Airfoil & wings

Munson, B. R., Cronin, D. J. “Airfoils/Wings” The Engineering Handbook. Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000

© 1998 by CRC PRESS LLC

36Airfoils/Wings

36.1 Nomenclature36.2 Airfoil Shapes36.3 Lift and Drag Characteristics for Airfoils36.4 Lift and Drag of Wings

Bruce R. MunsonIowa State University

Dennis J. CroninIowa State University

A simplified sketch of a wing is shown in Fig. 36.1. An airfoil is any cross section of the wingmade by a plane parallel to the xz plane. The airfoil size and shape usually vary along thespan.

Airfoils and wings are designed to generate a lift force, L, normal to the free stream flow that isconsiderably larger than the drag force, D , parallel to the free stream flow. The lift and drag arestrongly dependent on the geometry (shape, size, orientation to the flow) of the wing and the speedat which it flies, Vo , as well as other parameters, including the density, ½; viscosity, ¹; and speed ofsound, a, of the air. The following sections discuss some properties of airfoils andwings.

36.1 NomenclatureThe shape, size, and orientation of an airfoil can be given in terms of the following parameters(Fig. 36.2): the chord length, c, the chord line that connects the leading and trailing edges; theangle of attack, ®, relative to the free stream velocity, Vo ; the mean camber line that is halfwaybetween the upper and lower surfaces; and the thickness distribution, t, which is the distancebetween the upper and lower surfaces perpendicular to the camber line.

Various classes of airfoils have been developed over the years. These include the classicNational Advisory Committee for Aeronautics four-, five-, and six-digit series airfoils (forexample, the NACA 2412 airfoil used on the Cessna 150 or the NACA 64A109 used on the GatesLearjet [Anderson, 1991]) as well as numerous other modern airfoils [Hubin, 1992].

Performance characteristics of wings are normally given in terms of the dimensionless liftcoefficient and drag coefficient,


Figure 36.2 Airfoil geometry.

Figure 36.1 Wing geometry.

Figure 36.3 Typical lift and drag coefficients as a function of angle of attack.


CL =L

qoS(36:1)

CD =D

qoS(36:2)

where qo = 12½V 2

o is the dynamic pressure and S is the planform area of the wing. The planformarea is the area seen by looking onto the wing from above: the span times the chord for arectangular wing. Typical characteristics for lift and drag coefficients as a function of the angle ofattack are shown in Fig. 36.3. An efficient wing has a large lift-to-drag ratiothat is, a largeCL=CD .

FLYING MACHINE

Orville & Wilbur WrightPatented May 22, 1906#821,393An excerpt:

Our invention relates to that class of flying-machines in which the weight is sustained by thereactions resulting when one or more aeroplanes are moved through the air edgewise at a smallangle of incidence, either by the application of mechanical power or by the utilization of the forceof gravity.

The objects of our invention are to provide means for maintaining or restoring the equilibrium orlateral balance of the apparatus, to provide means for guiding the machine both vertically andhorizontally, and to provide a structure combining lightness, strength, convenience of construction,and certain other advantages which hereinafter appear.The Wrights became interested in flight after reading of successful glider flights in Germany. They builtand flew three glider bi-planes before attempting their unassisted powered flight at Kitty Hawk, N.Carolina in 1903. The U.S. Army was interested in powered flight and eventually awarded the Wrights acontract for the first military aircraft in 1909. (©1992, DewRay Products, Inc. Used withpermission.)


36.2 Airfoil ShapesAs shown in Fig. 36.4, typical airfoil shapes have changed over the years in response to changes inflight requirements and because of increased knowledge of flow properties. Early airplanes usedthin airfoils (maximum thickness 6 to 8% of the chord length), with only slight camber [Fig.36.4(a)]. Subsequently, thicker (12 to 18% maximum thickness) airfoils were developed and usedsuccessfully on a variety of low-speed aircraft [Fig. 36.4(b) and (c)].

Figure 36.4 Various airfoil shapes.

As the angle of attack is increased from small values, the lift coefficient increases nearly linearlywith ®. At larger angles there is a sudden decrease in lift and a large increase in drag. Thiscondition indicates that the wing has stalled. The airflow has separated from the upper surface, andan area of reverse flow exists (Fig. 36.3). Stall is a manifestation of boundary layer separation.This complex phenomenon is a result of viscous effects within a thin air layer (the boundary layer)near the upper surface of the wing in which viscous effects are important [Schlichting, 1979].

In addition to knowing the lift and drag for an airfoil, it is often necessary to know the locationwhere these forces act. This location, the center of pressure, is important in determining themoments that tend to pitch the nose of the airplane up or down. Such information is often given interms of a moment coefficient,

CM =M

qoSc(36:3)

where M is the moment of the lift and drag forces about some specified point, often the leadingedge.

For a given geometry, the lift and drag coefficients and the center of pressure (or momentcoefficient) may depend on the flight speed and properties of the air. This dependence can becharacterized in terms of the Reynolds number based on chord length, Re = ½Voc=¹ , and theMach number, Ma = Vo=a . For modern commercial aircraft the Reynolds number is typically onthe order of millions (106) . Mach numbers range from less than 1 (subsonic flight) to greater than1 (supersonic flight).


36.3 Lift and Drag Characteristics for AirfoilsLift and drag forces on airfoils are the result of pressure and viscous forces that the air imposes onthe airfoil surfaces. Pressure is the dominant factor that produces lift. A typical pressuredistribution is shown in Fig. 36.5. In simplistic terms, the air travels faster over the upper surfacethan it does over the lower surface. Hence, from Bernoulli's principle for steady flow, thepressure on the upper surface is lower than that on the bottom surface.

Figure 36.5 Typical pressure distribution on an airfoil.

For an unstalled airfoil, most of the drag is due to viscous forces. This skin friction drag is aresult of the shear stress distribution on the airfoil. For a stalled airfoil, pressure forces contributesignificantly to the drag.

For a two-dimensional body such as an airfoil (a wing of infinite span), the section lift, drag, andmoment coefficients (about a defined point) are based on the lift, drag, and moment per unit span,L0 [force=length ] , D0 [force=length ] , and M 0 [force ¢ length=length ] , respectively. Thatis,

A relatively recent development (c. 1970s) has been design and construction of laminar flowairfoils that have smaller drag than previously obtainable [Fig. 36.4(d)]. This has resulted fromnew airfoil shapes and smooth surface construction that allow the flow over most of the airfoil toremain laminar rather than become turbulent. The performance of such airfoils can be quitesensitive to surface roughness (e.g., insects, ice, and rain) and Reynolds numbereffects.

With the advent of commercial and business jet aircraft, it became necessary to develop airfoilsthat operate properly at Mach numbers close to unity. Since air, in general, accelerates as it passesaround an airfoil, the flow may be locally supersonic near portions of the upper surface, eventhough the flight speed is subsonic. Such supersonic flow can cause shock waves (discontinuitiesin the flow) that degrade airfoil performance. Airfoils have been developed (denoted supercriticalairfoils) to minimize the effect of the shock wave in this locally supersonic region [Fig. 36.4(e)].

Certain flow phenomena, such as shock waves, occur in supersonic flight that do not occur forsubsonic flight [Anderson, 1991]. The result is that supersonic airfoils tend to be thinner andsharper than those for subsonic flight [see Fig. 36.4(f)].


cl =L0

qoc(36:4)

cd =D0

qoc(36:5)

cm =M 0

qoc2(36:6)

For most airfoils, the lift coefficient is nearly linear with angle of attack up to the stall angle.According to simple airfoil theory [and verified by experiment (Fig. 36.6)], the lift-curve slope,dcl=d® , is approximately equal to 2¼ with ® in radians (or dcl=d® = 0:1096 deg¡1 when ® is indegrees) [Anderson, 1991].

Figure 36.6 Effect of camber on airfoil lift coefficient.

For symmetrical (no camber) airfoils, zero angle of attack produces zero lift; for airfoils withcamber, the zero-lift condition (® = ®0L ) occurs at nonzero angle of attack (Fig. 36.6).

The maximum lift coefficient for an airfoil (cl = cl;max ) is typically on the order of unity andoccurs at the critical angle of attack (® = ®CR ) (Fig. 36.3). That is, the lift generated per unit spanis on the order of the dynamic pressure times the planform area: L0 = clqoc ¼ q0c . The drag


coefficient, on the other hand, is on the order of 0.01. Hence, the maximum lift-to-drag ratio is onthe order of 100.

As illustrated in Fig. 36.7, the airfoil geometry may be altered by using movable trailing orleading edge flaps. Such devices can significantly improve low-speed (i.e., landing or takeoff)performance by increasing the maximum lift coefficient, thereby reducing the required landing ortakeoff speed.

Figure 36.7 Effect of flaps on airfoil lift coefficient.

All wings have a finite span, b , with two wing tips. The flow near the tips can greatly influence the

36.4 Lift and Drag of Wings

flow characteristics over the entire wing. Hence, a wing has different lift and drag coefficients thanthose for the corresponding airfoil. That is, the lift and drag coefficients for a wing are a functionof the aspect ratio, AR = b2=S . For a wing of rectangular planform (i.e., constant chord), theaspect ratio is simply b=c .

Because of the pressure difference between the lower and upper surfaces of a wing, the air tendsto "leak" around the wing tips (bottom to top) and produce a swirling flowthe trailing or wing tipvortices shown in Fig. 36.8. This swirl interacts with the flow over the entire length of the wing,thereby affecting its lift and drag. The trailing vortices create a flow that makes it appear as thoughthe wing were flying at an angle of attack different from the actual angle. This effect producesadditional drag termed the induced drag.


As shown by theory and experiment [Anderson, 1991], the larger the aspect ratio is, the largerthe lift coefficient is and the smaller the drag coefficient is (Fig. 36.9). A wing with an infiniteaspect ratio would have the properties of its airfoil section. Very efficient flyers (i.e., soaring birdsand sailplanes) have long, slender (large AR) wings.

Figure 36.8 Trailing vortex

Figure 36.9 Lift coefficient as a function

For many wings the chord length decreases from the wing root (next to the aircraft body) to thewing tip. In addition, the shape of the airfoil section may change from root to tip, as may the localangle of attack (i.e., the wing may have some "twist" to it).

Figure 36.10 Various wing planforms.of aspect ratio.


Although wind tunnel tests of model airfoils and wings still provide valuable (and sometimesunexpected) information, modern computational fluid dynamic (CFD) techniques are widely used.Techniques involving paneling methods, finite elements, boundary elements, finite differences, andviscous-inviscid interaction are among the powerful tools currently available to the aerodynamicist[Moran, 1984].

Defining Terms

Airfoil: The cross section of a wing, front to back.Angle of attack: The angle between a line connecting the leading and trailing edges of an airfoil

and the free stream velocity.Bernoulli's principle: Conservation of energy principle that states that an increase in flow speed

is accompanied by a decrease in pressure and vice-versa.Camber: Maximum distance between the chord line and the camber line.Center of pressure: Point of application of the lift and drag forces.Chord: Distance between the leading and trailing edges of an airfoil.Dynamic pressure: Pressure increase resulting from the conversion of kinetic energy into

pressure.Flaps: Leading and trailing edge devices used to modify the geometry of an

airfoil.Lift and drag coefficients: Lift and drag made dimensionless by dynamic pressure and wing

area.Moment coefficient: Pitching moment made dimensionless by dynamic pressure, wing area, and

chord length.Planform: Shape of a wing as viewed from directly above it.Span: Distance between the tips of a wing.Stall: Sudden decrease in lift as angle of attack is increased to the point where flow separation

occurs.

References

Anderson, J. D. 1990. Modern Compressible Flow with Historical Perspective, 2nd ed.McGraw-Hill, New York.

Anderson, J. D. 1991. Fundamentals of Aerodynamics, 2nd ed. McGraw-Hill, New York.Hubin, W. N. 1992. The Science of Flight: Pilot Oriented Aerodynamics. Iowa State University

Press, Ames, IA.Moran, J. 1984. An Introduction to Theoretical and Computational Aerodynamics. John Wiley

& Sons, New York.Schlichting, H. 1979. Boundary Layer Theory, 7th ed. McGraw-Hill, New York.

Further Information

Abbott, I. H. and van Doenhoff, A. E. 1949. Theory of Wing Sections. McGraw-Hill, New York.Anderson, D. A., Tannehill, J. C., and Pletcher, R. H. 1984. Computational Fluid Mechanics and

Heat Transfer. Hemisphere, New York.Anderson, J. D. 1985. Introduction to Flight, 2nd ed. McGraw-Hill, New York.

Many modern high-speed wings are swept back with a V-shaped planform; others are deltawings with a triangular planform (Fig. 36.10). Such designs take advantage of characteristicsassociated with high-speed compressible flow [Anderson, 1990].


Documents

Airfoil & wings