Marble RollerCoaster

In this post I’ll describe what I think was my first college project: a rollercoaster. My team and I finished it the night before the deadline and we had to work in the school’s common areas because we get kicked off the lab hahaha. Here is a video showing our work late at night and the final result.

                                               

Link to the youtube video.

Tips

From what I can remember, my general tips for building a rollercoaster in a cheap and easy way:

• Build the supports for your rails from wood, it is easy to cut and glue to fixed base. In this way you will not have to do extra soldering.
• If you decide to choose cooper wire to build your railways maybe you will find difficult in bending and keeping them in the form/shape you want. If this is case, fix one end to a press and stick the other end into a drill and set the RPMs to a low level to make the copper wire more malleable/ductile. You will notice that the longer you keep the wire turning it will turn easier to shape.
• From the materials I tried and the ones I saw my classmates using, I think an aluminum angle profile is the best way to go. You can bend them to make the shapes you want by making little straight cuts with a hacksaw in the angle corner of the aluminum, more or less as the red lines shown in the next picture.

                                                                   

• I ended up collecting some unused pipes from a hardware store, then cutting them in half with an electric chainsaw to make the rails. It is an easy way too, but the pipes are more difficult to bend to the shape you want. I used wood to make the base and the supports.

Interesting calculations on some components of a roller coaster

Ascendant and descendant slopes

A common force analysis is made in this type of railway as show in the next image.

This equation shows that the acceleration is proportional to the sine of the slope’s angle, so as the rollercoaster’s car goes down, the higher the slope the greater the acceleration. Same for when  it goes up hill, but since this acceleration is opposite to the direction of movement, it slows the car down.

Vertical loop

Vertical loops are very popular in rollercoasters. To make the car stay in the railway at the loop’s zenith, the centripetal acceleration has to be greater or equal to the acceleration due to gravity as the next diagram show. 

Based upon the free force diagram in Point C, the zenith, we compute the summatory of the forces. By convention, we consider the axis parallel to the acceleration to always positive.

When Nr=0,  as the railway does not exert any force on the car, the rollercoaster’s van attains the minimum velocity needed to reach the loop’s zenith. If the car had a speed lower than this, it could not make a complete loop. Thus, we compute this minimum velocity:

This relation can help us establish or adjust the radius of our loops in order for our marble, or whatever stuff you are using to simulate a rollercoaster, to complete the entire trajectory.  We just have to compute the velocity with which the marble enters the loop, and then solve for the radius in the previous equation. This velocity can be obtained using the conservation of energy law.

In actual rollercoasters, engineers do not make circular loops but clothoid loops in order to reduce the acceleration to which the riders are subjected to.