“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

f.leslie@ieee.org; (321) 768-6629

Renewable Energy in (and above) the Oceans

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?

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)

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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 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

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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

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

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

Figures in kW/m

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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

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Ref.: www.fujita.com/archive-frr/ TidalPower.html©1996 Ramage

http://acre.murdoch.edu.au/ago/ocean/wave.html

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

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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

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

2.2.2.2 020402http://www.bfi.org/Trimtab/summer01/oceanWave.htm

Photo by Wavegen

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 constantyielding 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

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

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

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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

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http://www.bfi.org/Trimtab/summer01/oceanWave.htm

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

Ref.: http://www.nrel.gov/otec/achievements.html

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Hybrid cycle uses open-cycle steam to vaporize closed-cycle ammonia

China also has experimented with OTEC

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 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.: www.freefoto.com/pictures/general/ windfarm/index.asp?i=2

Ref.: http://www.energy.ca.gov/education/story/story-

images/solar.jpeg

Photo of FPL’s Cape Canaveral Plant by F. Leslie, 2001 7.1 020315

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

www.strawbilt.org/systems/ details.solar_electric.html

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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

EnergyTransmission

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 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. 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

General: 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: 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/ 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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