Basics of RC Model Aircraft Design

BASICS OF

RIC

MODEL

CHOOSING AIRFOILS

•

WING LOADING

•

CG LOCATION

BASIC PROPORTIONS

•

AEROBATIC DESIGN

-and much more!

BY ANDY LENNON

~

... ----_....::::.:;"

From the Dublishers

of

Aboullhe Aulhor

L

ongtime modeler Andy Lennon

has been involved in aviation since the age of 15, when he went for a short ride in a Curtis Robin. He soon joined the Montreal Flying Club and began flying D. H. Gypsy Moths and early two-place Aeronca cabin monoplanes.

He was educated in Canada at Edward VII School, Strathcona

Academy,Montreal Technical School, McGill Universityand the University of Western Ontario, London,Ontario.

Andyentered the Canadian aircraft manufacturing industryand later moved to general manufacturing as an industrial engineer. Throughout his career,he continued to studyall things aeronauti-cal, particularly aircraft design, aviat ion texts, NACA and NASA reports and aviation periodicals. He has tested many aeronautics theories by designing, building and flying nearly25 experimental RIC models-miniatures of potential light aircraft. His favorite model,Seagull III,isa flying boat with wide aerobatic capabilities. Andy is a valued contributing editor toModelAirplane News,and he has written forModel Aviation,Model Builder,RC ModelerandRC Models and Electronics. His two other books are "RIC Model Airplane Design"and "Canard: A Revolution in Flight."

He continues to fly full-size airplanes and is licensed in both Canada and the U.S. And when he isn't at his drawing board or in his workshop, he'slikely to be at the flying field testing yet another model aircraft design ....

Copyright~1996 by Air Age Media Inc. ISBN:0-911295-40-2. Reprinted in 2002;2005.

All rights reserved, including the right of reproductionin whole or in partin any form.This book,or parts thereof,may not be

reproduced without the publisher'swrittenpermission. Published by Air Age Media Inc.

100 East Ridge Ridgefield,CT 06877-4066

AirAGE

ME 0 IA modelalrplanenews.com

PRINTED IN THE USA

Introdudion .•...•...•.4 Chapter 1 Airfoil Selection ...•..•....•5 Chapter 2 Understanding Airfoils .•9 Chapter 3 Understanding Aerodynamic Formulas ..13 Chapter 4 Wing Loading Design •.•.•...•...19 Chapter 5 Wing Design . ..••. ..••. ..•..21 Chapter 6

CG Location and the Balancing Ad ..•...•...27 Chapter 7

Horizontal Tail Design ••32 Chapter 8

Horizontal Tail Incidence and Downwash

Estimating ...•...•..••••.•37 Chapter 9

Vertical Tail Design and Spiral Stability .•....•.•..•42 Chapter 10

Roll Control Design •...47 Chapter 11 Weight Distribution in Design .•....•.•.•..••.•.•...••50 Chapter 12 Improve Performance by Reducing Drag ..•.••••....52 Chapter 13

Stressed-Skin Design and Weight Estimating ••.•.•..58

Chapter 14

Design for Flaps .•....•...63 Chapter 15

NASA "Safe Wing" 69 Chapter 16

Landing-Gear Design . ...72 Chapter 17

Ducted-Cowl Design 77

Chapter 18

Propeller Selection and Estimating Level Flight Speeds ....•...•....•...83 Chapter 19

Design for Aerobatics ..90 Chapter 20

High-Lift Devices and Drag Redudion .••...•...93 Chapter 21

Centrifugal Force and Maneuverability ••••••••••98 Chapter 22 Canards, Tandem-Wing and Three-Surface Design .••.•.•...•...•....•••.. 102

Contents

Chapter 23 Tailless Airplane Design 111 Chapter 24 Hull and Float

Design ...•...•...•..119 Chapter 25

Basic Proportions for RIC Aircraft Design ....125 Chapter 26

Construdion

Designs 129

Appendix ••••••••••••••••••••134

Introduction

~

,\

- •••

~.

~

•

•.

so with electric models, which are rapidlybecoming popular. They are clean, noiseless and thoroughly

enjoyable alternatives to gas/glow.

However, the design process chal-lenges our ability to build strong but light models with low zero-lift and induced drag and an optimized thrust system, be it prop or jet. Short of information on the design of electric powerplantsystems, this book gives you everythingyou ot h-erwise need,even the impactof car-rying heavy batteries.PerhapsAndy will tackle electricpowerplants at a fut ure date....

- Bob Kress

RetiredVicePresident, Grumman The design process begins with

weight estimation and structural

optim izati o n in the name of reduced weight. The book covers

thesetopics for modelsbetter than

any sources I have encoun tered previou sly. Next in design comes drag analysis and redu ction,which

arecove red professionally yet in an understandable way for the ama-teur design er. What a treat to see the consequences of flat-plate drag from seem ingly small items like landing-gear-wire legs properly illum inated. I recently had this top ic driven home dramatically when I wentall out to clean up the drag of myelectric fan A-6 Intruder prototype. The improved perfor-mance after the clean-up surprised me quite pleasantly. What I did

could have been drawn directly from thisbook .

Stability and control, after per-formance, is what we see as an immediate result of our efforts. Result svary from joy to the black-ness of the re-kitting process.

Andy's book will keep you away from the latt er end of the band through proper selection, arrange-mentandsizing of theaircraft com-pon entscontributingto both longi-tudinal an d lateral/d irectional sta-bilityand control.

The book is oriented mainly

tow ard gas/g low-powe red model aircraft design. With gas models, available powerrarelyisa problem.

Coping with marginal thrust sim-ply results in using a biggerengin e and a tendencyto ignoredrag! Not

A

ndy Lenno n has written

an outs tan ding book tha t covers all required aspects of the preliminary design process

for mod el aircraft. Fur the r, much of thecon ten t is eq ua llyapplicable to military RPV an d hom ebu ilt air-craft design. Reviewin g the book

was someth in g of a nostalgia trip

for me afte r 46 years of designing full-scal e and mod el aircra ft. Would that I had been able to

carry this book wit h me to an unsuspectin g aircra ft industr y

when I graduated college in 19S1!

My areas of disagreem ent here

and there as I read were mostly on exotic top ics and did not amo unt to much . When review ing my

not es jotted down while reading

the draft,Ifound that many ofmy

comments simply amplified what is said in thetext and reflected even ts from my own career relat edto the book topic at hand. The ch apters on pitch and lateral/d irection al s ta-bility and control remin ded me of

some Gru m man history. We

seemed to blow an aerodynamic fuse on every fifth aircraft prot

o-type-to wit, the XFSFSkyrocket, most of whic h lande d in Lon g

Islan d Sound, and the XF10F, which, abo utall axes, was said to be liasstable as an upside-down

pen-dulum." The only thin g that worked flawlessly was the variable sweep, which we feared the most!

Maybe Andy's book could have

helped. Sadly, Grumman nevergot the chance to go beyond the F-14 and tryan F-1SE

Chapter 1

-.6 .1 ~.,--. ""'-:. .Z.,, . Figure1.

Airfoildata forEppler E197:tift curves (right-hand illustra-tion)andpolar curves (left).

Figure 2.

Taper-wingconecuo«faclorfornon-elliptic lift distribution. .25 .50 .75 1.0 CHORD TIP/CHORDROOT .1 .20

r - - - -- - - ,

a::

'"

I -~.1

...

I -Z .... :;: ~.0 ::::J ... C < .0

ever, it isn't necessary to perform laborious calculations for each potent ialairfoil.Direct comparison of the curvesandcoefficien tsof the candidate airfoils is more easily done, without deterioration of the

results. This comparison calls for an understanding ofthe data.Start by examining the right -hand illust

ra-tion of Figure I- Eppler EI 97- in

detail.

EpplerE197is 13.42percent of its chord in depth. This plot is the result of win d-tunnel test s per

-formed atthe Universityof Stuttgart

in Germ any under the directionof Dr.Diete rAlthaus.

The horizon tallineisthe AoA(n, or alph a)line in degrees(measured from the airfoil 's chord line)-positivetotheright and negative to the left.

Airfo

il

Select

io n

In develop ing these airfoil plots, aero dy-nam ics scien tists have screene d out six of

these factors, leaving only the cha racter is-tics of lift, profiledrag andpitchingmoment unique to each indi

-vidual airfoil. The seventh, Rn, is refer

-ence d separately on

the airfo il plot.

Form ulas that in

cor-porate allsixvariables

and these coefficients permit accuratecalcu -lation ofthe lift,total drag and pitching moments for your wing and choice of airfoils.

In theairfoil se

lec-tion process, h

ow-10 14 18

• Spe ed. Lift, drag and pitching moment are proportional to the square of the speed.

• Wing area . Allthree are propor -tionalto wingarea.

• Reyn ol ds number (Rn). This reflectsboth speed and chord and is a measure of"scale effect."

• Angleof attack (AoA).In the u se-ful range of lift,from zeroliftto just before the stall, lift,profiledrag and pitching moment increase as the AoA increases.

• Wingchord(s). Pitch ing mom en t and Reynolds numb er are propor-tional to chord.

• Planform,i.e.,straigh t, tapered or elliptical. All impact lift, drag and pitching moment.

• Aspect rati o (AR). All three are affected by aspect ratio.

An(Reynolds Number) - -100,000 =~zoo,o o o - -Z50,000 Prollledrag coefficient (Coo)

-.2 -.4 -.6 1.6 1.4 1.2 1.0

it

.8

i

.6 U

=

.4 II 8.2 E

...

O

ne of the most importan t choices in mod el or full -scale airplane design is the selectio n of an airfoil. Thewing sec -tionchosenshould havecharacte ris-tics suited to theflight patternof the typeofmodelbeing designed.

There exist litera lly hundreds

of airfoil sections from which to choose.They are described in " air-foil plots" similar to EI97 (seeFigure

1).Selection of an airfoil demands a

reasonab le understanding of this data so that one can read, under -stand and use it to advantage.

Providing th is understanding is

the subjectofthis chap ter.Referring

to EI97,note that thedata is given

in terms of coefficien ts, except for the angle of attack. These co effi-cientsareCLfor lift,CDofor profile drag and

eM

for the pitching momen taround the 1/4-chord point. The actual lift, total drag and pitching moment of a wing depend on seven factors not directly related

toits airfoilsection.Theseare:

CHAPTER 1 A THE BASICS OF RIC MODEL AIRCRAFT DESIGN

1 1 0

WING DRAG COEFFICIENT I-z _0.8 w c:; ii: 0.6

....

_w Q '-' t: 0.4 :::; c:I _0.2 z 3

o

;?

1.0 5 10 15 20 25

WINGANGLE OF ATTACK-DEGREES AR = 18 AR=5 AR= 2.5 1.4 -::. 1.2 ~ I-Z _1.0 w c:; ii: _0.8

....

w Q '-' 0.6 t: :::; _0.4 c:I z 3 0.2 0 Figure 3.

How aspect ratio affects the stallangle ofattack.

Figure6.

How aspect ratio affects drag at a given lift. The vertical line, on the left,

pro-vides the C_L, positive above and negative below the horizontal line.

On the right of the vertical are the pitching moment coefficients, negative (or nose down) above, and positive (or nose up) below the horizontalline.

In the center are the three Rns covered by this plot, coded to iden -tify their respective curves.

.25.---- - - ---,

e

.20 u 1f.15 !z ~.10

....

~.05 i3

..

1 2 3 4 5 6 7 8 9 10 ASPECTRATIO FIgure 4.

Straight-wingcorrectionfactorfornon-elliptic lift distribution.

In the left-hand illustration, E197's chord line is straight and joins leading and trailingedges. The dotted, curved line is the "mean" or "camber" line, equidistant from both upper and lower surfaces.

The vertical line is graduatedide n-tically with the CLline on th e right. CL is positive above and negative below the horizontal line, which is itself graduated to providethe profile drag coefficientCoo'

Now, back to the curves in the right-hand illustration. The lift lines provide the C_L data on the E197 airfoil. Note that thissection

starts to lift at the negative AoA of minus 2 degrees and continues to lift to 16 degrees,for a total lift

spec-trum of 18 degrees.CLmax is 1.17.

These lift curves are section val-ues for "infiniteaspect ratios" and two-dimensional airflow. For wings of finite AR and three -dim en sio nal airflow, the slope of the lift curve decreases as shown in Figure 3.At these finite ARs, the AoA must be increased to obtain the same lift coefficient. These increases are called induced AoAs. Forexample, Figure 3 shows that if, with a wing of AR 5, you can achieve a C_Lof 1.2 with an AoA of 20 degrees, then with an AR of 9 you can achieve the same C_Lwith an AoA of 17 degrees.A higher AR wing will stall at a lower AoA.

In addition, the AoA must be increased to compensate for the fact that straight and tapered wings are not as efficient as the ideal elliptical wing planform. Figures 2 and 4 provide adjust-ment factors (T,or tau).

The pitching moment curves quantify the airfoil's nose-down tendency, increasing with i ncreas-ing AoA, but not linearly like thelift curves.

The curves in the left-hand illus -tration of Figure 1, called "polar curves," compare CL to Coo' Note

that E197 shows very little increase in profile drag despite increasing lift, except atthelowest Rn.

Again, these are section values. The profile drag values do not include induced drag, defined as

"the drag resulting from the pro-duction of lift" and which varies with AR as shown in Figure6.

Wing planform also affects induceddrag.As shown in Figures 2 and 4, the curves identified by 0, or

STALL 1.4 1.2- - .••~1 97

e

.

_. ,'- . ~-Rn 200,000

_..

: ,. it

"

... ./ '. E168

.

, " /

.

,

:

,

.

.

.

, I :2" +6 +10 +12+18

:

-.t

:

,

: .' ANGLE OF ATTACK E214 ... ,...4 (ALPHA)

.

.

:./ -.6 ,

".

,. I

,.'

iI . <1'..,.,' Figure5.

Lift curves of three airfoil types.Note that E168 lifts equally well inverted.

delta, provide the adjustment fac -tor to adjust induced drag to compensate for the wing's plan-form. The total wing Co is the sum of profile and induced drag coefficients.

___ Camber

(

~/7

;;

'

::

'

~

"

~

5

~

II

Heavily cambered

C?7??7

iii

Moderatelycambered-semisymmetrical

~

II

Symmetrical-nocamber Figure 7.

Broad types of airfoil sections.

l - I -Z Z

....

_z.o Rn =

....

.oz u_u:: u u::

...

_{~9.0 mill ion}

...

....

1.5

....

0 ...6.0 " 0 .01 u u Ii: ~3.0 " Cl ::;

~0

.

5

"

< z g; .01 0 0.1 " z ;::: 0 u

_t;

_.00

....

en

....

en -8-4 0 4 8 lZ 16 ZOZ4

A.SECTIONANGLEOFATTACK- DEGREES

-.5 0 .5 1.0 1.5

8.SECTIONLIFTCOEFFICIENT

Airfoil Selection ... CHAPTER 1

and higher profile drag.

The highest Rn in these plots is Rn250,000 .For a wing chordof 10 inches flying at sea level, this is equivalent to a speed of 3 2mph-ideal for sailplanes, but low for powered models,except at landing speeds. A lO-inch chord flying 90mph is at Rn700,000 atsealevel. Figure 8 indicates that both lift and drag improve at higher Rns, improving E197's good performance.

Figure 8.

Effects of Reynofds numberonsectioncharacteristics. In clarification, AoA isthe angle at

which the wing strikes the air (in flight) measuredfrom thechord line. Ang le of incidence is a drawing reference and is the angle of the win g's (or ho rizontal tail's) chord line relati ve to the aircraft's cen-terline or referen ce line.

AIRFOIL PLOT COMPARISONS There arethreebroad types of airfoil (as in Figure 7): heavily cambered (suchas E214), moderatelycambered (such as E197) and no camber, or sym metrical (such as EI68). Each typehasits own characteristics(see Figure 5). Greater camber increases C_Lmax, i.e.,moves the lift curve to the left so thattheangle of zero lift becomes increasingly negative, and the positive AoA of the stall is reduced.Note that symmetrical air-foils lift equally well upright or inverted.

STALL PATTERNS

There arethree major types of airfoil stall pattern,as in Figure 9:sharp, as for E168;sudden lift reduction; and the soft,gentlestall as for E197.

E168 has ano t he r airfoil quirk (see Append ix). At the stall, lift drops off but doesn 't return to fu ll value untilthe AoA isredu ced by a few degrees. This phenomenon is

r~"y

Sharp SuddenLin Gentle (E1 681 Loss (E197)

FigureS.

Types ofairfoilstall.

more pronounced at low Rn.This "hysteresis" is caused by separa -tion of the airflow on the wing's upper surface at the stall that does not re-attach until the AoA is reduced.Some airfoils have a more emphaticversion ofth is phe nome-non.

PITCHING MOMENT

Compare pitching momentsof air -foils E197,E168,E214 and E184in the appendix. The more heavily cambered the section is, the greater the negative pitch ing momen t.

The sym me trica lsection in E168 has virtually no pitch ing mom ent except at the stall, where it becomes violently negative.This is a stable reaction.The airfoil strives to lower its AoA.E168 would be an excellent pattern-shi p airfoil se lec-tion ; C_Lmax is good, and it'sthick eno ughforsturdywingstructures.

Airfoil E184 has a reflexed mean line toward its trailing edge. This acts like"up-elevator," reducing the pitching-moment coefficient, but also reducing C_L max. In airfoils, you don't get anythi ngfornothi ng. E184 is design ed for tailless mod -els-and not e thezero liftAoA shift to therightat low Rn.

DRAG AND

REYNOLDS NUMBER

The polar curves of airfoils E197, E168, E214 and E184 show the adverse reactio n, in both C_L and Co, to lower Rn an d to increasing AoA. Each airfoil has a different reaction-and this should be a seri-ous consideration for narrow wing-tips and small tail-surface chords, particu larly where, at low Rns, there's a reduction in the stall AoA

MISSION PROFILE

The final selection of an airfoil for your design depends on the design and on how youwant th e airfoil to perform, i.e.,its"mission profile."

For a sailplane, high lift, low drag and pitching moment at low Rns is the choice.For an aerobatic model, a symmetricalsection with low C_M and the capacity to ope r-ate both upright or inverted is desirable, along with a sha rp stall for spins and snap rolls and as high a C_L max as can be found. For a sport model, an airfoil like E197 is ideal. It has high CLmax, low drag and a moderate pitching moment.The stall is gentle. Note that the so-called "flat bottom" airfoils like the Clark Y(popular for sport models) are,in fact, mod -eratelycambered airfoils.

FORMULAS

Now forthose"d readed" formulas. Don't be alarmed; they're simple arith meticwithjust atou ch ofa lge-bra.Their solutions are easilyco m-puted on a hand calculatorthat has "square" and "square root" but -tons.

These formulas havebeen modi-fied for simplicity, and to reflect model airplane values of speed in mph,areas in squa re inches,chords in inches, pitching mome nts in inch/ounces and weight, lift and drag in ounces.

Fo rm ula 1:Reynolds num be r(Rn) Rn

=

speed (mph) xchord(in.) x K (K at sealevel is 780; at 5,000 feetis 690; and at 10,000feet is 610) Form u la 2: Aspe ct ratio (AR)

AR

=

span (in.)2 wingarea(sq.in.)

CHAPTER 1 .. THE BASICS OF RIC MODELAIRCRAFT DESIGN

Figure 10.

Method for locating themean aerodynamic chord (MAC).

B: Angle of attack (or incidence)

for level flight.CLrequireddivided

by CL per degree of angle of

attack.

Knowing wing area, weigh t and

cruising spee d, calculate the CL

needed asin Formula7.Divide th is

CL by CL per degree as above to

obt ain lift spectrum. Deduc t any negat ive AoAto zerolift.

wherein formulas6, 7,8,9 and 10:

C_L=liftcoefficien t(formula7);

CD= tot al drag coefficien t (fo

r-mula5);

V2=speed in mph squared; S

=

wing areain square inches;

C= mean aerody namicchord in inche s (seeFigure 10);

C_M

=

pitchi ng mo ment about the

%

MAC at the calculated C_L in

inc h/ounces;

o (sigma) = den sity of air (sea

level, 1.00; 5,000 feet, 0.861 6; 10,000 feet,0.7384).

SPECIAL PROCEDURES

A: Lift coefficient per degree of angle of attack adjusted for aspectratio and planform.

Referto Figure 1,Part 1E197.At CL

1.00 andAoA of 7degrees, plus the

2 degrees negati ve, a_ois9 degrees. ApplyForm ula4to obtai na.Divide

C_L 1.00 by a to obtain C_L per degree.

REFERENCES

Airfo ilDesignand Data. by Dr.RichardEppler, and Profilarenfurden Modellflug,by Dr.Dieter

Althaus,available fromSpringer-Verlag,New

Yorle Inc., P.O. Box 19386, Newarle, NJ

07195-9386.

Airfoils at Low Speeds(Soart ech #8), by Michael Selig, John Donovan and David Frasier. available from HA Stoleely, 1504 North Hor seshoe Cir., Virginia Beach, VA 23451.

Model Aircraft Dynamics, by Martin Simon, Zenith Booles, P.O. Box I/MN121, Osceola, WI54020.

C: Stall angleof attackadjusted for aspect ratio and plan.

Ad just the stallAoAforARand plan-form as in Formula 4. Dedu ct any negative AoA to zero lift to obtain positivevalue of stallAoA...

Sweep Angle

1;4MAC

Totaldrag

=

CDx a x V2xS 3519

Formula 10: Pitching moment

Pitching moment=CM xa x V2 xSx C

3519

Formula 6:Lift (or weight)

Lift (orweight)«CLx a x V2xS

3519

Formula 8:Model speed

Formula 9: Total profile and induced wing drag

v

= Ii x3519

a xC_LxS

Formula 7:Liftcoefficient required

C_L=liftx3519

axV2xS

"squa red";

AR=aspec t rat io;

I) (delta) = planform adjustment

factor(Figures2and4);

If you want to know the mod el's speedat a given C_Landweigh t: If you want to dete rm ine the lift

coefficien t needed for a given air

speed andweight:

COEFFICIENT CONVERSIONS

Up to this point, coefficien ts have

hadon ly abstract values. Toconvert these to meaningful figure s, we'll usethe sixvariables ment ion edpr e-viously in theseformulas.

1-

- I

C

C/2-

-1-

C-I

STRAIGHT

CIL--j-";'''''::<':'---i

I - I C

wherea = total of sectio n AoA and induced AoA;

a_o

=

sectionAoA from airfoilplot;

CL= lift coefficient at section

AoA from airfoil plot;

AR=aspect ratio;

T (ta u)

=

plan form ad just me n t

factors (Figures 2 and 4).

Form ula 5: Total of profile ( sec-tion)and induceddragcoefficien ts

a (alpha)«_{a o}+(18.24 xCJ x (1+1)

AR

Formula 3:Tape r ratio(A.-Iam bda)

Formula 4: To ta l of section and induced angle ofattack (AoA)

Taperratio = tip chord(in.) rootchord(in.)

where CD= tot al of profile and

induced dragcoefficients;

C_Do=section profile drag coeffi

-cient at CLchosen from airfoil plot ;

C_L2 _{= lift coefficient chosen} CD=C_Do+(0.3 18xC_L2) x(1+0)

AR

(A straight wing has a taper ratio of1.)

Mean aerodynamic ch ord (MAC) Figure 10 provides a graphic method for locating the MAC and

its lA-chord point. The MAC is

defined as "tha t cho rd rep resenta-tive of the wing as a who le and about which the lift, drag and pitching moment forces can be

consideredto act."

Chapter

·2

Figure1.

Characteristicsof NACA2412atvarious Reynoldsnumbers.

Figure2.

CharacteristicsofNACA 0012atvarious Reynoldsnumbers.

IJ':'-

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3l

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hJdJ~

'9 'fl~naldsNumEer.=t.J' y _c..._

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--,- .- - - -660.00 0

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001 -7 .- ..- --- 33ll000 o--·-~·l1a ooo

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,

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- --- - - -- - -- - --- -_A;rfo'~; N.A.C.AOO/ e

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Tes!:V-OT.IZj7-8

{k!~ul'~cor rec t ed 10infin/leQ~Ptlclrolio o

Airfoils

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j-. .0 .1 .0 <J

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In 193 7, NACA issued Report No.

586, whic h shows th e shocking

adverse impact of scale on airfoil characteristics (based on tests in a variable-density wind tunnel overa wide range of Rns, as shown in

Rn =Chord(in inches) x speed(in mph)x 780 (atsealevel). A full-scale airplane flying at 200mph with a wing chord of 5 feet

(60 inches) is operati ng at Rn 9,360,000. Ascale model flying at 60mph with a wing chord of 10

in che s flies at Rn 468,000. When landing at 25mph, the model's Rn isreduced to 195,000.

REYNOLDS NUMBERS

A most important consideration in airfoil selection is "scale effect."

The measure of scale effect is the

Rn. Itsformula is:

T

he selection of an airfoil section for most powered models is considered not to be critical by many modelers and kit designers.Models flyreasonably

well with anyold airfoil,and their high drag is beneficial in s

teepen-ing the glide for easier landings. Some years ago,there was a rumor that a well-known and respected Eastern model designer developed his airfoils with the aidof the sales ofhis size 12Florsheimshoes.

In con trast, the RIC soaring fr

a-ternity is very conscious of the

need for efficien t airfoils. Their models have on ly one power

so urce: gravity.The better the air-foil, the flatter the glide and the longer the glider maystay aloft.

This chapter is intended to

pro-vide readers with a practical, easy

understandingof airfoilch aracteris

-tics so that their selection will suit the type of performance they hope

to achieve from their designs. It doesnotgo into detailon such sub

-jects as laminar or turbulent flows,

turbulators, separation and

separa-tion bubbles, etc. (These are fully describedin Martin Simon's"Model

Aircraft Aerody nam ics" and S

elig-Donovan and Frasier's "Airfoils at Low Speeds"-see the source list at

th e end of this chapter.)

CHAPTER 2 .... THE BASICS OF RIC MODEL AIRCRAFTDESIGN

Figure 4.

Aerodynamiccharacteristics ofthe NACA641-412airfoil section,24-lnchchord.

reduced from 16 degrees to 11

degrees. Both lift and stall angles are higher than for NACA 0012.

Profile drag increases almost threefold at the lowest Rn.Owing to this airfoil's cambered mean line, the pitching moment is minus0.06 .

For NACA 6412 in Figure 3,the C_L max goes from 1.7 to 1.35 (79 per-cent).The stall angle is reduced from 16 degreesto12degrees.Profile drag doublesat thelowestRn.

It sh ould be noted, however,

that camber increase obviously

improvesC_Lmax and stall angle for this relativelythin(12 percent) sec

-tion at low Rns.

The pitching moment,due to its higher camber, is 0.135 negative.A

horizontal tail would need to pro-duce a heavy download to offset this pitching moment,resulting in an inc reased "trim drag."

In 1945,NACA issued Repor tNo.

824, "Sum mary of Airfoil Data";

it includes data on their "six-number" laminar-flow airfoils.

NACA64}"412 is typical(see Figure

4).The lowestRn is 3,000,000. These airfoils were developed

similarly to those in NACA Report

No. 460: a symme trical section wrapp ed around a cambered mean line.However,careful studyof pres-sure distribution allowed this type

of airfoil to obtain a very low

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moment, except beyond the stall where it's negative (nose down)and stabilizing.

NACA 2412 in Figure 1 isa pop

-ular spo rt-model airfoil. Com pared with NACA 0012, the maximum

lift coefficient isslightly high er at 1.6 at the highest Rn.At the lowest

Rn, with the turbulence factor

accounted for (4 1,500 x 2.64 ,

which equals109,560), the C_Lmax drops to 0.95, or 59 percentof th at of the highest Rn. Thestallangle is

- .. -

-t

-.3- _ - Ai rfo d:NACA.641a

• _ . Date:8-34 Tes/:V.O.T.ff65

~-.J _~$COrrec'~d'0 "'inileoSP Kf ratio -. 4 -.2 0 .2 .4 .6 .8 /0 l2 1.4 /.6 18

Lif! coe"jc ienI,C.

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~-.I

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".2 - - .-- ..- _.

·8 -4 0 4 8 /2 16 eo 24 28 .32

An9/~of olJoch(o r infin"'~o~pee.lrono.ct,(d~qrt!t!$)

Figure 3.

Characteristicsof NACA6412at variousReynolds numbers.

Figures I, 2 and 3). Note that the Rns shown are "test" results and requirecorrection for a"turbulence

factor"that wasn 't recognized dur-ing the tests. This factor is 2.64.

Each Rn in Figures 1, 2 and 3 should beincreasedbythisfactor.

The airfoilsinvolved in these fig-ures are "related sections." NACA 0012 is symmetrical ; NACA 2412 was develop ed by "wrapping" the

symmetrical section around a cam-bered mean line so that the upper

and lower sur faces were eq uidistan t from the cambe r line. For NACA

2412,this mean line has a camber height of 2 percent of the cho rd length,with itshighest point at 40 percent.

NACA0012 in Figure 2 shows a

shocking reduction in maximum

lift coefficient from 1.55 for the

highest Rn to 0.83 for the lowe

st-a difference of 54 percent of the

highervalue.

Similarly,the stall AoAissharply

reduced from 17 degrees for the highest Rn to 10 degrees for the

lowest. One very interesting ph

e-nomenon is this airfoil's beha vior beyond the stall at thelowerRns.It

continues to lift up to 28 degreesat almost full value.

Profile drag at low Rns is almost

double that at highRnsandincreases very significantly at the stall and beyond-not surprisin g, conside r-ing the post-stall lift behavior.

NACA0012 has a zero pitching

UnderstandingAirfo ils .. CHAPTER 2 Chordline

c===-=---=-E197

C

=====-E168 C

===-E226

c:=

==---=-E374

c=

====--E214

C

---E230

C

==-=-E211 Figure6. Eppler airfoils. THICKNESS

Thicker wings permit strong but light construction. They may also exact a small penalty in drag increase.Tapered wings with th ick root airfoils that taper to thinner, but related, tip airfoils, are strong, light and efficient. Laying out the intervening airfoils between root and tip calls for much calculation-or computer assistance.

For high speed, an airfoil such as E226 shown in Figure 6 is sug-gested. Drag and pitching moments are low, as is the C_L max, and the airfoil performs almost as well inverted as it does upright. E374 would also be a good high-speed airfoil section.

The authorhas had success withthe E197 for sport models.Ithas low pro-file drag, good lift and a gentle stall, but a fairly high pitching moment.

The E168 is suitable for strong hor

-izontalor vertical tail surfaces,or for wings of aerobatic models.Itperforms as well upright as it does inverted. trailing edge.This produces a posi-tive (nose-up) pitching moment. This airfoil would be suitable for a tailless or delta-wing model. Inevitably, C_L max is adversely affected.

MEAN LINE CAMBER

A symmetricalairfoil has thelowest C_L max and stall angle. An airfoil with increased camber produces a higher maximum C_L,but it starts to lift at higher negative angles of attack with a broader range of lift before stalling. Increased camber, however, produces increased pitch-ing moments.

Out of curiosity, the camber mean line for the E197 airfoil was straightened out and the envelope was redrawn as in Figure 5. The result was a symmetrical airfoil resembling the E168.

Some cambered airfoils have a lower surface trailing-edge "CUSp" created by a localized and increased curvature in the camber mean line, as in the E214, Figure 6. The cusp increases both C_Lmax and pitching moment; it's called "aft loading.II

E197 in Figure 6 has a slight cusp; airfoils E207 and E209 are similar to E197, but they lack the trailing

-edge cusp (reference 12). Airfoil E230 in Figure 6 has an upwardly reflexed camber mean line near its

100mph is operating at Rn

780,000.

The selection of an airfoil for a design should start with a review of airfoil plotsof the type in this chap-ter. In this author's experience, the plots of the University of Stuttgart published by Dieter Althaus are the clearest and most comprehensive. The airfoils developed by Dr. Richard Eppler are favored.

Straight meanline

(

E __

~

Figure5.

The cambered mean line of E197 (top)was straightenedoutandthe enveloperedrawn,resulting

inasymmetrical airfoil(boNom).

Cambered meanline

s~

profile drag (over a limited range of lower lift coefficients). The P-51 Mustang WW II fighter employed airfoils of this type. The "low drag bucket" at C_L0.4 shown in Figure 4 shows this drag reduction.

In 1949, NACA issued Technical Note 1945. This compared 15 NACA airfoil sections at Rns from 9,000,000 (9 x 106) to 700,000 (0.7X106)

The C_Lmax of NACA 64_1-412at

Rn 9 x 106 _{is 1.67, but it drops to}

1.18 (70 percent ofthe highestRn ) at Rn 0.7 x 106_{. Profile drag}

increases from 0.0045 to 0.0072 for the same Rn range, and the stall angleis 16 degrees, but it drops to 12 degrees at the low Rn. Pitching-moment coefficient is 0.063.

This report concluded that at low

Rns, the laminar-flow section did not offer substantial advantages over those in Report No. 460 and Report No. 610.NASA(NACA's suc-cessor) continued to do research into laminar-flow airfoils with much success; but at the high Rns of full-scale airfoils and aided by computer analysis.

The worldwide RIC soaring fra-ternity, however, has done much

wind-tunneltesting and computer

design of airfoils for model gliders (referen ces 10 to 15 inclusive). Though the Rn range of these tests seldom exceeds Rn 300,000, any airfoil that offers good perfor-mance at this low Rn can only improve at the higher Rns of pow-ered flight. A lO-inch-chord at

CHAPTER 2 .... THEBASICS OFRIC MODEL AIRC RAFT DESIGN

PITCHING MOMENT

The airfoil's pitching moment is

impo rtan t both st ruc tur ally an d aerodynamically. In flight -partic-ularly in maneuvers-the pitch ing moment triesto twistthewing in a

leadi ng-edge-down direction . This adds to the torsional stress placed

on the wing st ruc t ure by the

ailerons and ext ended flaps.

High-pitching-mo men t airfoils require

win gsth at are stiff in torsion, an d that favorsthickersectionsand full wing skins,particul arly for high-AR

wings.

Aerodynamically, the nose-down pitchin g momen t requ ires a hori-zontal tail downl oad for eq

uilib-rium.This adds to the lift thewing

must produce an d increases total

drag- called "t rim drag." The

pitchi n g moment is litt le affected

by variations in theRn.

STALL BEHAVIOR

One reason for preferring

wind-tun nel test data over com puter

-AIRFOil

CONSTRUCnON

Most poweredmodel aircraftoperatein anRn range from200,000towellover 1,000,000.Thisis above the critical rangeof Rnsat which turbulatorsare consideredto be effective.

Forthemore recently developeda ir-foils,there is a considerabledegree of laminar flowthat significantlyreduces their profile drag.This flowis easily upset byprotuberances on thewing's surfaces.

Forsmooth surfaces,fullwing sh eet-ing is suggested,with a film ov erlay-either overa foam-coreor built-upcon

-struction- thatwill promote the most

laminarflow andalsoresultin aw ing-stiffin torsion (see Chapter13,"Stressed SkinDesign").

Therearelarge modelswhosewings have multiple sparson both top and bot -tomsurfacesandarecoveredonlyin

plastic film.

Becauseitshrinks onapplication,the film tendsto flatten betweeneachrib

andeach spar.As a result. multiple ridges runboth chordwiseands pan-wise. renderinglaminarflow impossible.

Contrastthiswiththe verysmooth

surfaces of high-performanceRIC

soaring gliders.

12 THE BASICS OF RIC MODEL AIRCRAFT DESIGN

developed perfor ma nce curves is

that the former provides an a ccu-rat e "picture" ofthe airfoil'sbe

hav-ior at the sta lland beyond.

In general,there are th ree broad

typesof sta ll(asshown in Figure 9 of Cha pter 1, "Airfoil Select ion"):

sh arp;sudde nliftdrop; an dgentle.

For sport mod els, a gen tle sta llis

desira ble. Sha rp sta lls an d those

with a sudde n lift drop are appro

-priate for man euvers in whic h the

abili ty to stall a wing easily is

required, such as spins.

ZERO LIFT ANGLE

The angle of zero lift for a sy

m-metrical -secti on airfo il is zero

degrees AoA.Cam be redairfoil

sec-tio n s su ch as E21 4 shown in

Figure 6 sta rt to lift at almost 6

degrees negati ve AoA, butfor this

airfo il, that angle isunaffect ed by

variations in the Rn.

Con trast th is with airfoil E211.

This airfoil's angle of zero lift movesclo ser to zero degrees at th e

lowe r Rns.

The forward wing of a can ard

must sta ll befor ethe aft wing; but,

for longitudin al stability, the aft

wing mustreachits airfoil's zero-lift

ang le befor ethefron t wing'sairfoil.

If the for epl an e's airfoil reach es

zero lift first,a violen t diveresults

and, becau se the aft wing is still

lifting,acrash is almost in evit abl e.

The low-Rnbeh avior of th e E211

mean s that,at low speeds-or n

ar-row cho rds- t hisairfoil may reach

zero lift more readily. Its use as a

forward-wing airfoil on a cana rd is

to be avoided. Airfoil E214 is more suitable.

MAXIMUM LIFT COEFFICIENT

From zero lift, high er camber

results in a higher C_L max and

higher sta lli ng angles. This

impacts the model's takeo ff, sta ll

an d landing spee ds. A high CL

max permits slower flight in all three point s; a lo wer C_L max

reverses these con d itio ns .

SUMMARY

In aerodynam ics,nothing is free. In

gene ral, high lift mean s increased

drag an d pitching moments; for

high speeds,C_Lmax isredu ced and so on . The type of performa nce

sough t for a design dictates whic h

airfo il ch arac te ristics are sig

nifi-can t. Having selected these, any

adverse characteris tics must be

accepted and compensa ted for...

NACA AND NASA DATA

1. Report 460*: The characteristicsof 78

Related Airfoil Sections from Tests in the

Variable DensityWindTunnel;1933;Jacobs,

Ward and Pinkerton.

2.Report586 *:AirfoilSectionCharacteristics

asAff ected by Variations of the Reynolds

Number; 1937;Jacobs and Sherman.

3. Report 610*: Tests of Related Forward CamberAirfoilsinthe Variable-DensityWind

Tunnel; 1937; Jacobs, Pinkerton and

Greenberg.

4.Report 628*:AerodynamicCharacteristi cs

of a LargeNumber ofAirfoilsTestedinthe

Variabl e-Density Wind Tunnel; 1938;

Pinkerton andGreenberg.

5. Report 824*: Summaryof Airfoil Data; 1945; Abbott,von Doenhoffand Stivers.

6. Technical Note 194 5*: Aerodynamic

Characteristicsof 15 NACA AirfoilSectionsat

SevenReynoldsNumbers from0.7x 106 to

9.0x106;1949;LoftinandSmith .

7. Technical Note NASA TN 7428*: Low -Speed Aerodynamic Characteristicsof a 17 percent Thick Airfoil Designed for General AviationApplications;1973;McGhee,et.al. 8. NASA Technical Memorandum TM X 72697*:LowSpeedAerodynamiccharacter

is-tics of a 13-percent Thick Airfo il Section; 1977;McGhee,et.al.

9.NASA TechnicalPaper 1865*:Designand Experimental Results for a Flapped Natural

Laminar-Flow Airfoil for General Aviation

Applications;198 1; Somers.

10.Profilpolaren fOr den 1900Ellflug,Book1;

1980; Dieter Althus, Neckar-Verlag,

Klosterring#I,7730Villingen-Schwenningen, Germany.

11.Profilpolarenfur den 1900 Ellflug,Book2;

1986; Diet er Althus, Neckar-Verlag,

Klosterring#I,7730 Villingen-Schwenningen,

Germany.

12. Eppler Profile MTB 12; 1986; Martin

Hepperle.VerlagfUr Technikund Handwerk GMBH. Postfach 1128,7570Baden-Baden,

Germany.

13. Model Aircraft Aerodynamics, Second

Edition;1987; MartinSimons.

14.AirfoilsatLowSpeeds-Soartech8;1989;

Selig-Donovan and Fraser, Zenith Aviatio n

Books.P.O.Box I, Osceola,WI 54020.

15. AirfoilDesign and Data;1980;Dr.Richard

Eppler,SpringerVerlag,New York, NY.

'Available from U.s. Departmen t of

Commerce, National Technical Inform a-tion Service, 5285 Por t Royal Rd.,

Chapter

·3

T

h is book reflects a deep and lifelong interest in aviation;

a close study of the vast

amo unt of timeless aerodynamic research dat a, both full-scale and mod el, tha t isreadil yavailab le.

This, cou pled with the practica l

application of this data to the design, construction and flyingof a wide variety of model airplanes,

reflects those many years of study and experien ce.

(Th ese models perform well,and photos and 3-view drawings of them are incorporated into this book and are compiled in Chapter

26, "Con st ruction Designs.")

Layma n's language is used, but

inevitably some aerodyna mic jar-gon and symbols have to be in

tro-duced.The many charts,curves and

formulas may be intimidating to those readers who are not familiar with the use of the mass of infor

-mation they contain. Once actual numbersreplace symbolsin the for

-mulas, only plain, old, p

ublic-school arithmeti c is need ed . A

pocket calculatorwith "square"and

"sq uare-roo t" buttons simpli fies

the work.

The problem seem s to be "ho w and from where to obtainthe

num-bers." This chapter is designed to

answer this.The various figures are marked to illustr ate the sources of those numbers, and the speci fica-tions of an imagin ary model ai r-plane are used as sam ples.

The most import antformulas deal with lift,dragand pitching mom ent.

LIFT

The airfoil plot of Eppler E197 (see

Figure 1) showsthisairfoil's behavior

for "infinite AR,"i.e.,no wingtips.

Airplane wings, even very high-AR glider wings, have "finite" ARs and do havewingtips. Lift is lost at thosetips; the wider the tip cho rd, thegreater theloss.

The wing's AoA must be

increased (in duced AoA) to obtain the C_L needed as AR decreases.

Understanding

Aerodynamic

Formulas

Induceddrag incre asesat low ARs.

Airfoil plot smustbeadjusted to:

• reflectthe ARofyour wings; and • reflect the wing 's

planform-st raigh t (co n stan t chord) or tapered .

An elliptica l wing planform needs onlythe ad justme n t for AR.

The formula for both AR and plan form ad justments is:

a=a_o+ 18.24xCL x(1.+T)

A

R

a= 9°+ 18.24x1.00x1.17= 12.5°

6

where a =tot alAoA(AoA) needed;

aD

=

"sectio n" or airfoilplotAoA;

C_L

=

C_Lat thatAoA; AR

=

aspect ratio;

T

=

Plan for m ad justmen t factor.

Had the wing been tapered with a taper ratio of 0.6 (tip chord 7.5

inches divided by root chord 12.5

inch es, or 0.6), the planform

Referto Figure 2.E197 produces lift

of CL 1.00 at 9 degrees AoA, from

zerolift,forinfi n iteAR.

A constant-chord wing of AR6 has an adjustment factor T of0.17

(see Figure 4of Chapter 1).

Replace the symbols with these

numbers: Cl

c

L CM 1.6 RE 1.6 -.4

C

_==--==-

100000 _Lift + 200000 1.4 -.35 _C LYS.AoA 1.4 X 250000

/

CLmax1.17 1.2 .8 Profile drag YS.11ft .8 COYS.CL .6 .4 ~ .2 Pitchingmoment 0 C_MYSAoA -.2 .12 .14 6 10 14 18 -.4 Co Angle01attack -.4 .1 (AoA) -.6 E197(13.42"/0) -.6 .15 Figure1.

Eppler E197 airfoilplot.

CHAPTER 3 .... THE BASICS OFRIC MODELAIRCRAFTDESIGN

Figure 2.

Eppler airfoilE197 produces lilt of CL1.00at9degrees AoA,from zero lilt,for infiniteAR.

ofbothwin g and tail airfoilsset at zero degrees rela tive to thei r fuse -lage centerli nes. A sym metrical airfoil at zero degrees AoAwill pro -duce no lift.

What happen s is that, to take off,the pilot commands up-el

eva-tor, th us adjusti ng the wing to a

posit ive AoA, and it lifts. The lift

produ ces down wash that st rikes thehori zontaltail at a negative(or downward)angle caus ing a dow n-loadon thetailthat main tains the wing at a positive, lifting AoA. In bot h uprigh t and inverte d flight,

the fuse lage isincli ne d nose up at

a sma ll ang le, an d with some adde d drag.

SOLUTION No.

:z

Thismethod ismore accu rate and

invo lves one of the "d rea de d"

form ulas,asfollows:

CLof1.00af 9· from zero "" CL01 0.111per degree 1.6 -.4 HE

===---

100000 CL 1.4 -.3 CM + 200000 X 250000 _1.2 .25

c

.6 .8 .4 .2 .04 .06 .08 .1 .12 .14 -14 14 -.2 _{Co AoA}

'.4 Foraspect ratio6-constant chord

1

/

.1 CL011.00at 12.5 Irom zeroIi"

-.6 -.6 .15 E197 (13.42%)

_c..

_{of.08 degree} 1.6 1.4 CL 1.2

ad just mentfactorwould be0.0675,

reflecting the lower tip lift losses from the narrower tip chord.

A C_L of 1.00 for 12.5 degrees is 1.00 divided by 12.5, or 0.08 per degree. Th is is the"slope"of the lift curve at AR6 and cons tant chord.

Our exam ple mod el design has

the following specificatio ns: • Estima ted gross weigh t of 90 ounces;

• Wing area of 600 square inch es (4.17 squa refeet);

• Wing chordof 10 inch es;

• Spa nof 60inc hes;

• Estimated cruising speed of 50

mph; and

• Wing loading of 90 divided by

4.17, or21.6ouncesper squa refoot.

The three-surface"Wild Goose"was designedto theaerodynamic andstructural principlesin thisbook;specificallythose describedin Chapter 22, "Canard,Tandem Wing andThree-SurfaceDesign."It'san excellent flier.

The reare twosolutions tothed

eter-mination of the wing's AoAto s up-port the plane in level flight at th e estimated cruisingspeed.

SOLUTION No.1

Refer to Figu re 3. Ata wing loading of 21.6 ouncesper square foot and at a speed of 50m ph, the wing

needs a CLof closeto 0.20.

Our wing develops a C_L of 0.08 per degree AoA. ToproduceC_L0.20

would require an AoA of 0.20

dividedby 0.08,or 2.5degreesfrom

zero lift,which for E197isminus2

degrees.

The wing would thus be set at

(2.5 minus 2) or0.5 degree Ao A-and at0.5degreeangle ofincidence

to the fuselage cen terline on your

drawings.

Note that a symmetrical airfoil's angleof zerolift iszero degrees AoA.

If our wing used a symme trical

sec-tion,its AoAwould be 25degrees,as would itsangle ofinciden ce.

This is the "rigging" for a sport

model, using a cambered airfo il such as E197, i.e., 0.5 degree AoA. Mostpattern ships usesymmetrical

wing and horizont al tail airfoils;

such airfoils have no pitching

mom ent and perform aswell in vert-ed as they do upright, but with

lowermaximum liftcoefficients(CL max) compared with cam bered a

ir-foil sections. (See Cha pter 2, "Unde rstand ingAirfoils.")

These agile mode lshave chords

Lift

=

C_Lx a x V2x5 3519

Because we wan t to obtain the C_L needed,th isformulaismodif iedto:

C_L= Liftx 3519 a xV2 xS where CL

=

CLneeded; 100 1JY 95 V-

'>

90I - -f - -_coeffWing_icientsliff

~ 11~/ 85 / V 80 75 _II I~ / 70

/

V

65 _V I~n. / :I: 60

/

V

...

/ . / :IE 55 / / /

V

4JlV c 50 1/

_/

_/ V 5.~V

...

_./

...

₄₅

...

I / V V V _I~V

'"

₄₀ 1 / _V / V V V-

t!J

V 35 I I / /

_""

_V

_~v 30

V-I/V,

_~

_.>

V ,../... ~ I-(2225 l.--mph}20 V/, /...-: 1.17 ,../V ~~ I-(1615 '/'/'" 1:80

--

l::=

I -

...

mph)10 ~

::::::

::::::: -;::;--5 4 8 12 16 2

o

24 28 32 36 40 44 4 (21.6) WING LOADING Figure 3.

Nomographfor quickdeterminationof wing loading,lilt andspeedatsea level.

UnderstandingAerodynamicFormulas • CHAPTERJ CL _1.6 RE 1.6 -.4 _{C Stall C} Lmax

C

~ 100000 CL -.35

M

~

1.4 _{+ 200000} 1.4 Stall climax _{X 250000 C} L1.17 1.2 1.2 -.3 1.17 .8 .8

Pitchingmomentat

.6 0.5AoA ot0.060 .4 Profile drag atC_L 0.20 010.013 .2 .12 .14 _{10 14 18} -.2 Co

-.4 Profiledrag atCL .1 AoA

max011.17010.015

-.6 -.6 .15

E197(13.42%)

Figure 5.

Profile dragandpitchingmoments. A modeler living in Denver,CO,at

5,000 feetabove sea level would use a0 of 0.8616.

For our model, at sea level, this

would be C_L=(90 x 3519)divided

by(1.00 x 502 x 600),or 0.211.

Our sample wing has a C_Lof 0.08 per degree. The wing's AoA would be 0.211 divided by 0.08, or 2.64 degrees, less the E197's 2-degree negativeto zero lift,or 0.64 degree,

rounded out to the nearest 1;4

degree, or 0.75degree.

Lift

=

model's gross weight in ounces;

V2 _{= estimated cru ise speed in} mph "squared";

S=wing area in square inches;

o = density ratio of air (at sea level, it's 1.00; at 5,000 feet, it's

0.8616; and at 10,000 feet, it's

0.7384).

oursample model had slotted flaps that,when extended,increased the

wing's C_L max to 1.80, the stall

speed would decrease to 16mph from the unflapped 22mph, or becom e27 percent slower.

STALLING ANGLES

In Figure4,at infiniteAR,the E197

stallsverygen tly at about plus 11.5 degrees, or 13.5 degrees from zero lift.For our wing of AR 6 and con-stant chord,thiswould be:

a = 13.5 + (18.24 x 1.17 x 1.17 dividedby6),or 17.5degrees from

zero lift, or 15.5 degrees AoA at altitude.

For landing, however, this stall angleis greatlymodified by:

• _{At constant CL},changes in wing loading are reflected in the speed needed for level flight, and vice

versa.

• Ground effect. As shown in

Figure 6, at 0.15 of the Wingspan

(60 x 0.15, or 9 inches) above ground,thestall angleis reduced to 0.91of itsvalue at altitude,or to 14 degrees.

• The level flight wing AoA. Because thewing is at 0.5degree, it willstall at13.5 degreeshigher AoA. 18

Stalls 1.6 -.4

CL CM

1.4 -.35

good con trol,would be 26.4m ph .

Th is nomograph is most useful

in the early stages of a mode l's design . Forexample:

• At constant speed,it show sthe effect of cha ngesin wing loading,

i.e., wing area and/or weight, on the CL needed for level fligh t. As

wing loading in creases, so must

the _CL.

• At constant wing loading, it dis-plays the effect of the C_Lon speed

(or vice versa). For illustrati on, if

RE 100000 + 200000 X 250000 .12. .14 Stall at inliniteAR---'"'1-~--..., Stallat AR6-constantchord-~Lk~~:i::::~

E197(13.42%) 1.6 1.4

C

1.2 .8 .6 CL .4 .2 0 -.2 -.4 -.6 FIGURE J

This nomograph is one of the most

useful charts in this author's "bag of tricks."It compares three impor-tant factors: speed (m ph), wing loading (oz./sq. ft) and wing _CL.It reflects the impact of changes in these factors.

For example, our paper design has a wing loading of 21.6 ounces per square foot of wing area; the

wing has airfoil E197,which has a

C_Lmax of 1.17. Using Figure3, its

stall speed is 22mph. Adding 20 percent, its landing speed, under

Figure 4.

The stalling angles of Eppler airfoilE197.

• High-lift devices. As Figure 7

shows, slotted flaps extended 40 degrees would cause a further

CHAPTER:I ... THE BASICS OF RIC MODEL AIRCRAFTDESIGN .c;

..

~ <:

-...

<:

=

2

...

•

.25Cand.30Cslonedflaps

I - withleading-edgeslot

!

--

~ Plain split flaps / ' Sioned flap ~

---<,

-

-

-r-_

'"

..

<:

...

u

'"

:;; '0

..

e;, <: < 1. 10

-

l.--::::==:

E::::=:

r::::::::

I

1. 0 -

;;:::::

V--

V i-1--8~ -::::::"" 0.9

-~ 1-- 6 _V

-

~ _...

i-4~

V

....-

_{, /}

v

<, V

' " Wingaspect rallo 0.8 / 0.7 0.05 0.1 0.2 0.3 0.4 0.5 12 10 zen

_

...

8 ... encc ~ffi ccQ u l ₄ z"" ;;;u Q~ z< !:!... 0 1 - 0 u ... ::::> .... Qc:l "'z cc< -4

o

10 20 30 40 50 60

Heightot wing from ground

Wingspan

Figure 6.

Impact of ground effect onangfe of attack.

FLAP DEFLECTION ANGLE- DEGREES(@Rn 250,000)

Figure 7.

The effect onflaps andLEslotsontheangte of attack at maximum lift.

1 + - - - . 2 3 C

- - - . t

reduction of 4 degrees to 9.5 degrees stall angle. Had the slotted

slaps been combine d with fixed

leading-edge (LE) slots,there would

be a gain of 9 degrees, to 22.5 degrees stall angle.

The model'slanding stall angle has a major impact on landing-gear design. (Chapter 16, "Landing Gear

Design,"goesinto this in detail.)

Figure 8 shows the geometry of a fixed LE slot. Note how the slot

tapers from the lower entry to the upper exit.

Figure 9 displays the benefits of an LE slot in added CLand additional effective anglesof attack before the

stall.Dragislittle affected.

Figure 10 shows the additional

CL to be obtained from various types of flap alone,or in

combina-tion with LE slots.

Slotted flaps and fixed LE slots

com bine to mor e than dou ble the

CLof mostairfoilsections, produc-ing STOL performa nce .

For example,our E197 CLmax is 1.17. Equipped with deployed 30-percent-chord slotted flaps with extended lip and LE slots, both

full-spa n, the Wing's CLmax would

be 1.17plu s1.25, or 2.42.

Our sam ple model so equipped

would stall (Figure 7) at 14mph.

Figure 11 shows the added profile Co to be added to the section's pro-fileCD' when calculating the total of both profile and induced drags, discussedunder "drag," as follows. DRAG

The drag coefficients shown in Figures 5 and 11 are profile drag

only.The CLmax profile drag of the un flapped E197 is 0.015 (Figure 5) and for full-span slotted flap s would be an additional 0.121

(Figure 11), for a total of 0.136 in profile drag. Induced drag is not included. Note the very small increase in E197's profile drag for C_L0.20to C_Lmax 1.17.

The formula for calculation of

total wing drag is:

CD=CDo+0.318XCL2x (1+0)

AR

where CD= total of both profile and induced drags;

Coo

=

section profile drag coefficien tat thechosenwing C_L;

C_L2 _{= wing lift coefficient}

"squared";

AR=aspect ratio;

o

=

planform drag adjustment factors.

S l a t - - + - -...

.0185C

R.23C

Figure 8.

Geometry of thefixed leading-edge slot.

16 THE BASICSOF RIC MODELAIRCRAFTDESIGN

Our model's wing has a Coo of 0.013 at CL 0.20 (Figure 5) and a drag planform adjustment of 0.05

(see Figure 4 of Chapter 1).

Replacing symbols with numbers for the plain wing:

CD

=

0.013 + 0.318x0.22_x1.05

6 or 0.01523.

If our sample wing had full-span

slotted flaps that extended 40 degrees and thatwere 30 percent of

the wing chord, the total CD' at a C_L max totaling (1.17 + 1.05), or

Understanding Aerodynamic Formulas A CHAPTER 3 1.8 .36 I I ".. slOlledlWlngl- - - l / _\ / I \ 1.6

/

I \ .32 1I1llncrease / I

,

.:

_V

,

1.4

/

I .28

/

< ,

v:

1.2

//

/ I .24

"

/ 1I

//

L

1.0 '7'"1 I .20 Plainwing ~

t

_{V I} f! " u .8 L

j

.16 u

t:

I t:l ::; I I <_a:

....

rl

Q Q / I

....

...

_.6 I .12 Q z

/

V/

...

....

zs

z

_....

iI: I I

-/

c::;

....

Rn@609,000 iI:

....

0 _{.4 .08}

....

u

/

V'"

....

/

/ _CD 0 u ~/

_"..

_:;;

V _ADAIncrease .2

L

_p

:::..---- .04 0 0 .4 0 4 8 12 16 20 2 ANGLEOFArrACK-DEGREES (Rn 600,000) .30Cslolled flap withextended

lip and lead

ing-edge slot 1.80 ~ 1.60 ~

...

15 1.40 ~1mI1+---T~ 11l 1.20 ~m:J

....

- _"--,.,p;..- -=l ~ 1.00

~

:E .80 => :E

i

.60 ~ o ~ .40 !!1 ~ .20

TheWildGooseshown withslotted flaps on bothfrontandmain wings extended for slow,stable landings.

6 FLAP DEFlECTlON-llEGREES(@R250.000) Note th at a tapered wing's root

chord always flies at a highe r Rn than its tip chord at any speed, owing to th e narrower tips (whic h can bepron etotip-stalls as aresult). Fu ll-sca le airfo il research data may be used for model airplane

wing design-with carefu l regard

forth e majoreffect of scale on

par-ticularly lift,drag an d stall angles.

Figure 10.

Increments of maximumlift due toflapsand leading-edge slots.

o

r---"""T"-..,...~-+-~--I

PITCHING MOMENTS

These have noth in g to do with baseball! Allcamberedairfoilshave

nose-down, or negative, pitch ing mom ent s.Symmetricalairfoilshave

no pitchingmoments,exceptat the stall. Reflexed airfoils mayhavelow

nose-down or low nose-up pitch ing moments.

Nose-down pitc hi ng moments

must be offset by a horizontal tail do wnl o ad that is achieved by

havin g that tail'sAoA set ata neg

-ative ang leto the down wash from

the wing.(Ch a pter 8,"Hor izon tal

Tail In cid en ce and Downwas h

Esti ma ting," goes in to det ail.)

Rn

=

speed(mph)x chord(in.) x K K at sea level is 780; at 5,000 feet, it's690 ;and at 10,000 feet,it's 610. Our samp le model's wing chord is 10in ches, and atalan d in gspeed of 26.4m p h an d atsea level,itsRn wouldbe 26.4 x 10 x 780, or 205,920. In Denve r, th e Rn wou ld be 26.4 x 10 x 690,or 182,160.

A quickersolution at sea level is

given in Figure 12. Layin g a straightedge from "speed" left to "ch ord" right, Rn is read from the

cen te rcolum n .

(Note: in Figure2 ofCh apter I,the lower drag correction factor 0 for

the tapered wing ,of taper ratio 0.6,

is 0.02 compared to that for a

constan t-chordwingof 0.05.)

SCALE EFFECT

Scale effect is measur ed by Rn. In E197, lift and pitching moments

are little affected by the reduction

in Rn from 250,000to 100,000,but profiledragincreases substa n tially.

The form u lafor Rn is sim ple: Figure 9.

The benefits of thefixedleading-edge slot.

Repl acin g the symbo ls with num-bersforthe plain wing at50m ph: Drag (oz.)=0.410 x 1x 142_X600 3519 Drag(oz.)=0.01523x 1 x 502x 600 3519 (Figures 5 an d 11) Drag (oz.)=CDx a x V2_{x S} 3519 2.22(Figure 10),would be:

CD=(0.15+.121)+0.318x2.222x1.05

or 13.7 ounces.

or6.5 ounces.

An d for the full-span, slotte d-flap versio n at a sta lli ng speed of 14mph, 30-percen t-cho rd flaps at 40 degrees:

or 0.410.

The formulafor total wing drag is:

CHAPTER 3 ... THE BASICS OF RIC MODELAIRCRAFTDESIGN .28 Q Q ~ .24 w u u::: _.20

....

w Q yf Q <.> .16 C> V ~

~

c ~ .12 u:::

~~~

iit"

nd

1---:;

z-:

0 a: "-.08 BO~ z

0

0 t-SIOfl flaps

e

_~ w .04 en .... 0 en ... z w 0 10 20 30 40 50 60 ::E w a: <.>

iii!: _{FLAPDEFLECTIDN-DEGREES(@R250,000)}

Figure 11.

Increments of profiledrag coefficient atCL

max or increasingflapdeflections.

As Figure 5 shows, the E197air

-foil h_{as a negative CM of 0.060 at}

anAoAof 0.5degree.NotethatCM,

like

c.,

varieswith theAoA.

Also,t_{he CMapplies to the wi}ng's

V

4

MAC; on ourstraight wing of 10

inch es chord,ata point 2.5 inches

from its leadi ng edge.

The pitching moment formula is:

SPEED·MPH REYNOLDS CHORD·

NUM8ER INCHES 180 3₃400 000_,DOd,ooo 24₂₃ 160 2,5000,000 22 140 ₂₁ 120 2,000,000 20 100 1,5000,000 19 18 90 ₁₇ 80 1,000,000 ₁₆ 70 800,000 15 60 600,000 14 50 500,000 13 40 400,000 12 300,000 11 30 10

III

150,000 9 20 100,000 8 15 80,000 7 60,000 50,000 10 40,000 6 32,000 5 Figure12.

Nomograph for quickdeterminationof Reynolds numbers.

18 THEBASICSOF RIC MODEL AIRCRAFTDESIGN

PMillill-OZ. = C_Mx a x V2 x 5 xC

3519

where _CM

=

airfoil

pitching-moment coefficient at the AoA of

level flight;

V2 _{= speed in level flight}

"squared";

S

=

wing area in squareinches;

C

=

chordin inches;

a

=

density ratio of air.

Our sample Wing'snose-down PM is:

PM=0.060x1x 502 x 600 x 10

3519

or 255.75in-oz.

A moment is a force times a d

is-tance. In our sample, if a

tail-moment arm distance were 30

inches, the tail download to offset

the nose-down moment would be

255.75 divided by 30, or 8.52

ounces. (Chapter8 goesinto thisin detail.)

RPM, SPEED AND PITCH NOMOGRAM

Figure 13 was developed to help

model designers choose prop

pitches and diamete rs suitable for

both plane and engine to obtain

optimum performance.

This is explained in Chapter 8.

Figure 13 should be used with

Figure 3,"Wing Loading LiftSpeed

Nomograph." Don't use Figure 13

alone to estimate the speed of any

prop/plane/engine combina tio n; if

the prop pitch and diame teraren't

suitable for a model's character

is-tics, the nomogram will not be

accu rate.

Itwould obviously be poor judg

-ment to use a high -pitch,

low-diameterpropeller on a large, slow

flying,draggy modelwith low wing

loading. Similarly, a low-pitch,

large-diameter prop on a low-drag,

fast airplane with a high wing

load-ing would be a poor choice.

I hope thatthis chapterwillover

-come any problems some readers

may have with form ulas in this

book.To succee d,one musttry! No

effort,no success!...

STATIC RPM LEVELFLIGHT NOMINAL

X1,000 SPEED (MPH) PITCH 4 18.3 4 20 25 5 5 30 35 6 40 6 7 7 8 8 9 9 10 10 11 ₁₅₀ 11 12 12 13 ₂₀₀ 13 14 14 15 250 15 16 300 16 17 350 17₁₈ 18 _{400 19} 19 20 450 20 21 500 22 23 24 25 Figure13.

Nomogramforchoosing suitableprop pitchesanddiameters.