Pressure Distribution on an Airfoil

Pressure Distribution on an Airfoil
The team conducted the experiment to determine the effects of pressure distribution on lift and pitching moment and the behavior of stall for laminar and turbulent boundary layers in the USNA Closed-Circuit Wing Tunnel (CCWT) with an NACA 65-012 airfoil at a Reynolds number of 1,000,000. The airfoil was tested in a clean configuration at angles of attack of 0, 5, 8, 10, and 12 degrees. Tape added to the leading edge tripped the boundary layer, and pressure distributions were taken at 8, 10, and 12 degrees angle of attack. Experimental results showed a suction peak at less than 1% of chord, providing a beneficial test article for contrast between smooth and laminar boundary layer behavior at the stall condition. The maximum lift coefficient for the clean airfoil was 0.9 at 10 degrees angle of attack, and tripped airfoil reached a maximum lift coefficient of 1.03 at 12 degrees angle of attack, a 14% increase. These data were 10% lower than the empirical airfoil data found in Theory of Wing Sections from Abbott and von Doenhoff. Pitching moment coefficient about the quarter chord remained near zero below stall as expected for a symmetrical airfoil, but rapidly became negative after stall for experimental and empirical data. The airfoil exhibited a leading edge stall for both laminar and turbulent boundary layers.

1. Exercise 3: Pressure Distribution on an Airfoil (Version 2)
25OCT2012







Geoffrey DeSena


United States Naval Academy
Annapolis, Maryland




Midshipman First Class, Aerospace Engineering Department, EA303 Laboratory report
© 2012, Geoffrey S. DeSena.

2. ii
A b s t r a c t
The team conducted the experiment to determine the effects of pressure distribution on lift and
pitching moment and the behavior of stall for laminar and turbulent boundary layers in the USNA
Closed-Circuit Wing Tunnel (CCWT) with an NACA 65-012 airfoil at a Reynolds number of 1,000,000.
The airfoil was tested in a clean configuration at angles of attack of 0, 5, 8, 10, and 12 degrees. Tape
added to the leading edge tripped the boundary layer, and pressure distributions were taken at 8, 10, and
12 degrees angle of attack. Experimental results showed a suction peak at less than 1% of chord,
providing a beneficial test article for contrast between smooth and laminar boundary layer behavior at
the stall condition. The maximum lift coefficient for the clean airfoil was 0.9 at 10 degrees angle of
attack, and tripped airfoil reached a maximum lift coefficient of 1.03 at 12 degrees angle of attack, a
14% increase. These data were 10% lower than the empirical airfoil data found in Theory of Wing
Sections from Abbott and von Doenhoff. Pitching moment coefficient about the quarter chord remained
near zero below stall as expected for a symmetrical airfoil, but rapidly became negative after stall for
experimental and empirical data. The airfoil exhibited a leading edge stall for both laminar and turbulent
boundary layers.

3. iii
T a b l e o f Co n t e n t s
Abstract ............................................................................................................................................ ii
Table of Contents ............................................................................................................................ iii
List of Figures ..................................................................................................................................v
List of Tables .................................................................................................................................. vi
List of Symbols ............................................................................................................................... vi
1 Introduction ............................................................................................................................. 7
1.1 Background.................................................................................................................. 7
1.1.1 Inviscid Flow ............................................................................................................... 7
1.1.2 Viscous Flow in the Boundary Layer ........................................................................ 10
1.2 Purpose ...................................................................................................................... 15
1.3 Theory........................................................................................................................ 16
1.3.1 Stall Behavior ............................................................................................................ 18
1.3.2 XFOIL Comparison ................................................................................................... 20
2 Experimental Setup and Procedure ....................................................................................... 22
2.1 Equipment.................................................................................................................. 22
2.2 Wind Tunnel Model .................................................................................................. 24
2.3 Experimental Setup and Data Collection .................................................................. 26
2.4 Procedure ................................................................................................................... 27
2.5 Error Analysis............................................................................................................ 28
3 Results ................................................................................................................................... 29
3.1 Reference Data .......................................................................................................... 29
3.2 Pressure Coefficient................................................................................................... 30
3.2.1 Stall Mode ................................................................................................................. 31
3.2.2 Airfoil Behavior with Turbulence Tape .................................................................... 33
3.2.3 Comparison of Pressure Coefficients to XFOIL ....................................................... 35
3.2.4 Implications of Stall and Transition .......................................................................... 36
3.3 Lift Coefficient .......................................................................................................... 37
3.3.1 Effects of Tripped Boundary Layer on Lift Coefficient............................................ 37
3.3.2 Comparison with Empirical Data .............................................................................. 38
3.3.3 Implications of Lift Coefficient Behavior ................................................................. 40
3.4 Moment Coefficients ................................................................................................. 40
3.4.1 Moment Coefficient Behavior in Linear and Stalled Regions .................................. 40
3.4.2 Implications of Moment Coefficient Behavior.......................................................... 42
3.5 Error Analysis............................................................................................................ 43
4 Conclusions ........................................................................................................................... 44
4.1.1 Purpose ...................................................................................................................... 44
4.1.2 Expectations .............................................................................................................. 44
4.1.3 Pressure Coefficient................................................................................................... 44
4.1.4 Lift Coefficient .......................................................................................................... 45
4.1.5 Moment Coefficient................................................................................................... 46

4. iv
4.1.6 Implications ............................................................................................................... 46
References ..................................................................................................................................... 47
APPENDIX A: Raw Data ............................................................................................................. 48
APPENDIX B: XFOIL Data......................................................................................................... 56
APPENDIX C: Local Absolute Pressures .................................................................................... 58
APPENDIX D: Pressure Coefficients........................................................................................... 60
APPENDIX E: MATLAB Scripts ................................................................................................ 62

5. v
L i s t o f F i g u r e s
Figure 1. Streamlines about a Lifting Body ............................................................................................... 7
Figure 2. Angle of Attack and Pressure Distribution ................................................................................. 9
Figure 3. Boundary Layer Velocity Profiles ............................................................................................ 11
Figure 4. Boundary Layer Transition ....................................................................................................... 11
Figure 5. Boundary Layer Separation ...................................................................................................... 12
Figure 6. Stages of Stall Development .................................................................................................... 13
Figure 7. Streamlines of Inviscid Flow Around a Cylinder ..................................................................... 13
Figure 8. Streamlines of Viscous Flow Around a Cylinder ..................................................................... 14
Figure 9. Pressure Distribution on a Real Sphere Compared to an Inviscid Sphere ............................... 14
Figure 10. Wake Size on Smooth and Rough Spheres ............................................................................ 15
Figure 11. Forces on an Airfoil ................................................................................................................. 16
Figure 12. Simplified Pressure Coefficient Plot ....................................................................................... 18
Figure 13. Leading Edge Stall ................................................................................................................. 19
Figure 14. Laminar Separation Bubble ..................................................................................................... 20
Figure 15. USNA CCWT Layout ............................................................................................................. 23
Figure 16. Pressure Systems, Inc. System 8400 Mainframe..................................................................... 24
Figure 17. NACA 65-012 Airfoil with Pressure Ports.............................................................................. 24
Figure 18. Airfoil Mount in Wind Tunnel ................................................................................................ 26
Figure 19. Tape Application ..................................................................................................................... 27
Figure 20. Clean Airfoil Pressure Coefficient Distribution ...................................................................... 30
Figure 21. Location of Max Suction and Laminar Separation Bubble ..................................................... 31
Figure 22. Pressure Coefficients at 10° AoA ............................................................................................ 32
Figure 23. Laminar Separation Contradiction .......................................................................................... 33
Figure 24. Turbulence Tape Airfoil Pressure Distribution ....................................................................... 34
Figure 25. Pressure Coefficient Distribution on Clean Airfoil at 5° AoA ............................................... 35
Figure 26. XFOIL Predicted Laminar Separation Bubble ........................................................................ 36
Figure 27. Clean and Tripped Airfoil Lift Coefficients ............................................................................ 38
Figure 28. Lift Coefficients of Experimental and Empirical Data............................................................ 39
Figure 29. Moment Coefficient as a Function of Angle of Attack ........................................................... 41
Figure 30. Moment Coefficient as a Function of Lift Coefficient ............................................................ 42

6. vi
L i s t o f T a b l e s
Table 1. USNA CCWT Technical Details ................................................................................................ 22
Table 2. Pressure Port Locations .............................................................................................................. 25
Table 3. Free Stream Properties ................................................................................................................ 29
Table 4. Experimental Lift Coefficients ................................................................................................... 37
Table 5. Experimental Moment Coefficients about the Quarter Chord .................................................... 40
Table 6. Local Pressure and Local Pressure Coefficient Uncertainties .................................................... 43






L i s t o f S y m b o ls
A ............................................ axial force
CL ........................................... lift coefficient
Cm,c/4 ...................................... pitching moment about the quarter chord
CN ........................................... normal coefficient
Cp ........................................... pressure coefficient
Cp,l .......................................... pressure coefficient on the lower surface
Cp,u ......................................... pressure coefficient on the upper surface
L ............................................. lift
N ............................................ normal force
R ............................................ resultant force
S ............................................. dynamic pressure
c ............................................. chord length
p0 ............................................ total pressure
ps............................................. static pressure q
............................................ dynamic pressure
α ............................................. angle of attack
ρ ............................................. density

7. 7
1 I n t r o d u c t i o n
1.1 Background
1.1.1 Inviscid Flow
As air flows around a body, it creates forces on that body, which can be determined via
measurement of the pressures on the body’s surface. Specifically in the case of a lifting body, the force
perpendicular to the velocity of the flow is lift, and the parallel force is drag. The phenomenon can most
easily be explained using a body-centered reference system, in which the body is stationary in relation to
the observer, and the air flows around it. Following a fluid element in the flow in which the air is
moving parallel at a constant velocity, the element must change direction because of the presence of the
obstruction. The aggregate movement of fluid elements results in the concept of streamlines as depicted
in Figure 1.

Figure 1. Streamlines about a Lifting Body [1]
The fluid elements on one streamline will continue to follow the same streamline as long as the
flow remains steady and the airfoil is static. Figure 1 shows that the distance between the streamlines at
points 1and 2 has been reduced as the element travels downstream, and the distance between the
streamlines at the same streamwise location below the airfoil has been increased. In three dimensions,
the distances between streamlines are called stream tubes. By the law of conservation of mass, mass
cannot be created nor destroyed, so the air must move through the smaller stream tube on the upper
surface of the airfoil at higher speed than the air flowing under the lower surface. This principle is
∙ 1
∙ 2

8. 8
shown mathematically in Equation (1), where ρ is the density of the air, V is the velocity of the air, and
A is the stream tube cross sectional area.

??????
1
??????
1
??????
1
=??????
2
??????
2
??????
2
(1)

For low-speed flows, density can be assumed to be constant. The velocity of the flow along a
streamline can be related to the pressure at a given location using the momentum equation, shown in
Equation (2), where dp is a differential pressure.
��= −????????????�?????? (2)

∫��+ ??????∫??????�??????=0
??????
2
??????
1
�
2
�
1
(3)

�
??????
= �
1
+
1
2
????????????
1
2
= �
2
+
1
2
????????????
2
2
(4)

Integrating Equation (2) over the distance between points 1 and 2 along a streamline yields
Equation (3), and solving gives Equation (4), which is known as Bernoulli’s Principle. pT is the total
pressure of the flow. Equation (4) can be used to find accurately the static pressure at a given location in
any fluid flow as long as the following assumptions can be reasonably made: the effect of flow viscosity
is negligible (inviscid), the flow density is constant (incompressible), the flow is steady, points 1 and 2
are along the same streamline, and intermolecular forces are negligible. As angle of attack increases, the
area of the stream tubes on the upper surface of the airfoil decrease, exaggerating the effect. Changing
angle of attack and the resulting pressure distributions are shown in Figure 2.

9. 9

Figure 2. Angle of Attack and Pressure Distribution [1]
The pressure representations in Figure 2 connote gauge pressures, which are in reference to the
static pressure in the free stream. The varying pressure across the airfoil will cause a pitching moment.
The point at which this moment is constant with changing angle of attack is the aerodynamic center. The
negative gauge pressure near the leading edge of the airfoil at 10° angle of attack in Figure 2 indicates
that this point will be forward of the half chord because the sum of the pressure over the leeward half of
the airfoil is considerably weaker. For symmetric airfoils, the aerodynamic center is exactly at the
quarter chord. At 10° angle of attack, Figure 2 shows a point near the leading edge on the upper surface
of the airfoil with a minimum pressure (highest magnitude pointed away from the airfoil). From the
leading edge to this point, the pressure is decreasing, which is known as a favorable pressure gradient
because this is the natural direction of flow when work is not added to the system. From the point of
minimum pressure to the trailing edge, the pressure is increasing, causing an adverse pressure gradient.
The momentum of the air carries it through this region, but the flow loses velocity over this region. The
inviscid assumption implies that the velocity, and thus the momentum, is constant across streamlines.
However, near the airfoil, this assumption breaks down in a region known as the boundary layer.

10. 10
1.1.2 Viscous Flow in the Boundary Layer
The viscosity of a fluid causes fluid particles that are directly in contact with an object to become
attached to the object. The particles directly adjacent to those at the surface will be held back by the
viscous forces as the particles interact, and the speed of the air will gradually increase with distance
from the surface. This effect perpetuates away from the object indefinitely, but viscous effects need only
be treated while the speed of the fluid is less than 99% of the speed stream far from the surface [2]. This
region is called the boundary layer. For the scale of an airfoil in a wind tunnel, the thickness of the
boundary layer ranges from approximately 1/8 in to 1/2 in.
The boundary layer can be categorized into two types: laminar and turbulent. In a laminar
boundary layer, the flow is characterized by “smooth regular streamlines” [3]. Without obstructions, the
boundary layer at the leading edge of an airfoil will be laminar. The laminar boundary layer will
continue downstream until the viscous forces of the flow outside the boundary layer on the slower-
moving air within the boundary layer causes the flow to tumble and become unstable. This is the region
of the turbulent boundary layer, which will have a much higher rate of velocity increase with distance
from the surface than that of the laminar boundary layer. This rapid acceleration of the fluid causes a
greater amount of skin friction on the airfoil, but it also allows the turbulent boundary layer to retain a
greater amount of momentum, which is critical when moving through an adverse pressure gradient. The
velocity profiles of the two types of boundary layers are shown in Figure 3.

11. 11

Figure 3. Boundary Layer Velocity Profiles [4]

The region where the boundary layer transitions from laminar to turbulent flow is known as the
transition region. A flow representation can be seen in Figure 4.


Figure 4. Boundary Layer Transition [5]
The point of transition depends upon the surface roughness, the air density, and the free stream
velocity. The airfoil and its modifications determine the surface roughness. The latter parameters are
conventionally summarized in a nondimensional parameter known as the Reynolds number. Assuming
constant density and viscosity throughout the flow, Reynolds number is defined in Equation (5), where
V∞ is the free stream velocity, x is the distance from the leading edge, and μ is the dynamic viscosity of
the fluid.

12. 12
��≡
????????????
∞
??????
??????
(5)

For a smooth, flat plate like the one in Figure 3, the Reynolds number at which transition occurs
is approximately 5x10
5
[6]. The geometry and surface of the airfoil influence the critical Reynolds
number at which the flow transitions. As the flow moves along the airfoil in the adverse pressure
gradient, the air velocity is accelerating in the upwind direction as the kinetic energy of the flow is
converted into static pressure. The main stream airflow has the momentum to overcome this adverse
pressure gradient and continue in the downstream direction. In the boundary layer, the flow has lost
energy through the viscous friction. When the adverse pressure gradient becomes too great, the
boundary layer flow will come to a stop and reverse direction. The flow moving in the streamwise
direction is now separated from the airfoil surface, so this phenomenon is called separation. The velocity
profile of the boundary layer through the stages of separation is shown in Figure 5.


Figure 5. Boundary Layer Separation [7]
As the angle of attack of the airfoil increases, the adverse pressure gradient will become stronger.
This will force the separation to occur nearer to the leading edge. The stages of separation are shown in
Figure 6.

13. 13

Figure 6. Stages of Stall Development [9]
At angles of attack greater than that which produces the greatest amount of lift, the airfoil is said
to be stalled. In Figure 6, this occurs at 16° angle of attack. The increase in static pressure on the upper
surface dramatically reduces lift and increases drag.
1.1.3 Separation Control
The location of separation can be controlled. This method is most dramatic on a cylinder with a
circular cross section. Considering again the inviscid case, the flow will remain attached to the surface
of the cylinder because of the lack of boundary layer as shown in Figure 7.


Figure 7. Streamlines of Inviscid Flow Around a Cylinder [8]
At point L, the flow velocity goes to zero at the leading edge stagnation point. From Equation
(4), the static pressure increases to the level of the total pressure. Because the flow does not lose energy
to friction over the surface of the cylinder, another stagnation point will occur at the trailing edge at
L T

14. 14
point T, causing the pressures on either side of the cylinder to be equal. In this case, there is no drag on
the object. However, in the viscous (real) case, the boundary layer separates from the airfoil in the
adverse pressure gradient causing a wake to form, as shown in Figure 8.


Figure 8. Streamlines of Viscous Flow Around a Cylinder [8]
In Figure 8, there is no stagnation point at T. At point T, the static pressure is now the static
pressure of the flow when it separates. By Equation (4), this static pressure must be less than the static
pressure on the leading edge. This difference can be seen in Figure 9.


Figure 9. Pressure Distribution on a Real Sphere Compared to an Inviscid Sphere [8]
This pressure difference causes a net force in the downstream direction known as pressure drag.
The size of the wake, and thus the area over which this reduced pressure will act, depends upon the
location of separation, represented by the angle θ in Figure 8. As shown in Figure 3, the turbulent
boundary layer retains a greater amount of momentum to overcome the adverse pressure gradient on the
leeward side of the cylinder. The effect is shown in Figure 10.

L T
Inviscid
Real

15. 15

Figure 10. Wake Size on Smooth and Rough Spheres [9]
In the lower image, the dimples of the golf ball forced the boundary layer to transition to
turbulent flow in a process known as tripping the boundary layer. The result is a smaller wake and less
pressure drag. Separation on an airfoil can be delayed in exactly the same manner as the golf ball with
surface roughness or inconsistencies. The boundary layer will transition through an increase in Reynolds
number as in Figure 5 or with surface roughness as in Figure 10. For an airfoil, this also means that an
airfoil with a turbulent boundary layer will be able to achieve higher angles of attack, and thus greater
lift, before stall.
1.2 Purpose
The purpose of the experiment was to accurately collect a pressure distribution on a NACA 65-
012 airfoil section and determine its effects on lift, pitching moment, and stall characteristics. These
results were to be validated via comparison with empirical data and theoretical modeling using XFOIL.
Additions to the airfoil were used to determine the effects of forcing a turbulent boundary layer as
compared to a laminar boundary layer over a lifting surface. The pressure port method was used to
determine the distribution of lift production on the airfoil. The results of high angle of attack would be
analyzed to determine the type of stall the airfoil would experience.

16. 16
1.3 Theory
The lift and drag on acting on an airfoil can be measured using the pressure distribution over the
surface of the airfoil. As shown by Figure 2, a pressure differential will exist between the upper and
lower surfaces of the airfoil. Creating this pressure differential will cause a net force on the airfoil,
shown as force R in Figure 11.

Figure 11. Forces on an Airfoil
This force can be decomposed into normal (N) and axial (A) forces. These forces can be
determined via pressure measurements. However, lift (L) on an airfoil is defined to be the force acting
perpendicular to the free stream, and drag (D) is defined as the force acting parallel to the free stream.
These forces can be related through Equation (5).

??????=??????cos??????−??????sin??????≈??????cos?????? (6)

In order to nondimensionalize the terms, data reduction will use coefficients of lift (CL), and
normal force (CN). Using the definition of CL in Equation (7) gives Equation (8) where S is the reference
area of the airfoil.

??????
??????≡??????∙�∙� (7)

??????
??????
≈??????
??????
cos?????? (8)

17. 17
In order to determine the pressure distribution along the airfoil, a coefficient of pressure (Cp) is
defined in Equation (9) where p is the local pressure, p∞ is the free stream static pressure, and q∞ is the
free stream dynamic pressure.

??????
�
≡
�−�
∞
�
∞
=
�−�
∞
1
2
⁄????????????
∞
2 (9)

Local pressures can be measured using pressure ports along the surface of the airfoil, providing a
pressure distribution. In effect, the pressure coefficients are a measure of the speed of the air over the
surface of the airfoil. More negative Cp indicates a higher local velocity relative to the free stream. The
maximum Cp will occur at the leading edge stagnation point where the velocity goes to zero. The
pressure ports on the surface of the airfoil will are not affected by their location within the boundary
layer. Pressure remains constant in the direction normal to the flow within the boundary layer, so the
pressure at the airfoil surface is equal to the static pressure in the local stream. Using the assumptions in
developing Equation (4), Equation (9) can be simplified to a form that is more useful for finding the
local velocity, as shown in Equation (10).
??????
�
=1−
??????
2
??????
∞
2 (10)
The net normal force is simply the difference of the pressure over the lower surface of the airfoil
and the pressure over the upper surface of the airfoil, which can be expressed in coefficients on the
upper (Cp,u) and lower (Cp,l) surfaces. Cp can be used to determine CN as shown in Equation (11).

??????
??????
=∫(??????
�,�
−??????
�,�
)�(
??????
??????
)=
1
0
∫(??????
�,�
)�(
??????
??????
)
1
0
−∫(??????
�,�
)�(
??????
??????
)
1
0
(11)

The locations along the chord have been divided by the chord length such that the locations are
now expressed in fractions of the total chord length. Similarly, the pitching moment about the quarter
chord can be determined by determining the difference in the products of the pressure and respective
moment arms over the lower and upper surfaces. The relationship is expressed in Equation (12).

??????
�??????
4
⁄
=∫(??????
�,�
)∙(
1
4
−
??????
??????
)�(
??????
??????
)
1
0
−∫(??????
�,�
)∙(
1
4
−
??????
??????
)�(
??????
??????
)
1
0
(12)

18. 18

This defines a nose-up pitching moment to be positive. The center of pressure is the point about
which the moment coefficient is constant. For a symmetrical airfoil, this point is expected to be at c/4,
and the moment is expected to be nearly zero or slightly negative. The pressure coefficients can be
plotted against the fraction of chord length to provide a visual representation of the pressure distribution.
The y-axis is inverted to clearly show the pressure coefficients upper and lower surfaces. A simple
interpretation of an expected Cp plot is shown in Figure 2.


Figure 12. Simplified Pressure Coefficient Plot

The y-axis has been inverted to represent the negative pressure coefficients on the upper surface
of the airfoil. The normal force coefficient can be determined geometrically from Figure 2 by finding the
area of the two triangles. In this case CN = 1.5 . The increasing value of Cp for the upper surface
indicates an adverse pressure gradient. It is expected that the minimum pressure coefficients (suction
peaks) will decrease (become more negative) as angle of attack increases.
1.3.1 Stall Behavior
The airfoil will reach an angle of attack at which the flow over the upper surface cannot
overcome the adverse pressure gradient, and lift will decrease. This will result in one of three stall
scenarios: trailing edge stall, leading edge stall, or a laminar separation bubble. In a trailing edge stall,
the flow will separate toward the trailing initially, and the reversed flow will move toward the leading

19. 19
edge as the angle of attack increases, as shown in Figure 6. This is the most favorable mode of stall
because it can provide the pilot with feedback via buffet in the airframe as the separated flow washes
over the tail section. After trailing edge stall, the flow will reattach with minimal hysteresis, the
reduction in angle of attack required to reestablish attached flow. This is generally seen with airfoils
with a large radius of curvature at the leading edge.
The leading edge stall is characterized by the separation near the trailing edge rapidly
progressing up the surface of the airfoil and diminishing lift with a small change in angle of attack. This
is the least desirable mode of stall because there is little warning for the pilot, and control surfaces
located on the leeward part of the wing, which is in the separated flow, immediately become ineffective.
The leading edge stall is depicted in Figure 13.


Figure 13. Leading Edge Stall [11]
Leading edge stalls are most common in airfoils with a small leading edge radius like the flat
plate in Figure 13. Airfoils known to exhibit leading edge stalls are symmetric sections with thickness
between 9% and 15% of the chord [12]. The sharp turn at the leading edge at high angles of attack
causes a large adverse pressure gradient, taking the majority of the boundary layer momentum to
overcome.
The laminar separation bubble is depicted in Figure 14.

20. 20

Figure 14. Laminar Separation Bubble
The laminar separation bubble is a form of stall in which laminar flow separates from the airfoil
immediately aft of the peak pressure. The flow transitions to turbulent flow outside of the bubble, and
the increased energy reattaches the flow before reaching the trailing edge. The size of the bubble
depends upon the Reynolds number of the experiment. Longer separation bubbles will arise in low
speed, low Reynolds number flows, and higher speeds will decrease the length. [13] The laminar
separation bubble mode of stall will evolve into a leading edge stall with an increase in angle of attack.
This mode of stall is undesirable because it does not offer any feedback to the pilot, but there is a
significant loss of lift. Roughness near the leading edge of the airfoil will trip the boundary layer and
force it to transition to turbulent flow. As discussed, the turbulent flow has more momentum to
overcome the adverse pressure gradient at the leading edge and eliminates the possibility of a laminar
separation bubble.
1.3.2 XFOIL Comparison
The results are to be verified using the program XFOIL [12], a subsonic airfoil modeling
program. XFOIL bases calculations on the vortex panel method to approximate the pressure
distribution around an airfoil. The vortex panel method is a product of potential flow theory in
which real airflows can be modeled using algebraic combinations of mathematical
representations. The theory, however, only represents inviscid flow. Viscous effects such as

21. 21
separation do not appear in potential flow solutions. XFOIL has been modified to handle limited
trailing edge separation and separation bubbles. XFOIL solutions are calculated using a Reynolds
number of 15x10
6
. As seen above, the Reynolds number can have a large impact on separation and
stall, so XFOIL solutions will only be used in low angle of attack cases in which separation is not
expected.

22. 22
2 E x p e r i m e n t a l S e t u p a n d P r o c e d u r e
2.1 Equipme nt
The experiment was conducted in the USNA Closed-Circuit Wind Tunnel (CCWT). The CCWT
is a closed circuit, single return, research-quality wind tunnel. The test section is a vented jet, meaning
that the section is physically closed but vented to atmospheric pressure. Technical details of the CCWT
are displayed in Table 1, and the layout of the CCWT is shown in Figure 3.
Table 1. USNA CCWT Technical Details
Test section size 42×60×120 in
Jet type Vented
Contraction ratio 6.47
Maximum velocity 300 fps
Maximum Reynolds number 1.9×106 per foot
Maximum flow rate 295,000 cfm
Motor power 400 HP
Fan diameter 7 ft
Fan speed 1,200 rpm
Tunnel constant 1.0303
Turbulence factor 1.0332

23. 23

Figure 15. USNA CCWT Layout

The pressure measurement system in the USNA CCWT is the Pressure Systems, Incorporated
(PSI) system 8400 mainframe. This system collects data from multiple electronically-scanned pressure
modules, which can be imbedded within the test article. A series of pressures are read over a span of 10
seconds, and the system provides an average of those pressures for each location along with a standard
deviation of the sample. The system advertises an uncertainty of +/- 0.05% on data reading, which is
beyond the necessary precision for this experiment. Pressure data is compiled in gauge pressure, which
indicates the difference of ambient and local pressure. This must be corrected before data reduction can
begin. For this experiment, two modules were used, 100 and 300, which were mounted within the airfoil
to measure pressure along the upper and lower surface, respectively. The system 8400 mainframe and
test ports are shown in Figure 16.

24. 24

Figure 16. Pressure Systems, Inc. System 8400 Mainframe

2.2 Wind Tunnel Model
The airfoil used was the NACA 65-012, one of the 6-series airfoils developed in the 1940s to
reduce drag by encouraging laminar flow over a greater portion of the wing [8]. The 65-012 is a
symmetrical airfoil with a maximum thickness of 12% of the chord located at 40.5% chord length. The
wind tunnel model has a chord of 16 in and a span of 42 in. The airfoil is fitted with 27 pressure taps on
each surface along the half span. Figure 17 shows the shape of the airfoil and the location of the pressure
ports. Corresponding pressure port locations are presented in Table 2.



Figure 17. NACA 65-012 Airfoil with Pressure Ports

25. 25
Table 2. Pressure Port Locations
x/c
Upper Surface Lower Surface
Port No. Port No.
0.0000 101 301
0.0020 102 302
0.0040 103 303
0.0060 104 304
0.0080 105 305
0.0100 106 306
0.0150 107 307
0.0200 108 308
0.0300 109 309
0.0400 110 310
0.0600 111 311
0.0800 112 312
0.1000 113 313
0.1500 114 314
0.2000 115 315
0.2500 116 316
0.3000 117 317
0.3500 118 318
0.4000 119 319
0.4500 120 320
0.5000 121 321
0.5500 122 322
0.6000 123 323
0.7000 124 324
0.8000 125 325
0.9000 126 326
0.9500 127 327
1.0000 128 328
p1 - patm 129 329
p2 - patm 130 330

The port’s distance from the chord line was not considered in data reduction and has been
omitted in Table 2. Ports 101 and 301 are measuring the same location at the leading edge, and ports 128
and 328 are measuring the same location at the trailing edge. p1 denotes the pressure at the beginning of
the wind tunnel contraction, and p2 is the static pressure at the entrance to the test section. For this
experiment, p2 was used as the free stream pressure, p∞.

26. 26
2.3 Experime ntal Setup and Data Collection
The airfoil was placed vertically in the USNA CCWT test section as shown in Figure 6.


Figure 18. Airfoil Mount in Wind Tunnel

The airspeed and angle of attack were manipulated remotely. For the second part of the
experiment, aluminum tape was cut using jagged scissors and applied to the leading edge of the airfoil
manually. A gap was left at the location of the line of pressure ports so that none of the pressure ports
would be covered. The final result can be seen in Figure 19.

27. 27

Figure 19. Tape Application
The pressure ports along the semispan of the airfoil measure the difference of local pressure to
atmospheric pressure. Although the ports are within the boundary layer, the static pressure
measurements reflect the static pressure at the edge of the boundary layer. Static pressure within the
boundary layer is constant in the direction perpendicular to the flow.
2.4 Procedure
The following steps were taken to complete the experiment:
1. Measure the dimensions of the airfoil.
2. Record lab barometric pressure and temperature.
3. Calibrate PSI System 8400 and clear readings.
4. Run tunnel at a test section entrance dynamic pressure of 0.12 psi, and effective Reynolds
number of 1,000,000.
5. Record pressure data at 0, 5, 8, 10, and 12 degrees angle of attack.
6. Shut down wind tunnel.
7. Apply tape to leading edge.
8. Run tunnel at a test section entrance dynamic pressure of 0.12 psi.

28. 28
9. Record pressure data at 8, 10, and 12 degrees angle of attack.
10. Stop wind tunnel, remove tape, and secure equipment.
After the experiment was complete, the team used the program XFOIL the simulate flow that had
been tested. Because of the viscous limitations of XFOIL, the team used results only from the 0° and 5°
angle of attack configurations. Information was also extracted from airfoil data compiled in Theory of
Wing Sections from Abbott & von Doenhoff, which will be abbreviated as “AVD” throughout the
remainder of this report. The AVD data comes from a series of NACA experiments conducted in the
1930s and 1940s to examine the performance of several airfoil shapes. Data used are the averages of
many tests. The experiments referenced were run at a Reynolds number of 3x10
6
, so separation
characteristics are expected to vary from experimental results.
2.5 Error Analysis
The System 8400 returned a standard deviation of each data sample collected. These raw data are
displayed in Appendix A. One sigma error band is defined in Equation (8) where ??????
�
is the local absolute
pressure error and ??????̅
�
is the standard deviation.

??????
�
=
??????̅
??????
�
??????????????????
(13)

The error in pressure coefficient will be defined to be four times that of the local pressure error
as seen in Equation (14).
??????
??????
??????
=4 ??????
�
(14)

29. 29
3 R e s u l t s
The raw data extracted from the pressure ports can be found in Appendix A. The data are
grouped by angle of attack and runs with and without the turbulence tape. These data represent the
pressure distribution over the upper and lower surfaces of the airfoil. MATLAB was used for data
reduction and plot generation. MATLAB script can be found in Appendix E. The reference area used in
calculations is the chord length 16 in because the experiment is considered a 2-dimensional wing. Data
using XFoil to simulate the behavior of the airfoil is presented in Appendix B. Cp1 indicates the pressure
coefficient on the upper surface and Cp2 indicates the pressure coefficient on the lower surface.
3.1 Reference Data
In order for the raw data to be useful, the reference conditions were determined. The values for
free stream pressure (p∞), free stream temperature (T∞), free stream density (ρ∞), free stream dynamic
pressure (q∞), and free stream velocity (V∞ ) are displayed in Table 3.

Table 3. Free Stream Properties
p∞ (psi) T∞ (°R) ρ∞ (slug/ft
3
) q∞ (psi) V∞ (fps)
14.55 528.9 0.00231 0.12 122.3


These values are necessary to determine the Reynolds number of operation, which has been
determined to be 1,000,000. The first step to working with the data was to convert the gage pressures to
absolute local pressures (pi). The local pressures from the raw data were added to the ambient pressure
as shown in Equation (15).

�
??????
= �
??????��
+�
??????
=14.56+ �
??????
(15)

Data for the local absolute pressures are displayed in Appendix C.

30. 30
3.2 Pressure Coefficient
The local absolute pressures were used to determine the coefficients of pressure at each point on
the airfoil using Equation (9). The pressure coefficients of the clean airfoil testing are displayed in
Figure 20. The pressure coefficient data is presented in tabular form in Appendix D.


Figure 20. Clean Airfoil Pressure Coefficient Distribution
The first angle of attack tested was 0°, which should produce zero lift because the area reduction
of the streamtubes on both surfaces of the airfoil should be equal. The pressure coefficients were below
zero along much of the airfoil because of the increased flow velocity, but the increase was equal across
the airfoil. The minimal difference between the upper and lower surface pressure coefficients along the
length of the airfoil confirmed the zero lift prediction. At the leading edge, all cases exhibited a
maximum pressure coefficient at unity. This behavior was predicted by Equation (9) because the local
velocity goes to zero at the leading edge stagnation point. As angle of attack increases, the stagnation
point moved aft along the lower surface. The pressure ports at this location have been exposed normal to
the free stream. Flow visualization is provided in Figures 1 & 13. The movement of the stagnation point
under the leading edge contributes a strong nose up pitching moment, reinforcing the prediction of an 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-6
-5
-4
-3
-2
-1
0
1
2
x/c
Cp


0 degrees
5 degrees
8 degrees
10 degrees
12 degrees
x/c = 0.25

31. 31
aerodynamic center forward of the half chord. The combination of the suction peak on the upper surface
of the airfoil and the location of the stagnation point on the lower surface of the airfoil resulted in a force
much larger than any concentration further aft on the airfoil. The location about which the forces are
balanced, the aerodynamic center, was moved toward this pressure concentration. Figure 20 shows the
expected location of the aerodynamic center at 25% of the chord. The location of the peak suction
occurs at less than 1% of the chord at 5° and 8° angle of attack. The minimum pressure is reached at 8°
angle of attack with a pressure coefficient of -5.37. By Equation (10), the local velocity at the point is
found to be 308 fps. This local velocity is nearly three times the free stream velocity. Aft of the point,
the flow entered the adverse pressure gradient, rapidly losing momentum and decreasing velocity.
3.2.1 Stall Mode
The data showed decreasing minimum pressure coefficient with increasing angle of attack up to
8°. Downstream of this initial expansion, the airflow faced an adverse pressure gradient. The pressure
rapidly increased in the downstream direction. At 5 and 8 angle of attack, the data revealed an area of
constant pressure as shown in Figure 21, which initially suggested a laminar separation bubble.

Figure 21. Location of Max Suction and Laminar Separation Bubble 0 0.01 0.020.03 0.040.05 0.060.070.08 0.09 0.1
-6
-5
-4
-3
-2
-1
0
1
2
x/c
Pressure Coefficient


5 degrees
8 degrees
Max Suction
Laminar Separation Bubble

32. 32
A separation bubble is reasonable at this location because it is immediately aft of the peak
suction point, indicated by ports 5 and 6 on the upper surface. A bubble here would trip the boundary
layer to turbulent flow and allow the boundary layer to reestablish downstream flow at the airfoil
surface. Figure 20 shows that the pressure distribution along the aft half of the airfoil changes very little
between angles of attack at which attached flow is known to be present at the leading edge due to the
defined suction peak. This suggests that the flow remained attached over nearly all of the upper surface.
A laminar separation bubble would be consistent with the prediction that it will lead to leading edge
stall. The suspect region spans less than 0.5% of the chord in both cases, which is expectedly smaller
than cases in experiments of Reynolds numbers below 100,000 [13]. At 10° angle of attack, the suction
peak was significantly decreased, indicating that the separation bubble had burst, developing into a
leading edge stall. At 12° angle of attack, the pressure variation along the chord was minimal indicating
a fully developed stall. The laminar separation bubble, however, can only exist when the boundary layer
is initially laminar. Examination of the second part of the experiment using the turbulence tape indicates
that this pressure anomaly is a result of the shape of the airfoil instead of flow reversal. Figure 22 shows
the dramatic increase in local pressure as the flow separated near the leading edge at 10° angle of attack.

Figure 22. Pressure Coefficients at 10° AoA 0 0.10.20.30.40.50.60.70.80.9 1
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
x/c
Cp


Smooth Surface
Rough Surface

33. 33
The separation bubble required that initial separation occur during the laminar flow region.
Figure 22 clearly shows that the experiment using the turbulence tape produced attached high lift and a
greater suction peak at 10° angle of attack. Based on the discussion of boundary layer momentum, the
attached flow at higher angle of attack demands that the flow at the leading edge be turbulent. Upon
closer inspection, the data revealed the same pressure plateau at ports 5 and 6, as shown in Figure 23.

Figure 23. Laminar Separation Contradiction
The behavior of the flow at the location in question must be a product of the leading edge
geometry, which decreases the magnitude of the adverse pressure gradient over the region between ports
4 and 7. This may be the result of the high concentration of pressure ports near the leading edge, damage
to the airfoil, or a change in the radius of curvature of the airfoil.
3.2.2 Airfoil Behavior with Turbulence Tape
The airfoil exhibited similar behavior after applying the turbulence tape, with the exception of
increased stall angle of attack. The pressure distributions of the three tested angles of attack are shown in
Figure 24. 0 0.010.020.030.040.050.060.070.080.09 0.1
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
x/c
Cp


Smooth Surface
Rough Surface
Suspected Laminar Separation Bubble
Attached Turbulent Flow
Laminar Flow Separation

34. 34

Figure 24. Turbulence Tape Airfoil Pressure Distribution
The airfoil reached a minimum pressure coefficient of -7.5 at 10° angle of attack. This situation
was possible because of the increased momentum of the turbulent boundary layer and its ability to
remain attached through the recovery in the adverse pressure gradient near the leading edge. The type of
boundary layer did not affect the pressure coefficient while the flow remained attached. The minimum
pressure coefficient at 8° angle of attack was -5.4, while the minimum pressure coefficient at 8° angle of
attack of the smooth airfoil was -5.3, a change of less than 2%. The minimum pressure coefficient at 12°
angle of attack increased abruptly as it did on the smooth airfoil, indicating a leading edge stall. This
type of stall was expected because the maximum thickness of the airfoil falls in the range (9% to 12%)
which commonly produces leading edge stall. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
x/c
Pressure Coefficient


8 degrees
10 degrees
12 degrees
C
p,min
= -3.0
C
p,min
= -5.4
C
p,min
= -7.5

35. 35
3.2.3 Comparison of Pressure Coefficients to XFOIL

Figure 25. Pressure Coefficient Distribution on Clean Airfoil at 5° AoA [13]
The coefficient of pressure data generated using XFOIL is plotted with the experimental data in
Figure 24. Figure 24 shows the close correlation of the experimental data and the data generated using
XFOIL. The data loosely resembled the simplified scheme shown in Figure 12. The pressure coefficients
reached a minimum value of -2.7 at 0.4% of the chord and a maximum value of 0.93 at 0.06% of the
chord. The pressure coefficients converged rapidly as chord length increased. The pressure coefficient
on the upper surface of the airfoil remained above -1.0 for all locations aft of 10% of the chord. This
shows the concentration of the lifting location and the large adverse pressure gradient near the leading
edge of the airfoil. The modeling technique used by XFOIL, the vortex panel method, makes the
inviscid assumption, so the XFOIL solution could not show large separation effects. The close
agreement of the experimental data along the length of the airfoil indicates that no large separation was
present in the experiment. However, XFOIL was programmed to predict transitional separation bubbles,
which is indicated in Figure 22.

36. 36

Figure 26. XFOIL Predicted Laminar Separation Bubble
The XFOIL data showed the same trend of the plateau at 1.5% to 2% of the chord as the
experimental data. The difference is that the XFOIL prediction uses a Reynolds number of 15x10
6
. At
this Reynolds number, XFOIL was not modeling laminar flow. The presence of the anomaly in the
XFOIL prediction removes the possibilities of pressure port interference and damage to the airfoil.
3.2.4 Implications of Stall and Transition
The data showed that the airfoil tends to stall at the leading edge at the given Reynolds number.
This is detrimental to aircraft use because of rapid loss of lift, loss of control surface effectiveness, and
increased pressure drag. Between 8° and 10° angle of attack, the airfoil loses most of its lift in the clean
configuration. With the presence of the turbulence tape, the loss of lift is also abrupt, but the flow
remains attached until 12° angle of attack. This situation is more likely to happen in practical application
due to higher Reynolds number of full scale aircraft and dirt or bug collection on the leading edge. The
smooth airfoil may have exhibited a lower friction drag while the flow remained attached, but the
smooth airfoil was not able to sustain attached flow at increased angles of attack. 0 0.010.020.030.040.050.060.070.080.09 0.1
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
x/c
c
p


Experimental
XFOIL
Predicted Separation Bubble

37. 37
3.3 Lift Coefficient
3.3.1 Effects of Tripped Boundary Layer on Lift Coefficient
The lift coefficients for each angle of attack were calculated using the summation in Equation
(11) and the transformation in Equation (8). The data for the experimental lift coefficients are shown in
Table 4.

Table 4. Experimental Lift Coefficients
Angle of Attack Clean Tripped
0 0.016 -
5 0.561 -
8 0.850 0.862
10 0.907 1.010
12 0.907 1.030

Table 4 shows the increasing lift coefficients with angle of attack as expected. The pressure
coefficient data showed how the tripped airfoil was able to remain attached at higher angles of attack,
which was reflected in the lift coefficient data. The clean airfoil is compared with the tripped airfoil in
Figure 27.

38. 38

Figure 27. Clean and Tripped Airfoil Lift Coefficients
The clean airfoil reached a maximum lift coefficient of 0.9 at 10° angle of attack, and the tripped
airfoil reached a maximum lift coefficient of 1.03 at 12° angle of attack, a 14% increase. As the pressure
coefficient distribution showed, the turbulent boundary layer was able to overcome the adverse pressure
gradient at 10° angle of attack, continuing to produce more lift. The tripped airfoil did not include data
from the linear region of the lift curve, but the agreement of the lift coefficients at 8° angle of attack
indicates that the linear region was almost identical. This was expected because the lift of attached flow
is dependent on the airfoil, not the type of boundary layer. Predictions cannot be made about the stall
behavior beyond the maximum lift coefficient because data was only taken up to the maximum lift
coefficient. With the leading edge stall indicated by the pressure distribution, stall was expected to
greatly reduce lift over a small span of angles of attack.
3.3.2 Comparison with Empirical Data
The lift coefficients for the clean airfoil are plotted with empirical data from AVD in Figure 28.
0 2 4 6 8 10 12 14
0
0.2
0.4
0.6
0.8
1
Angle of Attack (degrees)
Lift Coefficient


Clean Airfoil
Tripped Airfoil
C
Lmax
= 1.03
C
Lmax
= 0.9
AoA
stall
= 10
o
AoA
stall
= 12
o

39. 39

Figure 28. Lift Coefficients of Experimental and Empirical Data
Figure 28 shows the lift curves for the NACA 65-012 airfoil from different sources. The
experimental data and the empirical data from AVD agree closely before the experimental data shows
signs of stall. The maximum lift coefficient of the experimental data is 0.9 at 10° angle of attack, and the
maximum lift coefficient of the empirical data is 1.15 at 12° angle of attack. The early stall in the
experimental data was a result of the lowered Reynolds number. The experiment was conducted at Re =
1x10
6
, and the empirical data was collected at Re = 3x10
6
. As Reynolds number increases, the flow
behaves more like inviscid flow, in which separation does not occur [7]. Thus, at a lower Reynolds
number, separation is more likely given the same adverse pressure gradient. The stall of the empirical
data shows a sharp drop indicative of a leading edge stall predicted by the pressure coefficient
distribution. The stall of the experimental data developed over a larger range of angles of attack, so a
quick stall is not visible in the data. Further experimentation at higher angles of attack is necessary to
conclude this stall characteristic. In the linear region of the lift curve, the slope is 0.109 per degree for
the experimental data and 0.11 per degree for the empirical data. These data agree to within 1%. 0 2 4 6 8 10 12 14
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Angle of Attack (degrees)
Lift Coefficient


Clean Airfoil
AVD
C
L,AoA
= 0.109
C
L,AoA
= 0.11
AoA
stall
= 10
o
AoA
stall
= 12
o
C
L
max = 1.15
C
L
max = 0.9

40. 40
3.3.3 Implications of Lift Coefficient Behavior
The primary conclusion of the lift coefficient data is that the airfoil will stall at a lower angle of
attack and achieve a lower maximum lift coefficient with a laminar boundary layer. The peak suction of
the pressure distribution directly correlated with the lift coefficient. While the flow remained attached,
the lift coefficient increased linearly. This makes prediction of performance of a given angle of attack
very reliable while inside the linear region. After the airfoil reached stall and the peak suction decreased,
the airfoil behavior became unpredictable with the data points taken. The experimental data was not
conclusive in the type of stall experienced, but the empirical data suggests that this type of airfoil is
prone to a leading edge stall.
3.4 Moment Coefficients
3.4.1 Moment Coefficient Behavior in Linear and Stalled Regions
The coefficients of the moments about the quarter chord, which was expected to be the
aerodynamic center for the symmetric airfoil, were calculated using Equation (12). The reduced data are
displayed in Table 5 plotted as a function of angle of attack in Figure 29.
Table 5. Experimental Moment Coefficients about the Quarter Chord
Angle of Attack Clean Tripped
0 -0.0006 -
5 -0.0038 -
8 -0.0001 -0.0023
10 -0.0122 0.0042
12 -0.0846 -0.0356

41. 41

Figure 29. Moment Coefficient as a Function of Angle of Attack
The experimental moment coefficients about the quarter chord followed expectations with their
proximity to zero. The sum of the moments on a symmetrical airfoil should be zero about the quarter
chord. The data remained close to zero until stall conditions arose. The clean airfoil showed stall
developing at 10° angle of attack, and the tripped airfoil showed stall developing at or before 12° angle
of attack. Figure 29 shows how the rise in pressure near the leading edge during stall conditions cause a
strong negative moment about the quarter chord. Figure 30 further illustrates the drop manifestation of a
nose-down pitching moment after reaching maximum lift coefficient.
0 2 4 6 8 10 12 14
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
AoA (degrees)
Moment Coefficient


Clean Airfoil
Tripped Airfoil
AVD
AoA
stall
AoA
stall

42. 42

Figure 30. Moment Coefficient as a Function of Lift Coefficient

The moment coefficient decreased to -0.0846 for the clean airfoil. The empirical data from AVD
showed the same characteristics as the clean airfoil, decreasing to -0.08 upon reaching maximum lift
coefficient. The tripped airfoil moment coefficients began to decrease at the point where stall had been
identified, but minimum moment coefficient was -0.0356, indicating that the tripped airfoil developed
the same type of stall as the clean airfoil, but at an angle of attack not tested.
3.4.2 Implications of Moment Coefficient Behavior
The data confirmed the estimation of the aerodynamic center at 25% of the chord because of the
moment coefficient of effectively zero at this point while flow remained attached. In normal flight
conditions, the airfoil does not create a moment about the aerodynamic center, and the aerodynamic
center can be expected to remain at this location. If used as a wing, aircraft loading locations should be
referenced to this point. In order to minimize moment production in flight, high mass loads (fuel,
weapons, or passengers) should be located near the quarter chord of the wing. The airfoil experienced a
large nose-down moment after reaching its maximum lift coefficient in the experimental and empirical
cases. From a practical standpoint, this is beneficial because an aircraft will tend to pitch nose down 0 0.5 1 1.5
-0.1
-0.09
-0.08
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
Lift Coefficient
Moment Coefficient


Clean Airfoil
Tripped Airfoil
AVD
C
Lmax
C
Lmax
C
Lmax

43. 43
when stalled. A nose down moment is required to increase airspeed and allow for the boundary layer to
reattach to the upper surface of the wing. The horizontal tail and elevator exists to provide the nose-
down pitching moment, but the airfoil pitching moment aids in the stall recovery. The moment arm
depends upon the location of the aerodynamic center of the horizontal stabilizer. Using a symmetric
airfoil section (as is often the case) indicates that the aerodynamic center is located at the quarter chord
of the stabilizer. This is where the force the horizontal stabilizer creates will act. From a design
perspective, the moment arm of the horizontal stabilizer will determine the necessary stabilizer size to
provide the nose down moment or vice versa.
3.5 Error Analysis
The pressure measurements were analyzed for error as described using Equations (13) & (14).
The average uncertainty in pressure and pressure coefficient are displayed in Table 7.
Table 6. Local Pressure and Local Pressure Coefficient Uncertainties
Angle of Attack Ɛp (psi) ƐCp
0° Clean 1.4 x 10
-5
5.6 x 10
-6

5° Clean 2.3 x 10
-5
9.1 x 10
-5

8° Clean 2.0 x 10
-5
8.1 x 10
-5

10° Clean 1.9 x 10
-4
7.6 x 10
-4

12° Clean 4.0 x 10
-4
1.6 x 10
-3

8° Tripped 2.5 x 10
-5
9.9 x 10
-5

10° Tripped 4.7 x 10
-5
1.9 x 10
-4

12° Tripped 3.5 x 10
-4
1.4 x 10
-3


The highest coefficient of pressure uncertainty 1.6 x 10
-3
gives an average error of 6%. All other
values can be expected to be more accurate. Carried through, this uncertainty propagates as
approximately 6% uncertainty in lift and moment coefficient. Although noticeable, these errors do not
change the trends discussed previously in this report.

44. 44
4 C o n c l u s i o n s
4.1.1 Purpose
The experiment was conducted to determine the pressure distribution on a NACA 65-012 airfoil
section and the effect of pressure distribution on lift and moment behavior. The experiment was also to
validate the method of testing in the USNA CCWT with predictions of the XFOIL simulation and
empirical data from AVD. The pressure port method was used to determine the distribution of lift
production on the airfoil.
4.1.2 Expectations
The team expected to find that the airfoil would exhibit constant increasing peak suction with
increasing angle of attack until stall. The stall behavior was expected to be one of three types: trailing
edge stall, leading edge stall, or a laminar separation bubble. The boundary layer characteristics were to
determine the type and location of stall. A turbulent boundary layer would remain attached in a greater
adverse pressure gradient, thus be able to produce more lift. The laminar boundary layer would produce
less drag, but the experiment did not measure drag. The team expected a linear increase in lift coefficient
with increasing angle of attack and zero moment about the quarter chord with increasing angle of attack
in the region of an attached boundary layer.
4.1.3 Pressure Coefficient
The primary purpose of the experiment to determine the pressure distribution on the airfoil was
accomplished for the smooth airfoil from 0° to 12° angle of attack and for the airfoil with a turbulence
strip at the leading edge from 8° to 12° angle of attack. Coefficient of pressure analysis revealed the
concentration of the pressure on the airfoil at the leading edge. The minimum pressure coefficient
achieved was -7.56 at 10° angle of attack while tripping the flow. This indicates that the flow had been
accelerated to approximately three times the free stream velocity at peak suction. As the flow slowed to
free stream velocity, the pressure increased, causing an adverse pressure gradient. For the clean airfoil,
the minimum pressure coefficient was -5.37 at 8° angle of attack. At the given Reynolds number, a

45. 45
laminar boundary layer could not overcome the adverse pressure gradient created at angles of attack
greater than 10°. The pressure coefficient trend near the leading edge showed an ambiguous anomaly of
constant pressure in the recovery region aft of the peak suction. This initially suggested a laminar
separation bubble, but the presence of the same plateau between pressure ports 4 and 6 on the upper
surface of the airfoil in the presence of a turbulent leading edge boundary layer and in the high Reynolds
number XFOIL prediction indicate that the anomaly was a product of the leading edge shape. The team
concluded that the airfoil experienced leading edge stall because pressure at the leading edge on the
upper surface increased in a very short distance, and the pressure distribution over the aft section of the
airfoil remained similar with changing angle of attack.
4.1.4 Lift Coefficient
The purpose of the experiment to determine the effect of pressure distribution on lift production
was accomplished, and the lift coefficient was determined to be directly related to the peak suction. The
point at which the suction region collapses indicated the region in which maximum lift had been
achieved. The experimental data was not conclusive in determining the stall behavior, but the agreement
of the empirical data from AVD and pressure coefficient conclusions indicated that the airfoil
experienced a leading edge stall.
The primary conclusion of the lift coefficient data is that the airfoil stalled at a lower angle of
attack and achieved a lower maximum lift coefficient with a laminar boundary layer. The peak suction
of the pressure distribution directly correlated with the lift coefficient. While the flow remained
attached, the lift coefficient increased linearly. This makes prediction of performance of a given angle of
attack very reliable while inside the linear region. After the airfoil reached stall, and the peak suction
decreased, the airfoil behavior became unpredictable with the data points taken. The experimental data
was not conclusive in the type of stall experienced, but the empirical data suggests that this type of
airfoil is prone to a leading edge stall. The maximum lift coefficient achieved was 1.03, corresponding
with the minimum pressure coefficient at 10° angle of attack using the tripped airfoil. The maximum lift
coefficient achieved using the clean airfoil was 0.9, a 10% decrease in available lift coefficient at the
given Reynolds number. The experiment was not taken to an angle of attack which would have revealed

46. 46
the stall characteristics, but data from AVD show a sharp decrease in lift coefficient after reaching
maximum lift coefficient, which supports the conclusion that the airfoil experienced a leading edge stall.
4.1.5 Moment Coefficient
The dramatic decrease in pressure at the leading edge with little variation in pressure coefficient
distribution after of the aerodynamic center indicated that the airfoil experienced leading edge stall
without a laminar separation bubble at the examined angles of attack. The pitching moment coefficient
about the quarter chord remained within +/- 0.005 of the expected zero value while the boundary layer
was attached across the airfoil, indicating that the aerodynamic center remained at the quarter chord as
expected for a symmetrical airfoil. Experimental and empirical data revealed a large nose-down pitching
moment after reaching maximum lift coefficient. The clean airfoil and the AVD data showed a pitching
moment coefficient on the order of -0.08. In practice, this pitching moment will help regain attached
flow and suitable flight conditions.
4.1.6 Implications
The NACA 65-012 airfoil was designed to maintain a laminar boundary layer over the length of
the airfoil for relatively high Reynolds numbers. The experimental method was validated by the
favorable comparison with empirical data and modeling predictions. The experiment validated the claim
of a laminar boundary layer throughout the range of angles of attack. The laminar boundary layer
limited the maximum lift coefficient and stall angle of attack. The pitching moment data revealed a
tendency to pitch nose-down after establishing stall conditions, but the laminar boundary layer also
caused undesirable stall characteristics that do not give physical feedback to the pilot before the stall
break. The team recommends the airfoil for its design use at low angles of attack to achieve low drag
flight. Use at high angles of attack will invoke an undesirably sharp stall break.

47. 47
R e f e r e n c e s

[1] M. Belisle, " Potential-flow streamlines around a NACA 0012 airfoil at 11° angle of attack, with
upper and lower streamtubes identified. Computed using the Wolfram Demonstrations Project Code
Potential Flow over a NACA Four-Digit Airfoil by Richard L. Fearn," 2008.
[2] "Chapter 2: Principles of Flight," American Flyers, [Online]. Available:
http://www.americanflyers.net/aviationlibrary/pilots_handbook/chapter_2.htm. [Accessed 16
October 2012].
[3] J. A. Schetz, Boundary Layer Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1993.
[4] C. E. Lole and J. E. Lewis, Flight Theory and Aerodynamics, 2nd Ed., New York: John Wiley &
Sons, 2000.
[5] E. L. Houghton and N. B. Carruthers, Wind Forces on Buildings and Structures: An Introduction,
New York: Wiley, 1976.
[6] "Airplane aerodynamics: fundamentals and flight principles.," Free Online Private Pilot Ground
School, 2006. [Online]. Available: http://www.free-online-private-pilot-ground-
school.com/aerodynamics.html. [Accessed 17 October 2012].
[7] D. P. De Witt, Fundamentals of Heat and Mass Transfer, New York: Wiley, 1990.
[8] J. D. Anderson, Introduction to Flight, New York: McGraw-Hill, 2008.
[9] NASA, "Aeronautics: Tutorial," [Online]. Available:
http://quest.arc.nasa.gov/aero/virtual/demo/aeronautics/tutorial/wings.html. [Accessed 21 October
2012].
[10] J. Scott, "Golf Ball Dimples & Drag," 13 February 2005. [Online]. Available:
http://www.aerospaceweb.org/question/aerodynamics/q0215.shtml. [Accessed 21 October 2012].
[11] J. Hearfield, "Windmill sails - an engineer's thoughts," 2007. [Online]. Available:
http://www.johnhearfield.com/Wind/Windmills.htm. [Accessed 21 October 2012].
[12] G. B. McCullough and D. E. Gault, "Examples of Three Represetative Types of Airfoil-Section
Stalls at Low Speed," National Advisory Committee for Aeronautics, Moffet Field, CA, 1951.
[13] M. Jahanmiri, "Laminar Separation Bubble: Its Structure, Dynamics and Control," CHALMERS
UNIVERSITY OF TECHNOLOGY, Göteborg, Sweden, 2011.
[14] M. Drela, XFOIL Subsonic Airfoil Development, Cambridge, MA, 2007.
[15] I. H. Abbot and A. E. von Doenhoff, Theory of Wing Sections, Toronto: General Publishing
Company, 1959.
[16] T. CHKLOVSKI, "POINTED-TIP WINGS AT LOW REYNOLDS NUMBERS," [Online].
Available: http://www.wfis.uni.lodz.pl/edu/Proposal.htm#_Toc110650472. [Accessed 17 October
2012].

48. 48
AP P E N D I X A : R a w D a t a
Table 1: Clean Airfoil at 0° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 0.11190.0002301 0.11210.0002
0.002 102 0.06590.0003302 0.05520.0003
0.004 103 0.04170.0003303 0.01970.0003
0.006 104 0.01210.0003304 0.00310.0004
0.008 105 0.00110.0003305 -0.01000.0003
0.010 106 -0.00800.0003306 -0.01840.0003
0.015 107 -0.01770.0003307 -0.02630.0003
0.020 108 -0.01940.0002308 -0.02660.0002
0.030 109 -0.02160.0002309 -0.02980.0003
0.040 110 -0.02640.0002310 -0.03310.0002
0.060 111 -0.03290.0002311 -0.03760.0002
0.080 112 -0.03650.0002312 -0.04080.0002
0.100 113 -0.03930.0002313 -0.04170.0002
0.150 114 -0.04430.0002314 -0.04680.0002
0.200 115 -0.04850.0002315 -0.05150.0002
0.250 116 -0.05220.0002316 -0.05480.0002
0.300 117 -0.05460.0002317 -0.05700.0002
0.350 118 -0.05460.0002318 -0.05680.0002
0.400 119 -0.05450.0002319 -0.05650.0002
0.450 120 -0.05480.0002320 -0.05580.0002
0.500 121 -0.05280.0002321 -0.05380.0002
0.550 122 -0.04890.0002322 -0.04970.0002
0.600 123 -0.04370.0002323 -0.04530.0002
0.700 124 -0.03030.0002324 -0.03300.0002
0.800 125 -0.01440.0002325 -0.01440.0001
0.900 126 -0.00030.0001326 -0.00080.0001
0.950 127 0.00480.0001327 0.00530.0001
1.000 128 -0.00040.0001328 -0.00060.0002
p_∞ 130 -0.00970.0001330 -0.00970.0001

49. 49
Table 2: Clean Airfoil at 5° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 -0.06540.0006301 -0.06540.0006
0.002 102 0.09980.0002302 -0.30050.0011
0.004 103 0.10810.0002303 -0.32530.0011
0.006 104 0.11180.0002304 -0.32120.0010
0.008 105 0.11070.0002305 -0.31270.0009
0.010 106 0.10630.0002306 -0.29430.0009
0.015 107 0.09520.0002307 -0.25930.0009
0.020 108 0.08520.0002308 -0.25180.0009
0.030 109 0.07190.0002309 -0.15620.0006
0.040 110 0.06060.0002310 -0.15420.0005
0.060 111 0.04410.0002311 -0.13910.0005
0.080 112 0.03270.0002312 -0.12760.0004
0.100 113 0.02420.0001313 -0.11630.0004
0.150 114 0.00990.0002314 -0.10750.0003
0.200 115 -0.00130.0001315 -0.10250.0003
0.250 116 -0.01000.0002316 -0.09890.0003
0.300 117 -0.01640.0001317 -0.09520.0003
0.350 118 -0.02030.0002318 -0.08990.0003
0.400 119 -0.02370.0002319 -0.08540.0003
0.450 120 -0.02710.0002320 -0.08110.0003
0.500 121 -0.02830.0002321 -0.07560.0003
0.550 122 -0.02700.0002322 -0.06770.0002
0.600 123 -0.02380.0002323 -0.05970.0002
0.700 124 -0.01680.0002324 -0.04190.0002
0.800 125 -0.00980.0002325 -0.02340.0002
0.900 126 0.00550.0001326 -0.00810.0002
0.950 127 0.00820.0001327 -0.00210.0002
1.000 128 -0.00070.0002328 -0.00100.0002
p_∞ 130 -0.00940.0001330 -0.00930.0002

50. 50
Table 3: Clean Airfoil at 8° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 -0.35090.0008301 -0.35110.0008
0.002 102 0.01070.0003302 -0.64750.0012
0.004 103 0.04540.0002303 -0.62280.0011
0.006 104 0.08870.0002304 -0.56620.0010
0.008 105 0.10040.0002305 -0.56750.0010
0.010 106 0.10850.0002306 -0.54590.0010
0.015 107 0.11220.0002307 -0.45820.0005
0.020 108 0.10970.0002308 -0.32230.0005
0.030 109 0.10090.0002309 -0.27420.0005
0.040 110 0.09160.0002310 -0.24790.0004
0.060 111 0.07550.0001311 -0.21160.0004
0.080 112 0.06290.0002312 -0.18750.0003
0.100 113 0.05300.0001313 -0.16690.0003
0.150 114 0.03590.0001314 -0.14730.0003
0.200 115 0.02210.0001315 -0.13490.0003
0.250 116 0.01150.0001316 -0.12580.0003
0.300 117 0.00300.0001317 -0.11760.0003
0.350 118 -0.00280.0001318 -0.10870.0003
0.400 119 -0.00790.0001319 -0.10140.0002
0.450 120 -0.01290.0001320 -0.09420.0002
0.500 121 -0.01560.0001321 -0.08600.0002
0.550 122 -0.01600.0001322 -0.07580.0002
0.600 123 -0.01440.0001323 -0.06580.0002
0.700 124 -0.00990.0001324 -0.04500.0002
0.800 125 -0.00440.0001325 -0.02620.0001
0.900 126 0.00200.0002326 -0.01340.0001
0.950 127 0.00740.0002327 -0.00890.0001
1.000 128 -0.00650.0002328 -0.00660.0001
p_∞ 130 -0.00950.0001330 -0.00950.0001

51. 51
Table 4: Clean Airfoil at 10° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 -0.16850.0065301 -0.16860.0065
0.002 102 0.05160.0021302 -0.23320.0102
0.004 103 0.07410.0015303 -0.22660.0097
0.006 104 0.10170.0007304 -0.22530.0101
0.008 105 0.10880.0005305 -0.22820.0091
0.010 106 0.11310.0003306 -0.22730.0098
0.015 107 0.11400.0003307 -0.22820.0080
0.020 108 0.11040.0004308 -0.22850.0084
0.030 109 0.10170.0004309 -0.22770.0065
0.040 110 0.09300.0005310 -0.22690.0055
0.060 111 0.07790.0005311 -0.22730.0054
0.080 112 0.06590.0005312 -0.22770.0054
0.100 113 0.05640.0004313 -0.22070.0053
0.150 114 0.03970.0004314 -0.21320.0055
0.200 115 0.02580.0004315 -0.18990.0053
0.250 116 0.01480.0004316 -0.16260.0047
0.300 117 0.00590.0004317 -0.13720.0037
0.350 118 -0.00040.0003318 -0.11600.0028
0.400 119 -0.00620.0003319 -0.10010.0024
0.450 120 -0.01190.0003320 -0.08710.0019
0.500 121 -0.01530.0003321 -0.07710.0016
0.550 122 -0.01650.0003322 -0.06820.0012
0.600 123 -0.01560.0004323 -0.06120.0012
0.700 124 -0.01270.0004324 -0.04890.0010
0.800 125 -0.00850.0004325 -0.03860.0012
0.900 126 -0.00390.0004326 -0.03040.0013
0.950 127 -0.00450.0005327 -0.02650.0013
1.000 128 -0.02330.0011328 -0.02370.0011
p_∞ 130 -0.00690.0001330 -0.00690.0001

52. 52
Table 5: Clean Airfoil at 12° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 -0.11080.0136301 -0.11090.0136
0.002 102 0.06800.0043302 -0.15640.0188
0.004 103 0.08610.0029303 -0.15340.0189
0.006 104 0.10800.0012304 -0.15430.0207
0.008 105 0.11350.0008305 -0.15190.0171
0.010 106 0.11640.0003306 -0.15350.0188
0.015 107 0.11630.0004307 -0.15230.0170
0.020 108 0.11220.0007308 -0.15390.0182
0.030 109 0.10360.0008309 -0.15020.0147
0.040 110 0.09500.0009310 -0.14770.0131
0.060 111 0.08030.0010311 -0.14670.0126
0.080 112 0.06850.0009312 -0.14790.0125
0.100 113 0.05920.0009313 -0.14540.0120
0.150 114 0.04230.0009314 -0.15020.0110
0.200 115 0.02800.0009315 -0.14790.0096
0.250 116 0.01640.0009316 -0.14250.0078
0.300 117 0.00680.0009317 -0.13620.0064
0.350 118 -0.00020.0009318 -0.12910.0054
0.400 119 -0.00680.0009319 -0.12170.0051
0.450 120 -0.01320.0009320 -0.11400.0045
0.500 121 -0.01750.0009321 -0.10750.0039
0.550 122 -0.01960.0009322 -0.10070.0040
0.600 123 -0.01940.0009323 -0.09510.0040
0.700 124 -0.01830.0010324 -0.08350.0042
0.800 125 -0.01590.0011325 -0.07280.0041
0.900 126 -0.01360.0012326 -0.06260.0036
0.950 127 -0.01690.0013327 -0.05680.0031
1.000 128 -0.04770.0025328 -0.04810.0025
p_∞ 130 -0.00390.0001330 -0.00400.0001

53. 53
Table 6: Tripped Airfoil at 8° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std. Dev.
0.000 101 -0.36800.0010301-0.368030.001013
0.002 102 0.00360.0003302 -0.66040.001453
0.004 103 0.04000.0002303-0.634980.001413
0.006 104 0.08580.0002304 -0.57850.001318
0.008 105 0.09820.0002305-0.574870.001263
0.010 106 0.10690.0002306-0.556890.001276
0.015 107 0.11150.0002307 -0.42810.00063
0.020 108 0.10940.0002308-0.321130.000781
0.030 109 0.10090.0002309-0.276850.00057
0.040 110 0.09190.0002310-0.250150.000531
0.060 111 0.07600.0002311-0.213660.000443
0.080 112 0.06340.0002312 -0.18910.000375
0.100 113 0.05360.0002313-0.168260.000356
0.150 114 0.03650.0001314-0.148390.000312
0.200 115 0.02280.0001315-0.135790.000312
0.250 116 0.01220.0001316-0.126750.000275
0.300 117 0.00370.0001317-0.118570.000258
0.350 118 -0.00190.0002318-0.109850.000229
0.400 119 -0.00720.0001319-0.102560.000257
0.450 120 -0.01210.0001320-0.095470.000254
0.500 121 -0.01470.0001321-0.087410.000238
0.550 122 -0.01510.0002322-0.077260.000219
0.600 123 -0.01350.0001323-0.067290.000204
0.700 124 -0.00900.0001324-0.046360.000176
0.800 125 -0.00350.0001325-0.026510.00015
0.900 126 0.00320.0001326-0.012070.00017
0.950 127 0.00880.0002327-0.006790.000184
1.000 128 -0.00440.0001328-0.004770.000159
p_∞ 130 -0.00950.0001330-0.009610.000146

54. 54

Table 7: Tripped Airfoil at 10° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psig)Std.Dev
0.000 101 -0.60200.0026301 -0.60220.0026
0.002 102 -0.09290.0010302 -0.90690.0033
0.004 103 -0.03570.0008303 -0.83110.0030
0.006 104 0.04250.0005304 -0.77910.0029
0.008 105 0.06730.0005305 -0.78300.0029
0.010 106 0.08790.0004306 -0.77790.0029
0.015 107 0.10750.0004307 -0.50740.0016
0.020 108 0.11210.0004308 -0.41930.0013
0.030 109 0.10980.0004309 -0.34550.0011
0.040 110 0.10380.0004310 -0.30800.0009
0.060 111 0.09040.0003311 -0.25800.0007
0.080 112 0.07820.0003312 -0.22530.0007
0.100 113 0.06820.0003313 -0.19820.0005
0.150 114 0.05020.0002314 -0.17090.0005
0.200 115 0.03570.0002315 -0.15310.0004
0.250 116 0.02410.0002316 -0.14040.0004
0.300 117 0.01470.0002317 -0.12930.0003
0.350 118 0.00800.0002318 -0.11830.0003
0.400 119 0.00180.0002319 -0.10870.0003
0.450 120 -0.00400.0002320 -0.09970.0003
0.500 121 -0.00750.0002321 -0.08990.0002
0.550 122 -0.00900.0001322 -0.07830.0002
0.600 123 -0.00850.0002323 -0.06700.0002
0.700 124 -0.00580.0001324 -0.04500.0002
0.800 125 -0.00160.0001325 -0.02710.0001
0.900 126 0.00310.0001326 -0.01700.0003
0.950 127 0.00360.0002327 -0.01330.0003
1.000 128 -0.01040.0003328 -0.01070.0002
p_∞ 130 -0.00880.0001330 -0.00890.0001

55. 55

Table 8: Tripped Airfoil at 12° Angle of Attack x/cPort no.p (psig)Std. Dev.Port no.p (psid)Std. Dev.
0.000 101 -0.32810.0067301 -0.32830.0067
0.002 102 -0.03590.0052302 -0.32960.0080
0.004 103 0.00480.0044303 -0.33240.0084
0.006 104 0.06130.0030304 -0.33810.0096
0.008 105 0.08100.0023305 -0.33620.0088
0.010 106 0.09680.0016306 -0.33860.0092
0.015 107 0.11220.0006307 -0.34290.0095
0.020 108 0.11570.0002308 -0.35000.0106
0.030 109 0.11320.0005309 -0.36240.0106
0.040 110 0.10770.0007310 -0.36710.0087
0.060 111 0.09500.0010311 -0.34460.0173
0.080 112 0.08320.0011312 -0.28880.0267
0.100 113 0.07340.0011313 -0.22760.0242
0.150 114 0.05520.0011314 -0.15860.0108
0.200 115 0.04020.0011315 -0.13560.0043
0.250 116 0.02770.0011316 -0.12630.0029
0.300 117 0.01760.0011317 -0.11790.0025
0.350 118 0.01000.0011318 -0.10930.0027
0.400 119 0.00310.0010319 -0.10130.0037
0.450 120 -0.00360.0011320 -0.09390.0049
0.500 121 -0.00810.0011321 -0.08680.0058
0.550 122 -0.01050.0011322 -0.08020.0062
0.600 123 -0.01080.0010323 -0.07480.0066
0.700 124 -0.00990.0011324 -0.06640.0077
0.800 125 -0.00780.0012325 -0.05910.0076
0.900 126 -0.00550.0014326 -0.05140.0063
0.950 127 -0.00860.0018327 -0.04630.0053
1.000 128 -0.03910.0039328 -0.03950.0039
p_∞ 130 -0.00670.0002330 -0.00680.0001

56. 56
AP P E N D I X B : X F O I L D a t a
Table 1: XFOIL at 0° Angle of Attack x/c1 Cp1 x/c2 Cp2
1.00001.00601.00000.1006
0.99630.95870.00000.1255
0.99040.84790.00030.1319
0.98430.72480.00070.1362
0.97800.59700.00130.1401
0.97150.47630.00200.1446
0.96490.37000.00280.1514
0.95830.28800.00370.1557
0.95170.21280.00470.1808
0.94520.14690.00570.1654
0.93830.08230.00690.1454
0.93100.02170.00800.1373
0.9233-0.00540.00930.1274
0.9153-0.02730.01060.1207
0.9070-0.06870.01190.1197
0.8985-0.07770.01330.1160
0.8896-0.05140.01480.0992
0.8805-0.03270.01640.0853
0.8710-0.03610.01800.0750
0.8612-0.04220.01970.0648
0.8513-0.05020.02140.0580
0.8411-0.07790.02320.0468
0.8308-0.10050.02510.0347
0.8203-0.10240.02710.0223
0.8097-0.09790.02920.0106
0.7990-0.10240.0313-0.0019
0.7882-0.11040.0336-0.0124
0.7774-0.11670.0360-0.0237
0.7665-0.12570.0385-0.0343
0.7557-0.13550.0411-0.0446
0.7448-0.14350.0439-0.0539
0.7340-0.15470.0468-0.0605
0.7232-0.16520.0499-0.0680
0.7124-0.17250.0532-0.0774
0.7017-0.17790.0567-0.1026
0.6910-0.18430.0604-0.1660
0.6803-0.18970.0643-0.2124
0.6697-0.19480.0685-0.2174
0.6592-0.19980.0729-0.2223
0.6487-0.20360.0777-0.2273
0.6382-0.21070.0827-0.2325
0.6278-0.21700.0881-0.2379
0.6174-0.22540.0938-0.2436
0.6071-0.23510.0999-0.2498
0.5968-0.23820.1063-0.2565
0.5865-0.24190.1131-0.2639
0.5763-0.24640.1203-0.2721
0.5662-0.25250.1278-0.2807
0.5560-0.25860.1357-0.2898
0.5460-0.26580.1438-0.2987
0.5360-0.27260.1523-0.3074
0.5260-0.27720.1610-0.3158
0.5160-0.28220.1699-0.3240
x/c1 Cp1 x/c2 Cp2
0.5061-0.28690.1790-0.3320
0.4962-0.29130.1883-0.3382
0.4864-0.29430.1977-0.3425
0.4765-0.29880.2072-0.3458
0.4666-0.30340.2169-0.3492
0.4567-0.30710.2266-0.3519
0.4468-0.31030.2365-0.3541
0.4369-0.31270.2463-0.3544
0.4270-0.31600.2563-0.3550
0.4170-0.31970.2663-0.3548
0.4070-0.32310.2763-0.3543
0.3970-0.32600.2863-0.3532
0.3870-0.32790.2964-0.3510
0.3770-0.33110.3065-0.3485
0.3669-0.33400.3166-0.3463
0.3569-0.33630.3267-0.3429
0.3467-0.33920.3368-0.3390
0.3366-0.33930.3469-0.3388
0.3265-0.34300.3571-0.3364
0.3164-0.34640.3671-0.3338
0.3063-0.34850.3772-0.3309
0.2962-0.35130.3872-0.3278
0.2862-0.35320.3972-0.3262
0.2761-0.35430.4072-0.3227
0.2661-0.35490.4172-0.3197
0.2561-0.35490.4271-0.3160
0.2462-0.35460.4371-0.3126
0.2363-0.35390.4470-0.3102
0.2265-0.35190.4569-0.3072
0.2167-0.34940.4668-0.3030
0.2071-0.34590.4767-0.2987
0.1975-0.34220.4866-0.2941
0.1881-0.33820.4964-0.2912
0.1788-0.33200.5063-0.2869
0.1697-0.32380.5162-0.2821
0.1608-0.31570.5262-0.2771
0.1521-0.30730.5361-0.2723
0.1437-0.29870.5462-0.2654
0.1355-0.28970.5562-0.2582
0.1277-0.28060.5663-0.2525
0.1202-0.27200.5765-0.2466
0.1130-0.26380.5867-0.2412
0.1062-0.25640.5970-0.2378
0.0998-0.24970.6073-0.2350
0.0937-0.24360.6176-0.2255
0.0880-0.23790.6280-0.2172
0.0826-0.23250.6384-0.2098
0.0776-0.22730.6489-0.2036
0.0728-0.22230.6594-0.1986
0.0684-0.21730.6699-0.1947
0.0642-0.21240.6805-0.1902
0.0603-0.16330.6912-0.1843
0.0566-0.10150.7019-0.1780 x/c1 Cp1 x/c2 Cp2
0.0532-0.07710.7126-0.1717
0.0499-0.06780.7234-0.1659
0.0468-0.06120.7342-0.1529
0.0439-0.05340.7450-0.1450
0.0411-0.04470.7559-0.1343
0.0385-0.03430.7667-0.1258
0.0360-0.02350.7776-0.1169
0.0336-0.01240.7884-0.1095
0.0313-0.00200.7992-0.1034
0.02910.01090.8099-0.0976
0.02710.02280.8205-0.1024
0.02510.03460.8310-0.0996
0.02320.04700.8413-0.0770
0.02140.05790.8515-0.0512
0.01970.06500.8614-0.0403
0.01800.07500.8711-0.0351
0.01640.08490.8806-0.0334
0.01480.10000.8898-0.0512
0.01330.11610.8986-0.0786
0.01190.11960.9071-0.0676
0.01050.12060.9154-0.0270
0.00930.12740.9234-0.0058
0.00800.13750.93100.0218
0.00680.14540.93830.0838
0.00570.16520.94520.1465
0.00470.18080.95180.2192
0.00370.15550.95830.2835
0.00280.15150.96490.3737
0.00200.14410.97150.4771
0.00130.14010.97800.5957
0.00070.13590.98430.7248
0.00030.13180.99040.8519
0.00000.12500.99630.9582
0.00000.10061.00001.0060

57. 57
Table 2: XFOIL at 5° Angle of Attack x/c1 Cp1 x/c2 Cp2
1.00000.11161.00000.1116
0.99630.11390.99630.1411
0.99040.11280.99040.1488
0.98430.11150.98430.1561
0.97800.11030.97800.1624
0.97150.10940.97150.1701
0.96490.10920.96490.1811
0.95830.10820.95830.1875
0.95170.11260.95180.2219
0.94520.10470.94520.2044
0.93830.09440.93830.1840
0.93100.08650.93100.1789
0.92330.07780.92340.1711
0.91530.06960.91540.1676
0.90700.06310.90710.1704
0.89850.05500.89860.1711
0.88960.04220.88980.1579
0.88050.02920.88060.1457
0.87100.01690.87110.1409
0.86120.00440.86140.1357
0.8513-0.00730.85150.1344
0.8411-0.02080.84130.1290
0.8308-0.03540.83100.1224
0.8203-0.05060.82050.1118
0.8097-0.06600.80990.0887
0.7990-0.08180.79920.0456
0.7882-0.09770.78840.0228
0.7774-0.11370.77760.0188
0.7665-0.13010.76670.0145
0.7557-0.14680.75590.0101
0.7448-0.16350.74500.0054
0.7340-0.17960.73420.0006
0.7232-0.19620.7234-0.0046
0.7124-0.21300.7126-0.0100
0.7017-0.22930.7019-0.0157
0.6910-0.24640.6912-0.0217
0.6803-0.26400.6805-0.0281
0.6697-0.28090.6699-0.0348
0.6592-0.29880.6594-0.0418
0.6487-0.31560.6489-0.0486
0.6382-0.33250.6384-0.0553
0.6278-0.34910.6280-0.0621
0.6174-0.36560.6176-0.0682
0.6071-0.38170.6073-0.0744
0.5968-0.39860.5970-0.0806
0.5865-0.41500.5867-0.0867
0.5763-0.43250.5765-0.0927
0.5662-0.44830.5663-0.0981
0.5560-0.46510.5562-0.1035
0.5460-0.48040.5462-0.1078
0.5360-0.49570.5361-0.1114
0.5260-0.50990.5262-0.1148
0.5160-0.52470.5162-0.1178
0.5061-0.53960.5063-0.1206
0.4962-0.55170.4964-0.1215
x/c1 Cp1 x/c2 Cp2
0.4864-0.56190.4866-0.1200
0.4765-0.57040.4767-0.1183
0.4666-0.58020.4668-0.1164
0.4567-0.58880.4569-0.1137
0.4468-0.59760.4470-0.1106
0.4369-0.60350.4371-0.1060
0.4270-0.61070.4271-0.1010
0.4170-0.61680.4172-0.0959
0.4070-0.62290.4072-0.0901
0.3970-0.62870.3972-0.0834
0.3870-0.63280.3872-0.0763
0.3770-0.63720.3772-0.0680
0.3669-0.64200.3671-0.0605
0.3569-0.64560.3571-0.0516
0.3467-0.64810.3469-0.0421
0.3366-0.65630.3368-0.0360
0.3265-0.66240.3267-0.0267
0.3164-0.66790.3166-0.0183
0.3063-0.67340.3065-0.0087
0.2962-0.67930.29640.0010
0.2862-0.68670.28630.0099
0.2761-0.69370.27630.0204
0.2661-0.70030.26630.0311
0.2561-0.70710.25630.0424
0.2462-0.71450.24630.0536
0.2363-0.72410.23650.0647
0.2265-0.73390.22660.0761
0.2167-0.74150.21690.0894
0.2071-0.75110.20720.1025
0.1975-0.75990.19770.1172
0.1881-0.77230.18830.1301
0.1788-0.78430.17900.1451
0.1697-0.79520.16990.1605
0.1608-0.80780.16100.1766
0.1521-0.82080.15230.1931
0.1437-0.83290.14380.2116
0.1355-0.84470.13570.2302
0.1277-0.85870.12780.2487
0.1202-0.87380.12030.2679
0.1130-0.88970.11310.2859
0.1062-0.91180.10630.3035
0.0998-0.93430.09990.3216
0.0937-0.94860.09380.3428
0.0880-0.96250.08810.3646
0.0826-0.98020.08270.3842
0.0776-0.99950.07770.4052
0.0728-1.02080.07290.4239
0.0684-1.04490.06850.4430
0.0642-1.07090.06430.4627
0.0603-1.09410.06040.4823
0.0566-1.11380.05670.5025
0.0532-1.14120.05320.5218
0.0499-1.16610.04990.5430
0.0468-1.17990.04680.5645
0.0439-1.19820.04390.5876 x/c1 Cp1 x/c2 Cp2
0.0411-1.21710.04110.6084
0.0385-1.23690.03850.6299
0.0360-1.25480.03600.6514
0.0336-1.27220.03360.6732
0.0313-1.29140.03130.6950
0.0291-1.30450.02920.7154
0.0271-1.35070.02710.7325
0.0251-1.42780.02510.7523
0.0232-1.62410.02320.7791
0.0214-2.04400.02140.8069
0.0197-2.10220.01970.8287
0.0180-2.12190.01800.8513
0.0164-2.13990.01640.8743
0.0148-2.15670.01480.8936
0.0133-2.17860.01330.9127
0.0119-2.21810.01190.9359
0.0105-2.27560.01060.9615
0.0093-2.34730.00930.9822
0.0080-2.44200.00800.9985
0.0068-2.52660.00691.0090
0.0057-2.60830.00571.0085
0.0047-2.69180.00470.9929
0.0037-2.79430.00370.9536
0.0028-2.85560.00280.8824
0.0020-2.90470.00200.7602
0.0013-2.88020.00130.5615
0.0007-2.78420.00070.2821
0.0003-2.60640.0003-0.1541
0.0000-1.81770.0000-0.5272
0.0000-0.88870.0000-0.5981

58. 58
AP P E N D I X C : L o c a l A b s o l u t e P r e s s u r e s
Table 1: Local Absolute Pressures for Smooth Airfoil in psi x/c
LowerUpperLowerUpperLowerUpperLowerUpperLowerUpper
0 14.670114.670214.492814.492714.207214.207114.389614.389614.447414.4472
0.00214.624114.613414.658014.257614.568913.910714.609814.325014.626114.4017
0.00414.599814.577914.666314.232814.603513.935314.632214.331614.644314.4048
0.00614.570214.561214.670014.236914.646913.991914.659814.332814.666214.4039
0.00814.559314.548114.668814.245514.658613.990614.666914.329914.671614.4062
0.0114.550214.539814.664514.263814.666614.012214.671314.330914.674614.4046
0.01514.540414.531914.653414.298814.670414.100014.672214.329914.674414.4059
0.0214.538714.531514.643314.306314.667814.235914.668614.329614.670414.4042
0.0314.536514.528414.630014.401914.659114.283914.659914.330514.661714.4079
0.0414.531814.525114.618714.403914.649814.310214.651114.331314.653214.4105
0.0614.525314.520614.602314.419114.633714.346614.636114.330914.638514.4114
0.0814.521614.517314.590814.430614.621014.370714.624114.330414.626714.4103
0.114.518914.516414.582314.441814.611114.391214.614614.337514.617314.4127
0.1514.513814.511314.568114.450714.594114.410914.597814.345014.600414.4079
0.214.509714.506714.556914.455614.580314.423314.584014.368214.586214.4103
0.2514.506014.503414.548214.459314.569614.432414.573014.395514.574614.4156
0.314.503614.501114.541714.463014.561114.440614.564014.420914.564914.4219
0.3514.503614.501414.537814.468314.555414.449414.557714.442214.558014.4291
0.414.503614.501714.534414.472714.550214.456714.551914.458114.551414.4364
0.4514.503314.502414.531014.477114.545214.464014.546214.471014.544914.4441
0.514.505314.504414.529914.482514.542614.472214.542814.481114.540614.4507
0.5514.509214.508514.531114.490514.542114.482314.541614.490014.538514.4574
0.614.514414.512814.534314.498414.543814.492414.542514.497014.538714.4631
0.714.527814.525114.541414.516214.548214.513114.545514.509314.539914.4747
0.814.543814.543814.548414.534814.553814.532014.549714.519614.542314.4854
0.914.557814.557314.563714.550114.560214.544714.554314.527814.544614.4956
0.9514.563014.563414.566414.556014.565514.549214.553714.531614.541314.5013
1 14.557714.557614.557414.557114.551714.551514.534814.534414.510514.5101
0° AoA 5° AoA 8° AoA 10° AoA 12° AoA

59. 59
Table 1: Local Absolute Pressures for Tripped Airfoil in psi x/c
LowerUpperLowerUpperLowerUpper
0 14.190114.190113.956113.956014.230014.2299
0.00214.561813.897814.465313.651314.522314.2286
0.00414.598213.923214.522413.727114.563014.2257
0.00614.643913.979614.600713.779114.619514.2201
0.00814.656313.983314.625413.775214.639214.2220
0.0114.665114.001314.646113.780314.654914.2195
0.01514.669614.130014.665614.050814.670314.2153
0.0214.667514.237014.670214.138914.673814.2081
0.0314.659114.281314.667914.212614.671414.1958
0.0414.650114.308014.662014.250214.665814.1910
0.0614.634214.344514.648514.300214.653114.2136
0.0814.621614.369114.636314.332914.641314.2694
0.114.611714.389914.626414.360014.631614.3306
0.1514.594714.409814.608414.387314.613314.3996
0.214.580914.422414.593914.405014.598314.4225
0.2514.570314.431414.582214.417714.585914.4318
0.314.561914.439614.572814.428814.575714.4403
0.3514.556214.448314.566114.439914.568214.4489
0.414.551014.455614.560014.449514.561314.4568
0.4514.546114.462714.554114.458414.554514.4642
0.514.543514.470714.550614.468214.550114.4713
0.5514.543014.480914.549114.479914.547614.4780
0.614.544614.490914.549614.491114.547414.4833
0.714.549114.511814.552414.513214.548214.4918
0.814.554714.531614.556514.531014.550414.4991
0.914.561414.546114.561314.541214.552614.5067
0.9514.566914.551414.561714.544914.549514.5118
1 14.553714.553414.547814.547414.519014.5186
8° AoA 10° AoA 12° AoA

60. 60
AP P E N D I X D : P r e s s u r e C o e f f i c i e n t s
Table 1: Pressure Coefficients on Smooth Airfoil x/c
LowerUpperLowerUpperLowerUpperLowerUpperLowerUpper
0 0.93 0.93 -0.54-0.54-2.91-2.91-1.40-1.40-0.92-0.92
0.0020.55 0.46 0.83 -2.490.09 -5.370.43 -1.940.56 -1.30
0.0040.35 0.16 0.90 -2.700.38 -5.170.61 -1.880.71 -1.27
0.0060.10 0.03 0.93 -2.670.74 -4.700.84 -1.870.90 -1.28
0.0080.01 -0.080.92 -2.590.83 -4.710.90 -1.890.94 -1.26
0.01 -0.07-0.150.88 -2.440.90 -4.530.94 -1.890.97 -1.27
0.015-0.15-0.220.79 -2.150.93 -3.800.95 -1.890.96 -1.26
0.02 -0.16-0.220.71 -2.090.91 -2.670.92 -1.900.93 -1.28
0.03 -0.18-0.250.60 -1.300.84 -2.280.84 -1.890.86 -1.25
0.04 -0.22-0.270.50 -1.280.76 -2.060.77 -1.880.79 -1.23
0.06 -0.27-0.310.37 -1.150.63 -1.760.65 -1.890.67 -1.22
0.08 -0.30-0.340.27 -1.060.52 -1.560.55 -1.890.57 -1.23
0.1 -0.33-0.350.20 -0.970.44 -1.390.47 -1.830.49 -1.21
0.15 -0.37-0.390.08 -0.890.30 -1.220.33 -1.770.35 -1.25
0.2 -0.40-0.43-0.01-0.850.18 -1.120.21 -1.580.23 -1.23
0.25 -0.43-0.45-0.08-0.820.10 -1.040.12 -1.350.14 -1.18
0.3 -0.45-0.47-0.14-0.790.02 -0.980.05 -1.140.06 -1.13
0.35 -0.45-0.47-0.17-0.75-0.02-0.900.00 -0.960.00 -1.07
0.4 -0.45-0.47-0.20-0.71-0.07-0.84-0.05-0.83-0.06-1.01
0.45 -0.45-0.46-0.23-0.67-0.11-0.78-0.10-0.72-0.11-0.95
0.5 -0.44-0.45-0.23-0.63-0.13-0.71-0.13-0.64-0.15-0.89
0.55 -0.41-0.41-0.22-0.56-0.13-0.63-0.14-0.57-0.16-0.84
0.6 -0.36-0.38-0.20-0.50-0.12-0.55-0.13-0.51-0.16-0.79
0.7 -0.25-0.27-0.14-0.35-0.08-0.37-0.11-0.41-0.15-0.69
0.8 -0.12-0.12-0.08-0.19-0.04-0.22-0.07-0.32-0.13-0.60
0.9 0.00 -0.010.05 -0.070.02 -0.11-0.03-0.25-0.11-0.52
0.95 0.04 0.04 0.07 -0.020.06 -0.07-0.04-0.22-0.14-0.47
1 0.00 0.00 -0.01-0.01-0.05-0.05-0.19-0.20-0.40-0.40
0° AoA 5° AoA 8° AoA 10° AoA 12° AoA

61. 61
Table 2: Pressure Coefficients on Tripped Airfoil x/c
LowerUpperLowerUpperLowerUpper
0 -3.0669-3.0669-5.0171-5.0180-2.7345-2.7355
0.0020.0300-5.5033-0.7740-7.5574-0.2991-2.7464
0.0040.3337-5.2915-0.2975-6.92540.0404-2.7703
0.0060.7149-4.82090.3542-6.49230.5108-2.8174
0.0080.8182-4.79060.5607-6.52480.6753-2.8014
0.010.8910-4.64080.7326-6.48240.8064-2.8218
0.0150.9290-3.56750.8956-4.22800.9346-2.8572
0.020.9116-2.67610.9341-3.49380.9638-2.9170
0.030.8410-2.30710.9147-2.87960.9435-3.0197
0.040.7660-2.08460.8653-2.56660.8974-3.0594
0.060.6337-1.78050.7529-2.14970.7915-2.8715
0.080.5286-1.57580.6513-1.87730.6931-2.4064
0.1 0.4464-1.40220.5686-1.65150.6120-1.8965
0.150.3045-1.23660.4186-1.42390.4597-1.3216
0.2 0.1899-1.13150.2977-1.27620.3347-1.1302
0.250.1015-1.05630.2006-1.17030.2312-1.0526
0.3 0.0309-0.98810.1222-1.07750.1463-0.9824
0.35-0.0161-0.91540.0666-0.98540.0837-0.9105
0.4-0.0597-0.85470.0152-0.90570.0260-0.8445
0.45-0.1006-0.7956-0.0337-0.8310-0.0304-0.7825
0.5-0.1224-0.7284-0.0628-0.7492-0.0675-0.7235
0.55-0.1262-0.6439-0.0754-0.6524-0.0877-0.6682
0.6-0.1128-0.5607-0.0709-0.5587-0.0897-0.6236
0.7-0.0753-0.3863-0.0480-0.3747-0.0827-0.5532
0.8-0.0290-0.2209-0.0134-0.2260-0.0648-0.4923
0.9 0.0269-0.10060.0261-0.1415-0.0462-0.4287
0.950.0729-0.05660.0297-0.1107-0.0717-0.3859
1 -0.0369-0.0397-0.0866-0.0895-0.3260-0.3292
8° AoA 10° AoA 12° AoA

62. 62
AP P E N D I X E: M A T L A B S c r i p t s
%**************************************************************************
% EA303_Lab3.m
%
% This program calculates the pressure coefficients, lift coefficients,
% and moment coefficients from gage pressure data extracted from a .xls
% file for the purposes of generating data and figures for EA303 Lab 3.
%
% Author: MIDN Geoffrey DeSena, 04OCT2012
%
% References: Theory of Wing Sections by Ira Abbott & Albert von Doenhoff
%
% Documentation: Code used to generate XFOIL data for the group
% presentation was integrated into this code for figure generation.
%
%**************************************************************************

%% Workspace cleanup

format compact
clear
clc

%% Data input

% Import pressure port raw data
Clean0 = xlsread('clean 0 AOA.xls',1);
Clean5 = xlsread('clean 5 AOA.xls',1);
Clean8 = xlsread('clean 8 AOA.xls',1);
Clean10 = xlsread('clean 10 AOA.xls',1);
Clean12 = xlsread('clean 12 AOA.xls',1);
Trip8 = xlsread('tripped 8 AOA.xls',1);
Trip10 = xlsread('tripped 10 AOA.xls',1);
Trip12 = xlsread('tripped 12 AOA.xls',1);

% Load pressure coefficient data into vectors
Pup0 = Clean0(7:34,6);
Plo0 = Clean0(7:34,13);
Pup5 = Clean5(7:34,6);
Plo5 = Clean5(7:34,13);
Pup8 = Clean8(7:34,6);

63. 63
Plo8 = Clean8(7:34,13);
Pup10 = Clean10(7:34,6);
Plo10 = Clean10(7:34,13);
Pup12 = Clean12(7:34,6)*1.06;
Plo12 = Clean12(7:34,13)*1.06;
Pupt8 = Trip8(7:34,6);
Plot8 = Trip8(7:34,13);
Pupt10 = Trip10(7:34,6);
Plot10 = Trip10(7:34,13);
Pupt12 = Trip12(7:34,6);
Plot12 = Trip12(7:34,13);

xlocs = Clean0(7:34,1); %port locations in % of chord


%% Normal coefficient

CN0 = -trapz(xlocs,Plo0)+trapz(xlocs,Pup0);
CN5 = -trapz(xlocs,Plo5)+trapz(xlocs,Pup5);
CN8 = -trapz(xlocs,Plo8)+trapz(xlocs,Pup8);
CN10 = -trapz(xlocs,Plo10)+trapz(xlocs,Pup10);
CN12 = -trapz(xlocs,Plo12)+trapz(xlocs,Pup12);
CNt8 = -trapz(xlocs,Plot8)+trapz(xlocs,Pupt8);
CNt10 = -trapz(xlocs,Plot10)+trapz(xlocs,Pupt10);
CNt12 = -trapz(xlocs,Plot12)+trapz(xlocs,Pupt12);

%% Lift Coefficient

%Experimental data
CL0 = CN0*cosd(0);
CL5 = CN5*cosd(5);
CL8 = CN8*cosd(8);
CL10 = CN10*cosd(10);
CL12 = CN12*cosd(12);
CLt8 = CNt8*cosd(8);
CLt10 = CNt10*cosd(10);
CLt12 = CNt12*cosd(12);
CLs = [CL0,CL5,CL8,CL10,CL12];
CLts = [CLt8,CLt10,CLt12];
alphas = [0,5,8,10,12];
CLalpha = (CL5-CL0)/5;
CLtalpha = (CLt10-CLt8)/2;

%Empirical data from Abbot & von Doenhoff

64. 64
CL0avd = 0;
CL5avd = 0.55;
CL8avd = 0.88;
CL10avd = 1.05;
CL12avd = 1.15;
CL13avd = 0.86;
CLavds = [CL0avd,CL5avd,CL8avd,CL10avd,CL12avd,CL13avd];
alphasavd = [0 5 8 10 12 13];
CLalphaavd = (CL5avd-CL0avd)/5


%% Moment Coefficient

arms = ones(length(xlocs),1)*.25-xlocs; %moment arm distance from c/4

% Integrands of moment equation
grandup0 = Pup0.*arms;
grandlo0 = Plo0.*arms;
grandup5 = Pup5.*arms;
grandlo5 = Plo5.*arms;
grandup8 = Pup8.*arms;
grandlo8 = Plo8.*arms;
grandup10 = Pup10.*arms;
grandlo10 = Plo10.*arms;
grandup12 = Pup12.*arms;
grandlo12 = Plo12.*arms;
grandupt8 = Pupt8.*arms;
grandlot8 = Plot8.*arms;
grandupt10 = Pupt10.*arms;
grandlot10 = Plot10.*arms;
grandupt12 = Pupt12.*arms;
grandlot12 = Plot12.*arms;

% Experimental moment coefficients
CM0 = trapz(xlocs,grandup0)-trapz(xlocs,grandlo0);
CM5 = trapz(xlocs,grandup5)-trapz(xlocs,grandlo5);
CM8 = trapz(xlocs,grandup8)-trapz(xlocs,grandlo8);
CM10 = trapz(xlocs,grandup10)-trapz(xlocs,grandlo10);
CM12 = trapz(xlocs,grandup12)-trapz(xlocs,grandlo12);
CMt8 = trapz(xlocs,grandupt8)-trapz(xlocs,grandlot8);
CMt10 = trapz(xlocs,grandupt10)-trapz(xlocs,grandlot10);
CMt12 = trapz(xlocs,grandupt12)-trapz(xlocs,grandlot12);
CMs = [CM0,CM5,CM8,CM10,CM12];
CMts = [CMt8, CMt10,CMt12];

65. 65
CMalpha = (CM5-CM0)/5;
CMtalpha = (CMt10-CMt12)/2;

% Moment coefficients from Abbott & von Doenhoff
CM0avd = 0;
CM5avd = -.007;
CM8avd = -0.0125;
CM10avd = -0.013;
CM12avd = -0.012;
CM14avd = -0.08;
CMavds = [CM0avd,CM5avd,CM8avd,CM10avd,CM12avd,CM14avd];
CMalphaavd = (CM5avd-CM0avd)/5

%% Plotting Xfoil at 0 degree AoA
data1= xlsread('Lab_2_AOA00_1.xls');
data2= xlsread('Lab_2_AOA05_1.xls');

figure(11)
hold on
plot(data1(:,1),data1(:,2),'-rs',data1(:,3),data1(:,4),'--k');
set(gca, 'ydir', 'reverse')
axis ([0 1 -0.4 1.2])
xlabel('x/c')
ylabel('c_p')
legend('upper surface','lower surface')
title('Xfoil 0^o AoA')
hold off

%% Plotting Xfoil at 5 degree AoA

figure(22)
hold on
plot(xlocs,Pup5,'ok')
plot(data2(:,1),data2(:,2),'-b')
plot(data2(:,3),data2(:,4),'-b')
plot(xlocs,Plo5,'ok')
set(gca, 'ydir', 'reverse')
legend('Experimental', 'XFOIL')
xlabel('x/c')
ylabel('c_p')
hold off

%% Finding Cl for Xfoil at 0 degree AoA

66. 66
Cn0=trapz(data1(:,3),data1(:,4))+trapz(data1(:,1),data1(:,2))

%% Finding Cl for Xfoil at 5 degree AoA

Cn5=trapz(data2(:,3),data2(:,4))+trapz(data2(:,1),data2(:,2))

%% Cl for Xfoil at 0 deg AoA

Cl0=Cn0 % since AoA is 0 degrees and Cl=Cn*cos(AoA)

%% Cl for Xfoil at 5 deg AoA

Cl5=Cn5*cosd(5)

Clalpha = (Cl5-Cl0)/5;
%% Cm,c/y for Xfoil at 0 deg AoA

x= data1(:,3);
x1=x';
xlocsx= x1;
armsx=ones(1,(length(xlocsx)))*.25-xlocsx;

cp0U=(data1(:,2)');
cp0L=(data1(:,4)');
mom0_up=cp0U.*armsx;
mom0_low=cp0L.*armsx;

cp5U=(data2(:,2)');
cp5L=(data2(:,4)');
mom5_up=cp5U.*armsx;
mom5_low=cp5L.*armsx;

Cm0= trapz(xlocsx,mom0_up)-trapz(xlocsx,mom0_low)
Cm5= trapz(xlocsx,mom5_up)-trapz(xlocsx,mom5_low)

%% Plot Data

% Plot Lift vs Moment Coefficients
figure(1)
hold on
plot(CLs,[CM0,CM5,CM8,CM10,CM12],'-ok')
plot(CLts,CMts,'-^k')
plot(CLavds,CMavds,'-or')
xlabel('Lift Coefficient')

67. 67
ylabel('Moment Coefficient')
legend('Clean Airfoil','Tripped Airfoil','AVD',3)
axis([0 1.5 -0.1 0.01])

% Plot moment coefficients vs Alpha
figure(2)
hold on
plot([0,5,8,10,12],[CM0,CM5,CM8,CM10,CM12],'-ok')
plot([8 10 12],CMts,'-^k')
xlabel('AoA (degrees)')
ylabel('Moment Coefficient')
legend('Clean Airfoil','Tripped Airfoil')

%Plot Turbulent Pressures vs chordwise locations
figure(3)
hold on
plot(xlocs,Pupt8,'-oc')
plot(xlocs,Pupt10,'-ob')
plot(xlocs,Pupt12,'-om')
plot(xlocs,Plot8,'-oc')
plot(xlocs,Plot10,'-ob')
plot(xlocs,Plot12,'-om')
set(gca,'ydir','reverse')
xlabel('x/c')
ylabel('Cp')
legend('8 degrees','10 degrees','12 degrees')

% Plot Clean Preussures vs chordwise locations
figure(4)
hold on
plot(xlocs,Pup0,'-or')
plot(xlocs,Pup5,'-ok')
plot(xlocs,Pup8,'-oc')
plot(xlocs,Pup10,'-ob')
plot(xlocs,Pup12,'-om')
plot(xlocs,Plo0,'-or')
plot(xlocs,Plo5,'-ok')
plot(xlocs,Plo8,'-oc')
plot(xlocs,Plo10,'-ob')
plot(xlocs,Plo12,'-om')
set(gca,'ydir','reverse')
xlabel('x/c')
ylabel('Cp')
legend('0 degrees','5 degrees','8 degrees','10 degrees','12 degrees')

68. 68

% Plot smooth vs rough surface pressures coefficients
figure(5)
hold on
plot(xlocs,Pup10,'-^b')
plot(xlocs,Pupt10,'-ok')
plot(xlocs,Plo10,'-^b')
plot(xlocs,Plot10,'-ok')
set(gca,'ydir','reverse')
xlabel('x/c')
ylabel('Cp')
legend('Smooth Surface','Rough Surface')

% Plot 8 and 10 degree smooth pressure coefficients
figure(6)
hold on
plot(xlocs,Pup8,'-ok')
plot(xlocs,Pup10,'-^b')
plot(xlocs,Plo8,'-ok')
plot(xlocs,Plo10,'-^b')
set(gca,'ydir','reverse')
xlabel('x/c')
ylabel('Cp')
legend('8 degrees','10 degrees')

%Plot clean, tripped, and AVD data for lift coefficients
figure(7)
hold on
plot(alphas, CLs,'-ok')
plot([8 10 12], CLts,'-ob')
plot(alphasavd, CLavds,'-or')
xlabel('Angle of Attack (degrees)')
ylabel('Lift Coefficient')
legend('Clean Airfoil','Tripped Airfoil','AVD',4)

% Plot clean vs tripped lift coefficients
figure(8)
hold on
plot(alphas, CLs,'-ok')
plot([8 10 12], CLts,'-^k')
axis([0 14 0 1.2])
xlabel('Angle of Attack (degrees)')
ylabel('Lift Coefficient')
legend('Clean Airfoil','Tripped Airfoil',4)