Abstract:
In this experiment, the use of a scale model airfoil section of an aircraft wing will be analyzed in a wind tunnel. The basic physical laws of engineering and science shall be applied to verify and to understand the principles of flight. A dimensional analysis will be applied to the model airfoil to represent a full-scale wing prototype. The basics of aerodynamics, as applied to standard NACA airfoil configurations, shall be applied to establish performance data regarding lift, drag and stall with respect to the various angles attack demonstrated throughout the experiment at a number of air speeds.
It should be noted that the Cessna 152 trainer aircraft uses a NACA 2412 airfoil, which is slightly thinner than the NASA 2415 airfoil currently available in this laboratory. Other airfoil models used in this laboratory include the NACA 4415 (normally used on the Lake Amphibious aircraft) and the NACA 0015 (used on helicopter blades and some acrobatic aircraft). The NACA 4415 is a very high lift airfoil designed to lift aircraft out of water quickly.

Table of Content

Abstract………..........................................................................................................................ii

1. Introduction....................................................................................................................4 2. Theory............................................................................................................................5 3. Results and Discussion.................................................................................................6,7 4. Conclusions………………………..............................................................................8,9 5. Appendix.......................................................................................................................10 6. References.....................................................................................................................19

LIST OF FIGURES

1. Figure 1: Airfoil nomenclature………………….............................................................5 2. Figure 2: Wind Tunnel ……………….………………..…………………….…....…….6 3. Figure 3: Drag, lift and angle of attack ………………………….………….…....……..6 4. Figure 4: Upper and lower pressure coefficient using chord position.............................10 5. Figure 5: Graph showing lift force from different AOA…………………………….....11

LIST OF TABLES

1. Table 1: Distance of pressure sensing port and X/C ratio………………….…………13 2. Table 2: Surface area of upper and lower ports………..……………………………...13 3. Table 3: Upper Lift force at 789 RPM…………………………………………….......14 4. Table 4: Lower lift force at 789 RPM…………...……………………….…………....14 5. Table 5: Upper lift force at 1168 RPM………...…….…………………………….….15 6. Table 6: Lower lift force at 1168 RPM …………………………………….…....…....15 7. Table 7: Upper lift force at 1300 RPM……………………………………...………...16 8. Table 8: Lower lift force at 1300 RPM…………………………….......…....…...…...16 9. Table 9: Pressure coefficients of upper pin at 3 wind velocities…………….………..17 10. Table 10: Lower pressure coefficient at 3 wing velocities………………….….……..18 11. Total lift force at different velocity……………………….……….......…....….……..18

Introduction:
In aerodynamics, researchers have tried to find the most efficient way to produce the highest lift in an aircraft while reducing the drag generated on the wing. By studying the wing in two parts, (1) the cross sectional area of an airfoil and (2) the modification of the airfoil properties along the finite wing, researchers are able to produce the maximum lift while achieving minimum drag. To test the airfoil wing, a scale model aircraft wing is tested using a wind tunnel that allows air to flow over the wing. Using the various flow velocities produced across a certain area of the wing, the pressure difference over that segment will help us calculate the amount of lift produced by the wing. This lab experiment will help understand the governing phenomena of the lift and drag on an aircraft foil and how these forces are differently affecting the wind velocity and angle of attach of the airfoil. By being able to calculate these forces and perform dimensional analysis, research engineers are able to use small prototypes to better understand how a full size aircraft will perform under these actual wind conditions.

Theory:
An airfoil consists of some dimensional nomenclature such as chord, chord line, mean camber line, camber, thickness, leading edge and trailing edge (Figure 1). The airfoil used for this experiment is a prototype of NACA 4415 which has a chord length of 42 inches (1). Due to the high cost of testing full size airfoils, the experiment uses a miniature scaled model of NACA 4415 with a chord length of 6 inches. This model has a scale factor of 7 by using the equation
S= CModel CPrototype [1] where S is the scale factor, CModel (in) is the chord length of the model and CPrototype (in) is the chord length of the prototype. This scale factor shows how large the prototype is compared to its model.

Figure 1: Airfoil nomenclature

Moreover, the scale factor (S) is used for finding the aerodynamic wing area of the model AModel (in^2) using the equation AModel= APrototype S2 [2] where APrototype (in ^2) is the wing area of the prototype. Another important parameter associated with the model scale is the lift force
LModel = LPrototypeS [3]
Where LModel (lbf) is the lift force of the model, LPrototype (lbf) is the lift force of the prototype and S is the scale factor.
The modeled NACA 4415 airfoil is placed inside a wind tunnel, FLOTEK 1440 (Figure 2), to simulate air velocity, from which pressure measurements are recorded. The wind tunnel generates various air speeds through the entrance cone into the test section by a variable speed fan. The air velocity through the test section had a variable up to 132 fps (40m/s).The test section has clear acrylic side walls and top to give a clear observation of the test in progress. The airfoil has a series of 16 Pitot tubes that are connected to 16 venturis. A Pitot tube is stationed at the front end of the test section to directly sense the static and total pressure of airflow. The Pitot tube was connected to a manometer to measure the pressure difference between its static and total pressure ports, providing a measure of the velocity pressure.

Figure 2: Wind Tunnel

Using the air flow of the wind tunnel, the speed of the moving airfoil is simulated. This speed creates two forces: lift force L and drag force D which is crucial to the flight of an aircraft. These two forces are related to the angle of attack α and relative wind velocity V (Figure 3).

Figure 3: Drag, lift and angle of attack

The relations for Lift and Drag forces have been developed and are written as functions of pressure, area, and lift or drag coefficients as
L = 12p∞ V2 ACl [4] where CL is the lift coefficient. The drag force is defined by
D = pv A Cd [5] where Cd is the drag coefficient.
The pressure exerted on the airfoil plays an important role in determining the lift. Therefore, it is important to establish a relationship between the pressures on different points of the surface. A new parameter, called the pressure coefficient (Cp), relates the pressure at different locations by
Cp = p-p∞12 p∞ V∞2 [6] where p∞ represents the air flow density.
In order to obtain the total lift produced by the airfoil, the pressure exerted on the top surface will be recorded as well as its airfoil area. The same procedure will be done for the lower or bottom surface of the airfoil and the difference between these two lifts will provide the net lift and the following equations can be derived:

Lus=P1A1+ P2A2+P3A3+ ……PnAn [7]
Lls=Pn+1An+1+ Pn+2An+2+Pn+3An+3+ ……Pn+mAn+n [8]
L=Lls-Lus [9]

where Lls (lbf) is the lift force of the lower surface, Lus (lbf) is the lift force of the upper surface, n is the number of pressure taps on the upper surface and m is the number of pressure taps on the lower surface.

Results and Discussion:
Table 1 shows the measurement of the upper eight measuring ports and lower eight measuring ports from the leading edge of the airfoil. The upper face of the airfoil has a total length of 6.55 inches with 8 Pitot tube ports located horizontally at the middle of the airfoil. Likewise, the lower side of the airfoil consists of 8 Pitot tube ports located horizontally at the middle of the airfoil (Table 1). Table 1 provides the ratio of length of the port with the chord length ranging from .042 for first port to .8 for the eighth port. Using the ratio from table 1, the surface area associated with each pressure sensing port on the airfoil is calculated (Table 2). Upper surface of the airfoil consists of surface area of 24.15 in^2 and whereas the lower surface has a surface area of 28.437 in^2. Moreover, using the surface area associated with individual ports, the lift force at individual ports is calculated using equation 7. This consists of summing all the individual lift forces from each port. The total lift force is then calculated by summing all the upper and lower lift force. Table 3 has all the airfoil pressure at different port with an angle of attack at -10, -6, -4, 0, 4, 6, 8, and 10 degrees. Table 4 shows the calculated lower surface lift force for individual ports and the sum of all the force that is acting downwards. This procedure continues for Table 5, 6, 7 and 8; however, the calculations are recorded for wind velocity of different magnitude. Wind velocities of 49.44, 73.03 and 81.66 ft/sec are used in this experiment. Further, two tables (Table 9 and 10) are constructed to establish the pressure coefficient (Cp) for each angle of attack (AOA) and to obtain the average pressure coefficient for each angle of attack. Finally, Table 11 shows the total lift force at various wing velocities. This total lift force is obtained by adding the total lift forces at the upper and lower surface of the airfoil.
Figure 4 shows the average pressure coefficient (Cp) of various angles of attack graphed relative to the chord position of different pins. Average pressure coefficient at the upper airfoil increased exponentially to the chord position, whereas the average pressure coefficient decreased exponentially with the chord position. The magnitude of the lift force varies with different wing velocities as shown in Figure 4. Figure 4 compares all three wind velocities of 49.44 (789 RPM), 73.03 (1168 RPM) and 81.66 (1300 RPM) ft/sec with the lift force generated. Lift force of the airfoil ultimately decreases from an AOA at -10 degrees to 10 degrees. However, comparing the neighboring angles along this range, the figure shows an increase in magnitude of lift force before it reaches the lower lift force at a positive 10 degree angle.
Conclusion:
This experiment demonstrated the aerodynamic forces of lift and drag that act on an airfoil. These forces occurred when airflow was introduced to the area around the model airfoil being tested in the wind tunnel. As a result, the drag and lift characteristics for the model airfoil were successfully measured and analyzed. The variation in measurements for each angle of attack may have occurred because errors in the design of the experiment. Various tubes were also not able to accurately read the displacement of fluid so proper analysis wasn’t able to be done on the pressure forces on certain cross sectional areas. Typically, airfoils intended for wind tunnel experimentation are constructed by computer controlled machines to ensure smooth and even surfaces with buildings large enough for the capacity of even the biggest airfoil wing from a plane. As this airfoils measurement was done by hand it was difficult to gauge measurements and produce proper geometries. Another error was involved with the pressure measurement using the Pitot tubes. Future work could use a wind tunnel designed specifically for airfoil testing so that a better measurement system could be devised, and the angle of attack and airflow velocity could be varied. A proper means of inspecting the airfoil for proper measurements would be useful as well.

Appendix
List of Figures

Figure 4: Upper and lower pressure coefficient using chord position

Figure 5: Graph showing lift force from different AOA

List of Tables

Table 5: Distance of pressure sensing port and X/C ratio Upper Ports (Xu) | Lower Ports (XL) | Port | X location (in) | X/C, c=6 | Port | X location (in) | X/C, c=6 | XU1 | 0.25 | 0.042 | XL1 | 0.25 | 0.042 | XU2 | 0.625 | 0.104 | XL2 | 0.625 | 0.104 | XU3 | 1.075 | 0.179 | XL3 | 1.025 | 0.171 | XU4 | 1.575 | 0.263 | XL4 | 1.525 | 0.254 | XU5 | 2.2 | 0.367 | XL5 | 2.025 | 0.338 | XU6 | 3.075 | 0.513 | XL6 | 2.9 | 0.483 | XU7 | 4.075 | 0.679 | XL7 | 3.9 | 0.65 | XU8 | 5.175 | 0.863 | XL8 | 5 | 0.833 | UEdge | 6.55 | 1.092 | LEdge | 6.25 | 1.042 |

Table 6: Surface area of upper and lower ports Upper Port (Xu) | Lower Port (XL) | Port | X/C, c=6 | Area(in^2) | Port | X/C, c=6 | Area(in^2) | XU1 | 0.042 | 0.4375 | XL1 | 0.042 | 0.4375 | XU2 | 0.104 | 0.85 | XL2 | 0.104 | 0.825 | XU3 | 0.179 | 0.875 | XL3 | 0.171 | 1.275 | XU4 | 0.263 | 1.8875 | XL4 | 0.254 | 1.775 | XU5 | 0.367 | 2.6375 | XL5 | 0.338 | 3.775 | XU6 | 0.513 | 3.575 | XL6 | 0.483 | 3.4 | XU7 | 0.679 | 4.625 | XL7 | 0.65 | 4.45 | XU8 | 0.863 | 5.8625 | XL8 | 0.833 | 5.625 | UEdge | 1.092 | 3.4 | LEdge | 1.042 | 6.875 | Total | | 24.15 | | | 28.4375 |

Table 7: Upper Lift force at 789 RPM Velocity @ 789 RPM | Xu/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Lu (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | -0.004 | 0.004 | 0.007 | 0.036 | 0.045 | 0.061 | 0.069 | 0.072 | 0.438 | 0.127 | 0.104 | -0.009 | 0.005 | 0.011 | 0.025 | 0.036 | 0.045 | 0.045 | 0.051 | 0.850 | 0.177 | 0.179 | -0.022 | -0.018 | -0.018 | -0.018 | -0.018 | -0.018 | -0.018 | -0.018 | 0.875 | -0.130 | 0.263 | 0.005 | 0.018 | 0.018 | 0.025 | 0.032 | 0.036 | 0.036 | 0.036 | 1.888 | 0.390 | 0.367 | 0.007 | 0.016 | 0.018 | 0.023 | 0.027 | 0.027 | -0.004 | -0.004 | 2.638 | 0.294 | 0.513 | 0.009 | 0.014 | 0.018 | 0.022 | 0.022 | 0.018 | 0.018 | 0.018 | 3.575 | 0.497 | 0.679 | 0.012 | 0.011 | 0.014 | 0.014 | 0.014 | 0.014 | 0.009 | 0.009 | 4.625 | 0.456 | 0.863 | 0.004 | 0.009 | 0.007 | 0.009 | 0.007 | 0.007 | 0.007 | 0.007 | 5.863 | 0.339 | Edge | | | | | | | | | 3.400 | | TOTAL | | | | | | | | | 24.150 | 2.150 |

Table 8: Lower lift force at 789 RPM Velocity @ 789 RPM | Xl/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Ll (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | 0.040 | 0.018 | 0.007 | -0.014 | -0.018 | -0.018 | -0.018 | -0.018 | 0.438 | -0.009 | 0.104 | 0.027 | 0.022 | 0.016 | 0.000 | -0.009 | -0.014 | -0.018 | -0.016 | 0.825 | 0.006 | 0.171 | 0.022 | 0.014 | 0.009 | 0.000 | -0.004 | -0.011 | -0.014 | -0.014 | 1.275 | 0.002 | 0.254 | 0.007 | 0.009 | 0.007 | 0.000 | -0.004 | -0.007 | -0.011 | -0.011 | 1.775 | -0.016 | 0.338 | 0.004 | 0.007 | 0.005 | 0.000 | 0.000 | -0.004 | -0.007 | -0.009 | 3.775 | -0.017 | 0.483 | 0.000 | 0.004 | 0.004 | 0.000 | 0.000 | -0.002 | -0.004 | -0.007 | 3.400 | -0.018 | 0.650 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | -0.004 | -0.004 | 4.450 | -0.032 | 0.833 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.625 | 0.000 | Edge | | | | | | | | | 6.875 | 0.000 | TOTAL | | | | | | | | | 28.438 | -0.085 |
Table 9: Upper lift force at 1168 RPM Velocity @ 1168 RPM | Xu/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Lu (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | -0.054 | -0.036 | -0.018 | 0.009 | 0.112 | 0.108 | 0.171 | 0.181 | 0.438 | 0.207 | 0.104 | -0.022 | 0.000 | 0.018 | 0.036 | 0.090 | 0.099 | 0.117 | 0.119 | 0.850 | 0.390 | 0.179 | -0.005 | -0.051 | -0.051 | -0.045 | -0.040 | 0.004 | -0.054 | -0.045 | 0.875 | -0.251 | 0.263 | 0.014 | 0.029 | 0.004 | 0.051 | 0.072 | 0.072 | 0.072 | 0.072 | 1.888 | 0.729 | 0.367 | -0.004 | 0.007 | -0.004 | -0.004 | -0.004 | -0.004 | -0.004 | 0.054 | 2.638 | 0.105 | 0.513 | 0.018 | 0.027 | 0.036 | 0.036 | 0.043 | 0.005 | 0.043 | 0.036 | 3.575 | 0.874 | 0.679 | 0.014 | 0.018 | 0.020 | 0.027 | 0.027 | 0.027 | 0.022 | 0.022 | 4.625 | 0.818 | 0.863 | 0.007 | 0.009 | 0.009 | 0.009 | 0.011 | 0.009 | 0.009 | 0.007 | 5.863 | 0.413 | Edge | | | | | | | | | 3.400 | | TOTAL | | | | | | | | | 24.150 | 3.284 | Table 10: Lower lift force at 1168 RPM Velocity @ 1168 RPM | Xl/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Ll (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | 0.108 | 0.054 | 0.022 | 0.004 | -0.045 | -0.047 | -0.060 | -0.045 | 0.438 | -0.004 | 0.104 | 0.072 | 0.054 | 0.040 | 0.022 | -0.022 | -0.032 | -0.036 | -0.043 | 0.825 | 0.045 | 0.171 | 0.043 | 0.036 | 0.027 | 0.018 | -0.014 | -0.018 | -0.027 | -0.032 | 1.275 | 0.041 | 0.254 | 0.027 | 0.025 | 0.018 | 0.009 | -0.011 | -0.014 | -0.022 | -0.027 | 1.775 | 0.010 | 0.338 | 0.018 | 0.014 | 0.014 | 0.007 | -0.011 | -0.011 | -0.018 | -0.022 | 3.775 | -0.027 | 0.483 | 0.009 | 0.007 | 0.007 | 0.004 | -0.007 | -0.011 | -0.014 | -0.018 | 3.400 | -0.080 | 0.650 | 0.000 | 0.000 | 0.000 | 0.000 | -0.007 | -0.007 | -0.011 | -0.016 | 4.450 | -0.185 | 0.833 | 0.000 | 0.000 | 0.000 | 0.000 | -0.007 | -0.007 | -0.009 | -0.011 | 5.625 | -0.193 | Edge | | | | | | | | | 6.875 | 0.000 | TOTAL | | | | | | | | | 28.438 | -0.393 | Table 11: Upper lift force at 1300 RPM Velocity @ 1300 RPM | Xu/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Lu (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | -0.051 | -0.022 | -0.004 | 0.065 | 0.155 | 0.199 | 0.235 | 0.235 | 0.438 | 0.355 | 0.104 | -0.018 | 0.018 | 0.032 | 0.083 | 0.126 | 0.144 | 0.162 | 0.155 | 0.850 | 0.598 | 0.179 | -0.047 | -0.047 | -0.047 | -0.054 | -0.018 | -0.054 | -0.054 | 0.036 | 0.875 | -0.250 | 0.263 | 0.018 | 0.047 | 0.054 | 0.087 | 0.105 | 0.105 | 0.108 | 0.099 | 1.888 | 1.175 | 0.367 | 0.029 | 0.051 | 0.058 | 0.083 | 0.090 | 0.090 | 0.087 | 0.079 | 2.638 | 1.495 | 0.513 | 0.029 | 0.043 | 0.051 | 0.065 | 0.065 | 0.061 | 0.054 | 0.051 | 3.575 | 1.497 | 0.679 | 0.025 | 0.036 | 0.040 | 0.040 | 0.040 | 0.032 | 0.029 | 0.022 | 4.625 | 1.219 | 0.863 | 0.018 | 0.018 | 0.018 | 0.018 | 0.014 | 0.014 | 0.011 | 0.014 | 5.863 | 0.741 | Edge | | | | | | | | | 3.400 | | TOTAL | | | | | | | | | 24.150 | 6.831 | Table 12: Lower lift force at 1300 RPM Velocity @ 1300 RPM | Xl/C | Airfoil pressure P (lb/in^2) at various angle of attack | Pin SA (in^2) | Lift force Ll (lb) | | -10° | -6° | -4° | 0° | 4° | 6° | 8° | 10° | | | 0.042 | 0.144 | 0.054 | 0.022 | -0.040 | -0.029 | -0.065 | -0.065 | -0.061 | 0.438 | -0.017 | 0.104 | 0.101 | 0.058 | 0.025 | 0.007 | -0.025 | -0.043 | -0.051 | -0.054 | 0.825 | 0.015 | 0.171 | 0.054 | 0.040 | 0.029 | 0.011 | -0.014 | -0.029 | -0.032 | -0.036 | 1.275 | 0.028 | 0.254 | 0.040 | 0.029 | 0.022 | 0.007 | -0.011 | -0.022 | -0.025 | -0.032 | 1.775 | 0.013 | 0.338 | 0.032 | 0.022 | 0.014 | 0.004 | -0.011 | -0.018 | -0.022 | -0.029 | 3.775 | -0.027 | 0.483 | 0.018 | 0.014 | 0.011 | 0.004 | -0.007 | -0.014 | -0.022 | -0.022 | 3.400 | -0.061 | 0.650 | 0.011 | 0.007 | 0.004 | 0.000 | -0.007 | -0.014 | -0.018 | -0.018 | 4.450 | -0.161 | 0.833 | 0.004 | 0.004 | 0.000 | -0.004 | -0.007 | 0.032 | -0.014 | -0.144 | 5.625 | -0.731 | Edge | | | | | | | | | 6.875 | 0.000 | TOTAL | | | | | | | | | 28.438 | -0.942 | Table 13: Pressure coefficients of upper pin at 3 wind velocities | | Upper Pressure Coefficient (Cp) at Various AOA | Xu/C | Wind Velocity (ft/sec) | -10 | -6 | -4 | 0 | 4 | 6 | 8 | 10 | 0.042 | 49.446 | -1.183 | -0.817 | -0.634 | 0.832 | 1.291 | 2.115 | 2.482 | 2.665 | | 73.037 | -3.749 | -2.832 | -1.916 | -0.542 | 4.681 | 4.497 | 7.704 | 8.162 | | 81.658 | -3.565 | -2.099 | -1.183 | 2.298 | 6.880 | 9.079 | 10.911 | 10.911 | 0.104 | 49.446 | -1.458 | -0.771 | -0.450 | 0.283 | 0.832 | 1.291 | 1.291 | 1.565 | | 73.037 | -2.099 | -1.000 | -0.084 | 0.832 | 3.581 | 4.039 | 4.956 | 5.047 | | 81.658 | -1.916 | -0.084 | 0.649 | 3.215 | 5.414 | 6.330 | 7.246 | 6.880 | 0.179 | 49.446 | -2.099 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | | 73.037 | -1.275 | -3.565 | -3.565 | -3.291 | -3.016 | -0.817 | -3.749 | -3.291 | | 81.658 | -3.382 | -3.382 | -3.382 | -3.749 | -1.916 | -3.749 | -3.749 | 0.832 | 0.263 | 49.446 | -2.099 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | -1.916 | | 73.037 | -0.267 | 0.466 | -0.817 | 1.565 | 2.665 | 2.665 | 2.665 | 2.665 | | 81.658 | -1.916 | -0.084 | 0.649 | 3.215 | 5.414 | 6.330 | 7.246 | 6.880 | 0.367 | 49.446 | -0.771 | -0.084 | -0.084 | 0.283 | 0.649 | 0.832 | 0.832 | 0.832 | | 73.037 | -1.183 | -0.634 | -1.183 | -1.183 | -1.183 | -1.183 | -1.183 | 1.749 | | 81.658 | -3.382 | -3.382 | -3.382 | -3.749 | -1.916 | -3.749 | -3.749 | 0.832 | 0.513 | 49.446 | -0.656 | -0.175 | -0.084 | 0.191 | 0.374 | 0.374 | -1.183 | -1.183 | | 73.037 | -0.084 | 0.374 | 0.832 | 0.832 | 1.199 | -0.771 | 1.199 | 0.832 | | 81.658 | -0.084 | 1.382 | 1.749 | 3.398 | 4.314 | 4.314 | 4.497 | 4.039 | 0.679 | 49.446 | -0.542 | -0.267 | -0.084 | 0.099 | 0.099 | -0.084 | -0.084 | -0.084 | | 73.037 | -0.267 | -0.084 | 0.008 | 0.374 | 0.374 | 0.374 | 0.099 | 0.099 | | 81.658 | 0.466 | 1.565 | 1.932 | 3.215 | 3.581 | 3.581 | 3.398 | 3.031 | 0.863 | 49.446 | -0.395 | -0.450 | -0.267 | -0.267 | -0.267 | -0.267 | -0.542 | -0.542 | | 73.037 | -0.634 | -0.542 | -0.542 | -0.542 | -0.450 | -0.542 | -0.542 | -0.634 | | 81.658 | 0.466 | 1.199 | 1.565 | 2.298 | 2.298 | 2.115 | 1.749 | 1.565 | Average Cp | | -1.337 | -0.796 | -0.588 | 0.241 | 1.294 | 1.373 | 1.569 | 2.043 |

Table 14: Lower pressure coefficient at 3 wing velocities | | Lower Pressure Coefficient (Cp) at Various AOA | Xl/C | Wind Velocity (ft/sec) | -10 | -6 | -4 | 0 | 4 | 6 | 8 | 10 | 0.042 | 49.446 | 1.016 | -0.084 | -0.634 | -1.733 | -1.916 | -1.916 | -1.916 | -1.916 | | 73.037 | 4.497 | 1.749 | 0.099 | -0.817 | -3.291 | -3.382 | -4.024 | -3.291 | | 81.658 | 6.330 | 1.749 | 0.099 | -3.016 | -2.466 | -4.298 | -4.298 | -4.115 | 0.104 | 49.446 | 0.374 | 0.099 | -0.175 | -1.000 | -1.458 | -1.733 | -1.916 | -1.825 | | 73.037 | 2.665 | 1.749 | 1.016 | 0.099 | -2.099 | -2.649 | -2.832 | -3.199 | | 81.658 | 4.131 | 1.932 | 0.283 | -0.634 | -2.283 | -3.199 | -3.565 | -3.749 | 0.171 | 49.446 | 0.099 | -0.267 | -0.542 | -1.000 | -1.183 | -1.550 | -1.733 | -1.733 | | 73.037 | 1.199 | 0.832 | 0.374 | -0.084 | -1.733 | -1.916 | -2.374 | -2.649 | | 81.658 | 1.749 | 1.016 | 0.466 | -0.450 | -1.733 | -2.466 | -2.649 | -2.832 | 0.254 | 49.446 | -0.634 | -0.542 | -0.634 | -1.000 | -1.183 | -1.366 | -1.550 | -1.550 | | 73.037 | 0.374 | 0.283 | -0.084 | -0.542 | -1.550 | -1.733 | -2.099 | -2.374 | | 81.658 | 1.016 | 0.466 | 0.099 | -0.634 | -1.550 | -2.099 | -2.283 | -2.649 | 0.338 | 49.446 | -0.817 | -0.634 | -0.771 | -1.000 | -1.000 | -1.183 | -1.366 | -1.458 | | 73.037 | -0.084 | -0.267 | -0.267 | -0.634 | -1.550 | -1.550 | -1.916 | -2.099 | | 81.658 | 0.649 | 0.099 | -0.267 | -0.817 | -1.550 | -1.916 | -2.099 | -2.466 | 0.483 | 49.446 | -1.000 | -0.817 | -0.817 | -1.000 | -1.000 | -1.092 | -1.183 | -1.366 | | 73.037 | -0.542 | -0.634 | -0.634 | -0.817 | -1.366 | -1.550 | -1.733 | -1.916 | | 81.658 | -0.084 | -0.267 | -0.450 | -0.817 | -1.366 | -1.733 | -2.099 | -2.099 | 0.65 | 49.446 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | -1.183 | -1.183 | | 73.037 | -1.000 | -1.000 | -1.000 | -1.000 | -1.366 | -1.366 | -1.550 | -1.825 | | 81.658 | -0.450 | -0.634 | -0.817 | -1.000 | -1.366 | -1.733 | -1.916 | -1.916 | 0.833 | 49.446 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | -1.000 | | 73.037 | -1.000 | -1.000 | -1.000 | -1.000 | -1.366 | -1.366 | -1.458 | -1.550 | | 81.658 | -0.817 | -0.817 | -1.000 | -1.183 | -1.366 | 0.649 | -1.733 | -8.330 | Average Cp | | 0.653 | 0.042 | -0.361 | -0.920 | -1.573 | -1.798 | -2.103 | -2.462 |

Table 15: Total lift force at different velocity Wing Velocity (RPM) | Total Lift force (lb) | 789 | 2.065 | 1168 | 2.892 | 1300 | 5.889 |
References

[1] Cengal, Y. A., & Ghajar, A. J. (2011). Heat and Mass Transfer. New York: Mc-Grawhill.
[2] Cladwell., E. A. (2005). McGrawHill Encyclopedia of Science and Technology. New York: McGraw Hill.
[3] Eberhardt, D. A. (2010). How Airplanes Fly: A physical Description of Lift. Wiley.
[4] Michael J Moran, H. N. (2009). Fundementals of Engineering Thermodyanmics. Chicago: Wiley.
[5] Incropera, Frank & De Witt, David. (1990) Fundamentals of Heat and Mass Transfer, 3rd ed., New York: Mc-Grawhill.