1. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
Chapter 5
Airfoils
Prof. Galal Bahgat Salem Aerospace Dept. Cairo University

2. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
Introduction
In this chapter the following will be studied:
1- Geometric characteristics of the airfoils.
2- Aerodynamic characteristics of the airfoils.
3- Flow similarity ( Dynamic similarity )
■ Airfoil Geometric Characteristics
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4. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
Airfoil geometric characteristics include:
1- Mean camber line : The locus of points halfway between
the upper and lower surfaces as measured perpendicular
to the mean camber line.
2- Leading & trailing edges: The most forward and rearward
points of the mean camber line.
3- Chord line: The straight line connecting the leading and
trailing edges.
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5. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
4- Chord C : The distance from the leading to trailing edge
measured along the chord line.
5- Camber : The maximum distance between the mean
camber line and the chord line.
6- Leading edge radius and its shape through the leading
edge.
7- The thickness distribution: The distance from the upper
surface to the lower surface, measured perpendicular
to chord line
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6. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
►Airfoil Families (Series)
# NACA (National Advisory Committee for Aeronautics) or
NASA (National Aeronautics and Space administration)
identified different airfoil shapes with a logical numbering
system.
# Abbott & Von Doenhoff “ Theory of Wing Sections” includes a summary of airfoil data ( geometric and aerodynamic data )
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7. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
■NACA Airfoil Series
1- NACA 4-digit series
2- NACA 5-digit series
3- NACA 1-series or 16-series
4- NACA 6- series
5- NACA 7- series
6- NACA 8- series
Prof. Galal Bahgat Salem Aerospace Dept. Cairo University

8. ►NACA Four-Digit Series Example: NACA 2412 NACA 2 4 12
Maximum thickness (t ) in percentage of chord (t/c)max = 0.12
Camber in percentage of chord
yc = 0.02 C
Position of camber in tenths of chord xc = 0.4 C xc yc C
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10. ►NACA Five-Digit Series Example: NACA 23012 NACA 2 30 12
When multiplied by 3/2 yields the design lift coefficient Cl in tenths.
Cl = 0.3
When divided by 2, gives the position of the camber in percent of chord xc = 0.15 C
Maximum thickness (t ) in percentage of chord (t/c)max = 0.12
Prof. Galal Bahgat Salem Aerospace Dept. Cairo University

11. ►Note that this is the series of laminar airfoils .
►NACA Six- Series
Example: NACA
NACA
Location of minimum pressure in tenths of chord (0.4 C)
Maximum thickness (t ) in percentage of chord (t/c)max = 0.12
Series designation 6
Design lift coefficient in tenths (0.2)
►Note that this is the series of laminar airfoils .
Comparison of conventional and laminar flow airfoils
is shown in the following Figure.
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Pressure distribution
On upper surface
Conventional Airfoil
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Pressure distribution
On upper surface
Laminar Airfoil
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The Handbook “Theory of Wing Sections” gives the shape of airfoils in terms of upper and lower surfaces station and ordinate as given in the following Tables.
Airfoils can be drawn using these Tables.
From airfoil drawing we can extract its geometric data:
- camber line
- maximum camber ratio and its position
- maximum thickness ratio and its position
-leading edge radius
-trailing edge angle
Assignment 1 : Meaning of numbering system for NACA 1-series, NACA 7-Series, and NACA 8- Series.
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Tabe for NACA 2410, 2412, 2415
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■Center of Pressure and Aerodynamic Center
# Center or pressure : The point of intersection between the chord line and the line of action of the resultant aerodynamic force R.
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# In addition to lift and drag, the surface pressure and shear stress distribution create a moment M which tends to rotate the wing.
# Moment on Airfoil
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Neglect shear stress
F1 is the resultant pressure force on the upper surface.
F2 is the resultant pressure force on the lower surface.
Points 1 & 2 are the points of action of F1 & F2 .
R is resultant force of F1 & F2 .
F1 ≠ F2 because the pressure distribution on the upper surface differs from the pressure distribution on the lower surface.
Thus, F1 & F2 will create an aerodynamic moment M which will tend to rotate the airfoil.
The value of M depends on the point about which we choose to take moment.
For subsonic airfoils it is common to take moments about the quarter-chord point. It is denoted by Mc/4 .
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Mc/4 is function of angle of attack α, i.e. its value depends on α .
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20. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
■ Aerodynamic Center
≠ Aerodynamic center: The point on the chord line about which moments does not vary with α.
●The moment about the aerodynamic center (ac) is designated Mac .
● By definition, Mac = constant
● For low-speed and subsonic airfoils, ac is generally very close to the quarter-chord point
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■Lift, Drag, and Moment Coefficients
For an airplane in flight, L, D, and M depend on:
1- Angle of attack α
2- Free-stream velocity V∞
3- Free-stream density ρ∞ , that is, altitude
4- Viscosity coefficient µ∞
5- Compressibility of the airflow which is governed by
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Mach number M∞ = V∞/a∞. Since V∞ is listed above, we can designate a∞ as our index for compressibility.
6- Size of the aerodynamic surface. For airplane we use the plan form wing area S to indicate size.
7- Shape of the airfoil.
● Hence, for a given shape of airfoil, we can write:
L = f1( α, V∞, ρ∞, µ∞ , a∞, S )
D = f2( α, V∞, ρ∞, µ∞ , a∞, S )
M = f3( α, V∞, ρ∞, µ∞ , a∞, S )
●The variation of L with (α, V∞, ρ∞, µ∞ , a∞, S) taking one at a time with the others constant could be obtained by experiment in a wind tunnel .
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(α, ρ∞, µ∞ , a∞, S)
(α, V∞, µ∞ , a∞, S) L
(V∞, ρ∞, µ∞ , a∞, S) L
= const
= const L
= const 1 2 3 V∞ α ρ∞
(α, V∞, ρ∞, a∞, S)
(α, V∞, ρ∞, µ∞, S)
(α, V∞, ρ∞, µ∞, a∞)
= const
= const L L L
= const 4 5 6 µ∞ S a∞
Therefore, 6 experiments are required for each dependent variable.
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24. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
● Then by cross plotting that data obtained, we could be able to get a precise functional relation for L, D, and M.
● This is the hard way which could be very time consuming and costly.
●Instead, we can use the theory of dimensional analysis.
●This theory can reduce time, effort, and cost by grouping α, V∞, ρ∞, µ∞ , a∞, S , and L or D or M into a fewer number of non-dimensional parameters.
●The results of this theory are:
CL= f1 (α,, M∞, Re)
CD = f2 (α,, M∞, Re)
CM = f3 (α,, M∞, Re)
-where CL = L/ q∞S = Lift coefficient
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- CD = D/ q∞S = Drag coefficient
- CM= M/ q∞S C = Moment coefficient
and q∞ = ½ ρ∞ V2∞ , C = Airfoil chord
Dynamic similarity parameters
- Re = ρ∞ V∞ C/μ∞ = Reynolds number
- M∞ = V∞ / a∞ = Mach number
►Note :
1- For airfoil ( 2D flow ) S = C x 1
2- CL cl , L l
3- CD cd , D d
4- CM cm , M m
Per unit span
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■ Airfoil Data
● A goal of theoretical aerodynamics is to predict values of cl, cd, and cm from the basic equations and concepts of physical science.
● However, simplifying assumptions are usually necessary to make the mathematics tractable.
● Therefore, when theoretical results are obtained, they are generally not “exact”.
● As a result we have to rely on experimental measurements.
● cl, cd, and cm were measured by NACA for large number of airfoils in low-speed wind tunnels.
● At low-speed the effect of M∞ is cancelled.
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●These measurements were carried out on straight, constant-chord wings completely spanned the tunnel test section from one side to the other.
● In this fashion, the flow essentially “ saw” a wing with no wing tips, and the experimental airfoil data were obtained for “infinite wings”
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● Results of airfoil measurements include cl, cd, cm,c/4, and cm,ac.
● The results are given in the form of graphs as follows:
- The 1st page of graph gives data for cl and cm,c/4 versus
angle of attack for the NACA airfoil.
- The 2nd page of graph gives cd and cm,ac versus cl for
the same airfoil.
Note: Some results of these airfoil data are given in Appendix D ( “Introduction to Flight”, Anderson )
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Example: Airfoil data for NACA 2415
cl and cm,c/4 versus α
NACA 2415
Mach number is not included
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31. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
cd and cm,ac versus cl
NACA 2415
Mach number is not included
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32. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
Mach number is not included
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Mach number is not included
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34. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
►Variation of cl with α
● This variation is shown in the following sketch.
* cl varies linearly with α over a large range of α.
* At α = cl ≠ 0 due to the positive camber.
* cl = 0 at αL=0 ( zero lift direction/zero lift angle of attack)
* For large values of α,the linearity breaks down.
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* As α is increased beyond a certain value; cl reaches to clmax and then drops as α is further increased.
* When cl is rapidly decreasing at high α , the airfoil is stalled.
Separated flow
Flow mechanism associated with stalling
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►Comparison of Lift Curves for Cambered and Symmetric Airfoils
* For symmetric airfoil the lift curve goes through the origin.
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37. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
►The Phenomenon of Airfoil Stall
*It is of critical importance
in airplane design.
*It is caused by flow
separation on the upper
surface of the airfoil due to
high adverse pressure
gradient.
*When separation occurs,
the lift decreases
drastically, and the drag
increases suddenly.
Separated flow
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■Compressibility Correction For Lift & Moment Coefficient
For 0.3 < M∞ ≤ 0.7 , the corrections for cl and cm , using <Prandtl-Glauert rule , are given as:
- cl = cl,0 / √ [1- M∞2]
- cm = cm,0 / √ [1- M∞2]
Where cl,0 is the low-speed value of the lift coefficient,
cm,0 is the low-speed value of the moment coefficient.
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■ Flow Similarity (Dynamic Similarity)
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Consider two different flow fields over two different bodies, as shown in figure.
By definition, different flows are dynamically similar if:
1- The bodies and any other solid boundaries are
geometrically similar for the flow.
2- The dynamic similarity parameters are the same for
flows ( i.e.Re and M∞ are the same for the flows).
# If different flows are dynamically similar, the following results are satisfied:
1- The streamline patterns are geometrically similar.
2- The distribution of v/v∞ , p/p ∞,T/T ∞ ,..etc throughout
the flow field are the same when plotted against
common non-dimensional coordinates.
3- The force and moment coefficients are the same (i.e.
cl, cd, and cm are the same.
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v/v∞
s1/d1 , s2/d2
* Thus we can say that flows over geometrically similar bodies
at the same Mach and Reynolds numbers are dynamically
similar.
Hence, the lift, drag, and moment coefficients will be identical
for the bodies.
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43. Prof. Galal Bahgat Salem Aerospace Dept. Cairo University
►This is the key point in the validity of wind-tunnel testing:
“ If a scale model of a flight vehicle is tested in a wind tunnel, the measured lift, drag, and moment coefficients will be the same as for free flight as long as the Mach and Reynolds numbers of the wind-tunnel test-section flow are the same as for the free-flight case”
# This means that:
[ M∞1 ]model = [ M∞2 ]prototype
[ Re1 ]model = [ Re2 ]prototype
and [ cl1 ]model = [ cl2 ]prototype
[ cd1]model = [ cd2 ]prototype
[ cm1 ]model = [ cm2 ]prototype
Prof. Galal Bahgat Salem Aerospace Dept. Cairo University