Roller Coaster Design Challenge

[Invisib1e]

Hello everyone,
My classmates and I have been assigned a project in which we are designing a miniature roller coaster as an interactive and engaging way to deepen our understanding of physics concepts while developing our critical thinking and hands-on skills.

Our physics teacher has provided us with a set of specific design parameters (outlined below), and we are seeking any advice or tips you might have on how to construct our roller coaster to achieve the maximum possible exit velocity while still meeting all the given requirements.

Any guidance or suggestions would be greatly appreciated. If you have any questions or need further details about the project, please feel free to ask. Thank you in advance for your support!

Design Criteria:
The scaled construction of your design is required to test your model roller coaster. The following design criteria must be followed to be considered:

• Create a scaled roller coaster that is self-standing.
• You can only use “tree-based” materials for this project; i.e., no metals or plastics.
• You cannot use pre-purchased building kits (i.e., LEGO, K-NEX, etc.).
• A marble, representing the roller coaster, will be provided on the testing day.
• The roller coaster must contain, at a minimum, one (1) initial hill and one (1) vertical loop.
• The initial hill cannot be larger than 0.7 m tall.
• The base of the roller coaster cannot have an area of greater than 0.3 m².

Goal:

• To have the provided marble reach the end of the track and obtain the greatest final exit velocity
• To verify the Law of Conservation of Energy.
• To demonstrate a knowledge of vectors, velocity, displacement, forces, energy, and other concepts learnt throughout the duration of the course.

 

[rb1957]

how big is the marble ? Can you get an example marble, so you can do some testing ? Friction is your enemy ...

 

[Gr8blu]

An internet search using the term "physics of roller coaster vertical loop" might give you some very useful results ...

One more thought: does rolling along a flat surface or slight downward incline result in higher "exit" speed - or does exiting the loop?

 

[rb1957]

one thought for the loop ... does the track need to be continuous ? could you launch the marble, and have it land on the other side of the loop (with less friction) ?

 

[rb1957]

what is the starting height ? or is this the "initial hill" (the marble starts at the top of the hill) ??

For a track I'd have 3 narrow pieces to constrain the position of the marble ... marble would ride on one and the other two would contact near the "horizontal" diameter (yes?)

 

[3DDave]

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[GregLocock]

Th optimum loop may not be circular.

 

[dvd]

Whether you incorporate the concepts of similitude and length and time scales, it would seem like some acknowledgment of how these might affect your design and results would be beneficial.

 

[IRstuff]

You can start with this Brachistochrone curve Wikipedia page, which supposedly gives you the fastest exit speed and then incorporate your loop into that curve

 

[Invisib1e]

what is the starting height ? or is this the "initial hill" (the marble starts at the top of the hill) ??

For a track I'd have 3 narrow pieces to constrain the position of the marble ... marble would ride on one and the other two would contact near the "horizontal" diameter (yes?)

Thank you for your interest in the project. The answers to all of your questions are:

• The starting height is the initial height of our marble which can range from 0-0.7m tall
• The size of our marble will be 16mm (0.63 inches) in diameter
• Track must be continuous and marble is not able to be launched across. The marble must be placed on the initial point and roll through all of the course without any external forces acting upon it ex.) pushing, blowing...

 

[GregLocock]

So, ignoring aero drag, m*g*h=1/2*m*v^2+integral F dx, and we want to maximise v. F is the friction force. So there's a tradeoff between minimizing F (ie low radial accelerations) and total path length. So a big part of the problem is deciding on the optimal shape and size of the loop. A big loop will minimise F, but increases the path length.

My lawyer tells me that there is no requirement that the path is of any particular horizontal dimension, or that the final velocity is expected to be horizontal, hence a dropped marble with a loop near the top will have the fastest exit speed, as there will be no friction while the marble is in freefall.

 

[waross]

I had to wonder;
Each marble has the same Ft:lb of energy, so should not the exit speeds be equal regardless of the transit time?
This video on exit speeds is interesting.
Exit speeds

 

[IRstuff]

I had to wonder;
Each marble has the same Ft:lb of energy, so should not the exit speeds be equal regardless of the transit time?
This video on exit speeds is interesting.
Exit speeds

That's answered by the Brachistochrone curve; this link has a video showing the results of different paths, particularly that the shortest path does not result in the fastest speed.

 

[GregLocock]

waross- yes I agree in the absence of friction etc then the shape of the path (ignoring the loop) is irrelevant. Brachistocrone is optimising for minimum total transit time, not exit velocty explicitly.

Personally I'd steal my grandson's Hotwheels and do some experiments rather than trying to solve it analytically.

 

[3DDave]

Providing that mgh + 1/2mv^2 = constant for a given starting point and starting speed, and neglecting friction, losses to displacing air, and the energy stored in the rotating of the marble, the main thing the Brachistochrone curve does is maximize the average speed of the item following it.

Since the goal is to confirm the students paid attention to the instruction given in class I would only supply two aids in this project.

The first is a suggestion to use cardboard for the track and cardboard tubes for the supports. For assembly I would use white or yellow waterbased glue. When I have done this with Elmer's white glue I turn the bottle over before opening the spout. Then squeeze firmly and twist the spout to open it until the glue barely comes out. Too often people pour on the glue as if more is better. In waterbased glue, more means more water has to evaporate or soak in which means the joint takes longer to dry. By applying a bead barely larger than a sewing needle in diameter, the water will be removed almost instantly on contact. Done right and this amount of glue can be used to join notebook paper together without causing it to wrinkle. If one needs a stronger joint, then come back with notebook paper and bridge the pieces of cardboard or, if even more strength is required, use additional cardboard. This applies to thin cardboard used as packaging as well as corrugated cardboard where the glue can be applied to each facing and the wavy part inside; it won't work so well to apply it to a cut made parallel to the corrugations. Give it some practice in applying less and less glue. I think you will find that an almost invisible amount is sufficient to initially hold parts in place.

And addition to the first suggestion is to get a plastic cutting mat from an art store and use a sharp knife or single-edged razor blade and a metal straightedge to ensure the joints have no gaps. Glue does a poor job of joining across gaps. While one might use hot-melt glue or epoxy to make up for this, they take too long to set up to make various experiments that are needed to see the effects of various changes.

The second is to make various experiments. You can build the track in sections with different slopes, different loop shapes, different runs to the end and then all that is needed is to vary the heights of the supports and the transitions between them. If you can build track quickly then you can run more experiments.

I'll give a third and final suggestion. Make a module for the end of the track a smooth curve upwards. Since 1/mv^2 => mgh when it gets to the end of the track, then the higher the marble gets, the greater the velocity it had when crossing the finish line.

This is a picture of a piece of card that is 0.020 inch/0.5 mm thick with an example amount of glue on it. More glue than this will slow the process. In case it isn't entirely clear, the black line in the middle is the edge of the card which is lit from the bottom side.

 

[waross]

In the video that I posted, a number of objects of differing mass were shot horizontally at varying speeds.
The velocity was gauged by the horizontal distance the object travelled before it dropped to the floor.
First demonstration:
The mass did not affect the horizontal distance to fall to the floor. eg: All of the objects at the same velocity followed the same drop trajectory.
Second demonstration:
The velocity at which the objects were shot did affect the horizontal distance to fall to the floor. eg: The horizontal speed did affect the horizontal distance to fall to the floor.
Third demonstration;
Four marbles were released simultaneously on four tracks of varying profile.
The transit time was different for each track profile, indicating different Average Speeds.
However all four marbles hit the floor at the same horizontal distance indicating equal exit speeds.

 

[3DDave]

You posted a link to a Google search; Google returns different answers to different people depending on their previous search history, so I saw no particular video.

I think this is what was supposed to be there;

 

[waross]

I think this is what was supposed to be there;

That's it. Thanks Dave.