Concept explainers
In designing transfer curves to connect sections of straight railroad tracks, it’s 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
is continuous and has continuous slope, but does not have continuous curvature. Therefore f is not an appropriate transfer curve.
(b) Find a fifth-degree polynomial to serve as a transfer curve between the following straight line segments:
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Chapter 13 Solutions
Bundle: Calculus, 8th + Enhanced WebAssign - Start Smart Guide for Students + WebAssign Printed Access Card for Stewart's Calculus, 8th Edition, Multi-Term
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