BiosystemsEngineering(2006)95(1),3541doi:10.1016/j.biosystemseng.2006.06.007PMPowerandMachineryStrasseopeningfordroppingthepotatointoafurrowinthesoil.plantersareequippedwithtwoparallelrowsofcupsperbeltinsteadofone.DoublingthecuprowallowsARTICLEINPRESSparametersofmachineperformance.Highaccuracyofplantspacingresultsinhighyieldandauniformsortingandthus,ahighercapacityatthesameaccuracyisexpected.Capacityandaccuracyofplantspacingarethemaindoublethetravelspeedwithoutincreasingthebeltspeed1537-5110/$32.0035r2006IAgrE.AllrightsreservedThefunctioningofmostpotatoplantersisbasedontransportandplacementoftheseedpotatoesbyacup-belt.Thecapacityofthisprocessisratherlowwhenplantingaccuracyhastostayatacceptablelevels.Themainlimitationsaresetbythespeedofthecup-beltandthenumberandpositioningofthecups.Itwashypothesisedthattheinaccuracyinplantingdistance,thatisthedeviationfromuniformplantingdistances,mainlyiscreatedbytheconstructionofthecup-beltplanter.Todeterminetheoriginofthedeviationsinuniformityofplacementofthepotatoesatheoreticalmodelwasbuilt.Themodelcalculatesthetimeintervalbetweeneachsuccessivepotatotouchingtheground.Referringtotheresultsofthemodel,twohypotheseswereposed,onewithrespecttotheeffectofbeltspeed,andonewithrespecttotheinfluenceofpotatoshape.Aplanterunitwasinstalledinalaboratorytotestthesetwohypotheses.Ahigh-speedcamerawasusedtomeasurethetimeintervalbetweeneachsuccessivepotatojustbeforetheyreachthesoilsurfaceandtovisualisethebehaviourofthepotato.Theresultsshowedthat:(a)thehigherthespeedofthecup-belt,themoreuniformisthedepositionofthepotatoes；and(b)amoreregularpotatoshapedidnotresultinahigherplantingaccuracy.Majorimprovementscanbeachievedbyreducingtheopeningtimeatthebottomoftheductandbyimprovingthedesignofthecupsanditspositionrelativetotheduct.Thiswillallowmoreroomforchangesinthecup-beltspeedswhilekeepingahighplantingaccuracy.r2006IAgrE.AllrightsreservedPublishedbyElsevierLtd1.IntroductionThecup-beltplanter(Fig.1)isthemostcommonlyusedmachinetoplantpotatoes.Theseedpotatoesaretransferredfromahoppertotheconveyorbeltwithcupssizedtoholdonetuber.Thisbeltmovesupwardstoliftthepotatoesoutofthehopperandturnsovertheuppersheave.Atthispoint,thepotatoesfallonthebackofthenextcupandareconfinedinasheet-metalduct.Atthebottom,thebeltturnsovertheroller,creatingtheofthetubersatharvest(McPheeetal.,1996；Pavek&Thornton,2003).Fieldmeasurements(unpublisheddata)ofplantingdistanceinTheNetherlandsrevealedacoefficientofvariation(CV)ofaround20%.EarlierstudiesinCanadaandtheUSAshowedevenhigherCVsofupto69%(Misener,1982；Entz&LaCroix,1983；Sieczkaetal.,1986),indicatingthattheaccuracyislowcomparedtoprecisionplantersforbeetormaize.Travellingspeedandaccuracyofplantingshowaninversecorrelation.Therefore,thepresentcup-beltAssessmentoftheBehaviourofH.Buitenwerf1,2；W.B.Hoogmoed1FarmTechnologyGroup,WageningenUniversity,P.Oe-mailofcorrespondingauthor:2KroneGmbH,Heinrich-Krone3IB-Lerink,LaanvanMoerkerken85,3271AJ4InstituteofAgriculturalEngineering,University(Received27May2005；acceptedinrevisedformPotatoesinaCup-beltPlanter1；P.Lerink3；J.Muller1,4Box.17,6700AAWageningen,TheNetherlands；willem.hoogmoedwur.nl10,48480Spelle,GermanyMijnsheerenland,TheNetherlandsofHohenheim,D-70593Stuttgart,Germany20June2006；publishedonline2August2006)PublishedbyElsevierLtdforhandlingandtransporting.Manyshapefeatures,usuallycombinedwithsizemeasurements,canbedistinguished(Du&Sun,2004；Taoetal.,1995；Zodler,1969).IntheNetherlandsgradingofpotatoesismostlydonebyusingthesquaremeshsize(Koningdeetal.,1994),whichisdeterminedonlybythewidthandheight(largestandleastbreadth)ofthepotato.Forthetransportprocessesinsidetheplanter,thelengthofthepotatoisadecisivefactoraswell.ARTICLEINPRESSH.BUITENWERFETAL.36Theobjectiveofthisstudywastoinvestigatethereasonsforthelowaccuracyofcup-beltplantersandtousethisknowledgetoderiverecommendationsfordesignmodifications,e.g.inbeltspeedsorshapeand78910Fig.1.Workingcomponentsofthecup-beltplanter:(1)potatoesinhopper；(2)cup-belt；(3)cup；(4)uppersheave；(5)duct；(6)potatoonbackofcup；(7)furrower；(8)roller；(9)releaseopening；(10)groundlevel564321numberofcups.Forbetterunderstanding,amodelwasdeveloped,describingthepotatomovementfromthemomentthepotatoenterstheductuptothemomentittouchestheground.Thus,thebehaviourofthepotatoatthebottomofthesoilfurrowwasnottakenintoaccount.Asphysicalpropertiesstronglyinfluencetheefficiencyofagriculturalequipment(Kutzbach,1989),theshapeofthepotatoeswasalsoconsideredinthemodel.Twonullhypotheseswereformulated:(1)theplantingaccuracyisnotrelatedtothespeedofthecup-belt；and(2)theplantingaccuracyisnotrelatedtothedimensions(expressedbyashapefactor)ofthepotatoes.Thehypothesesweretestedboththeoreticallywiththemodelandempiricallyinthelaboratory.2.Materialsandmethods2.1.PlantmaterialSeedpotatoesofthecultivars(cv.)Sante,ArindaandMarfonahavebeenusedfortestingthecup-beltplanter,becausetheyshowdifferentshapecharacteristics.TheshapeofthepotatotuberisanimportantcharacteristicThefieldspeedandcup-beltspeedcanbesettoachievetheaimedplantspacing.Thefrequencyfofpotpotatoesleavingtheductatthebottomiscalculatedasfpotvcxc(2)wherevcisthecup-beltspeedinmsC01andxcisthedistanceinmbetweenthecupsonthebelt.TheangularspeedoftherollerorinradsC01withradiusrrinmiscalculatedasorvcrr(3)Table1ShapecharacteristicsofpotatocultivarsandgolfballsusedintheexperimentsCultivarSquaremeshsize,mmShapefactorSante2835146Arinda3545362Marfona3545168Golfballs42C18100AshapefactorSbasedonallthreedimensionswasintroduced:S100l2wh(1)wherelisthelength,wthewidthandhtheheightofthepotatoinmm,withhowol.Asareference,alsosphericalgolfballs(withaboutthesamedensityaspotatoes),representingashapefactorSof100wereused.ShapecharacteristicsofthepotatoesusedinthisstudyaregiveninTable1.2.2.MathematicalmodeloftheprocessAmathematicalmodelwasbuilttopredictplantingaccuracyandplantingcapacityofthecup-beltplanter.Themodeltookintoconsiderationradiusandspeedoftheroller,thedimensionsandspacingofthecups,theirpositioningwithrespecttotheductwallandtheheightoftheplanterabovethesoilsurface(Fig.2).Itwasassumedthatthepotatoesdidnotmoverelativetothecuporrotateduringtheirdownwardmovement.ThetimeoffreefalltfallinsiscalculatedwithARTICLEINPRESSASSESSMENTOFTHEBEHAVIOUROFPOTATOES37Thegapintheducthastobelargeenoughforapotatoxclearrcafii9825releaseafii9853xreleaseLineALineCFig.2.Processsimulatedbymodel,simulationstartingwhenthecupcrosseslineA；releasetimerepresentstimeneededtocreateanopeningsufficientlylargeforapotatotopass；modelalsocalculatestimebetweenreleaseofthepotatoandthemomentitreachesthesoilsurface(freefall)；rc,sumoftheradiusoftheroller,thicknessofthebeltandlengthofthecup；xclear,clearancebetweencupandductwall；xrelease,releaseclearance；arelease,releaseangle；o,angularspeedofroller；lineC,groundlevel,endofsimulationtopassandbereleased.Thisgapxreleaseinmisreachedatacertainangleareleaseinradofacuppassingtheroller.Thisreleaseanglearelease(Fig.2)iscalculatedascosareleasercxclearC0xreleaserc(4)where:rcisthesuminmoftheradiusoftheroller,thethicknessofthebeltandthelengthofthecup；andxclearistheclearanceinmbetweenthetipofthecupandthewalloftheduct.Whentheparametersofthepotatoesareknown,theanglerequiredforreleasingapotatocanbecalculated.Apartfromitsshapeandsize,thepositionofthepotatoonthebackofthecupisdeterminative.Therefore,themodeldistinguishestwopositions:(a)minimumre-quiredgap,equaltotheheightofapotato；and(b)maximumrequiredgapequaltothelengthofapotato.Thetimetreleaseinsneededtoformareleaseangleaoiscalculatedastreleaseareleaseor(5)Calculatingtreleasefordifferentpotatoesandpossiblepositionsonthecupyieldsthedeviationfromtheaveragetimeintervalbetweenconsecutivepotatoes.Combinedwiththedurationofthefreefallandthefieldspeedoftheplanter,thisgivestheplantingaccuracy.yreleasevendtfall0C15gt2fall(8)wheregisthegravitationalacceleration(9C18msC02)andthefinalvelocityvendiscalculatedasvendv02gyrelease(9)withv0inmsC01beingtheverticaldownwardspeedofthepotatoatthemomentofrelease.ThetimeforthepotatotomovefromLineAtothereleasepointtreleasehastobeaddedtotfall.Themodelcalculatesthetimeintervalbetweentwoconsecutivepotatoesthatmaybepositionedindifferentwaysonthecups.Thelargestdeviationsinintervalswilloccurwhenapotatopositionedlengthwiseisfollowedbyonepositionedheightwise,andviceversa.2.3.ThelaboratoryarrangementAstandardplanterunit(MiedemaHassiaSL4(6)wasmodifiedbyreplacingpartofthebottomendofthesheetmetalductwithsimilarlyshapedtransparentacrylicmaterial(Fig.3).Thecup-beltwasdrivenviatheroller(8inFig.1),byavariablespeedelectricmotor.Thespeedwasmeasuredwithaninfraredrevolutionmeter.Onlyonerowofcupswasobservedinthisarrangement.Ahigh-speedvideocamera(SpeedCamPro,Wein-bergerAG,Dietikon,Switzerland)wasusedtovisualisethebehaviourofthepotatoesinthetransparentductandtomeasurethetimeintervalbetweenconsecutivepotatoes.Asheetwithacoordinatesystemwasplacedbehindtheopeningoftheduct,theXaxisrepresentingthegroundlevel.Timewasregisteredwhenthemidpointofapotatopassedthegroundline.StandarddeviationWhenthepotatoisreleased,itfallstowardsthesoilsurface.Aseachpotatoisreleasedonauniqueangularposition,italsohasauniqueheightabovethesoilsurfaceatthatmoment(Fig.2).Asmallpotatowillbereleasedearlierandthusatahigherpointthanalargeone.ThemodelcalculatesthevelocityofthepotatojustbeforeithitsthesoilsurfaceuendinmsC01.Theinitialverticalvelocityofthepotatou0inmsC01isassumedtoequaltheverticalcomponentofthetrackspeedofthetipofthecup:v0rcorcosarelease(6)ThereleaseheightyreleaseinmiscalculatedasyreleaseyrC0rcsinarelease(7)whereyrinmisthedistancebetweenthecentreoftheroller(lineAinFig.2)andthesoilsurface.ARTICLEINPRESSH.BUITENWERFETAL.38ofthetimeintervalbetweenconsecutivepotatoeswasusedasmeasureforplantspacingaccuracy.Forthemeasurementsthecamerasystemwassettoarecordingrateof1000framespersecond.Withanaveragefreefallvelocityof2C15msC01,thepotatomovesapprox.2C15mmbetweentwoframes,sufficientlysmalltoallowanaccurateplacementregistration.Thefeedingratesforthetestoftheeffectofthespeedofthebeltweresetat300,400and500potatoesmin