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
.
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?