. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . Fig. 26. 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 x^the radius being unchanged. (Fig. 26.) In this case the whole §64. ALINEMENT. 73 curve is moved bodily a distance 00=AA = VV =BB, andmoved parallel to the first tangent A V Bn X BB AA^ (15) sin nBB sin J c. To change the direction of the forward tangent at the pointof tangency. (Fig. 27.) This problem involves a change
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . Fig. 26. 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 x^the radius being unchanged. (Fig. 26.) In this case the whole §64. ALINEMENT. 73 curve is moved bodily a distance 00=AA = VV =BB, andmoved parallel to the first tangent A V Bn X BB AA^ (15) sin nBB sin J c. To change the direction of the forward tangent at the pointof tangency. (Fig. 27.) 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 use. R, A, a J AV, and BV are 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+/?).
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