. Let AM be the given radius = 1146 feet, the arc AB = 800feet, containing 40°, and D C perpendicular distance 30 logarithms : As versed sine 40° . . 9-369133 Is to R 10-000000 So is D C =r 30 feet .... 1-477121 To M iS=difference of radii given and required=128-22 .... 2-107988Then we have 1146 + 128 = 1272 = radius of a 4° 30 say: 1146 : 1272:: 800 : 888 = arc AC. This case is equally applicable to changing the last radius usedin a compound curve terminating in a parallel tangent. Locating Side Tracks, Etc. 377 P
. Let AM be the given radius = 1146 feet, the arc AB = 800feet, containing 40°, and D C perpendicular distance 30 logarithms : As versed sine 40° . . 9-369133 Is to R 10-000000 So is D C =r 30 feet .... 1-477121 To M iS=difference of radii given and required=128-22 .... 2-107988Then we have 1146 + 128 = 1272 = radius of a 4° 30 say: 1146 : 1272:: 800 : 888 = arc AC. This case is equally applicable to changing the last radius usedin a compound curve terminating in a parallel tangent. Locating Side Tracks, Etc. 377 PROPOSITION III. In case the preceding method should consume too much of the tangentC G, it is required to change the origin of the curve, also the lengthof radius, so that the required tangent may commence opposite to B,running parallel to B H, -% In this case the radiating point will be changed from M towardsA and B, the radius shortened, and the point A moved towards K. Let the required distance between tangents, the given radius,and curvature be .as in Proposition II., then we have by logarithms:As the external secant of 40° . 9-484879 ? ;Is to radius 10-000000 So is 30 feet rr: 1-477121 ? To difference of radii = 98*23 . 1 992242 By natural external secants = - 30 •305407 = 98- — And 1146—98 = 1048 = radius of a 5 28 , as 1146 : 1048:: 800 : 782 = length of 5° 28 (natural tangent of 40°= 83910) = 82 tangent 82 feet from A to K, and curve from thence 732feet of a 5° 28 curve. a 2* V J 3Y8 Formula for Running Lines, PROPOSITION^ r\^. Fij. 3. Raving located a curve with a given terminating in a givenpoint, it is required to change the origin of the curve, also theradius, so as to pass through the same terminating point, with adifferent direction of tangent. KALEV
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