ME438 Aerodynamics is offered by Dr. Bilal Siddiqui at DHA Suffa University. This lecture set deals with everything about airfoils.

1. Aerodynamics
ME-438
Spring’16
ME@DSU
Dr. Bilal A. Siddiqui

2. 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.

3. 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

4. Airfoil Evolution

5. Plan of Study

6. 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

7. 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.

8. 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.

9. NACA 4-series airfoil

10. Generating NACA 4-series Airfoils
• It is easy to think of the airfoil as being defined by
• The camber line (𝑦𝑐).
• Symmetric distribution of half thickness (𝑦𝑡) 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.

11. Generating NACA 4-series airfoils
• Leading edge radius is given by 𝑟𝐿𝐸 = 1.1019 𝑡2
• The NACA 4-series is defined by the following equations.
• Let 𝑦𝑡 be the half thickness at a given chord station
• The mean camber line is given by

12. NACA 4415 used on a number of UAVs
AAI Shadow 400
AAI Shadow 200
AAI RQ-2

13. 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.

14. 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 361.400
20 10 0.1260 51.640
30 15 0.2025 15.957
40 20 0.2900 6.643

15. 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

16. 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.

17. Aerodynamic Characteristics of Airfoils: Lift
Using potential flow, we can predict lift curve
slope, but not stall

18. Aerodynamic Characteristics of NACA 2412
Lift curve slope and moment coefficient in
linear range not affected by Re

19. 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.

20. An example
Consider 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.