The-Br′eguet-Richet-Quad-Rotor-Helicopter-of-1907

TheBr´eguet-RichetQuad-RotorHelicopterof1907byProfessorJ.GordonLeishmanAtthebeginningofthe20thcenturytheFrenchscientistandacademicianCharlesRichetbuiltasmall,un-pilotedhelicopter.Althoughthemachinewasunsuccessful,itinspiredoneRichet’sstudents,LouisBr´eguet,whowaslatertobecomeafamousaviationpioneer.Duringthelatterpartof1906,thebrothersLouisandJacquesBr´eguetbegantoconducthelicopterexperimentsoftheirown,undertheguidanceofProfessorRichet.TheBr´eguetBrotherswerefromthefamousBr´eguetclockmakingfamily,andhadagoodknowledgeofengineeringprinciplesandadequatefundstoproceedwithseriousdesignwork.LouisBr´eguetmademeticuloustestsofairfoilshapes,parallelingthoseoftheWrightBrothers–seeAnderson’sbookHistoryofAerodynamics.Withoutadoubt,theBr´eguet’sunderstoodtheessentialaerodynamictheoryofliftingwingsandhadatleastarudimentaryunderstandingoftherequirementsforverticalflight.In1907,theBr´eguetBrothersbuilttheirfirsthumancarryinghelicopter–theycalledittheBr´eguet-RichetGyroplaneNo.1,whichwasaquad-rotor.ClearlytheBr´eguet’sapproachedtheproblemofthehelicoptermorescientificallythanothersatthetime,andthoughthardaboutaconfigurationthatwasmostlikelytomeetwithsuccess.InthewordsofLouisBr´eguet:“....Start-ingfromfrommycalculationsIwaslead....tobuildanaircraftwithfourpropellers[rotors]of8.10meterdiameter.”Theissueofstabilitywasaconsiderationinthedesign,butthefirstrequirementforthemachinewassimplytoliftitselfandapilotoffthegroundunderitsownpower.TheBr´eguet-Richetquad-Figure1:TheBr´eguet-RichetquadrotorGyroplaneNo.1,circa1907rotorconsistedoffourlonggird-ersmadeofweldedsteeltubesandarrangedintheformofahorizontalcross,lookingsome-whatlikeanassemblageoflad-ders.Eachrotorconsistedoffourlight,fabriccoveredbiplane-typeblades,givingatotalof32separateliftingsurfaces.Therotorswereplacedateachofthefourcornersofthecross.Diagonallyoppositepairsofrotorsrotatedinoppositedirections,therebycancelingtorquereactionontheairframe.Thepilotsatinthecenterofthestructurebelowan8-1cylinderAntoinetteinternalcombustionengine,whichproducedabout40hp(29.8kW),althoughsomesourcessuggestthattheengineproducedperhapsasmuchas50hp(37.3kW).Theenginedrovetherotorsthroughasimplebeltandpulleytransmission.Thebareairframeweighed-inatasubstantial760lb(345kg),andtheAntoinetteengineandfuelweighedabout364lb(165kg),givingthemachineanemptyweightofabout1,124lb(510kg).TheBr´eguet’swereabletofindawillinghelperasapilot–aMonsieurVolumard–whoweighedonly68kg(150lb),resultinginamachinewithanetgrosstake-offweightofsome578kg(1,274lb).ThefirstexperimentswiththeirGyroplaneNo.1werecarriedoutatDouai,FrancebetweenAugustandSeptember1907.Themachineisreportedtohaveliftedintoflight,andcarriedthepilotashigha1.5m(5ft),albeitbriefly.However,therewasnomeansofcontrolprovidedtothepilototherthanathrottlefortheenginetochangetherotorspeed,andthestabilityofthemachinewasfoundtobeverypoor.Themachinewassubsequentlytetheredsothatitcouldmoveonlyverticallyupward.Photographsofthenumerousattemptsatflightshowtheassistanceofseveralmen,oneateachcornerofthecross-likestructure,stabilizingandperhapsevenliftingthemachine.Thereisconsiderabledebateastowhetherflightwasevenpossiblewithsuchalargeandrelativelyheavymachinewithanengineofonly40-50hp(29.8-37.3kW)installed.Therefore,itisinstructivetoobjectivelyreviewtheliftingcapabilityoftheBr´eguet-Richetmachineusingsimplerotortheory.ItisrecordedthateachrotoroftheBr´eguet-Richetmachinewasapproximately8.1m(26.6feet)indiameter,andthemachinehadagrossweight(withpilot)ofabout578kg(1,274lb).Theabsoluteminimumpowerrequiredtoliftthemachineverticallybytherotorscanbeestimatedfromthe“momentumtheory,”whichformallyembodyNewton’slawsofmotionappliedtoafluidmovingthroughtherotors.Assumingeachrotorliftedone-quarterofthetotalaircraftweight,thenthemomentumtheorygivesaresultfornetminimumpossiblepower(oridealpower,Pideal)requiredtodriveallfourrotorsusingtheequationPideal=4(W/4)3/2√2ρAlbfts−1wherethetotaltake-offweightW=1,274lb,andwhereeachrotorhadasweptdiskarea,A=πD2/4≈554.5ft2.Whiletherotorswereactuallycomprisedofbi-planeblades,theperformanceoftherotorsisprimarilyafunctionoftheirprojectedsweptarea.WorkinginImperialunitsandassumingsea-levelairdensity(ρ=0.00238slugs/ft3)thisgivestheidealshaftpowerrequiredto2driveallfourrotorsoftheBr´eguetmachineasPideal=4550(1,274/4)3/2√2×0.00238×554.5≈25.5hp(19kW)Withtherelativelyprimitivetypesofbi-planerotorsusedbytheBr´eguetBrothers,andwithfarfromoptimalbladeshapeorbladetwistdistributionsandalsohighprofiledragfromthebracingbetweentheblades,wecouldexpecttheaerodynamicefficiencyoftheirrotorstobequitepoor.Onecanoptimisticallyestimatethattherotorefficiencycouldbenobetterthan50%(afigureofmeritof0.5).Thissuggestsanetpowerforflightofatleast51hpwasrequiredtobedeliveredattherotorshafts.TheBr´eguet’salsousedaninefficientbeltandpulleysystemtodrivetherotors.Sotakingintoaccountaconservativeestimateoftransmissionlossesofsome20%,fortheirmachinetohoverfreeoftheground,theinstalledpowerrequiredwouldhaveneededtobeinexcessof60hp(47.8kW).Remember,thattheBr´eguet-Richetmachineusedaenginethatoptimisticallyproducedonlya