P A P E R S

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An experiment on wind energyVincenzo Lombardo1, Emilio Fiordilino1,Aurelio Agliolo Gallitto1,3 and Pasquale Aglieco2

1 Dipartimento di Fisica, Universita di Palermo, Via Archirafi 36, I-90123 Palermo, Italy2 Istituto Tecnico Industriale Statale ‘Alessandro Volta’, Passaggio dei Picciotti 1, I-90123Palermo, Italy

E-mail: aurelio.agliologallitto@unipa.it

AbstractWe discuss an experiment on wind energy performed with home-madeapparatus. The experiment reproduces a laboratory windmill, which canpump water from a lower level to a higher one. By measuring the gain of thegravitational potential energy of the pumped water, one can determine thepower extracted from the wind. The activity was carried out withhigh-school students, in the framework of the Italian National Plan forScientific Degrees—Physics. The proposed experiment allows teachers todiscuss renewable energy sources with students whose knowledge of physicsis limited to mechanics. It gives students the possibility to gain experiencewith energy and to increase their awareness of this renewable energy source.

Introduction

Wind energy has been exploited since prehistory,with early historical applications including sailingvessels and windmills [1]. Windmills were usedto pump water from at least the 9th century andwere later used extensively in Europe. Since the14th century, in the Netherlands windmills werebuilt to pump out the redundant water from thepolder, land reclaimed from the sea or riversand protected by dykes, to improve agriculturaldevelopment.

Early immigrants to the United States ofAmerica brought with them the technology ofwindmills from Europe; in 1930, an estimated600 000 units were in use, so that a multi-bladedwind turbine atop a bar-lattice tower was acharacteristic of the rural landscape [2].

Wind energy can be obtained everywhere;it is renewable and endless. However, it hasgained economic significance only recently and

3 Author to whom any correspondence should be addressed.

today one can see everywhere modern wind farmsthat transform the kinetic energy of wind intoelectric energy, based on the well known Faraday–Neumann–Lenz law. Wind turbines allow one tofulfil any energy need at any level of growth and tohelp significantly developing countries or isolatedcommunities, for whom the installation of mini-turbines is more convenient than extension of thenational electric grid [3].

The inclusion of wind energy topics in schoolprogrammes, as well as of other renewable-energy-source topics [4, 5], could give studentsthe possibility to gain experience with energy-supply systems and could raise their awareness ofthe benefits that can be obtained in daily life byusing renewable energy sources.

In this paper, we discuss an experimenton wind energy performed using home-madeapparatus and carried out with high-schoolstudents, during the activities of the ItalianNational Plan for Scientific Degrees—Physics.The activities were carried out with the aim

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Figure 1.of increasing the interest of young people inscientific studies [4–7]. Further activity carriedout with high-school students, as well assecondary-school students, has also been putforward, such as, for example, the so-called‘School adopts an experiment’ programme [8, 9].Here, we propose a quantitative experiment toexploit the wind’s kinetic energy to increase thepotential gravitational energy of some amount ofwater by pumping it from a lower level to a higherone.

Theoretical descriptionTo exploit wind energy, the kinetic energy ofmoving air, a wind turbine is necessary. This isa device that converts the kinetic energy fromthe wind into rotational mechanical energy. If themechanical energy is used to produce electricity,the device is often called a wind generator. If themechanical energy is used to drive machinery,such as for grinding grain or pumping water, thedevice is called a windmill or wind pump [10].

In order to explain the physical origin of thewind energy, let us consider an air flux tube inwhich a blade rotor is located, as illustrated infigure 1.

By applying Bernoulli’s equation betweentwo sections of the flow tube and considering theair as an ideal fluid, one has

p1 +12ρv2

1 + ρgh1 = p2 +12ρv2

2 + ρgh2, (1)

where p1, v1 and h1 are respectively the pressure,speed and height of the fluid in the section infront of the rotor; p2, v2 and h2 are respectivelythe pressure, speed and height of the fluid inthe section behind the rotor; ρ = m/V is the airdensity and g the gravitational acceleration; the

air density at atmospheric pressure, p0, and atroom temperature, T0 ≈ 20 ◦C, is ρ ≈ 1.2 kg m−3

(the density of water is ρw = 1000 kg m−3).In the presence of the rotor, part of the kinetic

energy of the air flow is extracted by the rotor.The extracted power P is given by the productof the extracted energy per volume unit times thevolume of air that flows through the rotor in thetime unit. By equating the kinetic energy of theair lost when it goes through the rotor with theenergy gained by the rotor [11], one easily obtainsthe following relation:

12ρSv(v2

1 − v22) = ρSv2(v1 − v2), (2)

which gives v = (v1 + v2)/2. From this analysis,it results that the velocity of the air at the planeof the rotor blades is always the averaged valueof the velocity of the upstream air and that of thedownstream air. Therefore, the extracted power is

P =Pnom

2

(1+

v2

v1

)2 (1−

v2

v1

), (3)

where we have defined the nominal theoreticalpower Pnom that can be extracted from the windas

Pnom =12ρSv3

1. (4)

The power that can be transferred from the windto the rotor as a function of the ratio v2/v1 isplotted in figure 2. The maximum power thatcan be transferred from the wind to the rotorsis obtained for v2 = v1/3, therefore the powerextracted from the wind is

Pmax =1627

12ρSv3

1 =1627 Pnom ≈ 0.59Pnom. (5)

The result of equation (5) is known asBetz’s law, from the German physicist AlbertBetz, who first formulated this law [12]. Thephysical interpretation of Betz’s law comes outfrom the fact that the air flowing through therotor cannot reduce its velocity to zero, because itmust maintain a constant flux (stationary air flow)and because otherwise it would accumulate justafter the rotor blades. All of the upstream windpower cannot be extracted by the rotor, as somepower is left in the downstream air that continuesto move with reduced speed. Consequently, thekinetic energy of the wind cannot be transferredcompletely to the rotor, but a part of it remains

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An experiment on wind energy

Figure 2.

for the air to escape from the rotor. This is atheoretical limit that cannot be overcome. It isworth noting that often it is convenient to definethe nominal energy flux as 8nom =

12ρv3 (v is the

wind velocity), which is measured in W m−2 inthe SI unit system.

So far, we have only considered the powerthat the rotor can ideally extract from the wind.However, during the energy conversion process,due to the mechanical movement of differentparts of the apparatus, friction wastes energy.Furthermore, parasitic aerodynamic effects, suchas turbulence and swirl, during the air flowthrough the rotor blades contribute to reduce theconversion efficiency. Finally, in our measure-ments the centrifugal pump has its own efficiencythat affects also the global energy conversionprocess. All these effects can be included in theaverage efficiency η of the apparatus, which isdefined as

η = Pe/Pnom, (6)

where Pe is the extracted power and Pnom isthe impinging power of the wind given byequation (4).

Modern wind turbines start working whenthe wind velocity is 4–5 m s−1, reach themaximum efficiency for a wind velocity of about10–15 m s−1 and stop when the wind velocityreaches values greater than 20–25 m s−1; theirefficiency ranges from about η ≈ 0.2 to aboutη ≈ 0.3.

Figure 3. A picture of the experimental apparatusconsisting of two fans, a small hydraulic pump and twowater tanks.

Experimental apparatus and results

To perform the experiment, we built a prototypeof a windmill by using two fans of 38 cm indiameter, a small hydraulic centrifugal pump andtwo five-litre water tanks. The primary fan isused to generate a useful air flow with controlledvelocity; it is powered by an electric motor withvariable angular velocity. The velocity of the windis measured by an anemometer with an accuracyof about 5% of the reading. The secondary fanis used to extract energy from the air flowingthrough it; it is connected to a small centrifugalhydraulic pump that pumps water from a tank,located at the same level as the pump, to anotherone located h = 1 m higher than the previous one.On the lateral surface of the latter tank, a scaleis marked that allows one to measure the volumeof pumped water as a function of time. Figure 3shows the experimental apparatus.

The experiment was performed by measuringthe quantity of water pumped as a function oftime at different wind velocities, which were set

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Figure 4.by changing the angular velocity of the primaryfan. Typical results are shown in figure 4.

Discussion and conclusionThe measurements performed allowed us todetermine the power extracted by the rotor fromthe wind. Considering that the height to whichthe water rises is h = 1 m, the gain in potentialenergy is 1U = ρwVgh = mgh (ρw is the waterdensity). The slope dU/dt indicates the rate atwhich the potential energy is gained; thereforefrom the slope of the 1U versus time curves wecan calculate the extracted power. Multiplying themeasured volume V of the pumped water by thefixed factor ρwgh one obtains the plots shownin figure 4; the slope of the best-fit curves givesthe extracted power. In figure 5, we report theextracted power as a function of the wind velocity.

In ‘Theoretical description’, we have foundthat the extracted power from the wind dependson the cubic power of the wind velocity.Therefore, we have fitted the experimental datawith the function f (v) = A+ Bv3. The theoreticalcurve is shown in figure 5. From the fitting oneobtains that our apparatus works for velocitiesgreater than 5.2 m s−1. This result is mainly dueto the presence of mechanical friction.

In order to evaluate the efficiency of theapparatus, we calculate the ratio between theextracted power and the corresponding idealpower of equation (4). The obtained efficiency isabout 5%, evaluated at v = 9 m s−1. At lower

Figure 5.velocities, the efficiency reduces and eventuallybecomes zero at v = 5.2 m s−1. For a practicalwind turbine, losses in efficiency are mainly dueto mechanical-power losses in the transmissionand pump systems, turbulence and swirl impartedby the rotor to the air flow and viscous drag on therotor blades.

In conclusion, we have carried out anexperiment on wind energy performed with ahome-made windmill to pump water from a lowerlevel to a higher one. This activity was carried outwith high-school students, aiming at exploitingthe wind energy to produce mechanical work bypumping water uphill.

We propose a simple but quantitativeexperiment, which can be addressed to studentsbeginning their studies on physics, with theirknowledge of physics limited to mechanics; thisconsideration suggested to us the developmentof suitable apparatus for measurement of theextracted wind energy by using the conceptof the mechanical potential energy gained bywater and not by involving concepts of electricalenergy. From the pedagogical point of view, thisfeature should not be overlooked; the feasibilityof the experiment is rather simple and allows theteacher to discuss renewable energy solely from amechanical point of view.

Finally, we suggest the inclusion of windenergy topics in school programmes to give stu-dents the possibility to gain experience with windenergy. Our aim is to stimulate physics teachersto explain this subject in their classrooms, to

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improve learning through experimental activitiesand increase students’ awareness of renewableenergy sources. Furthermore, we believe that thepresentation of the rather abstract concept ofenergy can benefit greatly from the use of topicslike that presented here and may be considered tobe of deep social impact by young pupils.

Acknowledgments

This work was carried out in the framework of theItalian National Plan for Scientific Degrees, underthe financial support of the Italian Ministry ofEducation, University and Research. The authorsthank V Mazzola for technical assistance.

Received 25 July 2012, in final form 3 August 2012doi:10.1088/0031-9120/47/6/755

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Vincenzo Lombardo is a student ofmathematics at the University of Pavia,Italy. He was awarded his mathematicsbachelor’s degree by the University ofPalermo, Italy, defending a thesis thatconcerned the preparation and realizationof the wind energy experiment.

Emilio Fiordilino teaches quantum andstatistical mechanics at the University ofPalermo, Italy. His research activitymainly concerns the physics of theinteraction of strong electromagneticfields with molecules and nanoparticles,but also volcanism. He spends part of histime lecturing on quantum mechanics inhigh schools. He is the author of aphysics book for secondary schools.

Aurelio Agliolo Gallitto is an associateprofessor of experimental physics at theUniversity of Palermo, Italy, and worksin the field of superconductivity atmicrowave frequencies. From 2008 to2010 he was the local coordinator of theItalian National Plan for ScientificDegrees. He is the author of a physicsbook for secondary schools.

Pasquale Aglieco is a secondary-schoolteacher of physics. He is involved in theactivities of the Italian National Plan forScientific Degrees—Physics, making avaluable contribution to the organizationof activities with schools.

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