Energy, Power, and Climate Change 8.8 Wave Power WAVES Common water waves are produced by the sun-driven winds passing over the water's surface. The height of the waves depends on the following three factors: The speed of the wind The duration of the wind The fetch FYI: The FETCH is thePower, length of the waterClimate over which the wind passes. Energy, and Change FYI: A NNE wind on Lake8.8 Michigan produces a much larger amplitude... Wave Power than a west wind. FETCH FYI: The course of the Edmund Fitzgerald on Lake Superior. Energy, Power, and Climate Change 8.8 Wave Power POWER IN A WATER WAVE A L The power of a water wave is complicated to calculate, so we'll simplify it some. Think of the crest as storage of potential energy, and the falling water as conversion into kinetic energy. FYI: The AVERAGE HEIGHT of theand water Climate is A / 2. Energy, Power, Change FYI: This much potential 8.8 energyWave is converted into kinetic energy each Power period T. POWER IN A WATER WAVE FYI: Power is energy per time: U FYI: Power is proportional to the SQUARE of the AMPLITUDE A. U Power is proportional to the WAVE SPEED V. Power is porportional to the LENGTH of the WAVEFRONT L. U U A = mgh = mgA/2 = VgA/2 = LAgA/2 A/2 L U = LgA2/2 = VT K = LgA2/2 K = VTLgA2/2 P = gVLA2 2 Power Generated By A Wave 3. FYI: The mass densityPower, of water is 1000 Energy, andkg/m Climate Change 8.8 Wave Power POWER IN A WATER WAVE Waves having an amplitude of 2 m roll onto a beach at a rate of one every 8 seconds. The wave crests are 75 meters apart. (a) What is the wave velocity? V = d/t = /T = 75/8 = 9.75 m/s (b) How much wave power is there, per unit length? P = gVLA2 2 2 2 gVA (1000)(10)(9.75)2 P / L = = 195 kW/m = 2 2 (c) How much wave power is there along 25 km of beach? P = (195 kW/m)L P = (195 kW/m)(25000 m) P = 4875 MW Energy, Power, and Climate Change 8.8 Wave Power POWER GENERATION FROM A WATER WAVE THE OSCILLATING WATER COLUMN Air Column - Compressed and rarefied by rising and falling wave. Wind Turbine Generator Turbine generates both ways FYI: A pelamis can generate 750 kW of power. Energy, Power, and Climate Change 8.8 Wave Power POWER GENERATION FROM A WATER WAVE THE PELAMIS The pelamis is named after the sea snake for obvious reasons. Each of four sections is hinged to the previous one. Fluid inside moves back and forth. The moving fluid drives a generator.