1. January 2011
Basics of Aerofoil
Rajesh Kumar
EDC-Fans
Bap Ranipet
BHEL
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2. History:
The serious work on the development of airfoil sections began in the late 1800's.
It was known that flat plates would produce lift when set at an angle of incidence, some suspected that shapes
with curvature, that more closely resembled bird wings would produce more lift or do so more efficiently.
H.F. Phillips patented a series of airfoil shapes in 1884 after testing them in wind tunnels (artificial currents of
air produced from induction by a steam jet in a wooden conduit)
Octave Chanute writes in 1893, "...it seems very desirable that further scientific experiments be made on
concavo-convex surfaces of varying shapes, for it is not impossible that the difference between success and failure of
a proposed flying machine will depend upon the sustaining effect between a plane surface and one properly curved
to get a maximum of 'lift'.”
Otto Lilienthal, in 1894, after measuring the shapes of bird wings, tested the airfoils on a 7m diameter
"whirling machine". He believed that the key to successful flight was wing curvature or camber. He also
experimented with different nose radii and thickness distributions .
Wright Brothers aerofoil closely resembled Lilienthal's sections: thin and highly cambered. (This was possible
because early tests of airfoil sections were done at extremely low Reynolds number, where thin and cambered
sections behave better than thicker ones.)
Some of the first airplanes (Wright Brothers Flyer) were biplanes reason being erroneous belief that efficient
airfoils must be thin and highly cambered. A biplane is a fixed-wing aircraft with two main wings. A biplane wing
structure has a structural advantage, but produces more drag than a similar monoplane wing. It become obsolete
by the late 1930s.
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3. A wide range of airfoils developed
A family of sections used and tested by the NACA in the early 1920's
Eastman Jacobs, in 1939, at the NACA in Langley, designed and tested the first laminar flow airfoil section
having extremely low drag and a high lift to drag ratio of about 300.
The reasons airfoils looks quite different from one another is that the flow conditions and design goals changes
from one application to the next.
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4. The Reynolds number Re is a dimensionless number which gives a measure of the ratio of inertial forces to
viscous forces and quantifies the relative importance of these two types of forces for given flow conditions.
It is used to characterize different flow regimes, as laminar or turbulent flow:
laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by
smooth, constant fluid motion while turbulent flow occurs at high Reynolds numbers and is dominated by
inertial forces, which tend to produce random, erratic, chaotic eddies, vortices and other flow .
At very low Reynolds numbers (<10,000 based on chord length) efficient airfoil sections looks peculiar as the
sketch of a dragonfly wing.
The Eppler 193 is a good section for model airplanes.
The Lissaman 7769 was designed for human-powered aircraft.
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5. The various terms related to airfoils are defined below:
1. The mean camber line is the locus of points midway between the upper and lower surfaces.
2. The chord line is a straight line connecting the leading and trailing edges of the airfoil, at the ends of the
mean camber line.
3. The chord is the length of the chord line and is the characteristic dimension of the airfoil section.
4. The maximum thickness and the location of maximum thickness are expressed as a percentage of the chord.
5. For symmetrical airfoils both mean camber line and chord line pass from centre of gravity of the airfoil and
they touch at leading and trailing edge of the airfoil.
6. The aerodynamic centre is the chord wise length about which the pitching moment is independent of the lift
coefficient and the angle of attack.
7. The centre of pressure is the chord wise location about which the pitching moment is zero.
8. The aspect ratio is defined as the span-to-mean-chord ratio of an airfoil. The aspect ratio of a wing is the
length of the wing compared with the breadth (chord) of the wing. A high aspect ratio indicates long,
narrow wings, whereas a low aspect ratio indicates short, stubby wings. For most wings, the length of the
chord varies along the wing so the aspect ratio (AR) is defined as the square of the wingspan divided by the
area of the wing platform i.e. AR=b2/S; where, b is the wingspan, and S is the area of the wing platform.
9. The solidity ratio is defined as the sum of tip widths divided by the fan circumference. Solidity is Measure of
a fan’s pressure capability.
10. The stall point is the fan operating condition where the boundary layer of air separates from the airfoil and
causes turbulence.
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6. Airfoil Geometry
Airfoil geometry can be characterized by the coordinates of the upper and lower surface.
One can generate a reasonable airfoil section given these parameters:
Chord length,
maximum thickness,
maximum camber,
position of max thickness,
position of max camber,
and nose radius
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7. NACA aerofoil (Eastman Jacobs)
The NACA 4 digit and 5 digit airfoils were created by superimposing a simple mean line shape with a thickness
distribution that was obtained by fitting a couple of popular airfoils of the time:
y = (t/0.2) * (.2969*x0.5 - .126*x - .3537*x2 + .2843*x3 - .1015*x4)
The camber line of 4-digit sections was defined as a parabola from the leading edge to the position of maximum
camber, then another parabola back to the trailing edge.
4 4 12
Max camber in % chord Position of maximum Maximum thickness in % of chord
camber in 1/10 of chord
NACA 4412
2 30 12
Approx Max camber in Position of maximum Maximum thickness in % of
% chord camber in 2/100 of chord chord
NACA 23012
NACA 5 – digit sections had the same thickness distribution, but used a camber line with more curvature near
the nose.
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8. The 6-series of NACA airfoil sections were generated
1. from a more or less prescribed pressure distribution and
2. were meant to achieve some laminar flow.
6 3 2 2 12
Six series Location of minimum Half width of low drag Ideal CL in Max thickness in
Cp in 1/10 of chord bucket in 1/10 of CL tenths % of chord
After the six-series sections,
1. airfoil design became much more specialized
2. particular application specific
3. these sections form basis of several airfoil sections and then the entire geometry is modified based on
its 3-D characteristics.
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9. Airfoil Pressure Distributions and Performance
The aerodynamic performance depends on the distribution of pressure over the airfoil.
This distribution is expressed in terms of the pressure coefficient which is the difference between local static
pressure and free stream static pressure, non-dimensionalized by the free stream dynamic pressure.
Cp = (P-P∞)/(1/2 ρU2∞)
Plot Cp vs. x/c:
x/c varies from 0 at the leading edge to 1.0 at the trailing edge.
1. Stagnation Point : The stagnation point occurs near the leading edge.
It is the place at which V = 0,
In incompressible flow Cp = 1.0,
In compressible flow it may be somewhat larger.
2. The upper surface pressure is lower than the lower surface in this case. But it doesn't have to be always.
3. The lower surface sometimes carries a positive pressure, and pulls the wing downward (near the mid-chord).
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10. 4. The region of the pressure distribution is called the pressure recovery region or region of adverse pressure
gradient. The pressure increases from its minimum value to the value at the trailing edge.
5. Adverse pressure gradient is associated with boundary layer transition and separation, if the gradient is too
severe.
6. The pressure at the trailing edge is related to the airfoil thickness and shape near the trailing edge. For
infinitely thin sections Cp = 0 at the trailing edge.
7. Large positive values of Cp at the trailing edge imply more severe adverse pressure gradients.
severity of the adverse pressure gradient.
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11. Effect of pressure on flow:
• For equilibrium we must have a pressure gradient when the flow is curved
• The pressure must increase as we move further from the surface (negative Cp)
• Depends on angle of attack and aerofoil shape
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12. Effects of changes in camber, leading edge radius, trailing edge angle, and local distortions in the airfoil surface.
Cp vs. x/c plots 2
1
4
3
5 1. Reduced camber at aft/rear section pushing the
surface downward
2. Sharp nose leads to favourable gradients over 50% of
the section
3. A thicker section will have a less prominent peak
(pressure peak near the nose)
4. Only one line because at zero lift (symmetric upper
6 and lower section with 00 attack), the upper and lower
surface pressure coincide.
5. A conventional cambered section.
6. An aft-loaded section, the opposite of a reflexed
airfoil carries more lift over the aft part of the airfoil.
Supercritical airfoil sections look like this.
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13. Airfoil Design
Airfoils may be designed to produce
1. low drag without generating any lift
2. low drag while producing a given amount of lift
3. very high lift to drag ratio
4. maximum lift and drag doesn't really matter
To achieve any of these, constraints may apply on
1. thickness, or
2. stagger angle, or
3. pitching moment, or
4. off-design performance, or
5. stall characteristics, etc.
1. pitch chord ratio/ solidity, or
2. blade spacing, or
Design Approach
1. Design by authority
2. Use of an already designed airfoil
3. Works well if the goals of a particular design problem matches with the goals of the original airfoil design
4. The availability of the test data ensures, with the available tools now airfoil section can be designed with
accurate predictability without testing
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14. Methods for airfoil design
Direct design
Inverse design
Direct Methods involve
A specified section geometry (such as a NACA airfoil)
Ready calculation methods for pressures and performance
Evaluation based on given shape
Identifying the problems in the performance characteristics
Modification of the shape to improve the performance
The two main problems of direct methods are
1. The identification of the problems in performance
2. Shape optimization for improved performance
Inverse Design Methods involve
The objective function as the target pressure distribution or the least squares difference between the
actual and target Cp
Changing the airfoil shape to improve the performance.
This may be done in several ways:
1. By hand, using knowledge of the effects of geometry changes on Cp and Cp changes on
performance.
2. By numerical optimization, using shape functions to represent the airfoil geometry and letting
the computer decide on the sequence of modifications needed to improve the design. 14

15. Typical Problems
1. Thick Airfoil Design
The minimum pressure decreases due to thickness
A more severe adverse pressure gradient and the need to start recovery sooner
The section with maximum thickness must recover pressure with almost steepest possible gradient
This problem addressed by Liebeck in connection with maximum lift
The thickest possible section has a boundary layer just on the verge of separation throughout the recovery
2. High Lift Airfoil Design
Requires large negative pressures on the upper surface of the airfoil. The limit to this suction is associated with
i. compressibility effects, and
ii. the boundary layer to be capable enough of negotiating the resulting adverse pressure recovery.
For maximum lift, it is best to keep the boundary layer on the verge of separation
For maximum airfoil lift, the best recovery location is chosen and the airfoil is made very thin so that the lower
surface produces maximum lift as well. (Since the upper surface Cp is specified, increasing thickness only reduces
the lower surface pressures.)
3. Laminar Airfoil
Useful for reducing skin friction drag, increasing maximum lift, or reducing heat transfer.
At low Reynolds numbers it is achieved by maintaining a smooth surface and using an airfoil with a favourable
pressure gradient.
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16. Typical Problems
4. Transonic Airfoil Design
Severe instability can occur at transonic speeds. Shock waves move through the air at the speed of sound. When
an object also moves at the speed of sound, these shock waves build up in front of it to form a single, very
large shock wave. During transonic flight, the body must pass through this large shock wave, as well as cope
up with the instability caused by air moving faster than sound over parts of the wing and slower in other
parts.
Objective is to limit shock drag losses at a given transonic speed.
Since both lift and thickness reduce (increase in magnitude) the minimum Cp, the transonic design problem is to
create an airfoil section with high lift and/or thickness without causing strong shock wave.
Supercritical airfoil are designed to operate efficiently with substantial regions of supersonic flow. But the
maximum local Mach numbers should not exceed about 1.2 to 1.3 on a well-designed supercritical airfoil.
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17. Mach number, Ma
It is the speed of an object moving through air, or any other fluid media, divided by the speed of sound in that
medium at that particular condition of temperature and pressure.
Ma=V/Vs
where, Ma is the Mach number
V is the relative velocity of the source to the medium and
Vs is the speed of sound in the medium
At Standard Sea Level conditions (150C temperature), the speed of sound is 340.3 m/s in the Earth's atmosphere.
High-speed flow around objects
High-
Regime Subsonic Transonic Sonic Supersonic Hypersonic
hypersonic
Mach No, Ma <1.0 0.8–1.2 1.0 1.2–5.0 5.0–10.0 >10.0
When an aircraft exceeds Mach 1 (i.e. the sound barrier) a large pressure difference is created just in front of the
aircraft, called a shock wave. This spreads backward and outward from the aircraft in a cone shape (called as a
Mach cone). It causes the sonic boom as heard when fast moving aircraft travels overhead.
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18. Mach number, Ma
High-
Regime Subsonic Transonic Sonic Supersonic Hypersonic
hypersonic
Mach No, Ma <1.0 0.8–1.2 1.0 1.2–5.0 5.0–10.0 >10.0
in a subsonic compressible flow
in a supersonic compressible flow
where, M is Mach number
is impact pressure and
P is static pressure and
γ is the ratio of specific heat of a gas at a constant pressure to that at constant volume (1.4 for air)
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19. Typical Problems
5. Low Reynolds Number Airfoil Design
Too much laminar flow
Restricted severe pressure gradients and maximum lift capability
The boundary layer is much less capable of handling an adverse pressure gradient without separation
Laminar separation bubbles are common can lead to excessive drag and low maximum lift
6. Multiple Design Point Airfoils
One of the difficulties in designing a good airfoil is the requirement for acceptable off-design performance.
Low drag section must perform well without separation at an angle of attack slightly away from its design
point.
Airfoils with high lift capability may perform poorly at lower angles of attack.
To overcome these one can design the upper and lower surface of the section to satisfy separate design point
operation. Often it is clear that the upper surface will be critical at one of the points and we can design the upper
surface at this condition. The lower surface can then be designed to make the section behave properly at the
second point.
Variable geometry can be employed (at some expense) as in the case of high lift systems.
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