AE303 – Lab 5: DC-6B
Fredy Gomez Cruz, 821602191
San Diego State University, San Diego, CA, 92115
The purpose of this lab was to measure the aerodynamic forces on an Model airplane DC-6B using wind tunnel
force measurements. Measuring the force values from the model we are able to find the forces of lift, drag and
the aerodynamic pitching and yawing moments. Using the wind tunnel, we are able to determine aerodynamic
force. Most importantly the purpose of this experiment was the variation of this data when the tail of the model
was on and off. We first set up the experiment by placing the model DC-6B into the wind tunnel and measuring
the drag, lift and moment forces at 10 distinctive angles. Using the SDSU wind tunnel at a constant velocity and
dynamic pressure we were able to gather data from this experiment. This experiment was highly beneficial
when understanding the relation of angle of attack versus lift and drag and the relation between moments and
the yawing and pitch angles. I learned from this experiment that the coefficient of drag increased with the
increased angle of attack. This seemed to increase further when the tail was attached to the model. Interesting
enough the lift coefficient also increased when the tail was attached. This makes sense as the tail serves to
increase stability and increase efficiency. The vital information extracted from this lab was the forces on the
model and how the angle of attack changed the performance of the model. Results presented and increase in
the lift coefficient with the tail attached, an increase in stability presented through an increase pitching moment
coefficient. Also an increase in yaw moment coefficients when the angle of yaw increase. However, when the
tail was attached the stability of the airfoil grew. While the airfoil seemed to be more aerodynamic without the
tail, ultimately the tail serves to be a stabilizer of the model to produce a more aerodynamic model overall.
Nomenclature
𝑐
S
b
𝑞
𝐶𝑀
𝐶𝑁
𝐶𝐿
𝐶𝐷
e
AR
𝑥
𝑦
𝑣
𝜌
𝛼
= chord length
= Area of Airfoil
= wing span
= Dynamic Pressure
= Pitching Moment Coefficient
= Yaw Moment Coefficient
= Lift
= Drag
= Oswald Efficiency
= Aspect Ratio
= Distance Along the Chord Line
= Coordinate Perpendicular to Chord Line
= Velocity of the Air Flow Upstream of the Airfoil
= Density
= Angle of Attack
ᵦ
= Angle of Yaw
𝐹𝑥
𝐹𝑦
𝐹𝑧
𝑀𝑥
𝑀𝑦
𝑀𝑧
= Drag Force
= Side Force
= Lift Force
= Rolling Moment
=Pitching Moment
=Yawing Moment
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Introduction
The goal of this experiment was to measure the aerodynamic forces of a model using the wind tunnel force
measurements. The wind tunnel aerodynamic forces allows the investigation of aerodynamic forces, the change in
them when the angle of attack changes and then the effect of these changes when the airfoil has a tail and when it
doesn’t. This experiment was performed in the SDSU wind tunnel with the proper lab safety technique.
First the airfoil is placed at a -6-degree angle of attack and a velocity is set. At this point the wind tunnel will begin
to measure forces on a model placed inside the wind tunnel. Having multiple angles of attack will allow for the analysis
of the most accurate data. The data collected from the experiment will allow us to find the relationship of the change
in angle of attack and yaw angle on the coefficients of lift, drag and moments. Using two data group, one where the
model has a tail and more where the model does not, we will also be able to analyze which setting is the most effective
at reducing drag while increasing lift. The data will then be compared and the relationship between the coefficient of
lift versus angle of attack will be analyzed when the tail is on and off to determine which is more efficient. The same
analysis will be applied with the yaw moment and the yaw angle.
Theory
First the lift, drag, pitching moment and yaw moment are measured by the wind tunnel. For each force and moment,
F, are provided a equation that allows for the forces of just the model to be presented:
F(model) = [F(model on, wind on) – F(model on, wind off)] – [F(model off, wind on) – F(model off, wind off)]
The equation provides the ability to remove the influence of the shafts on the overall performance of the model.
Using the several measurements of the forces of lift, drag, pitching moment and yaw moment. These forces are then
used to find the coefficients of lift and drag. The forces measured by the wind tunnel also calculate the pitching
moment coefficient and the yaw moment coefficient.
𝐿
𝑐𝑙 = 𝑞𝑠
(1)
𝐷
(2)
𝐶𝐷 =
𝑞𝑠
𝐶𝑀 =
𝑞𝑆𝑐̅
𝐶𝑁 =
𝑞𝑆𝑏
𝑀𝑦
(3)
:
𝑁
(4)
Finally, the Oswald Coefficient was also discovered using the aspect ration of the airfoil. The aspect ratio is
plugged into the equation and is able to account into the Oswald efficiency factor. The Oswald efficiency is important
because it helps calculate the efficiency factor for the straight wing aircraft with data such as the span, area of the
wing and chordline. The Oswald efficiency is used to interpret the change in drag with lift for a airfoil area.
ⅇ = 1.78(1 − .045𝐴𝑅 .68 ) − 0.64
(6)
Procedure
This procedure dictates the steps necessary to perform this experiment correctly. This experiment was not
performed by a different group and data was presented for students to analyze.
General Experiment Procedure



Read Barometer and Temperature
Zero the balance system such that yaw angle and Angle of Attack are at 0 degrees respectively.
Assure that the model is on and the wind is off
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

Record dynamic pressure, temperature and forces and moment for the angles of attack:
o 𝛼 =[ -6 -4 -2 0 2 4 6 8 10 15]
o ᵦ = [0 5 10]
Complete 6 run with the following 5 iteration and repeat the steps above
o Model On, Tail On, Wind Off
o Model On, Tail On, Wind On
o Model On, Tail Off, Wind On
o Model Off, Tail Off, Wind On
o Model Off, Tail Off, Wind Off
Equipment




San Diego State University Subsonic Wind Tunnel
o Constructed 1963
o Range: 0-180 mph
o TF : 1.27
o 150 Hp
o 6-Load Cell Strain Gauge Balance System
2.2 Full Model Airplane: DC-6B
o Model reference area S = 93.81 in. 2
o Model reference length c = 3.466 in.
o Model reference wing span b = 27.066 in.
2.3 Wind tunnel test setting
o Free stream dynamic pressure q = 7 in H2O
Computer
Results and Discussion
The results presented below are the result of the coefficients of lift, coefficients of drag and the pitching and yaw
moment. This data was gathered separate from the student body and all results presented are the analysis component
of measured data. Results presented showcase a similar shape in curve when comparing figure (1) and figure (2) data.
This result is important because it showcases that both models have similar behaviors. However, even though the
model with the tail on presents a higher ration of lift to drag meaning that it creates more drag, that it also manages to
create more lift. Figure 2 showcases similar behaviors when the angle of attack increases. The model with and without
the tail follow the same behavior and after the critical angle of attack, lift decreases. Both lines showcase this behavior.
The model with the tail, has a higher coefficient of lift than the model without the tail. This means that the tail is able
to create more stability while also being able to assist in the increase of the coefficient of lift.
Figure 1: Coefficient of Lift v Coefficient of Drag
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Figure 2: Coefficient of Lift v AoA
The results below showcase the Yawing moment coefficient versus the yaw angle, and the pitching moment
coefficient versus the angle of attack. In Figure 1, a positive slope indicates that the model is stable. In the graph the
yawing moment coefficient is reaching a positive slope as opposed to the negative slope that is presented with the tail
off results, this means that the yawing moment is more stable when the tail is attached to the model. When the tail is
not attached to the model there is less stability in the model.
Furthermore, there is the pitching moment coefficient versus the angle of attack. The pitch coefficient is what
prevents pitch moment when the model experiences a high clockwise moment. When the pitching moment increases
a positive slope means that the model increasingly becomes more unstable. This instability is not noticeable when it
comes to the tail on because the pitching moment coefficient decreases when the angle of attack increases. This
decrease in the pitching moment coefficient means that as the angle of attack increases that the pitching momement
decreases. This creates a more stable aircraft. Having a lower pitching coefficient when angle of attack increases
creates a more stable aircraft at higher angles of attack. The opposite behavior is seen with the tail off. This means
that as the angle of attack increases that instead of decreasing pitching moment, it also increases further increase
destabilization.
Figure 3: Yawing Moment Coefficient v Yaw Angle
Figure 4: Pitching Moment Coeff v AoA
The results presented above showcase the behaviors of a model with and without its tail and the effects that is has
on the lift, drag, pitch and yaw moments. The results supported the idea that the tail serves as both an stabilizer and
increases the lift to drag ratio The results clearly support the idea that the tail increases the overall efficiency of the
airfoil Furthermore, as seen by the last two figures, the tail serves to increase the performance of stabilization when
the aircraft experiences yaw and pitching moments. Results undeniably support the model performance increases when
the tail is attached.
Lab 5: Full Model Aircraft Performance
TITLE
Oswald Efficiency
TITLE
Maximum Lift-to-Drag Ratio
Zero-lift Angle of Attack
Lift-Curve Slope
Maximum Lift Coefficient
VAR
𝒆
VAR
(𝑪𝑳 /𝑪𝑫 )𝒎𝒂𝒙
(𝑪𝑳 /𝑪𝑫 )𝒎𝒂𝒙
𝜶𝑳=𝟎
𝜶𝑳=𝟎
𝒅𝑪𝑳 /𝒅𝜶
𝒅𝑪𝑳 /𝒅𝜶
(𝑪𝑳 )𝒎𝒂𝒙
(𝑪𝑳 )𝒎𝒂𝒙
Tail Config.
On
Off
On
Off
On
Off
On
Off
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VALUE
.81596
VALUE
12.384
13.134
3.75
3.9
.075
.062
.932
.832
UNITS
UNITS
𝒅𝒆𝒈𝒓𝒆𝒆
𝒅𝒆𝒈𝒓𝒆𝒆
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
-
Critical Angle of Attack
Pitching Moment-Curve Slope
Yawing Moment-Curve Slope
TITLE
VAR
UNITS
VALUE
TITLE
VAR
UNITS
VALUE
Angle of
Attack
𝜶
−6
-4
-2
0
2
4
6
8
10
15
Coeff. of
Lift
𝑪𝑳
-0.23818
-0.06064
0.11797
0.30554
0.49023
0.68005
0.82162
0.93212
0.83309
0.77552
Sideslip Angle
𝜷
0
5
10
𝜶𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍
𝜶𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍
𝒅𝑪𝑴 /𝒅𝜶
𝒅𝑪𝑴 /𝒅𝜶
𝒅𝑪𝑵 /𝒅𝜷
𝒅𝑪𝑵 /𝒅𝜷
On
Off
On
Off
On
Off
Tail ON
Coeff. of
Pitching
Moment
𝑪𝑴
0.19291
0.12505
0.07557
0.0300
-0.01345
-0.06913
-0.12113
-0.16732
-0.39494
-0.53298
Coeff. of
Drag
8
8
-.0322
.0169
.0022
-8.6305E-4
Coeff. of
Lift
𝑪𝑫
0.06724
0.05332
0.04755
0.04797
0.04781
0.05632
0.06256
0.07527
0.16388
0.31825
Tail ON
Yawing Moment Coefficient
(𝑪𝑵 )𝒕𝒂𝒊𝒍 𝒐𝒏
0.00287
0.00429
0.02477
𝑪𝑳
-0.17100
-0.01638
0.14308
0.28554
0.46555
0.62891
0.74434
0.83202
0.66823
0.58263
Tail OFF
Coeff. of
Pitching
Moment
𝑪𝑴
-0.10679
-0.04159
0.00121
0.05377
0.09936
0.14172
0.17762
0.21223
0.16165
0.16689
𝒅𝒆𝒈𝒓𝒆𝒆
𝒅𝒆𝒈𝒓𝒆𝒆
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
𝒅𝒆𝒈𝒓𝒆𝒆−𝟏
Coeff. of
Drag
𝑪𝑫
0.05784
0.04837
0.04327
0.04077
0.03939
0.04506
0.05028
0.06324
0.15150
0.27136
Tail OFF
Yawing Moment Coefficient
(𝑪𝑵 )𝒕𝒂𝒊𝒍 𝒐𝒇𝒇
-0.00131
-.00541
-.00809
Conclusion
The purpose of this lab experiment was to compare the forces on an on the model DC-6B from a wind tunnel
when the tail is attached and when there is no tail. Most importantly the aerodynamic force on the model provided
information of the coefficient of lift drag and yawing and pitching moment. These aerodynamic forces were
compared when testing the behavior of the model with and without its tail. The results showcased the relationship
between a coefficient of lift and the angle of attack , the ratio of lift and drag and the yaw and pitching moments
versus the yaw and pitch angles respectively. The results presented the difference in these changes with the
model when it had a tail attached and no tail. The results showcase that there was an increase in stability, lift,
drag and overall efficiency when a tail was on.
In conclusion, the data supported the idea that the tail improves the overall efficiency of the performance of the
model. The wind tunnel first measured the aerodynamic forces of the model. Using the data gathered from the
force measurements, the calculations for the coefficients of lift, drag yaw and pitching moment were derived in
order to determine the behavior of a model in a wind tunnel at different angles of attack and yaw angles with the
tail on and the tail off. We obtained a better understanding of airplane aerodynamic performance through the
analysis of these forces with respect to the change in angle of attack. The theories presented in previous classes
supported the behaviors of the model as the tail served to provide stability and increase effectiveness. The
theories state that the tail is used for stability and even though it may increase drag that it is also a factor in
increasing lift. Figure 1 strongly supported this claim because the lift to drag was greater with the tail on than
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the tail. This figure displayed that the lift and the drag was greater in the test with the tail on. Theories also
explained the tail helped with yaw stability. These results were supported through Figure 3 as the tail increased
the Yaw Moment coefficient as the angle of yaw increased. This means that the tail is actively preventing a yaw
moment that would destabilize the airplane. Overall, the results supported the theories presented our courses.
Some ways that this experiment could be improved is to be able to find shafts that will provide even less effects
on our results, The fact that the struts may be affecting the experiment can create some artificial drag that may
not be created by the airplane. A big factor of error in the experiment is also the fact that no students were able
to participate and perform the lab. This means we are at the mercy of the data and factors such as debris inside
of the wind tunnel or an incorrect dynamic pressure may affect the results. This data as far as we know is the
most correct or can also be full of errors. Finally the results may have suffered from skewed answers if the
balance was not properly zeroed out. This may increase drag and yaw moment without the testers of the
experiment ever noticing.
Sample Calculations
Temperature Correction:
Y1=72
Y=76.5
Y2=76
𝑃𝑎𝑚𝑏 =
=
X1=29
0.114
Latitude Correction:
X=29.75
X2=30
0.118
Y1=32
Y=32.7157
Y2=34
P1
0.124
0.128
X1=29
0.035
X
X2=30
0.036
P2
0.030
0.031
(𝑥2 − 𝑥)(𝑦2 − 𝑦)
(𝑥 − 𝑥1 )(𝑦2 − 𝑦)
(𝑥2 − 𝑥)(𝑦 − 𝑦1 )
(𝑥 − 𝑥1 )(𝑦 − 𝑦1 )
𝑄 +
𝑄 +
𝑄 +
𝑄
(𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 ) 11 (𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 ) 21 (𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 ) 12 (𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 ) 22
(𝑥2 − 𝑥)(𝑦2 − 𝑦)
(𝑥 − 𝑥1 )(𝑦2 − 𝑦)
(𝑥2 − 𝑥)(𝑦 − 𝑦1 )
(𝑥 − 𝑥1 )(𝑦 − 𝑦1 )
𝑄11 +
𝑄21 +
𝑄12 +
𝑄 =
(𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 )
(𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 )
(𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 )
(𝑥2 − 𝑥1 )(𝑦2 − 𝑦1 ) 22
𝑃𝑎𝑚𝑏 = 29.567 𝑖𝑛𝐻𝑔
Corrected Pressure in (psi) Scanivalve:
𝑃𝑎𝑚𝑏 = 29.567 𝑖𝑛𝐻𝑔 ∗
0.491154𝑝𝑠𝑖
= 14.522𝑝𝑠𝑖
1 𝑖𝑛𝐻𝑔
Density:
𝑃𝑎𝑚𝑏
𝜌=
=
𝑅𝑇
29.567𝑖𝑛𝐻𝑔 ∗
3386.39 𝑃𝑎
1 𝑖𝑛𝐻𝑔
5
287 ∗ (76.5℉ + 459.17 ∗ ( ))
9
= 1.057
𝑘𝑔
𝑚3
Velocity:
248.84 𝑃𝑎
2 (( 7𝑖𝑛𝐻2𝑂) ×
)
1𝑖𝑛𝐻2𝑂
2𝑞 √
𝑚
𝑉=√ =
= 57.40
𝑘𝑔
𝜌
𝑠
1.057 3
𝑚
Sutherland Equation: Dynamic Viscosity
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American Institute of Aeronautics and Astronautics
𝜇=
𝑎𝑇 1∕2
𝑏
𝑇
(1+ )
=
1.458×106
𝐾𝑔
𝑚⋅𝑠⋅𝐾1∕2
5
9
(76.5℉+459.17∗( ))
1∕2
= 1.835 × 10−5
110.4𝐾
)
5
(76.5℉+459.17∗(9))
(1+
Reynold’s Number:
𝑘𝑔
𝑚
𝜌𝑣𝑐 1.057 𝑚3 × 57.40 𝑠 × 0.0880364𝑚
𝑅ⅇ =
=
= 2.91 × 105
𝜇
1.835 𝑥10−5
Coefficient of Lift:
𝐶𝐿 =
𝐿
−5.6448
=
= −.23818
𝑞𝑠 7𝑖𝑛𝐻2𝑂 × 93.81𝑖𝑛2
Coefficient of Drag:
𝐶𝐷 =
𝐷
1.5936
=
= .06724
𝑞𝑠 7𝑖𝑛𝐻2𝑂 × 93.81𝑖𝑛2
Pitching Moment Coefficient :
𝐶𝑀 =
𝑀𝑦
15.8464
=
= .19291
𝑞𝑆𝑐̅ 7𝑖𝑛𝐻2𝑂 × 93.81𝑖𝑛2 × 3.466𝑖𝑛
Yaw Moment Coefficient:
𝐶𝑁 =
𝑁
1.0675
=
= .00166
𝑞𝑆𝑏
7𝑖𝑛𝐻2𝑂 × 93.81𝑖𝑛2 × 27.066𝑖𝑛
Aspect Ratio:
𝐴𝑅 =
𝑏 2 27.066𝑖𝑛2
=
= 7.8091
𝑆
93.81𝑖𝑛2
Oswald Efficiency:
ⅇ = 1.78(1 − .045𝐴𝑅.68 ) − 0.64 = 1.78(1 − .045(7.8091.68 ) − 0.64 = .81596
Lift Slope:
𝜕𝐶𝐿 𝑦2 − 𝑦1
. 49023 − .30554
=
=
= .0923
𝜕𝛼
𝑥2 − 𝑥1
2−0
Acknowledgments
This lab was under the supervision of Dr. Xiaofeng Liu and laboratory teaching assistant Nate Abrenilla. A
lecture was prepared and delivered by Dr. Liu who guided the class towards producing the statistical results of this
lab. Lab technician Nate Abrenilla overlooked the data readings. This lab was performed at SDSU facilities and results
were produced through numerical analysis at home.
References
[1] Figliola and Beasley, 6th Ed., 2015
[2] Latitude Correction, (n.d.). [online] Available at: https://blackboard.sdsu.edu/bbcswebdav/pid-5431224-dtcontent-rid108216837_1/courses/A_E303-01-Spring2020/LattitudeCorrectionForBarometerHeightReading.pdf
[3] Temperature Correction, (n.d.). [online] Available at: https://blackboard.sdsu.edu/bbcswebdav/pid-5431224-dtcontent-rid108216837_1/courses/A_E303-01-Spring2020/TemperatureCorrectionForBarometerHeightReading.pdf
[4] Liu, X. (n.d.). AE 303 Experimental Aerodynamics: Lecture 2.
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Appendix A Proof:
F(model) = [F(model on, wind on) – F(model on, wind off)] – [F(model off, wind on) – F(model off, wind off)]
F(model) = [F(model) + F(struts)] – [F(struts)]
F(model) = F(model)
Given the following equations, we are asked to prove that the Aerodynamic forces on the model equate to the difference of two
forces. The forces on a model with a wind tunnel on minus the forces of on a model with the wind tunnel off and the forces on two
support shafts with the wind tunnel on minus the forces on two shafts minus with the wind tunnel off. Both parts of the equation
present the aerodynamic forces on the model being experimented on.
The results of the first array will present the aerodynamic forces on a model as well in addition to the aerodynamic forces on
the shafts that are holding the model in place.
The results on the second array part of the equation will be the aerodynamic forces on two supporting shafts.
When subtracting these arrays, it is proved that the only forces being calculated will be the aerodynamic forces of the model
which are the complete aerodynamic forces being measured.
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Appendix B Raw Data:
Model
on
Tail
on
Wind
off
VAR
UNITS
a
(deg)
-6
-4
-2
0
2
4
6
8
10
15
0
0
b
(deg)
0
0
0
0
0
0
0
0
0
0
5
10
T
(deg F)
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
Fx
Fy
Fz
Mx
My
Mz
(lbs)
-0.005908
0.017053
-0.004624
-0.015708
0.001453
-0.027536
-0.022835
-0.018871
-0.008925
-0.028839
-0.165008
-0.01854
(lbs)
0.018442
0.01273
0.032428
0.01016
0.018352
0.004237
0.02523
0.014524
-0.005993
-0.025351
-0.36162
-0.059068
(lbs)
0.088777
0.00262
0.056704
-0.000327
0.034289
0.070536
-0.068748
-0.080231
0.036908
0.064041
-0.006624
0.112114
(lbs-in)
0.244822
0.501834
0.786183
0.891143
0.829477
0.967714
0.228854
0.939119
1.110047
0.342711
-21.97348
-32.66918
(lbs-in)
-2.022044
-0.113281
-0.353426
0.182135
-0.209594
0.419119
0.996239
1.732817
1.466205
2.223806
7.012855
8.128888
(lbs-in)
-0.184967
-0.47868
-0.28054
-0.36136
-0.402864
-0.477849
-0.090122
0.220062
0.046479
0.819693
6.294042
2.020689
Model
on
Tail
on
Wind
on
VAR
UNITS
WIND OFF
a
(deg)
0
-6
-4
-2
0
2
4
6
8
10
15
0
0
b
(deg)
0
0
0
0
0
0
0
0
0
0
0
5
10
T
(deg F)
80.4
84.6
85.4
86
86.6
87.2
87.7
88.5
89
89.7
90.1
91.1
91.3
Fx
Fy
Fz
Mx
My
Mz
(lbs)
0.026864
7.194787
6.872995
6.70594
6.720269
6.738783
6.922296
7.088431
7.382709
9.485697
13.18478
6.876539
7.396124
(lbs)
-0.044216
-0.727597
-0.682756
-0.776686
-0.809907
-0.8867
-0.929877
-0.866889
-0.904505
-0.67123
-0.560931
-4.703029
-10.19293
(lbs)
0.126754
-4.404358
-0.277936
4.027154
8.362796
12.72379
17.34721
20.57334
23.20206
20.92874
19.49249
8.462686
8.582788
(lbs-in)
-0.657393
1.024059
2.924975
2.127815
1.409047
-0.099865
0.673774
0.622432
0.021775
-6.206694
-18.03564
-30.55221
-67.04751
(lbs-in)
0.280259
-37.0396
-41.57501
-45.48488
-49.73383
-53.56722
-57.82892
-61.61265
-64.92059
-83.36735
-95.43278
-44.14704
-39.30335
(lbs-in)
-0.416469
-0.253064
-0.145788
-0.204641
-0.009391
0.312847
0.090355
0.205982
0.104649
0.571622
0.740256
12.63188
13.97878
Model
on
Tail
off
Wind
on
VAR
UNITS
WIND OFF
a
(deg)
0
-6
-4
-2
0
2
4
6
8
10
15
0
0
b
(deg)
0
0
0
0
0
0
0
0
0
0
0
5
10
T
(deg F)
73.6
80.5
82
82.9
83.7
84.3
85.1
85.9
86.8
87.3
88
89.1
89.5
Fx
Fy
Fz
Mx
My
Mz
(lbs)
0.010781
6.988701
6.749577
6.619873
6.576237
6.548442
6.693852
6.831214
7.127326
9.212098
12.11298
6.672617
6.916518
(lbs)
-0.012032
-0.431059
-0.489058
-0.614657
-0.52314
-0.525255
-0.682469
-0.563192
-0.433677
-0.537551
-0.460777
-3.585717
-8.235045
(lbs)
-0.028225
-2.929299
0.740092
4.537245
7.86108
12.07634
16.03649
18.78229
20.88168
16.95631
14.82893
8.375125
8.65658
(lbs-in)
0.600087
1.959986
2.579629
2.285295
1.453093
0.307181
0.522041
0.586327
2.351817
-7.763657
-16.60592
-34.65988
-72.47628
(lbs-in)
-0.092476
-59.72863
-55.24239
-51.33245
-48.05553
-44.18394
-41.02078
-38.16047
-35.56841
-39.2055
-40.25858
-41.54384
-39.36234
(lbs-in)
-0.289459
-2.805113
-2.725257
-1.759101
-2.615784
-2.747644
-2.055718
-3.400231
-4.553399
0.051615
-1.63751
-0.169411
-9.403744
Model
off
Tail
off
Wind
on
VAR
UNITS
a
(deg)
0
0
0
b
(deg)
0
5
10
T
(deg F)
78.1
80.1
82.5
Fx
Fy
Fz
Mx
My
Mz
(lbs)
(lbs)
(lbs)
(lbs-in)
(lbs-in)
(lbs-in)
5.635527 -0.31733 1.091942 -1.04235 -51.22485 -1.646912
5.587263 -3.091032 1.1648 -44.88395 -44.69973 4.779194
5.850228 -7.145455 1.467987 -88.16304 -45.84466 -2.486216
Model
off
Tail
off
Wind
off
VAR
UNITS
a
(deg)
-6
-4
-2
0
2
4
6
8
10
15
0
0
b
(deg)
0
0
0
0
0
0
0
0
0
0
5
10
T
(deg F)
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
72.3
Fx
Fy
Fz
Mx
My
Mz
(lbs)
0.028441
0.043177
0.05192
0.036337
0.031385
0.02045
0.00682
0.017846
0.024835
-0.03553
0.00777
0.040518
(lbs)
-0.012549
-0.010251
-0.034881
-0.011717
-0.008431
-0.001672
-0.015034
-0.044704
-0.01952
0.003813
-0.082482
-0.11664
(lbs)
-0.059705
-0.064655
-0.082625
-0.029994
0.020906
-0.067541
-0.077728
-0.099026
-0.055599
0.043188
-0.043057
-0.060447
(lbs-in)
0.082251
0.631329
0.719338
0.438986
-0.061458
0.286625
0.64602
-0.260985
0.161507
0.4527
-16.26275
-32.34356
(lbs-in)
-0.360937
0.508962
0.114283
1.155168
1.028247
1.344672
1.433802
1.684247
1.166787
2.650371
5.272538
8.832101
(lbs-in)
-0.511322
-0.265324
-0.142598
-0.159895
-0.24703
-0.279926
0.062034
0.26886
0.189853
0.025815
1.191334
1.441786
9
American Institute of Aeronautics and Astronautics
Tamb
Pamb
74
29.67
Tamb
Pamb
76.5
29.73
Tamb
Pamb
74
29.74
Tamb
Pamb
74.3
29.73
Tamb
Pamb
74
29.67
Appendix C: MATLAB Code
Cd_tailon
Cl_tailon
Cm_tailon
Cn_tailon
Cd_tailoff
Cl_tailoff
Cm_tailoff
Cn_tailoff
=
=
=
=
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AF22:AF33');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AH22:AH33');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AJ22:AJ33');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AK22:AK33');
=
=
=
=
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AF41:AF52');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AH41:AH52');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AJ41:AJ52');
xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AK41:AK52');
figure (1)
x= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'E20:E29');
y= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AH22:AH31');
y1= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AH41:AH50');
plot(x,y)
hold on
plot(x,y1)
title('Cl v {\alpha}')
xlabel('{\alpha}')
ylabel('Cl')
legend("tail on", "tail off")
legend('Location',"best")
grid on
hold off
figure (2)
x= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'E20:E29');
y= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AJ22:AJ31');
y1= xlsread("LIU_AE303_Lab-5-Data.xlsx","Sheet1",'AJ41:AJ50');
plot(x,y)
hold on
plot(x,y1)
title('Cm v {\alpha}')
xlabel('{\alpha}')
ylabel('Cm')
legend("tail on", "tail off")
legend('Location',"best")
10
American Institute of Aeronautics and Astronautics
grid on
hold off
figure (3)
beta= Cm_tailoff([4 11 12]);
y= Cn_tailon([4 11 12]);
y1= Cn_tailoff([4 11 12]);
plot(beta,y)
hold on
plot(beta,y1)
title('Cm v {\beta}')
xlabel('{\beta}')
ylabel('Cm')
legend("tail on", "tail off")
legend('Location',"best")
grid on
hold off
figure (4)
Cdoff= Cd_tailoff([1:10]);
y1= Cl_tailoff([1:10]);
Cdon= Cd_tailon([1:10]);
y= Cl_tailon([1:10]);
plot(Cdoff,y1)
hold on
plot(Cdon,y)
title('C_l v C_d')
xlabel('C_d')
ylabel('C_l')
legend("tail on", "tail off")
legend('Location',"best")
grid on
hold off
%7
Cl_Cd_Max_tailon = .932124/.0752701
Cl_Cd_Max_tailoff = .821622/.0625553
%8
y = Cl_tailon([1:10]);
x = transpose([-6 -4 -2 0 2 4 6 8 10 15]);
11
American Institute of Aeronautics and Astronautics
dCl_dalfaon= x\y
y1 = Cl_tailoff([1:10]);
x1 = transpose([-6 -4 -2 0 2 4 6 8 10 15]);
dCl_dalfaoff= x1\y1
%10 dCm/dalfa
y2 = Cm_tailon([1:10]);
x2 = transpose([-6 -4 -2 0 2 4 6 8 10 15]);
dCm_dalfaon= x2\y2
y3 = Cm_tailoff([1:10]);
x3 = transpose([-6 -4 -2 0 2 4 6 8 10 15]);
dCm_dalfaoff= x3\y3
%11 dCn/dBeta
y4 = Cn_tailon([4 11 12]);
x4 = transpose([0 5 10]);
dCm_dbetaon= x4\y4
y5 = Cn_tailoff([4 11 12]);
x5 = transpose([0 5 10]);
dCm_dbetaoff= x5\y5
12
American Institute of Aeronautics and Astronautics