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
f.leslie@ieee.org; (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
 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 windblown 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?
 Renewable energy systems transform incoming solar energy and its
alternate forms (wind and river flow, etc.), usually without pollutioncausing 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)
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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
 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
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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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Economics
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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
 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
 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
 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
 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”
 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
http://acre.murdoch.edu.au/ago/ocean/wave.html
Ref.: www.fujita.com/archive-frr/ TidalPower.html
©1996 Ramage
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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
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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
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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
http://www.earthsci.org/esa/energy/wavpwr/wavepwr.html
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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
http://www.bfi.org/Trimtab/summer01/oceanWave.htm
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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 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)
 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
 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
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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
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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
 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)
 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
 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
http://www.bfi.org/Trimtab/summer01/oceanWave.htm
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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
Ref.: http://www.nrel.gov/otec/achievements.html
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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)
 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
 Energy trade-offs required to
make rational decisions
 PV is expensive ($4 to 5 per
Ref.: www.freefoto.com/
pictures/general/
windfarm/index.asp?i=2
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.:
http://www.energy.ca.gov/
education/story/storyimages/solar.jpeg
Photo of
FPL’s
Cape
Canaveral
Plant by
F. Leslie,
2001
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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
www.strawbilt.org/systems/ 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
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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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Conclusion
 Renewable energy offers a longterm 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.
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General:
 Sørensen, Bent. Renewable Energy, Second Edition. San Diego: Academic Press, 2000, 911 pp. ISBN 012-656152-4.
 Henry, J. Glenn and Gary W. Heinke. Environmental Science and Engineering. Englewood Cliffs: PrenticeHall, 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. 0-471-083569, 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 0-84931605-7, 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
 General:
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http://www.google.com/search?q=%22renewable+energy+course%22
http://www.ferc.gov/ Federal Energy Regulatory Commission
http://solstice.crest.org/
http://dataweb.usbr.gov/html/powerplant_selection.html
http://mailto:energyresources@egroups.com
http://www.dieoff.org. Site devoted to the decline of energy and effects upon population
 Tidal:
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http://www.unep.or.kr/energy/ocean/oc_intro.htm
http://www.bluenergy.com/technology/prototypes.html
http://www.iclei.org/efacts/tidal.htm
http://zebu.uoregon.edu/1996/ph162/l17b.html
 Waves:
 http://www.env.qld.gov.au/sustainable_energy/publicat/ocean.htm
 http://www.bfi.org/Trimtab/summer01/oceanWave.htm
 http://www.oceanpd.com/
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
http://www.newenergy.org.cn/english/ocean/overview/status.htm
http://www.energy.org.uk/EFWave.htm
 http://www.earthsci.org/esa/energy/wavpwr/wavepwr.html
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References: Internet
 Thermal:
 http://www.nrel.gov/otec/what.html
 http://www.hawaii.gov/dbedt/ert/otec_hi.html#anchor349152 on OTEC systems
 Wind:
 http://awea-windnet@yahoogroups.com. Wind Energy elist
 http://awea-wind-home@yahoogroups.com. Wind energy home powersite elist
 http://telosnet.com/wind/20th.html
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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
 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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