. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . Fig. 21. radius. If the radius is not to be changed, the point of curvemust be altered as follows: b. To move the forward tangent parallel to itself a distance a?,the radius being unchanged. (Fig. 21.) In this case the whole 34 RAILROAD CONSTRUCTION. §34. curve is moved bodily a distance 00^-moved parallel to the first tangent AV Bn ^ Xsin nBB^ sin J =AA = VV==BB% and BB = -r^ -AA (15) c. To change the direction of the forward tangent at the pointof tangency. (Fig. 22.) This pro
. Railroad construction. Theory and practice. A textbook for the use of students in colleges and technical schools . Fig. 21. radius. If the radius is not to be changed, the point of curvemust be altered as follows: b. To move the forward tangent parallel to itself a distance a?,the radius being unchanged. (Fig. 21.) In this case the whole 34 RAILROAD CONSTRUCTION. §34. curve is moved bodily a distance 00^-moved parallel to the first tangent AV Bn ^ Xsin nBB^ sin J =AA = VV==BB% and BB = -r^ -AA (15) c. To change the direction of the forward tangent at the pointof tangency. (Fig. 22.) This problem involves a change (a) in the central angle and also requires anew radius. An error in the deter-mination of the central angle fur*nishes an occasion for its , Ay a, AVy and BV are Bs=R vers A, R=R- Bs^RveTsA,vers A (16) vers {A —a)Fig. 22. ^s=i^ sin i. As=Rsin A. .\ AA=As-As==Rsin 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 AFP=/?. It is required to determinethe radius (R) and the tangentdistance (AV). A is = i(180-A)-1^=90°-(ii+/?).PP=2VP sin PVG -2yPcos(ii+/?).PSV^iA.
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