Coaster Dynamics: Coaster Lab #8



Coaster Dynamics
Coaster Lab

Lesson #8:   Circular Motion:   Everything's Loopy

TOPICS:   Roller Coaster Loops and G Forces.

1.   Starting with the default track configuration in Coaster Dynamics, set the height of the first 2 elements to:

        Spiral Hill = 45 m
        Round Loop = 40 m.

Run the roller coaster ride and stop it after the car passes the Round Loop. Use the Coaster Lab feature to determine the velocity at the entrance to the Round Loop (ie., at Watchpoint 2).




2.   Using the following equations for centripetal force and the G force,

        Fc = (mv²)/(R)
        Fg = (Fc)/(mg)

calculate the loop height that would have a maximum force (at the entrance point) of 5.0 G's.

Set the Round Loop height to your calculated value, and run the ride again. What is the G force at the top of the loop (ie., Watchpoint 6)?


















3.   When designing a loop, it's desirable to have the centripetal force at the top of the loop -1.0 G (or greater magnitude) so that the riders will be held firmly in their seats while they're upside down (the centripetal force is pointing downward, and thus negative). If the force at the top of the loop is near zero, the riders would fall out of their seats if no seatbelts were used. If the force is -1.0 G, the riders would seem to "float" on their seats, and if -2.0 G's, the riders would be pushed into their seats with a magnitude equal to their normal weight. While maintaining the force at the top of the loop, you must also avoid large forces of magnitude 5 G's or more at the bottom (or bones/eyeglasses may get broken).

For the Round Loop above, why is it not possible to achieve -1.0 G at the top and less than 5.0 G's at the bottom simultaneously?











4.   Change the Round Loop of Module 2 to a Teardrop Loop, and set its height equal to the same value you used in Part 2.

Run the ride again, and determine the G forces at the entrance and at the top of the loop.










5.   Why is the Teardrop Loop preferable to the Round Loop?
      What would you do to improve the loop design even more?


















NOTE:   On your next visit to an amusement park, or the next time you see a picture or film of a roller coaster, look very carefully at the shape of the loops. This geometric shape has a special name... called a klothoid (sometime also spelled clothoid). All real roller coasters use loops shaped like this. What makes this shape preferable to the Round and Teardrop Loops modeled in Coaster Dynamics?
















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