Basics of RC Model Aircraft Design

BASICS OF

RIC MODEL CHOOSING AIRFOILS • WING LOADING • CG LOCATION BASIC PROPORTIONS • AEROBATIC DESIGN -and much more!

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BY ANDY LENNON

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From the Dublishers of

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Aboullhe Aulhor 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 University and the University of Western Ontario, London, Ontario. Andy entered the Canadian aircraft manufacturing industry and later moved to general manufacturing as an industrial engineer. Throughout his career, he continued to stud y all things aeronautical, particularly aircraft design, aviat ion texts, NACA and NASA reports and aviation periodicals. He has tested many aeronautics theories by designing, building and flying nearl y 25 experimental RIC models-miniatures of potential light aircraft. His favorite model, Seagull III, is a flying boat with wide aerobatic capabilities. Andy is a valued contributing editor to Model Airplane News , and he has written for Model Aviation, Model Builder, RC Modeler and RC 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's likely to be at the flying field testing yet another model aircraft design . ...

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Copyright ~

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

All rights reserved , including the right of reproduct ion in whole or in part in any form. This book, or parts thereof , may not be reproduced without the publisher 's written permission. Published by Air Age Media Inc. 100 East Ridge Ridgefield , CT 06877-4066

AirAGE

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modela lrplanenews.com PRINTED IN THE USA

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THE BASICS OF RIC MODEL AIRCRAFTDESIGN

Contents 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 14 Design for Flaps .•....•... 63 Chapter 15 NASA "Safe Wing"

69

Chapter 16 Landing-Gear Design .... 72 Chapter 17 Ducted-Cowl Design

77

Chapter 23 Tailless Airplane Design

111

Chapter 18 Propeller Selection and Estimating Level Flight Speeds ....•.......•....•......83

Chapter 24 Hull and Float Design ......•.......•......•.. 119

Chapter 19 Design for Aerobatics .. 90

Chapter 25 Basic Proportions for RIC Aircraft Design .... 125

Chapter 20 High-Lift Devices and Drag Redudion .••...•..... 93

Chapter 26 Construdion Designs

Chapter 21 Centrifugal Force and Maneuverability •••••••••• 98

129

Appendix •••••••••••••••••••• 134

Chapter 22 Canards, Tandem-Wing and Three-Surface Design .••.•.•...•...•....•••.. 102

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 THE BASICS OF RIC MODEL AIRCRAFT DESIGN

3

Introduction ~. ~ ~ ,\

- •••

ndy Lenno n ha s written an outstan ding book tha t covers all required aspects of the preliminary design process for mod el aircraft. Fur the r, much of the con ten t is equally applicable to military RPV an d h om ebu ilt aircraft design . Reviewin g the book was som eth in g of a nostalgia trip for me afte r 46 years of designi ng full -scal e and mod el aircra ft. Would that I h ad been able to carr y thi s book wit h me to an unsuspectin g aircraft 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 mu ch . When review ing my not es jotted down while reading the draft, I found that many of my comments simply amplified what is said in th e text and reflected even ts from my own career related to the book topic at hand. The ch apters on pitch and lateral/d irection al stability and control remin ded me of some Gru m man his tory. We seem ed to blow an aerodynamic fuse on every fifth aircraft prot otype-to wit, th e XFSF Skyrocket, mo st of whic h lande d in Lon g Islan d Sound, and the XF10F, which, abo ut all axes, was said to be lias stabl e as an up side-down pendulum ." Th e only thin g that worked flawlessly was th e variable sweep, which we feared th e mo st! Maybe Andy's book could ha ve helped. Sadly, Grumman never got the chance to go beyond th e F-14 and try an F-1S E

A

4

THE BASIC S OF RIC MODEL AIRCRAFT DESIGN

The design process begins with weight estimation and structural optimization in the name of reduced weight. The book covers th ese topics for models better than any sources I have encoun tered previou sly. Next in design comes drag analysis and redu ction, which are cove red professionally yet in an understandable way for the amateur designer. Wh at a treat to see the consequences of flat-plate drag from seemingly small items like land ing-gear-wire legs properly illuminated. I recently had this top ic driven home dramatically wh en I wen t all out to clean up the drag of my electric fan A-6 Intruder prototype. The improved performance after the clean-up surprised me quite pleasantly. What I did could have been drawn directly from thi s book. Stability and control, after performance, is what we see as an immediate result of our efforts. Result s vary from joy to th e blackness of the re-kitting process. Andy's book will keep you away from the latt er end of th e band through proper selection, arrangement and sizing of th e aircraft compon ents contributing to both longitudinal an d lateral /d irectional stability and control. The book is ori ented mainly toward gas/g low-powe red model aircraft design. With gas models, available power rarely is a problem. Coping with marg inal thrust simply results in using a bigger engin e and a tendency to ignore drag! Not

••.

so with electric models, which are rapidly becoming popular. They are clean, noi seless and thoroughly enjoyable alternatives to gas/glow. However, the design process challenges our ability to build strong but ligh t 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 powerplant systems, this book gives you everything you ot herwise need , even the impact of carrying heavy batteries. Perhaps Andy will tackle elect ric power plants at a fut ure date. ... - Bob Kress Retired Vice President, Grumman

Chapter 1

ne of th e most important choices in mod el o r fullscale airplane design is the selectio n of an airfoil. The wing section chosen should have charac teristics suited to th e flight pattern of the type of model being designed. There exis t litera lly h undreds of airfoil sectio ns from which to choose. They are described in "airfoil plots" similar to EI9 7 (see Figure 1). Selection of an airfoil demands a reasonable understanding of this data so that one can read, understand and use it to advantage. Providing th is understanding is th e subject of thi s chap ter. Referring to EI97 , note that the data is given in terms of coefficien ts, except for th e angle of attack. These coefficien ts are C L for lift, CDo for profile d rag and eM for the pitching moment around the 1/4-chord point. The actual lift, total drag and pitching moment of a wing depend on seven factors no t directl y related to its airfoil section . These are:

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

Airfoil

• Wing area. All three are proportional to wing area.

Selectio n

• Wing chord(s). Pitch ing mom en t and Reynol ds number are proportional to chord. • Angle of attack (AoA). In the useful range of lift, from zero lift to just before the stall, lift, profile drag and pitching moment increase as the AoA increases. • Aspect rati o (AR). All three are affected by aspect ratio. • Planform, i.e., straight, tapered or elliptical. All impac t lift, drag and pitching moment. • Reyn ol ds number (Rn). Th is reflects bot h speed and chord and is a measure of "scale effect."

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Figure 1. Airfoil data for Eppler E197: tift curves (right-hand illustration) andpolar curves (left).

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In develop ing thes e airfoil plots, aerodynamics scientists have screene d out six of these factors, leaving onl y the cha racteristics of lift, profile drag and pitching moment unique to each individua l airfo il. The seventh, Rn, is reference d separately on the airfo il plot. Formulas th at incorporate all six variables and these coefficients permit accurate calculation of th e lift, total drag and pitching moments for your wing and choice of airfoils. In the airfoil selection process, h ow-

ever, it isn 't necessary to perform lab or ious calcula tion s for each potent ial airfoil. Direct co mparison of th e curves an d coefficients of the candidate airfoils is more easil y done, wit hout deterioration of the result s. Th is com parison calls for an understanding of the data . Start by examin ing th e right -hand illustration of Figure I- Eppler EI 97- in deta il. Eppler E197 is 13.42 percent of its chord in depth. This plot is th e result of win d-tun n el test s perform ed at th e University of Stuttgart in Germ any under the direction of Dr. Dieter Althaus. The horizon tal lin e is th e AoA (n, or alph a) line in degrees (measured from th e airfoil 's ch o rd line)positive to th e right and negative to the left. .20

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THE BASICS OF RIC MODEL AIRC RAFTDESIGN

5

CHAPTER 1 A THE BASICS OF RIC MODEL AIRCRAFT DESIGN

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Figure 3. How aspect ratio affects the stallangle ofattack.

The vertical line, on the left, provides the CL, 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 horizontal line. In the center are the three Rns covered by this plot, coded to identify their respective curves. .25 .---- - - - - - - - - ---,

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FIgure 4. Straight-wing correctionfactor fornon-elliptic lift distribution.

In the left-hand illustration, E197's chord line is straight and joins leading and trailing edges. The dotted, curved line is the "mean" or "camber" line, equidistant from both upper and lower surfaces. The vertical line is graduated identically with the CL line on th e right. CL is positive above and negative below the horizontal line, which is itself graduated to provide the profile drag coefficient Coo' Now, back to the curves in the right-hand illustration . The lift lines provide the CL data on the E197 airfoil. Note that this section starts to lift at the negative AoA of minus 2 degrees and continues to lift to 16 degrees, for a total lift spec6

THE BASICS OF RIC MODEL AIRC RAFTDESIGN

1

1

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WING DRAG COEFFICIENT

Figure 6. How aspect ratio affects drag ata given lift.

trum of 18 degrees. CL max is 1.17. These lift curves are section values for "infinite aspect ratios" and two-dimensiona l airflow. For wings of finite AR and threedimensional 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. For example, Figure 3 shows that if, with a wing of AR 5, you can achieve a CL of 1.2 with an AoA of 20 degrees, then with an AR of 9 you can achieve the same CL with an AoA of 17 degrees. A higher AR wing will stall at a lower AoA. In addition, the AoA m ust be increased to compensate for the fact that straight and tapered wings are not as efficient as the idea l elliptical wing planform . Figures 2 and 4 provide adjustment factors (T, or tau). The pitching moment curves quantify the airfo il's nose-down tendency, increasing with increasing AoA, but not linearly like the lift curves. The curves in the left-hand illustration of Figure 1, called "polar curves," compare CL to Coo' Note that E197 shows very little increase in profile drag despite increasing lift, except at the lowest Rn. Again, these are section values. The profile drag values do not include induced drag, defined as "the drag resulting from the production of lift" and which varies with AR as shown in Figure 6. Wing planform also affects induced drag . As shown in Figures 2 and 4, the curves identified by 0, or

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CHAPTER 7

TAIL AIRFOIL SECTION S Since th e hori zo n tal tail surface has to pro vide lift-both u p and down-sym metrical airfo ils suc h as Eppler E168 are recommended . Many m od el s in co rpo rat e flat balsa sheet or flat built-up tail surfaces. These are less effect ive, aerodynamicall y, th an sym metrical airf oil s. Figure 1 shows polar curves (CL versus Co) for a flat plate airfoil at low Rns. Lift is greater, and drag is less for E168. As explain ed in Chapter 13, "Stressed Skin Design ," symme trical tail surfaces may be made lighter an d stronger than shee t balsa and much stronger th an built-up surfaces (and only slightly heavier).

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Figure 2. Effect of aspect ratio on wing characteristics.

Based on experience, this author uses a simp le meth od for establishing the horizontal-tail area (HTA). If you have a wing AR of 6 and a tailmo ment arm that is 2.5 times the wing's MAC, th en a tail area of 20 percent of th e wing area is adequate. Here is the formula : HTA = 2.5 x MA C x 20 % x WA TMA

where HTA = horizontal-tail are a in square inches; TMA =tail-moment arm in inches; WA = wing area in square inches; MAC = Wing's mean aerodynamic chord in inches. For short TMAs, this formula will increase th e tail area ; for long TMAs, area is reduced , but wha t aerodynamicists call "tail vo lume, " i.e., area times TMA, will remain constant.

TAIL ASPECT RAT IOS The upper portion of Figure 2 illustrates the effect of AR on lift and AoA. For AR 5, th e stall occurs at a 20-degree AoA, and at AR 2.5, the stall is at 27 degrees-both at a lift coefficient of 1.2. Thus, at AR 5, the tail surface responds more quickly to changes in AoA th an at AR 2.5 since the lift per degree of AoA is greater. For sma ller models, however, th e tail 's ch ord sho uld not be less than 5 inches to avo id unfavorable low Rn effect s. An AR of 4 to 5 with constant cho rd is reco mmen ded . SLOTTED FLAP EFFECT When slotted flap s ar e full y extended, several things occur :

• Both lift and d rag increase substa ntially, and th e model's speed dec reases. • The wing's nose-down pitc hi ng moment increases sha rply. • Th e down was h angle also increases in proportio n to th e lift increase from th e lowered flap s. Thi s increases th e horizon tal tail download . Experienc e with th e Seagull III, th e Seahawk and th e Swift indicates th at the flap chord (in percen t of th e wing's chor d) influ ences th e model's flaps-down beh avior. Flaps with wider ch ord s-up to 30 percent of th e win g's cho rd- gene rate very little pitch cha nge when extended. The increase in tail downTHE BASICS OF RIC MODEL AIRCRAFT DESIGN

33

CHAPTER 7 ... THE BASICS OF RIC MODEL AIRCRAFT DE SIGN

level, "gro und effect" occurs. When a plane is in grou nd effect: 1.0

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load th at tends to cause a noseup reactio n is equalized by th e Wing's hig h er nose-down pitching m om en t. It is very satisfying to lower full flap, after th rott ling back and have th e model continue on its m erry way, with out nosi ng up or down , but flying noticeably slower. For narrower chord (2S percent) flaps, th e flap-induced tail down load is greater th an th e nose-down wing pitching moment. When th e flaps are extended, this causes the model to nose up sha rply an d rather alarmingly. GROUND EFFECT

Wh en an airplan e is on fina l approach and descen ds to half its wingspan abov e ground (or water) 34

Lowering flaps causes an increase in th e down wash angle and in the nose-down pitch; but th e severe downwash angle reduction , du e to gro un d effect, red uces th e tail 's dow nlo ad, causing the mod el to nose-down in a sha llow dive. This is part icularly noticeable for models with wide-chord (up to 30 percent of th e Wing's cho rd) slotte d flaps. This beh avior requi res consider able up-elevator force to sto p th e dive and to raise th e aircraft's nose to th e n ear- st all touch down posture.

THE BASIC S OF RIC MODEL AIRC RAFT DESIGN

The larger th e elevato r area , in proportio n to the ho rizontal ta il's tot al are a, th e mor e effective th e elevato r, as shown in Figur e S. For slotted flapped mode ls, an elev ator are a of 40 perc ent of th e h ori zontal tail's area is suggested. Th is prop ortion provides adeq ua te elevator auth or ity to achi eve n earfu ll-st all lan d in gs, with fla ps ex te n ded an d in gro u nd effect. Wit h out flaps , a pro po rtion of 30 to 3S percent is adequate. Full eleva to r deflection of 2S degrees, both up and down , is appropriate. Th is m ay, at first, prove sensitive but , with practice, has proven to be no problem . At high speeds, elevator low dua l rate is suggested. CG LOCATIONS

The o ptim um CG is vertically in lin e wit h th e wing 's aero dy nam ic center at 2S percent of its MAC. Th ere are, h owever, ad vantages and di sadvantages in h eren t in positioning the CG ah ead of o r behind the Win g's aerodynamic cen te r.

FORWARD CG

See Figur e 6. A CG ahead of the wing 's aerodynam ic center ha s only one advantage: it improves longitudin al stability, since it increases the "stability margin." (See Ch apter 6, "CG Location .") A forward CG has th ese consequences: • The model's maneuverability is reduced , particularly when centrifugal for ce comes into play. (More on th is subject further on. ) • The tail download to balance the for ward CG adds to the load the wing mu st support, in addition to the model 's weight. Profile and in duce d dr ags (called "trim drag") of both wing and tail increase. • In gro und effect, and particularly for a flapp ed model, more powerful tail downlift is needed to raise th e model' s nose for a flapsdown landing. This is more pron ounced for wings using cambered , i.e. , semisymmetrical or flat-bottom ed, airfoils owing to the Wing's nose-down pitching moment. For sym m et rical-win g airfoils, the tail download need o n ly balance the nose-down moment of the forw ard CG and the nose-down pitch from the ex ten ded flaps . • The forward CG should be no farthe r forward than a point 16 percent of the MAC, i.e., measured aft of th e lead ing edge. • With respe ct to an y m aneuver involving centrifugal force (an d there are few that don 't ), that force acts at the CG and also substan tially increases the load the wing must support. (See Chapter 4, "Win g Loading Design ."). In a tight turn at h igh speed, centrifu gal forc e increases the wing lift and the weight at the CG ahea d of the wing's aerodynamic cen ter. A force couple results that resists the turn . Th is imposes a he avy addit io n al load on the horizontal tail th at , even with full up elevato r, it ma y be unable to su ppo rt- an d it stalls-limiting the model's maneuverability. For a CG vertically in line with the Wing 's center of lift , these

Horizontal Tail Design

tio ns for stability and flight control.

A CHAPTER 7

• The relative size of the areas of th e hori zo n tal tail and wing. En larging the tail will move the NP rearward for a larger static margin .

• Attempting to redu ce trim d rag Tail download by movin g th e CG • Sim ilarly, a longer tail moment arm will move the NP aft . too far aft can ca use problem s. download Th is requires an • The relat ive vertical positioning in crease in the of the wing and horizontal tail has a tail's positive AoA significant bearing on the tail 's effectiveness, or efficiency. A tail Figure 6. for equili brium. In Forward CG force diagrams. located close to the wing's wake, in a sha llow dive, th e heavy downwash, loses effective wi ng's AoA an d Cl both decrease. ness . At this location, the tail is in Since th e downreduced dynamic air pressure Tail upload wa rd angle of caused by the drag of both wing and w 'n g lilts NP _ _ _ fuselage. This redu ces that ta il's the down wash is Down~ effectiveness to un der 50 perce nt. In prop ortional to Pitch moment CG co ntrast, a T-tail is 90 percen t th e wing's Cl , th e /.. Wing lift effective. dive reduces the C--,"_--,..:=--NP Downwash .... do wnwash ang le, which becomes This reduced efficiency affects the Cambered Taildownload CG NP locati on . It acts like a red uct ion more nearly paralin tail area : it moves the NP forlel with th e fuse ward and reduces the static ma rlage cen te rline . Figure 7. The tail's AoA and gin. The larger the vertica l sepa raAffCG force diagrams. lift increase, resulttio n between wing and tail, the ing in a so mebetter. For models whose wing is forces are directly opposed and do on or in th e middle of the fuse lage, times violent "tuck under." Soaring not add to the tail 's load. a 'l-tall is best . For high wings gliders with CGs so located have lost above the fuselage , a low tail is wings in the resulting steep dive. AFTCG Moving th e CG forward and redu cindicat ed. There is another aspect to all See Figure 7. A CG behind th e ing th e tail's AoA is th e rem edy. wing's aerodynamic center offers this. For the same NP, a high , more • This author is nervous about advantages, but ha s seriou s pot enefficient tail may be red uced in th e use of an aft CG coupled with area, yet would have the same tial disadvantages: slotted or Fowler flaps. The large effectiveness as the lower, larger increase in down wash angle created tail. If made larger in area , th e • Maneuverability is increasedby th e extended flaps could cha nge centrifugal force acting on th e aft more efficient hi gh er tail will th e tail's AoA substa ntially, conver tmove the NP aft, thereby en larg ing CG actually reduces the tail load s ing a positive upneeded for these maneuvers. load (or mild negative dow nload) to a • Owing to th e nos e-down pit ching h eavy download . moment of a cambered airfoil, th e horizontal tail normally has a The combination of an aft CG and a download requirement. The aft Basic airfoil , NACA 2412, maximum Iltt coellicient 1.00at stall speed of 24mph , angle of atta ck14 degrees , Rn 183,000 and wing loading of 24 heavy tail downCG's moment about the wing's ounces persquare foot. load might well aerody n amic center redu ces this result in a disastail download. /'.......

CHAPTER 10

ot her types of h ingin g, some form of gap seal is advised. Figure 7 provides sugges te d propor tions for ailerons, strip ailerons and spo ilers that were deve loped by NACA. They are goo d sta rting poi nts when yo u are creating your own designs. A

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STABILATORS

Some recent jet fighters use such tails . They move in opposite directions for roll control, and up or down for elevator action---or any combination of the two. They seem very effective and, for a model, higher ARs would provide longer moment arm s. Adverse yaw would be small. Pivoting on the spanwise pivots at 1;4 MAC wou ld result in low operating loads, as for all moving wings. This form of roll control might have app lication on pattern ships, leavin g the wing free for fullspan flaps .

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AILERON DIFFERENTIAL

Figure 6 shows how to use a servo's rotation to produce aileron differen tial. GAP SEALING

Wind-tunnel tests have proven that a 1132-inch gap on a lO-inchchord wing will cause a loss of rolling moment of approximately 30 percent. A gap seal for all control surfaces is suggested. The sidebar "Flap and Aileron Actuation Hin ges" of Chapter 14, "Des ign for Flaps," provide s a hinging method that has proven durable and inherently gap sealing. For

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Figure 7. Typical control-surface geometries.

THE BASICS OF RIC MODEL AIRCRAFT DESIGN

49

Chapter 11

Weight Distribution in Design

n anal ysis of th e weight of th e average .40 to .50 glowpowered, rad io-con trolled mod el aircraft with ailerons discloses th at th e power and con tro l uni ts, combined, weigh very close to SO percen t of the aircraft's gross weight. The power un it (PU) is composed of spinner, pro p, engine, muffler, engine mou nt, fuel tank, fuel, cowl, fuel tubing and nuts and bolt s. The contro l unit (CU) is made up of receiver, battery, servos, swit ch , extension cables, foam protection for receiver and batt ery and servo screws. In th e design of a mod el,

A

Figure 1. Three-view drawing o(Granville canard.

50

THE BASICS OF RIC M ODEL AIRCRAFT DESIGN

the distributio ns of th ese heavy unit s alon g th e length of the fuselage has a major effect on th at model's man euverability. Massing both units as close togeth er an d as close to the CG as possible while keeping th at CG in its design locati on will result in a highl y man euverable model. Moving th e power unit for ward by elongating the fuselage ahe ad of the wing requi res that the control un it move aft to keep th e CG at its de sign location. Man euverability will be redu ced as a result . A few sim ple defi nition s will h elp in unde rsta nding thi s reduction: • Moment. A force times a distan ce. • Inertia. The resistan ce of an ob ject to any cha nge in its motion or to being moved from a state of rest. • Moment of inertia. The inertia resista nce tim es its distance from some related point. In our case, that "related point" is th e mod el's CG. • Momentum. An ob ject in motion has mom entum equal to its mass times its veloci ty. In maneuvers, both th e PU and CU acquire momentum in a direction different from th e origin al line of flight. The PU's weigh t multiplied by its dista nce from th e mod el's CG is its "momen t of in ertia. " The same app lies to th e CU. Obviously, th e greater th e dista nce of both th e PU and CU from th e mod el's design CG, the great er those mom ents of inertia will be and th e greater th e resistan ce to the man euver. Also, lon ger moment arm s (in th is case, distance of the PU and CU from th e CG) requ ire bo th PU and CU to move th rough greater distances, for a given angular displaceme nt, as the aircraft maneuvers.

Lon gitudinally, the moment to ov ercome the moments of in ertia of both units for maneuvers is the model's TMA multipli ed by the force gene rated by deflecting the elev ato rs. Th e model's TMA is mea sur ed from CG to 1/4 MAC of the hor izontal ta il. For a given TMA an d elev ato r force , the greater the moments of inertia of th e PU and CU, th e slower the model's reaction . Loops will ha ve greate r diameter, and th e model will be less agile. With th e man euver underway, both the PU and CU acquire mom entum. To stop the maneuver, thi s mom entum mu st be overcome. Larger mom en ts of inertia produce larger momentum and slow the recovery from that maneuver. Directionally, the same applies. The rudder will have less effect in yawing the model. Also, as explaine d in Chapter 9, "Vertical Tail Design and Spiral Stability, " elongating the fuselage ahead of th e CG in creases its directionally destabilizing side area, requiring increa sed vertical tail area for stabil ity and control, further aggravating the situation. Greater moments of in ertia h ave one advantage: they offer more resistance to any disturbance. In level flight , the model will "groove." SPINNING

In a ta ilspin, one wing panel is fully stalled, but th e opposite panel continues to lift. The model rotates rapidl y, nose-down, around a vertical axis through its CG. Up-elevator and rudder into the spin maintain the rotation. Cen trifugal force acting on the model's components comes into play. The long er moment arms of both the PU and CU result in these uni ts rotating at higher speeds, gen erating greater centrifugal forces, wh ich act horizontally, away from

Weight Distribution in Design ... CHAPTER 11

dangerou s ailero n flutter greatly outweighs th e small reduction in maneu verability that 's occasioned b y th e ma s s -balan ce weights. Th e same comments appl y to mass balancing of elevators and rudd er. REAR·ENGINE CANARDS

For con vent ion al designs, it is not difficult to position both power an d con tro l un its so as to minimize th eir mom ents of inertia. Rear-engin e canards, without aft win g sweep, are a different matt er. Such aircra ft ha ve t he ir CGs betw een fore and aft wings, closer to the latt er. The PU at or behind the aft wing is balanced by locating the CU as far forward as possible. In most cases, additional ballast is requ ired up fron t to locate th e CG corre ctly. The mo ments of iner tia of both uni ts (and ballast) could not be greater. My Swan canard was not intend ed to be aerobati c, but in level flight , it grooved beautifully. The re are canard configur ati on s that h ave lower moments of inerti a.

Figure 2. Three-view drawing of Long-fl.

the spin axis. Th is action flatt ens the spin . The lon ger mom ent arms increase th e momentum, reduce th e rudd ers' effectiveness in sto pping the spin and delay th e spin recove ry, which could lead to a damaging crash.

servos to be positioned in the wing center sectio n. While aileron mass-balance weights work against lat eral maneuverability, keeping th e ailerons light reduces the mass-balance weight correspo ndingly. Freedom from

LATERAL CONTROL

Inertia roll coupling is a con sideration in lateral control. For those designs in wh ich th e aerod ynamic and inertia axes coincide, axial rolls are little affected by larger moments of in ertia . In snap rolls and barrel rolls, centrifugal force comes into play, as it does for spins , resulting in slower initiation of and recovery from these maneuvers. The model's wing is a factor, as it weighs close to 2S percent of the model's gross weight. For good lateral maneuverability, keeping th e wing panel's CG as close to the fuselage center line h elps. Th is results from :

• Ru ta n 's Long-EZ (Figure 2). The sweptback aft win g perm its th e PU to move forward , shortens th e fuselage and permits th e CU (pilot) to mo ve aft, close to th e CG. The big wing-root strakes house th e fuel on th e CG. The wingtip vertica l surfaces have reason able mom en t arm s for good direction al control, but th eir loca tio n increases th e wing 's mom ent of ine rtia, redu cin g lateral man euverab ility. • Miles Libellula (Figure 3). This was a British wartime design. The twin engines ahea d of th e moderately swept aft wing br ing th e power units closer to th e CG longitudinally. Both fore and aft wings have flaps. Note th e h igh-AR foreplanes on bot h the Long-EZ an d th e Libellula. ...

• Tapered win g of mod erate AR. • Ailerons, mass balanced to avoid flutter, permit aileron and flap

• Granville canard (Figu re 1). Both PU and CU (th e pilot) are located close to the CG for good maneu verabi lit y. A modernized version of th is clever design would be interesting.

Figure 3. . Three-viewdrawing of the Miles M.39S Libel/uta.

THE BASICS OF RIC MODE L AIRC RAFT DESIGN

51

Chapter 12

Reducing Drag t will come as a surprise to most mod elers (an d some model design ers, too) to find how much air resistance, or drag, their miniature aircraft generate in flight . The sources of much of it are such things as expos ed or partially cowled eng in es; wire landing-gear legs; fat tires; dowels and rubber bands that are used to hold down th e wing s; large, exposed control horns and linkag es; and thick TEs on wings and tail surfaces. This doesn 't impl y that the models don 't fly well; they do! In fact, th e h igh drag is benefi cial: it causes fairly stee p glides-engine throttled-that ma ke the landings of th ese relat ively low-wing -loading model s easy to judge. Their performance suffers in all other flight aspects, however. Many years ago, Model A irplane News published a very sign ificant article by Hewitt Phillips and Bill Tyler, titl ed "Cutt ing Down the Drag." It was based on wind-tunnel tests conducted at the Massach usetts Institute of Technology Aeron autical Laborat or y at model airplane speeds of from 15 to 40mph. Th e test models were 48 inc hes long and of typical mod el airplane con struction. Figure 1 sum marizes the results, wh ich are given in term s of their Cos. The actua l drag in ounces of a mod el fuselage depends on three factors:

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• airspeed; • cross-section area; and • sha pe of the fuselage. The CD for each reflects the drag value of that shape. When used in a formula th at include s cross-section

52

THE BASICS OF RIC MODELAIRCRAFT DESIGN

area and speed, it will accurately prolooks rep resentati ve of ma ny of vide the actual drag in ounces. For toda y's fuselage shapes. From its CD our purposes, the CD provides the of 1.261, deducting th e prop CD of relative drag value of each shape . .577 and adding th e extra drag of Analysis of the Cos in Figure 1 will .260 for tricycle gear/tires and of provide some surprising results. .336 for the fully exposed engine, Deducting the .198 CD of fuseresults in a worst-case CDof 1.28. At 40mph, this would gene rate a 19lage 1 from that of fuselage 8 (0458 ) gives a CD of .260 for the landing ounce drag; at 50mph, a 30-ounce gear on ly-or more th an the drag of drag. Surprised? Th is doesn 't fuselage 1. This gear was lI8-inchinclude wing and tail-surface drag. diameter music wire , and the A good drag-redu cing design could wheels were the thin, symmetrical, lower this to a CD of .38 (5.7 ounces) at 40mph but, again , th is cross-sectioned type that was popular at the time. Current tricycle wouldn't include wing and tail-surlanding gear with their large, fat face drag. Figures 3 and 4 from tires would, con servatively, double the CD to .520Fuselage Nose or more than 2112 times that of .198 1 fuselage 1. Deducting the .340 .198 CD of fuse2 lage 1 from that of fuselage 9 (.775) .237 3 provide s a CD of .577 for the sta.225 tionary propeller. 4 From fuselage II's CD of 1.261, .242 5 deducting the prop CD of .577, .269 the landing gear 6 CDof .260 and the Elastic band .340 CD of fuse.261 7 lage 2, resul ts in th e exposed .458 engine-cylinder drag of CD .084. A fully exposed .775 engine, muffler and firewall wou ld, conserva1.034 tively, have a CD four times as great : .336. 1.261 Fuselage 11, which is 48 inches long and 33 inches Figure 1. square in cross-section, Drag coefficients of various fuselages.

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