WingFinding

the right

blend of airfoil,

span, chord,

and planform

DesignNeal Willford, EAA 169108

well-designed airplane is one where its designer

carefully weighs the many—and often conflict-

ing—requirements and makes the best compro-

mises possible to achieve the design objectives.

No place is this more evident than in the wing

design, where the designer must effectively combine area,

span, and planform with airfoil(s) and flap size, and factor in

the construction method.

As the renowned airplane designer John Thorp said, “The

best airplane is the least airplane which will exactly do the

job.” So let’s look at what you need to consider when sizing

the minimum wing to “do the job.” Like the other article in

our series, a downloadable spreadsheet on the EAA Sport

Aviation web page will help you with this process.

If you only remember these two points, you will at least

have a basic understanding of the major factors in sizing a

wing:

■ The wing area is determined by the stall speed ortakeoff/landing requirements.

■ The wingspan is determined by the rate of climb,sink rate, or ceiling requirements.

A

42 MAY 2004

MA

RK

GO

DFR

EY

MA

RK

SC

HA

IBLE

042-050 WINGS 405 4/13/04 3:01 PM Page 2

EAA Sport Aviation 43

Wing Area & PlanformWhen a maximum stall speed is the design limit, therequired wing area (in square feet) can be determinedusing this equation: Wing Area = 295 x GrossWeight/(Vkts

2 x CLMAX)Table 1 shows the maximum stall speeds for several

different categories of airplanes. The first three typeshave fairly low limits and will likely be the design cri-teria.

The maximum stall speed for FAR 23 certificated air-planes is pretty high; therefore, it is not often thedesign factor for small, general aviation airplanes.Instead, takeoff and landing considerations may be thedesign condition. The following equations (derivedfrom References 2 and 3) can be used to estimate thewing area for these cases:

The equations show that weight, distance, and theCLMAX all affect the needed wingarea. So does power loading (theratio of gross weight to the engine’smaximum rated horsepower) whentakeoff distance is critical. A lowerpower ratio indicates higher horse-

power for a given gross weight, and this reduces theneeded wing area proportionally. The takeoff distanceused in the equation is for a fixed-pitch propeller.Using a constant-speed propeller shortens the takeoffdistance by about 30 percent or more and, like a lowerpower loading, reducesthe needed wing area.

The distances usedin the equations arefor ground roll only.The distance needed toclear a 50-foot obstacleon takeoff or landingcan be 50 percent to100 percent higher. Itis desirable, but notalways possible, to size the airplane so the takeoff andlanding distances are roughly equal, and the greater ofthe two will determine the minimum runway lengths.Airplanes built in the 1930s and ‘40s were designed forshorter grass strips and consequently have more wingarea than those designed for today’s longer paved run-ways.

Gross weight and CLMAX are the two variablespresent in all the wing area equations. An airplane’sgross weight is roughly 2.5 times its useful load, so oneway to control wing area is to decide on a reasonable

useful load. We always want more use-ful load, but realize that there is aprice to pay for it. CLMAX is the max-imum lift coefficient an airplane canachieve before it stalls. The equationsshow that the needed wing area is

Formula 1

Formula 2

MA

RK

GO

DFR

EY

DEK

EVIN

TH

OR

NTO

N

JIM

KO

EPN

ICK

042-050 WINGS 405 4/13/04 3:02 PM Page 3

44 MAY 2004

inversely proportional to the CLMAX, indicating thathigher lift coefficients mean a smaller and possiblylighter wing.

When laying out a wing, designers have a variety ofplanform options—elliptical, tapered, constant chord,or a combination thereof—and their choice will affectthe drag due to lift (or induced drag). A wing produc-ing lift deflects the air behindit downward, and Germanresearchers found that theresulting drag would be mini-mized when the downwashwas constant along the span.The elliptical planform down-wash was constant along thespan. The elliptical planformaccomplishes this, making itthe theoretical “gold stan-dard.”

Few airplanes have ellipticalwings because research provedthat a straight tapered wing,which is easier to build, isalmost as good (except athigher aspect ratios). Testingrevealed that the best taperratio (tip chord/root chord) forthe lowest induced drag wasabout 0.4. Unfortunately,there’s a nasty side effect ofusing too low a taper ratio.Taper causes the wing to startstalling outboard, and thelower the ratio, the farther outthe stall starts. Stalling out-board renders the aileronsineffective, and aircraft controlis the last thing we want tosurrender. Wing sweep alsoaffects the lift distribution,with sweep back moving thestall initiation outboard andforward sweep moving itinboard.

To move the stall inboard,designers use a moderate taperratio of 0.5 to 0.6 and wing

twist. Figure 1, calculat-ed with this month’sspreadsheet, shows thelift distribution for atapered wing with andwithout twist. Theupper curves representa wing close to stall andshow that adding twist

moves the lift coefficient peak inboard from theailerons (which usually start at 50 percent to 65 per-cent semi-span).

The black line represents the maximum available 2-d lift coefficient of airfoils used for this example. Thestall starts where the line first intersects the wingcurves. It slopes down because of the Reynolds num-

Figure 1. cl comparison for different wing planforms and twist.

Figure 2. Two Different Airfoils Designed Using XFOIL

Type of Aircraft Sea Level Maximum Stall Speed (Knots)

Ultralight 24Light-Sport Aircraft 39 (landing configuration), 45 (flaps up)JAR/VLA 45FAR 23 Single Engine 61

Table 1. Sea Level Maximum Stall Speeds for Various Types of Aircraft

042-050 WINGS 405 4/12/04 08:04 PM Page 4

EAA Sport Aviation 45

ber effect, which is a function of the airspeed, air den-sity, and airfoil chord length.

An airfoil’s clMAX (cl represents 2-d lift coefficient)often decreases with lower Reynolds numbers (whichoccur as the chord shrinks) and in this case causes a 9percent loss in clMAX at the tip airfoil. Using a tip air-foil with a higher clMAX at a lower Reynolds numberwould help raise the black line and allow the intersec-tion point to move further inboard, away from theailerons.

Adding wing twist increases induced drag and can

cause other drag problems. You can see this inthe lower curves on Figure 1, which representthe wing at cruise. Because of the twist thewing’s outer portion is flying at a lower angleof attack and would require a tip airfoil withlow drag at low lift coefficients to keep theouter-wing drag from being excessive.

Airfoils with low drag at low lift coefficientsoften have low maximum lift coefficients—which reduce the slope on the black line butdrive the stall outboard. Often, designerschoose better stalling characteristics and use atip airfoil with a higher clMAX and accept theextra drag penalty.

These compromises help reduce the drag differencesbetween tapered and constant-chord wings. Using aconstant-chord wing results in about a 1 percent dragpenalty at cruise, but structural weight savings—notlower drag—is usually the tapered wing’s main benefit.But the aerodynamic savings is important for some air-craft, such as sailplanes that often fly at speeds wherethe parasite and induced drag is nearly equal. This iswhy most high-performance sailplanes have taperedor even multi-tapered wings.

Figure 1 shows one of the benefits of a constant-

CONCORDE BATTERY CORPORATION2009 San Bernardino Road

West Covina, California 91790 USA(626) 813-1234 • Fax (626) 813-1235

www.concordebattery.comISO 9001:2000 Certified

Recombinant Gas (RG) Valve Regulated Sealed Lead Acid (VRSLA)

Aircraft Batteries• MAINTENANCE FREE •

CONCORDE BATTERY CORPORATION2009 San Bernardino Road

West Covina, California 91790 USA(626) 813-1234 • Fax (626) 813-1235

www.concordebattery.comISO 9001:2000 Certified

Photograph Courtesy of: Dr. Mike SchlossOwner/Operator of “Naked Fanny”

Airplanes built in the 1930s and

‘40s were designed for shorter

grass strips and consequently

have more wing area than those

designed for today’s longer

paved runways.

042-050 WINGS 405 4/12/04 08:09 PM Page 5

chord wing. Its maximum local lift coefficient occursat the root, so the wing will start stalling well inboardof the ailerons. A downside is that it will stall beforethe wing reaches its maximum lift coefficient along itswhole span, and this results in the wing CLMAX beingabout 7 percent less than the airfoil’s maximum 2-d cl.A tapered wing does a bit better because its lift distri-bution is flatter and its wing CLMAX is about 4 per-cent to 5 percent less in maximum 2-d cl of the airfoilsused. Probably one of the constant-chord wing’sbiggest benefits is that it’s easier and cheaper to make.

Every wing has tips, and over the years designershave tried just about every shape imaginable. One ofthe best performing, however, is a squared-off ending!Usually, sharp edges aren’t good aerodynamically, buton wingtips they force the tip vortex a little fartherout, which effectively results in a little extra wingspan.They aren’t too pretty, but they are easy to make.

Another wingtip that gives good results looks like itwas created by a table saw set at 15 degrees to 45degrees from the wing’s bottom surface. This is basi-cally the Hoerner wingtip, and variations include a cir-

cular or parabolic shape (as viewed from thefront) that replaces the “saw cut” transitionfrom the wing’s lower to upper surface.Keeping the edge of the wingtip as sharp aspossible is important, as data from Reference5 shows that fully rounded tips (as viewedfrom the front) have the worst performance.

Starting before World War I, wind tunneldata show that a raked or sheared tip offers aslight aerodynamic advantage over a more“conventional” tip shape. These tips have aleading edge sweep of 45 degrees to 70degrees as viewed from the top. Do not use a

tip shape that buries the aileron tip too far inboard, oraileron performance will suffer. Running the aileronall the way to the tip is also not a good idea becausethis can result in undesirable aileron forces.

Airfoil ConsiderationsBuilding a wind tunnel to verify the Lilienthal wing“curves” data is one reason the Wright brothers suc-ceeded. Finding that data incorrect, they developedand tested their own airfoil shapes and used them toproperly size their gliders and, eventually, their pow-ered Flyer. Since then the wind tunnel has played animportant role in airfoil development, and tremen-dous strides were made from the 1920s through the1940s.

In 1933 the National Advisory Committee forAeronautics (NACA) conducted an extensive investi-gation of airfoil shapes. It varied the camber line (theresulting curve drawn through the middle of an air-foil) as well as the airfoil thickness distribution (thesymmetrical airfoil shape draped over the camberline). Starting with the thickness distribution from the

Clark Y airfoil (used on the Spiritof St. Louis), researchers scaled it toget the desired airfoil thicknesses.

In testing 96 different thicknessand camber combinations NACAcreated its series of four-digit air-foils. The first digit is the maxi-mum camber height, the secondthe camber location, and the lasttwo the maximum thickness. Thebest overall airfoils are the 24 and44 series, and they have success-fully served many airplanes foryears. The four-digit symmetricalairfoils also turned out to be goodairfoils for tail surfaces.

The four-digit, 12 percent thicksections had the highest maxi-mum lift coefficient, which is whythey are popular with airplanedesigners. The 2412 is on all the

46 MAY 2004

Figure 3. Estimated Lift Coefficients for Figure 2 Airfoils

Starting before World War I, wind

tunnel data show that a raked or

sheared tip offers a slight

aerodynamic advantage over a

more “conventional” tip shape.

Reynolds Number = 3,000,000Mach Number=0.05

042-050 WINGS 405 4/12/04 08:29 PM Page 6

EAA Sport Aviation 47

Cessna strutted singles, except the208 Caravan. The Aeronca Champ,Fly Baby, Volksplane, and othersall wear the 4412. These airfoils arepretty tolerant to manufacturingimperfections and insects, and arestill worth consideration for light-sport type aircraft.

NACA testing showed that themaximum lift coefficient increasedwhen the maximum camber posi-tion was closer to the leading ortrailing edge. Moving the maxcamber point aft of 50 percentchord was not desirable because ofthe high pitching moments. Eventhe 44 series airfoils have prettyhigh pitching moments that cancause high trim drag at highspeeds.

Instead, NACA explored movingthe maximum camber position far-ther forward while using a different camber shape. Theresult was the five-digit airfoils, with the best being the230 series. These airfoils offered high lift, low drag, and

very low pitching moment—just what designers werelooking for as airplane speeds and wing loadings wereincreasing. They have probably been used on more dif-

Bring Your Panel Into The 21st Century. Only $1995!The Dynon Avionics EFIS-D10gives you all the benefits of asolid-state AHRS platform in onecompact package.Instruments:• Attitude Indicator• Airspeed• Altitude• Gyro stabilized magnetic heading• Turn rate• Slip/skid ball• Angle-of-attack (optional)• Clock or Up/Down timer• G-meter• Vertical Speed• Voltmeter

Actual SizeWith over 500 sold in the first six months, the EFIS-D10 has proven to be therunaway best seller in low cost electronic flight information systems. Call usat 425-402-0433 or visit us on the web at www.dynonavionics.com

Figure 4. Estimated Drag Coefficients for Figure 2 Airfoils

Reynolds Number = 6,000,000Mach Number=0.20

042-050 WINGS 405 4/12/04 08:18 PM Page 7

ferent airplanes—from the Taylorcraft to the earlyCitation jets—than any other. Their downside is thatthey have a rather abrupt stall, which can be some-what tamed by the wing planform and thickness used.

By the 1940s researchers had designed airfoils withthe potential for much lower drag. They allowed theair to flow at cruise lift coefficients at a constant orslightly accelerating speed over 40 percent to 60 per-cent of the airfoil’s surface. If the surface were smoothand free from waviness, the result would be a long runof laminar flow and much lower drag.

NACA’s systematic investigation of laminar airfoilsresulted in the six-series airfoils. They have been usedon many airplanes over the years, but often withoutthe desired drag reduction (for reasons we will discussshortly). Reference 4 includes wind tunnel data forsome of the best NACA airfoils.

Computer programs now enable aerodynamiciststo design custom airfoils for particular applications.One of the best available is XFOIL, now a public domainprogram (available at http://raphael.mit.edu/xfoil/). It doesa good job of estimating an airfoil’s drag and CLMAXand has powerful design features, making it a goodway to custom design airfoils for new airplanes (thetypical approach now used in the aircraft industry).

Factors other than aerodynamics should also beconsidered when choosing an airfoil. For example,strut-braced wings can use a 12 percent thick airfoilwithout a severe weight penalty. Cantilever wingsrequire a beefier spar and usually have thicker root air-foils to reduce the spar weight. Often 15 percent to 18percent thick root airfoilstransition to a 12 percentto 15 percent thick tip air-foil. Thicker airfoils usual-ly have higher drag, butoften the drag differenceis minimal compared tothe wing weight savingsthey afford. Avoid airfoilsthinner than 12 percentbecause they usually havesharp stall characteristicsand a lower clMAX. Theexception is the single sur-face airfoils used on someultralights, which bydesign are “thin” yet stillhave a high lift coefficient(and drag).

Construction methodand materials can alsoinfluence airfoil selection.Extensive laminar flowairfoils offer low drag—provided the wing con-

tour is smooth and accurate. Extensive laminar flow isdifficult to obtain with aluminum skins thinner than0.032 inch. Schreder sailplanes achieve laminar flowbecause their thinner aluminum skins are bonded toclosely spaced foam ribs. Metal bonding in a home-building environment can be very difficult, soapproach it cautiously. Composite or plywood wingshave more potential for achieving laminar flow.

Ultimately it’s low wing drag that counts. Figure 2shows two different airfoils designed with XFOIL. Thetop one was designed for high clMAX lift by using agenerous leading edge and a carefully shaped uppersurface, but the compromise is that it is capable ofonly 20 percent to 30 percent laminar flow. The sec-ond airfoil was designed for 40 percent to 50 percentlaminar flow and a moderate clMAX.

Figure 3 shows the estimated CL comparison forboth “clean” airfoils and with the laminar flowtripped at 5 percent chord top and bottom. The lami-nar airfoil clMAX is barely affected by early transition,compared to a 10 percent loss for the high-lift airfoil.Assuming the wing is sized for one of the require-ments mentioned earlier, a wing using the high lift air-foil could be 10 percent smaller (even accounting forthe lift loss due to the tripped flow).

Figure 4 shows the estimated drag of the two air-foils, and that the laminar one is definitely superior inthe cruise cl range. However, if the wing constructionmethod only allows a maximum of 25 percent laminarflow, then the drag difference disappears. The drag ofthe high-lift wing would actually be less because it

48 MAY 2004

Figure 5. Oswald Efficiency Factor Trend

042-050 WINGS 405 4/12/04 08:19 PM Page 8

could be smaller (and probably lighter). While developing the Bonanza, Beechcraft did wind

tunnel and flight testing with two different wings—onewith a laminar airfoil and another with the 230-seriesairfoil. Both tests revealed that the laminar wing didn’twork with Beech’s particular construction needs andmethods, so the airplane wears the 230-series airfoil.

We saw earlier that the wing CLMAX is less thanthe airfoil 2-d clMAX. It still needs to be corrected fur-ther to obtain the airplane CLMAX used in the wingsizing equations or, if the wing area is known, to esti-mate stall speeds. This correction depends on the typeand size of the flaps, the extra pitching moment thatthey generate, and the center of gravity (CG) location.Approximate 2-d lift increment and pitching moment

can be found in Reference 6.The CG location can have a noticeable

impact on CLMAX—negative when for-ward of the wing’s aerodynamic center andpositive when aft. Because of this, it is agood idea to use the airplane’s CLMAX forthe most forward CG/gross weight combi-nation when sizing the wing. This month’sspreadsheet can be used to help estimate

this.

WingspanAn airplane’s maximum rate of climb and ceilingdepend on excess thrust horsepower, where thrusthorsepower equals the available engine horsepowertimes the propeller efficiency. The thrust horsepowerrequired to keep an airplane in level flight is equal to:Thrust Horsepower = (Ap x ó x Vkts

3)/96170 + [0.3/(ex ó x Vkts)] x (Weight/Span) 2

The amount depends on the drag area (Ap), air den-sity ratio (ó), airspeed, span loading (weight/span),and Oswald’s efficiency factor (e). The first part of theequation shows the power required to overcome theparasite drag and is multiplied by the airspeed cubed,indicating that it becomes increasingly dominant at

EAA Sport Aviation 49

By the 1940s researchers haddesigned airfoils with the potential for much lower drag.

042-050 WINGS 405 4/12/04 08:20 PM Page 9

higher speeds. The power required to overcome the induced drag is

the second part, and here it is divided by the airspeed(not cubed), indicating that this term becomes domi-nant at lower speeds. The span loading term is squared,showing that a longer span has a powerful effect inlowering this term. Oswald’s factor accounts for fuse-lage and planform effects. Figure 5 shows it for variousairplanes and indicates a general decline with increas-ing wing aspect ratio.

As we saw earlier, a low power loading reduces theneeded wing area for takeoff. Along with a constant-speed prop, it can also reduce the required span. Weneed to be careful though, because high span loadingcombined with a high stall speed can cause an uncom-fortably high sink rate and landing speed in the eventof an emergency off-field landing. You may find thatadding a few extra feet of wingspan may be worth it toreduce the power-off sink rate. Hopefully you wouldnever need the extra span for this reason, and the addi-tional benefit would be a boost in rate of climb—some-thing that is always desirable when flying on a hotsummer day!

50 MAY 2004

Take the Easy Approach Through Appleton for

EAA AirVenture 2004!

I 27 daily flights on United Express, Northwest Airlink,

Comair (Delta Connection), or Midwest Airlines.

I Located just 20 minutes north of Oshkosh with easy

access to Hwy 41

I Daily bus service between the airport and EAA and

to several nearby hotels

I On-site car rental agencies

I Grass and pavement parking for transient aircraft

www.ATWairport.com

AAero EEnhancements, Inc.636-527-2120, Toll Free: 1-888-821-AEROFAX: 636-256-0370 (2376)

www.aeroenhancements.com

“GIVE YOUR INSTRUMENTPANEL THE ULTIMATE

ENHANCEMENT”

Glare ShieldLighting with

BlackoutProtection

Panel Lightingwith Blackout

Protection

CustomInstrument

Panels• Exotic Real Wood

• Carbon Fiber• Machined Plastic

more at www.eaa.org�

References“Airplane Design 101,” Willford, Neal, EAA Sport

Aviation, February 2002. Airplane Performance, Stability and Control,

Perkins and Hage, 1949, Wiley and Sons.Aviation Handbook, Warner and Johnston, 1931,

McGraw Hill.Theory of Wing Sections, Abbot and Von

Doenhoff, 1959, Dover Publications.Fluid Dynamic Drag, Hoerner, Sighard, 1951, pub-

lished by author.“Looking for Lift,” Willford, Neal, EAA Sport

Aviation, March 2004.

While developing the Bonanza,

Beech did wind tunnel and

flight testing with two different

wings—one with a laminar air-

foil and another with the 230-

series airfoil.

042-050 WINGS 405 4/12/04 08:21 PM Page 10