[PDF] Applied Aerodynamics - Forgotten Books

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:LATEQUPERINTKNDRNfIeOPTKR AFEODYNANICSDEPARTMENTOPTHRNATIONALPHYSICALLABORATORY

ILL0sdTIONSAND

NEWYORK

LONGMANS,GREENANDCO.

FOURTHAVENUEAND3015STREET

39,PATERNOSTERROW,LONDON

BOMBAY.CALCUTTA,ANDMADRAS

1920

A11right:hram!

233672E

APR10moCkg?Kl?g

lac. EYTS Bic

PREFACE

Tnaworkaimaattheextractionofprinciplesof6ightfrom,andthe

illustrationoftheuseof,detailedinformationonaeronauticsnowavailablefrommanysources;notablythepublicationsoftheAdvisory

CommitteeforAeronautics.Themainoutlinesofthetheoryof6ightaresimple,butthestageofapplicationnowreachednecessitatescarefulexaminationofsecondaryfeatures.Thisbookiscastwiththisdistinction

inViewandstartswithadescriptionofthevariousclassesofaircraft,bothheavierandlighterthanair,andthenproceedstodevelopthe

lawsofsteady6ightonelementaryprinciples.Laterchapterscomplete

thedetailasknownatthepresenttimeandcoverpredictionsandanalysesofperformance,aeroplaneacrobatics,andthegeneralproblems

ofcontrolandstability.Thesubjectofaerodynamicsisalmostwholly basedonexperiment,andmethodsaredescribedofobtainingbasic informationfromtestsonaircraftin6ightorfromtestsinawindchannelonmodelsofaircraftandaircraftparts. Theauthorisanxioustoacknowledgehisparticularindebtednessto

theAdvisoryCommitteeforAeronauticsforpermissiontomakeuseofreportsissuedunderitsauthority.Extensivereferenceismadetothosereportswhich,priortothewar,wereissuedannually;itisunderstood

thatallreportsapprovedforissuebeforethebeginningof1919arenowreadyforpublication.Tothismaterialtheauthorhashadaccess,but

itWillbeunderstoodbyallintimatelyuaiutedwiththereportsthat

thecontentscannotbefullyrepresenbyextracts.Thepresentvolumeisnotanattemptatcollectionoftheresultsofresearch,butacontributiontotheirapplicationtoindustry.

Forthelastyearofthewartheauthorwasresponsibletothe

DepartmentofAircraftProductionfortheconductofaerodynamicresearchonaeroplanesin6ight,andhisthanksaredueforpermission

tomakeuseofinformationacquired.ForpermissiontoreproducephotographsacknowledentismadetotheAdmiraltyAirshipDepartment,Messrs.HandleyageandCc.,theBritishandColonialAeroplane

Cc.,thePliw-nixDynamoCc.,Messrs.D.NapierandCc.,andELM.

StationeryOjice.

L.BAIBSTOW.mumsWren,

October6th,1919.

viiiCONTENTS

AERIALBIANOEUVRESANDTHEEQUATION01"MOTION

CONTENTS

ofpetrolandoildMoreaccuratemethodofprediction-GeneraltheorydData ofclimbdTheoryofreductionfromactualtostandardatmospheredLevelkights

CONTENTS

LISTOFPLATES

Fourteentensofmatterinkight

FightingBiplaneScout

CockpitofanAeroplane

RotaryEnginedAir-cooledStationaryEngine

Waiter-cooledEngine

NearlycompletedRigidAirship

C000Q0O0Q0Q

ExperimentalarrangementofTubeAnemometeronanAeropla 0

ModelAeroplanearrangedtoshowAutorotation

EddiesbehindCylinder

FlowofWaterpastanInclinedPlate.LowandHighSpeeds

FlowofAirpastanInclinedPlate.LowandHighSpeeds

VeryStableModeldSlightlyStableModel

StableModelwithtwoRealFinsdModelwhichdevelopsanUnstable OscillationdModelwhichillustratesLateralInstabilities

CHAPTERI

GENERALDESCRIPTIONOFSTANDARDFORMSOFAIRCRAFT

In'raonvcrron

IntheOpeningreferencestoaircraftasrepresentedbyphotographsof moderntypes,bothheavier-than-airandlighter-than-air,attentionwill bemoreespeciallydirectedtothosepointswhichspecijcallyrelatetothe subject-matterofthisbook,i.e.toappliedaerOdynamics.Strictlyin terpreted,thewordaerodynamicsisusedonlyforthestudyoftheforces

onbodiesduetotheirmotionthroughtheair,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 forceshasextensionswhichak' ecttheexternalformtakenbyaircraft. Oneofthemostimportantitemsinaircraftdesignistheeconomical distributionofmaterialsoastoproduceasufjcientmarginofstrength fortheleastweightofmaterial.Acceptingthestatementthatadditional aconsequenceofincreasedweight,itwillbeappreciatedthat theproblemofexternalformcannotbedeterminedsolelyfromaerodynamic considerations.Asanexampleofasimpletypeofcompromisemaybe instancedtheproblemofwingform.Thegreatestliftforagivenresistance isobtainedbytheuseofsinglelongandnarrowplanes,theadvantagebeing lessandlessmarkedastheratiooflengthtobreadthincreases,butremaining appreciablewhentheratioisten.MostaerOplaneshavethisaspect ratiomorenearlyequaltosixthenten,andinsteadofthesingleplaneadoublearrangementispreferred,theek' ectofthedoublingbeingan appreciablelossofaerodynamicekiciency.Thereasonswhichhaveled

tothisresultarepartlyaccountedforbyaspecialconvenienceinjghtingwhichaccompaniestheuseofshortplanes,butafactorofgreaterimportanceisthatarisingfromthestrengthdesiderata.Theweightof

wingsoflargeaspectratioisgreaterforagivenliftingcapacitythanthat ofshortwings,andtheexternalsupportnecessaryinalltypesofaerOplane ismoredifjculttoachievewithaerodynamiceconomyforasinglethan foradoubleplane.Aerodynamically,alimitisjxedtotheweight 1n

2APPLIEDAERODYNAMICS

carriedbyawingatachosenspeed,andforsafealightingthetendency

hasbeentojxthisspeedatalittleoverfortymilesanhour.ThisgivesalowerlimittothewingareaofanaerOplanewhichhastocarryaspecijed

weight.Thegeneralexperienceofdesigiershasbeenthatthislimitisaseriousrestrictioninthedesignofamonoplane,butoffersverylittle

biplane.Inafewcases,threeplaneshavebeensuperposed,butthetypehasnotreceivedanygeneraldegreeofacceptance.For

smallaerOplanes,thefurtherlossofaerodynamicefjciencyinatriplane hasbeenacceptedforthesakeofthegreaterrapidityofmanaauvrewhich canbemadetoaccompanyreducedspanandchord,whilstinverylarge aerOplanesthechiefadvantageofthetriplaneisareductionoftheoverall dimensions.Uptothepresenttimeitappearsthatanadvantageremains withthebiplanetypeofconstruction,althoughverygoodmonOplanesand triplaneshavebeenbuilt. Theillustrationshowsthataircrafthaveenteredthestageofengineer ingasdistinctfromaerodynamicalsciencehinthatthejnalproduct

isdeterminedbyanumberofconsiderationswhicharemutuallyrestrictiveandinwhichthepracticalknowledgeofusageisaveryimportantfactor

intheattainmentofthebestresult. Althoughairisthe6uidindicatedbythetermaerodynamics,it hasbeenfoundthatmanyofthephenomenaof6uidmotionareindependent

oftheparticular6uidmoved.Advantagehasbeentakenofthisfactinarrangingexperimentalwork,andinalaterchapterastrikingOptical

illustrationofthetruthoftheaboveobservationisgiven.Thedistinction betweenaerodynamicsandthedynamicsof6uidmotiontendstodisappear inanycomprehensivetreatmentofthesubject. Intheconsiderationofaerialmanoeuvresandstabilitytheaero

dynamicsofthemotionmustberelatedtothedynamicsofthemovingmasses.Itisusualtoassumethataircraftarerigidbodiesforthepurposes

indicated,andingeneraltheassummionisjustijable.Inafewcases,as incertainjnsofairshipswhichde6ectunderload,greaterrejnementmay benecessaryasthescienceofaeronauticsdeveIOps. Itwillreadilybeunderstoodthataerodynamicsinitsstrictinter pretationhaslittledirectconnectionwiththeinternalconstructionof aircraft,theimportantitemsbeingtheexternalformandthechangesof itwhichgivethepilotcontroloverthemotion.Asthesubjectisinitself

extensive,andastheinternalstructureisbeingdealtwithbyotherwriters,thepresentbookaimsonlyatsupplyingtheinformationbymeansof

whichtheforcesonaircraftinmotionmaybecalculated. Thescienceofaerodynamicsisstillveryyoung,anditisthirteenyears onlysincethejrstlongheponanaeroplanewasmadeinpublicbySantos Dumont.ThecircuitoftheEiffelTowerinadirigibleballoonpreceded thisfeatbyonlyashortperiodoftime.Aeronauticsattractedthe attentionofnumerousthinkersduringpastcenturies,andmanyhistorical accountsareextantdealingwiththeresultsoftheirlabours.Formany reasonsearlyattemptsat6ightallfellshortofpracticalsuccess,although theyadvancedthetheoryofthesubjectinvariousdegrees.Thepresent epochofaviationmaybesaidtohavebegunwiththepublicationofthe

STANDARDFORMSOFAIRCRAFT3

experimentsmadeby'LangleyinAmericaintheperiod1890to1900. Theapparatususedwasawhirlingarmjttedwithvariouscontrivances forthemeasurementoftheforcesonkatplatesmovedthroughtheairat theendofthearm. Onelineofexperimentmayperhapsbedescribedbrie6y.Anumber ofplatesofequalareaweremadeandarrangedtohavethesametotal weight,afterwhichtheywereconstrainedtoremainhorizontalandto falldownverticalguidesattheendofthewhirlingarm.Thetimeoffall

oftheplatesthroughagivendistancewasmeasuredandfoundtodepend,notonlyontheSpeedoftheplatethroughtheair,butalsoonitsshape.

Atthesamespeeditwasfoundthattheplateswiththegreatestdimension acrossthewindfellmoreslowlythanthoseofsmalleraspectratio.For smallvelocitiesoffallthetimeoffallincreasedmarkedlywiththeSpeed oftheplatethroughtheair.Byachangeofexperimentinwhichthe plateswereheldonthewhirlingarmataninclinationtothehorizontal andbyrunningthearmatincreasingspeedsthevalueofthelatterwhen theplatejustlifteditselfwasfound.Repetitionofthisexperiment showedthataparticularinclinationgavelessresistancethananyother fortheconditionthattheplateshouldjustbeairborne.

FromLangleyfsexperimentsitwasdeducedthataplateweighingtwopoundspersquarefootcouldbesupportedat85m.p.h.iftheinclination

wasmadeeightdegrees.Theresistancewasthenone-sixthoftheweight,andmakingallowanceforotherpartsofanaeroplaneitwasconcluded

thatatotalweightof750lbs.couldbecarriedfor.theexpenditureof25 horsepower.Earlyexperimenterssetthemselvesthetaskofbuildinga completestructurewithintheselimitations,andsucceededinproducing aircraftwhichliftedthemselves. Langleyputhisexperimentalresultstothetestofa6ightfromthe tOpofahouseboatonthePotomacriver.Owingtoaccidenttheaero planedivedintotheriverandbroughttheexperimenttoaveryearlyend. InEngland,MaximattemptedthedesignofalargeaerOplaneand engine,andachievedanotableresultwhenhebuiltanengine,exclusive ofboilersandwater,whichweighed180lbs.anddeveloped860horse power.Toavoidthedifjcultiesofdealingwithstabilityin6ight,the aerOplanewasmadecaptivebyjxingwheelsbetweenupperandlower rails.Theexperimentscarriedoutwereveryfewinnumber,butalift oflbs.wasobtainedbeforeoneofthewheelscarriedawayafter contactwiththeupperrail. Forsometenyearsaftertheseexperiments,aviationtookanew direction,andattemptstogainknowledgeofcontrolbytheuseofaero planeglidersweremadebyPilcher,LilienthalandChanute.Fromahill builtforthepurposeLilienthalmadenumerousglidesbeforebeingcaught inapowerfulgustwhichhewasunabletonegotiateandwhichcosthim hislife.Inthecourseofhisexperimentshediscoveredthegreatsuperiority ofacurvedwingovertheplanesonwhichLangleyconductedhistests. Byasuitablechoiceofcurvedwingitispossibletoreducetheresistance tolessthanhalfthevalueestimatedfor6atplatesofthesamecarrying capacity,Theonlycontrolattemptedintheseearlyglidingexperiments

4APPLIEDAERODYNAMICS

wasthatwhichcouldbeproducedbymovingthebodyoftheaeronaut inadirectiontocounteracttheek' ectsofthewindforces. InthesameperiodveryrapidprogresswasmadeinthedeveIOpmvnt ofthelightpetrolmotorforautomobileroadtransport,andbetween1900

and1908itbecameclearthattheprospectsofmechanical6ighthadmateriallyimproved.Thejrstachievementsofpower-drivenaeroplanes

tocallforgeneralattentionthroughouttheworldwerethoseoftwo Frenchmen,HenriBarmanandBleriot,whomadenumerousshort6ights whichwerelimitedbylackofadequatecontrol.Thesetwopioneerstook Oppositeviewsastothepossibilitiesofthebiplaneandmonoplane,but intheendthefirstproducedanaeroplanewhichbecameverypopular asatrainingaeroplanefornewpilots,whilstthesecondhadthehonour ofthejrstcrossingoftheEnglishChannelfromFrancetoDover. Thelackofcontrolreferredto,existedchie6yinthelateralbalanceof theaeroplanes,itbeingdikiculttokeepthewingshorizontalbymeans oftherudderalone.TherevolutionarystepcamefromtheBrothersWright inAmericaastheresultofapatientstudyoftheproblemsofgliding.A lateralcontrolwasdevelopedwhichdependedonthetwistingorwarping oftheaeroplanewingssothattheliftonthedepressedwingcouldbe increasedinordertoraiseit,withacorrespondingdecreaseoflift ontheotherwing.Asthechangesofliftduetowarpingwereaccompanied

bychangesofdragwhichtendedtoturntheaeroplane,theBrothersWrightconnectedthewarpandruddercontrolssoastokeeptheaeroplane

onastraightcourseduringthewarping.Theprincipleofincreasingthe liftonthelowerwingbyaspecialcontrol18nowuniversallyapplied,but therudder1snotconnectedtothewingkapcontrolwhichhastakenthe placeofwingwarping.FromthetimeoftheWrights'jrstpublic6ights inEuropein1908theaviatorsoftheworldbegantomcreasetheduration oftheirkightsfromminutestohours.Progressbecameveryrapid,and thespeedof6ighthasrisenfromthe85m.p.h.oftheHenriFarmanto nearly140m.p.h.inamodernjghtingscout.Therangehasbeen increasedtoover2000milesinthebombingclassofaeroplane,andthe AtlanticOceanhasrecentlybeencrossedfromNewfoundlandtoIrelandby theVickersfVimybomber. Assoonastheproblemsofsustainingtheweightofanaemplaneand ofcontrollingthemotionthroughtheairhadbeensolved,manyinvestiga tionswereattemptedofstabilitysoastoelucidatetherequirementsin anaeroplanewhichwouldrenderitabletocontrolitself.Partialattempts

weremadeinFrancefortheaeroplanebyFerber,Seeandothers,butthemostsatisfactorytreatmentisduetoBryan.Startingin1908incollabora

tionwithWilliams,Bryanappliedthestandardmathematicalequations ofmotionofarigidbodytothedisturbedmotionsofanaeroplane,andthe culminationofthisworkappearedin1911.Themathematicaltheory remainsfundamentallyintheformproposedbyBryan,butchangeshave beenmadeinthemethodofapplicationastheresultofthedevelopment ofexperimentalresearchundertheAdvisoryCommitteeforAeronautics. Themathematicaltheoryisfoundedonasetofnumbersobtainedfrom experiment,anditischie6yinthedeterminationofthesenumbersthat

STANDARDFORMSOFAIRCRAFT5

developmenthastakenplaceinrecentyears.Someextensionsofthe mathematicaltheoryhavebeenmadetocover6ightinanaturalwind andinspiralpaths. ExperimentalworkonstabilityonthemodelscaleattheNational PhysicalLaboratorywascc-ordinatedwith6yingexperimentsatthe RoyalAircraftFactory,andtheresultsofthemathematicaltheoryof

stabilitywereappliedbyBuskintheproductionoftheRE.20.aeroplane,which,withcontrolontherudderonly,was6ownfordistancesof60or70milesonseveraloccasions.Bythistime,1914,themainfoundationsof

aviationaswenowknowithadbeenlaid.Thelaterhistoryislargely thatofdetaileddevelopmentunderstressoftheGreatWar. Thehistoryofairshipshasfollowedadifferentcourse.Theproblem ofsupportneveraroseinthesamewayasforaeroplanesandseaplanes, asballoonshadbeenknownformanyyearsbeforetheadventoftheair ship.Thejrstchangefromthefreeballoonwaslittlemorethanthe attachmentofanengineinordertogiveitindependentmotionthrough theair,andthepoweravailablewasverysmall.Thesphericalballoon hasahighresistance,itscourseisnoteasilydirected,andthedirigible balloonbecameelongatedatitsearlieststages.Thelongcigar-shaped formsad0ptedbroughttheirownspecialdifjculties,astheytooaredikicult tosteerandareinclinedtobuckleandcollapseunlesssukicientprecautions aretaken.Steeringandmanagementhasbeenattainedinallcasesby thejttingofjns,bothhorizontalandvertical,totherearoftheairship envelope,andtheproblemofafjxingjnsofsufjcientareatothe6exible envelopeofanairshiphasimposedengineeringlimitationswhichprevent asimpleapplicationofaerodynamicknowledge. Theproblemofmaintenanceofformofanairshipenvelopehasledto severalsolutionsofverydifferentnatures.Inthenon-rigidairshipthe

envelopeiskeptin6atedbytheprovisionofsufjcientinternalpressure,eitherbyautomaticvalveswhichlimitthemaximumpressureorbythe

pilotwholimitstheMum.Theinterioroftheenvelopeisdivided bygastightfabricintotwoorthreecompartments,thelargestofwhich isjlled .withhydrogen,andthesmalleronesarefullyorpartiallyin6ated withaireitherfromtheslipstreamofanairscreworbyaSpecial fan.Astheairshipascendsintoairatlowerpressurethevalvestothe airchambersopenandallowairtoescapeasthehydrogenexpands,and solongasthisispossiblelossofliftisavoided.Thegreatestheightto whichanon-rigidairshipcangowithoutlossofhydrogenisthatforwhich theairchambersorballoonetsareempty,andhencethesizeofthe balloonetsispreportionedbytheceilingoftheairship. Ifthecarofanairshipissuspendednearitscentre,theenvelopeat resthasgasforcesactingonitwhichtendtoraisethetailandhead.The undersideoftheenvelopeisthenintensiononaccountofthegaslift, whilsttheupperside ,isincompression.Asfabriccannotwithstand compression,sufjcientinternalpressureisappliedtocounteracttheeffect oftheliftinproducingcompression. Thecarofthenon~rigidairshipisattachedbycablestotheunderside oftheenvelope,andastheseareinclined,aninwardpullisexertedwhich9

6APPLIEDAERODYNAMICS

tendstoneutralisethetensioninthefabric.Forsomeparticularinternal pressurethefabricwilltendtopucker,andSpecialexperimentsaremade todeterminethispressureandtodistributethepullinthecablessoas tomakethepressureassmallaspossiblebeforepuckeringoccurs.The" experimentismadeonamodelairshipwhichisinvertedandjlledwith water.Theloadsinthecables,theirpositionsandthepressureareall undercontrol,andthenecessarymeasurementsareeasilymade.The theoryoftheexperimentisdealtwithinalaterchapter. Inkighttheexterioroftheenvelopeissubjectedtoaerodynamic pressureswhichareintensenearthenose,butwhichfalloffvery rapidlyatpointsbehindthenose.Fromatendencyofthenosetoblow inunderpositivepressure,achangeoccurstoatendencytosuckoutat

adistanceoflessthanhalfthediameteroftheairshipbehindthenose,andthissuction,invaryingdegrees,persistsoverthegreaterpartofthe

envelope.AthighSpeedsthetendencyofthenosetoblowinisvery greatascomparedwiththeinternalpressurenecessarytoretaintheform oftherestoftheenvelope,andareductionintheweightoffabricusedis obtainedifthenoseisreinforcedlocallyinsteadofmaintainingitsshape byinternalpressurealone.Inoneofthephotographsofthischapterthe reinforcementofthenoseisveryclearlyshown. Theproblemofthemaintenanceofformofanon-rigidairshipis appreciablysimplijediftheweighttobecarriedisnotallconcentrated inonecar. Inthesemi-rigidairshiptheenvelopeisstilloffabricmaintainedto formbyinternalpressure,butbetweentheenvelopeandcarisinterposed alonggirderwhichdistributestheconcentratedloadofthecaroverthe wholesurfaceoftheenvelope.Thistypeofairshiphasbeenusedin France,buthasreceivedmostdevelopmentinItalyitisnotusedinthis country. Rigidairshipsdependuponametalframeworkforthemaintenance oftheirform,andinGermanyweredevelopedtoaveryhighdegreeof efjciencybyCountZeppelin.Thelargestairshipsareofrigidconstruction andhaveagrossliftofnearlyseventytons.Theframeworkisusually

ofalightaluminiumalloy,occasionallyofwood,andinthefuturesteelmaypossiblybeused.Thestructureisalightlatticeworksystemofgirders

runningalongandaroundtheenvelopeandbracedbywiresintoastiff frame.Inmoderntypesakeelgirderisprovidedinsidetheenvelopeat thebottom,whichservestodistributetheloadfromthecarsandalso

furnishesacommunicationway.Thenumberofcarsmaybefourormore,andthebendingundertheliftofthehydrogen1skeptsmallbyacareful

choiceoftheirpositions.Someofthetransversegirdersarebracedinside theenvelopebyanumberofradialwires,thecentresofwhicharejoined byawirerunningthewholelengthoftheairshipalongitsaxis.Inthe compartmentssoproducedthegas-containersare6oated,andtheliftis transferredtotherigidframebythepressureonanettingofsmallcord. Thelatticeworkiscoveredbyfabricinordertoproduceasmooth unbrokensurfaceandsokeepdowntheresistance.Speedsof75m.p.h. havebeenreachedinthelatestBritishtypesofrigidairship,andthereturn

8APPLIEDAERODYNAMICS

thedirectionofPrandtl,ofwhichnoresultshavebeenobtainedinthis country.SomeoftheGermanwritersonstabilitywerefollowingclosely

alongparallellinestothoseofBryaninBritain,andhad,priorto1914,arrivedattheideaofmaximumlateralstability.

TheotherEuropeanlaboratoryofnotewasatKoutchinonearMoscow,withD.Riabouehinskyasdirector.Thislaboratoryappearstohavebeen

aprivateestablishment,andplayedayeryusefulpartinthedevelopment ofsomeofthefundamentaltheoriesof6uidmotion.Thepracticaldemand onthetimeoftheexperimentersappearstohavebeenlessseverethanin themoreWesterncountries.

ANationalAdvisoryCommitteeforAeronauticswasformedatWashingtononApril2,1915,bythePresidentoftheUnitedStates.

Reportsofworkhaveappearedfromtimetotimewhichlargelyfollow thelinesoftheolderBritishCommitteeandaddtothegrowingstockof valuableaeronauticaldata.BeforedealingwithSpecijccasesofaircraftitmaybeusefultocompare andcontrastmanfseffortswiththemostnearlycorrespondingproducts ofnature.Betweenthebirdsandtheman-carryingaeroplanethereare pointsofsimilarityanddifferencewhichstrikeanobserverimmediately.

Bothhavewings,thoseinthebirdbeingmovablesoastoallowof6apping,whilstthoseintheaeroplanearejxedtothebody.Boththebirdand

theaeroplanehavebodieswhichcarrythemotivepower,inonecase muscularandintheothermechanical.Bothhavetheintelligencefactor inthebody,theaerOplaneasapilot.Theaeroplanebodyisjttedwith anairscrew,anorganwhollyunrepresentedinbirdandanimallife,the propulsionofthebirdthroughtheairaswellasitssupportbeingachieved bythe6appingofitswings.Inbothcasesthebodiesterminateinthin surfaces,ortails,whichareusedforcontrol,butwhilsttheaerOpIanehas averticaljnthebirdhasnosuchorgan.Thewingsofabirdaresomobile atwillthatmanceuvresofgreatcomplexitycanbemadebyalteringtheir positionandshape,manceuvreswhicharenotpossiblewiththerigidwings ofanaeroplane.Inadditiontothedik' erencebetweenairscrewandkappingwings,aeroplanesandbirdsdiffergreatlyinthearrangementsfor alighting,theskidsandwheelsoftheaeroplanebeingtotallydissimilar tothelegsofthebird. Thestudyofbird6ightasabasisforaviationhasclearlyhadamarked in6uenceontheparticularformwhichmodernaer0planeshavetaken, andnomethodofaerodynamicsupportisknownwhichhasthesame valueasthatobtainedfromwingssimilartothoseofbirds.Thefactthat 6appingmotionhasnotbeenadopted,atleastforextensivetrial,appears tobedueentirelytomechanicaldifjculties.Inthisrespectnatural developmentindicatessomelimitationtothesizeofbirdwhichcan6y. Thesmallerbirds6ywitheaseandwithaveryrapid6appingofthewings largerbirdsSpendlongperiodsonthewing,butgeneralinformation indicatesthattheyaresoaringbirdstakingadvantageofupcurrents behindclik' soralargesteamer.Withthestilllargerbirdstheemuand ostrich,6ightisnotpossible.Thehistoryofbird-lifeisinstrxctaccordance withthemechanicalprinciplethatstructuresofasimilarnatureget

STANDARD~FORMSOFAIRCRAFT9

relativelyweakerastheygetlarger.Man,althoughhehassteelanda largeselectionofothermaterialsathisdisposal,hasnotfoundanything somuchbetterthanthemuscleofthebirdastomaketheproblemof supportinglargeweightsby.6apping6ightanymorepromisingthanthe resultsforthelargestbirds.Inlookingforanalternativeto6apping thescrewpropellerasdevelopedforsteamshipshasbeenmodijedforaerial use,andatpresentistheuniversalinstrumentofpropulsion. Theadeptionofrigidwingsinlarge6yingmachinesinordertoobtain sufjcientstrengthalsobroughtnewmethodsofcontrol.Mechanical principlesrelatingtotheej' ectofsizeonthecapacityformanuauvreShow thatrecoveryfromadisturbanceisslowerforthelargerconstruction. Thegustsencounteredaremuchthesameforbirdsandaeroplane,and theslownessofrecoveryoftheaemplanemakesitimprobablethatthe beautifulevolutionsofabirdincounteringtheeffectsofagustwillever beimitatedbyaman-carryingaeroplane.Inonerespecttheaeroplane hasadistinctadvantage:itsSpeedthroughtheairisgreaterthanthat ofthebirds,andSpeedisitselfoneofthemosteffectivemeansofcombating theeffectofgusts.

Furtherreferencetobird6ightisforeigntothepurposeofthisbook,whichrelatestoinformationobtainedwithoutspecialattentiontothe

studyofbird6ight. Theairshipenvelopeandthesubmarinehavemoreresemblanceto thejshesthantoanyotherlivingcreatures.GenerallySpeaking,theform ofthelargerjshesprovidesaverygoodbasisfortheformofairships. Itiscuriousthatthejnsofthejshareusuallyverticalasdistinctfrom thehorizontaltailfeathersofthebird,andthejnsoverandunderthe centralbodyhavenocounterpartintheairship.Boththeartijcialand livingcraftobtainsupportbydisplacementofthemediuminwhichthey aresubmerged,andrisingandfallingcanbeproducedbymoderatechanges ofvolume.Theresemblancebetweenthejshesandairshipsisfarless closethanthatbetweenthebirdsandaeroplanes.

GENERALDESCRIPTIONorPaarrcvnxaAxacnarr

Anumberofphotographsofmodernaircraftandaeroenginesare reproducedastypicalofthesubjectofaeronautics.Theywillbeusedto dejnethosepartswhichareimportantineachtype.Thedetailsofthe motionofaircraftarethesubjectoflaterchaptersinwhichtheconditions ofsteadymotionandstabilityaredevelopedanddiscussed. TheAntoninadThefrontispieceshowsalargeaer0planein6ight. BuiltbyMessrs.HandleyPageCc.,theaerOplane'istheheaviestyet 6ownandweighsaboutlbs.whenfullyloaded.Itsenginesdevelop

1500horsepowerandpropeltheaeroplaneataSpeedofabout100miles

anhour.Iteisofnormalbiplaneconstructionforitswings,theSpecial characteristicsbeingintheboxtailandinthearrangementofitsfour engines.Eachenginehasitsownairscrew,thepowerunitsbeingdivided intotwobythebodyoftheaer0plane,eachhalfconsistingofapairof enginesarrangedbacktoback.Oneairscrewofeachpairisworkingin

10APPLIEDAERODYNAMICS

thedraughtoftheforwardscrew,andthistandemarrangementisasyet somewhatnovel.

Biplane(Fig.dFig.1showsaSingle-seaterjghtingscofut,theSE.5,muchusedinthelaterstagesofthewar.Itsfourwingsareofequallength,

andformthetwoplaneswhichgivethenametothetype.Thelowerwings areattachedtotheundersideofthebodybehindtheairscrewandengine cowl,whilsttheupperwingsarejoinedtoashortcentresectionsupported fromthebodyonaframeworkofstrutsandwires.Awayfromthebodythe upperandlowerplanesaresupportedbywingstrutsandwirebracing, andthewholeformsastiffgirder.In6ighttheloadfromthewingsis transmittedtothebodythroughthewingstrutsandthewiresfromtheir upperendstotheundersideofthebody.Thesewiresarefrequently referredtoasliftwires.Thedownwardloadonthewingswhichaecom paniestherunningoftheaeroplaneoverroughgroundistakenbyanti liftwires,whichrunfromthelowerendsofthewingstrutstothecentre sectionoftheupperplane. Inthedirectionofmotionoftheaeroplanein6ightareanumberof bracingwiresfromthebottomofthevariousstrutstothetopofthe

neighbouringmember.Thesewiresstiffenthewingsinawaywhichmaintainsthecorrectangletothebodyoftheaeroplane,andareknown

asincidencewires.Thebracingsystemisredundant,oneormore membersmaybreakwithoutcausingthecollapseofthestructure. Thewingsofeachplanewillbeseenfromthephotographtobebent upwardsinwhatisknownasadihedralangle,theobjectofwhichisto assistinobtaininglateralstability.Forthelateralcontrol,wing6aps areprovided,theextentofwhichcanbeseenonthewingsontheleftof thejgure.Onthelower6aptheleverforattachmentoftheoperating cableisvisible,thelatterbeingledintothewingatthefrontspar,and hencebypulleystothepilotfscockpit.Thepositionsofthefrontandrear sparsareindicatedbytheendsofthewingstrutsintheforeandaft direction,andrunalongthewingsparalleltotheleadingedges.

ThebodyrestsontheSparsofthebottomplane,andcarriestheengineandairscrewintheforwardend.Theengineiswater-cooled,andthe

necessaryradiatorsaremountedmthenoseimmediatelybehindtheair screw.Blinds,shownclosed,arerequiredinaer0planeswhichclimbto greatheights,sincethetemperatureisthenwellbelowthefreezingpoint ofwater,andunrestricted6owofairthroughtheradiatorduringaglide wouldleadtothefreezingofthewaterandtolossofcontroloftheengine. Theblindscanbeadjustedtogiveintermediatedegreesofcoolingto correspondwithenginepowersintermediatebetweenglidingandthe maximumpossible. Alongsidethe'bodyandstretchingbackbehindthepilotfsseatisone oftheexhaustpipeswhichcarrythehotgaseswelltotherearoftheaero plane.Thepilot'sseatisjustbehindthetrailingedgeoftheupperwing. Abovetheexhaustpipeandnearthefrontofthebodyisacoveroverthe cylindersononesideoftheengine,thecoverbeingusedtoreducetheair resistance. Theairscrewisintheextremeforwardpositionontheaeroplane,and

DigtizedbyGoogle

STANDARDFORMSOFAIRCRAFT11

hasfourblades.ThediameterisjxedinthiscasebythehighSpeedof

theairscrewShaft,andnot,asinmanycases,bythegroundclearancerequiredforsafetywhenrunningovertheground.Belowthebodyandunderthewingsofthelowerplaneisthelanding

chassis.Theframeconsistsofapairofvee-Shapedstrutsbasedonthe bodyandjoinedatthebottomendsbyacrosstube.Thestructure eis supportedbyadiagonalcross-bracingofwires.Thewheelsandaxleare heldtotheundercarriagebybindingsofrubbercordsoastoprovide 6exibility.Theshocksoflandingaretakenpartlybythisrubbercord andpartlybythepneumatictyresonthewheels.Withtheaer0plane bodynearlyhorizontalthewheelaxleisaheadofthecentreofgravity oftheaeroplane,sothattheeffectofthejrstcontactwiththegroundis tothrowupthenose,increasingtheangleofincidenceanddrag.Ifthe Speedofalightingistoogreattheliftmayincreasesufjcientlytoraise theaeroplaneofftheground.Theartofmakingacorrectlandingisoneof themostdifjcultpartstobelearntbyapilot. ThetailoftheaeroplaneisnotclearlyShowninthisjgure,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 anemometerisusuallyjxedtooneofthewingstruts,astheeffectofthe presenceofthewingonthereadingislessmarkedthaninthecasenow illustrated. InthistypeofaerOplane,madebytheBritishdzColonialAeroplane Coyhtheenginerotates,andtheairscrewhasasomewhatunusualfeature inthespinnerwhichisattachedtoit.Theairscrewhastwoblades only,andthistypeofconstructionhasbeenmorecommonthanthefour bladedtypeforreasonsofeconomyoftimber.Thedifferencesof efjciencyarenotmarked,andeithertypecanbemadetogivegood service,thechoicebeingdeterminedinsomecasesbytheSpeedofrotation oftheairscrewshaftofanavailableengine. TheundercarriageisverysimilartothatshowninFig.1.Onone ofthefrontstrutsisasmallwindmillwhichdrivesapMpforthepetrol feed.Windmillsarenowfrequentlyusedforauxiliaryservices,suchas theelectricalheatingofclothingandthegenerationofcurrentforthe. wirelesstransmissionofmessages. Thetailisclearlyvisible,andunderneaththeextremeendofthebody

12APPLIEDAERODYNAMICS

isthetail-skid.Thisskidishingedtothebody,andissecuredbyrubber cordatitsinnerend,soastodecreasetheshockofcontactwiththeground. Thehorizontalplaneatthetailisseentobedivided,thefrontpartor tailplanebeingjxed,whilsttherearpartorelevatorismovableatthe pilotfswish.Thecontrolcablesgoinsidethefuselageattherootofthe tailplane.Underneath,thetailplane18seentobebracedtothebody above,thebracingwiresareattachedtothejn,which,likethetailplane, isjxedtothebody.Therudderishiddenbehindthejn,buttherudder leverforattachmentofthecontrolcablecanbeseenabouthalfwayup thejn. Thepilotsitsunderthecabane,andhisdownwardviewishelped byholesthroughthewings.Immediatelyinfrontofhimisawindscreen, andalsointhisinstanceamachine-gun,whichjresthroughtheairscrew.

Flying-boat(Fig.dThedij'

erenceofShapefromthelandtypesis markedinseveraldirections,aswillbeseenfromtheillustrationrelatingto thePhoenixCorkkying-boatP.5.Theparticularfeaturewhichgives itsnametothetypeistheboatstructureunderthelowerwing,andthis replacesthewheelundercarriageoftheaeroplaneinordertorenderpossible alightingonwater.The6yingboatisshownmountedonatrolleyduring transitfromtheshedstothewater.Ontheundersideoftheboat,just behindthenationalitycircles,isastepwhichplaysanimportantpartin thepreliminaryrunonthewater.Asecondstepoccursunderthewings attheplaceoflastcontactwiththeseaduringakight,butishiddenby thedeepShadowofthelowerwing. Underneaththelowerwingattheouterstrutsisawing6oatwhich keepsthewingoutOfthewaterinanySlightroll.Thewingstructureis muchlargerthanthoseofFigs.1and2,andtherearesixpairsOfinter planestruts.Theupperplaneisappreciablylongerthanthelower,the extensionsbeingbracedfromthefeetoftheouterstruts.Theleverson thewing6apsoraileronsarenowveryclearlyshownowingtothe proximityofwavestothelowerwing,aileronsarenotjttedtothem. ThetailisraisedhighabovetheboatandisintheSlipstreamsfrom thetwoairscrews.Asthecentrelineoftheairscrewsisfarabovethe

centreOfgravity,switchingontheenginewouldtendtomakethekyingboatdive,wereitnotsoarrangedthattheslip-streameffectonthetail

isarrangedtogiveanOppositetendency.Thejnandrudderareclearly shown,asarealsotheleversontherudderandelevators.Besideshaving adihedralangleonthewings,smalljnshavebeenjttedabovethetop wingsaspartofthelateralbalanceOfthekying-boat. Theenginesarebuiltonstrutsbetweenthewings,andeachengine drivesatractorairscrew.Theenginesareruninthesamedirection, althoughatanearlystageofdevelopmentofkying-boatstheekectsof geSOOpicactionoftherotatoryairscrewswereeliminatedbyarranging forrotationinOppositedirections.Thiswasfoundtobeunnecessary. Thetailofthekying-boathasbeenespeciallyarrangedtocomeintothe slipstreamoftheairscrews,butinaeroplanesthisoccurswithout Specialprovisionordesire.Notonlydoestheairscrewincreasetheair Speedoverthetail,butitalterstheangleofincidenceandblowsthetail

Flo.4.dCockpitofanaeroplane.

DgtzedbyG

STANDARDFORMSOFAIRCRAFT18

upordowndependingonitssetting.ThereisalsoatwistintheSlipstream whichisfrequentlyunsymmetricallyplacedwithreSpecttothejnandrudder andtendstoproduceturning.Theeffectsofswitchingtheengineonand

Offmaybeverycomplex.

Inordertoeasethepilotfseffortsmanyaeroplanesarejttedwithan adjustabletailplane,andiftheyarestabletheadjustmentcanbemade soastogiveanychosen6yingspeedwithouttheapplicationofforceto thecontrolstick. PilotfsCockpit(Fig.dThephotographofthePantherwastaken fromabovetheaeroplanelookingdownandforward.Atthebottomofthe jgureistheedgeoftheseatwhichrestsonthetopofthepetroltank.Along thecentreofthejgureisthecontrolcolumnhingedatthebottomtoarock. ingshaftsothatthepilotisabletomoveitinanydirection.Bysuitable cableconnectionsitisarrangedthatfore-and-aftmovementdepressesor

raisestheelevators,whilstmovementtorightorleftraisesorlowersvtherightailerons.Someoftheconnectionscanbeseen;behindthecontrol

columnisaleverattachedtotherockingshaftandhavingatitsendsthe cablesfortheailerons.Thecablescanbeseenpassingininclineddirections infrontofthepetroltank.OnthenearSideofthecontrolcolumnbut partlyhiddenbytheseatisthelinkwhichoperatestheelevators. Inthecaseofeachcontrolthemotionofthecolumnrequiredisthat whichwouldbemadewereitjxedtotheaeroplaneandthepilotheld independentlyandheattemptedtopulltheaeroplaneintoanydesired position.Inotherwords,ifthepilotpullsthesticktowardshimthe.nose oftheaeroplanecomesup,whilstmovingthecolumntotherightbrings theleftwingup. Onthetopofthecontrolcolumnisasmallswitchwhichisusedbythe pilottocutouttheenginetemporarily,anOperationwhichisfrequently requiredwitharotaryenginejustbeforelanding. Acrossthephotographandalittlebelowtheenginecontrolswitches istherudderbar,thehingeofwhichisverticalandbehindthecontrol column.Thetwocablestotherudderareseentocomestraightback underthepilotfsseat.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

rotatesaboutajxedcrankshaft.Thecylinders,nineinnumber,developa netbrakehorsepowerofabout280ataSpeedof1100to1800revolutionsper minute.Thecylindersareprovidedwithgills,whichgreatlyassistthecool ingofthecylinderduetotheirmotionthroughtheair.Withoutanyforward

motionoftheaerOplane,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-bedjgures.Forengines withstationarycylinderstest-bedjguresusuallygivebrakehorsepower 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,thelattermaking

1800to2000r.p.m.Totherightofandbelowtheairscrewhubisoneof

themagnetoswithitsdistributingwiresforthecorrecttimingOfthe explosionsintheseveralcylinders.Atthebottomofthephotographare

theinletpipes,carburettors,petrolpipesandthrottlevalves.Water-cooledEngine(Fig.dWater-cooledengineshavebeenused

morethananyothertypeinbothaeroplanesandairships.Thetwo photographsoftheNapier450h.p.engineshowwhatanintricate mechanismtheaeroenginemaybe.Thecylindersarearrangedinthree rowsoffour,eachonebeingsurroundedbyawaterjacket.Thefeed pipesofthewater-circulatingsystemcanbeseeninFig.6bgoingfrom thewaterpumpatthebottomofthepicturetothelowerendsofthe cylinderjackets,whilstabovethemarethepipeswhichconnectthe

Fla.5(a).dRotaryengine.

Fla.5(b).dAir-cooledstationaryengine.

DigntizedbyGoc

16APPLIEDAERODYNAMICS

theshipandringsrunningroundit.Twotypesofringarevisible,oneofwhichiswhollycomposedofsimplegirders,whilstthesecondhasking

postsasstik' enersontheinside.Fromthecornersofthissecondframe

radialwirespasstothecentreoftheenvelopeandformoneofthedivisionsoftheairship.Thecentresofthevariousradialdivisionsareconnected

byanaxialwire,whichtakestheendpressureofthegasbagsinthecase ofde6ationofoneofthemorofinclinationoftheairship.Thecordnetting againstwhichthegasbagsrestcanbeseenveryclearly.Theairshipis onebuiltfortheAdmiraltybyMessrsBeardmore. TheNon-rigidAirship(Fig.dThenon-rigidtypeofconstruction isessentiallydifferentfromthatdescribedabove,theshapeoftheenvelope beingmaintainedwhollybytheinternalgaspressure.TheN.S.typeof airshipillustratedinFig.9hasagrossweightof11tons,and travelsatalittlemorethan55m.p.h.Thelength-is

0262feet,andthemaximumwidthoftheenvelope57feet.Fig.9bgivesthebestideaof

thecross-sectionofthistypeofairship,andshowsthreelobesmeetingin well-dejnedcorners.ThetypewasoriginatedinSpainbyTorresQuevedo anddevelopedinParisbytheAstraCompany.Itcontainsaninternal ropesandfabricbetweenthecorners.The satisfactorydistributionofloadsonthefabricduetotheweightofthe carandenginesispossiblewiththisconstructionwithoutnecessitating suspensionfarbelowthelowersurfaceoftheenvelope.Fig.90,taken frombelowtheairship,showsthewiresfromthecartothejunctionof thelobesatthebottomoftheenvelope,andthesetakethewholeload underlevel-keeleconditions.Tobracethecaragainstrolling,wiresare carriedoutoneithersideandjxedtothelobesatsomedistancefromthe 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-pressureairisobtainedfromscoopsloweredintothe

slipstreamsfromtheairscrews,thescoopsbeingvisibleinallthejgures,butarefoldedagainsttheenvelopeinFig.9a.Valvesareprovidedin

thefeedpipesforusebythepilot,whoin6atesordekatestheballoonets asrequiredtoallowforchangesinvolumeofthehydrogenduetovariations

STANDARDFORMSOFAIRCRAFT17

ofheight.Automaticvalvesarearrangedtoreleaseairifthepressure Theweightoffabricnecessarytowithstandthepressureofthegas isgreatlyreducedbyreinforcingthenoseoftheairshipasshownin Fig.9b.Themaximumexternalairforceduetomotionoccursatthe noseoftheairship,andathighspeedsbecomesgreaterthantheinternal pressureusuallyprovided.Theregionofhighpressureisextremelylocal, andbytheadditionofstiffeningribstheexcessofpressureoverthe internalpressureistransmittedbacktoapartoftheenvelopewhereitis easilysupportedbyasmallinternalpressure.Occasionallythenoseof anairship1sblowninathighSpeed,butwiththearrangementsadopted theconsequencesareunimportant,andthecorrectshape18recoveredbyanincreaseofballoonetpressure. Thein6ationofoneballoonetandthede6ationoftheotherisacontrol bymeansofwhichthenoseoftheairshipcanberaisedorlowered,andso effectachangeoftrim,buttheusualcontrolisbyelevatorsandrudders. IntheN.8.typeofairshiptherudderisconjnedtothelowersurface,and theupperfinisofreducedsize.This,thelargestofthenon-rigidairships, istheproductoftheAdmiraltyAirshipDepartmentfromtheirstation atKingsnorth,andhasseenmuchserviceasasea-scout. KiteBalloons(Fig.dTheearlykiteballoonwasprobablyaGerman type,withastringofparachutesattachedtothetailinordertokeep theballoonpointingintothewind.Theliftonakiteballoonispartly duetobuoyancyandpartlyduetodynamiclift,thelatterbeinglargely

predominantinwindsof40or50m.p.h.Theballooniscaptive,andmayeitherbesentaloftinanaturalwindorbetowedfromaship.Twotypes

ofmodernkiteballoonareshowninFig.10,(a)and(b)showingthelatest andmostsuccessfuldevelopment.Tothetailoftheballoonarejxed threejns,whicharekeptin6atedinawindbythepressureofairina swapattachedgtothelowerjn.Withthisarrangementtheballoon swingsslowlybackwardsandforwardsaboutaverticalaxis,andtravels sidewaysasanaccompanyingmovement. ThekitewireisshowninFig.lobascomingtoamotorboat.The secondropewhichdipsintotheseaisanautomaticdeviceformaintaining theheightoftheballoon.Thegeneralsteadinessoftheballoondepends onthepointofattachmentofthekitewire,andtheimportantdifference illustratedbythetypesFig.10(a)and(c)isthatthelatterbecomes

longitudinallyunstableathigh-windspeedsandtendstobreakaway,theformerdoesnotbecomeunstable.Thegeneraldisposition

oftheriggingisshownmostclearlymFig.10a,whereariggingband isshownfortheattachmentofthecarandkiteline.

CHAPTER11

THEPRINCIPLESOFFLIGHT

(i)TunAsaopnxns Indevelopingthematterundertheaboveheading,anendeavourwillbe madetoavoidthejnerdetailsbothofcalculationandofexperiment.In thelaterstagesofanyengineeringdevelopmenttheamountoftimedevoted tothedetailsinordertoproducethebestresultsisapttodullthesense ofthoseimportantfactorswhicharefundammtalandcommontoall discussionsofthesubject.Itusuallyfallstoafewpioneerstoestablish themainprinciples,andaviationfollowstherule.Therelationsbetween lift,resistanceandhorsepowerbecamethesubjectofgeneraldiscussion amongstenthusiastsintheperiod1896-1900mainlyowingtotheresearches ofLangley.Maximmadeanaeroplaneembodyinghisviews,andwecan nowseethatonthesubjectsofweightandhorsepowertheseestablishedthefundamentaltruths.Methodsof dataandofmakingcalculationshaveimmovedandhavebeenextended tocoverpointsnotarisingintheearlydaysof6ight,andoneextension istheconsiderationof6ightataltitudesofmanythousandsoffeet. Themainframeworkofthepresentchapteristherelatingofexpo mentaldatatotheconditionsofkight,andtheexperimentaldatawillbe takenforgranted.Laterchaptersinthebooktakeuptheexamination oftheexperimentaldataandthejnerdetailsoftheanalysisandprediction ofaeroplaneperformance.WingsdThemostprominentimportantpartsofanaeroplanearethe wings,andtheirfunctionisthesupportingoftheaeroplaneagainstgravita tionalattraction.Theforceonthewingsarisesfrommotionthroughthe air,andisaccompaniedbyadownwardmotionoftheairoverwhichthe wingshavepassed.Theprincipleofdynamicsupportina6uidhasbeen calledthesacrijcialhprinciple(byLordRayleigh,Ibelieve),andstated broadlyexpressesthefactthatifyoudonotwishtofallyourselfyoumust makesomethingelsefall,inthiscaseair. IfAB,Fig.11;betakentorepresentawingmoviuginthedirectionofthe arrow,itwillmeetairatrestatCandwillleaveitatEEenduedwitha downwardmotion.Now,fromNewtonfslawsofmotionitisknownthat therateatwhichdownwardmomentumisgiventothe6uidisequalto thesupportingforceonthewings,andifweknewtheexactmotionof theairroundthewingtheupwardforcecouldbecalculated.Theproblem

is,however,toodifjcultforthepresentstateofmathematicalknowledge,andourinformationisalmostentirelybasedontheresultsoftestson

modelsofwingsinanartijcialaircurrent. 18

THEPRINCIPLESOFFLIGHT19

Thedirectmeasurementofthesustainingforceinthiswaydoesnot involveanynecessityforknowledgeofthedetailsofthe6ow.Itisusual todividetheresultantforceRintotwocomponents,Lthelift, eandD thedrag,buttheessentialmeasurementsintheaircurrentarethemagni tudeofRanditsdirection7,thelatterbeingreckonedfromthenormal tothedirectionofmotion.Theresolutionintoliftanddragisnotthe onlyusefulform,anditwillbefoundlaterthatinsomecalculationsitis convenienttousealinejxedrelativetothewingasabasisforresolution 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.Ofcourseinanygiven6yingmachinethe weightofthemachineisjxed,andthereforetheliftisjxed,anditfollows

fromtheabovestatementthatonlyonespeedof6ightcancorrespondmthagivenangleofincidence,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.12foranangleofincidenceof

17°orForanglesofincidencegreaterthanthisitisnotpossibleto

carrysomuchloadat40m.p.h.Withoutanyfurtherexperimentsitis nowpossibletodrawtheremainder:ofthecurvesofFig.12.AtBthelift for40m.p.h.hasbeenfoundtobe610lbs.AtB1itwillbe610XGS)hlbs., 24300
eQkjk

BSaeA

-sAomcunarlonorCHORD(DEGREES)

Fro.l2.dWingliftandspeed.

at610X(jglbsandsoon,theliftforagivenanglebeingproportional tothesquareofthespeed. NowsupposethatthewingsforwhichFig.12waspreparedarctobe usedonanaeroplaneweighing2000l.At85m.p.h.thewingscannotbe

madetocarrymorethan1580lbs.,andconsequentlytheaeroplanewillneedtogetupaspeedofmorethan85m.p.h.beforeitcanleavetheground.

At40asweseeatD,theweightcanjustbelifted,andthiscon stitutestheslowestpossible6yingspeedofthataeroplane.Theangleof incidenceisthen17to18degrees.Ifthespeedisincreasedto50m.p.h. therequiredliftisobtainedatanangleofincidenceratherlessthan andsoon,untiliftheengineispowerfulenoughtodrivetheaerOplaneat

100m.p.h.theangleofincidencehasasmallnegativevalue.

22APPLIEDAERODYNAMICS

ItisnowpossibletomakeTable]showingtheresistanceoftheaeroplaneatvariousspeeds,andtoestimMethenethorsepowerrequiredto

propelanaeroplaneweighing2000lbs.Thelossesintheorgansofpro pulsionwillnotbeconsideredatthispoint,butwillbedealtwithalmost diatelywhendeterminingthehorsepoweravailable. Aroughideaofthebrakehorsepoweroftheenginerequiredfor

ANGLEOFINCIDENCEDEGREES

Fro.13.dWingdragandspeed.

horizontal6ightcanbeobtainedbyassumingapropellerof

60percent.inallcases.Itwillthenbeseenthattheaeroplanewould

justbeableto6ywithanengineof45horsepowerataspeedof approximately50m.p.h.At70m.p.h.thebrakehorsepowerofthe enginewouldneedtobenearly80,whilstto6yat100m.p.h.would neednolessthan225horsepower.Byvariousmodijcationsofwingarea thehorsepowerforagivenspeedcanbevariedconsiderably.butthe examplegivenillustratesfairlyaccuratelythelimitsofspeedofan

THEPRINCIPLESOFFLIGHT28

aeroplaneoftheweightassumed;c.g.anenginedeveloping100horse powermaybeexpectedtogiveakight-speedrangeoffrom40m.p.h. to80m.p.h.toanaeroplaneweighing2000lbs.

ResistanceofreatofTotalresistance

aeroplane(lbs),(lbs). ThePropulllve[comm-Uptothepresentthecalculationshave referredtothebehaviouroftheaeroplane,withoutdetailedreferenceto themeansbywhichmotionthroughtheairisproduced. proposedtoshowhowthenecessaryhorsepowerisestimatedinorderthat theaeroplanemay6y.Thisestiniatefinvolvestheconsiderationofthe 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.andarotationalspeedof

600r.p.m.theforwardspeedbeincreasedto80m.p.h.andthe

rotationalspeedto1200thethrustwillbeincreasedfourtimes. Givenatableofjgures,suchasTable2,whichshowsthethrustof anairscrewatseveralSpeedsofrotationwhentravellingat40m.p.h. throughtheair,resultscanbededucedforthethrustatothervaluesof theforwardspeedinthemannerdescribedbelow. nethorsepowerisheremeantthepowernecessarytodriveB perfectlgrefjcientmeansofpropulsionexisted.Theconditionsarevery anaeroplanewhengliding;

24APPLIEDAERODYNAMICS

ThejguresinTable2wouldbeobtainedeitherbycalculationorby 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.Theterm

pitchisobtainedfromananalogybetweenanairscrewandascrew,theadvanceofthelatteralongitsaxisforonecompleterevolutionbeingknownasthepitch.hWhilstthereareobviousmechanicaldifferences

betweenasolidscrewturninginitsnutandanairscrewmovingina mobile6uid,theexpressionhasmanyadvantagesinthelattercaseand willbereferredtofrequently.Forthepresentitisnotnecessarytoknow howpitchisdejned. ThenumbersgiveninTable2correspondwiththecurvemarked ABCinFig.14.Todeducethoseforanyotherspeed,say60the jrstcolumnismultipliedby38andthesecondby,givingthe followingtable:

Forwardspeed00m.p.h.

Revs.perminute.Thrust(M).

Itwillbenoticedthattheairscrewmustnowberotatingmuchmore rapidlythanbeforeinordertoproduceathrust.Theremainingcurves ofFig.14wereproducedinasimilarway,andrelatetospeedsofthe

THEPRINCIPLESOFFLIGHT25

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.Forhighervelocitiesof6ightthe

AlRSCREWREVOLUTIONS0

F10.leadThrustandspeed.

revolutionsincreasesteadily,untilat100m.p.h.therateofrota tion18over1600r.p.m.Theenginemay,however,notbepowerfulenough todrivethepropellerattheserates,anditisnownecessarytoestimate, inamannersimilartothatforthrust,howmuchhorsepower18required. TheinitialdatagiveninTable4areagainassumedtohavebeen

TABLE4.dArasonxwHoasnrowxnarmSeam).

Forwardspeed40m.p.h.

26APPLIEDAERODYNAMICS

obtainedexperimentally,andthejguresfromthistable' areplottedin

Fig.15inthecurveABC.Toobtainthecurvefor60m.p.h.thejrstcolumnofTable4ismultipliedby$23andthesecondby(jgobtaimngthenumbersgiveninTable5.

r.pm

AIRSCREWREVOLUTIONS.

Thecurvessoobtainedforvariouskightspeedsindicate

powerbeforetheairscrewhasstepped.TheSpeedsarelowerthanthoseforwhichthethrusthasbecomezero,andindicatethepointsatwhich

theairscrewbecomesawindmill.Inanaeroplane,however,theresistancetoturningoftheenginewouldgreatlyreducethespeedatwhichthewindmillbecomesekf

ectivebelowthatindicatedforno-horsepower,andstoppage ofthepetrolsupplytotheenginewouldoftenresultinthestoppageoftheairscrew.

THEPRINCIPLESOFFLIGHT27

FromFigs.14and15it18noweasytojndthebrakehorsepowerof theenginewhichwouldbenecessarytodrivetheaeroplanethroughthe atspeedsfrom40to100m.p.h.FromFig.14itisfoundthatthe aeroplanewhentravellingat50m.p.hthroughtheairneedsanairscrew

speedof980r.p.m.Todrivetheairscrewatthisspeed18seenfromFig.pointC,,toneed89horsepower.ForotherSpeedsthehorsepoweris

indicatedbythepointsC,02,C3andC4,andthecollectedresultsare giveninTable6.

8ofamplancHomewardMme.)neon-cantor

OnFig.15alineOPhasbeendrawnwhichrepresentstheworkwhich particularenginecoulddoatthevariousspeedsofrotation,thisagain

isanexperimentalcurve.Theengineissupposedtobegiving120h.p.at1200r.p.m.Itwillbeseen,fromFig.15,thattheengineisnotpowerful

enoughtodrivetheaeroplaneateitherthelowestorthehighestSpeedsfor thecalculationshavebeenmade.Formanypurposestheinformation

giveninFig.15ismoreconvenientlyexpressedintheformshowninFig.16,wheretheabscissa18the6ightSpeedoftheaerOplane.ThecurveABCDE

ofthelatterjgure18plottedfromthepointsC,01,Oz,03andC4ofFig.15,whilethelineFGHcorrespondswiththepointsB,E,,BJB,andB4.

Thejrstcurveshowsthehorsepowerrequiredfor6ight,andthesecond thehorsepoweravailable.Fromthediagram1nthisformitiseasilyseen thatthepointFrepresentstheslowestspeedatwhichtheaeroplanecan ky,inthiscase403m.p.h.,andthatHshowsthepossibilityofreachinga speedofnearly98m.p.h. Fig.16showsmorethanthis,foritgivesthereservehorsepoweratany speedof6ight.Thisreservehorsepowerisroughlyproportionaltothe Speedatwhichtheaeroplanecanclimb,andthecurveshowsthatthebest climbingSpeedismuchnearertothelowerlimitofspeedthantothe GenealncmarksonFigc.12d16dCalculationsrelatingtothe6ightspeed ofanaeroplaneareillustratedfairlyexactlybythecurvesinFig.12-16. Asthesubjectisenteredintoindetailmanysecondaryconsiderationswill beseentocomein.Thedifjcultieswillbefoundtoconsistverylargely

inthedeterminationofthestandardcurvesmarkedABCDEinthejgures,andtheanalysisofresultstoobtainthesedataconstitutesoneofthemore

laboriouspartsoftheprocess.Thecomplicationisverylargelyoneof detail,andshouldnotbeallowedtoobscurethecommonbasisof6ight conditionsforallaeroplanesastypijedbythecurvesofFigs.12d16.

28APPLIEDAERODYNAMICS

ClimbingFlightdInthemoregeneraltheoryoftheaeroplaneitis ofinteresttoShowhowthepreviouscalculationsmaybemodijedto include6ightsotherthanthoseinahorizontalplane.Therateatwhich aerOplanecanclimbhasalreadybeenreferredtoincidentallyincon naotienwithFig.16. Itisclearfromtheoutsetthattheairforcesactingontheaeroplane dependonitsspeedandangleofincidence,andarenotdependent acting forceswillvarywiththeattitudeoftheaeroplane.Iftheaeroplane hingtheairscrewthrustwillneedtobegreaterthanforhorizontal 6ight,whilstifdescendingthethrustisreducedandmaybecomezero ornegative.Thereisaminimumangleofdescentforanyaeroplanewhen coco70ac

SPCEDOF(wasoutnounTHROUGHam)

Fm.16.dHorsepowerandspeedforlevelkight.

theairscrewisgivingnothrust,andthisangleisoftenreferredtoastheangleofglidefortheaeroplane.hMorecorrectlyitshouldbereferred

toastheleastangleofglide.h Themethodofcalculationofglidingandclimbing6ightisillustrated

inFig.17,whichisadiagramoftheforcesactingonanaeroplaneinfree6ightbutwithits6ightpathinclinedtothehorizontal.

Inhorizontal6yingitwillbeassumedthatthedirectionofthethrustis horizontal,inwhichcaseitdirectlybalancestheresistanceoftheremainder oftheaerOplanetomotionthroughtheair.'Intheabovediagramthis statementmeansthatT=D.SimilarlytheweightoftheaerOplaneis exactlycounterbalancedbytheliftonthewings,i.e.LW.Theangleof incidenceofthewingsmaybevariedbyadjustmentoftheelevator,in whichcasethethrustwouldnotstrictlyliealongthewind.Ifnecessary aslightcomplicationofformulacouldbeintroducedtomeetthiscase,but theek' ectofthisvariationissmall,and,inaccordancewiththeideaon

30APPLIEDAERODYNAMICS

Equation(2)cannowbeusedtoshowhowdiagrams12and18maybe alteredtoallowforinclinedkight.Inthejrstplacetheordinatesof Fig.18,which,afteradditionofthedragofthebody,showthevalue ofDformanyanglesofincidence,needtobedecreasedbymultiplying bycos0togiveDcos0.Theeffectofthismultiplicationisverysmall asarule.At10°thefactoris0985,andat0940.Foravery steepSpiralglideatsaythedifferencebetweencos0andunitybecomes important,cos0beingthen0707. TothevalueofDcos0istobeaddedatermWsin9inordertoobtain

thethrustoftheairscrewwhenclimbingatanangle0.Wemaythenmakeatableasbelow,usingjguresfromTable1toobtainthesecond

column.

TABLE7.-T1mva'rwwwmama.

DraginbcrlmntalAlrmvthrustwhen

nightxcos9climbingat6h(lbs). Theangleofclimbwaschosenarbitrarilyatandtocompletethe investigationofthepossibilitiesofclimbTable7wouldberepeatedfor otherangles.UsingFigs.14and15fortheairscrewasforhorizontal 6ight,wemaynowcalculatethehorsepowerrequiredfor6ightwhen climbing,andsoobtainthejguresofTable8.

TABLE8.dHoasxrownawantcamma.

Atthelowestandhighestspeedsofthetablethehorsepowerrequired isfarg'reaterfthanthatavailable,andthejguresarenotwithintherange ofFi16.maynowproceedtoplotthehorsepowerofTable8againstspeed toobtainadiagramcorrespondingwithFig.16.Thenewcurvemarked A1B101D1inFig.18comparedwithABCDEasreproducedfromFig.16 showsanincreaseofnearly50h.p.atallSpeedsduetotheclimbat ThehighestSpeedof6ightisshownbytheintersectionofAlBlclwith FGHatH5.FGHisthehorsepoweravailable,andisthesameasthe similarlymarkedcurveofFig.16.ThehighestSpeedis7and

THEPRINCIPLESOFFLIGHT81

sincetheangle0isconstantalongAlBlcltherateofclimbwillbe greatestatthispointfortheconditionsassumed.Rateofclimb,V,his commonlyestimatedinfeetperminute,andwethenhave

Max.V,ford5°88XVah,xsin0

88Xx00875

ThecalculationsshowninTables7and8havebeenrepeatedforother anglesofclimbandoneangleofdescenttoobtaincorrespondingcurves

ODKIOOIPLIOPIY(MILESPERHOUR)

Fm.18.dHorsepowerandspeedforclimbingflight.

i brlig.18.TheintersectionsH4,H0,etcthenprovidedataforTable9ow.

TABLE9.dRu'zor0mmumSeas».

Unimnmratsa!climbAnglectclimb.torlivenI

5915
582
5113

Flightnotpossible.

Table9showsthattherateofclimbvariesrapidlywiththe6ightspeed theneighbourhOOd100m.p.h.to80butthatfrom ,65m.p.h.to

56m.p.h.thevalueofrateofclimbvariesonlyfrom725to780.This

illustratesthewell-knownfactthatthebestrateofclimbofanaeroplane isnotmuchaffectedbysmallinaccuraciesinthe6ightspeed. Thetableshowsanotherinterestingdetail;themaximumangleof

82APPLIEDAERODYNAMICS

climbisbutthegreatestrateofclimboccursatasmallerangle. Forreasonsconnectedwiththecontroloftheaeroplaneanangleof8°or thereaboutswouldprobablybechosenbyapilotinsteadofthe showntobethebest.

Dim-Bydivingismeantdescentwiththeengineon,as

distinguishedfromaglidemwhichtheengineiscutok' .Iftheenginebe keptfullyonitisfoundthatthespeedofrotationoftheairscrewrises

higherandhigherastheangleofdescentincreases.Thereis,however,anupperlimittotheSpeedatwhichanaeroplaneenginemayberunwith

safety.andmourillustrationanappropriatelimitwouldbe1600r.p.m. ThespeedofrotationcorrespondingwithH4was1550r.p.m.,anditwill beseenthatthenewrestrictionwillcomeintooperationforsteeper descent.Fig.14,ifextended,wouldnowenableustodeterminethethrust oftheairscrewatany13dwithoutreferencetothehorsepower,butit willbeevidentthatthe'limitsofusefulnessofeachofthepreviousjgures 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

levelkightathighSpeedsisnotdeterminedinanyothercalculation.IncompilingTable11someangleofpathsuchasd10°ischosen,andvarious

speedsof6ightareassumed.FromtheseSpeedsthethirdcolumnis

THEPRINCIPLESOFFLIGHT88

ulstedandgivesoneofthequantitiesofFig.19.Thevalue-0197 ble11)occursatanangleofd0°16(Fig.andfromthesamejgure

ANGLEO

Politique de confidentialité -Privacy policy