. Railroad construction. Theory and practice . h the tangents and the longchord are obstructed. The above methods are but samplesof a large number of similar methods which have been choice of the particular method to be adopted must bedetermined by the local conditions. 32. Obstacles to location. In this section will be given onlya few of the principles involved in thisclass of problems, with illustrations. Theengineer must decide, in each case, whichis the best method to use. It is frequentlyadvisable to devise a special solution forsome particular case. a. When the vertex is inac
. Railroad construction. Theory and practice . h the tangents and the longchord are obstructed. The above methods are but samplesof a large number of similar methods which have been choice of the particular method to be adopted must bedetermined by the local conditions. 32. Obstacles to location. In this section will be given onlya few of the principles involved in thisclass of problems, with illustrations. Theengineer must decide, in each case, whichis the best method to use. It is frequentlyadvisable to devise a special solution forsome particular case. a. When the vertex is inaccessible. Asshown in § 26, it is not absolutely essentialthat the vertex of a curve should belocated on the ground. But it is very evi-dent that the angle between the terminaltangents is determined will far less prob-able error if it is measured by a singlemeasurement at the vertex rather than asthe result of numerous angle measurementsFig. 17. along the curve, involving several posi- tions of the transit and comparatively short sights Some-. § 32. ALIGNMENT. 31 times the location of the tangents is already determined onthe ground (as b}^ bn and am, Fig. 17), and it is required tojoin the tangents by a curve of given radius. Method. Measureab and the angles Vba and baV. A is the sum of these distances bV and aV are computable from the above J and R, the tangent distances are computable, and thenBb and a A are found by subtracting bV and aV from the tan-gent distances. The curve may then be run from A, and thework may be checked by noting whether the curve as run endcat B—previously located from b. Example. Assume a?>=546 82; angle a = 15° 18; angleb = 18° 22; D =3° 40; required a A and bB,J = 15° 18 + 18° 22 = 33° 40 Eq. (4) R (3° 40) tan JJ =tan 16° 50 r = sin 18° 22 ab ^^ ~ sin 33° 40 log sin 18° 22 co-log sin 33° 40 aF = AF = aA = ^ sin 33° 40 log sin
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