Answer: In designing transfer curves to connect sections

Chapter 13, Problem 13.266

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In designing transfer curves to connect sections of straight railroad tracks, its important to realize that the acceleration of the train should be continuous so that the reactive force exerted by the train on the track is also continuous. Because of the formulas for the components of acceleration in Section 13.4, this will be the case if the curvature varies continuously. (a) A logical candidate for a transfer curve to join existing tracks given by for and for might be the function , , whose graph is the arc of the circle shown in the figure. It looks reasonable at first glance. Show that the function is continuous and has continuous slope, but does not have continuous curvature. Therefore is not an appropriate transfer curve. ; (b) Find a fifth-degree polynomial to serve as a transfer curve between the following straight line segments: for and for . Could this be done with a fourth-degree polynomial? Use a graphing calculator or computer to sketch the graph of the connected function and check to see that it looks like the one in the figure. y 0 x y=x y=0 transfer curve