. Fy.,. Suppose the curve A C to have been described containing 60° ofcurvatiire, and that the distance G D equal 50 feet. We have by logarithms : Sine 60° (total amount of curvature), . OOSTSSl Is to R 10-000000 So is G D, 50 feet 1-698970 To AB rz 5778 feet, .... 1-76T439 r. I . GD 50 ^^„ Or by nat. sines = -. = = 6773. ^ sin. 60° -86608 Produce the tangent from A to B =: 57-73 feet; then make the * The diagrams in this work are not drawn to any exact scale, but are designedto represent merely the abstract geometrical relation of l
. Fy.,. Suppose the curve A C to have been described containing 60° ofcurvatiire, and that the distance G D equal 50 feet. We have by logarithms : Sine 60° (total amount of curvature), . OOSTSSl Is to R 10-000000 So is G D, 50 feet 1-698970 To AB rz 5778 feet, .... 1-76T439 r. I . GD 50 ^^„ Or by nat. sines = -. = = 6773. ^ sin. 60° -86608 Produce the tangent from A to B =: 57-73 feet; then make the * The diagrams in this work are not drawn to any exact scale, but are designedto represent merely the abstract geometrical relation of linos. 376 Formula for Running Lines, j curve B D equal A C ; that is A M C = B X D ; then the tangents ;! will be parallel. j This rule will apply to the origin of a compound curve, using the :total amount of curvature run. PROPOSITION II. Fig. 2. | Having a curve A B terminating in a tangent D F, it is required to jfind the radius of a curve that will give a tangent C G parallel to\D F at any given distance therefrom, as at D C say 30 feet, i. 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, -%3.
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Keywords: ., bookcentury1800, bookdecade1850, booksubjectenginee, bookyear1856
