AerodynamicsME-438

Spring’16ME@DSU

Dr. Bilal A. Siddiqui

Airfoils• An airfoil is the shape of a wing, blade or sail as seen in

cross-section.• Subsonic flight airfoils have a rounded leading edge,

sharp trailing edge, with curved upper and lower surfaces which may not be symmetric

• Supersonic airfoils have sharp leading edge, sharp trailing edge and are often symmetric.

• Transonic airfoils are similar to subsonic airfoils but have a rather flat upper surface.

• Reasons for these changes will become apparent later.• Airfoil choice/design is critical to flight performance…and

by no means trivial.

From top to bottom:• Laminar flow airfoil for a RC park flyer• Laminar flow airfoil for a RC pylon racer• Laminar flow airfoil for a manned prop• Laminar flow at a jet airliner airfoil• Stable airfoil used for flying wings• Aft loaded airfoil allowing for a large main spar and late stall• Transonic supercritical airfoil• Supersonic leading edge airfoil

Black = laminar flow,red = turbulent flow,grey = subsonic stream,blue = supersonic flow volume

Airfoil Evolution

Plan of Study

Airfoil NACA Nomenclature

NACA= National Advisory Committee for Aeronautics was the name of the government agency founded in 1915, later transformed into NASA in 1958

Some airfoil definitions

• Mean camber line is the locus of points halfway between the upper and lower surfaces as measured perpendicular to the mean camber line.

• Forward & rearward points of mean camber line are leading and trailing edges.• Straight line connecting leading and trailing edges is chord line c of airfoil.• Camber is the maximum distance between the mean camber line and the chord

line, measured perpendicular to the chord line. • Thickness is the distance between the upper and lower surfaces, also measured

perpendicular to the chord line.• The shape of the airfoil at the leading edge is usually circular, with a leading-edge

radius of approximately 0.02c.• Angle of attack, lift and drag directions are defined w.r.t. the chord.

NACA Airfoil Numbering – 4 series NACA airfoils

• NACA identified different airfoil shapes with a logical numbering system.• The first family of NACA airfoils, developed in 1930s, was the “four-digit” series, e.g. NACA 2412 airfoil.• 1st digit is the maximum camber in hundredths of chord• 2nd digit is the location p of maximum camber m along the chord from the leading edge in tenths of

chord.• Last two digits give the maximum thickness in hundredths of chord. • For NACA 2412 airfoil, the maximum camber is m=0.02c located at p=0.4c from the leading edge, and

the maximum thickness is t=0.12c. • Or, m/c=2% camber at p/c=40% chord, with t/c=12% thickness. • An airfoil with no camber, (camber line coincides chord line) is called a symmetric airfoil. • NACA 0012 airfoil is a symmetric airfoil with a maximum thickness of 12 percent.

NACA 4-series airfoil

Generating NACA 4-series Airfoils• It is easy to think of the airfoil as being defined by

• The camber line ().• Symmetric distribution of half thickness () perpendicular to camber line.

• Thickness needs to be applied perpendicular to the camber line, coordinates of upper/lower surfaces become

Plot of a NACA 2412 foil. The camber line is shown in red, and the thickness – or the symmetrical airfoil 0012 – is shown in purple.

Generating NACA 4-series airfoils• Leading edge radius is given by • The NACA 4-series is defined by the following equations. • Let be the half thickness at a given chord station

• The mean camber line is given by

NACA 4415 used on a number of UAVs

AAI Shadow 400

AAI Shadow 200

AAI RQ-2

NACA 5-series Airfoils• The second family of NACA airfoils was the 5-series, e.g. NACA 23015.• For more complex airfoil shapes. • 1st digit when multiplied by 1.5 gives the design lift coefficient in tenths• 2nd and 3rd digits when multiplied by 0.5 give the location of maximum

camber along the chord from the leading edge in hundredths of chord• Final two digits give the maximum thickness in hundredths of chord. • For the NACA 23012 airfoil, the design lift coefficient is cl,des=0.3, the

location of maximum camber is at p=0.15c, and the airfoil has t/c=12% maximum thickness.

Aero Commander 200 uses NACA 23015

Design lift coefficient is lift coefficient for the airfoil when the slope of the camber line at the leading edge is parallel to the freestream.

Generating the 5-series airfoils• The camber line is given by

Where m and k1 depend on the 2nd and 3rd digit of the airfoil series.

• Having calculated the camber line, the thickness distribution, calculation of the airfoil envelope and plotting of coordinates is done in the same way as the NACA 4 digit airfoils.

2nd and 3rd Digits Camber position(%) m K1

10 5 0.0580 361.40020 10 0.1260 51.64030 15 0.2025 15.95740 20 0.2900 6.643

NACA 6-series airfoils• One of the most widely used family of NACA airfoils is the 6-series laminar

flow airfoils, developed during World War II, e.g. NACA 65-215.• 1st digit identifies the series• 2nd gives the location of minimum pressure in tenths of chord from the

leading edge• 3rd digit is the design lift coefficient in tenths• Last two digits give the maximum thickness in hundredths of chord. • For NACA 65-215 airfoil, the 6 is the series designation, the minimum

pressure occurs at 0.5c, the design lift coefficient is 0.2, and the airfoil is 15 percent thick.

NACA 65-215

Abaris Golden Arrow uses NACA 65-215

Other airfoils• NACA/NASA has other airfoil series as well: 7-series, 8-series, S-series etc.• Eppler airfoils, based on Prof. Eppler’s famous inverse design code are also

very efficient and widely used airfoils, e.g. E 1098• Many of the large aircraft companies today design their own special-purpose

airfoils.• Clark-Y is a very popular general purpose airfoil.• Boeing 727, 737, 747, 757, 767, and 777 have specially designed Boeing

airfoils.• This is done using potential flow (panel) methods or full Navier Stokes CFD

techniques.

Aerodynamic Characteristics of Airfoils: Lift

Using potential flow, we can predict lift curve slope, but not stall

Aerodynamic Characteristics of NACA 2412

Lift curve slope and moment coefficient in linear range not affected by Re

Drag Characteristics of NACA 2412

Drag consists of pressure and friction components, so partly dependent on Re. Using panel codes, we can predict the pressure drag to some accuracy.

An exampleConsider an NACA 2412 airfoil with a chord of 0.64 m in an airstream at standard sea level conditions. The freestream velocity is 70 m/s. The lift per unit span is 1254 N/m.• Calculate the angle of attack and the drag per unit span.• Calculate the moment per unit span about the aerodynamic center.• Calculate and compare the lift-to-drag ratios at angles of attack of 0,

4, 8, and 12 degrees. The Reynolds number is 3.1 × 106.