570 Lab 1 Report
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1
Aerodynamic Characteristics of Aerofoils
ENME 570
Lab B02
October 20, 2023
Marcus Gregory UCID: 30115997
Rachel Mah UCID: 30114083
James Williams UCID: 30061201
Ayman Malkawi UCID: 30117701
2
TABLE OF CONTENTS
EXECUTIVE SUMMARY
3
1
–
INTRODUCTION & BACKGROUND
3
2
–
METHODS & PROCEDURE
5
3 - RESULTS
6
4 - DISCUSSION
12
5 - CONCLUSION
17
6 - REFERENCES
18
3
EXECUTIVE SUMMARY
The purpose of this laboratory experiment is to gain a better understanding of wind tunnel testing
and to analyze the collected data to gain further knowledge regarding the pressure distribution around
an aerofoil. Further objectives include analyzing how lift is generated by different aerofoils and how shape
and angle of attack affect the lift and drag forces. Two aerofoils are tested in the wind tunnel; a
symmetrical aerofoil NACA 0012 with pressure taps and a cambered airfoil NACA 2412 with a variable
flap. An open-loop, subsonic wind tunnel is used which contains a force transducer to measure lift or drag
as well as a 32-way manometer to obtain the 20 pressure measurements for NACA 0012. In completing
this lab, the coefficient of lift for NACA 0012 was obtained using the pressure distribution for each angle
of attack and compared with the values from the force transducer measurements. The plot showed that
discrepancies between the two methods increased at higher angles of attack. Plots of lift coefficient vs
angle of attack, drag coefficient vs angle of attack, and lift coefficient vs drag coefficient were produced
for both aerofoils and compared. Many conclusions were drawn from the plots. Firstly, the coefficient of
lift for the symmetric airfoil was approximately zero at zero angle of attack as opposed to the cambered
aerofoil which did produce lift initially. It was expected that the cambered airfoil would produce a greater
amount of lift than the symmetrical airfoil however, the trend in the data showed that as the angle of
attack increased, the coefficient of lift was greater in the symmetric aerofoil which could be due to a
variety of sources of error present in the experiment. It is concluded that a cambered aerofoil can
generate a greater amount of lift than a symmetric aerofoil before stalling. The plots reinforced that the
cambered aerofoil produced less drag than the symmetric. Multiple sources of error were identified in
the experiment including bias errors found in the calibration of certain tools, misalignment in the system,
and instrument drift. Additional random errors could be due to turbulence within the wind tunnel,
environmental fluctuations, vibrations, as well as human error. Overall, the lab was a success and the
trends found in the results were similar to those found in literature.
1
–
INTRODUCTION & BACKGROUND
Aero foil theory and wind tunnels play integral roles in the field of aerodynamics, shaping our
understanding of how objects interact with fluids, particularly in the field of aerospace engineering. The
airfoil theory serves as a fundamental framework for understanding and predicting these aerodynamic
behaviors. Wind tunnels, on the other hand, are invaluable tools that allow engineers and scientists alike
to conduct controlled experiments, test models, and collect data to better understand, validate, and
refine aerodynamic concepts including the airfoil foil theory.
Airfoil theory revolves around the study of airfoils, which are specifically designed shapes that
optimize lift and minimize drag when an object moves through a fluid, particularly in air. The distinctive
shape of an airfoil is characterized by a curved upper surface and a flatter lower surface, designed to
manipulate the airflow around it. This manipulation leads to the generation of lift, a force that enables
aircraft to overcome gravity and achieve flight. This manipulation also attempts to minimize the drag
forces acting upon it. There are 2 main components of drag, both of which arise due to the viscosity of
the fluid:
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5
1.
Frictional Drag: This component results from the resistance of air as it flows over the surface of
an object, such as the wing of an aircraft.
2.
Pressure Drag: This component emerges from the variations in air pressure around the object.
This pressure difference results in an aerodynamic force that acts in the direction of the higher
pressure, which is typically towards the upper surface.
The shaping of immersed bodies is crucial for generating lift. This lift is produced by manipulating
pressure distributions around the body. Symmetric bodies can also create lift by adjusting the angle of
attack, which is the angle relative to
the free stream direction (α). An airfoil serves as a prime example
of
a body that is designed to generate lift. They can be symmetric or asymmetric in cross-section.
Importantly, asymmetric airfoils can
produce lift even at α = 0 degrees, while symmetric airfoils require a
nonzero α to generate lift.
This foundational knowledge underpins aerodynamics and is pivotal in
designing wing profiles and optimizing performance.
The drag and lift forces can be found by taking the surface integral of the body and is represented by
equations 1 and 2.
𝐹
?
= ∮ 𝑃
?
sin 𝜃 ?𝐴 + ∮ 𝜏
𝑜
cos 𝜃
?
?𝐴
(1)
𝐹
𝐿
= ∮ 𝑃
?
cos 𝜃 ?𝐴 − ∮ 𝜏
𝑜
sin 𝜃
?
?𝐴
(2)
In computing the drag and lift forces, the coefficient of lift and the coefficient of drag can also be
determined using the relations in equations 3 and 4.
𝐶
?
=
𝐹
𝐷
1
2
𝜌
∞
𝑈
∞
2
𝐴
(3)
𝐶
𝐿
=
𝐹
𝐿
1
2
𝜌
∞
𝑈
∞
2
𝐴
(4)
Wind tunnels are controlled environments for simulating the flow of air over objects, providing
an experiment to further verify and refine the airfoil theory. They typically consist of a test section, where
the models or prototypes are placed, and a powerful fan system to propel air over these objects at
controlled speeds. Wind tunnels allow engineers and researchers to study the effects of factors such as
airspeed, angle of attack, and airfoil shape in a consistent manner. Wind tunnels can appear in many
different fashions depending on the use. The wind tunnel in this lab is an open-loop, subsonic wind tunnel
with a square intake, test section, and outtake. The speed ranges from 0 to 36 m/s, and the 600 mm-long
test section has a 305 mm by 305 mm cross-section.
An important parameter for any wind tunnel testing is the freestream velocity (U∞), which can
be measured using a pitot tube, by placing it normal to the flow which creates a stagnation point at the
tip where the stagnation pressure may be measured. On the side of the pitot tube, the flow closely
approximates the velocity of the free stream, and it is possible to measure the static pressure of the fluid.
The difference between these values represents a pressure corresponding to the reduction in potential
energy from stagnation to static. Assuming energy conservation, this reduction is equivalent to the kinetic
energy of the flow at the free stream velocity.
6
2
–
METHODS & PROCEDURES
For the experiment the two aerofoils being tested in the wind tunnel are NACA 0012 with pressure
taps and NACA 2412 with a variable flap.
The open-loop, subsonic wind tunnel contains a force transducer
to measure lift or drag as well as a 32-way manometer to obtain the 20 pressure measurements for NACA
0012.
Figure 1: Schematic of Wind Tunnel Setup
1.
Turn on the power for the data acquisition system, the fan, and the force transducer.
2.
Connect the force transducer using TeqQuipment’s data acquisition s
oftware on the computer.
3.
After ensuring the lift and drag balance are in the lift position, level the aerofoil at an angle of
attack of 0 degrees. To ensure it is level and secure, use the screws and ensure the tip of the edges
of the aerofoil are 153mm from the bottom wall of the wind tunnel.
4.
Record the tare value of the pressure in manometers one to twenty as well as the last manometer
(static pressure), this value should be approximately 300 mm.
5.
Ensure the pitot tube is pointed upstream and lowered to 30 mm from the tunnel wall to measure
accurate air speed.
6.
Next, tare the force balance and turn the fan speed dynamometer completely counterclockwise.
7.
After switching on the fan, turn the speed up until the pitot tube manometer has reached 40 mm
and avoid touching or moving the equipment as it will affect the accuracy of the results obtained.
8.
After waiting two minutes for the air speed to steady, use the software to collect force data at a
frequency of 2 Hz for 60 seconds.
9.
Pressure data can now be collected for the corresponding angle of attack. Record each pressure
measurement in the data table provided.
10.
Repeat steps 1-9 for the required angle of attacks.
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7
11.
Once the data for lift has been collected for all angles of attack, turn the fan off and repeat the
procedure after setting the balance to drag instead of lift.
12.
Repeat the above steps 1-11 for the NACA 2412 aerofoil, disregarding steps required for
measuring pressure as NACA 2412 has no pressure taps. The variable flap should be set to zero
degrees.
13.
The data collected by the software can be exported to an excel file once all tests are complete.
3
–
RESULTS
After collecting the data from the experiments there were two sets of data that are important in
analyzing the performance of different aerofoils. There are two important data sets that were collected
and will be used to determine the lift and drag coefficients. The first method is using the pressure
distribution around the airfoil measured by the 32-way manometer. The other set collected was using the
data acquisition software that monitors the lift and drag balance to measure the force that the aerofoil
induces. This can be used to measure the lift and drag forces.
Firstly, the characteristics of the flow such as the freestream velocity
, Reynold’s Number, and
dynamic pressure in the wind tunnel was determined using the pitot static tube:
Table 1: Calculated Characteristics of the Flow in the Wind Tunnel
Pitot static (mm)
Calculated Velocity
(m/s)
Re
c
Dynamic Pressure
(Pa)
40
25.34
271118
340.4
A subset of the pressures measured around the aerofoil for an angle of attack of 0
˚
is shown
below:
Table 2: Subset of the Measurements from Pressure Taps
Angle of inclination (deg)
0
2
Pressure Taps
Tare (mm)
Pressure measurement (mm)
1
298
266
254
2
299
283
288
3
298
254
244
4
299
254
260
5
298
243
234
Static (P
∞
)
300
260
260
8
The lift coefficient CL was computed from the pressure distribution using the drag and lift forces
along the surface of the aerofoil using the following equation:
𝐹
𝐿
= ∮ 𝑃??𝑠𝜃?𝐴 − ∮ 𝜏
𝑜
𝑠𝑖?𝜃?𝐴
𝑆
𝑆
Assuming the frictional coefficient is very small compared to the first term, the pressure acts only
in the vertical direction, and the lifting pressure is P = P
i
-P
∞
.
The equation can be rewritten:
𝐶
?
=
𝐹
𝐿
1
2
𝜌
∞
𝑈
∞
2
= ∮
(𝑃
𝑖
− 𝑃
∞
)
1
2
𝜌
∞
𝑈
∞
2
?𝐴
𝑆
The pressure is computed using the 32-way manometer. Thus, the static pressure for each tap
was computed:
𝑃
𝑖
= 𝜌
𝑤𝑎?𝑒?
∗ 𝑔 ∗ (ℎ − ℎ
?𝑎?𝑒
)
Using Excel, the pressure around the aerofoil was determined for the 20 pressure taps. This
pressure data was used to find the coefficient of pressure, then integrated along the top and bottom
surface to determine the sectional lift coefficient. This integration was done using MATLAB, using the
polyfit command to fit a polynomial to the data and integrating this curve the sectional lift coefficients
were computed. However, it is important to note that this is the sectional lift coefficient at midspan.
Hence multiplying the C
l
value by a span of 0.3m results in the C
L
for the aerofoil.
Table 3: Computed C
L
from the pressure distribution around the aerofoil
Angle of
Attack
Cl Computed
Using MATLAB
CL
0
0.1789
0.05367
2
0.3541
0.10623
4
0.5048
0.15144
6
0.7025
0.21075
8
0.8008
0.24024
10
0.8676
0.26028
12
0.7818
0.23454
14
0.9218
0.27654
16
0.9681
0.29043
The coefficient of pressure was used to find the lift coefficient thus, a plot comparing the
coefficient of pressure vs. the angle of attack can be plotted:
9
Figure 2: C
P
vs
α
The lift coefficient can also be computed using the force balance that the airfoil is attached to. A
subset of the force balance data acquired by the data acquisition software is shown below:
Table 4: Subset of the Force Balance Data Set to Lift Mode for
α
=0
Time
AF1300Z Basic Balance
Manual
Angle
Input
Operating Conditions
Time
Force
Orientation
Manual
Angle
Atmospheric
Temperature
Atmospheric
Pressure
Ambient Air
Density
(s)
(N)
(°)
(°C)
(mbar)
(kg.m
-3
)
Data
Series 1
0
-0.05
Lift
0
22.0
900.00
1.06
0.5
0.04
Lift
0
22.0
900.00
1.06
1
0.03
Lift
0
22.0
900.00
1.06
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cp
Cp vs.
α
alpha=2
alpha=6
alpha=10
alpha=14
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10
The force that the aerofoil produces in the lift direction is recorded. Taking the absolute value of
the forces and then the average, the force that the corresponding angle of attack is determined. Plugging
this force into equation (2), the lift coefficients were determined. The same procedure can be carried out
for the drag coefficient.
Table 5: Computed C
L
and C
D
for NACA 0012,2412 Aerofoils
NACA 0012
Angle of attack
FL AVG [N]
FD AVG [N]
CL
CD
0
0.01
0.33
0.000644386
0.02126475
2
1.46
0.77
0.094080409
0.04961775
4
2.08
2.2
0.134032364
0.141765
6
2.83
2.31
0.182361341
0.14885325
8
3.9
2.19
0.251310682
0.141120614
10
5.57
2.26
0.358923205
0.145631318
12
7.2
1.61
0.463958182
0.103746205
14
8.17
4.39
0.526463659
0.282885614
16
7.73
N/A
0.498110659
N/A
NACA 2412
Angle of attack
FL AVG [N]
FD AVG [N]
CL
CD
0
1.32
0.13
0.085059219
0.008377044
2
1.79
0.15
0.115345456
0.00966582
4
2.4
0.57
0.154653126
0.036730117
6
2.73
0.53
0.175917931
0.034152565
8
3.06
0.94
0.197182736
0.060572474
10
3.31
1.11
0.213292436
0.071527071
12
3.27
1.58
0.210714884
0.101813308
14
3.31
2.47
0.213292436
0.159163842
16
1.69
3.76
0.108901576
0.242289897
Using this data and comparing between the two measurement methods as well as between the
two aerofoils, the following plots were created:
11
Figure 3: Comparing Lift Coefficient vs. Angle of Attack for the Two Methods
Figure 4: Lift Coefficient vs. Angle of Attack for the Different Aerofoils
0
0.1
0.2
0.3
0.4
0.5
0.6
0
2
4
6
8
10
12
14
16
18
CL
α
NACA 0012 CL vs.
α
Pressure Distribution
Force Transducer
0
0.1
0.2
0.3
0.4
0.5
0.6
0
2
4
6
8
10
12
14
16
18
CL
α
CL vs.
α
NACA0012
NACA2412
12
Figure 5: Drag Coefficient vs. Angle of Attack for the Different Aerofoils
Figure 6: Lift Coefficient vs. Drag Coefficient for the Different Aerofoils
0
0.05
0.1
0.15
0.2
0.25
0.3
0
2
4
6
8
10
12
14
16
18
CD
α
CD vs.
α
NACA0012
NACA2412
0
0.1
0.2
0.3
0.4
0.5
0.6
0
0.05
0.1
0.15
0.2
0.25
0.3
CL
CD
CL vs. CD
NACA0012
NACA2412
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4
–
DISCUSSION
From the results, coefficients of lift, drag, and pressure were determined using the force balance
and pressure distribution. These relations were plotted and can be useful in characterizing the aerofoils.
It is important to note that this experiment only measured the sectional lift coefficient. The difference
between the lift coefficient and the sectional lift coefficient is important when comparing aerofoils, so it
is important to distinguish the two.
The lift coefficient is a dimensionless parameter that characterizes the lift generated by an entire
airfoil
. It’s typically used to describe the lift performance of an
entire airfoil or aircraft. This coefficient
represents the lift force in relation to dynamic pressure and the reference area. The lift coefficient can
vary with different angles of attack, airspeeds, and other flight conditions. It is typically used to monitor
an aircraft or airfoil’s characterist
ics, including lift curves, stall behavior, and performance.
The Sectional lift coefficient, on the other hand, represents the lift generated at a particular
section of the airfoil per unit span. This coefficient is often studied to understand the variations of lift
distribution along the span of a wing. Engineers and aerodynamicists often use this to design different
wing shapes to achieve desired lift distribution characteristics or features such as twist, taper, and
winglets.
These lift and drag coefficients are very important in characterizing the aerofoils. As shown in
Figures 4 and 5 plotting the C
L
and C
D
coefficients as a function of the angle of attack, the two aerofoils
can be compared. First, looking at the lift coefficient curves, the main difference between a cambered
airfoil and a symmetric airfoil can be observed. At an angle of attack of 0
˚
NACA 2412 produces lift, while
NACA 0012 does not.
The gradient of the CL curve represents the lift curve slope, which is a measure of the change in
lift per unit change in angle of attack. If this value were to be high, it would imply that the aerofoil can
generate more lift for a given change in angle of attack. The gradient of the CD curve is related to the drag
increase with angle of attack. The magnitude of this increases and its trend can be indicative of how prone
the aerofoils are to drag. A flatter CD vs angle of attack curve indicates lower drag increase with angle of
attack.
Significant changes in the shape of curves may indicate flow separation, stall, or other
aerodynamic phenomena. A sudden change in the CL curve, such as a sudden drop in lift, indicates the
stall point, which can be crucial for aircraft safety. A sudden change in the CD curve, such as a sharp
increase, can indicate a significant drag due to flow separation or other factors.
Not only can these coefficients be compared to the angle of attack, but they can be plotted against
each other. As shown in Figure 6, after plotting CL vs CD, the aerodynamic performance can be evaluated.
The plot can be used to see the produced lift for a corresponding drag coefficient. This is important
because it can be used to optimize the wing depending on its requirements. For example, it shows the
amount of drag present for lift being produced. These can be used to find the most efficient angles of
attack to operate the aerofoil depending on if it is being used to produce lift or minimize drag. The most
efficient angles of attack can be determined from the figures below:
14
While the CL vs. CD graph is useful, the results we obtained from the lab were not what was
expected, there are discrepancies for the NACA 0012 aerofoil. This large deviation could be due to the
experiment failing during the session due to the force balance being bumped causing the results to differ.
It is possible that after restarting the experiment, the given angle of attack was not held constant after
restarting the apparatus.
Holding a given angle of attack for a test period of 60 seconds serves several different, yet important
purposes. These are explained below:
•
Steady-State Data: Holding a constant angle of attack for 60 seconds allows the forces to stabilize
and reach a steady-state condition where the measurements are reliable, accurate, and
consistent.
•
Reduce fluctuations: Aerodynamic forces tend to fluctuate during the initial moments as the flow
adjusts to the new angle of attack. By holding the angle of attack for 60 seconds, it allows the
possibility of averaging the data over the time period, to reduce these short-term fluctuations and
provide a more representative measurement.
•
Observe Stability: Maintaining a 60 second angle of attack allows engineers or researchers to
observe the long-term stability of the airfoil and ensure that the data collected is not being
influences by transient effects in the wind tunnel’s airflow,
providing a more accurate depiction
of performance.
•
Capture Key Moments: In certain cases, specific aerodynamic behaviors may take some time to
fully develop. A 60 second period allows for the capture of these critical points, ensuring that
important characteristics are not missed.
Holding the given angle is important, however it is not the only source for error during the experiment.
Errors such as bias error and random error can be present in the results.
Bias error refers to a consistent and predictable deviation of measurements from the true or correct
value. Some of the potential sources of bias error that may have taken effect throughout the experiment
includes:
1.
Calibration Issues: Inaccurate calibration of certain tools such as speed sensors, pressure sensors,
or balance systems.
2.
Misalignment: Misalignment of the model, balance, systems, or any wind tunnel components can
lead to consistent bias errors in measurements.
3.
Instrument Drift: Over time, measurement instruments may experience drift, which may impact
the accuracy of the measurements due to environmental or wear-like conditions.
Random error refers to unpredictable deviations in measurements that occur due to uncontrollable
factors. Some potential sources include:
1.
Turbulence: Inconsistent airflow or minor turbulence within the wind tunnel can lead to a random
variation in measurements.
2.
Changes in Environment: Random fluctuations in temperature, pressure, or humidity can affect
the properties of the air, which could cause random changes to the measurements.
3.
Vibrations: Vibrations from the wind tunnel or external sources, such as sound or movement of
outside object, may introduce randomness into the measurements.
15
4.
Human Error: Misreading certain values or a variation in a human’s attention can lead to random
error in measurements.
Bias Error Correction: Identifying and correcting bias errors can be addressed through regular
equipment maintenance and calibration.
Random Error Mitigation: Mitigating random errors includes taking a larger number of measurements
and ensuring stable testing conditions within the wind tunnel during experimentation.
It is very challenging to mitigate all these errors, this is why it is important to compare data to
other experiments as well as expected values found in literature.
Shown below are some comparisons between the results obtained in this lab and literature
values:
Figure 7: Comparing C
P
vs. x/C of the NACA 0012 Aerofoil at
α
=10 and 9
˚
Compared to Figure 4.3
Literature Values From [textbook pg 374]
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Cp (Experimental) alpha=10
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16
Figure 8: Comparing Cl vs.
α
of the NACA 0012 Aerofoil Compared to Figure 4.25 Literature
Values from [1, pg.353].
Figure 9: Comparing CD vs.
α
of the NACA 0012 Aerofoil Compared to Literature Values From [3]
-1.6
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
2.4
-24
-16
-8
0
8
16
24
32
Cl
α
Cl vs.
α
0
0.05
0.1
0.15
0.2
0.25
0.3
0
5
10
15
CD
α
CD vs.
α
17
Figure 10: Computed Sectional Lift Coefficient vs.
α
of the NACA 2412 Aerofoil Compared to Figure 4.10
Literature Values from [1, pg 330]
Figure 11: Comparing CD vs.
α
of the NACA 2412 Aerofoil Compared to Literature Values From
[4]
These comparisons show promising results for this experiment. While the values do differ from
literature slightly, the trends that the aerofoils demonstrate match up to the literature values in all the
plots.
-1.2
-0.8
-0.4
0
0.4
0.8
1.2
1.6
2
-8
0
8
16
24
Cl
α
Cl vs.
α
NACA2412
0
0.05
0.1
0.15
0.2
0.25
0.3
0
5
10
15
20
CL
α
CD vs.
α
18
The last performance characteristic of aerofoil design is the aerodynamic that is of intertest during
this experiment is the aerodynamic center. The aerodynamic center is the point along the chord line of an
airfoil where the total aerodynamic force can be considered to act. The aerodynamic center plays a crucial
role in an aircraft’s stability and controll
ability. Its position relative to the center of gravity influences the
stability of the aircraft. This center should be positioned ahead of the center of gravity for a stable flight.
Finding the location of the aerodynamic center is also crucial to evaluate stall behavior, since locating the
aerodynamic center after the center of gravity can lead to a nose-up pitching moment during a stall, which
can be problematic.
The aerodynamic center of symmetrical and asymmetrical airfoils may be calculated using the following
equation:
𝑋
𝑎
𝑐
= 0.25 −
?
?
𝛼𝑐
4
?
?
𝛼
[2]
Given that the slope of the lift curve,
𝐶
?
𝛼
, and the pitching moment coefficient about the quarter chord,
𝐶
?
𝛼𝑐
4
, are known it is possible to determine the exact location,
𝑋
𝑎
𝑐
, of the aerodynamic center on a given
airfoil.
In our case since we have collected the pressure distribution, we know the lifting force across the chord
length we are able to calculate the lifting curve per unit length
𝐶
?
and thus its slope at varying angles of
attack.
To determine
𝐶
?
𝛼𝑐
4
we can use the following equation:
𝐶
?
𝛼𝑐
4
=
?
𝑐𝛼
4
1
2
𝜌𝑉
2
𝑐
2
Where
?
𝑐
4
is the moment about the quarter chord,
? = 𝐹
?
𝑥
𝑐
1
4
. We know the air density, chord length and
air speed from supplied data.
It is important to note that the aerodynamic center of symmetrical airfoils is simply 0.25 because the
moment about the aerodynamic center is zero for all angles of attack.
5
–
CONCLUSION
Overall, this lab experiment was a success. The wind tunnel equipped with a 32-way manometer
and force balance, was used to quantify the pressure distribution, the lift, and the drag forces around
two different aerofoils. This data was used to determine the lift, drag, and pressure coefficients of the
aerofoils. The effects of changing angle of attack and the difference between a symmetric and cambered
aerofoil were observed.
These relations and plots were analyzed for possible sources of error and compared with
literature values to back up their validity. It turns out the results from this lab were close to literature
values, however, some slight deviations were observed. These sources of error were identified and the
significance of holding attack angles was investigated.
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19
Lastly, other aerodynamic properties were investigated. Such as the aerodynamic center and the
use of lift and drag coefficient in aerodynamic optimization. These properties are important in
aerodynamics and give insight on other possible experiments that can be performed on aerofoils in a
wind tunnel.
20
6 - REFERENCES
[1] Anderson, J.D.
Fundamentals of Aerodynamics
. 6
ed. New York: McGraw-Hill Education, 2017.
Accessed October 19, 2023.
[2]
Aerodynamic centre
. Aerodynamic Centre - an overview | ScienceDirect Topics. (n.d.). Accessed
October 20, 2023.
https://www.sciencedirect.com/topics/engineering/aerodynamic-centre.
[3] Airfoil Tools.
NACA 0012 Airfoils.
Airfoil Tools. Accessed October 20, 2023.
http://airfoiltools.com/airfoil/details?airfoil=n0012-il
[4] Airfoil Tools.
NACA 2412 Airfoils
. Airfoil Tools. Accessed October 20, 2023.
http://airfoiltools.com/airfoil/details?airfoil=naca2412-il
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Activity 3-3
A | + %00L
E区
Reading a Scale
Name
Tanner Francis
Identify the portion of a foot (12") as indicated by the reading from the zero mark (0) on the scales below. Place your answers
in the spaces provided.
1.
78
88
92
4.
2.
6.
3.
9 6
1
3.
8.
O.
14
13
ju 3
here to search
直 0
85°F
F2
F4
F5
F7
%23
F8
prt sc
2
home
F10
pua
F12
F11
insert
3.
4.
0.
6.
6.
K
H.
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University of Babylon
Collage of Engineering\Al-Musayab
Department of Automobile
Engineering
Under Grad/Third stage
Notes:
1-Attempt Four Questions.
2- Q4 Must be Answered
3-Assume any missing data.
4 تسلم الأسئلة بعد الامتحان مع الدفتر
Subject: Mechanical
Element Design I
Date: 2022\01\25
2022-2023
Time: Three Hours
Course 1
Attempt 1
Q1/ Design a thin cylindrical pressure tank (pressure vessel) with hemispherical ends to the
automotive industry, shown in figure I below. Design for an infinite life by finding the
appropriate thickness of the vessel to carry a sinusoidal pressure varied from {(-0.1) to (6) Mpa}.
The vessel is made from Stainless Steel Alloy-Type 316 sheet annealed. The operating
temperature is 80 C° and the dimeter of the cylinder is 36 cm. use a safety factor of 1.8.
Fig. 1
(15 Marks)
Q2/ Answer the following:
1- Derive the design equation for the direct evaluation of the diameter of a shaft to a desired
fatigue safety factor, if the shaft subjected to both fluctuated…
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■Review
Determine the maximum constant speed at which the pilot can travel, so that he experiences a maximum acceleration
an = 8g = 78.5 m/s².
Express your answer to three significant figures and include the appropriate units.
μΑ
v =
Value
Units
Submit
Request Answer
Part B
?
Determine the normal force he exerts on the seat of the airplane when the plane is traveling at this speed and is at its lowest
point.
Express your answer to three significant figures and include the appropriate units.
о
HÅ
N =
Value
Submit
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?
Units
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SOLUTION
B
PROBLEM 12.16
Block 4 has a mass of 40 kg, and block B has a mass of 8 kg. The
coefficients of friction between all surfaces of contact are μ, = 0.20
H = 0.15. Knowing that P = 50 N→, determine (a) the acceleration of
block B, (b) the tension in the cord.
Constraint of cable: 2x + (x-x1) = x + x = constant.
a+ag = 0,
or
aB = -a
Assume that block A moves down and block B moves up.
Block B: +/ΣF, = 0: NAB - WB cos 0 = 0
=ma: -T+μN + Wsin
=
We as
g
+ ΣΕ
We
Eliminate NAB and
aB-
NAB
B
Nas
HN
UNA
A
NA
-T+W(sin+μcоsе) = WB-
g
VD"M-
g
Block A: +/ΣF, = 0: NA-NAB - W₁cos + Psinė = 0
N₁ = N AB+W cose - Psin
=
(WB+WA)cose - Psinė
ΣF=ma -T+Wsino-FAB-F + Pcos =
CIVE 281 X
+
Ждал
g
Q |
го
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Gate AB in Figure below is 1.0 m long and 0.9 wide. Calculate force F on the gate and position X of its centre of
Not yet
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Fv = 390 N
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Mountaineers often use a rope to lower themselves
down the face of a cliff (this is called rappelling). They
do this with their body nearly horizontal and their feet
pushing against the cliff (Eigure 1). Suppose that an
78.6-kg climber, who is 1.88 m tall and has a center of
gravity 1.0 m from his feet, rappels down a vertical cliff
with his body raised 40.4° above the horizontal. He
holds the rope 1.54 m from his feet, and it makes a
20.7° angle with the cliff face.
✓ Correct
Part D
Figure
1 of 1
What minimum coefficient of static friction is needed to prevent the climber's feet from slipping on
the cliff face if he has one foot at a time against the cliff?
Express your answer using two significant figures.
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- O Week 2- 20527 22110L x a MasteringEngineering Mastering x M Inbox (10,309) - usmikail@gmail x a Product Detail Page a Central Service Technical Manual x O 21) YouTube i session.masteringengineering.com/myct/itemView?assignmentProblemiD=12443395&offset=next KHW 1 Problem 12.3 6 of 16 I Review A particle travels along a straight line with a velocity v = (12 – 3t2) m/s, where t is in seconds. When t = 1 s, the particle is located 10 m to the left of the origin. Express your answer to three significant figures and include the appropriate units. As = 437 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining Part C Determine the distance the particle travels during the time period given in previous part. Express your answer to three significant figures and include the appropriate units. ? ST = Value Unitsarrow_forwardK mylabmastering.pearson.com Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... P Pearson MyLab and Mastering Mastering Engineering Back to my courses Course Home Scores Course Homearrow_forwardNeeds Complete typed solution with 100 % accuracy.arrow_forward
- + P 4. 5. 1/4 R %24 2. Bb Basic BIM/REVIT Drafting (CAD) X Bb Unit 03 - Reading Measuring loo X uaptc.edu/bbcswebdav/pid-4073050-dt-content-rid-22008907_1/courses/DFT.1005.A10.2021.S0/pdf_activities_03-03.pdf pdf 1 / 2 - Activity 3-3 A | + %00L E区 Reading a Scale Name Tanner Francis Identify the portion of a foot (12") as indicated by the reading from the zero mark (0) on the scales below. Place your answers in the spaces provided. 1. 78 88 92 4. 2. 6. 3. 9 6 1 3. 8. O. 14 13 ju 3 here to search 直 0 85°F F2 F4 F5 F7 %23 F8 prt sc 2 home F10 pua F12 F11 insert 3. 4. 0. 6. 6. K H.arrow_forwardmylabmastering.pearson.com Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... P Pearson MyLab and Mastering Scoresarrow_forwardUniversity of Babylon Collage of Engineering\Al-Musayab Department of Automobile Engineering Under Grad/Third stage Notes: 1-Attempt Four Questions. 2- Q4 Must be Answered 3-Assume any missing data. 4 تسلم الأسئلة بعد الامتحان مع الدفتر Subject: Mechanical Element Design I Date: 2022\01\25 2022-2023 Time: Three Hours Course 1 Attempt 1 Q1/ Design a thin cylindrical pressure tank (pressure vessel) with hemispherical ends to the automotive industry, shown in figure I below. Design for an infinite life by finding the appropriate thickness of the vessel to carry a sinusoidal pressure varied from {(-0.1) to (6) Mpa}. The vessel is made from Stainless Steel Alloy-Type 316 sheet annealed. The operating temperature is 80 C° and the dimeter of the cylinder is 36 cm. use a safety factor of 1.8. Fig. 1 (15 Marks) Q2/ Answer the following: 1- Derive the design equation for the direct evaluation of the diameter of a shaft to a desired fatigue safety factor, if the shaft subjected to both fluctuated…arrow_forward
- Chapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... Scores ■Review Determine the maximum constant speed at which the pilot can travel, so that he experiences a maximum acceleration an = 8g = 78.5 m/s². Express your answer to three significant figures and include the appropriate units. μΑ v = Value Units Submit Request Answer Part B ? Determine the normal force he exerts on the seat of the airplane when the plane is traveling at this speed and is at its lowest point. Express your answer to three significant figures and include the appropriate units. о HÅ N = Value Submit Request Answer Provide Feedback ? Units Next >arrow_forwardthis is a practice problem, not a graded assignmentarrow_forwardChapter 12 - Lecture Notes.pptx: (MAE 272-01) (SP25) DY... Scoresarrow_forward
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