cot U. In the special case in which P is on the median Hne OF,^ = 90°-J J, and (JJ+,5)=90°. Eq. 18 then reduces to ^F = -^il +COS iJ)=VP cot ii,sm iJ 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 abo\e. 35. Determination of the curvature of existing track, (a) Usinga transit. Set up the transit at any point in the center of thetrack. Measure in each 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 equals the deg
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