Basic Aeronautics for Modellers

Basic

FO

ODELLERS

FOR MODELLERS

©2002Tra p let PublicationsLimited

All rightsre serv ed.All tradem ark sand register ed nam es ackno w ledge d.Nopart of thisbook maybe copie d, rep ro du ced or tran smitt ed inany fo rmwithoutthe writte nconsen tof thePublish e rs.

The informati on in thisbook istruetothebest of ourknowl ed geat thetime ofco mp ilatio n. Recom mendati ons are madewithout anygua rantee,implied orothe rw ise,on thepartof the autho ror publish er,who also discl aim any

liabilityincurred inconnec tion with the useof data orspecificinformatio ncontaine d within thispublicat ion.

First ed ition publish ed by Trapl etPublicat ionsLimited in 1995 Publish edby Trap let Publication sLimited 2002

Trap let House, Seve rn Drive, Up to n-u p o n-Seve rn, Worces te rsh ire . WR8 OJ L

United Kingdom.

ISBN1900371413

Front Couer. Stefan If/u rlllseen bere exercising someofb isconsiderableflyingskills ioitbbis 1:2scale Pitts 51. Stefa n brought tbePittsbackwards,balancing thethrustoftbeeng ine againsttbe stlffbrecze, until tberudder

tou chedbim! (Photo: PeterDauison)

TecbnicalDra uiingsby Lee\\7isedale Ca rtoons by Simo nBates

TRAPLET

~v;=---"=:P r U l J l l C AT I O N S

Print ed andbou nd byStephen s&George Limited ,

Acknowledgements

C

onven t io nally this is a pa g e of sycop ha n t ic

ramblings wher ein I thank everyo ne in my life from the midwife who delivered me to my dent ist's receptio nist. Well ,thank youone and all.

I owe my parents a sma ll apo logy, as I rem ember buyin g a mod el ae ro plane and then promi sin g that it would be my last ; not once but three or four times. I made no suc h rash promi s e s to mywife Anne who unwittingl y made the mistake of marr yin g a dormant Ae rom od elle r, who ever since then has been erupting with increasingmagnitudeand frequen cy, sprinkling the hou se with success ive layer s of styrene be ad s, wood shav ings, balsa dust, glass fib re stra nds and Solarfilm frag men ts.Sorry Anne .

Asfor my daughters Ron a and Shee na, if they ever live in Ame rica the ir analysts will make much of the socialand paternal depri vat ion the y have endured by being theoffspringofa ferve ntaeromode ller.

Passing quic kly over my educatio n at Le n z ie Acade my, Glasgow Universi ty and the Hambl e College of Air Training, the grea t mileston e in mymo dellin g life was when Jo hn Michie had the time and pat ien ce to teach metoflyproporti on al R/C aeroplanes.And it was Brian Davies who introduced metoaeroba ticsandword processing, whic h is whe n thisbo ok germina ted . I have learn ed a grea t deal from my friends in the Alde rsho t club and W'ind sor Park, and contin ue to learn from my present circle offriends inScotland.Itwas due to one of these , Bob McGill , tha t I be came immersed in water plan es.

Finally, thank yo u to Dr. Fra n k Cot on of the Depa rtm ent of Ae ro s pace Eng inee r ing at Glas g o w University who re ad throu gh the manu script to check that I wou ld not em ba rr ass the Dep artm ent to o ex te ns ively by pre a ch ing fundam entalaero dy na mic fallacies.

Foreword

O

ne of the first technical questions my son ever aske d me was"Howdoplan esfly?"Well,weall know how plan esfly .. .don'twe?Think again! If you were asked that simpl equestion,couldyo u givea concis e comprehensible ans wer? If you co u ld, how would you dealwith the retor t, deliv ered bythe son of one of my co lleagues . . . "How do plan es fly upside down?".

One of the most fascinating aspec ts of the modern world is the science of flight. Whethe r it be a bird, helic o pter , fighter aircr aft or eve n the marvellous bu mble bee ,people have always been intriguedbythe same basicquestion- "How does it fly?".Unfor tunately, the answe r is not always straig h tfo rward an d is comp lica te d by the wid e varie ty ofme chanisms and physicalphenomena whic h interacttoproduceflight.

Man's interestin model aircraftis alon g stand ing one. Over the years,the motivation for this has largelybeen recreation al altho ugh since scientificstud ies have been conduc ted, mostnotabl y those inGermany betweenthe World Wars. As ares ult, tod ay's aeromo de ller is a fairly well info rm ed ind ivid ua l who , inst e ad of ask ing the basic natureof flight question,ismore inter est ed in how to improve the performance of an aircraft or how to avoid problems during fligh t. The answers to most of these question s can be found in Basic Aeronautics for Mod ellers.

This book skillfully guides the reade r through the basics of airc r a ft flight an d perform anc e before ad dress ing issues specific to model aircraft. Alasdair Su the rl a n d draws on his pe rs onal exp erience as a stude nt, a pilot, and most importantly an aeromodeller, to present fundamental inform ati on in a friendly and easily accessib le form. He doe s so by building the knowled ge base of the read er in a steady progressive mann er, highlight in g a number of co m m o n miscon ception s along the way. In this way, he ensures that the reade r is prepared for each new sectio n of the book as it is reache d. Thankfully,the useofcomplica ted equa tions or tedi ou sderivation s which,if excessive,can ofte n det er the laym an , is either avoided or they are provided inap pend ices.

Throu gh ou t the book, use is mad e of observat io ns from flow visua lisation experi me nts to illustrate asp ects offluid behav iour. Overthe years,flow visua lisation has beenoneof themostpowerful tools in thedevelopment ofour current understanding offluid dynam ics.Indeed , smo ke flow visua lisatio n wind tunnels are still used in many unive rsitie s for researc h an d stu d e n t dem on str ations. It is obvio us that the demonst rations given to AlasdairSutherland in his stude nt days had a considerableimpact;after allseeing isbelieving!

Whether you consider yoursel f to be a novice or a

well-season ed aerornode ller, there issometh ing in this bo ok fo r you . Beginner s ca n le arn abo u t the basic mechani sms of lift generation and the manner inwhich for ce s actonan aircraft. The more experience d,on the othe r hand , can contemplate the detailed influence of model scaleand the role of the Re ynold s number. The bo ok mayeven encou rage so me to raid the library for mor e info rmatio n or carry ou tsome res earch of their own. Most importantly though,this book waswritten by anenthus iast for its readers to enjoy.I hope you do!

Dr. Frank Cotton Department of Aerospace Engineering University of Glasgow. Ala sd a ir Sutherl and was born an d ed ucated in the Glasgow area, progre ssing from Lenzie Academy to Glasgo w Univers ity where he earned a B.Sc. with Honours inAeronau ticalEngi neering.Afte rtra ining fora career as an airline pilot at Ham ble,near Southampton, he joine d BEA in 1973 to fly Trident aircraft arou nd Euro peand Lockheed LlD11aircraftworldwi de.

An aerorno de lle r sinc e the age of eleve n, he flies most types of radio co ntro lled aircraftespeci allyspo rts and aerobatic,and particul arly enjoys designin g models of vario us typ e s . After man y years as a member of Alder sh ot Model Club he mov ed back to Scotland as Capta in of British Airways turbop rop aircra ft, first the H.S. 748 and latt erly the British Aerospace ATP. He is now a member of both the Clyde Valley Fliers and the Garn ockValley!vIAe.

Contents

Page Intro duction 11 Chapter1 Chapter 2 Chapter 3 Chapter 4 Cha pter 5 Chapter 6 Chapter 7 Chapter8 Chapter9 Chapter10 Cha pter 11 Chapt er 12

The Aeroplane'sEnvironment 13

Tbe air.Masstoeigbtand grauity. Newton

s

Laws.Inertia.Vectors.Moments.

Re qu irement for Flight - Lift 16

\fiatcbing tbeairfloto.Pressure variation.Pressureexert s a force.Windtunneltesting.

The Stall'sthe Limit 20

Theliftcu rve.17Jestall,tbe reason.Variation insta lling cbaracteristtcs.

TheDrawback Drag 23

17Jeboundarylayer.Wing drag;dragpolar,effectof tbicknessandcamber, la mtn a rfloui sections.Fuselage drag, strea m lin ing.A bitfor golfers.

Haveyou aMoment? 26

17Je mom ent on tbe wing.Centreofpressure.Aero dyna mic centre.

Aerofoil sectionsu m m a ry, tbe effectoftbicknessandca m ber. Section classification and use.

The Vor texSyste m 30

Theuortexaroundtbewing. Seeingtbe cortices.Even moredrag,tbereason . Complications. Simp lifica tio ns. 17Jeimp orta nceofAspect Ratio.

Lessonsforpracticalmodellers.Ground effect,

Planform and Twist 35

Ellipticallift distribution.Localangleofattack.Differentplanform shapes.

Tipstalling.Wasbout,aerodynamicioasbout.Sweep ba ck. Mean chord.Horsesfor courses.

CG and Stability .41

17Je CG.Stabilityingen eral. Motionofan aeroplane.Stability ofaerop lanesinPitcb, CGPosition.Complications.We can work it out?Simplerequations.

Variationson tbeformula.

Directionaland Late ralStability .49

Directionalsta bility , the fin. Lateralsta bility,sideslip.Fin sideforce,wing position , dihedral,sweep back.Aspectsofdesign.Directionaland lateralinteraction, spiral divergen ce,dutchro ll.

Control .56

Rudder.Elevators.Ailerons, aileron drag,aileronalternatives.Control su rface balances. Control effective ness, rotationalinertia, sta bility,aerodynamicdamping.

Otberflying con trols,throttle,air brakes,flaps, sla ts.Controlcombinations,tailerons, flaperons, eleuons, V-ta il.

Turning Flight 63

Mecbanics of turning.Turning aeroplanes,loa d f actor in a turn,refinem ent, stdeslipp tng andsk idd ing,dragin a turn,stallingspeed. Higb aspectratio. Turningusingrudder.Specialeffects.Wben isarudderaneleva tor?

A DelicateBalance 67

Equilibrium.Tail lift to trim.Elevatorangletotrim. Tail Settingangle. Theeffec tof thrust on trim.

Cha p te r13 Cha p te r 14 Cha p ter15 Cha p te r16 Cha p te r 17 Cha pte r18 Cha p te r19 Cha p te r 20 Cha pter21 Cha pter22 GliderPerformance 72

Lift/Dragratio.Speed range.Aerodyn a m ic data.Optimising performance,strea m lin ing, toeigbt.Iiffectofto indonperformance, down trim,ballast.

Power ed Performance 76

Propellerthrust,slipstrea meffec ts.Levelflight, top speed,sta llingspeed, effecton toeigbt.Take oJ(. Clim b.Descentand landing.

TheAe ro d yn am icsofAeroba tics 80

77Je sta ll.Sp in.Snap . Loop.Inoerted.Roll.Yatu.Aerobat ictrim set up.

SpecialCases 85

Lowasp ect ratio,handling,CGposition. Ca nard.sta bility,CGPositi on,

Tail-lessaeroplane,sta bility,trim,con trol.Multitoing,performance,CGposition.

Reyn oldsNumber 90

Definition,importance,nontogra nt.Intbeboundary layer,situationnormal,

lam inar separation,separation bubble,tbeunderside.Re-eff ecton aerodynamicdata. 77Je problem area .Hysteresisloop.77Je effect011modeldesignandperformance, wingtips,classrules,optim u mweigbt.Tu rbu latorstrips.surfacefinish, Using publisb eddata.

Aeroelasticity 96

Effecton stability,ta ilbend, wingtwist.Aileron reversal.Wingdivergen ce. Aileronflutter,tbe ca use,tbecure.117ingflutter.TailFlutter.

Tuck Under 102

Description.77Je villa in unmasked.Wingtwist.ta il bending.flexible con trols. 77Je eleva tor trimgrap h.Critica lspeed.Tuckunder speed.Getting away witb it. Tailplane insta bility. Rem edies/ortuckunder. Conclusions.

The Air on theMo ve 109

Navigatio n.Slopelift.Tbennallift,Windsb earand WindGrad ien t.Gusts.

Mytbsand miscon ceptions.Momentum.Kinetic energy.Analogies.77Jemeaningofl ife?

ModelAircraftStructures 114

Defining some words,compositestructures,tobatairdoestowings, bendingmom ents,stru tted wings,torsionalstiff ness,fuselages,tailplanes.

Centre ofGrav ity Position .123

Rigbt andwrongCGs,Fligbttesting,popula r misunderstand ings,tobatma tters, meancbords,tbeflyingtoing,biplanes,tbeneutralpoint, adjustm ents, pu ttingittogeth er,sta bility marg in.

Appendices 131

A Bemoulli'sequation BBoundaryLayer Cvortices

D Dibedralandsweep E Usefu lNomograms

Glos sa ry 143

Sym bols,Abb rev iatio nsandCommo nAerody na m ic Terms

Index 145

Introduction

W

hen the cold rawwind howlsdown from the

North bringinggrey fragme nted clouds which scud low over the damp da rk forbidd in g landscap e like ademon army.When sheets of icy rain deluge incessantly from a leaden sky and the puddles join fo rcestothreaten uswith anoth er gre at flood.When the great oak trees bow down to the unseen forces of the wind like frightened pe asants befor e their Gods. When ever the outside environment beco mes hostile to man and his aeroplane,I cu rl up in a cha ir bythe fire with some books and magazin es ,to absorb all the fact, fiction and folkloreof our fascinatinghobby.

Itis on nightslike theseasI lie inbed listeningto the wind howlin g or the rain lash ing or the deathl y silence of th e snow fa ll that I he ar voices, vo ices from my past. They are the voices ofaerodyna mics le cturers and authors an d the y remi nd me ho w little accu ra te knowledge of aerodyna mics is available to the ave rage mo deller, and they tell me whose fault it is. Mine! My faultfornotwritingthisbo ok soone r!

I haveth re e main aims inwriting this boo k.The first istodisp el thehalf-truths and old wivestalespassed on, usu ally ingood faith,into the folkloreofthe hobby.

I once had a very puzzling conversa tio n with a modell e r abo u t the use of "flaps ", until he cla rifi ed matt e rs by ex plai ni ng that he meant the "bac k flaps" (eleva tors).So the second aim is to get us allspeaking the same lan gu age as fa r as po ssible so that our inevit abl e dis cussions and arg u me n ts can be more meaningful.

The third aim of my book is an introduction to aero-dynamics so that youcan understandhowto make use of the data available elsewhere when designing your own mod els .Understandingsome simp le theorywill not turnyouovern ight intothedesign e r ofthe most elegant andsuper-efficient models (thatstillrequiresexperienc e, ins pirati on an d talent) , but you can learn what is po s s ibl e under the laws of Ph ys ic s, an d wh a t is impossible- unlike the alche mis ts of old who was te d the irlivestryingto turn lead into gold.

Now let me plea for pati ence especially from the more knowledgeable readers. I have started off with a simple,rosy,idealisedview oftheworldandI introduce the realcomplications littlebylittle.

Chapter

I

The Aeroplane's Environment

The Air

Pleasetry this simple experiment.Take a can of beer, openit,and drink the contents. Now wha tare you left with?Mostpeopl e say "anempty can"but thatis wrong . Ifyou answered"acanfullofair"give yourselfapat on the back . We aero mode llers must be conscious of the air. We are depending on it to sup p ly the lift for our aerop lanes.Next time yousee a Jumbojetlumberin g off the runw a y remem ber tha t the air is providi ng the upward force ofup to400to ns.

So how heavyis, say a roomfullofair, 4met res by 3 and2.36met re shigh? Wouldyou believe 35 kg or 77Ib? At abou t 1.22 ou nces pe r cubic fo ot air is not very dens e , bu t you wou ldn't call a room empty if it conta ine d77Ib of balsa wood!

Now, how stro ng is the air?In a schoolexperiment thehalves of afourinch(lOOmm)diam et erhollow stee l sphere were placed togeth er and as much aspossibleof the air ins ide was remo ved. The air held the halv e s togethe r. It too k a lot of effort from the four strongest lad s in the class to pull thetw ohalves apa rt. Pressure is defined as a force per unit area.The force whic h theair pressu re exerts ona sur facewithavacu u m on theothe r sideis14.7 pounds per square inch or nearly a ton pe r squ are foot! The pull ne ed ed to sepa rat e the hemisphere s in schoo l was almos t 180 Ib (800 N). Natura lly the air exerts its fo rce on a sur face whe ther the re is a vacuu m on the other side or not. Hold up a square foot ofpaperand there isa ton of force on each side , butso what?Thetwo forces cancel ou t. Pressureis not dire ction al, or rather it isomnidirection al; it acts in all direction s at once .And it acts perpendicular to the surface atevery point. So whichever wayup you hold the paperthe re is exactly the same one ton force on eachside.

You canseetheair pressure varyingsligh tlyfrom day to day on your barometer. Both density and pressure reduce with altitud e but we aeromo de lle rs can igno re these sma ll differences.The reductionin air pressure is abou tatenth ofone per cent for every 30 fe et climb ed. Incidentally it isbymeasuringthatreduction in pressure that an aeropl an e's altimeterworks.

Low speed airflow iscalled"incompressible" because, althoughthe pressurewiIIvary,densitydo esnot.We all kno w air can be co mp ressed, and its den sity change d, but only in a co n tainer. Aeroplanes in fre e air do not comp ress it unlesstheytravel at near so nicspeeds .

Mass, Weight Gravity

An object's mass is the amo untof mate rial whic h it contain s.Becau se we live on the earth'ssurface we tend

BasicAeronauticsforModellers

to use the word weigh t instea d and to us there is no differ ence. Whe re an object's mass (as opposed to its weigh t) shows itse lf is in its resistan ce to be ing accelerate d . Take an iron canno nba llinto space and it wiII be "we ightless" but try kicking the canno nball and yo u will bre a k you r fo ot. Its resistan c e to being accelerated ,its mass , has not changed . The weight of the ball is just the force of the earth 's gra vi tatio n al attra ctio n on its mass. To get the weight of a body, multiply its mass times "g", the "gravitational consta nt" which on the earth' s surface is 32.2 It/sec/sec or 9.8 1 m/sec/se c.The weight ofa"kilogram"of massis aforce of9.81Newtonsand the weightof a "slug"(yes really) ofmass is a force of 32.2 pounds.(Butyou don't need toremember all that).

Newton's Laws

If a body is in "equilibrium" it is either at rest or movingat constan tspee d in a straight line (tha t is, not accelerating). Man y years ago SirIsaac Newto n put into wo rdsthree fu nda me n tal Law s of Motion.

• 1.The first says that a body wiII be inequilibri umif all the fo rce s on it canc el out, Le. if there is no resultantforce.

• 2.The second says that the force nee de d to cause an accelerationequalsthe masstimesthe acceleration . • 3. The third is the old favouri te abo u t each force

having anequa l and oppositerea ction.

Inertia

Whenyou kicked the can no nba llinsp ace,itapp lied aneq ua land opposite fo rce to your fo ot. Tha tkind of for ce is called an "inertia force", and is the for ce with whic h a body resists be ing accelera ted.Similarly,when you catc h a ball yo u apply a force to slow it down , overcoming its "ine rtia"which makes itwant to carryon theway it was going.

Vectors

A riddle! The re was a car sitting on a level road with the brakes off and three men pushing it bu t it wasn't moving!Why not? One waspushing the front, one the back,and one was pushing theside. An important little detail!

Any quant ity whos e direct ion must be specified as well as its amou n t, for exam p le forces, is calle d a "Vector".Othe rexamp lesof vectors are distance moved, acceleratio n and velocity. I prefer the word velocity to speed because itis arem ind e r that itis a vector.

Vecto rs can be added to g eth er by ad d ing their amounts only if they are in the sam e direc tio n. If two

..:...

The "moment"of a force abo ut a point is the size of the force times thedistanceoftheforce from the point. force s are in op pos ite directions, like two men pushing at eithe r en d of a ca r, the y will canceleach othe r out. If ve ct ors are at an angl e to eac h othe r the y can be added by drawing a "vectordiagram"using a ruler an d protract or. A vecto r diagr am is a scale drawin g in which the len gth of the li ne s represen ts the amo u n t, and the direction r epre-sents thedirection of the vectors.Figure 1.1could represe n t a treasure map."Sta rting at A walk ten metres north to B, then go ten metres east to c."The eq uivalent,or re su ltant , of the tw o vecto rs AB and BC ad de d together is the vecto r ACwhich is 14.14 metres to the northeast. Figure 1.1 co uld just as eas ily hav e represented the addition of two for cesor velocities.

Vectors can als o be split up, or "resolved", into two or more "com -ponents" which will ha v e the sa m e effec t (Fig ure 1.2) . The tre a sure is in a cav e, "C". The inscrip tio n on the Azt e c Temple, "A" says ; Go five kilometres on a bearing0370

East ofNo rth(b ut beware of the Dragon at "0"). Preferring an easy life to he ctic ad ve ntur e,our hero"Tri gon o metry"]onesinstead goes 4 km due No rth, sto p s for a few beers at "B", and then goes 3 km due East where he finds the cave, treasure etc. etc. Very precise and scien tific but no use for a moviescript.

From thevectordiagramin Figure 1.2, vecto r AC ca n be split in to its two co m p o ne nts, AB the No rtherly co m po ne ntand BCthe Easterly com p o nent. The bigger ang le A is,the smaller AB become s as a proportion of ACand the bigger BCbecome s as a proportion of AC. Theratio of BCto ACiscalled thesine of theangle ,the ra tio of ve ctor AB to AC is called the co s in e of the angle,and the ratio of BCto AB is called the tangent of the angle A.These ratios are usually sho rte ne d to sin, cos and tan an d can be lo o ked up in table s for any angle.

Using his mathematical tabl e s "T r ig"jones could work out the components for an y angl e without reso rting to scale drawing.The sine of37degrees is0.6 and cos 370 _{= 0.8. Of co urse the sa me goes for othe r} vecto rslikeforce sor velocities etc.

Moment

c

10 ..

_

.

...

B A Fig u re 1.1

5 Pivo t Moment

=5

.'\"10

=

50 5 10

~-

- - - --- -- -- --- - - --- --- --- - ----

-

--~

Figure1.4

groundsp eed vec tor. Wind has no othereffec t(b utsee the cha pte ron wind near the endanyway). To save any argument I shall Iassume still air conditions in all the cha pte rs until then.

Figure1.2 Figure1.3 B 3 C 100 50 Easterly Component

~

5 10

J:

~ 4 A Nortbernly Component

Fig ure 1.3 represents a seesaw the plank of wh ich is exactly balanced .Ther e isach ild weighing100 lb5feet from the pivot and a ch ild weighing 50 Ib 10 feet from thepivot.The ch ildon the right has amoment of500 ft. Ib clock wise abo ut the pivot,and the ch ild on the left has a mom entof 500 ft. lbanticloc kw ise ab outthepivot. The two moments are eq ua l but in opposit e directions and so the y ca nce l ou t which le a v e s the seesaw balanced. It is in eq u ilibrium as ther e is zero resultant mom en t.

In Figure 1.4two equa lbut opposite fo rces act on a bod y. The two force vectors canc el out, the y have no resultant but the ywill obvious ly tend to turn the body. The turning effect , or moment, of the pair of for ces is the same abo ut any po int youca re to choose.The tot al momentis Force times the distan ce between them.This kindofsyste m is called a couple and its momentis the same 5 x10= 50aboutany pivot poin t.InCha p ter 5I'll remi nd you that yo u can hav e a force syste m with no resu lta ntexcep t a mom entwhich isthesame about any point.

You will ofte n see some quanti ty like airs peed (V) with a number su pe rsc rip t. For exam p le V3 me an s V "cu bed" or V "to the powe r 3" or speed x speed x speed.Simila rly the"cube root"of V(w ritte n3jV)isthe numb er which , when multiplied together thre e times ,. givesV.

Win

d

I could have used the wind as ano ther exam ple on vectors.To find the effec tofthewind,just ad d the wind vector to the aero pla ne's veloci ty ve ct or to get the

Chapter 2

Requirementfor Flight - Lift

W

hat makes an aer oplane specia l is its wing.

The question is, ho w do es it produce lift?I wish I could tak e you to a wind tunnel with

ap pro p ria te models and mea surement eq u ip me n t. I

could then dem on strate how lift is produced just as it

was shown to me. Inste ad I sha ll have to attempt to

describ eitin words and diagr am s.

D

efinitions

Figure 2.1 sho ws the cross-sectio n of a wing. The

straig ht line from the ce ntre of the leadi ng ed ge (L.E.)

the trailing edge (T.E.) is the chord line.The len gth of

the chord line isthe cho rd of the wing (the wing tip to

wing tip distan ce is the spa n). The maximum distan ce

bet w e en the top an d bottom surfaces is the wing

th ickne ss, usu all y exp ressed as a percen tage of the

cho rd.The line drawn midway betweentop andbotto m surfaces is calle d the me an line or camber line. The

maximu mdistan ce betweenthemean lineand the cho rd

line isthe cambe rof the sectio nand it too is give n as a

perce ntageof thechord.

The leading edge is always smoothly rou nded and

thetrailin g edge is always sha rp.

A typica l test wing fo r a wind tunnel has a uniform chord and aerofoilsectio n from one end to the othe r and fits exactly in the

width of the tunnel

which do e s awa y with Fig ure2.2

the comp licat io n of tip

effec ts which we don't need at this stage.

I sha ll give you fair

warnin g whe n I come

to a wingwith tips. For

the mom ent the flow is

assume d to be the same

at any po sit ion alo ng

the spa n (two

dimen-sional flow).

Figure2.1

Wa

tching t

h e Airflo

w

It is interesting towatch the flowinasmo ke tunnel,

which is a speciallow speed wind tunnel inwhich many

small st re a ms of smo ke are fed in to the airstream

upwind of the wing. The thin st re a ms of sm o ke

travellin gwiththe air as it flows over the wing help to

visualise the airflow.Figure 2.2 is adiagram sho wing a

typ icalflow pattern around a wing.The lines sho w the

position ofthe smo kestreams.Thisis a commonway of

sho w ing an airflow and the line s drawn are called

"streamlines".

Streamli nes are lines drawn in the dire ction of the airflow suc h that no wh er e does the air flo w across a line.

As the airflow ap proaches the Lead ing Edge(L.E.)of the wing it sp lits in two, part going above and pa rt below.The strea mline which divid es the air which will go overthe wing from the air whic h will flow unde r it

meetsthe wingatpoint A.Airmolecul esflo win g exactly

along th is line will me et the wing head on an d be brou ght to a de ad stop at A. Po int A is called the "stagnation point" becau se the air's velocity is reduced

to zero. .

Wa tching the smo ke strea ms over the top surface

very closel y, itcan be seen that the airspeeds up as it

16

Cam ber Line • Call/be" • ChordLbw • .L E. T.E.• • • ~--- --- --- - - ---- --- --- - -~ CIJOI'd

the air me etsthe wing head on.See Figure 2.5in whic h the len gth of eacharrowrep resents the pressure at that point.

Pressureis define d as for ce per unitarea .Imagine in Figure 2.5 th at these pressure arrows, one inch apart, each represent the fo rce on the one squa re inch arou nd each hole. If all those force vectorsare added togeth er, the resultan twillbe the total force on a one inc h wide strip of wing. Its size and direc tion depend upon the aerofoil sectio n, the ang le to the airflow, the speed of the airflow, ete. See Figure 2.6 in wh ich the resu ltant force is sho w n as force F. The po int where th is force crossesthe chord line ofthe sectio nis called the Centre of Pressur e (orCP.). It is the poin tth rough wh ich the total pressure effecton the wing can be repl aced by a sing leforce.

Pressure Exerts a Force

~ -

_---

---Figure2.4

Figure2,3

Figure 2.5

passes over the thick part of the wing and resumes its pre vi o u s speed by the Trailing Edge (T.E.). Under the wing the smoke bunches up as itslowsdown , and then it accelerates to its originalspeedat the T.E. Ifthe smoke strea msare pulsed, Le. released in sho rt burs ts, it can be seenthat the start of the smoke pu lse above the wing re ach esthetrailing edge before the smo ke below the wing as illustrated in Figure 2.3. Obvio us ly the air over the top surface hashad to speed up to cover a longer path in the same tim e. Notice also th a t where th e flow ha s speede d up the stream-lin e s are closer and whe re the flow is slo we r the stream lines arefurthe rapart.

As the ang le of attack is incr e ased the stag n at io n po int A mov es down arou nd the cu rve ofthe leading edgeincreasingthe distance the air travels overthe to p, and reduci ng the distance alo ng the underside .On a wing with a symme trica lsectio n at an angle to the airflow, the stagna tio n poin tis below the cent re of the le ad in g edge (as in Figure 2.4) so jus t as with the cambered section the air flowi ng over the to p su rface has further to go in the same time, and must therefor e speed up.

You can't get a change in velocity withou t app lying aforce (Newton'sFirstLaw).The only for ce available to th e free air is its pressu re so the pr e s su re must be changing as speed cha nges across the chord of the wing(SeeAppen dix A,Bern oull i's equation).

If we wish tomeasur e accurately thepressur e cha nges we have dedu ced must

be occurri ng ove r our aerofo il, we can drill a row of tiny holes in the top and bottom surfaces andconnec teachone to a pre ss u re measuring de v ice. Each pre s su re measured acts at right ang les to the surface at the poin twhe re itwas measured. The pressur e is, as expected, less on the upper surface tha n on th e unde r surface an d the re is a high pre s su r e pe ak at the stag na tio n point where

Pressure Variation

Figu re2.6 Ailflow ~ Figure2. 7 Ailflow ~ Figure 2.8 L

,

,

,

,

,

,

,

,

, ,

,

,

c

.r.

lV

It is inc on veni ent to have a fo rc e act ing in an

arbitrarydirection like that andso it is split up into two compo ne n tsat right anglesto eachothe r.

The dire cti ons chose n are the obvio us one s for a

wind tunnel. The co m po ne n t in the dire cti on of the

airflow is called Drag ,and the co m po ne ntat right ang les

to the airflow is calle d Lift(See Figure 2.7). Note that I did not sayverticaland hor izontal! It istrue if the wind tunnel is built horizontal, but lift will not be ve rt ical when we co me to an aeroplane clim bing ordescendi ng

or ban kin g.Figures 2.8and 2.9sh ow whatImean.Note

thatitis amathematical conven ience to sho w forceslike

F,orLandD at the centreofpressure.Theyare mer el y representingthetrue situa tion of Figure 2.5.

Some pre ssure mea suring de v ic e s mea sure the

diffe rencein pressur ebetween thedesired pointand the static pressure of the air in the room.Or if you like the pressure differ en ce between the insid e and outside of a hollow wing.Figure 2.10is simila r to Figure 2.5but this time sho w ing the pre ssure difference betwe en inside

and ou tside.The reduction in pressure whe re the air is

speed ed up causesan upwardforce over the top surface

and whe re the air is slowed down ther e isan upward

force on thelower surface.Thisisacom mo n meth od of

sho w ing the lift distribution which you mayhave come

across befor e (some times only the line joining the tops

18

of thearrows is shown).The resultantof allthes e for ce s

(or pressur es )is exac tly the same asin Figure 2.6.

Just togetall thisin perspective , consider how much pressure cha nge is needed to su p port the weight of a mod el with a typ ical wing lo a d ing of 20 oz./ft- . Atmospheric pressure is about 14.7 pounds per square

inc h. An ave rage pre ssure rise on the unders id e of

0.02%, and an aver ag e pressure reduction of 0.04% on

thetopsurface willsuffice.

We are not asking much are we ?To call this a "vacu u m" would be misleadin g. I exag gera te d

enormously the arro ws on mydiagram s 2.5and 2.10 to

makethem mean ingful.

Wind

T

u nnel

T

esting

Of co urse we don't really go throu gh all this

rig m a role of me a surin g pre s sure s an d inv ol v ed

ca lcu latio n to work out the lift and drag in a wind

tunnel. Beside s the co m p lica tion involved, the sk in friction draghasbeen igno red .

The wing cou ld simplybe mounted on a balan ce to

mea sur ethe forcesdirectly.

The force must be mea sured through the attac h me nt point (e.g.the L.E.or quarte r cho rd point)together with

the moment abo ut this poin t. Th is mom ent iscalled the

Pitch in g Mom ent. As mom ent eq ua ls force time s dist a nce, if the lift an d moment are kno wn then the position whe re the liftacts(the CentreofPress u re) can be calcu lated . The wind tunnel sho uldbe equip p ed with a bala nce capa b le of me a su rin g ho ri zontal force s , vertica l forces, and pitch ing moments all at the same time.

This eq uipmentcan beused totest awing,adjus ting one variable ata time and kee pi ng everythi ng else the sametofind ou t the effec tofeachvariable.For instan ce test ing the same wing in the same position at differ ent airspeeds shows that Lift, Drag an d Moment are all prop ort ionaltothespeed squared.

In otherwords at twicethespeed youget fourtimes the for ce , and at three times the speed, nine times the for ce etc.

By similar means it is found that Liftand Drag are also proport ion alto theair den sitypand thewingarea. The mom ent is proportional to the speed squared, the air den sityand thewing area time sthe chord.

To turn these relationships into use ful eq ua tions for estima ting the lift from a wing , a cons ta n t has to be intro ducedand its valuemustbefound expe rime ntally.

50for exa mp le • L= PV2_{5 x cons t.}

Figure2.9

Figure2.10

Adifferent cons tan t is ne ed ed ineach case but to save running outofsu itable lett ers ,the lett er C isused inall th ree equations with a different subscri p t.The people who mad e up the eq ua tions put ina!1 as well becau se the term !1 pV2had turned up in Berno u lli's equ ation (see AppendixA again).

We end up withthesethree familiarequa tions • L= !1PV25CL

• D=!1pV2_{5 C} D • M = !1PV25CC~I

Where CL is the lift coeffic ie n t and CD is the dra g coefficie ntand CM is the pitchi ng mom ent coefficien t. They allvary withang le of attack as you willsee.

!

1 I

t

t

BasicAeronauticsforModellers

t

t

t

+

~

Chapter 3

The Stall's the Limit

Notice the shape of the graph! It is straight from Ato Cand then curves up to amaximumat D then down to E and beyond.

At point B theangleof attack is ze ro asthe winghas been arranged as in Figure3.3 suc h that the chord line is parallelto the airflow. Although the angl e of attack is zero,thewing isstillproducinglift.

At point A the wing has been tilted further lead ing edge down as in Figure 3.4 and is now producing no lift. The zero lift angle ofattack is written as a_o (the su bsc r ip t 0 denoting no lift). The normal way of measuring angle of attack is to mea sure UP from the direction of moti on to the chord line.Because thechord

E

0<

=0 Figure 3.1sho ws a wing sectio n in an airflow.The

anglebetween the chord lineand and the airflow is called theangle of attack.It is usuallyrepresent ed bythe greek lett er a (alp ha). Occa sionall y a different datum line is used ins teadofthe cho rd line. It maybe a straight line on theundersid eofaflat bottom ed or undercarnbered Wing, orthe wing's zero lift line. Asthe name suggests, if the airflow isparallelto the ze rolift line,theliftis zero (usefu l in mathem aticalformulae).

The inciden ce of the wing is the angle betwe en its cho rd line (or other datum line) and the fusela ge datum line.It bearsnorelation totheairflow and angleofattack at all.It isjust ariggin g angle.It maybemeasured on the aeroplanewith an incidence meter oron the plan with a protractor.Thoseare theusu aldefinition sandIshallstick to them, but it is not uncommon to see the word incide nceused meaningangleof attack.

Testinga wing at manydifferent angles of attack and working out the Cl. eac h time (from the form u la in Chapter2)enables agraph of liftcoefficie nt again stangle of attacktobedrawnfor thatparticularsection.For most normal sectio ns the graph looks like Figure 3.2. This gra p h is true for this sectio n regardle ss of the size or spee d an d ca n be us ed to est im a te the lift in any cond ition.

The

Lift Curve

Definitions

I

nwind tunnels the wing is stationa ryand the air is drawnove r it,so that ishow it isusuallydescrib ed in the or y. It is just as valid to think of the air as stationaryand the wing moving. Its directionof motion is exactlyopposite to the arrow marked "a irflo w". The directi on ofthe airflow must be measured far enough

aheadof the wingso that itis not affected by thewing's app roach. Figure3.1 Angle ofAtta ck (measur edfrom ch o r d U1Ie) Ang le ofAttack (measuredfrom zerolift U1Ie)

C

Zero lift l .

--- - -

Cb';;"';-;'

- - - -

~"~

_

_

~

Directionof Motion " " , ,

Airflo w

lin e is DOWN in this case the ang le ofattack is a negative ang le (for ex ample the an g le of

attack forzerolift on an

Eppler 19 5 sec t ion is give n as - 3 de gre es).

The zero lift line (ZLL)

drawn on thewing is by defin itio n parallel to the

airflow.

At po int D the lift

coefficie nt is CLma x which is the maximum liftcoefficient which the

sectioncan produce and

occurs atas the stalling angleof attac k.

The Stall

Figu re3.3 Figu re 3.4 _ _ _.~~ ZLL

----:----c--

-0<;[ - - -

-

-~ Figure 3.5 DirectionOfMotioll At points C,Dand E the wing is mounted as in Figur e 3.5 with a la rge po sit ive ang le of attack but somet h ing strange happens to th e

liftin thisarea. Asa has

been increase d, the lift has been increa si ng

ste a d ily in proportion

but now itsuddenlyreachesapeak and drops off again.

The phenomenon whereby lift drops beyond a certain

angleofattack,rather than incre asingas before,iscalled

the "STALL".The wing issaidto have stalled because it

ca n n o t be pe rsu a d e d to prod uce any greate r lift coefficient.

towards the lead ing edge , Figure 3.7. Atthis pointthe

wing is fully stalled (p o in t E on Figure 3.2). The air

makes no atte mpt to fo llow the wing's top surface but

breaks up into turbulence. The result is a reduction in

liftcoefficient. Note that there isstillquite a lot of lift, but less than the re was when the ang le of attack was

justlessthan thestallingangle.

The Reason

To find the reasons in the airflow for the stall it is

back to the smo ke tunnel.Atsmall angles of attack the

airflow over the wingissmooth butasangle ofattack is

incre ased ther e co mes a po int when the flow starts to breakaway before it get s tothetrailing edge ,Figure 3.6.

The aircan'tquitemak eitdown theback ofthe aero fo il

so the smooth flow en ds as the strea m lines abru ptly

brea k away, or "sepa rate", fro m the su rface at the "separation point".

If the angle of attac k is increased even more the

sepa ra tion poin t mo ve s progressively fu rther for wa rd

Figure 3.6

~

:

BasicAerona uticsforModellers

Variations

Different sectio ns havedifferent stallingcharacteristics

dep endin g upon the ir thick nes s, camber and the

sharpness or blun tne ss of their le ading edges. Some se ctions miss ou t the Figure 3.6 stage and the flo w separation starts suddenly at the leading edge giving a very abrup t sta ll as in Fig u re 3.8 (NACA 23012 for exa mple). Others hav e a mor e progressive stall as in

Figure3.9(forexam pleNACA4415).

In the special case of an unc ambered (i.e.

symmetrical) wing sectio n, the graphof lift coefficient

Figure3. 7

---==

Figure3.8

0<

againstangleof attackwill lo ok likeFigure 3.10. Thatis, the liftcoefficient is zero atzero angleof attack ,which

Figure 3.9

isjust whatyouexpect,and ofco urse it perform sjustas wellinverted .

Anysection willhave a graph like Figure 3.10 ifthe angle of attack is measured from the sectio n's ze ro lift

line. Itis merelya caseof movingthevertical axis alo ng

towhere the lift is zero.Then,for the straight bit of the graph belowthestall,the liftco efficie n t equals the slope of the line times the angle of attack. Co nve nie ntly it is found thatCL = 0.1 per degree (ap prox) forall aerofoil se ctio ns. I sha ll use this idea in the cha pte r on Pitch Stability.

Notice To

Air

men

I hate to lab our the point but not ice wha t ison the graph on Figure 3.2, not speed but angle of attac k. A wing do es not have a stalling speed .It has a stalling angle of atta c k at wh ic h it will sta ll more or le s s reg ardl e ss of the speed. Tha t is one reason why lift coefficie nt isplotted ,to get rid of airspeed and den sity variables whic h are unimportant to the prop ert ies of a section .Itistrue that an aeroplane hasastallingspeed, but it is only a little true.

When I come to mention the stalling spe e ds of an aeroplane Isha ll remindyou that it isthe stalling angle of thewingwhich matters.

Figure 3.10

0<

0<

Chapter

4

The Drawback

_•

_{• •}

Drag

I

nmybook Drag is no thin g to do with dressin g up. It is a force resisting mo tio n. To be mo re exact, DRAG is a force exerted by the air on a moving aerop lane,and itactsin exactly the oppositedirection to the direc tio nofmotion of the aeroplane.

Drag as measu red in the wind tunnel is mad e up of tw o parts. First th e re is th e drag from the pre ssu re dist ribu tio n men tio ne d in Chapte r 2. Ifthe pressure dist ributi on dep ict e d in Figure 2.4 is adde d up to produce a single resul tant force on the wing (Figu re 2.5),then the componen tin the direction ofthe airflow is the Pressure Drag.That is one part,the other is good oldfriction.

\V'he n one object slides over ano ther, the re is a friction force re sisting motio n. A friction force

Cal

;

exist even witho u tmotion whic h is why the hand brake can hold the car on a hill. In fluids (e.g. helium,air, water, .oil, treacle)the friction effec tis called"viscosity" and the differ ence in this case is that the viscous forces can not existwithou t mot io n.The viscous drag onan aeroplane is,for tu nately, sma lldue to the air'slow viscosity and it occursin the"bou ndarylaye r".

The bounda ry layer is a very thi n layer of air, the bott o m of whichis stuc k tothe aeroplane'ssurface, and th e to p of which is

mo v in g with the air-strea m (See appen dix B). The flow in this re g io n may be smooth or roug h (larn ina r or turb ul e n t in te c h n ical jargo n) or more usually a bit of each. It starts off la m in ar and the n usu al ly changes into a turb ule nt bounda ry la yer fu rt h e r dow n-stream. Alami n ar boundary layerhasless drag butis more prone to separate from the surface.

Wing Drag

In the wind tunne l each aerofoil section canbe tested to find its drag by sim p ly me a s-ur in g it on a bala nce. Usingthe formu laatthe end of Chapter 2 the drag coefficient can be

Basic Aerona uticsfor Modellers

calcu lated. In the case of a test on a wing section, the drag is divided by Y, pVl and the wing area, and the re sult in g Drag Coefficient, CD is a property of th e section,independentof speed and size,and can be used to estimate the drag of any othe r wing using th a t section.It willvary with the angleofattack however,so itis normal to testitata wide range ofangles ofattack andthen plota grap hof drag coefficient against angleof attackfor that section.

The typicalshape ofsucha graph is showninFigure 4.1.Drag coefficient tu rns out to be a very smallnumbe r which at small angles of attack does not vary much. There is a minim u m drag angle of attack (point A) which is not necessarily where (J. is zero. Approachi ng the stallingangleof attack (point B) the drag increaseis more rapid while above th e stalling angle the dra g increases veryrapidlyindeed.

Whe n the wing stallsatpoint B,the drag increase is proba b ly more significant than the reduction in lift coefficient.

Drag Polar

Knowing the drag of a wing at a certain angle of

Figure 4.1

B

the resulting graph would look rather sq uashed so the drag isalw ays show n greatly exaggerated. From the drag polar you can read off the value of C_Lrnaxand CDrnin• Notice that the minimum drag does not necessarily

occurwhere lift is zero.

The Lift/Dragratio is often taken as ameasure of the "efficie ncy"of a section,and it can easily be worked out from the polar diagram. At any point on the graph divide the lift coefficient by the drag coefficient.The best VD ratio occurs at the point C where thestra ight line just touches the graph.

Thickness and Camber

attack is only part of the story. The "drag polar"(as in Figure 4.2) is useful in showing how much drag the wing produces when generating a certain amount of lift. If lift and drag coefficients were shown to the same scale

The amount of the minimum drag depends mainly upon the section thickness.The less the thickness, the less the minimum drag,but thin wingsare not strong so a compromise has to be reached.In addition,a very thin wing has a sharp leading edge,and that is one of the things which can cause an abrupt leading edge stall as on Figure 3.8,in the previous chapter.

The angle of attack, or lift coefficient, at which the minimum drag occurs varies with the sectio n's camber. The more the camber, the higher the angle of attack at which the minimum drag occurs.Therefore the drag on an aeroplane which usually flies slowly can be minimisedby usinga section with quite a lot of camber. There is however a large increase in drag if the aeroplane is flown fast. In other words it does not penetrate well. Highly cambered sections are often called"low speed sections".

A wind tunnel can be used to measure the drag of a fuselag e (o r undercarriage or any other part of an aeroplane). It too will consist of two parts. Surface friction drag will depend on the surface roughness, and on thesurface area.

The more surface area exposed to the airflow (the

"w e tt e d area"), and the greater the proportion of turbulent boundary layer, the more the surface friction drag,but more important is the pressure drag which will depend on theshape of the body.

Certain sections have a drag curve like Figure 4.3, with a region of particularly low drag from point A to B. This is known as the "d rag bucket",and it takes little imaginationto see why.The drag coefficientis virtually constant in the drag bucket and rises stee p ly on either side.

By careful design, and keeping the surface very smooth, the designers of the sections have managed to keep the boundary layers laminar (see Appendix B) as long as possible to take maximum advantage of the lower drag.If the section is not built accurately,or if it is not kept smooth and clean, the drag bucket will disappear.

As with other sections the more the camber the larger the angleof attackwhere the minimum drag occurs,and the more the thickness the more the minimum drag will be. Curiously also, the thicker the section,the wider the drag bucket will be.

Fuselage Drag

Laminar

Flow Sections

01. 01. S B ..- --_.._....-- ---....---:..;-

-..,

---....

A Figure4,3 Cl) Figure4.2

24

Basic AeronClutics/orModellers

Scaleair cr aft like this SkJ1walkeroftenuse wheel spats whichsignificantly

reduceprofiledrag.

Streamlining

Pressur e drag can be min im is ed by ca re fu l "stre am lin ing " of the bo d y, that is shapin g the bod y suc h that the stre amlin e s in the a ir-flo w foll ow the sha pe of the bod y rather than

break ing away from the

su r face to leave a turbulent wake.

For examp lesu p pose the drag of a flat disc at

right angles to the air

-flow is 100 units. The

drag of a sphere of the

same diam eter would

be on ly 45 units while

the drag ofa care fu lly

streamline d body, again

of the same diameter , could be reduced to on ly four

units.Yes ,theprofiledrag ofa strea mline d body can be

redu ced to only fou r per cen t of that of the same

dia me te rof flat disc.

The drag due to the wake ca use d by the flow sepa rating from the surface is so much more important

than the sur face fricti on drag in the boundary laye r,

wheth er laminaror turbulen t.

A B

it

fo

r

Golf

e r s

Why, you are wond erin g, does a golf ball have

dimples?Well as it fliesthrough the air atgrea tspeed, it hasa boundarylayer.

The dimpl es are ther e to ens ure that itisa turbulent

boundarylaye r,asturbulentboundarylayers clingto the

surface lon gerbefore they separate. \'(Thichreduces the

Figure4.4

Smooth Ball

..

Dimpled Ball

BasicAeronauticsfor Modellers

size ofthe turbul ent wakewhich reduces pressuredrag

by a subs ta ntialamount. It more thanco mpe nsates for

the slight increas e in skin friction drag. Hen ce the ball

goesfurther foragivenclout. SeeFigure 4.4.

/

TurbulentWake

Chapter 5

Have You

A

Moment

A

lmost certainly! It do es not matteratwhic h poin t on th e wing you choose to attac h the balance,

you will almost certainly be able to measur e a mo me nt about that point. The le ad ing edge might be chosen as a convenient po int as itsimplifies the ensuing calculat ions.As withliftand dragthe momentcoefficient CM is worked ou tfrom the formu la ata wide range of different ang les of attack and then plo tte d on a grap h.

For mathe mat icalreasons it was decid ed th at nose up moments wou ld be defin ed as positive, bu t of course the mo ment about the leading edge willbe nose down,

Le.negative. Figure 5,1 C~ILE Nose Up 0(0 0( B A Nose Doum D E Figure 5.2

Th e gra ph will lo o k lik e Figure 5.1 in which the poin tsA, B, C, D and E correspond to tho se on Figure 3.2.Theline is straightfrom poi n t A,the angle of attack for nolift,to point C,where the wingstarts to stall,and then curvesdown to D and E as the wing stalls.In other words,the mo ment getsprogressivelymore nose down as angle of attack is incre ased and then at the stalling angle there is a furt he r increase in the nose down moment. Please notice also that atpointA, where lift is zero and ang le of attack isa_{o (t}he 0 meaning"no lift"),

there is stilla nose down moment.The corresponding momen t coefficient is called _{CMo (where t}he 0 again me ans "no lift ") and it is always ne ga tive , Le. nose down, for normal sections.

BUT, But, but! I he ar you say. The moment is the turningeffect ofthe lift force so how can no lifthave a moment? Well remember that all this stuffabout Lift forces, Drag forces, Moments and the Centreof Pressure is just for administra tive convenience. \Vh a t we are trying to describe is a pressure distributio n around the wing, so let us go back to tha t; look at Figure 2.10 again. Atthe angleof attack at which the balance says there is no lift, th e pressure distribution will ha ve cha nged to somethinglike that inFigure 5.2.The re will be a smalldownward pressure on the front part of the wing and a small upward pre ssure on the re ar part of th e wing, but the angle of attack has been carefully adjustedso that these cancel out. Howeverthey willstill have a moment abou t the lead ing edge, or any other point youcare to name (see Figure 1.4),

Centre ofPressure

If the lift and drag and the moment about a known point like the le ad ing edge are known, then the position ofthe Centreof Pressure (CP) can be calculated .As you

CP Position

"$0,TO LO$ETilE IIUN,tDIVED IIEK $TKAIGIIT DOWN••••ANDTilE COFP $LlPPED klGIITOFFTilE WING, ZIPPED PA$THY EAK,ANDGOT TANGLED

IN TilE TAIL KIGGING WIKE$I"

:

.1

1

I am a mathemati cal

~concep tyo u knoui

CP "'"'"

other way.You are perhaps wondering if itis possible tochoose a point in betweensuch thatthe grap h will be in betw een the others,dead levellikethe dotted line in fact?Yes,it'spossible!

Back in the day s when Ca me ls fou ght ag a inst Albat rosse s, the Centre of Pressure was the phrase on eve ryo ne's lips, in aerodynamic circle s that is. But in lat er years whe n aerodyn am icistsfoundthatthere wasa po int on the aero foilabou t which the moment did not vary withang le of,attack,theywere so ple ased thatthey gave it a spe cial name, the ae rod yn amic cen tre of the section(some times shortened to aerocentre or justA.C.). Here at last wasa pointatwhich they could place th e lifton their diagrams and in their little calculations and all they had to do was adda mom ent on the aero plan e which varied only with airspeed, not angle of attack. This new mathematical con ce pt described the pressure

distribu tion (reme mber Chapter 2) just aswellasthe old

Centre of Pressuremathematicalco nce p t. The beauty of

~Chord I Stall ____ __ __ J_ _ _ CLll ltu: Figure5.3 know, the CP mo v e s

around and Figure 5.3 shows the trend of the movem ent. The Centre of Pre ssure moves for-ward on the wing as ang le of att ac k is increased. It nearly gets to the quarte r ch o r d po sit ion but then the sta ll move s it back again. At the other end a cu r io us thing hap -pens. When CL is ve ry small the Cen tr e of Pre ssure disappears off

the ba ck of th e wing.

That ca n happen becau s e it is a mathematical con -venience ,nottied to the wing'with a piece of string. The distance of the cen tre of pressure behindthe leading edge

is calculate d bydividing the momentabout the leading edg e by the lift co effic ie nt. When the lift coeffic ie n t bec om es very very small,the ans wer becomesvery very large. When the lift is zero, the ans we r is infinity!You can imaginethatthe idea of a minisculeforce agigantic distan ce beh in d the wing would have the same effec t as the pressure distribution in Figure 5.2.Lift is definedas the compone nt of the resultant force atright angles to theairflow so in Figure5.2there isze rolift.

In the spe cialcase of asymmetricalaerofo il there is no mom ent at zero lift, and when the CP position is calculated it turns out to beat abo ut the quarter chord point atall anglesofattack right up tothestall,whereit moves backa bit as before.A fixed point like this is so much more satisfying . It can be marked on diagrams, an d you can take momentsabout various pointsanddo little calculations (if that

iswhat turns youon). Wouldn't it be just thrilling if we could do that for camber ed sec tions aswell?

Well, Figure 5.4 is just like 5.1 except that in ad d itio n to the mo -ment abou t the leading edge, it also sh ows the gra p h of the moment abo u t the trailing edge as well. This line als o passes through point A sho w ing that the zero lift mom ent is the sam e no matter abo u t which pointitismeasured.The only difference is th e slope,which is now the

A

erodynamic

Centre

Figure5.4 _dthe_istributioeffect _nof t_{, b}he_{ut do}sa m e co_{not fo}mp l_{rge t th}e x ai_arflow_{t it is}a_tnd pr_{he pr}e s_esss u r_ure_e dist rib u tio n which creates th e lift, not the arrows or form ulae which are just co nvenie nt ways of attempting to describe it.

Aerofoil Section Summary

/

/ /

Increasing the thickness will • 1.increasethe minimum drag,CDmin

• 2.widenthe drag bucketon lami na rflo w sectio ns • 3.increa se streng th/weight ratio.

Increasing the camber will

• 1.incre ase CU11:IX(verythick or verythin sectio ns have

areducedCl.llm due to anearlystall).

• 2. make the zero lift angle of attack, 0:₀ more

negative.

• 3.increase the liftcoefficient at which minim um drag occurs.

Now that I have mentioned all the se ctio n characteristics,Iwould like tode scr ib e , with the hel p of

Figure 5.6, how an aerofoil section may be made up , and ho w we can influenceits ae ro dynamic coefficients.

Firstdrawa straight line whichwillbethe cho rd line of the section.

Next draw in the camber line. The maximum gap

between it an d th e chord line is the camb er of th e section,whic h may be from zero to 6%or possibly8% ofth e chord.The max cambercan occurbet w ee n 15% and 60%of the chordfromthe le ad ingedge.

Then a thickness distribution is wrap ped around the cam ber line. This may be done by drawi n g lines of

appropria te le ngth across the camber line and jo ining

thei r ends,or drawing a series of circleswith centres on

the camber lineandjo in ingthe ir tangentsas shown.The maximu mthickness isusually between 6%and 18% and

occ urs from 15%to 50%ofthe chord from the leadi ng

edge.

Thickness and Camber

,

\

IIIBettoeen

z

_

/ A / / / / /

it isthat for a partic ularsection,th eco efficie nt C'\lnis a constan t, just a small negative number, like -0.05 for NACA 2415 for example (but it is co nstant only below

th e section'sstalling angle) .

Now the pressure distribu tionmay be representedby forces in fou rdiffe re nt ways.They are shown inFigure 5.5.The first is the resu lta nt force throu g h the CP. Or

one cou ld show the tw o separate compone n ts, Liftand Drag,atthe CP.

But since that is imprac tica l whe n you come to measureitin a wind tunnel,theforces can be measured as Lift and Drag at a fixed point like the lead ing edge together with a momen t abou t the leadi ng edge, and

finally the Liftand Drag at theae rodyn amic cen tre and a momen t )'1'10. This last metho d is mo st convenient for

calcula tions.These areallequallyvalidways of showing

Figure 5.5 L AC L D L

(

Figure5.6

Ma.'\: Camber

t

Cambe,.Line

Cb o r d Line

Il(/If

Th ic k ness Distributton

Tbickne ss

HalfThick ness added eacb sideofca m bel'

• 4. increase the negative value of C~IO' wh ich will be between-0.02 and -0.03 for each 1%ofcambe r.

• 5. reducethenegative (inverted flight ) C_{lm a},

Section Classification and Use

SYMl'l'JET RICAL sections hav e zero cam be r and ther efor e

ao

and CMoare also ze ro.\Vithou tcamber they

haverath eralo w Culla, butat leastit isasgood inverted

asup right. Theleast drag occursatzerolift. Symmetri cal sectio ns are th us best for high speed and ae ro ba tic aeroplanes. Their thickness is a com p romise between

strength and drag , typically 10%to 18% fo r wings and

6%to 10%for tailpl an es.

All other sections are cambered

sections.

An UNDERCAMBERED section IS Just a thin high ly cambe redsectio n.Sometimes thecamber isjustenough to mak e the underside slig h tly concave as on WWI

aero planes.On some freeflight floater stheundersideis

veryconcave bec ausethe perce ntage cambe r is as much as thethickn ess.Suchsectionsare very good at large lift

coefficients(lowspeed) but poor atsmallliftcoefficients

(highspeed), which mean s theydo not pen etr at ewell. Theyarealso uselessinverted.

The BICO NVEX (orSEMI-SYMMETRICAL)sectio n is

so ca lle d because both top an d bott om su rfaces are

con ve x, but the top one is mo re so. That is be cause

the cambe r issmallco mpa re d to the thickn ess,and the fa ster or more aerobatic the aeroplan e will be, the smaller the cambersho uld be.

The FLAT-BOTTOMED section, like the Clark Y or Gottingen 796,isa specialcase of acambe redsec tio n.If

BasicAeronauticsfor Modellers

th e percentage thickne ss is chose n to be abou t 3.33

tim e s the cam ber then the rea r 70% or 80% of the aerofo il underside often turns out flat. That makes it

easy to build, it hasa good upright perfo rma nce but is

po orinvert ed.

Chapter 6

The Vortex System

W

ith no wingin the wind tun nelthe streamlines in the flow would be straightand parallelas in Figure 6.1. Putting in a wing changes the airflow somewhatas shown in Figure 6.2.The changes imposedon theair'svelocitybythewingare an upwash just in front of the wing, a speed inc rease abo ve and a decrease below the wing, anda downwash behin d the wing. Figure 6.3 shows these velocity changes (sh ow n asdV) in isolation.The effectofthewing seems tobeto

Figure6.1

Figure6.2

induceakindofsw irling mot ion tothe air,around itself. A rotating flow is calle d a VORTEX (Ap pe n d ix C ex plains vortices in mo re detail). \'V'henever a wing is produci ng lift it tend s to induce this circu la ting flo w arou nd itself, andthemor eliftthemorecircu lation.This vortex iscalled the "bound vortex"as it isfixed around thewing.

Vortices canno tend abruptlyin mid air. In the wind tu n nel they en d on the wind tun nelwallwhich is fine. Butwhat happen s ifthe wing doe s not extend from the wall to wall? What happ en s if th e wing has . . . (wait for it) . . .TIPS!YES folks we are now intoTHREE DIMENSIONALFLOW.

er

did promise to warn you). Well you know very well what happens, the Figu re 6.3 ~ dV dV

I

dV

!

dV

..

~

LotoPressure

~Wi"gT

iP

High Pres sure

~

TopSurfaceFlow

SlightlyInuiard

BottomSurfaceFlow

Slightly Outward

I

I

LE TE

I

I

I

I

,

(

Figu re6.4

vortices do not justend,they trail off in the flow behi nd th e wing tips . The se vortices are called the Traili ng

Vortices.They wouldgo on for ever if the air'sviscosity did not dissipate them and absorb their energy.I have watched the condensa tion trails of a Boeing 747 still

gently rotating when followi ng 2000 feet below and nine teenmiles behind.

Thereis anotherequa llyvalid way ofloo king at these trailing vortices.At ournewly acquired wingtips,the air pressure is lower above the wing than below.The air

inevitabl ytriesto go from high pressure tolow,around

the tips, whic h gives rise to a degree of spanwise flow , outward on the lo wer surface and inward on the top.

The trendcontinuesto a decreasing exten tsome way in

from thetip.When th e to p and bottom flows re u nite at the traili ng edge, they are mo vin g in slight ly different

directions,sligh tlyoutwardon theundersid e andslight ly

inwardontop.

In Figu re6.4I havetriedto show theresult of all this.

Alongthe trailing edge,especially nearthetips , vortices

are formedwhichall rollup togeth er to form onela rge vortex trailingbeh ind eachwing tip.

Seeing The Vortices

There is an easy way you can see your mod el's

trailing vortices.Attach three streamers twelve to fifteen

feet lo ng to each wing tip of a su itab le model

er

used a Gangs ter 63).Laythem out straig ht on the grou nd for

take off.Onclimb ou tit willbe seen that the strea mers

are being whirled round by the airflow, clockwise on theleft andanticlockwiseonthe right.

TIY a slow flypast. Th e stre ame rs will be swi rled in

large slow swirls.Now try ahigh speed beat up.Notice the diffe re n ce in the way the strea me rs are swirling

sugges ting a le ss stro ng vortex. The lift equa ls the weight in both cases sugges ting that at low speed a strongervortex is needed to generate the same lift.On

the nexthigh speed pass trypulling a tightloop as the mod el passes.The swirling noticeabl yincreases as soon

as you pulltheup elevator to inc rease thelift.

Now do a low inverted pass.Fromyourp~intofview

nothing is differe nt. The lift is still up and the vortices stillgo clockwise onyourleft,andanticlockwiseonyour right (fro m the aeroplane's po int of view the direc tions

of rotation andlift have all rever sed).The lift isrelated to

the vortices in dire ction as well as strength.Check that

by coming inslowandhigh and doingabunt,oroutside loo p.

Watch the strea mers carefu lly as you app ly do wn eleva tor. You will see the mstop rotating and then star t rotat ing again the othe rwayround.This willcontin ue all the way round the bu n t until when you release the

do wn eleva tor to continue no rmal fligh t, the rotations

reverse again.

The lessonto learn fromthis is that thestre ngthof the vor tices increases with the lift coefficient of the wing.

After abou t five min u tes of this the streamers had

flap ped themselves to pie ces andwere down to two or

thre efeet long.

Figure 6.5 AR=Infinite AR=Infinite 1

,.-,6

/ / ..--, 3

.>:

"

\

I , ' ,/ 1/ / I ,' 1 / / 1:/'

,:

1,/' ~,r :~

Even More Drag

The ASPECT RATIOofa 3-D wing is defin ed as the spa n dividedbythe averagechord.It isfound tha t when a realwing withtips istested ina windtu nne l itsdragis

mor e than if it fitted perfectly fromwall to wall,and the

lift isless.Thelo ss in per formancedepends on its aspect rat io as illustr ated in Figure 6.5.The high e r the Aspect Rat io ofthe wing,thene are r isitspe rformance to that of

the idea l tw o dimensional wing(infiniteaspectratio).

The Reason

Th issho rtfallin performance iscaused bythe trailing vortices whichcreate a reg ion of descending air behind the wing, after all the energy to crea te them must be

paid for somehow. That the s e vor tices als o cause

downwashin the airflow as itap proaches the wing can

bepro ven bythe ory ,or dem on strat ed athom eby filling

atallglasswith waterand placin g afew grains of riceat thebottom .\Vith aspoo n,stirthe water in theglassnear

the top and you willso on see the rice grains begin to

swirl.Becauseofthefluid's viscositya SWirling motionis

inducedright tothe bottom ofthe glass. If the spoo n is

the wingtip vortex stirring the air beh ind the wing, the rice is be ing swirle d round ahead ofthe wing , in the

same direction,buttoalesse r extent.

Fig ure 6.6 shows the airflow around a re al thre e

dimen sion al wing in more deta il. A long wayahead of the wing the airflow is undistur bed by its presence. As the air approaches, it is angled down sligh tly by the

downwash ahead of the wing ind uced by the trailing

vortices and the n jus t in front of the wing the air is sweptup andover by the boun d vortex as in 2-D flow.

We started by defining the ang leof attack as the angle

betwee n the wing an d the und isturbed airflo w aw ay

aheadof the wing.No w we cansee thatthe "real"angle

of attac k of theair meetingthe wing has been reduced

by the downwash. And the lift relat e s well to the lift

predicted from 2-Dtests at th is reduced angle of attack. So the loss of lift is expla in ed by the downwa sh

reducing the angle of atta ck. But what abou t the

increaseindrag?

Lo okingbackatFigure 6.6again,the aeroplane must

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