Energy Losses in a Speed Monster

How much energy is lost as the train moves along the track? The layout of the Speed Monster makes it possible to obtain an estimate, by using the Speed Monster panorama photo above, which shows how the hills and valleys of the corkscrew become slightly lower with every coil.

Make a larger copy of the photo and draw a line beteen the highest points in the corkscrew. You can also draw a similar line between the lowest points. Measure (in mm on the photo) how much the altitude, H, changes for a given horizontal distance, D. Before working out a number, we should also account for the additional distance due to the circular motion. The diameter, 2R, of the circle can be obtained from the distance between the lines connecting the upper and lower points, respectively. As the train moves a distance L to the right, while completing a whole turn, it also moves a distance 2piR around the circle, giving a total distance


The ratio
can be taken as an estimate of the "effective" friction coefficient, which includes air resistance and other losses. For cold and empty trains, the relative energy losses can be more than twice as large [10]. This must, of course, be allowed for in roller coaster design, so that even these trains can make it safely back to the station.

How does the estimate from the photo agree with the comparison of train speed just after launch and just before the brakes?
2007-08-02 AMP