. Railroad construction. Theory and practice . 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 =AA ==VV =BB, andmoved parallel to the first tangent AV Bn X BB = =AA, (15) sin nBB sin J 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.
. Railroad construction. Theory and practice . 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 =AA ==VV =BB, andmoved parallel to the first tangent AV Bn X BB = =AA, (15) sin nBB sin J 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 use. Ry J J a, AVj and BV are 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^^hA.
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