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[PDF] AERODYNAMICS, AERONAUTICS, AND FLIGHT MECHANICS
IPREFACE This second edition of Aerodynamics, Aeronautics, and Flight Mechanics marks fifty If the pilot pulls back on the control column as the throttle is advanced value of 1 20 for CL,,,, agrees almost exactly with the airplane's manual
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2623_3AppliedAerodynamics_10526036.pdf APPLIEDAERODYNAMICS
ByL.BAIRSTOW,Amiateofthe
RoyalCollegeofScienceinMechanics;Whitworth
Scholar;FellowandMemberofCounciloftheRoyal
AeronauticalSociety,etc.
AEROPLANESTRUCTURES
ByA.J.SUTTONPIPPARD,M.Sc..ArmoM.
FellowoftheRoyalAeronauticalSociety,
andCapt.I.LAURENCEPancuun.lateR.A.l AssociateFellowoftheRoyalAeronauticalSociety.WithanIntroductionbyL.BAtRS'row,F.R.S.THEAEROENGINE
ByMajorA.T.EVANSandCaptainW.GRYLLS
ADAMS,M.A.
THEDESIGNOFSCREW
PROPELLERS
LONGMANS,GREENANDC0.
NEWYORK.LONDON,BOMBAY,CALLUTTA,ANDMADRAS
APPLIEDAERODYNAMICS
BY LEONARDBAIRSTOW,ADVISE!ONAERODYNANICSTOTHEAIRMINISTRY:MEMBEROFTHEADVISORYCOMMITTEE FORAEEONAUTICS.All!INVENTIONSCOMMITTEE.ACCIDENTSINVESTIGATIONCONMITTRE. ANDADVISORYONCIVILAVIATION:LATEQUPERINTKNDRN fI eOPTKR AFEODYNANICSDEPARTMENTOPTHRNATIONALPHYSICALLABORATORYILL0sdTIONSAND
NEWYORK
LONGMANS,GREENANDCO.
FOURTHAVENUEAND3015STREET
39,PATERNOSTERROW,LONDON
BOMBAY.CALCUTTA,ANDMADRAS
1920A11right: hram!
233672E
APR10moCk g?Kl? g
lac. EYTS BicPREFACE
Tnaworkaimaattheextractionofprinciplesof 6ightfrom,andtheillustrationoftheuseof,detailedinformationonaeronauticsnowavailablefrommanysources;notablythepublicationsoftheAdvisory
CommitteeforAeronautics.Themainoutlinesofthetheoryof 6ightaresimple,butthestageofapplicationnowreachednecessitatescarefulexaminationofsecondaryfeatures.Thisbookiscastwiththisdistinction
inViewandstartswithadescriptionofthevariousclassesofaircraft,bothheavierandlighterthanair,andthenproceedstodevelopthe
lawsofsteady 6ightonelementaryprinciples.Laterchapterscompletethedetailasknownatthepresenttimeandcoverpredictionsandanalysesofperformance,aeroplaneacrobatics,andthegeneralproblems
ofcontrolandstability.Thesubjectofaerodynamicsisalmostwholly basedonexperiment,andmethodsaredescribedofobtainingbasic informationfromtestsonaircraftin 6ightorfromtestsinawindchannelonmodelsofaircraftandaircraftparts. TheauthorisanxioustoacknowledgehisparticularindebtednesstotheAdvisoryCommitteeforAeronauticsforpermissiontomakeuseofreportsissuedunderitsauthority.Extensivereferenceismadetothosereportswhich,priortothewar,wereissuedannually;itisunderstood
thatallreportsapprovedforissuebeforethebeginningof1919arenowreadyforpublication.Tothismaterialtheauthorhashadaccess,but
itWillbeunderstoodbyallintimatelyuaiutedwiththereportsthatthecontentscannotbefullyrepresenbyextracts.Thepresentvolumeisnotanattemptatcollectionoftheresultsofresearch,butacontributiontotheirapplicationtoindustry.
ForthelastyearofthewartheauthorwasresponsibletotheDepartmentofAircraftProductionfortheconductofaerodynamicresearchonaeroplanesin 6ight,andhisthanksaredueforpermission
tomakeuseofinformationacquired.ForpermissiontoreproducephotographsacknowledentismadetotheAdmiraltyAirshipDepartment,Messrs.HandleyageandCc.,theBritishandColonialAeroplane
Cc.,thePliw-nixDynamoCc.,Messrs.D.NapierandCc.,andELM.StationeryO jice.
L.BAIBSTOW.mumsWren,
October6th,1919.
viiiCONTENTSAERIALBIANOEUVRESANDTHEEQUATION01"MOTION
CONTENTS
ofpetrolandoil dMoreaccuratemethodofprediction-Generaltheory dData ofclimb dTheoryofreductionfromactualtostandardatmosphere dLevel kightsCONTENTS
LISTOFPLATES
Fourteentensofmatterin kight
FightingBiplaneScout
CockpitofanAeroplane
RotaryEngine dAir-cooledStationaryEngine
Waiter-cooledEngine
NearlycompletedRigidAirship
C000Q0O0Q0Q
ExperimentalarrangementofTubeAnemometeronanAeropla 0ModelAeroplanearrangedtoshowAutorotation
EddiesbehindCylinder
FlowofWaterpastanInclinedPlate.LowandHighSpeeds
FlowofAirpastanInclinedPlate.LowandHighSpeeds
VeryStableModel dSlightlyStableModel
StableModelwithtwoRealFins dModelwhichdevelopsanUnstable Oscillation dModelwhichillustratesLateralInstabilitiesCHAPTERI
GENERALDESCRIPTIONOFSTANDARDFORMSOFAIRCRAFT
In'raonvcrron
IntheOpeningreferencestoaircraftasrepresentedbyphotographsof moderntypes,bothheavier-than-airandlighter-than-air,attentionwill bemoreespeciallydirectedtothosepointswhichspeci jcallyrelatetothe subject-matterofthisbook,i.e.toappliedaerOdynamics.Strictlyin terpreted,thewordaerodynamicsisusedonlyforthestudyoftheforcesonbodiesduetotheirmotionthroughtheair,butformanyreasonsitisnotconvenienttoadheretoocloselytothisdefinition.Inthecaseof
heavier-than-aircraftoneoftheaerodynamicforcesisrequiredtocounter balancetheweightoitheaircraft,andisthereforedirectlyrelatedtoa non-dynamicforce.Inlighter-than-aircraft,sizedependsdirectlyon theweighttobecarried,buttheweightitselfisbalancedbythebuoyancy ofamassofentrappedhydrogenwhichagainhasnodynamicorigin.As thesizeofaircraftincreases,theresistancetomotionatanypredetermined speedincreases,andtheaerodynamicforcesforlighter-than-aircraft dependuponandareconditionedbynon-dynamicforces. Theinter-relationindicatedabovebetweenaerodynamicandstatic forceshasextensionswhicha k' ecttheexternalformtakenbyaircraft. Oneofthemostimportantitemsinaircraftdesignistheeconomical distributionofmaterialsoastoproduceasuf jcientmarginofstrength fortheleastweightofmaterial.Acceptingthestatementthatadditional aconsequenceofincreasedweight,itwillbeappreciatedthat theproblemofexternalformcannotbedeterminedsolelyfromaerodynamic considerations.Asanexampleofasimpletypeofcompromisemaybe instancedtheproblemofwingform.Thegreatestliftforagivenresistance isobtainedbytheuseofsinglelongandnarrowplanes,theadvantagebeing lessandlessmarkedastheratiooflengthtobreadthincreases,butremaining appreciablewhentheratioisten.MostaerOplaneshavethisaspect ratiomorenearlyequaltosixthenten,andinsteadofthesingleplaneadoublearrangementispreferred,thee k' ectofthedoublingbeingan appreciablelossofaerodynamice kiciency.Thereasonswhichhaveledtothisresultarepartlyaccountedforbyaspecialconveniencein jghtingwhichaccompaniestheuseofshortplanes,butafactorofgreaterimportanceisthatarisingfromthestrengthdesiderata.Theweightof
wingsoflargeaspectratioisgreaterforagivenliftingcapacitythanthat ofshortwings,andtheexternalsupportnecessaryinalltypesofaerOplane ismoredif jculttoachievewithaerodynamiceconomyforasinglethan foradoubleplane.Aerodynamically,alimitis jxedtotheweight 1n2APPLIEDAERODYNAMICS
carriedbyawingatachosenspeed,andforsafealightingthetendencyhasbeento jxthisspeedatalittleoverfortymilesanhour.ThisgivesalowerlimittothewingareaofanaerOplanewhichhastocarryaspeci jed
weight.Thegeneralexperienceofdesigiershasbeenthatthislimitisaseriousrestrictioninthedesignofamonoplane,butoffersverylittle
biplane.Inafewcases,threeplaneshavebeensuperposed,butthetypehasnotreceivedanygeneraldegreeofacceptance.For
smallaerOplanes,thefurtherlossofaerodynamicef jciencyinatriplane hasbeenacceptedforthesakeofthegreaterrapidityofmanaauvrewhich canbemadetoaccompanyreducedspanandchord,whilstinverylarge aerOplanesthechiefadvantageofthetriplaneisareductionoftheoverall dimensions.Uptothepresenttimeitappearsthatanadvantageremains withthebiplanetypeofconstruction,althoughverygoodmonOplanesand triplaneshavebeenbuilt. Theillustrationshowsthataircrafthaveenteredthestageofengineer ingasdistinctfromaerodynamicalscience hinthatthe jnalproductisdeterminedbyanumberofconsiderationswhicharemutuallyrestrictiveandinwhichthepracticalknowledgeofusageisaveryimportantfactor
intheattainmentofthebestresult. Althoughairisthe 6uidindicatedbythetermaerodynamics,it hasbeenfoundthatmanyofthephenomenaof 6uidmotionareindependentoftheparticular 6uidmoved.Advantagehasbeentakenofthisfactinarrangingexperimentalwork,andinalaterchapterastrikingOptical
illustrationofthetruthoftheaboveobservationisgiven.Thedistinction betweenaerodynamicsandthedynamicsof 6uidmotiontendstodisappear inanycomprehensivetreatmentofthesubject. Intheconsiderationofaerialmanoeuvresandstabilitytheaerodynamicsofthemotionmustberelatedtothedynamicsofthemovingmasses.Itisusualtoassumethataircraftarerigidbodiesforthepurposes
indicated,andingeneraltheassummionisjusti jable.Inafewcases,as incertain jnsofairshipswhichde 6ectunderload,greaterre jnementmay benecessaryasthescienceofaeronauticsdeveIOps. Itwillreadilybeunderstoodthataerodynamicsinitsstrictinter pretationhaslittledirectconnectionwiththeinternalconstructionof aircraft,theimportantitemsbeingtheexternalformandthechangesof itwhichgivethepilotcontroloverthemotion.Asthesubjectisinitselfextensive,andastheinternalstructureisbeingdealtwithbyotherwriters,thepresentbookaimsonlyatsupplyingtheinformationbymeansof
whichtheforcesonaircraftinmotionmaybecalculated. Thescienceofaerodynamicsisstillveryyoung,anditisthirteenyears onlysincethe jrstlongheponanaeroplanewasmadeinpublicbySantos Dumont.ThecircuitoftheEiffelTowerinadirigibleballoonpreceded thisfeatbyonlyashortperiodoftime.Aeronauticsattractedthe attentionofnumerousthinkersduringpastcenturies,andmanyhistorical accountsareextantdealingwiththeresultsoftheirlabours.Formany reasonsearlyattemptsat 6ightallfellshortofpracticalsuccess,although theyadvancedthetheoryofthesubjectinvariousdegrees.Thepresent epochofaviationmaybesaidtohavebegunwiththepublicationoftheSTANDARDFORMSOFAIRCRAFT3
experimentsmadeby'LangleyinAmericaintheperiod1890to1900. Theapparatususedwasawhirlingarm jttedwithvariouscontrivances forthemeasurementoftheforceson katplatesmovedthroughtheairat theendofthearm. Onelineofexperimentmayperhapsbedescribedbrie 6y.Anumber ofplatesofequalareaweremadeandarrangedtohavethesametotal weight,afterwhichtheywereconstrainedtoremainhorizontalandto falldownverticalguidesattheendofthewhirlingarm.Thetimeoffalloftheplatesthroughagivendistancewasmeasuredandfoundtodepend,notonlyontheSpeedoftheplatethroughtheair,butalsoonitsshape.
Atthesamespeeditwasfoundthattheplateswiththegreatestdimension acrossthewindfellmoreslowlythanthoseofsmalleraspectratio.For smallvelocitiesoffallthetimeoffallincreasedmarkedlywiththeSpeed oftheplatethroughtheair.Byachangeofexperimentinwhichthe plateswereheldonthewhirlingarmataninclinationtothehorizontal andbyrunningthearmatincreasingspeedsthevalueofthelatterwhen theplatejustlifteditselfwasfound.Repetitionofthisexperiment showedthataparticularinclinationgavelessresistancethananyother fortheconditionthattheplateshouldjustbeairborne.FromLangley fsexperimentsitwasdeducedthataplateweighingtwopoundspersquarefootcouldbesupportedat85m.p.h.iftheinclination
wasmadeeightdegrees.Theresistancewasthenone-sixthoftheweight,andmakingallowanceforotherpartsofanaeroplaneitwasconcluded
thatatotalweightof750lbs.couldbecarriedfor.theexpenditureof25 horsepower.Earlyexperimenterssetthemselvesthetaskofbuildinga completestructurewithintheselimitations,andsucceededinproducing aircraftwhichliftedthemselves. Langleyputhisexperimentalresultstothetestofa 6ightfromthe tOpofahouseboatonthePotomacriver.Owingtoaccidenttheaero planedivedintotheriverandbroughttheexperimenttoaveryearlyend. InEngland,MaximattemptedthedesignofalargeaerOplaneand engine,andachievedanotableresultwhenhebuiltanengine,exclusive ofboilersandwater,whichweighed180lbs.anddeveloped860horse power.Toavoidthedif jcultiesofdealingwithstabilityin 6ight,the aerOplanewasmadecaptiveby jxingwheelsbetweenupperandlower rails.Theexperimentscarriedoutwereveryfewinnumber,butalift oflbs.wasobtainedbeforeoneofthewheelscarriedawayafter contactwiththeupperrail. Forsometenyearsaftertheseexperiments,aviationtookanew direction,andattemptstogainknowledgeofcontrolbytheuseofaero planeglidersweremadebyPilcher,LilienthalandChanute.Fromahill builtforthepurposeLilienthalmadenumerousglidesbeforebeingcaught inapowerfulgustwhichhewasunabletonegotiateandwhichcosthim hislife.Inthecourseofhisexperimentshediscoveredthegreatsuperiority ofacurvedwingovertheplanesonwhichLangleyconductedhistests. Byasuitablechoiceofcurvedwingitispossibletoreducetheresistance tolessthanhalfthevalueestimatedfor 6atplatesofthesamecarrying capacity,Theonlycontrolattemptedintheseearlyglidingexperiments4APPLIEDAERODYNAMICS
wasthatwhichcouldbeproducedbymovingthebodyoftheaeronaut inadirectiontocounteractthee k' ectsofthewindforces. InthesameperiodveryrapidprogresswasmadeinthedeveIOpmvnt ofthelightpetrolmotorforautomobileroadtransport,andbetween1900and1908itbecameclearthattheprospectsofmechanical 6ighthadmateriallyimproved.The jrstachievementsofpower-drivenaeroplanes
tocallforgeneralattentionthroughouttheworldwerethoseoftwo Frenchmen,HenriBarmanandBleriot,whomadenumerousshort 6ights whichwerelimitedbylackofadequatecontrol.Thesetwopioneerstook Oppositeviewsastothepossibilitiesofthebiplaneandmonoplane,but intheendthefirstproducedanaeroplanewhichbecameverypopular asatrainingaeroplanefornewpilots,whilstthesecondhadthehonour ofthe jrstcrossingoftheEnglishChannelfromFrancetoDover. Thelackofcontrolreferredto,existedchie 6yinthelateralbalanceof theaeroplanes,itbeingdi kiculttokeepthewingshorizontalbymeans oftherudderalone.TherevolutionarystepcamefromtheBrothersWright inAmericaastheresultofapatientstudyoftheproblemsofgliding.A lateralcontrolwasdevelopedwhichdependedonthetwistingorwarping oftheaeroplanewingssothattheliftonthedepressedwingcouldbe increasedinordertoraiseit,withacorrespondingdecreaseoflift ontheotherwing.Asthechangesofliftduetowarpingwereaccompaniedbychangesofdragwhichtendedtoturntheaeroplane,theBrothersWrightconnectedthewarpandruddercontrolssoastokeeptheaeroplane
onastraightcourseduringthewarping.Theprincipleofincreasingthe liftonthelowerwingbyaspecialcontrol18nowuniversallyapplied,but therudder1snotconnectedtothewing kapcontrolwhichhastakenthe placeofwingwarping.FromthetimeoftheWrights' jrstpublic 6ights inEuropein1908theaviatorsoftheworldbegantomcreasetheduration oftheir kightsfromminutestohours.Progressbecameveryrapid,and thespeedof 6ighthasrisenfromthe85m.p.h.oftheHenriFarmanto nearly140m.p.h.inamodern jghtingscout.Therangehasbeen increasedtoover2000milesinthebombingclassofaeroplane,andthe AtlanticOceanhasrecentlybeencrossedfromNewfoundlandtoIrelandby theVickers fVimybomber. Assoonastheproblemsofsustainingtheweightofanaemplaneand ofcontrollingthemotionthroughtheairhadbeensolved,manyinvestiga tionswereattemptedofstabilitysoastoelucidatetherequirementsin anaeroplanewhichwouldrenderitabletocontrolitself.PartialattemptsweremadeinFrancefortheaeroplanebyFerber,Seeandothers,butthemostsatisfactorytreatmentisduetoBryan.Startingin1908incollabora
tionwithWilliams,Bryanappliedthestandardmathematicalequations ofmotionofarigidbodytothedisturbedmotionsofanaeroplane,andthe culminationofthisworkappearedin1911.Themathematicaltheory remainsfundamentallyintheformproposedbyBryan,butchangeshave beenmadeinthemethodofapplicationastheresultofthedevelopment ofexperimentalresearchundertheAdvisoryCommitteeforAeronautics. Themathematicaltheoryisfoundedonasetofnumbersobtainedfrom experiment,anditischie 6yinthedeterminationofthesenumbersthatSTANDARDFORMSOFAIRCRAFT5
developmenthastakenplaceinrecentyears.Someextensionsofthe mathematicaltheoryhavebeenmadetocover 6ightinanaturalwind andinspiralpaths. ExperimentalworkonstabilityonthemodelscaleattheNational PhysicalLaboratorywascc-ordinatedwith 6yingexperimentsatthe RoyalAircraftFactory,andtheresultsofthemathematicaltheoryofstabilitywereappliedbyBuskintheproductionoftheRE.20.aeroplane,which,withcontrolontherudderonly,was 6ownfordistancesof60or70milesonseveraloccasions.Bythistime,1914,themainfoundationsof
aviationaswenowknowithadbeenlaid.Thelaterhistoryislargely thatofdetaileddevelopmentunderstressoftheGreatWar. Thehistoryofairshipshasfollowedadifferentcourse.Theproblem ofsupportneveraroseinthesamewayasforaeroplanesandseaplanes, asballoonshadbeenknownformanyyearsbeforetheadventoftheair ship.The jrstchangefromthefreeballoonwaslittlemorethanthe attachmentofanengineinordertogiveitindependentmotionthrough theair,andthepoweravailablewasverysmall.Thesphericalballoon hasahighresistance,itscourseisnoteasilydirected,andthedirigible balloonbecameelongatedatitsearlieststages.Thelongcigar-shaped formsad0ptedbroughttheirownspecialdif jculties,astheytooaredi kicult tosteerandareinclinedtobuckleandcollapseunlesssu kicientprecautions aretaken.Steeringandmanagementhasbeenattainedinallcasesby the jttingof jns,bothhorizontalandvertical,totherearoftheairship envelope,andtheproblemofaf jxing jnsofsuf jcientareatothe 6exible envelopeofanairshiphasimposedengineeringlimitationswhichprevent asimpleapplicationofaerodynamicknowledge. Theproblemofmaintenanceofformofanairshipenvelopehasledto severalsolutionsofverydifferentnatures.Inthenon-rigidairshiptheenvelopeiskeptin 6atedbytheprovisionofsuf jcientinternalpressure,eitherbyautomaticvalveswhichlimitthemaximumpressureorbythe
pilotwholimitstheMum.Theinterioroftheenvelopeisdivided bygastightfabricintotwoorthreecompartments,thelargestofwhich is jlled .withhydrogen,andthesmalleronesarefullyorpartiallyin 6ated withaireitherfromtheslipstreamofanairscreworbyaSpecial fan.Astheairshipascendsintoairatlowerpressurethevalvestothe airchambersopenandallowairtoescapeasthehydrogenexpands,and solongasthisispossiblelossofliftisavoided.Thegreatestheightto whichanon-rigidairshipcangowithoutlossofhydrogenisthatforwhich theairchambersorballoonetsareempty,andhencethesizeofthe balloonetsispreportionedbytheceilingoftheairship. Ifthecarofanairshipissuspendednearitscentre,theenvelopeat resthasgasforcesactingonitwhichtendtoraisethetailandhead.The undersideoftheenvelopeisthenintensiononaccountofthegaslift, whilsttheupperside ,isincompression.Asfabriccannotwithstand compression,suf jcientinternalpressureisappliedtocounteracttheeffect oftheliftinproducingcompression. Thecarofthenon~rigidairshipisattachedbycablestotheunderside oftheenvelope,andastheseareinclined,aninwardpullisexertedwhich96APPLIEDAERODYNAMICS
tendstoneutralisethetensioninthefabric.Forsomeparticularinternal pressurethefabricwilltendtopucker,andSpecialexperimentsaremade todeterminethispressureandtodistributethepullinthecablessoas tomakethepressureassmallaspossiblebeforepuckeringoccurs.The" experimentismadeonamodelairshipwhichisinvertedand jlledwith water.Theloadsinthecables,theirpositionsandthepressureareall undercontrol,andthenecessarymeasurementsareeasilymade.The theoryoftheexperimentisdealtwithinalaterchapter. In kighttheexterioroftheenvelopeissubjectedtoaerodynamic pressureswhichareintensenearthenose,butwhichfalloffvery rapidlyatpointsbehindthenose.Fromatendencyofthenosetoblow inunderpositivepressure,achangeoccurstoatendencytosuckoutatadistanceoflessthanhalfthediameteroftheairshipbehindthenose,andthissuction,invaryingdegrees,persistsoverthegreaterpartofthe
envelope.AthighSpeedsthetendencyofthenosetoblowinisvery greatascomparedwiththeinternalpressurenecessarytoretaintheform oftherestoftheenvelope,andareductionintheweightoffabricusedis obtainedifthenoseisreinforcedlocallyinsteadofmaintainingitsshape byinternalpressurealone.Inoneofthephotographsofthischapterthe reinforcementofthenoseisveryclearlyshown. Theproblemofthemaintenanceofformofanon-rigidairshipis appreciablysimpli jediftheweighttobecarriedisnotallconcentrated inonecar. Inthesemi-rigidairshiptheenvelopeisstilloffabricmaintainedto formbyinternalpressure,butbetweentheenvelopeandcarisinterposed alonggirderwhichdistributestheconcentratedloadofthecaroverthe wholesurfaceoftheenvelope.Thistypeofairshiphasbeenusedin France,buthasreceivedmostdevelopmentinItalyitisnotusedinthis country. Rigidairshipsdependuponametalframeworkforthemaintenance oftheirform,andinGermanyweredevelopedtoaveryhighdegreeof ef jciencybyCountZeppelin.Thelargestairshipsareofrigidconstruction andhaveagrossliftofnearlyseventytons.Theframeworkisusuallyofalightaluminiumalloy,occasionallyofwood,andinthefuturesteelmaypossiblybeused.Thestructureisalightlatticeworksystemofgirders
runningalongandaroundtheenvelopeandbracedbywiresintoastiff frame.Inmoderntypesakeelgirderisprovidedinsidetheenvelopeat thebottom,whichservestodistributetheloadfromthecarsandalsofurnishesacommunicationway.Thenumberofcarsmaybefourormore,andthebendingundertheliftofthehydrogen1skeptsmallbyacareful
choiceoftheirpositions.Someofthetransversegirdersarebracedinside theenvelopebyanumberofradialwires,thecentresofwhicharejoined byawirerunningthewholelengthoftheairshipalongitsaxis.Inthe compartmentssoproducedthegas-containersare 6oated,andtheliftis transferredtotherigidframebythepressureonanettingofsmallcord. Thelatticeworkiscoveredbyfabricinordertoproduceasmooth unbrokensurfaceandsokeepdowntheresistance.Speedsof75m.p.h. havebeenreachedinthelatestBritishtypesofrigidairship,andthereturn8APPLIEDAERODYNAMICS
thedirectionofPrandtl,ofwhichnoresultshavebeenobtainedinthis country.SomeoftheGermanwritersonstabilitywerefollowingcloselyalongparallellinestothoseofBryaninBritain,andhad,priorto1914,arrivedattheideaofmaximumlateralstability.
TheotherEuropeanlaboratoryofnotewasatKoutchinonearMoscow,withD.Riabouehinskyasdirector.Thislaboratoryappearstohavebeen
aprivateestablishment,andplayedayeryusefulpartinthedevelopment ofsomeofthefundamentaltheoriesof 6uidmotion.Thepracticaldemand onthetimeoftheexperimentersappearstohavebeenlessseverethanin themoreWesterncountries.ANationalAdvisoryCommitteeforAeronauticswasformedatWashingtononApril2,1915,bythePresidentoftheUnitedStates.
Reportsofworkhaveappearedfromtimetotimewhichlargelyfollow thelinesoftheolderBritishCommitteeandaddtothegrowingstockof valuableaeronauticaldata.BeforedealingwithSpeci jccasesofaircraftitmaybeusefultocompare andcontrastman fseffortswiththemostnearlycorrespondingproducts ofnature.Betweenthebirdsandtheman-carryingaeroplanethereare pointsofsimilarityanddifferencewhichstrikeanobserverimmediately.Bothhavewings,thoseinthebirdbeingmovablesoastoallowof 6apping,whilstthoseintheaeroplaneare jxedtothebody.Boththebirdand
theaeroplanehavebodieswhichcarrythemotivepower,inonecase muscularandintheothermechanical.Bothhavetheintelligencefactor inthebody,theaerOplaneasapilot.Theaeroplanebodyis jttedwith anairscrew,anorganwhollyunrepresentedinbirdandanimallife,the propulsionofthebirdthroughtheairaswellasitssupportbeingachieved bythe 6appingofitswings.Inbothcasesthebodiesterminateinthin surfaces,ortails,whichareusedforcontrol,butwhilsttheaerOpIanehas avertical jnthebirdhasnosuchorgan.Thewingsofabirdaresomobile atwillthatmanceuvresofgreatcomplexitycanbemadebyalteringtheir positionandshape,manceuvreswhicharenotpossiblewiththerigidwings ofanaeroplane.Inadditiontothedi k' erencebetweenairscrewand kappingwings,aeroplanesandbirdsdiffergreatlyinthearrangementsfor alighting,theskidsandwheelsoftheaeroplanebeingtotallydissimilar tothelegsofthebird. Thestudyofbird 6ightasabasisforaviationhasclearlyhadamarked in 6uenceontheparticularformwhichmodernaer0planeshavetaken, andnomethodofaerodynamicsupportisknownwhichhasthesame valueasthatobtainedfromwingssimilartothoseofbirds.Thefactthat 6appingmotionhasnotbeenadopted,atleastforextensivetrial,appears tobedueentirelytomechanicaldif jculties.Inthisrespectnatural developmentindicatessomelimitationtothesizeofbirdwhichcan 6y. Thesmallerbirds 6ywitheaseandwithaveryrapid 6appingofthewings largerbirdsSpendlongperiodsonthewing,butgeneralinformation indicatesthattheyaresoaringbirdstakingadvantageofupcurrents behindcli k' soralargesteamer.Withthestilllargerbirdstheemuand ostrich, 6ightisnotpossible.Thehistoryofbird-lifeisinstrxctaccordance withthemechanicalprinciplethatstructuresofasimilarnaturegetSTANDARD~FORMSOFAIRCRAFT9
relativelyweakerastheygetlarger.Man,althoughhehassteelanda largeselectionofothermaterialsathisdisposal,hasnotfoundanything somuchbetterthanthemuscleofthebirdastomaketheproblemof supportinglargeweightsby. 6apping 6ightanymorepromisingthanthe resultsforthelargestbirds.Inlookingforanalternativeto 6apping thescrewpropellerasdevelopedforsteamshipshasbeenmodi jedforaerial use,andatpresentistheuniversalinstrumentofpropulsion. Theadeptionofrigidwingsinlarge 6yingmachinesinordertoobtain suf jcientstrengthalsobroughtnewmethodsofcontrol.Mechanical principlesrelatingtothee j' ectofsizeonthecapacityformanuauvreShow thatrecoveryfromadisturbanceisslowerforthelargerconstruction. Thegustsencounteredaremuchthesameforbirdsandaeroplane,and theslownessofrecoveryoftheaemplanemakesitimprobablethatthe beautifulevolutionsofabirdincounteringtheeffectsofagustwillever beimitatedbyaman-carryingaeroplane.Inonerespecttheaeroplane hasadistinctadvantage:itsSpeedthroughtheairisgreaterthanthat ofthebirds,andSpeedisitselfoneofthemosteffectivemeansofcombating theeffectofgusts.Furtherreferencetobird 6ightisforeigntothepurposeofthisbook,whichrelatestoinformationobtainedwithoutspecialattentiontothe
studyofbird 6ight. Theairshipenvelopeandthesubmarinehavemoreresemblanceto the jshesthantoanyotherlivingcreatures.GenerallySpeaking,theform ofthelarger jshesprovidesaverygoodbasisfortheformofairships. Itiscuriousthatthe jnsofthe jshareusuallyverticalasdistinctfrom thehorizontaltailfeathersofthebird,andthe jnsoverandunderthe centralbodyhavenocounterpartintheairship.Boththearti jcialand livingcraftobtainsupportbydisplacementofthemediuminwhichthey aresubmerged,andrisingandfallingcanbeproducedbymoderatechanges ofvolume.Theresemblancebetweenthe jshesandairshipsisfarless closethanthatbetweenthebirdsandaeroplanes.GENERALDESCRIPTIONorPaarrcvnxaAxacnarr
Anumberofphotographsofmodernaircraftandaeroenginesare reproducedastypicalofthesubjectofaeronautics.Theywillbeusedto de jnethosepartswhichareimportantineachtype.Thedetailsofthe motionofaircraftarethesubjectoflaterchaptersinwhichtheconditions ofsteadymotionandstabilityaredevelopedanddiscussed. TheAntonina dThefrontispieceshowsalargeaer0planein 6ight. BuiltbyMessrs.HandleyPageCc.,theaerOplane'istheheaviestyet 6ownandweighsaboutlbs.whenfullyloaded.Itsenginesdevelop1500horsepowerandpropeltheaeroplaneataSpeedofabout100miles
anhour.It eisofnormalbiplaneconstructionforitswings,theSpecial characteristicsbeingintheboxtailandinthearrangementofitsfour engines.Eachenginehasitsownairscrew,thepowerunitsbeingdivided intotwobythebodyoftheaer0plane,eachhalfconsistingofapairof enginesarrangedbacktoback.Oneairscrewofeachpairisworkingin10APPLIEDAERODYNAMICS
thedraughtoftheforwardscrew,andthistandemarrangementisasyet somewhatnovel.Biplane(Fig. dFig.1showsaSingle-seater jghtingsco fut,theSE.5,muchusedinthelaterstagesofthewar.Itsfourwingsareofequallength,
andformthetwoplaneswhichgivethenametothetype.Thelowerwings areattachedtotheundersideofthebodybehindtheairscrewandengine cowl,whilsttheupperwingsarejoinedtoashortcentresectionsupported fromthebodyonaframeworkofstrutsandwires.Awayfromthebodythe upperandlowerplanesaresupportedbywingstrutsandwirebracing, andthewholeformsastiffgirder.In 6ighttheloadfromthewingsis transmittedtothebodythroughthewingstrutsandthewiresfromtheir upperendstotheundersideofthebody.Thesewiresarefrequently referredtoasliftwires.Thedownwardloadonthewingswhichaecom paniestherunningoftheaeroplaneoverroughgroundistakenbyanti liftwires,whichrunfromthelowerendsofthewingstrutstothecentre sectionoftheupperplane. Inthedirectionofmotionoftheaeroplanein 6ightareanumberof bracingwiresfromthebottomofthevariousstrutstothetopoftheneighbouringmember.Thesewiresstiffenthewingsinawaywhichmaintainsthecorrectangletothebodyoftheaeroplane,andareknown
asincidencewires.Thebracingsystemisredundant,oneormore membersmaybreakwithoutcausingthecollapseofthestructure. Thewingsofeachplanewillbeseenfromthephotographtobebent upwardsinwhatisknownasadihedralangle,theobjectofwhichisto assistinobtaininglateralstability.Forthelateralcontrol,wing 6aps areprovided,theextentofwhichcanbeseenonthewingsontheleftof the jgure.Onthelower 6aptheleverforattachmentoftheoperating cableisvisible,thelatterbeingledintothewingatthefrontspar,and hencebypulleystothepilot fscockpit.Thepositionsofthefrontandrear sparsareindicatedbytheendsofthewingstrutsintheforeandaft direction,andrunalongthewingsparalleltotheleadingedges.ThebodyrestsontheSparsofthebottomplane,andcarriestheengineandairscrewintheforwardend.Theengineiswater-cooled,andthe
necessaryradiatorsaremountedmthenoseimmediatelybehindtheair screw.Blinds,shownclosed,arerequiredinaer0planeswhichclimbto greatheights,sincethetemperatureisthenwellbelowthefreezingpoint ofwater,andunrestricted 6owofairthroughtheradiatorduringaglide wouldleadtothefreezingofthewaterandtolossofcontroloftheengine. Theblindscanbeadjustedtogiveintermediatedegreesofcoolingto correspondwithenginepowersintermediatebetweenglidingandthe maximumpossible. Alongsidethe'bodyandstretchingbackbehindthepilot fsseatisone oftheexhaustpipeswhichcarrythehotgaseswelltotherearoftheaero plane.Thepilot'sseatisjustbehindthetrailingedgeoftheupperwing. Abovetheexhaustpipeandnearthefrontofthebodyisacoveroverthe cylindersononesideoftheengine,thecoverbeingusedtoreducetheair resistance. Theairscrewisintheextremeforwardpositionontheaeroplane,andDigtizedbyGoogle
STANDARDFORMSOFAIRCRAFT11
hasfourblades.Thediameteris jxedinthiscasebythehighSpeedoftheairscrewShaft,andnot,asinmanycases,bythegroundclearancerequiredforsafetywhenrunningovertheground.Belowthebodyandunderthewingsofthelowerplaneisthelanding
chassis.Theframeconsistsofapairofvee-Shapedstrutsbasedonthe bodyandjoinedatthebottomendsbyacrosstube.Thestructure eis supportedbyadiagonalcross-bracingofwires.Thewheelsandaxleare heldtotheundercarriagebybindingsofrubbercordsoastoprovide 6exibility.Theshocksoflandingaretakenpartlybythisrubbercord andpartlybythepneumatictyresonthewheels.Withtheaer0plane bodynearlyhorizontalthewheelaxleisaheadofthecentreofgravity oftheaeroplane,sothattheeffectofthe jrstcontactwiththegroundis tothrowupthenose,increasingtheangleofincidenceanddrag.Ifthe Speedofalightingistoogreattheliftmayincreasesuf jcientlytoraise theaeroplaneofftheground.Theartofmakingacorrectlandingisoneof themostdif jcultpartstobelearntbyapilot. ThetailoftheaeroplaneisnotclearlyShowninthis jgure,and Withanenginedeveloping210horsepowerandaloadbringingthegross weightoftheaemplaneto2000lbs.,theaerOplaneillustratediscapable ofaspeedofover180m.p.h.andcanclimbtoaheightoffeet. Thelimittotheheighttowhichaircraftcanclimbisusuallycalledthe ceiling. h Monoplane(Fig. dThemoststrikingdifferencefromFig.1isthe changefromtwoplanestoasingleone,andinordertosupportthewings againstlandingShocks,apyramidofstrutsorcabanehasbeenbuilt overthebody.Fromtheapexofthepyramidbracingwiresarecarried topointsontheuppersidesofthefront ,andrearspars.Thelowerbracing wiresgofromtheSparstotheundersideofthebody,andeachisduplicated. Ontherightwingnearthetipisatubeanemometerusedaspartof theequipmentformeasuringthespeedoftheaeroplane.Inbiplanesthe anemometerisusually jxedtooneofthewingstruts,astheeffectofthe presenceofthewingonthereadingislessmarkedthaninthecasenow illustrated. InthistypeofaerOplane,madebytheBritishdzColonialAeroplane Coy htheenginerotates,andtheairscrewhasasomewhatunusualfeature inthespinnerwhichisattachedtoit.Theairscrewhastwoblades only,andthistypeofconstructionhasbeenmorecommonthanthefour bladedtypeforreasonsofeconomyoftimber.Thedifferencesof ef jciencyarenotmarked,andeithertypecanbemadetogivegood service,thechoicebeingdeterminedinsomecasesbytheSpeedofrotation oftheairscrewshaftofanavailableengine. TheundercarriageisverysimilartothatshowninFig.1.Onone ofthefrontstrutsisasmallwindmillwhichdrivesapMpforthepetrol feed.Windmillsarenowfrequentlyusedforauxiliaryservices,suchas theelectricalheatingofclothingandthegenerationofcurrentforthe. wirelesstransmissionofmessages. Thetailisclearlyvisible,andunderneaththeextremeendofthebody12APPLIEDAERODYNAMICS
isthetail-skid.Thisskidishingedtothebody,andissecuredbyrubber cordatitsinnerend,soastodecreasetheshockofcontactwiththeground. Thehorizontalplaneatthetailisseentobedivided,thefrontpartor tailplanebeing jxed,whilsttherearpartorelevatorismovableatthe pilot fswish.Thecontrolcablesgoinsidethefuselageattherootofthe tailplane.Underneath,thetailplane18seentobebracedtothebody above,thebracingwiresareattachedtothe jn,which,likethetailplane, is jxedtothebody.Therudderishiddenbehindthe jn,buttherudder leverforattachmentofthecontrolcablecanbeseenabouthalfwayup the jn. Thepilotsitsunderthecabane,andhisdownwardviewishelped byholesthroughthewings.Immediatelyinfrontofhimisawindscreen, andalsointhisinstanceamachine-gun,which jresthroughtheairscrew.Flying-boat(Fig. dThedi j'
erenceofShapefromthelandtypesis markedinseveraldirections,aswillbeseenfromtheillustrationrelatingto thePhoenixCork kying-boatP.5.Theparticularfeaturewhichgives itsnametothetypeistheboatstructureunderthelowerwing,andthis replacesthewheelundercarriageoftheaeroplaneinordertorenderpossible alightingonwater.The 6yingboatisshownmountedonatrolleyduring transitfromtheshedstothewater.Ontheundersideoftheboat,just behindthenationalitycircles,isastepwhichplaysanimportantpartin thepreliminaryrunonthewater.Asecondstepoccursunderthewings attheplaceoflastcontactwiththeseaduringa kight,butishiddenby thedeepShadowofthelowerwing. Underneaththelowerwingattheouterstrutsisawing 6oatwhich keepsthewingoutOfthewaterinanySlightroll.Thewingstructureis muchlargerthanthoseofFigs.1and2,andtherearesixpairsOfinter planestruts.Theupperplaneisappreciablylongerthanthelower,the extensionsbeingbracedfromthefeetoftheouterstruts.Theleverson thewing 6apsoraileronsarenowveryclearlyshownowingtothe proximityofwavestothelowerwing,aileronsarenot jttedtothem. ThetailisraisedhighabovetheboatandisintheSlipstreamsfrom thetwoairscrews.AsthecentrelineoftheairscrewsisfarabovethecentreOfgravity,switchingontheenginewouldtendtomakethe kyingboatdive,wereitnotsoarrangedthattheslip-streameffectonthetail
isarrangedtogiveanOppositetendency.The jnandrudderareclearly shown,asarealsotheleversontherudderandelevators.Besideshaving adihedralangleonthewings,small jnshavebeen jttedabovethetop wingsaspartofthelateralbalanceOfthe kying-boat. Theenginesarebuiltonstrutsbetweenthewings,andeachengine drivesatractorairscrew.Theenginesareruninthesamedirection, althoughatanearlystageofdevelopmentof kying-boatsthee kectsof geSOOpicactionoftherotatoryairscrewswereeliminatedbyarranging forrotationinOppositedirections.Thiswasfoundtobeunnecessary. Thetailofthe kying-boathasbeenespeciallyarrangedtocomeintothe slipstreamoftheairscrews,butinaeroplanesthisoccurswithout Specialprovisionordesire.Notonlydoestheairscrewincreasetheair Speedoverthetail,butitalterstheangleofincidenceandblowsthetailFlo.4. dCockpitofanaeroplane.
DgtzedbyG
STANDARDFORMSOFAIRCRAFT18
upordowndependingonitssetting.ThereisalsoatwistintheSlipstream whichisfrequentlyunsymmetricallyplacedwithreSpecttothe jnandrudder andtendstoproduceturning.TheeffectsofswitchingtheengineonandOffmaybeverycomplex.
Inordertoeasethepilot fseffortsmanyaeroplanesare jttedwithan adjustabletailplane,andiftheyarestabletheadjustmentcanbemade soastogiveanychosen 6yingspeedwithouttheapplicationofforceto thecontrolstick. Pilot fsCockpit(Fig. dThephotographofthePantherwastaken fromabovetheaeroplanelookingdownandforward.Atthebottomofthe jgureistheedgeoftheseatwhichrestsonthetopofthepetroltank.Along thecentreofthe jgureisthecontrolcolumnhingedatthebottomtoarock. ingshaftsothatthepilotisabletomoveitinanydirection.Bysuitable cableconnectionsitisarrangedthatfore-and-aftmovementdepressesorraisestheelevators,whilstmovementtorightorleftraisesorlowersvtherightailerons.Someoftheconnectionscanbeseen;behindthecontrol
columnisaleverattachedtotherockingshaftandhavingatitsendsthe cablesfortheailerons.Thecablescanbeseenpassingininclineddirections infrontofthepetroltank.OnthenearSideofthecontrolcolumnbut partlyhiddenbytheseatisthelinkwhichoperatestheelevators. Inthecaseofeachcontrolthemotionofthecolumnrequiredisthat whichwouldbemadewereit jxedtotheaeroplaneandthepilotheld independentlyandheattemptedtopulltheaeroplaneintoanydesired position.Inotherwords,ifthepilotpullsthesticktowardshimthe.nose oftheaeroplanecomesup,whilstmovingthecolumntotherightbrings theleftwingup. Onthetopofthecontrolcolumnisasmallswitchwhichisusedbythe pilottocutouttheenginetemporarily,anOperationwhichisfrequently requiredwitharotaryenginejustbeforelanding. Acrossthephotographandalittlebelowtheenginecontrolswitches istherudderbar,thehingeofwhichisverticalandbehindthecontrol column.Thetwocablestotherudderareseentocomestraightback underthepilot fsseat.Intheruddercontrolthepilotpushestherudder bartotherightinordertoturntotheright. Severalinstrumentsareshowninthephotograph.Inthetapleft corneristheaneroidbarometer,whichgivesthepilotanapproximate ideaOfhisheight.Inthecentreisthecompass,aninstrumentSpecially designedforaircraftwheretheconditionsofusearenotveryfavourable togoodresults.Immediatelybelowthecompassandpartlyhiddenby itistheairspeedindicator,whichisusuallyconnectedtoatubeanemometer suchaswasshowninFig.2ontheedgeOfthewing. eStillloweronthe instrumentboardandbehindthecontrolcolumnisthecross-levelwhich indicatestoapilotwhetherheisside-Slippingornot.Totherightof thecross-levelarethestartingswitchesfortheengine,twomagnetosbeing usedasaprecautionarymeasure.Belowandtotherightoftherudder baristheenginerevolution-indicator.14APPLIEDAERODYNAMICS
ENGINESO
Air-cooledRotaryEngine(Fig.5a). dInthistypeofengine,theRR:2,theairscrewisboltedtothecrankcaseandcylinders,andthewholethen
rotatesabouta jxedcrankshaft.Thecylinders,nineinnumber,developa netbrakehorsepowerofabout280ataSpeedof1100to1800revolutionsper minute.Thecylindersareprovidedwithgills,whichgreatlyassistthecool ingofthecylinderduetotheirmotionthroughtheair.WithoutanyforwardmotionoftheaerOplane,coolingisprovidedbytherotationOfthecylinders,andanappreciablepartofthehorsepowerdevelopedisabsorbedinturning
theengineagainstitsairresistance.Airandpetrolareadmittedthrough pipesshownatthesideofeachcylinder,andboththeinletandexhaust valvesaremechanicallyoperatedbytherodsfromtheheadofthecylinder tothecrankcase.Thecammechanismforoperatingtherodsisinside thecrankcase.Thehubfortheattachmentoftheairscrewisshownin thecentre. Atypeofengineofgenerallysimilarappearance.hasstationary cylindersandisknownasradial. hItisprobablethatthecoolinglosses inaradialenginearelessthanthoseinarotaryengineofthesamenet power,butnodirectcomparisonappearstohavebeenmade.The effectivenessofanenginecannotbedissociatedfromthemeanstakento coolitscylinders.Theresistanceofcylindersinaradialengineand radiatorsinawater-cooledengineshouldbeestimatedandallowedfor beforecomparisoncanbemadewitharotaryengine,thelossesofwhich havealreadybeendeductedintheenginetest-bed jgures.Forengines withstationarycylinderstest-bed jguresusuallygivebrakehorsepower withoutallowanceforaerodynamiccoolinglosses. Vac-typeAir-cooledEngine(Fig.5b). dTheengineshownhastwelve cylinders,developsabout240horsepowerandisknown ,asthe R.A.F.4d.Thecylindersarearrangedabovethecrankcasein tworowsofsix,withananglebetweenthem,hencethenamegiven tothetype.Inordertocoolthecylindersacowlhasbeenprovided, sothattheforwardmotionoftheaerOplaneforcesairbetweenthe cylindersandoverthecylinderheads.Attheextremeleftofthephoto graphistheairscrewhub,andinthisparticularenginetheairscrewis gearedsoastoturnathalftheSpeedofthecrankshaft,thelattermaking1800to2000r.p.m.Totherightofandbelowtheairscrewhubisoneof
themagnetoswithitsdistributingwiresforthecorrecttimingOfthe explosionsintheseveralcylinders.Atthebottomofthephotographaretheinletpipes,carburettors,petrolpipesandthrottlevalves.Water-cooledEngine(Fig. dWater-cooledengineshavebeenused
morethananyothertypeinbothaeroplanesandairships.Thetwo photographsoftheNapier450h.p.engineshowwhatanintricate mechanismtheaeroenginemaybe.Thecylindersarearrangedinthree rowsoffour,eachonebeingsurroundedbyawaterjacket.Thefeed pipesofthewater-circulatingsystemcanbeseeninFig.6bgoingfrom thewaterpumpatthebottomofthepicturetothelowerendsofthe cylinderjackets,whilstabovethemarethepipeswhichconnecttheFla.5(a). dRotaryengine.
Fla.5(b). dAir-cooledstationaryengine.
DigntizedbyGoc
16APPLIEDAERODYNAMICS
theshipandringsrunningroundit.Twotypesofringarevisible,oneofwhichiswhollycomposedofsimplegirders,whilstthesecondhasking
postsassti k' enersontheinside.Fromthecornersofthissecondframeradialwirespasstothecentreoftheenvelopeandformoneofthedivisionsoftheairship.Thecentresofthevariousradialdivisionsareconnected
byanaxialwire,whichtakestheendpressureofthegasbagsinthecase ofde 6ationofoneofthemorofinclinationoftheairship.Thecordnetting againstwhichthegasbagsrestcanbeseenveryclearly.Theairshipis onebuiltfortheAdmiraltybyMessrsBeardmore. TheNon-rigidAirship(Fig. dThenon-rigidtypeofconstruction isessentiallydifferentfromthatdescribedabove,theshapeoftheenvelope beingmaintainedwhollybytheinternalgaspressure.TheN.S.typeof airshipillustratedinFig.9hasagrossweightof11tons,and travelsatalittlemorethan55m.p.h.Thelength-is0262feet,andthemaximumwidthoftheenvelope57feet.Fig.9bgivesthebestideaof
thecross-sectionofthistypeofairship,andshowsthreelobesmeetingin well-de jnedcorners.ThetypewasoriginatedinSpainbyTorresQuevedo anddevelopedinParisbytheAstraCompany.Itcontainsaninternal ropesandfabricbetweenthecorners.The satisfactorydistributionofloadsonthefabricduetotheweightofthe carandenginesispossiblewiththisconstructionwithoutnecessitating suspensionfarbelowthelowersurfaceoftheenvelope.Fig.90,taken frombelowtheairship,showsthewiresfromthecartothejunctionof thelobesatthebottomoftheenvelope,andthesetakethewholeload underlevel-keel econditions.Tobracethecaragainstrolling,wiresare carriedoutoneithersideand jxedtothelobesatsomedistancefromthe planeofsymmetryoftheairship.Theprincipleofreliefofstressby' distributionofloadhasbeenutilisedinthisship,-thecarandengine nacellesbeingsupportedasseparateunits.Communicationispermitted acrossagangwaywhichaddsnothingofvaluetothedistributionof load.Theenginesaretwoinnumber,situatedbehindtheobservationcar,andeachisprovidedwithitsownairscrew.Beneaththeenginesandalso
belowthecararebumpingbagsforuseonalighting. Astheshapeoftheairshipisdependentontheinternalgaspressure, specialarrangementsaremadetocontrolthisquantity,andthefabricpipes showninFig;90showhowairisadmittedforthispurposetoenclosed portionsoftheenvelope.Theenvelopeisdividedinsidebygastight fabric,sothatinthelowerlobesbothoftheforeandrearpartsofthe airship,smallchambers,orballoonets,areformedintowhichaircanbe pumpedorfromwhichitcanbereleased.Thepositionoftheseballoonets canbeseeninFig.90,attheendsofthepairoflonghorizontalfeed pipes;theyarecrossconnectedbyfabrictubeswhicharealsoclearly visible.Thehigh-pressureairisobtainedfromscoopsloweredintotheslipstreamsfromtheairscrews,thescoopsbeingvisibleinallthe jgures,butarefoldedagainsttheenvelopeinFig.9a.Valvesareprovidedin
thefeedpipesforusebythepilot,whoin 6atesorde katestheballoonets asrequiredtoallowforchangesinvolumeofthehydrogenduetovariationsSTANDARDFORMSOFAIRCRAFT17
ofheight.Automaticvalvesarearrangedtoreleaseairifthepressure Theweightoffabricnecessarytowithstandthepressureofthegas isgreatlyreducedbyreinforcingthenoseoftheairshipasshownin Fig.9b.Themaximumexternalairforceduetomotionoccursatthe noseoftheairship,andathighspeedsbecomesgreaterthantheinternal pressureusuallyprovided.Theregionofhighpressureisextremelylocal, andbytheadditionofstiffeningribstheexcessofpressureoverthe internalpressureistransmittedbacktoapartoftheenvelopewhereitis easilysupportedbyasmallinternalpressure.Occasionallythenoseof anairship1sblowninathighSpeed,butwiththearrangementsadopted theconsequencesareunimportant,andthecorrectshape18recoveredbyanincreaseofballoonetpressure. Thein 6ationofoneballoonetandthede 6ationoftheotherisacontrol bymeansofwhichthenoseoftheairshipcanberaisedorlowered,andso effectachangeoftrim,buttheusualcontrolisbyelevatorsandrudders. IntheN.8.typeofairshiptherudderiscon jnedtothelowersurface,and theupperfinisofreducedsize.This,thelargestofthenon-rigidairships, istheproductoftheAdmiraltyAirshipDepartmentfromtheirstation atKingsnorth,andhasseenmuchserviceasasea-scout. KiteBalloons(Fig. dTheearlykiteballoonwasprobablyaGerman type,withastringofparachutesattachedtothetailinordertokeep theballoonpointingintothewind.Theliftonakiteballoonispartly duetobuoyancyandpartlyduetodynamiclift,thelatterbeinglargelypredominantinwindsof40or50m.p.h.Theballooniscaptive,andmayeitherbesentaloftinanaturalwindorbetowedfromaship.Twotypes
ofmodernkiteballoonareshowninFig.10,(a)and(b)showingthelatest andmostsuccessfuldevelopment.Tothetailoftheballoonare jxed three jns,whicharekeptin 6atedinawindbythepressureofairina swapattached gtothelower jn.Withthisarrangementtheballoon swingsslowlybackwardsandforwardsaboutaverticalaxis,andtravels sidewaysasanaccompanyingmovement. ThekitewireisshowninFig.lobascomingtoamotorboat.The secondropewhichdipsintotheseaisanautomaticdeviceformaintaining theheightoftheballoon.Thegeneralsteadinessoftheballoondepends onthepointofattachmentofthekitewire,andtheimportantdifference illustratedbythetypesFig.10(a)and(c)isthatthelatterbecomeslongitudinallyunstableathigh-windspeedsandtendstobreakaway,theformerdoesnotbecomeunstable.Thegeneraldisposition
oftheriggingisshownmostclearlymFig.10a,whereariggingband isshownfortheattachmentofthecarandkiteline.CHAPTER11
THEPRINCIPLESOFFLIGHT
(i)TunAsaopnxns Indevelopingthematterundertheaboveheading,anendeavourwillbe madetoavoidthe jnerdetailsbothofcalculationandofexperiment.In thelaterstagesofanyengineeringdevelopmenttheamountoftimedevoted tothedetailsinordertoproducethebestresultsisapttodullthesense ofthoseimportantfactorswhicharefundammtalandcommontoall discussionsofthesubject.Itusuallyfallstoafewpioneerstoestablish themainprinciples,andaviationfollowstherule.Therelationsbetween lift,resistanceandhorsepowerbecamethesubjectofgeneraldiscussion amongstenthusiastsintheperiod1896-1900mainlyowingtotheresearches ofLangley.Maximmadeanaeroplaneembodyinghisviews,andwecan nowseethatonthesubjectsofweightandhorsepowertheseestablishedthefundamentaltruths.Methodsof dataandofmakingcalculationshaveimmovedandhavebeenextended tocoverpointsnotarisingintheearlydaysof 6ight,andoneextension istheconsiderationof 6ightataltitudesofmanythousandsoffeet. Themainframeworkofthepresentchapteristherelatingofexpo mentaldatatotheconditionsof kight,andtheexperimentaldatawillbe takenforgranted.Laterchaptersinthebooktakeuptheexamination oftheexperimentaldataandthe jnerdetailsoftheanalysisandprediction ofaeroplaneperformance.Wings dThemostprominentimportantpartsofanaeroplanearethe wings,andtheirfunctionisthesupportingoftheaeroplaneagainstgravita tionalattraction.Theforceonthewingsarisesfrommotionthroughthe air,andisaccompaniedbyadownwardmotionoftheairoverwhichthe wingshavepassed.Theprincipleofdynamicsupportina 6uidhasbeen calledthesacri jcial hprinciple(byLordRayleigh,Ibelieve),andstated broadlyexpressesthefactthatifyoudonotwishtofallyourselfyoumust makesomethingelsefall,inthiscaseair. IfAB,Fig.11;betakentorepresentawingmoviuginthedirectionofthe arrow,itwillmeetairatrestatCandwillleaveitatEEenduedwitha downwardmotion.Now,fromNewton fslawsofmotionitisknownthat therateatwhichdownwardmomentumisgiventothe 6uidisequalto thesupportingforceonthewings,andifweknewtheexactmotionof theairroundthewingtheupwardforcecouldbecalculated.Theproblemis,however,toodif jcultforthepresentstateofmathematicalknowledge,andourinformationisalmostentirelybasedontheresultsoftestson
modelsofwingsinanarti jcialaircurrent. 18THEPRINCIPLESOFFLIGHT19
Thedirectmeasurementofthesustainingforceinthiswaydoesnot involveanynecessityforknowledgeofthedetailsofthe 6ow.Itisusual todividetheresultantforceRintotwocomponents,Lthelift, eandD thedrag,buttheessentialmeasurementsintheaircurrentarethemagni tudeofRanditsdirection7,thelatterbeingreckonedfromthenormal tothedirectionofmotion.Theresolutionintoliftanddragisnotthe onlyusefulform,anditwillbefoundlaterthatinsomecalculationsitis convenienttousealine jxedrelativetothewingasabasisforresolution ratherthanthedirectionofmotion. Nomatterbywhatmeanstheresultsareobtained,itisfoundthatthe supportingforceorliftofanaeroplanewingcan~berepresentedbycurves suchasthoseofFig.12.Theliftingforcedependsontheanglea.(Fig.11) theaerofoilmakestherelativewind,anditisinterestingto jndthatthebepositivewhena.isnegative,i.e.whenthe relativewindisapparentlyblowingontheuppersurface.Thechord,is. thestraightlinetouchingthewingontheundersurface,isinclineddown wardsat8°ormorebeforeawingofusualformceasestolift. Theliftonthewingdependsnotonlyontheangleofincidenceand ofcoursethearea,butalsoonthevelocityrelativetotheair,andfor full-scaleaeroplanestheliftisproportionaltothesquareoftheSpeedat thesameangleofincidence.Ofcourseinanygiven 6yingmachinethe weightofthemachineis jxed,andthereforetheliftis jxed,anditfollowsfromtheabovestatementthatonlyonespeedof 6ightcancorrespondmthagivenangleofincidence,andthatthespeedandangleofincidencemustchangetogetherinsuchawaythattheliftisconstant.Thisrelation
caneasilybeseenbyreferencetoFig.12.ThecurveABCDEisobtainedbyexperimentasfollowsAwing(inpracticeamodelofitisusedand
20APPLIEDAERODYNAMICS
multiplyingfactorsapplied)ismovedthroughtheairataspeedof40m.p.h. Inoneexperimenttheangleofincidenceismadezero,andthemeasured liftis840lbs.ThisgivesthepointPofFig.12.Whentheangleof incidenceis5°theliftis900lbs.,andsoon.Inthecourseofsuchan experiment,thereisreachedanangleofincidenceatwhichtheliftisa maximum,andthisisshownatDinFig.12foranangleofincidenceof17°orForanglesofincidencegreaterthanthisitisnotpossibleto
carrysomuchloadat40m.p.h.Withoutanyfurtherexperimentsitis nowpossibletodrawtheremainder:ofthecurvesofFig.12.AtBthelift for40m.p.h.hasbeenfoundtobe610lbs.AtB1itwillbe610XGS) hlbs., 24300eQ k j k
BSa eA
-sAomcunarlonorCHORD(DEGREES)Fro.l2. dWingliftandspeed.
at610X( jglbsandsoon,theliftforagivenanglebeingproportional tothesquareofthespeed. NowsupposethatthewingsforwhichFig.12waspreparedarctobe usedonanaeroplaneweighing2000l.At85m.p.h.thewingscannotbemadetocarrymorethan1580lbs.,andconsequentlytheaeroplanewillneedtogetupaspeedofmorethan85m.p.h.beforeitcanleavetheground.
At40asweseeatD,theweightcanjustbelifted,andthiscon stitutestheslowestpossible 6yingspeedofthataeroplane.Theangleof incidenceisthen17to18degrees.Ifthespeedisincreasedto50m.p.h. therequiredliftisobtainedatanangleofincidenceratherlessthan andsoon,untiliftheengineispowerfulenoughtodrivetheaerOplaneat100m.p.h.theangleofincidencehasasmallnegativevalue.
22APPLIEDAERODYNAMICS
ItisnowpossibletomakeTable]showingtheresistanceoftheaeroplaneatvariousspeeds,andtoestimMethenethorsepowerrequiredto
propelanaeroplaneweighing2000lbs.Thelossesintheorgansofpro pulsionwillnotbeconsideredatthispoint,butwillbedealtwithalmost diatelywhendeterminingthehorsepoweravailable. AroughideaofthebrakehorsepoweroftheenginerequiredforANGLEOFINCIDENCEDEGREES
Fro.13. dWingdragandspeed.
horizontal 6ightcanbeobtainedbyassumingapropellerof60percent.inallcases.Itwillthenbeseenthattheaeroplanewould
justbeableto 6ywithanengineof45horsepowerataspeedof approximately50m.p.h.At70m.p.h.thebrakehorsepowerofthe enginewouldneedtobenearly80,whilstto 6yat100m.p.h.would neednolessthan225horsepower.Byvariousmodi jcationsofwingarea thehorsepowerforagivenspeedcanbevariedconsiderably.butthe examplegivenillustratesfairlyaccuratelythelimitsofspeedofanTHEPRINCIPLESOFFLIGHT28
aeroplaneoftheweightassumed;c.g.anenginedeveloping100horse powermaybeexpectedtogivea kight-speedrangeoffrom40m.p.h. to80m.p.h.toanaeroplaneweighing2000lbs.ResistanceofreatofTotalresistance
aeroplane(lbs),(lbs). ThePropulllve[comm-Uptothepresentthecalculationshave referredtothebehaviouroftheaeroplane,withoutdetailedreferenceto themeansbywhichmotionthroughtheairisproduced. proposedtoshowhowthenecessaryhorsepowerisestimatedinorderthat theaeroplanemay 6y.Thisestiniate finvolvestheconsiderationofthe airscrew. Anairscrewactsontheairinamannersomewhatsimilartothatof awing,andthrowsairbackwardsinacontinuousstreaminorderto produceaforwardthrust.Thethrustisobtainedfortheleastex penditureofpoweronlywhentherevolutionsoftheengineareinavery specialrelationtotheforwardspeed. Increaseofthespeedofrevolutionwithoutalterationoftheforward speedoftheaeroplaneleadstoincreasedthrust,butthelawofincreaseis complex.Increasingthespeedoftheaeroplaneusuallyhastheeffectof decreasingthethrust,againinamannerwhichitisnoteasytoexpress simply.Calculationscanbemadetoshowwhattheairscrewwilldo underanycircumstances,butthediscussionwillbelefttoaspecialchapter. Onesimwelawcan,however,bededucedfromthebehaviourofair screws,andisofmuchthesamenatureasthatalreadypointedoutforthe supportingsurfaces.Itwasstatedthat,iftheangleofincidenceiskept constant,theliftanddragofawingincreaseinproportiontothesquare ofthespeed.Nowintheairscrew,itwillhefoundthattheangleof incidenceofeachbladesectioniskeptconstantiftherevolutionsare increasedinthesamepreportionastheforwardspeed,andthatunder suchconditionsthethrustandtorquebothvaryasthesquareofthe speed.Iffromaforwardspeedof40m.p.h.andarotationalspeedof600r.p.m.theforwardspeedbeincreasedto80m.p.h.andthe
rotationalspeedto1200thethrustwillbeincreasedfourtimes. Givenatableof jgures,suchasTable2,whichshowsthethrustof anairscrewatseveralSpeedsofrotationwhentravellingat40m.p.h. throughtheair,resultscanbededucedforthethrustatothervaluesof theforwardspeedinthemannerdescribedbelow. nethorsepowerisheremeantthepowernecessarytodriveB perfectlgref jcientmeansofpropulsionexisted.Theconditionsarevery anaeroplanewhengliding;24APPLIEDAERODYNAMICS
The jguresinTable2wouldbeobtainedeitherbycalculationorby anexperiment.Testsonairscrewsarefrequentlymadeattheendofa longarmwhichcanberotated,sogivingtheairscrewitsforwardmotion. Actualairscrewsmaybetestedonalargewhirlingarm,oramodelair screwmayheusedinawindchannelandmultiplyingfactorsemployed toallowforthechangeofscale.Forwardspeed40m.p.h.
Revs.perminute.Thrust
ItwillbenoticedfromTable2thattheairscrewgivesnothrustuntil rotatingfasterthan500r.p.m.Atlowerspeedsthanthistheairscrew wouldopposearesistancetotheforwardmotion,andwouldtendtobe turningasawindmill.Whenthesubjectisenteredintoinmoredetail itwillbefoundthatthenumberofrevolutionsnecessarybeforeathrust isproducedisdeterminedbythepitchoftheairscrew.Thetermpitchisobtainedfromananalogybetweenanairscrewandascrew,theadvanceofthelatteralongitsaxisforonecompleterevolutionbeingknownasthepitch. hWhilstthereareobviousmechanicaldifferences
betweenasolidscrewturninginitsnutandanairscrewmovingina mobile 6uid,theexpressionhasmanyadvantagesinthelattercaseand willbereferredtofrequently.Forthepresentitisnotnecessarytoknow howpitchisde jned. ThenumbersgiveninTable2correspondwiththecurvemarked ABCinFig.14.Todeducethoseforanyotherspeed,say60the jrstcolumnismultipliedby38andthesecondby,givingthe followingtable:Forwardspeed00m.p.h.
Revs.perminute.Thrust(M).
Itwillbenoticedthattheairscrewmustnowberotatingmuchmore rapidlythanbeforeinordertoproduceathrust.Theremainingcurves ofFig.14wereproducedinasimilarway,andrelatetospeedsoftheTHEPRINCIPLESOFFLIGHT25
ing2000lbs.Thethrustnecessarytosupporttheaeroplaneintheairat speedsof40,50,60,70and100m.p.h.hasbeenobtainedinTable1,and usingFig.14itisnowpossibletoobtainthepropellerrevolutionswhich arenecessarytoproducethisrequiredthrust.Thepointsaremarked C,C,,03,C3and04.Toproduceathrustof610lbs.at40m.p.h.the propellermustbeturningatabout1880asshownatthepoint0. speedrisesto50m.p.h.theenginemaybeshutdownveryappro therevolutionsbeingonly980.Forhighervelocitiesof 6ighttheAlRSCREWREVOLUTIONS0
F10.lea dThrustandspeed.
revolutionsincreasesteadily,untilat100m.p.h.therateofrota tion18over1600r.p.m.Theenginemay,however,notbepowerfulenough todrivethepropellerattheserates,anditisnownecessarytoestimate, inamannersimilartothatforthrust,howmuchhorsepower18required. TheinitialdatagiveninTable4areagainassumedtohavebeenTABLE4. dArasonxwHoasnrowxnarmSeam).
Forwardspeed40m.p.h.
26APPLIEDAERODYNAMICS
obtainedexperimentally,andthe jguresfromthistable' areplottedinFig.15inthecurveABC.Toobtainthecurvefor60m.p.h.the jrstcolumnofTable4ismultipliedby$23andthesecondby( jgobtaimngthenumbersgiveninTable5.
r.pmAIRSCREWREVOLUTIONS.
Thecurvessoobtainedforvarious kightspeedsindicate
powerbeforetheairscrewhasstepped.TheSpeedsarelowerthanthoseforwhichthethrusthasbecomezero,andindicatethepointsatwhich
theairscrewbecomesawindmill.Inanaeroplane,however,theresistancetoturningoftheenginewouldgreatlyreducethespeedatwhichthewindmillbecomese k f
ectivebelowthatindicatedforno-horsepower,andstoppage ofthepetrolsupplytotheenginewouldoftenresultinthestoppageoftheairscrew.THEPRINCIPLESOFFLIGHT27
FromFigs.14and15it18noweasyto jndthebrakehorsepowerof theenginewhichwouldbenecessarytodrivetheaeroplanethroughthe atspeedsfrom40to100m.p.h.FromFig.14itisfoundthatthe aeroplanewhentravellingat50m.p.hthroughtheairneedsanairscrewspeedof980r.p.m.Todrivetheairscrewatthisspeed18seenfromFig.pointC,,toneed89horsepower.ForotherSpeedsthehorsepoweris
indicatedbythepointsC,02,C3andC4,andthecollectedresultsare giveninTable6.8ofamplancHomewardMme.)neon-cantor
OnFig.15alineOPhasbeendrawnwhichrepresentstheworkwhich particularenginecoulddoatthevariousspeedsofrotation,thisagainisanexperimentalcurve.Theengineissupposedtobegiving120h.p.at1200r.p.m.Itwillbeseen,fromFig.15,thattheengineisnotpowerful
enoughtodrivetheaeroplaneateitherthelowestorthehighestSpeedsfor thecalculationshavebeenmade.FormanypurposestheinformationgiveninFig.15ismoreconvenientlyexpressedintheformshowninFig.16,wheretheabscissa18the 6ightSpeedoftheaerOplane.ThecurveABCDE
ofthelatter jgure18plottedfromthepointsC,01,Oz,03andC4ofFig.15,whilethelineFGHcorrespondswiththepointsB,E,,BJB,andB4.
The jrstcurveshowsthehorsepowerrequiredfor 6ight,andthesecond thehorsepoweravailable.Fromthediagram1nthisformitiseasilyseen thatthepointFrepresentstheslowestspeedatwhichtheaeroplanecan ky,inthiscase403m.p.h.,andthatHshowsthepossibilityofreachinga speedofnearly98m.p.h. Fig.16showsmorethanthis,foritgivesthereservehorsepoweratany speedof 6ight.Thisreservehorsepowerisroughlyproportionaltothe Speedatwhichtheaeroplanecanclimb,andthecurveshowsthatthebest climbingSpeedismuchnearertothelowerlimitofspeedthantothe GenealncmarksonFigc.12 d16 dCalculationsrelatingtothe 6ightspeed ofanaeroplaneareillustratedfairlyexactlybythecurvesinFig.12-16. Asthesubjectisenteredintoindetailmanysecondaryconsiderationswill beseentocomein.Thedif jcultieswillbefoundtoconsistverylargelyinthedeterminationofthestandardcurvesmarkedABCDEinthe jgures,andtheanalysisofresultstoobtainthesedataconstitutesoneofthemore
laboriouspartsoftheprocess.Thecomplicationisverylargelyoneof detail,andshouldnotbeallowedtoobscurethecommonbasisof 6ight conditionsforallaeroplanesastypi jedbythecurvesofFigs.12 d16.28APPLIEDAERODYNAMICS
ClimbingFlight dInthemoregeneraltheoryoftheaeroplaneitis ofinteresttoShowhowthepreviouscalculationsmaybemodi jedto include 6ightsotherthanthoseinahorizontalplane.Therateatwhich aerOplanecanclimbhasalreadybeenreferredtoincidentallyincon naotienwithFig.16. Itisclearfromtheoutsetthattheairforcesactingontheaeroplane dependonitsspeedandangleofincidence,andarenotdependent acting forceswillvarywiththeattitudeoftheaeroplane.Iftheaeroplane hingtheairscrewthrustwillneedtobegreaterthanforhorizontal 6ight,whilstifdescendingthethrustisreducedandmaybecomezero ornegative.Thereisaminimumangleofdescentforanyaeroplanewhen coco70acSPCEDOF(wasoutnounTHROUGHam)
Fm.16. dHorsepowerandspeedforlevel kight.
theairscrewisgivingnothrust,andthisangleisoftenreferredtoastheangleofglidefortheaeroplane. hMorecorrectlyitshouldbereferred
toastheleastangleofglide. h Themethodofcalculationofglidingandclimbing 6ightisillustratedinFig.17,whichisadiagramoftheforcesactingonanaeroplaneinfree 6ightbutwithits 6ightpathinclinedtothehorizontal.
Inhorizontal 6yingitwillbeassumedthatthedirectionofthethrustis horizontal,inwhichcaseitdirectlybalancestheresistanceoftheremainder oftheaerOplanetomotionthroughtheair.'Intheabovediagramthis statementmeansthatT=D.SimilarlytheweightoftheaerOplaneis exactlycounterbalancedbytheliftonthewings,i.e.LW.Theangleof incidenceofthewingsmaybevariedbyadjustmentoftheelevator,in whichcasethethrustwouldnotstrictlyliealongthewind.Ifnecessary aslightcomplicationofformulacouldbeintroducedtomeetthiscase,but thee k' ectofthisvariationissmall,and,inaccordancewiththeideaon30APPLIEDAERODYNAMICS
Equation(2)cannowbeusedtoshowhowdiagrams12and18maybe alteredtoallowforinclined kight.Inthe jrstplacetheordinatesof Fig.18,which,afteradditionofthedragofthebody,showthevalue ofDformanyanglesofincidence,needtobedecreasedbymultiplying bycos0togiveDcos0.Theeffectofthismultiplicationisverysmall asarule.At10°thefactoris0985,andat0940.Foravery steepSpiralglideatsaythedifferencebetweencos0andunitybecomes important,cos0beingthen0707. TothevalueofDcos0istobeaddedatermWsin9inordertoobtainthethrustoftheairscrewwhenclimbingatanangle0.Wemaythenmakeatableasbelow,using jguresfromTable1toobtainthesecond
column.TABLE7.-T1mva'rwwwmama.
DraginbcrlmntalAlrmvthrustwhen
nightxcos9climbingat6 h(lbs). Theangleofclimbwaschosenarbitrarilyatandtocompletethe investigationofthepossibilitiesofclimbTable7wouldberepeatedfor otherangles.UsingFigs.14and15fortheairscrewasforhorizontal 6ight,wemaynowcalculatethehorsepowerrequiredfor 6ightwhen climbing,andsoobtainthe jguresofTable8.TABLE8. dHoasxrownawantcamma.
Atthelowestandhighestspeedsofthetablethehorsepowerrequired isfarg'reater fthanthatavailable,andthe jguresarenotwithintherange ofFi16.maynowproceedtoplotthehorsepowerofTable8againstspeed toobtainadiagramcorrespondingwithFig.16.Thenewcurvemarked A1B101D1inFig.18comparedwithABCDEasreproducedfromFig.16 showsanincreaseofnearly50h.p.atallSpeedsduetotheclimbat ThehighestSpeedof 6ightisshownbytheintersectionofAlBlclwith FGHatH5.FGHisthehorsepoweravailable,andisthesameasthe similarlymarkedcurveofFig.16.ThehighestSpeedis7andTHEPRINCIPLESOFFLIGHT81
sincetheangle0isconstantalongAlBlcltherateofclimbwillbe greatestatthispointfortheconditionsassumed.Rateofclimb,V, his commonlyestimatedinfeetperminute,andwethenhaveMax.V,ford5°88XVa h,xsin0
88Xx00875
ThecalculationsshowninTables7and8havebeenrepeatedforother anglesofclimbandoneangleofdescenttoobtaincorrespondingcurvesODKIOOIPLIOPIY(MILESPERHOUR)
Fm.18. dHorsepowerandspeedforclimbingflight.
i brlig.18.TheintersectionsH4,H0,etcthenprovidedataforTable9ow.TABLE9. dRu'zor0mmumSeas».
Unimnmratsa!climbAnglectclimb.torlivenI
5915582
5113
Flightnotpossible.
Table9showsthattherateofclimbvariesrapidlywiththe 6ightspeed theneighbourhOOd100m.p.h.to80butthatfrom ,65m.p.h.to56m.p.h.thevalueofrateofclimbvariesonlyfrom725to780.This
illustratesthewell-knownfactthatthebestrateofclimbofanaeroplane isnotmuchaffectedbysmallinaccuraciesinthe 6ightspeed. Thetableshowsanotherinterestingdetail;themaximumangleof82APPLIEDAERODYNAMICS
climbisbutthegreatestrateofclimboccursatasmallerangle. Forreasonsconnectedwiththecontroloftheaeroplaneanangleof8°or thereaboutswouldprobablybechosenbyapilotinsteadofthe showntobethebest.Dim-Bydivingismeantdescentwiththeengineon,as
distinguishedfromaglidemwhichtheengineiscuto k' .Iftheenginebe keptfullyonitisfoundthatthespeedofrotationoftheairscrewriseshigherandhigherastheangleofdescentincreases.Thereis,however,anupperlimittotheSpeedatwhichanaeroplaneenginemayberunwith
safety.andmourillustrationanappropriatelimitwouldbe1600r.p.m. ThespeedofrotationcorrespondingwithH4was1550r.p.m.,anditwill beseenthatthenewrestrictionwillcomeintooperationforsteeper descent.Fig.14,ifextended,wouldnowenableustodeterminethethrust oftheairscrewatany13dwithoutreferencetothehorsepower,butit willbeevidentthatthe'limitsofusefulnessofeachoftheprevious jgures havebeenreached,andanextensionofexperimentaldataisnecessaryto coverthehigherspeeds. Thefactthatundercertaincircumstancesforcesvaryasthesquare offorwardSpeedoftheaeroplanesuggestsamorecomprehensiveformof presentationthanthatofFigs.12,18,14and15,andthenewcurvesof Figs.19and20showanextensionoftheoldinformationtocoverthe newpointsoccurringintheconsiderationofdiving.Thevaluesofthe extendedportionaresosmallthatonanyappreciablescaleitisonly possibletoshowtherangecorrespondingwithsmallanglesofincidence andforsmallvaluesofthrustandhorsepower.TABLElo. dA1asoa:wTnausrwussnrvmo.
thrustThecurveconnectingV3m.p.h.andspeedisshowninFig.21.Insteadofequation(2)willbeusedtheequation
Va nish.Vzm.TheuseofD1insteadofDcos0isconvenientnowsincethe
level kightathighSpeedsisnotdeterminedinanyothercalculation.IncompilingTable11someangleofpathsuchas d10°ischosen,andvarious
speedsof 6ightareassumed.FromtheseSpeedsthethirdcolumnis