1. “It is pleasant, when the sea is high and the winds are dashing the waves about, to watch from shore the struggles of another.” Lucretius, 99-55 B.C. An Introduction to Wave and Tidal Energy Frank R. Leslie, BSEE, MS Space Technology 5/25/2002, Rev. 1.7 fleslie @fit.edu; (321) 674-7377 www.fit.edu/~fleslie f.leslie @ieee.org; (321) 768-6629 Renewable Energy in (and above) the Oceans

2. 15.O Overview of Ocean Energy lOcean energy is replenished by the sun and through tidal influences of the moon and sun gravitational forces lNear-surface winds induce wave action and cause wind- blown currents at about 3% of the wind speed lTides cause strong currents into and out of coastal basins and rivers lOcean surface heating by some 70% of the incoming sunlight adds to the surface water thermal energy, causing expansion and flow lWind energy is stronger over the ocean due to less drag, although technically, only seabreezes are from ocean energy 1.0 020402

3. 15. Available Energy lPotential Energy: PE = mh lKinetic Energy: KE = ½ mv 2 or ½ mu 2 lWave energy is proportional to wave length times wave height squared (LH 2 )per wave length per unit of crest length ŸA four-foot (1.2 m), ten-second wave striking a coast expends more than 35, 000 HP per mile of coast [Kotch, p. 247] lMaximum Tidal Energy, E = 2HQ x 353/(778 x 3413) = 266 x 10 -6 HQ kWh/yr, where H is the tidal range (ft) and Q is the tidal flow (lbs of seawater) lE = 2 HQ ft-lb/lunar day (2 tides) or E = 416 x 10 -4 HV kWh, where V is cubic feet of flow 1.2 020412

4. 15. Ocean Energy lThe tidal forces and thermal storage of the ocean provide a major energy source lWave action adds to the extractable surface energy lMajor ocean currents (like the Gulf Stream) may be exploited to extract energy with underwater rotors (turbines) lThe oceans are the World’s largest solar collectors (71% of surface) lThermal differences between surface and deep waters can drive heat engines lOver or in proximity to the ocean surface, the wind moves at higher speeds over water than over land roughness 2.0 020329

5. 15. Wave Energy lEnergy of interchanging potential and kinetic energy in the wave lCycloidal motion of wave particles carries energy forward without much current lTypical periodicities are one to thirty seconds, thus there are low-energy periods between high-energy points lIn 1799, Girard & son of Paris proposed using wave power for powering pumps and saws lCalifornia coast could generate 7 to 17 MW per mile [Smith, p. 91] 2.0 020402

6. 15. Ocean Energy: Wave Energy lWave energy potential varies greatly worldwide Source: Wave Energy paper. IMechE, 1991 and European Directory of Renewable Energy (Suppliers and Services) 1991 Figures in kW/m 2.0 20329

7. 15. Concepts of Wave Energy Conversion lChange of water level by tide or wave can move or raise a float, producing linear motion from sinusoidal motion lWater current can turn a turbine to yield rotational mechanical energy to drive a pump or generator ŸSlow rotation speed of approximately one revolution per second to one revolution per minute less likely to harm marine life ŸTurbine reduces energy downstream and could protect shoreline lArchimedes Wave Swing is a Dutch device [Smith, p. 91] 2.1 020402

8. 15. Salter “Ducks” lScottish physicist Prof. Stephen Salter invented “Nodding Duck” energy converter in 1970 lSalter “ducks” rock up and down as the wave passes beneath it. This oscillating mechanical energy is converted to electrical energy lDestroyed by storm lA floating two-tank version drives hydraulic rams that send pressurized oil to a hydraulic motor that drives a generator, and a cable conducts electricity to shore 2.2.1 020402 Ref.: www.fujita.com/archive-frr/ TidalPower.html ©1996 Ramage http://acre.murdoch.edu.au/ago/ocean/wave.html

9. 15. Fluid-Driven Wave Turbines lWaves can be funneled and channeled into a rising chute to charge a reservoir over a weir or through a swing-gate ŸWater passes through waterwheel or turbine back to the ocean ŸAlgerian V-channel [Kotch, p.228] lWave forces require an extremely strong structure and mechanism to preclude damage lThe Ocean Power Delivery wave energy converter Pelamis has articulated sections that stream from an anchor towards the shore ŸWaves passing overhead produce hydraulic pressure in rams between sections ŸThis pressure drives hydraulic motors that spin generators, and power is conducted to shore by cable Ÿ750 kW produced by a group 150m long and 3.5m diameter 2.2.2.1 020402

10. 15. Fluid-Driven Wave Turbines lDavis Hydraulic Turbines since 1981 ŸMost tests done in Canada Ÿ4 kW turbine tested in Gulf Stream lBlue Energy of Canada developing two 250 kW turbines for British Columbia lAlso proposed Brothers Island tidal fence in San Francisco Bay, California 1000 ft long by 80 ft deep to produce 15 – 25 MW lAustralian Port Kembla (south of Sydney) to produce 500 kW 2.2.2.1 020402

11. 15. Air-Driven Wave Turbines (Con’t) l A floating buoy can compress trapped air similar to a whistle buoy lThe oscillating water column (OWC) in a long pipe under the buoy will lag behind the buoy motion due to inertia of the water column lThe compressed air spins a turbine/alternator to generate electricity at $0.09/kWh 2.2.2.2 020402 The Japanese “Mighty Whale” has an air channel to capture wave energy. Width is 30m and length is 50 m. There are two 30 kW and one50 kW turbine/generators http://www.earthsci.org/esa/energy/wavpwr/wavepwr.html

12. 15. Air-Driven Wave Turbines lBritish invention uses an air-driven Wells turbine with symmetrical blades lIncoming waves pressurize air within a heavy concrete box, and trapped air rushes upward through pipe connecting the turbine lA Wavegen™, wave-driven, air compressor or oscillating water column (OWC) spins a two-way Wells turbine to produce electricity lWells turbine is spun to starting speed by external electrical power and spins the same direction regardless of air flow direction lEnergy estimated at 65 megawatts per mile 2.2.2.2 020402 http://www.bfi.org/Trimtab/summer01/oceanWave.htm Photo by Wavegen

13. 15. Ocean Energy: Tidal Energy lTides are produced by gravitational forces of the moon and sun and the Earth’s rotation lExisting and possible sites: ŸFrance: 1966 La Rance river estuary 240 MW station  Tidal ranges of 8.5 m to 13.5 m; 10 reversible turbines ŸEngland: Severn River ŸCanada: Passamaquoddy in the Bay of Fundy (1935 attempt failed) ŸCalifornia: high potential along the northern coast lEnvironmental, economic, and esthetic aspects have delayed implementation lPower is asynchronous with load cycle 3.1 020402

14. 15. Tidal Energy lTidal mills were used in the Tenth and Eleventh Centuries in England, France, and elsewhere lMillpond water was trapped at high tide by a gate (Difficult working hours for the miller; Why?) ŸRhode Island, USA, 18 th Century, 20-ton wheel 11 ft in diameter and 26 ft wide ŸHamburg, Germany, 1880 “mill” pumped sewage ŸSlade’s Mill in Chelsea, MA founded 1734, 100HP, operated until ~1980 ŸDeben estuary, Woodbridge, Suffolk, England has been operating since 1170 (reminiscent of “the old family axe”; only had three new handles and two new heads!) ŸTidal mills were common in USA north of Cape Cod, where a 3 m range exists [Redfield, 1980] ŸBrooklyn NY had tidal mill in 1636 [?] 3.1 020402

15. 15. Tidal Energy (continued) lPotential energy = S integral from 0 to 2H (ρgz dz), where S is basin area, H is tidal amplitude, ρ is water density, and g is gravitational constant yielding 2 S ρ gH 2 lMean power is 2 S ρ gH 2 /tidal period; semidiurnal better lTidal Pool Arrangements ŸSingle-pool empties on ebb tide ŸSingle-pool fills on flood tide ŸSingle-pool fills and empties through turbine ŸTwo-pool ebb- and flood-tide system; two ebbs per day; alternating pool use ŸTwo-pool one-way system (high and low pools) (turbine located between pools) 3.1 020402

16. 15. Tidal Water Turbines lCurrent flow converted to rotary motion by tidal current lTurbines placed across Rance River, France lLarge Savonius rotors (J. S. Savonius, 1932?) placed across channel to rotate at slow speed but creating high torque (large current meter) lHorizontal rotors proposed for Gulf Stream placement off Miami, Florida 3.2 020402

17. 15. Tidal Flow: Rance River, France l240 MW plant with 24, 10 MW turbines operated since 1966 lAverage head is 28 ft lArea is approximately 8.5 square miles lFlow approx, 6.64 billion cubic feet lMaximum theoretical energy is 7734 million kWh/year; 6% extracted lStorage pumping contributes 1.7% to energy level lAt neap tides, generates 80,000 kWh/day; at equinoctial spring tide, 1,450,000 kWh/day (18:1 ratio!); average ~500 million kWh/year lProduces electricity cheaper than oil, coal, or nuclear plants in France 3.3 020329

18. 15. Tidal Flow: Passamaquoddy, Lower Bay of Fundy, New Brunswick, Canada lProposed to be located between Maine (USA) and New Brunswick lAverage head is 18.1 ft lFlow is approximately 70 billion cubic feet per tidal cycle lArea is approximately 142 square miles lAbout 3.5 % of theoretical maximum would be extracted lTwo-pool approach greatly lower maximum theoretical energy lInternational Commission studied it 1956 through 1961 and found project uneconomic then lDeferred until economic conditions change 3.3 020329 [Ref.: Harder]

19. 15. Other Tidal Flow Plants under Study lAnnapolis River, Nova Scotia: straight-flow turbines; demonstration plant was to be completed in 1983; 20 MW; tides 29 to 15 feet; Tidal Power Corp.; ~$74M lExperimental site at Kislaya Guba on Barents Sea ŸFrench 400 kW unit operated since 1968 ŸPlant floated into place and sunk: dikes added to close gaps lSea of Okhotsk (former Sov. Union) under study in 1980 lWhite Sea, Russia: 1 MW, 1969 lMurmansk, Russia: 0.4 MW lKiansghsia in China 3.3 020402

20. 15. Other Tidal Flow Plants under Study (continued) lSevern River, Great Britain: range of 47 feet (14.5 m) calculated output of 2.4 MWh annually. Proposed at $15B, but not economic. lChansey Islands:20 miles off Saint Malo, France; 34 billion kWh per year; not economic; environmental problems; project shelved in 1980 lSan Jose, Argentina: potential of 75 billion kWh/year; tidal range of 20 feet (6m) lChina built several plants in the 1950s lKorean potential sites (Garolim Bay) 3.3 0203402

21. 15. Hydraulic Pressure Absorbers lLarge synthetic rubber bags filled with water could be placed offshore where large waves pass overhead ŸAlso respond to tides ŸA connecting pipe conducts hydraulic pressure to a positive displacement motor that spins a generator ŸThe motor can turn a generator to make electricity that varies sinusoidally with the pressure 4.0 020402 http://www.bfi.org/Trimtab/summer01/oceanWave.htm

22. 15. Ocean Thermal Energy: OTEC (Ocean Thermal Electric Conversion) lFrench Physicist Jacque D’Arsonval proposed in 1881 lGeorges Claude built Matanzos Bay, Cuba 22 kW plant in 1930 [Smith, p.94] lKeahole Point, Hawaii has the US 50 kW research OTEC barge system lOTEC requires some 36 to 40°F temperature difference between the surface and deep waters to extract energy lOpen-cycle plants vaporize warm water and condense it using the cold sea water, yielding potable water and electricity from turbines-driven alternators lClosed-cycle units evaporate ammonia at 78°F to drive a turbine and an alternator Ref.: http://www.nrel.gov/otec/achievements.html 5.0 020402 lHybrid cycle uses open-cycle steam to vaporize closed-cycle ammonia lChina also has experimented with OTEC

23. 15. Wind Energy Equations (also applies to water turbines) lAssume a “tube” of air the diameter, D, of the rotor ŸA = π D 2 /4 lA length, L, of air moves through the turbine in t seconds ŸL = u·t, where u is the wind speed lThe tube volume is V = A·L = A·u·t lAir density, ρ, is 1.225 kg/m 3 (water density ~1000 kg/m 3 ) lMass, m = ρ·V = ρ·A·u·t, where V is volume lKinetic energy = KE = ½ mu 2 6.1 020402

24. 15. Wind Energy Equations (continued) lSubstituting ρ·A·u·t for mass, and A = π D 2 /4, KE = ½·π/4·ρ·D 2 ·u 3 ·t lTheoretical power, P t = ½·π/4·ρ·D 2 ·u 3 ·t/t = 0.3927·ρ a ·D 2 ·u 3, ρ (rho) is the density, D is the diameter swept by the rotor blades, and u is the speed parallel to the rotor axis lBetz Law shows 59.3% of power can be extracted lP e = P t ·59.3%·ή r ·ή t ·ή g, where P e is the extracted power, ή r is rotor efficiency, ή t is transmission efficiency, and ή g is generator efficiency lFor example, 59.3%·90%·98%·80% = 42% extraction of theoretical power 6.1 020402

25. 15.C Conclusion lRenewable energy offers a long- term approach to the World’s energy needs lEconomics drives the energy selection process and short-term (first cost) thinking leads to disregard of long-term, overall cost lWave and tidal energy are more expensive than wind and solar energy, the present leaders lIncreasing oil, gas, and coal prices will ensure that the transition to renewable energy occurs lOffshore and shoreline wind energy plants offer a logical approach to part of future energy supplies 8.0 0201402

26. References: Books, etc. lGeneral: ŸSørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 0- 12-656152-4. ŸHenry, J. Glenn and Gary W. Heinke. Environmental Science and Engineering. Englewood Cliffs: Prentice- Hall, 728pp., 1989. 0-13-283177-5, TD146.H45, 620.8-dc19 ŸBrower, Michael. Cool Energy. Cambridge MA: The MIT Press, 1992. 0-262-02349-0, TJ807.9.U6B76, 333.79’4’0973. ŸDi Lavore, Philip. Energy: Insights from Physics. NY: John Wiley & Sons, 414pp., 1984. 0-471-89683-7l, TJ163.2.D54, 621.042. ŸBowditch, Nathaniel. American Practical Navigator. Washington:USGPO, H.O. Pub. No. 9. ŸHarder, Edwin L. Fundamentals of Energy Production. NY: John Wiley & Sons, 368pp., 1982. 0-471-08356- 9, TJ163.9.H37, 333.79. Tidal Energy, pp. 111-129. lWind: ŸPatel, Mukund R. Wind and Solar Power Systems. Boca Raton: CRC Press, 1999, 351 pp. ISBN 0-8493- 1605-7, TK1541.P38 1999, 621.31’2136 ŸGipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co., 1993. 0-930031-64-4, TJ820.G57, 621.4’5 ŸJohnson, Gary L, Wind Energy Systems. Englewood Cliffs NJ: Prentice-Hall, Inc. TK 1541.J64 1985. 621.4’5; 0-13-957754-8. lWaves: lSmith, Douglas J. “Big Plans for Ocean Power Hinges on Funding and Additional R&D”. Power Engineering, Nov. 2001, p. 91. lKotch, William J., Rear Admiral, USN, Retired. Weather for the Mariner. Annapolis: Naval Institute Press, 1983. 551.5, QC994.K64, Chap. 11, Wind, Waves, and Swell. lSolar: ŸDuffie, John and William A. Beckman. Solar Engineering of Thermal Processes. NY: John Wiley & Sons, Inc., 920 pp., 1991. 9.1 020402

27. References: Internet lGeneral: Ÿhttp://www.google.com/search?q=%22renewable+energy+course%22 Ÿhttp://www.ferc.gov/ Federal Energy Regulatory Commission Ÿhttp://solstice.crest.org/ Ÿhttp://dataweb.usbr.gov/html/powerplant_selection.html Ÿhttp://mailto:energyresources@egroups.com Ÿhttp://www.dieoff.org. Site devoted to the decline of energy and effects upon population lTidal: Ÿhttp://www.unep.or.kr/energy/ocean/oc_intro.htmhttp://www.unep.or.kr/energy/ocean/oc_intro.htm Ÿhttp://www.bluenergy.com/technology/prototypes.htmlhttp://www.bluenergy.com/technology/prototypes.html Ÿhttp://www.iclei.org/efacts/tidal.htmhttp://www.iclei.org/efacts/tidal.htm Ÿhttp://zebu.uoregon.edu/1996/ph162/l17b.html lWaves: Ÿhttp://www.env.qld.gov.au/sustainable_energy/publicat/ocean.htm Ÿhttp://www.bfi.org/Trimtab/summer01/oceanWave.htmhttp://www.bfi.org/Trimtab/summer01/oceanWave.htm Ÿhttp://www.oceanpd.com/http://www.oceanpd.com/ Ÿhttp://www.newenergy.org.cn/english/ocean/overview/status.htmhttp://www.newenergy.org.cn/english/ocean/overview/status.htm Ÿhttp://www.energy.org.uk/EFWave.htmhttp://www.energy.org.uk/EFWave.htm Ÿhttp://www.earthsci.org/esa/energy/wavpwr/wavepwr.html 9.2 020329

28. References: Internet lThermal: Ÿhttp://www.nrel.gov/otec/what.htmlhttp://www.nrel.gov/otec/what.html Ÿhttp://www.hawaii.gov/dbedt/ert/otec_hi.html#anchor349152 on OTEC systems lWind: Ÿhttp://awea-windnet@yahoogroups.com. Wind Energy elist Ÿhttp://awea-wind-home@yahoogroups.com. Wind energy home powersite elist Ÿhttp://telosnet.com/wind/20th.html 9.2 020329

29. Units and Constants lUnits: ŸPower in watts (joules/second) ŸEnergy (power x time) in watt-hours lConstants: Ÿ1 m = 0.3048 ft exactly by definition Ÿ1 mile = 1.609 km; 1m/s = 2.204 mi/h (mph) Ÿ1 mile 2 = 27878400 ft 2 = 2589988.11 m 2 Ÿ1 ft 2 = 0.09290304 m 2 ; 1 m 2 = 10.76391042 ft 2 Ÿ1 ft 3 = 28.32 L = 7.34 gallon = 0.02832 m 3 ; 1 m 3 = 264.17 US gallons Ÿ1 m 3 /s = 15850.32 US gallons/minute Ÿg = 32.2 ft/s 2 = 9.81 m/s 2 ; 1 kg = 2.2 pounds ŸAir density, ρ (rho), is 1.225 kg/m 3 or 0.0158 pounds/ft 3 at 20ºC at sea level ŸSolar Constant: 1368 W/m 2 exoatmospheric or 342 W/m 2 surface (80 to 240 W/m 2 ) Ÿ1 HP = 550 ft-lbs/s = 42.42 BTU/min = = 746 W (J/s) Ÿ1 BTU = 252 cal = 0.293 Wh = 1.055 kJ Ÿ1 atmosphere = 14.696 psi = 33.9 ft water = 101.325 kPa = 76 cm Hg =1013.25 mbar Ÿ1 boe (42- gallon barrel of oil equivalent) = 1700 kWh 9.3 020402

30. Energy Equations lElectricity: ŸE=IR; P=I 2 R; P=E 2 /R, where R is resistance in ohms, E is volts, I is current in amperes, and P is power in watts Ÿ Energy = P t, where t is time in hours lTurbines: ŸP a = ½ ρ A 2 u 3, where ρ (rho) is the fluid density, A = rotor area in m 2, and u is wind speed in m/s ŸP = R ρ T, where P = pressure (Nm -2 = Pascal) ŸTorque, T = P/ω, in Nm/rad, where P = mechanical power in watts, ω is angular velocity in rad/sec lPumps: ŸPm = gQ m h/ή p W, where g=9.81 N/kg, Q m is mass capacity in kg/s, h is head in m, and ή p is pump mechanical efficiency 9.4 020402