Here is the final presentation for my PJAS Project 2011-2012. Not only does in include roller coasters, but was completely tested with K'Nex. My speech is included underneath each slide, but will not be verbatim to what I say; I will be memorizing the speech and will be presenting it tomorrow. This is almost exactly what I say. My meet in which I present this is tomorrow. This presentation/speech can not exceed 10 minutes, but must be well over 5 minutes. Today, my speech was exactly 9 minutes.
If anyone knows why I chose the colors for the slide, you'll get a cookie!!!! (I'll give you a hint: LaMbChOpZ )
Hopefully you may find this interesting, or maybe help you decide which inversion to choose if having a speed issue and why. Thanks for taking an interest!
Good morning, my name is Liam Chambers and I am in the 10th grade at Springfield High School. The title of my project is A Test of Inversions for a Roller Coaster.
This year I chose to do a continuation of my previous year's project that tested maintaining velocity in different loops, I’ve built with K’Nex from a young age, and I have a strong interested in roller coasters and the physics behind them.
I first researched what inversions are. Inversions are a type of element found on a roller coaster where the riders are turned upside down, then right side up again. Some of the most common elements are the Clothoid Loop, the Corkscrew, the Zero-G-Roll, and the Immelmann.
I chose these four inversions because I conducted an online poll to users who are fans of roller coasters. The Clothoid Loop and Corkscrew were already determined, so 49 users voted on which element would be the remaining two popular inversions. The 3rd inversion is the Zero-G-Roll; the 4th should be the Cobra Roll, but the complexity of building that element to scale and have the car travel through it realistically was not possible. Therefore, the final inversion to be tested is the Immelmann.
Friction is a force that opposes motion between objects, and a loss of energy simultaneously occurs. An example of this is between the wheels of the cars and the track that are constantly moving against each other. Kinetic Friction occurs again between the wheels and the track, but instead, it occurs while the car is in motion along the track. Velocity is expressed as the distance over time. Lateral Forces are forces that push and pull riders to the side of the car, perpendicular to normal force.
Normal Force is the force exerted upon an object in constant contact with another stable object perpendicularly. For example, when a car is on a straight piece of track parallel to the ground, it pushes down on the track with a weight of mg, the cars mass times the acceleration due to gravity. Since the car is not sinking through the track, there has to be an equal and opposite force pushing up on it, this is the normal force. Frictional Force is expressed as the Work of Non-Conservative Forces over the distance traveled. It describes how much energy is lost in a given amount of track.
The Law of Conservation of Energy that states the energy an object can possess will remain equal in the absence of non-conservative forces; a non-conservative force would be friction. It’s expressed as the sum of the Work of Non-Conservative Forces, the initial Potential Energy, and initial Kinetic Energy is equal to the sum of the final Potential and Kinetic Energy. Potential Energy is the energy the car possesses from height, and Kinetic Energy is the energy the car possesses from velocity.
The 4 diagrams represent different stages of a roller coaster’s circuit with the first diagram showing the car at the top of the lift hill, increasing potential energy as it gains height. At this point, the car’s potential energy is converted into kinetic energy as the car enters the element. When the car enters the element, most of the car’s potential energy has been converted into kinetic energy since it increased velocity but decreased its height. After the car’s kinetic energy is converted back into potential energy at the top of the inversion, it is once again converted back into Kinetic energy, with an increase in velocity as it exits the inversion. The sum of the Potential Energy and Kinetic Energy should remain equal, but because of non-conservative forces, this total decreases over time.
After researching, the following hypothesis was developed: If the tracks are tested, then the Clothoid Loop will maintain the highest final velocity because it minimizes the frictional force between the car and track. I believe this because the Clothoid Loop has the smallest amount of lateral forces due to its design, and will have the smallest frictional force compared to other elements.
The materials I used to conduct this experiment are K’Nex parts, a 4 car train and 3.5 centimeter fin, 2 photogates, a digital timer, and a tape measure.
These were the steps taken to build the procedure. One thing I would like to note is that the lift hill, drop, and brake run were kept constant in my experiment.
This slide depicts the actual variables tested in my experiment: the Clothoid Loop, Corkscrew, Zero-G-Roll, and the Immelmann.
To test the experiment, establish the variable groups as the Clothoid Loop, the Corkscrew, the Zero-G-Roll, and the Immelmann. Then, gather materials and place the cars on the lift hill after installing the 3.5 centimeter fin to set off the photogates. Next, place photogates on the set up and start the trial by turning on the motor.
Record the times displayed on the digital timer and calculate the velocity for each trial. Then calculate the Potential Energy, Kinetic Energy, Normal Force, Work of Non-Conservative Forces, and Frictional Force for each inversion. Create graphs of the velocity, and then a table of values for a comparison. Then repeat steps 4 through 7 for each trial and step 8 and 9 for each variable group. Finally, analyze results and draw conclusions.
These are photos of my set up including an overview during testing and how the photogates are attached to my setup.
The title of the graph for the Clothoid Loop is distance versus time. On the X axis is the distance from start and on the Y axis is the velocity. This first section is where the car was being pulled up the lift hill, then where the car is released from the chain lift and enters the Clothoid Loop. This line represents the point of inverting in the Clothoid Loop, with the 1st half and 2nd half of the inversion, followed by the brake run.
Similar to the graph of the Clothoid Loop, the Corkscrew’s graph has the same general shape. One substantial difference is the varying velocities at the point of inverting. This could be caused from the excess room for the car to move laterally and vertically around the track. After retesting this section, the velocities were similar up to the thousandth decimal place.
The graph for the Zero-G-Roll also looks similar to the graph of the Corkscrew with the varying velocities. One point to notice is that the car’s velocity continues to slow down even after the car begins to un-invert and travel back down to ground level.
Finally, the graph for the Immelmann has the same general shape as the Clothoid loop, maintaining a very gradual change in velocity during the first half of the inversion, but as it begins to un-invert, the car seems to have more varying velocities, possibly due to the space for the car to move.
On the graph for the averages, you can see the velocity for the lift hill and drop are the same for all inversions, whereas the ending points of the graphs are all different. This has to do with keeping the elements to scale when compared to the cars. I will find the difference of each inversion by subtracting the value at the start of the inversion and the end of the inversion, depicted in the respective color of the graph that intersects that line. For example, the velocity difference for the Corkscrew is the difference from the start of the inversion to the blue line, representing the end of the inversion.
These are key equations used in this experiment that were also used on the following slide for a comparison.
This table shows the information needed to come to a conclusion, with the best value in yellow. The Immelmann has the smallest velocity difference between the start and end of each inversion, meaning it had the highest exit velocity. The Clothoid loop had a very close difference. These two elements and the Corkscrew and Immelmann have very similar differences because of the general shape of the inversions. The difference in Kinetic Energy also shows that my Immelmann had the smallest difference. The Work of Non-conservative Forces difference and the Frictional Force difference is the least for the Immelmann again, but one thing to notice is that the Normal Force and the Potential Energy difference is neither highlighted nor different. This is because they are the same for each inversion.
In this experiment, my hypothesis is unsupported because the Immelmann maintained a higher velocity and had the smallest frictional force. However, I do believe that there are a few reasons why. First, the inversions are not perfectly shaped and my entire set up was completely hand built with the possibility of human error. Also in this experiment, I learned that there are many other factors involved to come to a definite conclusion. I originally planned to focus on Velocity, Potential Energy, and Kinetic Energy, but research led me to include more factors to come to a conclusion. For next year, I would like to possibly test uncommon inversions.
Thank you for listening, are there any questions?
Edited by LaMbChOpZ, 29 October 2016 - 06:45 PM.
