1 Introduction

You work for a small engineering consulting company. Your company has just won a brief contract from a consortium of home-owners in the small coastal settlement of Vanishing Bay in SW Victoria. The contract is to make a preliminary assessment of whether wave energy could allow the home owners to save their homes while providing a long-term income.

The home-owners live on a beach that is gradually being eroded by Southern Ocean swell. Estimates are that their land will be permanently flooded by the sea in roughly 10 years, making it completely worthless. Since everyone knows the properties are doomed, no-one will buy them and insurance companies have refused to insure them. They have to save enough money over the coming years to buy land on a nearby hill where they can rebuild (effectively, they must self-insure), but most cannot afford that.

The home-owners realised that they could generate and sell electricity from ocean waves that might reduce their self-insurance costs. Meanwhile, removing energy from the waves would slow down or even reverse the erosion rate, buying them more time to save the money. The formed a consortium, and with help from the local council, won a government grant to pay your company.

Your supervisor is a mechanical engineer but has no experience with wave calculations. Your supervisor contracted a coastal engineer for advice, resulting in the brief report in Appendix A. Your supervisor also paid a maritime engineer to suggest how you should calculate the power output and the annual cost of a wave-energy development, resulting in the report in Appendix B. Your company’s accountant has provided financial guidance in Appendix C.

2 Key data

The sea level is rising globally at about 0.0035 m per year. A wave-rider buoy (an instrument that measures waves) is located off Vanishing Bay in 30 m depth of water; its data give a significant wave height of Hm0 = 2.16 m at a frequency of 0.135 Hz. Measurements determined the rate of vertical elevation change of the beach is given by −0.001087H3 m0+0.010427 m/day, where Hm0 is the significant wave height. Today, the beach is only 15 m wide, from mean sea level to the properties’ boundary. The beach and seabed slope at a gradient of 0.05 for a distance of 20 km, then drops to the ocean floor. There are 44 properties, each occupying an average 15 m length of beachfront. The replacement land and house on the hill will cost each home-owner an average of $1.5 million. Electricity must be sold at or below the annual-average wholesale price of $450/MWh1. Multiple wave-energy converters cannot be installed closer than half a wavelength apart, from centre to centre.  

3 Questions your report must address

1. Can electricity sales from wave energy, minus development costs and self-insurance costs, deliver income to the consortium in the long term?

2. What is your preliminary design for the best wave-energy development to defend Vanishing Bay? 

You do not have to use any or all of Appendices A, B and C. These are guides. You are free to doubt the accuracy or relevance of Appendices A, B and C, make your own investigations and come up with your own data and formulae. However, you must use the Key Data in section 2 above and you must include a table with all the input data values you used, whether you used the data in Appendices A-C or better data you found yourself.

Appendix A and B