(Courtesy  the Center for Innovation in Engineering and Science Education, Stevens Institute of Technology). Level: grades 6-12.

Overview

In this activity for grades 6-12, students design a seawall to protect a major coastal highway from erosion by ocean waves and address these questions: Erosion–can you fight it? How much energy is involved with waves and erosion? Can humans stop erosion of the shoreline? Should we? Is it cost effective?

Procedure

Problem Statement
Your engineering team has been charged to submit a bid for a design for a 600 meter seawall to protect a major coastal highway. Your team must design the wall right at the edge of the water. The structure must be able to withstand the impact of the ocean waves. You cannot spend any more money on the project than is necessary, so it is crucial that the team know what materials can be used in construction and how much each material will cost. It is also important to know that there will be no funding available for beach nourishment (replenishment) in the future. Your team will have to give a 10 minute presentation on the seawall design and submit the bid to the Project Manager (teacher).

1. To determine the amount of wave energy, use an equation to calculate the amount of energy based on the height of a wave. First, determine the amount of energy for every square meter of wave, the energy (joules) is equal to 1260.6 times the square of the wave height.

Wave Energy = 1260.6 (Wave Height)2

2. To determine the Total Energy in a wave, calculate the total surface area of the wave and multiply that by the wave energy.

Total Energy = Wave Energy (surface area of wave)

For example, calculate the energy for an average open water wave that is 2 meters high, 7 meters wide and 500 meters long:

Wave Energy = 1260.6 (Wave Height)2
Wave Energy = 1260.6 (2)m2
Wave Energy = 1260.6 (4)m2
Wave Energy = 5042.4 Joules/m2

Total Energy = Wave Energy (surface area of wave)
Total Energy = Wave Energy (7 meters x 500 meters)
Total Energy = 5042.4 Joules/m2 (3,500m2)
Total Energy = 17,648,400 Joules or 1.76484 x 107 Joules

3. For this activity, the waves will be 8 meters wide, and the section of the seawall that the waves will hit is 300 meters long. Determine the highest water height for this month for this location.

4. Calculate the Total Energy of the wave.

5. Using the table of materials below, your team must design a wall to withstand the wave energy calculated above.

Note: The strength represents how much energy the material can absorb PER WAVE before it structurally fails. The Amount Needed column represents how much material needed to supply the stated strength. For example, a wall of 2,000 cubic meters of wood can absorb a maximum of 4 million joules from each wave that hits it.

6. One of the highest waves in recorded history for this site was 5 meters high. This wave occurred during an exceptionally large storm. Would this information change your design? If so, explain.

7. The following links may be of assistance for research: NOAA pictures of shoreline types; NOAA Beach Nourishment.

8. Using all of this information, create a bid for a design for the seawall project described in the Problem Statement.

Your team must create a 10 minute presentation on the seawall design and submit the bid to the Project Manager (teacher).

When preparing your project, your group might also want to consider if the project will be cost effective, possible alternatives, tourism dollars, etc.

Any mix of materials is allowable, but remember that your bid and presentation will be judged according to:

• calculations
• structural integrity
• projected longevity
• aesthetics
• environmental concerns
• cost

Additional Activity

Erosion Comic Strips: Choose one agent of erosion, and allow students to create a comic strip (handout) that shows the cause of the erosion, the results of the erosion, and the effect this has on humans. (combining art with science, using alternate literacy practices, valuing
creativity) Thanks to Christopher Young, a Robert Noyce Teacher Scholar at the University of Rochester.

Filed under: Class Activities, Grades 6-8, Grades 9-12

Tags: Marine engineering, Math Lesson Plans, Mathematics