Amusement Park Ride: Ups and Downs in Design

Mechanical and civil engineers are involved in the design of roller coasters. Engineers must understand how the basic physics concepts of energy apply to successful roller coasters. The challenge is to make the roller coasters fast and fun, without compromising structural integrity, which is critical for ride safety.

After this activity, students should be able to:

• Identify situations in which kinetic energy is transformed into potential energy and vice versa.
• Identify key steps in the engineering design process.
• Model, test, evaluate and modify a design.
• Invent a product to meet a need.
• Create a prototype and final model, taking design criteria into consideration.
• Use science, math, and engineering principles to design and optimize a product.

The city of Wahoo wants to build a new roller coaster ride on their town common as part of the celebration of their 300th year. For consistency with the round number, they want a design to be as "loopy" as possible while keeping cost to a minimum. They are looking for engineering designs that optimize the ratio (material costs/inches of loop diameter) and are aesthetically pleasing (look good!). Every section of a roller coaster has different characteristics. Some portions have very light turns while others have more gentle curves and turns. Each scenario has its limits for whether or not it will work.

Background

Roller coasters at amusement parks utilize potential energy and kinetic energy. Typically, a motor pulls up the roller coaster car to gain its initial potential energy. Once at the peak point, no motors are connected to the car in any way. The car begins its winding and looping decent along a track that has been designed to safely convert potential energy into kinetic energy while making it a thrilling ride.

If the car goes through a loop-de-loop and does not have enough kinetic energy, it will not stay on the track as it reaches the peak of the loop. Kinetic energy is measured as KE=(mv²)/2, where m is the mass of the object and v is the velocity. Potential energy is measured as PE=mgh, where m is the mass, g is the gravitational force, and h is the distance above the reference point where the mass starts.

Ideally, all the potential energy is converted to kinetic energy, but in reality, this never holds true, since some of the energy is lost to friction. Because of the loss of energy, the peak of the loops must be lower than the initial starting point of the car. See Worksheet 3 for a reference diagram.

With the Students

Part 1: Preliminary Design and Testing

1. Show Worksheet 1: Reference Diagram (PDF) as an overhead transparency OR make copies and distribute as a student handout. Discuss the energy concepts illustrated on the worksheet.
2. Hand out Worksheet 2: Design and Building Guidelines (PDF) to all students. Review the task, design criteria and scoring.
3. Discuss the engineering design process (refer to the figure below) and how engineers use it to design structures like roller coasters.
4. Divide the class into groups of three students each.
5. Give each group 1 marble, a container to catch the marble, 1 foam piece, 1 toothpick, and a one-foot piece of masking tape.
6. Have each team design and test a preliminary prototype using the provided materials.
7. As they test, advise the groups to plan their final designs and the amount of materials that they will need. Have them sketch their ideas on paper and fill in quantities of materials on Worksheet 3: Cost and Evaluation Sheet (PDF).
8. After 20 minutes, have students return the materials from the preliminary prototypes and obtain the materials they listed on Worksheet 3 from the "store." If this is done at two separate class times, the materials can be ready for students when they arrive for the second meeting.

The steps of the engineering design process.CopyrightCopyright 2019 TeachEngineering.org. All rights reserved.

Part 2: Final Design and Testing

1. Permit additional materials to be purchased during the first phase of design and testing, about 30 minutes. Once materials have been obtained from the store, they may not be returned or exchanged.
2. Give teams 10 minutes to finalize their designs. Give each group 1 "P" sticker and 1 "K" sticker. Remind groups to use the stickers to mark the places on their roller coasters that have the greatest kinetic and potential energy.
3. When time is up, have groups step back from their roller coasters. Test each roller coaster individually by having a team member release the marble to run through it. Remember, each roller coaster must be able to stand alone and the marble must travel completely from start to finish. Permit at least two tries per coaster, though more testing can be done if time allows.
4. Identify an "aesthetic rating." Have each group look at all of the roller coaster designs and come up with an aesthetic rating, such as 1-6 if six groups, with 1 being the best. Based on the group responses, the leader announces the ratings.
5. Have groups measure the diameter of each loop in the roller coaster and total the cost of purchased materials in Worksheet 3.
6. Have students compute the loop diameter to cost ratio, then add the aesthetic ranking.
7. After all groups have completed the tests, come to a consensus as a class about the results. Lead a discussion on observations about effective and non-effective solutions. Was there a stronger design/construction that seemed to work? How did potential and kinetic energy play a role? Along with justifying the best design, did your group consider structural integrity? Is the ride safe?

Pre-Activity Assessment

Discussion: Observe student participation in class discussion on potential and kinetic energy.

Activity Embedded Assessment

Observation: Observe student participation and contribution within groups during the preliminary and final design stages.

Circumferece: Have students calculate the circumference of the loops (assuming they are true circles) using the measured diameter.

Post-Activity Assessment

Estimating Velocity: Have students estimate the velocity at the point where the kinetic energy is the highest (the lowest point of the track). Start by estimating the potential energy at the start (PE = m*g*h ) and then assume that all of this energy is converted to kinetic energy. Solve the equation KE = (1/2)mv² for the velocity. Note: if you set the two equal (m*g*h = (1/2) mv²), you do not need to measure the mass of the ball!

Graph: As a class, create a scatter plot of the maximum height of each track vs. calculated theoretical velocity. Discuss the relationship between the variables. 

Recap: Assign students to individually describe their roller coaster designs with sketches, explaining what worked and what did not work. Review their recaps to gauge their depth of comprehension.

Making Sense: Have students reflect about the science phenomena they explored and/or the science and engineering skills they used by completing the Making Sense Assessment (PDF).

Marden, Duane. Roller Coaster Database. A comprehensive, searchable database with information and statistics on 5,000+ roller coasters throughout the world. http://www.rcdb.com/