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An Introduction to Wave and Tidal Energy Renewable Energy in (and above) the Oceans Frank R. Leslie, BSEE, MS Space Technology 5/25/2002, Rev. 1.7; (321) 768-6629

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An Introduction to Wave and Tidal Energy

Renewable Energy in (and above) the Oceans

Frank R. Leslie,

BSEE, MS Space Technology

5/25/2002, Rev. 1.7; (321) 768-6629

“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.

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

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what s renewable energy
What’s renewable energy?
  • Renewable energy systems transform incoming solar energy and its alternate forms (wind and river flow, etc.), usually without pollution-causing combustion
  • This energy is “renewed” by the sun and is “sustainable”
  • Renewable energy is sustainable indefinitely, unlike long-stored, depleting energy from fossil fuels
  • Renewable energy from wind, solar, and water power emits no pollution or carbon dioxide
  • Renewable energy is “nonpolluting” since no combustion occurs (although the building of the components does in making steel, etc., for conversion machines does pollute during manufacture)

1.1 020302

renewable energy continued
Renewable Energy (Continued)
  • Fuel combustion produces “greenhouse gases” that are believed to lead to climate change (global warming), thus combustion of biomass is not as desirable as other forms
  • Biomass combustion is also renewable, but emits CO2 and pollutants
    • Biomass can be heated with water under pressure to create synthetic fuel gas; but burning biomass creates pollution and CO2
  • Nonrenewable energy comes from fossil fuels and nuclear radioactivity (process of fossilization still occurring but trivial)
    • Nuclear energy is not renewable, but sometimes is treated as though it were because of the long depletion period

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the eventual decline of fossil fuels
The eventual declineof fossil fuels
  • Millions of years of incoming solar energy were captured in the form of coal, oil, and natural gas; current usage thus exceeds the rate of original production
  • Coal may last 250 to 400 years; estimates vary greatly; not as useful for transportation due to losses in converting to liquid “synfuel”
  • We can conserve energy by reducing loads and through increased efficiency in generating, transmitting, and using energy
  • Efficiency and conservation will delay an energy crisis, but will not prevent it

1.1 020402

available energy
Available Energy
  • Potential Energy: PE = mh
  • Kinetic Energy: KE = ½ mv2 or ½ mu2
  • Wave energy is proportional to wave length times wave height squared (LH2)per wave length per unit of crest length
    • A four-foot (1.2 m), ten-second wave striking a coast expends more than 35, 000 HP per mile of coast [Kotch, p. 247]
  • Maximum 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)
  • E = 2 HQ ft-lb/lunar day (2 tides)or E = 416 x 10-4 HV kWh, where V is cubic feet of flow

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  • Cost of installation, operation, removal and restoration
  • Compare cost/watt & cost/watt-hour vs. other sources
  • Relative total costs compared to other sources
  • Externality costs aren’t included in most assessments
  • Cost of money (inflation) must be included (2 to 5%/year)
  • Life of energy plant varies and treated as linear depreciation to zero
  • Tax incentives or credits offset the hidden subsidies to fossil fuel and nuclear industry
  • Environmental Impact Statements (EIS) require early funding to justify permitting

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

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

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ocean energy wave energy
Ocean Energy: Wave Energy
  • Wave energy potential varies greatly worldwide

Figures in kW/m

Source: Wave Energy paper. IMechE, 1991 and European Directory of Renewable Energy (Suppliers and Services) 1991

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concepts of wave energy conversion
Concepts of Wave Energy Conversion
  • Change of water level by tide or wave can move or raise a float, producing linear motion from sinusoidal motion
  • Water current can turn a turbine to yield rotational mechanical energy to drive a pump or generator
    • Slow rotation speed of approximately one revolution per second to one revolution per minute less likely to harm marine life
    • Turbine reduces energy downstream and could protect shoreline
  • Archimedes Wave Swing is a Dutch device [Smith, p. 91]

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salter ducks
Salter “Ducks”
  • Scottish physicist Prof. Stephen Salter invented “Nodding Duck” energy converter in 1970
  • Salter “ducks” rock up and down as the wave passes beneath it. This oscillating mechanical energy is converted to electrical energy
  • Destroyed by storm
  • A 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

Ref.: TidalPower.html©1996 Ramage

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

fluid driven wave turbines14
Fluid-Driven Wave Turbines
  • Davis Hydraulic Turbines since 1981
    • Most tests done in Canada
    • 4 kW turbine tested in Gulf Stream
  • Blue Energy of Canada developing two 250 kW turbines for British Columbia
  • Also proposed Brothers Island tidal fence in San Francisco Bay, California 1000 ft long by 80 ft deep to produce 15 – 25 MW
  • Australian Port Kembla (south of Sydney) to produce 500 kW 020402

air driven wave turbines con t
Air-Driven Wave Turbines (Con’t)
  • A floating buoy can compress trapped air similar to a whistle buoy
  • The oscillating water column (OWC) in a long pipe under the buoy will lag behind the buoy motion due to inertia of the water column
  • The compressed air spins a turbine/alternator to generate electricity at $0.09/kWh

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 020402

air driven wave turbines
Air-Driven Wave Turbines
  • British invention uses an air-driven Wells turbine with symmetrical blades
  • Incoming waves pressurize air within a heavy concrete box, and trapped air rushes upward through pipe connecting the turbine
  • A Wavegen™, wave-driven, air compressor or oscillating water column (OWC) spins a two-way Wells turbine to produce electricity
  • Wells turbine is spun to starting speed by external electrical power and spins the same direction regardless of air flow direction
  • Energy estimated at 65 megawatts per mile

Photo by Wavegen 020402

ocean energy tidal energy
Ocean Energy: Tidal Energy
  • Tides are produced by gravitational forces of the moon and sun and the Earth’s rotation
  • Existing and possible sites:
    • France: 1966 La Rance river estuary 240 MW station
      • Tidal ranges of 8.5 m to 13.5 m; 10 reversible turbines
    • England: Severn River
    • Canada: Passamaquoddy in the Bay of Fundy (1935 attempt failed)
    • California: high potential along the northern coast
  • Environmental, economic, and esthetic aspects have delayed implementation
  • Power is asynchronous with load cycle

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

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tidal energy continued
Tidal Energy (continued)
  • Potential 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 gH2

  • Mean power is 2 S ρ gH2/tidal period; semidiurnal better
  • Tidal Pool Arrangements
    • Single-pool empties on ebb tide
    • Single-pool fills on flood tide
    • Single-pool fills and empties through turbine
    • Two-pool ebb- and flood-tide system; two ebbs per day; alternating pool use
    • Two-pool one-way system (high and low pools) (turbine located between pools)

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tidal water turbines
Tidal Water Turbines
  • Current flow converted to rotary motion by tidal current
  • Turbines placed across Rance River, France
  • Large Savonius rotors (J. S. Savonius, 1932?) placed across channel to rotate at slow speed but creating high torque (large current meter)
  • Horizontal rotors proposed for Gulf Stream placement off Miami, Florida

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tidal flow rance river france
Tidal Flow: Rance River, France
  • 240 MW plant with 24, 10 MW turbines operated since 1966
  • Average head is 28 ft
  • Area is approximately 8.5 square miles
  • Flow approx, 6.64 billion cubic feet
  • Maximum theoretical energy is 7734 million kWh/year; 6% extracted
  • Storage pumping contributes 1.7% to energy level
  • At neap tides, generates 80,000 kWh/day; at equinoctial spring tide, 1,450,000 kWh/day (18:1 ratio!); average ~500 million kWh/year
  • Produces electricity cheaper than oil, coal, or nuclear plants in France

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tidal flow passamaquoddy lower bay of fundy new brunswick canada
Tidal Flow: Passamaquoddy, Lower Bay of Fundy, New Brunswick, Canada
  • Proposed to be located between Maine (USA) and New Brunswick
  • Average head is 18.1 ft
  • Flow is approximately 70 billion cubic feet per tidal cycle
  • Area is approximately 142 square miles
  • About 3.5 % of theoretical maximum would be extracted
  • Two-pool approach greatly lower maximum theoretical energy
  • International Commission studied it 1956 through 1961 and found project uneconomic then
  • Deferred until economic conditions change

[Ref.: Harder]

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other tidal flow plants under study
Other Tidal Flow Plants under Study
  • Annapolis 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
  • Experimental site at Kislaya Guba on Barents Sea
    • French 400 kW unit operated since 1968
    • Plant floated into place and sunk: dikes added to close gaps
  • Sea of Okhotsk (former Sov. Union) under study in 1980
  • White Sea, Russia: 1 MW, 1969
  • Murmansk, Russia: 0.4 MW
  • Kiansghsia in China

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

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hydraulic pressure absorbers
Hydraulic Pressure Absorbers
  • Large synthetic rubber bags filled with water could be placed offshore where large waves pass overhead
    • Also respond to tides
    • A connecting pipe conducts hydraulic pressure to a positive displacement motor that spins a generator
    • The motor can turn a generator to make electricity that varies sinusoidally with the pressure

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ocean thermal energy otec ocean thermal electric conversion
Ocean Thermal Energy: OTEC (Ocean Thermal Electric Conversion)
  • French Physicist Jacque D’Arsonval proposed in 1881
  • Georges Claude built Matanzos Bay, Cuba 22 kW plant in 1930 [Smith, p.94]
  • Keahole Point, Hawaii has the US 50 kW research OTEC barge system
  • OTEC requires some 36 to 40°F temperature difference between the surface and deep waters to extract energy
  • Open-cycle plants vaporize warm water and condense it using the cold sea water, yielding potable water and electricity from turbines-driven alternators
  • Closed-cycle units evaporate ammonia at 78°F to drive a turbine and an alternator
  • Hybrid cycle uses open-cycle steam to vaporize closed-cycle ammonia
  • China also has experimented with OTEC


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wind energy equations also applies to water turbines
Wind Energy Equations(also applies to water turbines)
  • Assume a “tube” of air the diameter, D, of the rotor
    • A = π D2/4
  • A length, L, of air moves through the turbine in t seconds
    • L = u·t, where u is the wind speed
  • The tube volume is V = A·L = A·u·t
  • Air density, ρ, is 1.225 kg/m3 (water density ~1000 kg/m3)
  • Mass, m = ρ·V = ρ·A·u·t, where V is volume
  • Kinetic energy = KE = ½ mu2

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wind energy equations continued
Wind Energy Equations (continued)
  • Substituting ρ·A·u·t for mass, and A = π D2/4 , KE = ½·π/4·ρ·D2·u3·t
  • Theoretical power, Pt = ½·π/4·ρ·D2·u3·t/t = 0.3927·ρa·D2·u3, ρ (rho) is the density, D is the diameter swept by the rotor blades, and u is the speed parallel to the rotor axis
  • Betz Law shows 59.3% of power can be extracted
  • Pe = Pt·59.3%·ήr·ήt·ήg, where Pe is the extracted power, ήr is rotor efficiency, ήt is transmission efficiency, and ήg is generator efficiency
  • For example, 59.3%·90%·98%·80% = 42% extraction of theoretical power

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generic trades in energy
Generic Trades in Energy
  • Energy trade-offs required to make rational decisions
  • PV is expensive ($4 to 5 per watt for hardware + $5 per watt for shipping and installation = $10 per watt) compared to wind energy ($1.5 per watt for hardware + $5 per watt for installation = $6 per watt total)
  • Are Compact Fluorescent Lamps (CFLs) always better to use than incandescent?

Ref.: windfarm/index.asp?i=2


Photo of FPL’s Cape Canaveral Plant by F. Leslie, 2001

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energy storage
Energy Storage
  • Renewable energy is often intermittent, and storage allows alignment with time of use.
  • Compressed air, flywheels, weight-shifting (pumped water storage at Niagara Falls)
  • Batteries are traditional for small systems and electric vehicles; first cars (1908) were electric
  • Hydrogen can be made by electrolysis
  • Energy is best stored as a financial credit through “net metering”
    • Net metering requires a utility to bill at the same rate for buying or selling energy details.solar_electric.html

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energy transmission
  • Electricity and hydrogen are energy carriers, not natural fuels
  • Electric transmission lines lose energy in heat (~2% to 5%); trades loss vs. cost
  • Line flow directional analysis can show where new energy plants are required to reduce energy transmission
  • Hydrogen is made by electrolysis of water, cracking of natural gas, or from bacterial action (lab experiment level)
  • Oil and gas pipelines carry storable energy
    • Pipelines (36” or larger) can transport hydrogen without appreciable energy loss due to low density and viscosity
    • More efficient than 500 kV transmission line and is out of view

7.3 020402

legal aspects and other complications
Legal aspects and other complications
  • PURPA: Public Utility Regulatory Policy Act of 1978. Utility purchase from and sale of power to qualified facilities; avoided costs offsetting basis of purchases
  • Energy Policy Act of 1992 leads to deregulation
  • “NIMBYs” rally to shrilly insist “Not In My Backyard”!
  • Investment taxes and subsidies favor fossil and nuclear power
  • High initial cost dissuades potential users; future is uncertain
  • Lack of uniform state-level net metering hinders offsetting costs
  • Environmental Impact Statements (EIS) require extensive and expensive research and trade studies
  • Numerous “public interest” advocacy groups are well-funded and ready to sue to stop projects

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  • Renewable energy offers a long-term approach to the World’s energy needs
  • Economics drives the energy selection process and short-term (first cost) thinking leads to disregard of long-term, overall cost
  • Wave and tidal energy are more expensive than wind and solar energy, the present leaders
  • Increasing oil, gas, and coal prices will ensure that the transition to renewable energy occurs
  • Offshore and shoreline wind energy plants offer a logical approach to part of future energy supplies

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references books etc
References: Books, etc.
  • General:
    • Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 0-12-656152-4.
    • Henry, 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
    • Brower, Michael. Cool Energy. Cambridge MA: The MIT Press, 1992. 0-262-02349-0, TJ807.9.U6B76, 333.79’4’0973.
    • Di Lavore, Philip. Energy: Insights from Physics. NY: John Wiley & Sons, 414pp., 1984. 0-471-89683-7l, TJ163.2.D54, 621.042.
    • Bowditch, Nathaniel. American Practical Navigator. Washington:USGPO, H.O. Pub. No. 9.
    • Harder, 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.
  • Wind:
    • Patel, 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
    • Gipe, Paul. Wind Energy for Home & Business. White River Junction, VT: Chelsea Green Pub. Co., 1993. 0-930031-64-4, TJ820.G57, 621.4’5
    • Johnson, Gary L, Wind Energy Systems. Englewood Cliffs NJ: Prentice-Hall, Inc. TK 1541.J64 1985. 621.4’5; 0-13-957754-8.
  • Waves:
  • Smith, Douglas J. “Big Plans for Ocean Power Hinges on Funding and Additional R&D”. Power Engineering, Nov. 2001, p. 91.
  • Kotch, 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.
  • Solar:
    • Duffie, John and William A. Beckman. Solar Engineering of Thermal Processes. NY: John Wiley & Sons, Inc., 920 pp., 1991.

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references internet
References: Internet
  • General:
    • Federal Energy Regulatory Commission
    • Site devoted to the decline of energy and effects upon population
  • Tidal:
  • Waves:

9.2 020329

references internet36
References: Internet
  • Thermal:
    • on OTEC systems
  • Wind:
    • Wind Energy elist
    • Wind energy home powersite elist

9.2 020329

units and constants
Units and Constants
  • Units:
    • Power in watts (joules/second)
    • Energy (power x time) in watt-hours
  • Constants:
    • 1 m = 0.3048 ft exactly by definition
    • 1 mile = 1.609 km; 1m/s = 2.204 mi/h (mph)
    • 1 mile2 = 27878400 ft2 = 2589988.11 m2
    • 1 ft2 = 0.09290304 m2; 1 m2 = 10.76391042 ft2
    • 1 ft3 = 28.32 L = 7.34 gallon = 0.02832 m3; 1 m3 = 264.17 US gallons
    • 1 m3/s = 15850.32 US gallons/minute
    • g = 32.2 ft/s2 = 9.81 m/s2; 1 kg = 2.2 pounds
    • Air density, ρ (rho), is 1.225 kg/m3 or 0.0158 pounds/ft3 at 20ºC at sea level
    • Solar Constant: 1368 W/m2 exoatmospheric or 342 W/m2 surface (80 to 240 W/m2)
    • 1 HP = 550 ft-lbs/s = 42.42 BTU/min = = 746 W (J/s)
    • 1 BTU = 252 cal = 0.293 Wh = 1.055 kJ
    • 1 atmosphere = 14.696 psi = 33.9 ft water = 101.325 kPa = 76 cm Hg =1013.25 mbar
    • 1 boe (42- gallon barrel of oil equivalent) = 1700 kWh

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energy equations
Energy Equations
  • Electricity:
    • E=IR; P=I2 R; P=E2/R, where R is resistance in ohms, E is volts, I is current in amperes, and P is power in watts
    • Energy = P t, where t is time in hours
  • Turbines:
    • Pa = ½ ρ A2 u3, where ρ (rho) is the fluid density, A = rotor area in m2, and u is wind speed in m/s
    • P = R ρ T, where P = pressure (Nm-2 = Pascal)
    • Torque, T = P/ω, in Nm/rad, where P = mechanical power in watts, ω is angular velocity in rad/sec
  • Pumps:
    • Pm = gQmh/ήp W, where g=9.81 N/kg, Qm is mass capacity in kg/s, h is head in m, and ήp is pump mechanical efficiency

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