Fig.1:StructureofPZT,acrystalcommonlyusedforpiezoelectricapplications(Source:WikimediaCommons)

PiezoelectricRoadsinCaliforniaRexGarlandApril26,2013

SubmittedascourseworkforPH240,StanfordUniversity,Fall2012

Introduction

Alternative energy will become increasinglyimportantas fossil fuel supplies inevitably runoutor environmental damage sparks consumerawareness. The search for a viable energyalternativewillcontinueuntilthesealternativescanaddressthedynamicdemandsoftheelectricalgridandstoragelimitations.Piezoelectricdevices,usedfor harvesting the vibrational energy of roads andwalkways due to traffic, can produce electricalenergy that is predictable (based on trafficpatterns),andlocallystorable.

Piezoelectric devices generate electrical energybymeansofapiezoelectriccrystal.Thecrystal,placedabout 5 centimeters below the surface of theasphalt, slightlydeformswhenvehicles travel across the road, therebyproducing electrical current.ThesedeviceshavebeenimplementedbytheEastJapanRailwayCompany(underpedestriansubwaystation gates) and by Innowattech (under roads in Israel). Innowattech has advertised that thesedevices, if planted along a onekilometer stretch of road, could provide an average of 400 kW ofpower,enoughtopower162WesternU.S.homes.[1,2]Thesedatasuggestthatpiezoelectricenergyharvesting is a competitive, clean alternative energy source. In response to these findings, in 2011CaliforniastateassemblymanMikeGattoproposedAssemblyBill306todevelopthistechnologyforCalifornianroads.[3,4]However,itisunclearwhetherthedatatrulyreflectthephysicallimitationsofpiezoelectricenergyharvesting.

Capacity

Thegeneratingcapacityofpiezoelectricdevicescanbecrudelyoverapproximatedbyassumingthatthevibrationsintheroadarecausedbytrafficalone,andthateach"vibrationevent"fromonevehicleis independent of another (i.e. the vibrations are sufficiently dampened before the next vehiclepasses).Under these assumptions, the total energy harvested by piezoelectric devices along a onekilometerstretchisatmostthenumberofcarsthatpassmultipliedbythevibrationalenergythatonecartransferstotheroad.Thisvibrationalenergycanbeoverapproximatedbytheenergythateachcarconsumesandputs tomechanicalworkacross thisstretch.Inotherwords, theenergyacarlosestovibrations in asphalt must be less than the energy a car puts to mechanical work over the onekilometerstretch.Thisvaluecanbecomputedbymultiplyingtheenergyconsumedfromgasolinebythermalefficiency.

ExpendedEnergy = (GasolineUsed)(EnergyDensityofGasoline)(ThermalEfficiency)

= 1km0.621mi/km2.8kg/gal4.43107J/kg0.4

20mi/gal

= 1.54MJ

This overestimation provides an appropriate upper bound to the amount of energy absorbed bypiezoelectricdevicesfromonecarmovingacrossaonekilometerstrip(i.e.nomorethan1.5MJ).Ofcourse, someof this "mechanical" (i.e.nonthermal) energy is lost asvarious formsof friction andused for other processes inside the vehicle (such as air conditioning), and not nearly all of thevibrationalenergywillbeabsorbedbythedevicesintheroad.Ifthedevicesareembeddedonabusystreet,thensuchastreetwillgenerateatmostthisamountofenergymultipliedbythenumberofcarsmoving across the street. If such a street or highway sees an average of 600vehicles per hour (asassumedbyInnowattech),thentheenergyprovidedbythesedevicesonaonekilometerstretchcouldpower at most 105 WesternU.S. homes (with a total of 257 kW). [1,2] If the calculation wererepeatedforonly18wheelers(withabout5mpg), themaximumamountofhomesaonekilometerstripcouldpowerwouldincreaseto421homes(with1MW).

However,amorereasonableapproximationcanbemadebyusingthefactthatapproximately5%oftheenergyconsumedbythecarislostasrollingfriction,althoughrollingfrictionaccountsforbothinternalfrictioninthewheelsandfrictionduetotheasphalt.[5]Byreplacingthermalefficiencyintheaboveequationwith5%, theamountofenergy released into theground forone20mpgcarwoulddecreaseto0.19MJ.Thisonekilometerstripcouldthenpoweratmost13homes(32kW)forthe20mpg car, or 52 homes (128 kW) for an 18wheeler. For this calculation, there is still a majorassumptionthatallthevibrationalenergyoftheroadiscapturedbypiezoelectricdevices.

It isnotclearwhether thenumberscurrentlyused toquantifygeneratingcapacityaremisguidedorsimplymisreported,butunder theoptimisticassumptionsstatedabove,piezoelectricdevicesover aonekilometerstripofroadwillgeneratepowerforonlyabout15homes.Unlesstheroadcarriesonly5mpgvehicles(ormanymorethan600vehiclesperhour),itisunlikelythatanywherenear400kWofpowercanbegeneratedfromonekilometer.

Profitability

Withthepriceofgasolinehoveringaround$4agallonforthepastyear,thecostofdrivinga20mpgcaracrossonekilometerisabout$0.124.AndbyrecentretailpricesofresidentialelectricityontheWestCoast,the0.19MJgeneratedbyonecarcostsabout$0.0064,oraboutonetwentieththecostofthegasolineburnedacrossthisonekilometerstrip.[6]Atthisrate,theroadwillgeneratearevenueof$33,565peryear.

Asanapproximate,thepriceofapiezoelectricdevicecanbeestimatedbyitsmostexpensiveelement,namelythepiezoelectriccomponent.Thiscomponent,accordingtoInnowattech'spatent,iscomprisedof about 50% leadzirconate titanate (PZT) ceramic and is about 14142 cm3 in dimension. [7]Giventhatpiezoelectricsheetsofthesamematerialcurrentlycost$165inbulkfromPiezoSystems(for100sheetsof10.64cm3each),thecostpercm3ofthismaterialisabout$0.155.Sincethedevicesareembedded30cmapartfromeachotherandintworowsperlane,akilometerofatwowaystreetwillcontain13,333devices,eachdevicecosting$30.39,addingtoatotalof$405,253.Evenwithoutconsidering themanufacturing or installation costs, itwould take about 12 years to earn back thisamountfromthedevicerevenue.

Conclusion

Generating capacity and profitability are two important factors to consider in choosing this energyalternative.There is currently a significant capon thegenerating capacity.Net profitswill onlybeseen after at least 12 years, as an underestimate. There are also many more "costs," besides thefinancial costs of manufacturing and installation, to take into account, such as the environmentalimpactofmanufacturingthePZTceramicsusedinInnowattech'sdevices.Whilepiezoelectricdevicesaregainingpopularity,theyarelesscapablethanpreviouslyclaimedbecauseofphysicallimitations.

RexGarland.Theauthorgrantspermissiontocopy,distributeanddisplay thiswork inunalteredform,with attribution to the author, for noncommercial purposes only. All other rights, includingcommercialrights,arereservedtotheauthor.

References

[1] K. Diamond, "Climate Change, Sustainable Development, and Ecosystems CommitteeNewsletter,"AmericanBarAssociation,July2009.

[2]"AnnualEnergyReview2011,"U.S.EnergyInformationAdministration,DOE/EIA0384(2011),September2012.

[3]"AssemblyBillNo.306,"CaliforniaLegislature,9Feb11.

[4]"LegislativeIndexandTableofSectionsAffected,"CaliforniaLegislature,30Nov12.

[5] A. Bandivadekar et al., "On The Road In 2035: Reducing Transportation's PetroleumConsumptionAndGHGEmissions,"MassachusettsinstituteofTechnology,LFEE200805RP,July2008.

[6]"ElectricPowerMonthlywithData forAugust2012,"U.S.Energy InformationAdministration,October2012.

[7]H.Abramovichetal., "PowerHarvestingFromRailwayApparatus,SystemandMethod,"U.S.Patent7812508,12Oct10.