NA520 Final Project Report
Simulations of Drag Lift and Separation of the Flow past an Elliptical Cylinder
Shiyu Wang
Abstract
The model of the flow past the circular
cylinder has been widely applied to marine
engineering. To generalize the case, the project
uses elliptical cylinders with varying axial
length ratios instead. The project considers the
2-D profile of the cylinder. In order to
determine the pressure distribution, lift
coefficients, drag coefficients, and separation
locations under different cases, a program called
Xfoil is adopted to analyze the problem. In
addition, the software Ansys-Fluent is also used
so that the results calculated by these two
methods can be validated mutually. The results
show that the lift coefficients remain zero, the
drag coefficients increases as axial length ratios
become larger. In addition, the project gives the
equation to predict the separation locations.
Finally, the reasons for error by using these two
methods are also provided.
Xfoil and Fluent. By analyzing the results, the
project also shows relations between these
factors and shapes.
2. Methodology
The assumption is that the elliptical cylinder
is long enough, so the project uses its 2-D
profile to simplify the model. In the following
part A and B, two methods have been induced to
solve this problem, and the results can be
validated mutually. Part A uses Xfoil which is
based on viscous formulation which is
essentially the same as that of the transonic
ISES code [2]. However, some changes have
been incorporated to improve the prediction of
“base drag” from blunt trailing edges. Part B
uses Ansys-Fluent which is based on
computational fluid dynamics (CFD). This
method uses numerical methods and algorithms
to perform the calculations which are required
to simulate the interaction of liquids with
surfaces defined by boundary conditions.
Keywords: Pressure Distribution, Drag, Lift,
Separation, Elliptical Cylinder, Xfoil, Fluent
1. Introduction
2.1. Using Xfoil to analyze the elliptical
cylinder
The project uses elliptical cylinders with
varying axial length ratios as the model to
analyze. The background conditions are set that
the 20°C seawater flows uniformly past the
cylinder with 0° angle of attack. According to
fresh water and seawater properties [1], the
density  is 1024.87 kg/m3, the viscosity  is
0.001077 kg/m/s, the kinematic viscosity  is
1.0508 106 m2/s. The speed of the flow U is
3.1524 m/s, and the fixed length of the long axis
of the ellipse L is 1m. So the Reynolds number
Re is 3 106 , the Mach number Ma is
0.009264. The objective of this project is to
determine the pressure distribution, lift
coefficients, drag coefficients, and separation
locations under cases of different axial length
ratios. The results are calculated and verified by
The project uses Xfoil to calculate the
pressure distribution, the lift coefficient, the
drag coefficient, and the separation location
under different axial length ratios of the
elliptical cylinder. Each case considers that
Reynolds number is 3 106 and the angle of
attack is 0 . In addition, all the solutions below
are based on one case of the project
( a  0.5m, b  0.1m ).
Step1. Establish the geometry of the
elliptical cylinder
In this project, the ellipse parameter equation
is used to establish the geometry of the elliptical
cylinder. The angle is defined in the
1
NA520 Final Project Report
counterclockwise direction and the trailing edge
is of the angle of 0 degree.
 x  a cos  

 ,  [0, 2 ]
 y  b sin  
command. Although using the PANE command
also dose this, CADD allows the point addition
to be restricted to location with excessive corner
angles, and also to locations which fall within a
specified x-range. Thirdly, the initial conditions
(Reynolds number and angle of attack) are
inputted into the program to calculate.
(1)
For this case of the project
( a  0.5m, b  0.1m ), the whole angle 2 is
discretized into 50 pieces, so the whole
continuous elliptical geometry is discretized by
50 points, which are determined by equation (1).
Then, the x, y coordinate values for each point
are created in a formatted Xfoil coordinate file
for the program to establish the geometry of
elliptical cylinder. The geometry can be seen in
the following figure.
In the figure 2, the pressure coefficient, the
lift coefficient, and the drag coefficient are
demonstrated along the cylinder.
Figure 2. Cp along the elliptical cylinder
Step3. Analyze different cases by varying
the geometry in a non-dimensional manner
The geometry can be varied by using
different axial length ratios  , which indicates
that the length of the short axis to the length of
the long axis. By fixing the length of the long
axis and varying  from 0.05 to 1.0, the
geometry is changing from a thin elliptical
cylinder to a round cylinder. Then, the results
can be obtained by repeating the first two steps.
Figure 1. The geometry of the elliptical cylinder
Step2. Use the program to analyze the case
Firstly, the number of panel nodes needs to be
enlarged to generate more precise results. The
project increases the default panel nodes from
51 to 250 so that the maximum panel angle is
reduced from 64.35 to 11.67 , which can be
tolerated within the 15 degree angle criteria.
Secondly, it is also necessary to ensure that the
loaded geometry does not contain panels that
create very sharp edges. Therefore, the PANE
command in Xfoil is adopted to smooth out the
geometry. Furthermore, in case that the cylinder
has an excessively coarse point spacing,
additional points can be added with the CADD
2.2. Using Ansys-Fluent to analyze the
elliptical cylinder
Step1. Establish and mesh the geometry of
the elliptical cylinder
The whole geometry contains two parts; one
is the cylinder and the other is the c-mesh
domain which represents the flow. Both of them
can be created by stretching the surfaces from
2
NA520 Final Project Report
the sketches which are drawn in the geometry
modeler. However, the latter needs Boolean
subtract to deduct the cylinder area from the
original c-mesh area.
In addition, the minimum required thickness
of the refined structured mesh region can be
determined by the equation below.
 1 4
 max  0.373( ) 5 L5
The reason for using c-mesh is that when
considering the viscous effect, the boundary
layer and the wake has to be adapted in the
streamwise direction. For viscous flow, the cmesh allows you to resolve the wake which is
the nice resolution of the region right behind the
trailing edge. However this is not the case for
the o-mesh. So o-mesh is acceptable in inviscid
flow but often unacceptable in viscous flow.
U
(6)
By inserting the known values into the
equation (5) and (6), the maximum thickness of
the first cell mesh is calculated as 4.4 107 m ,
the minimum required thickness of the refined
structured mesh region is calculated as 0.0189m.
The final mesh can be seen from the figures
below.
After establishing the two parts, the geometry
needs to be meshed. The closer the mesh is to
the cylinder, the denser the mesh needs to be.
For the purpose of more precise results, the
closer mesh also needs to be regular structured
grids which are typically quadrilaterals with
four equal sides.
Another important factor needs to be consider
is the mesh around the boundary layer region.
As the Reynolds number is 3 106 which is
within the turbulent boundary layer region and
the cylinder is thin, the project uses the 1/7power approximation to calculate the boundary
layer thickness.

y 
Step2. Set up the material and boundary
conditions
The material is the 20°C seawater with the
parameters mentioned before. Since the
Reynolds number of the flow is in the range of
turbulent, the project chooses the viscous model
k-epsilon to simulate. The boundary conditions
for the inlet are controlled by the velocity. Since
the angle of attack is 0 degree, the x velocity is
the speed of the flow and y velocity is 0. The
boundary conditions for the outlet are controlled
by the pressure and its gauge pressure is set as
0. The boundary conditions for the cylinder are
that the cylinder is treated as the solid wall,
which means no penetration into the wall.
1
 w  0.029 U 2 Re x 5
w

u 
Figure 3. The refined structured mesh around
the elliptical cylinder
(2)
(3)
u  y
(4)

Set the y  equals to 1 and combine the three
equations above, the maximum thickness of the
first cell mesh can be calculated by the equation
below.
ymax 

0.029U
Re
1
10
L
Step3. Solve the model and obtain the
result
(5)
Change the residual absolute criteria to
1104 , which ensures some further trust of the
3
NA520 Final Project Report
solutions. Then change the number of iterations
to 3000 and let the solver compute the model
from the inlet. Finally, the result can be seen in
the following figure.
blunter, the separation region becomes larger;
therefore the error appears.
1.2
Xfoil b/a=0.1
Fluent b/a=0.1
1
0.8
Cp
0.6
0.4
0.2
0
-0.2
0
100
200
-0.4
θ(°)
1.2
Figure 4. Cp along the elliptical cylinder
300
Xfoil b/a=0.2
Fluent b/a=0.2
1
0.8
All the results computed by Xfoil are
compared against the results calculated by
Ansys-fluent.
0.6
Cp
3. Results
0.4
0.2
0
3.1. The pressure coefficient
-0.2
The data of the pressure coefficient of all
cases (   0.05 ~ 1.0 ) can be seen from the
table in the appendix. To illustrate the result
clearly, the project uses five cases below that
have different axial length ratios  . Because of
the symmetry of the ellipse and the 0 degree
angle of attack, the pressure coefficient of the
upper side and the lower side is symmetrical. As
can be seen from the figures, the pressure
coefficient calculated by two methods fits each
other well. However, the main difference exists
around the surface after the separation location.
This is mainly because that the entire viscous
solution (boundary layers and wake) used by
Xfoil is strongly interacted with the
incompressible potential flow via the surface
transpiration model (the alternative
displacement body model is used in ISES code).
This only permits proper calculation of limited
separation regions. As the cylinder becomes
0
100
200
300
-0.4
-0.6
θ(°)
1.5
Xfoil b/a=0.5
Fluent b/a=0.5
1
Cp
0.5
0
0
100
200
-0.5
-1
-1.5
4
θ(°)
300
NA520 Final Project Report
circle. The result calculated by the Xfoil is
validated against the values by Fluent. As the
limitation of simulating the large separation
regions by Xfoil, which can also be seen in the
error mentioned before in the Cp distribution, the
blunter shape’s drag coefficient are not fitted so
well as the thinner shape.
1.5
Xfoil b/a=0.7
Fluent b/a=0.7
1
0.5
Cp
0
0
100
200
300
-0.5
0.18000
0.16000
-1
0.14000
0.12000
-2
Coefficient
-1.5
θ(°)
0.10000
0.08000
0.06000
0.04000
0.02000
1.5
Xfoil b/a=1.0
1
Fluent b/a=1.0
0.00000
-0.02000 0
0.2
0.4
Cp
0
-0.5
0.6
0.8
λ
0.5
0
100
200
300
drag coefficient (Xfoil)
lift coefficient (Xfoil)
drag coefficient (fluent)
lift coefficient (fluent)
-1
Figure 6. Cd and CL along the cylinder
-1.5
-2
3.3. The separation location
-2.5
-3
At the separation location, the velocity
gradient at the wall and the wall shear stress are
zero. Therefore the project uses the chart based
on the results calculated by Xfoil to find the
separation location which lets the friction
coefficient (Cf) equals to zero. Then, the project
finds the relation between separation locations 
and axial length ratios  as the equation below.
θ(°)
Figure 5. Cp along the elliptical cylinder (Xfoil
versus Fluent)
3.2. The drag coefficient and the lift
coefficient
  2.0019 6  6.289 5
As can be seen in the figure, the lift
coefficient is almost zero no matter how thin or
thick the cylinder is. This is because that the
symmetrical shape and 0 degree angle of attack
make the pressure and wall shear stresses acting
on the body be cancelled. However, due to the
viscous effect, the drag can be accumulated. The
blunter the body is, the larger the drag
coefficient is. In the figure, the maximum drag
coefficient appears when the cylinder becomes a
7.1291 4  3.7795 3
1.2034 2  0.0012  1.0035
5
(7)
1
Cf
NA520 Final Project Report
As can be seen in the figure above, the points
calculated by Fluent fit the equation (7) well.
Similarly, the error comes from the limitation of
analyzing large separation regions by Xfoil.
0.01
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0
-0.001 0
4. Conclusions
0.2
0.4
0.6
0.8
The project establishes the elliptical cylinder
model with varying axial length ratios  from
0.05 to 1.0. The pressure distribution, lift
coefficients, drag coefficients and separation
locations have been studied. In addition, the
results are validated between two program Xfoil
and Fluent and the results fit well mutually.
1
x(m)
b/a=0.05
b/a=0.2
b/a=0.35
b/a=0.5
b/a=0.65
b/a=0.8
b/a=0.95
b/a=0.1
b/a=0.25
b/a=0.4
b/a=0.55
b/a=0.7
b/a=0.85
b/a=1.0
b/a=0.15
b/a=0.3
b/a=0.45
b/a=0.6
b/a=0.75
b/a=0.9
Under the same characteristic area, the results
illustrate that the drag coefficient increases as
the body becomes blunter. However, the lift
coefficient remains almost zero because of the
symmetry of the body and the zero angle of
attack. Besides, the project also predicts the
relation of the axial length ratio and the location
of separation by the equation (7).
Figure 7. Cf along the cylinder
Separation Location(m)
1.05
y = -2.0019x6 + 6.289x5 - 7.1291x4 + 3.7795x3 1.2034x2 + 0.0012x + 1.0035
R² = 0.9994
1
0.95
The error between the two methods mainly
comes from two parts. Firstly, the Xfoil is
precise to analyze most thin foil shapes.
However, as can be seen in the result, when the
shape becomes blunter without sharp trailing
edge, the separation region becomes larger. So
the error will appear. Secondly, the first cell
mesh around the cylinder is required to be very
thin, which results in the appearance of longnarrow grids. The long-narrow grids can save
the calculating time but the quality of the mesh
is not as high as the quadrilaterals with equal
sides.
0.9
0.85
0.8
0.75
0.7
0
0.2
0.4
0.6
0.8
1
Axial Length Ratio
result points (Xfoil)
result points (Fluent)
Poly. (result points (Xfoil))
Figure 8. The relationship between separation
locations and axial length ratios
6
NA520 Final Project Report
Reference
[1] International Towing Tank Conference (2011). Fresh Water and Seawater Properties (2nd revision).
ITTC, pp.7-8.
[2] Mark Drela. XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils. MIT, Dept.
of Aeronautics and Astronautics.
[3] Bruce R. Munson, Theodore H. Okiishi, Wade W. Huebsch, Alric P. Rothmayer (2013).
Fundamentals of Fluid Mechanics (7th edition). New York. J. Wiley
[4] Pietro Catalano, Meng Wang, Gianluca Iaccarino, Parviz Moin. “Numerical Simulation of the Flow
around a Circular Cylinder at High Reynolds Numbers”, International Journal of Heat and Fluid Flow,
Vol.24, pp. 463-469, 2003
[5] Yazan Taamneh. “CFD Simulations of Drag and Separation Flow around Ellipsoids”, Jordan
Journal of Mechanical and Industrial Engineering, Vol.5, pp. 129-132, 2011
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NA520 Final Project Report
Appendix
1. Nomenclature
 : Density of water (kg/m3)
 : Parameter of the angle (rad)
 : Viscosity of water (kg/m/s)
 : Axial length ratio
 : Kinematic viscosity of water (m2/s)
 : Separation location (m)
U : Inflow speed (m/s)
 w : Wall shear stress (pa)
L : Fixed length of the long axis of the ellipse
(m)
u : Friction velocity (m/s)
Re : Reynolds number
y  : Non-dimensional length
Ma : Mach number
 : Boundary layer thickness (m)
C p : Pressure coefficient
x : X location of discretized points of the
cylinder (m)
CD : Drag coefficient
y : Y location of discretized points of the
cylinder (m)
CL : Lift coefficient
a : Half length of the long axis (m)
C f : Friction coefficient
b : Half length of the short axis (m)
2. Cp along the cylinder
Table1. Cp along the cylinder by Xfoil (   0.05  0.25 )
x(0.05)
Cp
x(0.1)
Cp
x(0.15)
Cp
x(0.2)
Cp
x(0.25)
Cp
0.999
0.996
0.989
0.981
0.972
0.964
0.955
0.946
0.937
0.929
0.920
0.911
0.902
0.893
0.884
0.876
0.867
0.279
0.213
0.003
0.011
-0.031
-0.060
-0.077
-0.086
-0.095
-0.097
-0.094
-0.095
-0.097
-0.097
-0.098
-0.098
-0.098
0.999
0.997
0.994
0.990
0.985
0.978
0.970
0.962
0.955
0.947
0.939
0.930
0.921
0.913
0.904
0.895
0.887
0.208
0.203
0.198
0.189
0.176
0.113
0.024
-0.047
-0.103
-0.146
-0.151
-0.156
-0.162
-0.167
-0.173
-0.177
-0.181
0.999
0.998
0.995
0.992
0.988
0.983
0.977
0.971
0.965
0.958
0.951
0.943
0.935
0.927
0.918
0.909
0.900
0.266
0.263
0.260
0.257
0.252
0.245
0.234
0.173
0.089
0.011
-0.052
-0.107
-0.170
-0.231
-0.235
-0.239
-0.245
0.999
0.998
0.995
0.992
0.988
0.984
0.979
0.974
0.969
0.963
0.957
0.951
0.944
0.936
0.928
0.920
0.912
0.292
0.290
0.289
0.289
0.288
0.288
0.287
0.293
0.265
0.198
0.110
0.021
-0.052
-0.112
-0.159
-0.198
-0.228
0.999
0.998
0.995
0.992
0.988
0.984
0.979
0.974
0.969
0.963
0.957
0.951
0.944
0.937
0.930
0.922
0.914
0.301
0.298
0.296
0.294
0.293
0.291
0.288
0.286
0.284
0.284
0.239
0.155
0.058
-0.031
-0.105
-0.165
-0.212
8
NA520 Final Project Report
0.858
0.849
0.840
0.831
0.823
0.814
0.805
0.796
0.787
0.778
0.769
0.761
0.752
0.743
0.734
0.725
0.716
0.707
0.699
0.690
0.681
0.672
0.663
0.654
0.645
0.637
0.628
0.619
0.610
0.601
0.592
0.583
0.575
0.566
0.557
0.548
0.539
0.530
0.521
0.512
0.504
0.495
0.486
0.477
0.468
0.459
-0.099
-0.098
-0.100
-0.099
-0.100
-0.099
-0.101
-0.100
-0.101
-0.100
-0.101
-0.101
-0.101
-0.101
-0.101
-0.101
-0.101
-0.100
-0.101
-0.101
-0.101
-0.101
-0.101
-0.101
-0.101
-0.102
-0.101
-0.101
-0.102
-0.102
-0.101
-0.102
-0.102
-0.101
-0.101
-0.102
-0.101
-0.102
-0.101
-0.101
-0.102
-0.101
-0.102
-0.102
-0.101
-0.102
0.878
0.869
0.860
0.852
0.843
0.834
0.825
0.816
0.807
0.798
0.789
0.781
0.772
0.763
0.754
0.745
0.736
0.727
0.718
0.709
0.700
0.691
0.682
0.673
0.664
0.656
0.647
0.638
0.629
0.620
0.611
0.602
0.593
0.584
0.575
0.566
0.557
0.548
0.539
0.530
0.521
0.512
0.503
0.494
0.485
0.476
-0.184
-0.186
-0.189
-0.191
-0.193
-0.194
-0.196
-0.197
-0.198
-0.199
-0.201
-0.201
-0.202
-0.203
-0.204
-0.204
-0.204
-0.205
-0.205
-0.206
-0.206
-0.207
-0.207
-0.207
-0.208
-0.208
-0.208
-0.208
-0.208
-0.209
-0.209
-0.209
-0.209
-0.209
-0.209
-0.210
-0.209
-0.210
-0.210
-0.210
-0.210
-0.210
-0.211
-0.210
-0.209
-0.211
0.891
0.881
0.872
0.862
0.853
0.843
0.833
0.823
0.813
0.804
0.794
0.784
0.774
0.764
0.754
0.744
0.734
0.724
0.714
0.704
0.693
0.683
0.673
0.663
0.653
0.643
0.633
0.623
0.612
0.602
0.592
0.582
0.572
0.562
0.551
0.541
0.531
0.521
0.511
0.501
0.490
0.480
0.470
0.460
0.450
0.440
-0.251
-0.257
-0.263
-0.268
-0.274
-0.278
-0.282
-0.286
-0.289
-0.292
-0.295
-0.297
-0.299
-0.301
-0.303
-0.304
-0.306
-0.307
-0.308
-0.309
-0.311
-0.311
-0.312
-0.313
-0.314
-0.315
-0.314
-0.316
-0.316
-0.316
-0.317
-0.317
-0.318
-0.317
-0.318
-0.318
-0.318
-0.318
-0.318
-0.319
-0.318
-0.319
-0.319
-0.319
-0.318
-0.318
9
0.903
0.893
0.884
0.874
0.864
0.854
0.844
0.833
0.822
0.812
0.801
0.790
0.779
0.767
0.756
0.745
0.734
0.722
0.711
0.699
0.688
0.676
0.665
0.653
0.642
0.630
0.619
0.607
0.595
0.584
0.572
0.560
0.549
0.537
0.525
0.514
0.502
0.490
0.478
0.467
0.455
0.443
0.432
0.420
0.408
0.397
-0.253
-0.273
-0.290
-0.303
-0.314
-0.327
-0.346
-0.372
-0.387
-0.387
-0.389
-0.392
-0.396
-0.398
-0.402
-0.405
-0.407
-0.410
-0.412
-0.414
-0.417
-0.418
-0.419
-0.421
-0.422
-0.424
-0.424
-0.425
-0.426
-0.427
-0.428
-0.428
-0.429
-0.429
-0.429
-0.430
-0.430
-0.430
-0.431
-0.430
-0.430
-0.432
-0.429
-0.430
-0.428
-0.428
0.906
0.897
0.888
0.878
0.869
0.858
0.848
0.837
0.826
0.815
0.803
0.791
0.779
0.767
0.755
0.743
0.730
0.718
0.705
0.692
0.679
0.666
0.653
0.640
0.627
0.614
0.600
0.587
0.574
0.561
0.547
0.534
0.521
0.507
0.494
0.481
0.467
0.454
0.441
0.427
0.414
0.401
0.388
0.374
0.361
0.348
-0.250
-0.284
-0.323
-0.384
-0.436
-0.441
-0.447
-0.454
-0.462
-0.470
-0.478
-0.486
-0.494
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-0.512
-0.518
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-0.531
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-0.541
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-0.547
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-0.551
-0.554
-0.553
-0.554
-0.556
-0.556
-0.556
-0.555
-0.558
-0.555
-0.555
-0.557
-0.554
-0.556
-0.552
-0.551
-0.552
-0.548
NA520 Final Project Report
0.450
0.442
0.433
0.424
0.415
0.406
0.397
0.388
0.380
0.371
0.362
0.353
0.344
0.335
0.326
0.317
0.309
0.300
0.291
0.282
0.273
0.264
0.255
0.247
0.238
0.229
0.220
0.211
0.202
0.194
0.185
0.176
0.167
0.159
0.150
0.141
0.133
0.124
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0.108
0.099
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0.061
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0.467
0.458
0.449
0.440
0.431
0.422
0.414
0.405
0.396
0.387
0.378
0.369
0.360
0.351
0.342
0.333
0.324
0.315
0.306
0.297
0.288
0.279
0.270
0.261
0.252
0.244
0.235
0.226
0.217
0.208
0.199
0.190
0.181
0.172
0.164
0.155
0.146
0.137
0.128
0.120
0.111
0.102
0.093
0.085
0.076
0.068
-0.209
-0.211
-0.209
-0.211
-0.209
-0.209
-0.211
-0.209
-0.211
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-0.207
-0.207
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-0.207
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-0.205
-0.204
-0.205
-0.206
-0.200
-0.206
-0.201
-0.203
-0.196
-0.204
-0.199
-0.194
-0.197
-0.194
-0.195
-0.189
-0.190
-0.180
-0.177
-0.173
0.429
0.419
0.409
0.399
0.389
0.379
0.368
0.358
0.348
0.338
0.328
0.318
0.308
0.298
0.287
0.277
0.267
0.257
0.247
0.237
0.227
0.217
0.207
0.198
0.188
0.178
0.168
0.158
0.149
0.139
0.129
0.120
0.111
0.101
0.092
0.083
0.075
0.067
0.059
0.052
0.045
0.039
0.034
0.029
0.025
0.021
-0.320
-0.318
-0.319
-0.319
-0.316
-0.317
-0.318
-0.315
-0.317
-0.316
-0.314
-0.316
-0.313
-0.315
-0.312
-0.313
-0.314
-0.310
-0.306
-0.311
-0.306
-0.305
-0.302
-0.303
-0.302
-0.299
-0.295
-0.290
-0.291
-0.294
-0.281
-0.275
-0.276
-0.266
-0.268
-0.246
-0.246
-0.229
-0.222
-0.210
-0.198
-0.168
-0.137
-0.119
-0.075
-0.025
10
0.385
0.373
0.362
0.350
0.339
0.327
0.316
0.304
0.293
0.281
0.270
0.259
0.247
0.236
0.225
0.214
0.203
0.192
0.181
0.171
0.160
0.150
0.140
0.130
0.120
0.111
0.102
0.094
0.086
0.078
0.071
0.065
0.059
0.053
0.048
0.044
0.040
0.036
0.032
0.029
0.026
0.023
0.021
0.018
0.016
0.014
-0.427
-0.431
-0.424
-0.426
-0.424
-0.425
-0.422
-0.417
-0.423
-0.419
-0.415
-0.412
-0.413
-0.409
-0.405
-0.406
-0.397
-0.393
-0.398
-0.380
-0.384
-0.377
-0.369
-0.364
-0.357
-0.344
-0.335
-0.320
-0.321
-0.293
-0.287
-0.260
-0.253
-0.231
-0.214
-0.185
-0.155
-0.139
-0.107
-0.080
-0.042
-0.010
0.032
0.077
0.117
0.151
0.335
0.322
0.309
0.297
0.284
0.271
0.259
0.247
0.234
0.223
0.211
0.199
0.188
0.177
0.167
0.156
0.147
0.137
0.128
0.120
0.112
0.104
0.097
0.090
0.084
0.078
0.072
0.067
0.062
0.058
0.053
0.049
0.045
0.042
0.039
0.035
0.032
0.030
0.027
0.025
0.022
0.020
0.018
0.016
0.014
0.013
-0.548
-0.543
-0.544
-0.540
-0.535
-0.538
-0.528
-0.523
-0.523
-0.519
-0.513
-0.506
-0.498
-0.495
-0.480
-0.478
-0.468
-0.462
-0.450
-0.436
-0.428
-0.403
-0.404
-0.382
-0.360
-0.355
-0.325
-0.316
-0.294
-0.265
-0.255
-0.233
-0.198
-0.165
-0.163
-0.108
-0.105
-0.032
-0.016
0.009
0.054
0.111
0.143
0.178
0.246
0.263
NA520 Final Project Report
0.054
0.048
0.043
0.037
0.030
0.026
0.023
0.020
0.015
0.012
0.009
0.007
0.003
0.001
0.000
0.000
0.000
0.000
0.001
0.003
0.007
0.009
0.012
0.015
0.020
0.023
0.026
0.030
0.037
0.043
0.048
0.054
0.061
0.069
0.076
0.083
0.091
0.099
0.108
0.116
0.124
0.133
0.141
0.150
0.159
0.167
-0.098
-0.099
-0.104
-0.089
-0.063
-0.030
-0.013
-0.014
-0.062
-0.131
-0.151
-0.088
0.141
0.304
0.564
0.913
0.886
0.512
0.274
0.112
-0.119
-0.173
-0.153
-0.079
-0.026
-0.033
-0.041
-0.074
-0.101
-0.113
-0.114
-0.105
-0.098
-0.095
-0.095
-0.099
-0.100
-0.102
-0.105
-0.104
-0.105
-0.103
-0.103
-0.104
-0.105
-0.103
0.060
0.051
0.042
0.034
0.028
0.022
0.017
0.012
0.007
0.005
0.003
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.003
0.005
0.007
0.012
0.017
0.022
0.028
0.034
0.042
0.051
0.060
0.068
0.076
0.085
0.093
0.102
0.111
0.120
0.128
0.137
0.146
0.155
0.164
0.172
0.181
-0.168
-0.175
-0.163
-0.140
-0.096
-0.055
-0.039
-0.072
0.015
0.202
0.361
0.528
0.667
0.796
0.933
0.991
0.997
0.912
0.795
0.654
0.498
0.390
0.205
0.017
-0.075
-0.036
-0.059
-0.099
-0.139
-0.162
-0.176
-0.170
-0.171
-0.177
-0.181
-0.192
-0.190
-0.192
-0.196
-0.199
-0.194
-0.199
-0.202
-0.197
-0.203
-0.201
0.018
0.016
0.013
0.011
0.009
0.007
0.006
0.004
0.003
0.003
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.003
0.003
0.004
0.006
0.007
0.009
0.011
0.013
0.016
0.018
0.021
0.025
0.029
0.034
0.039
0.045
0.052
0.059
0.067
0.075
0.083
0.092
0.101
0.111
-0.012
0.042
0.041
0.111
0.133
0.239
0.330
0.436
0.501
0.647
0.709
0.800
0.854
0.921
0.981
0.998
0.997
0.973
0.913
0.858
0.783
0.702
0.621
0.507
0.393
0.308
0.212
0.132
0.099
0.023
0.027
-0.022
-0.047
-0.086
-0.127
-0.160
-0.176
-0.206
-0.217
-0.235
-0.241
-0.248
-0.265
-0.271
-0.274
-0.283
11
0.012
0.011
0.009
0.008
0.006
0.005
0.004
0.003
0.003
0.002
0.001
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.001
0.002
0.003
0.003
0.004
0.005
0.006
0.008
0.009
0.011
0.012
0.014
0.016
0.018
0.021
0.023
0.026
0.029
0.032
0.036
0.040
0.044
0.048
0.053
0.059
0.193
0.255
0.299
0.365
0.457
0.504
0.567
0.671
0.717
0.802
0.827
0.905
0.919
0.947
0.998
0.998
0.995
0.990
0.947
0.917
0.885
0.805
0.772
0.669
0.651
0.542
0.448
0.421
0.360
0.239
0.207
0.167
0.141
0.056
0.062
-0.019
-0.037
-0.074
-0.104
-0.149
-0.154
-0.202
-0.207
-0.248
-0.253
-0.272
0.011
0.010
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.002
0.001
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.001
0.002
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.010
0.011
0.013
0.014
0.016
0.018
0.020
0.022
0.025
0.027
0.030
0.032
0.035
0.039
0.042
0.045
0.356
0.384
0.453
0.490
0.578
0.613
0.691
0.737
0.801
0.835
0.891
0.912
0.956
0.976
0.992
0.997
0.997
0.990
0.983
0.944
0.919
0.890
0.836
0.807
0.730
0.678
0.626
0.566
0.500
0.432
0.409
0.318
0.303
0.208
0.205
0.140
0.101
0.048
0.020
-0.023
-0.046
-0.107
-0.098
-0.165
-0.168
-0.198
NA520 Final Project Report
0.176
0.185
0.194
0.202
0.211
0.220
0.229
0.238
0.247
0.255
0.264
0.273
0.282
0.291
0.300
0.309
0.317
0.326
0.335
0.344
0.353
0.362
0.371
0.380
0.388
0.397
0.406
0.415
0.424
0.433
0.442
0.450
0.459
0.468
0.477
0.486
0.495
0.504
0.512
0.521
0.530
0.539
0.548
0.557
0.566
0.575
-0.104
-0.105
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-0.106
-0.106
-0.105
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
0.190
0.199
0.208
0.217
0.226
0.235
0.244
0.252
0.261
0.270
0.279
0.288
0.297
0.306
0.315
0.324
0.333
0.342
0.351
0.360
0.369
0.378
0.387
0.396
0.405
0.414
0.422
0.431
0.440
0.449
0.458
0.467
0.476
0.485
0.494
0.503
0.512
0.521
0.530
0.539
0.548
0.557
0.566
0.575
0.584
0.593
-0.207
-0.199
-0.208
-0.205
-0.205
-0.206
-0.205
-0.206
-0.208
-0.206
-0.208
-0.210
-0.208
-0.207
-0.210
-0.207
-0.210
-0.208
-0.211
-0.209
-0.209
-0.210
-0.210
-0.209
-0.210
-0.210
-0.210
-0.209
-0.213
-0.208
-0.211
-0.210
-0.211
-0.211
-0.210
-0.210
-0.210
-0.210
-0.210
-0.210
-0.210
-0.210
-0.210
-0.209
-0.209
-0.210
0.120
0.129
0.139
0.149
0.158
0.168
0.178
0.188
0.198
0.207
0.217
0.227
0.237
0.247
0.257
0.267
0.277
0.287
0.298
0.308
0.318
0.328
0.338
0.348
0.358
0.368
0.379
0.389
0.399
0.409
0.419
0.429
0.440
0.450
0.460
0.470
0.480
0.490
0.501
0.511
0.521
0.531
0.541
0.551
0.562
0.572
-0.291
-0.291
-0.289
-0.302
-0.299
-0.301
-0.308
-0.305
-0.306
-0.313
-0.309
-0.311
-0.317
-0.311
-0.320
-0.319
-0.316
-0.319
-0.317
-0.323
-0.320
-0.320
-0.321
-0.322
-0.322
-0.321
-0.325
-0.321
-0.326
-0.323
-0.323
-0.325
-0.323
-0.324
-0.325
-0.323
-0.325
-0.324
-0.325
-0.323
-0.324
-0.324
-0.324
-0.323
-0.323
-0.323
12
0.065
0.071
0.078
0.086
0.094
0.102
0.111
0.120
0.130
0.140
0.150
0.160
0.171
0.181
0.192
0.203
0.214
0.225
0.236
0.247
0.259
0.270
0.281
0.293
0.304
0.316
0.327
0.339
0.350
0.362
0.373
0.385
0.397
0.408
0.420
0.432
0.443
0.455
0.467
0.478
0.490
0.502
0.514
0.525
0.537
0.549
-0.295
-0.306
-0.316
-0.344
-0.344
-0.357
-0.365
-0.370
-0.384
-0.389
-0.398
-0.401
-0.403
-0.409
-0.414
-0.414
-0.424
-0.424
-0.422
-0.429
-0.429
-0.431
-0.431
-0.436
-0.436
-0.435
-0.439
-0.439
-0.440
-0.439
-0.444
-0.440
-0.443
-0.443
-0.443
-0.442
-0.444
-0.446
-0.444
-0.443
-0.444
-0.443
-0.444
-0.443
-0.444
-0.442
0.049
0.053
0.058
0.062
0.067
0.072
0.078
0.084
0.090
0.097
0.104
0.112
0.120
0.128
0.137
0.147
0.156
0.167
0.177
0.188
0.199
0.211
0.223
0.234
0.247
0.259
0.271
0.284
0.297
0.309
0.322
0.335
0.348
0.361
0.374
0.388
0.401
0.414
0.427
0.441
0.454
0.467
0.481
0.494
0.507
0.521
-0.230
-0.258
-0.276
-0.289
-0.313
-0.329
-0.355
-0.369
-0.383
-0.400
-0.411
-0.432
-0.432
-0.445
-0.462
-0.468
-0.478
-0.494
-0.487
-0.502
-0.508
-0.514
-0.519
-0.519
-0.530
-0.528
-0.535
-0.541
-0.534
-0.547
-0.543
-0.550
-0.550
-0.551
-0.554
-0.553
-0.553
-0.556
-0.557
-0.555
-0.558
-0.558
-0.557
-0.557
-0.556
-0.557
NA520 Final Project Report
0.583
0.592
0.601
0.610
0.619
0.628
0.637
0.645
0.654
0.663
0.672
0.681
0.690
0.699
0.707
0.716
0.725
0.734
0.743
0.752
0.761
0.769
0.778
0.787
0.796
0.805
0.814
0.823
0.831
0.840
0.849
0.858
0.867
0.876
0.884
0.893
0.902
0.911
0.920
0.929
0.937
0.946
0.955
0.964
0.972
0.981
-0.106
-0.106
-0.107
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
-0.106
-0.107
-0.106
-0.107
-0.107
-0.106
-0.106
-0.106
-0.107
-0.107
-0.106
-0.107
-0.106
-0.108
-0.107
-0.107
-0.107
-0.107
-0.107
-0.108
-0.117
-0.117
-0.107
-0.091
-0.084
-0.085
-0.087
-0.086
-0.088
-0.087
-0.093
-0.091
-0.086
-0.057
-0.021
0.602
0.611
0.620
0.629
0.638
0.647
0.656
0.664
0.673
0.682
0.691
0.700
0.709
0.718
0.727
0.736
0.745
0.754
0.763
0.772
0.781
0.789
0.798
0.807
0.816
0.825
0.834
0.843
0.852
0.860
0.869
0.878
0.887
0.895
0.904
0.913
0.921
0.930
0.939
0.947
0.955
0.962
0.970
0.978
0.985
0.990
-0.210
-0.209
-0.209
-0.209
-0.208
-0.208
-0.208
-0.208
-0.208
-0.207
-0.207
-0.206
-0.207
-0.205
-0.206
-0.205
-0.204
-0.204
-0.203
-0.202
-0.202
-0.201
-0.200
-0.199
-0.198
-0.196
-0.195
-0.193
-0.191
-0.189
-0.187
-0.184
-0.181
-0.178
-0.173
-0.168
-0.163
-0.157
-0.153
-0.143
-0.101
-0.047
0.023
0.113
0.176
0.190
0.582
0.592
0.602
0.612
0.623
0.633
0.643
0.653
0.663
0.673
0.683
0.693
0.704
0.714
0.724
0.734
0.744
0.754
0.764
0.774
0.784
0.794
0.804
0.813
0.823
0.833
0.843
0.853
0.862
0.872
0.881
0.891
0.900
0.909
0.918
0.927
0.935
0.943
0.951
0.958
0.965
0.971
0.977
0.983
0.988
0.992
-0.323
-0.322
-0.321
-0.322
-0.321
-0.320
-0.320
-0.319
-0.319
-0.318
-0.317
-0.316
-0.315
-0.314
-0.313
-0.312
-0.311
-0.309
-0.307
-0.306
-0.304
-0.302
-0.299
-0.296
-0.294
-0.290
-0.286
-0.282
-0.277
-0.272
-0.266
-0.260
-0.254
-0.248
-0.243
-0.249
-0.180
-0.121
-0.069
-0.009
0.069
0.157
0.230
0.247
0.252
0.257
13
0.560
0.572
0.584
0.595
0.607
0.619
0.630
0.642
0.653
0.665
0.676
0.688
0.699
0.711
0.722
0.734
0.745
0.756
0.767
0.779
0.790
0.801
0.812
0.822
0.833
0.844
0.854
0.864
0.874
0.884
0.893
0.903
0.912
0.920
0.928
0.936
0.944
0.951
0.957
0.963
0.969
0.974
0.979
0.984
0.988
0.992
-0.443
-0.442
-0.441
-0.440
-0.439
-0.439
-0.437
-0.437
-0.434
-0.433
-0.432
-0.431
-0.428
-0.426
-0.424
-0.421
-0.418
-0.415
-0.412
-0.408
-0.404
-0.399
-0.394
-0.388
-0.382
-0.375
-0.368
-0.361
-0.355
-0.349
-0.344
-0.339
-0.268
-0.214
-0.172
-0.128
-0.074
-0.004
0.082
0.174
0.247
0.278
0.277
0.280
0.283
0.285
0.534
0.547
0.561
0.574
0.587
0.600
0.614
0.627
0.640
0.653
0.666
0.679
0.692
0.705
0.718
0.730
0.743
0.755
0.767
0.779
0.791
0.803
0.815
0.826
0.837
0.848
0.858
0.869
0.878
0.888
0.897
0.906
0.914
0.922
0.930
0.937
0.944
0.951
0.957
0.963
0.969
0.974
0.979
0.984
0.988
0.992
-0.556
-0.555
-0.553
-0.552
-0.552
-0.549
-0.547
-0.546
-0.544
-0.541
-0.538
-0.535
-0.532
-0.528
-0.523
-0.519
-0.513
-0.508
-0.501
-0.495
-0.487
-0.479
-0.471
-0.463
-0.455
-0.448
-0.443
-0.439
-0.372
-0.320
-0.286
-0.253
-0.215
-0.168
-0.108
-0.034
0.055
0.152
0.237
0.284
0.285
0.287
0.289
0.291
0.293
0.294
NA520 Final Project Report
0.989
0.996
0.999
-0.043
0.170
0.280
0.994
0.997
0.999
0.198
0.203
0.208
0.995
0.998
0.999
0.260
0.263
0.266
0.995
0.998
0.999
0.287
0.289
0.292
0.995
0.998
0.999
0.296
0.298
0.301
Table2. Cp along the cylinder by Xfoil (   0.3  0.5 )
x(0.3)
Cp
x(0.35)
Cp
x(0.4)
Cp
x(0.45)
Cp
x(0.5)
Cp
0.999
0.998
0.995
0.992
0.988
0.984
0.979
0.975
0.969
0.964
0.958
0.952
0.946
0.939
0.932
0.925
0.917
0.910
0.901
0.893
0.884
0.874
0.865
0.854
0.844
0.833
0.822
0.811
0.799
0.787
0.775
0.762
0.749
0.736
0.723
0.710
0.696
0.682
0.668
0.290
0.287
0.285
0.283
0.281
0.279
0.277
0.275
0.273
0.270
0.269
0.272
0.234
0.155
0.056
-0.041
-0.124
-0.193
-0.249
-0.296
-0.335
-0.368
-0.398
-0.441
-0.521
-0.544
-0.550
-0.557
-0.566
-0.576
-0.586
-0.595
-0.605
-0.613
-0.621
-0.629
-0.635
-0.642
-0.647
0.999
0.998
0.996
0.993
0.989
0.986
0.982
0.977
0.973
0.968
0.963
0.958
0.952
0.946
0.940
0.934
0.927
0.920
0.913
0.905
0.897
0.889
0.880
0.871
0.862
0.852
0.842
0.831
0.820
0.809
0.797
0.785
0.773
0.761
0.748
0.734
0.721
0.707
0.693
0.269
0.266
0.263
0.261
0.259
0.256
0.255
0.253
0.251
0.248
0.246
0.244
0.242
0.239
0.240
0.228
0.166
0.074
-0.027
-0.120
-0.200
-0.268
-0.326
-0.374
-0.416
-0.452
-0.482
-0.514
-0.573
-0.651
-0.657
-0.665
-0.674
-0.685
-0.697
-0.709
-0.720
-0.730
-0.740
0.999
0.998
0.996
0.993
0.990
0.987
0.983
0.979
0.975
0.971
0.966
0.962
0.957
0.952
0.946
0.940
0.934
0.928
0.921
0.915
0.907
0.900
0.892
0.884
0.875
0.866
0.857
0.847
0.837
0.827
0.816
0.805
0.793
0.781
0.769
0.756
0.743
0.730
0.716
0.246
0.243
0.240
0.237
0.235
0.233
0.231
0.228
0.226
0.224
0.222
0.220
0.217
0.215
0.212
0.210
0.207
0.205
0.207
0.166
0.084
-0.019
-0.121
-0.213
-0.292
-0.359
-0.418
-0.469
-0.513
-0.550
-0.582
-0.616
-0.681
-0.763
-0.771
-0.780
-0.792
-0.805
-0.819
0.999
0.998
0.996
0.993
0.991
0.987
0.984
0.981
0.977
0.973
0.969
0.964
0.959
0.955
0.949
0.944
0.938
0.933
0.926
0.920
0.913
0.906
0.899
0.891
0.883
0.875
0.867
0.858
0.848
0.838
0.828
0.818
0.807
0.795
0.784
0.772
0.759
0.746
0.733
0.221
0.217
0.214
0.212
0.209
0.207
0.205
0.202
0.200
0.198
0.195
0.193
0.190
0.188
0.185
0.183
0.180
0.177
0.174
0.171
0.168
0.171
0.145
0.068
-0.037
-0.148
-0.248
-0.336
-0.412
-0.478
-0.536
-0.586
-0.630
-0.667
-0.700
-0.743
-0.862
-0.881
-0.892
0.999
0.998
0.996
0.994
0.991
0.988
0.985
0.981
0.977
0.974
0.970
0.965
0.961
0.956
0.951
0.946
0.941
0.935
0.929
0.923
0.917
0.910
0.903
0.896
0.888
0.880
0.872
0.864
0.855
0.845
0.836
0.826
0.815
0.805
0.793
0.782
0.770
0.758
0.745
0.194
0.191
0.188
0.186
0.183
0.181
0.179
0.176
0.174
0.171
0.169
0.166
0.164
0.161
0.158
0.155
0.152
0.149
0.146
0.142
0.139
0.135
0.131
0.128
0.131
0.100
0.014
-0.101
-0.219
-0.325
-0.418
-0.498
-0.569
-0.631
-0.685
-0.733
-0.772
-0.809
-0.862
14
NA520 Final Project Report
0.654
0.640
0.626
0.612
0.597
0.583
0.569
0.554
0.540
0.525
0.510
0.496
0.481
0.467
0.452
0.438
0.423
0.409
0.395
0.380
0.366
0.352
0.338
0.324
0.311
0.297
0.284
0.271
0.258
0.245
0.233
0.221
0.209
0.198
0.187
0.177
0.166
0.157
0.148
0.139
0.130
0.122
0.115
0.108
0.101
0.095
-0.652
-0.656
-0.661
-0.664
-0.667
-0.670
-0.671
-0.674
-0.676
-0.676
-0.677
-0.677
-0.680
-0.678
-0.678
-0.679
-0.675
-0.676
-0.675
-0.671
-0.671
-0.669
-0.663
-0.663
-0.657
-0.652
-0.652
-0.641
-0.639
-0.631
-0.624
-0.621
-0.611
-0.597
-0.589
-0.586
-0.570
-0.554
-0.549
-0.534
-0.524
-0.502
-0.489
-0.473
-0.453
-0.432
0.679
0.665
0.650
0.636
0.621
0.606
0.591
0.576
0.561
0.546
0.531
0.515
0.500
0.485
0.470
0.454
0.439
0.424
0.409
0.394
0.379
0.365
0.350
0.336
0.321
0.307
0.294
0.280
0.267
0.254
0.241
0.229
0.217
0.205
0.194
0.183
0.173
0.163
0.154
0.144
0.136
0.128
0.120
0.112
0.105
0.099
-0.749
-0.757
-0.765
-0.772
-0.777
-0.783
-0.787
-0.791
-0.794
-0.798
-0.800
-0.801
-0.804
-0.802
-0.804
-0.804
-0.803
-0.802
-0.800
-0.797
-0.795
-0.793
-0.787
-0.783
-0.779
-0.770
-0.769
-0.761
-0.751
-0.744
-0.735
-0.722
-0.714
-0.704
-0.687
-0.683
-0.655
-0.644
-0.632
-0.610
-0.592
-0.575
-0.556
-0.528
-0.511
-0.482
0.702
0.688
0.674
0.659
0.644
0.629
0.614
0.599
0.583
0.568
0.552
0.536
0.521
0.505
0.489
0.473
0.458
0.442
0.426
0.411
0.395
0.380
0.365
0.350
0.335
0.321
0.307
0.293
0.279
0.266
0.253
0.240
0.228
0.216
0.204
0.193
0.182
0.172
0.162
0.153
0.144
0.135
0.127
0.120
0.112
0.105
-0.832
-0.845
-0.858
-0.870
-0.879
-0.889
-0.897
-0.905
-0.911
-0.916
-0.921
-0.925
-0.928
-0.930
-0.931
-0.933
-0.933
-0.932
-0.929
-0.930
-0.923
-0.920
-0.918
-0.911
-0.906
-0.898
-0.890
-0.882
-0.872
-0.859
-0.851
-0.838
-0.819
-0.810
-0.793
-0.778
-0.756
-0.738
-0.718
-0.696
-0.674
-0.643
-0.633
-0.595
-0.571
-0.539
15
0.720
0.706
0.692
0.678
0.663
0.648
0.633
0.618
0.602
0.586
0.571
0.555
0.539
0.523
0.507
0.491
0.475
0.459
0.443
0.427
0.411
0.396
0.380
0.365
0.350
0.335
0.321
0.306
0.292
0.279
0.265
0.252
0.240
0.227
0.216
0.204
0.193
0.183
0.173
0.163
0.153
0.145
0.136
0.128
0.120
0.113
-0.905
-0.919
-0.936
-0.952
-0.967
-0.982
-0.995
-1.007
-1.018
-1.026
-1.036
-1.042
-1.048
-1.052
-1.057
-1.058
-1.060
-1.061
-1.060
-1.058
-1.053
-1.052
-1.046
-1.039
-1.032
-1.027
-1.014
-1.007
-0.992
-0.983
-0.965
-0.950
-0.937
-0.915
-0.898
-0.879
-0.854
-0.831
-0.809
-0.779
-0.756
-0.731
-0.695
-0.668
-0.633
-0.597
0.732
0.719
0.705
0.691
0.677
0.662
0.647
0.632
0.617
0.601
0.586
0.570
0.554
0.538
0.522
0.506
0.490
0.474
0.458
0.442
0.426
0.410
0.395
0.379
0.364
0.349
0.335
0.320
0.306
0.292
0.278
0.265
0.252
0.240
0.228
0.216
0.205
0.194
0.184
0.174
0.164
0.155
0.146
0.137
0.129
0.121
-0.990
-1.000
-1.013
-1.028
-1.046
-1.064
-1.083
-1.100
-1.116
-1.130
-1.144
-1.154
-1.164
-1.172
-1.179
-1.182
-1.187
-1.189
-1.188
-1.190
-1.186
-1.183
-1.177
-1.172
-1.163
-1.156
-1.143
-1.132
-1.119
-1.103
-1.088
-1.069
-1.053
-1.029
-1.004
-0.991
-0.953
-0.934
-0.903
-0.875
-0.839
-0.816
-0.773
-0.746
-0.700
-0.664
NA520 Final Project Report
0.089
0.083
0.078
0.072
0.068
0.063
0.059
0.055
0.051
0.047
0.044
0.040
0.037
0.034
0.032
0.029
0.026
0.024
0.022
0.020
0.018
0.016
0.014
0.012
0.011
0.009
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.002
0.001
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.001
-0.422
-0.399
-0.370
-0.348
-0.335
-0.293
-0.293
-0.255
-0.211
-0.198
-0.157
-0.137
-0.093
-0.061
-0.016
0.025
0.049
0.099
0.146
0.194
0.225
0.286
0.327
0.403
0.435
0.492
0.532
0.600
0.656
0.696
0.763
0.796
0.845
0.873
0.919
0.947
0.959
0.981
0.995
0.999
0.999
0.992
0.986
0.953
0.945
0.912
0.093
0.087
0.081
0.076
0.070
0.066
0.061
0.057
0.053
0.049
0.045
0.042
0.039
0.035
0.032
0.030
0.027
0.025
0.022
0.020
0.018
0.016
0.014
0.013
0.011
0.010
0.008
0.007
0.006
0.005
0.004
0.003
0.002
0.002
0.001
0.001
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0.683
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0.811
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0.892
0.917
0.932
0.957
0.975
0.988
0.995
1.000
1.000
0.994
0.991
0.973
0.961
0.933
16
0.106
0.099
0.093
0.087
0.081
0.075
0.070
0.065
0.061
0.056
0.052
0.048
0.044
0.041
0.037
0.034
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0.025
0.023
0.021
0.018
0.016
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0.013
0.011
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0.008
0.007
0.005
0.004
0.003
0.003
0.002
0.001
0.001
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0.098
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0.261
0.316
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0.576
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0.670
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0.790
0.828
0.862
0.898
0.921
0.941
0.960
0.979
0.989
0.995
1.000
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0.997
0.989
0.980
0.956
0.942
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0.100
0.094
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0.076
0.071
0.066
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0.031
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0.020
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0.439
0.481
0.535
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0.629
0.684
0.723
0.753
0.810
0.834
0.870
0.899
0.924
0.947
0.961
0.980
0.987
0.996
1.000
1.000
0.995
0.987
0.982
0.962
0.948
NA520 Final Project Report
0.002
0.002
0.003
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0.006
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0.008
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0.918
0.890
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0.822
0.771
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0.694
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-0.786
17
0.002
0.003
0.003
0.004
0.005
0.007
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0.009
0.011
0.013
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0.128
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0.145
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0.173
0.183
0.193
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0.216
0.923
0.900
0.865
0.826
0.787
0.760
0.712
0.670
0.619
0.578
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0.482
0.419
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0.318
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0.107
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0.022
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0.037
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0.057
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0.066
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0.076
0.082
0.088
0.094
0.100
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0.114
0.121
0.129
0.137
0.146
0.155
0.164
0.174
0.184
0.194
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0.216
0.228
0.922
0.901
0.869
0.836
0.807
0.753
0.728
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0.480
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-1.008
NA520 Final Project Report
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0.311
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0.730
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0.816
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0.847
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18
0.227
0.240
0.252
0.265
0.279
0.292
0.306
0.321
0.335
0.350
0.365
0.380
0.396
0.411
0.427
0.443
0.459
0.475
0.491
0.507
0.523
0.539
0.555
0.571
0.586
0.602
0.618
0.633
0.648
0.663
0.678
0.692
0.706
0.720
0.733
0.746
0.759
0.772
0.784
0.795
0.807
0.818
0.828
0.838
0.848
0.858
-0.913
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0.379
0.395
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0.442
0.458
0.474
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0.506
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0.570
0.586
0.601
0.617
0.632
0.647
0.662
0.677
0.691
0.705
0.719
0.732
0.745
0.758
0.770
0.782
0.793
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0.815
0.826
0.836
0.845
0.855
0.864
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-0.731
-0.683
-0.629
-0.567
-0.496
-0.416
-0.323
-0.216
-0.098
NA520 Final Project Report
0.822
0.833
0.844
0.854
0.865
0.874
0.884
0.893
0.901
0.910
0.917
0.925
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0.867
0.875
0.883
0.891
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0.906
0.913
0.920
0.926
0.933
0.938
0.944
0.949
0.955
0.959
0.964
0.969
0.973
0.977
0.981
0.984
0.987
0.991
0.993
0.996
0.998
0.999
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0.069
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0.168
0.170
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0.880
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0.896
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0.923
0.929
0.935
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0.946
0.951
0.956
0.961
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0.970
0.974
0.977
0.981
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0.988
0.991
0.994
0.996
0.998
0.999
0.017
0.102
0.131
0.128
0.131
0.135
0.139
0.142
0.146
0.149
0.152
0.155
0.158
0.161
0.164
0.166
0.169
0.171
0.174
0.176
0.179
0.181
0.183
0.186
0.188
0.191
0.194
Table3. Cp along the cylinder by Xfoil (   0.55  0.75 )
x(0.55)
Cp
x(0.6)
Cp
x(0.65)
Cp
x(0.7)
Cp
x(0.75)
Cp
0.999
0.998
0.996
0.994
0.991
0.988
0.985
0.981
0.978
0.974
0.970
0.966
0.961
0.957
0.952
0.170
0.166
0.163
0.161
0.158
0.156
0.154
0.151
0.149
0.147
0.144
0.141
0.139
0.136
0.133
0.999
0.998
0.996
0.993
0.991
0.988
0.985
0.981
0.978
0.974
0.970
0.966
0.961
0.957
0.952
0.144
0.141
0.138
0.135
0.133
0.131
0.128
0.126
0.124
0.121
0.119
0.116
0.114
0.111
0.108
0.999
0.998
0.996
0.993
0.991
0.988
0.984
0.981
0.977
0.974
0.970
0.966
0.961
0.957
0.952
0.120
0.117
0.114
0.111
0.109
0.106
0.104
0.102
0.100
0.097
0.095
0.092
0.090
0.087
0.084
0.999
0.998
0.996
0.993
0.990
0.987
0.984
0.981
0.977
0.973
0.969
0.965
0.960
0.956
0.951
0.090
0.087
0.084
0.081
0.079
0.077
0.075
0.072
0.070
0.068
0.066
0.063
0.061
0.058
0.055
0.999
0.998
0.996
0.993
0.990
0.987
0.984
0.980
0.977
0.973
0.968
0.964
0.960
0.955
0.950
0.062
0.058
0.055
0.053
0.050
0.048
0.046
0.044
0.042
0.039
0.037
0.034
0.032
0.029
0.026
19
NA520 Final Project Report
0.947
0.942
0.936
0.931
0.925
0.918
0.912
0.905
0.898
0.891
0.883
0.875
0.867
0.858
0.849
0.840
0.830
0.820
0.810
0.799
0.788
0.776
0.765
0.752
0.740
0.727
0.714
0.700
0.686
0.672
0.658
0.643
0.628
0.613
0.598
0.582
0.566
0.551
0.535
0.519
0.503
0.487
0.471
0.455
0.440
0.424
0.130
0.127
0.123
0.120
0.116
0.113
0.109
0.105
0.100
0.096
0.092
0.088
0.087
0.023
-0.089
-0.219
-0.340
-0.447
-0.539
-0.620
-0.691
-0.753
-0.808
-0.856
-0.896
-0.942
-1.077
-1.112
-1.126
-1.143
-1.163
-1.184
-1.204
-1.224
-1.242
-1.259
-1.273
-1.284
-1.295
-1.303
-1.309
-1.315
-1.316
-1.317
-1.317
-1.314
0.947
0.942
0.936
0.931
0.925
0.919
0.912
0.906
0.899
0.891
0.884
0.876
0.868
0.859
0.851
0.841
0.832
0.822
0.812
0.802
0.791
0.780
0.768
0.756
0.744
0.732
0.719
0.706
0.692
0.679
0.665
0.650
0.636
0.621
0.606
0.591
0.576
0.560
0.545
0.529
0.514
0.498
0.483
0.467
0.451
0.436
0.105
0.102
0.098
0.095
0.091
0.087
0.083
0.078
0.074
0.069
0.065
0.060
0.054
0.050
0.053
0.001
-0.114
-0.253
-0.386
-0.503
-0.604
-0.693
-0.771
-0.840
-0.900
-0.952
-0.996
-1.045
-1.201
-1.229
-1.245
-1.264
-1.286
-1.310
-1.333
-1.354
-1.374
-1.391
-1.406
-1.418
-1.428
-1.435
-1.440
-1.444
-1.445
-1.444
0.947
0.941
0.936
0.930
0.924
0.918
0.912
0.905
0.898
0.891
0.883
0.876
0.867
0.859
0.850
0.841
0.832
0.822
0.813
0.802
0.792
0.781
0.770
0.758
0.746
0.734
0.721
0.709
0.696
0.682
0.669
0.655
0.641
0.627
0.612
0.597
0.583
0.568
0.553
0.538
0.522
0.507
0.492
0.477
0.462
0.446
0.081
0.078
0.074
0.071
0.067
0.063
0.059
0.054
0.049
0.045
0.039
0.034
0.029
0.023
0.017
0.011
0.013
-0.052
-0.182
-0.334
-0.474
-0.596
-0.702
-0.795
-0.876
-0.948
-1.012
-1.066
-1.116
-1.207
-1.337
-1.353
-1.372
-1.394
-1.419
-1.445
-1.470
-1.492
-1.512
-1.528
-1.544
-1.554
-1.563
-1.568
-1.571
-1.573
20
0.946
0.941
0.935
0.929
0.923
0.917
0.910
0.904
0.897
0.889
0.882
0.874
0.866
0.858
0.849
0.840
0.831
0.821
0.811
0.801
0.791
0.780
0.769
0.758
0.746
0.734
0.722
0.710
0.697
0.684
0.671
0.657
0.644
0.630
0.616
0.602
0.588
0.573
0.559
0.544
0.529
0.514
0.500
0.485
0.470
0.456
0.052
0.049
0.046
0.042
0.038
0.034
0.030
0.025
0.020
0.015
0.010
0.004
-0.002
-0.008
-0.014
-0.021
-0.028
-0.034
-0.037
-0.127
-0.279
-0.441
-0.586
-0.711
-0.820
-0.914
-0.999
-1.073
-1.136
-1.189
-1.244
-1.429
-1.462
-1.481
-1.504
-1.530
-1.559
-1.586
-1.611
-1.634
-1.653
-1.668
-1.681
-1.688
-1.697
-1.698
0.945
0.939
0.934
0.928
0.922
0.915
0.909
0.902
0.895
0.887
0.880
0.872
0.864
0.855
0.847
0.838
0.829
0.819
0.809
0.799
0.789
0.778
0.768
0.756
0.745
0.733
0.721
0.709
0.697
0.684
0.672
0.659
0.645
0.632
0.618
0.605
0.591
0.577
0.563
0.549
0.534
0.520
0.506
0.492
0.477
0.463
0.024
0.020
0.017
0.014
0.010
0.006
0.001
-0.003
-0.008
-0.013
-0.019
-0.025
-0.031
-0.038
-0.044
-0.051
-0.059
-0.066
-0.074
-0.074
-0.126
-0.273
-0.447
-0.611
-0.751
-0.872
-0.978
-1.071
-1.153
-1.223
-1.283
-1.343
-1.525
-1.582
-1.602
-1.626
-1.654
-1.684
-1.714
-1.741
-1.765
-1.785
-1.802
-1.815
-1.824
-1.830
NA520 Final Project Report
0.408
0.393
0.378
0.363
0.348
0.334
0.319
0.305
0.292
0.278
0.265
0.253
0.241
0.229
0.217
0.206
0.195
0.185
0.175
0.165
0.156
0.147
0.139
0.131
0.123
0.115
0.108
0.101
0.095
0.089
0.083
0.077
0.072
0.067
0.062
0.057
0.053
0.048
0.044
0.041
0.037
0.034
0.030
0.027
0.025
0.022
-1.309
-1.302
-1.295
-1.286
-1.275
-1.258
-1.247
-1.228
-1.210
-1.190
-1.172
-1.145
-1.121
-1.095
-1.065
-1.034
-1.004
-0.969
-0.932
-0.901
-0.856
-0.824
-0.775
-0.733
-0.693
-0.644
-0.602
-0.543
-0.503
-0.451
-0.401
-0.344
-0.297
-0.230
-0.191
-0.119
-0.073
-0.014
0.046
0.100
0.155
0.222
0.268
0.327
0.379
0.445
0.421
0.405
0.390
0.376
0.361
0.346
0.332
0.318
0.305
0.291
0.278
0.266
0.253
0.241
0.230
0.218
0.207
0.197
0.186
0.176
0.167
0.158
0.149
0.140
0.132
0.124
0.117
0.110
0.103
0.096
0.090
0.084
0.078
0.073
0.067
0.062
0.057
0.053
0.049
0.045
0.041
0.037
0.034
0.030
0.027
0.024
-1.440
-1.435
-1.427
-1.415
-1.407
-1.388
-1.375
-1.358
-1.336
-1.314
-1.291
-1.266
-1.237
-1.205
-1.176
-1.140
-1.106
-1.071
-1.030
-0.989
-0.946
-0.909
-0.852
-0.807
-0.768
-0.709
-0.665
-0.605
-0.556
-0.501
-0.441
-0.386
-0.331
-0.268
-0.213
-0.152
-0.092
-0.035
0.028
0.089
0.143
0.207
0.265
0.325
0.377
0.433
0.431
0.417
0.402
0.387
0.373
0.358
0.344
0.331
0.317
0.304
0.291
0.278
0.266
0.254
0.242
0.230
0.219
0.208
0.198
0.188
0.178
0.168
0.159
0.150
0.142
0.134
0.126
0.118
0.111
0.104
0.097
0.091
0.085
0.079
0.073
0.068
0.063
0.058
0.053
0.049
0.045
0.041
0.037
0.033
0.030
0.027
-1.570
-1.565
-1.559
-1.549
-1.536
-1.523
-1.506
-1.486
-1.464
-1.439
-1.416
-1.386
-1.356
-1.325
-1.289
-1.252
-1.214
-1.172
-1.132
-1.084
-1.038
-0.993
-0.941
-0.891
-0.837
-0.784
-0.726
-0.672
-0.610
-0.559
-0.492
-0.434
-0.368
-0.317
-0.241
-0.187
-0.121
-0.060
0.008
0.059
0.134
0.189
0.249
0.309
0.369
0.427
21
0.441
0.426
0.412
0.398
0.383
0.369
0.356
0.342
0.329
0.315
0.303
0.290
0.277
0.265
0.254
0.242
0.231
0.220
0.209
0.199
0.189
0.179
0.170
0.160
0.152
0.143
0.135
0.127
0.119
0.112
0.105
0.098
0.092
0.085
0.079
0.074
0.068
0.063
0.058
0.053
0.049
0.044
0.040
0.036
0.033
0.029
-1.699
-1.695
-1.690
-1.682
-1.669
-1.655
-1.637
-1.616
-1.595
-1.568
-1.542
-1.512
-1.480
-1.441
-1.407
-1.366
-1.323
-1.280
-1.234
-1.188
-1.134
-1.085
-1.029
-0.977
-0.917
-0.859
-0.799
-0.740
-0.675
-0.615
-0.549
-0.485
-0.420
-0.357
-0.286
-0.223
-0.152
-0.091
-0.023
0.044
0.107
0.168
0.233
0.294
0.359
0.413
0.449
0.435
0.421
0.407
0.393
0.379
0.366
0.353
0.339
0.326
0.314
0.301
0.289
0.277
0.265
0.253
0.242
0.231
0.220
0.210
0.199
0.190
0.180
0.171
0.161
0.153
0.144
0.136
0.128
0.120
0.113
0.106
0.099
0.092
0.086
0.080
0.074
0.068
0.063
0.058
0.053
0.048
0.044
0.040
0.036
0.032
-1.832
-1.829
-1.826
-1.818
-1.807
-1.792
-1.775
-1.752
-1.731
-1.704
-1.673
-1.644
-1.605
-1.569
-1.532
-1.485
-1.440
-1.394
-1.344
-1.292
-1.240
-1.182
-1.124
-1.065
-1.007
-0.943
-0.877
-0.809
-0.748
-0.679
-0.610
-0.543
-0.474
-0.403
-0.336
-0.260
-0.196
-0.123
-0.058
0.013
0.082
0.146
0.210
0.276
0.337
0.400
NA520 Final Project Report
0.020
0.017
0.015
0.013
0.011
0.010
0.008
0.007
0.005
0.004
0.003
0.002
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.002
0.003
0.004
0.005
0.007
0.008
0.010
0.011
0.013
0.015
0.017
0.020
0.022
0.025
0.027
0.030
0.034
0.037
0.041
0.044
0.048
0.053
0.487
0.538
0.596
0.633
0.686
0.722
0.772
0.802
0.842
0.871
0.904
0.923
0.948
0.962
0.980
0.989
0.995
1.000
0.999
0.996
0.989
0.980
0.963
0.946
0.926
0.902
0.875
0.839
0.800
0.767
0.729
0.684
0.639
0.592
0.534
0.492
0.438
0.388
0.322
0.275
0.213
0.155
0.104
0.046
-0.012
-0.076
0.022
0.019
0.017
0.014
0.012
0.011
0.009
0.007
0.006
0.005
0.004
0.003
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.009
0.011
0.012
0.014
0.017
0.019
0.022
0.024
0.027
0.030
0.034
0.037
0.041
0.045
0.049
0.053
0.057
0.484
0.543
0.588
0.636
0.685
0.726
0.765
0.808
0.839
0.874
0.898
0.927
0.947
0.962
0.980
0.989
0.996
1.000
1.000
0.996
0.990
0.979
0.963
0.946
0.925
0.903
0.871
0.837
0.811
0.766
0.726
0.684
0.635
0.589
0.541
0.487
0.434
0.376
0.325
0.264
0.204
0.142
0.091
0.030
-0.035
-0.092
0.024
0.021
0.018
0.016
0.014
0.012
0.010
0.008
0.007
0.005
0.004
0.003
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.003
0.004
0.005
0.007
0.008
0.010
0.012
0.014
0.016
0.018
0.021
0.024
0.027
0.030
0.033
0.037
0.041
0.045
0.049
0.053
0.058
0.063
0.476
0.539
0.581
0.636
0.677
0.725
0.768
0.803
0.837
0.872
0.901
0.925
0.945
0.964
0.978
0.989
0.996
1.000
1.000
0.995
0.989
0.978
0.964
0.945
0.925
0.899
0.874
0.838
0.804
0.764
0.724
0.680
0.633
0.586
0.534
0.484
0.420
0.370
0.305
0.254
0.189
0.134
0.062
0.008
-0.064
-0.117
22
0.026
0.023
0.020
0.018
0.015
0.013
0.011
0.009
0.007
0.006
0.005
0.003
0.002
0.002
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.002
0.002
0.003
0.005
0.006
0.007
0.009
0.011
0.013
0.015
0.018
0.020
0.023
0.026
0.029
0.033
0.036
0.040
0.044
0.049
0.053
0.058
0.063
0.068
0.465
0.526
0.578
0.626
0.675
0.719
0.762
0.800
0.837
0.869
0.896
0.924
0.946
0.962
0.979
0.989
0.996
1.000
1.000
0.996
0.988
0.978
0.963
0.946
0.924
0.897
0.867
0.837
0.802
0.759
0.719
0.675
0.628
0.577
0.524
0.471
0.411
0.357
0.292
0.235
0.169
0.112
0.037
-0.022
-0.092
-0.155
0.029
0.025
0.022
0.019
0.017
0.014
0.012
0.010
0.008
0.007
0.005
0.004
0.003
0.002
0.001
0.001
0.000
0.000
0.000
0.000
0.001
0.001
0.002
0.003
0.004
0.005
0.007
0.008
0.010
0.012
0.014
0.017
0.019
0.022
0.025
0.029
0.032
0.036
0.040
0.044
0.048
0.053
0.058
0.063
0.068
0.074
0.456
0.513
0.568
0.616
0.670
0.710
0.759
0.795
0.834
0.865
0.894
0.923
0.943
0.963
0.977
0.989
0.996
0.999
0.999
0.996
0.988
0.978
0.963
0.942
0.922
0.897
0.864
0.833
0.795
0.757
0.713
0.664
0.622
0.562
0.514
0.459
0.399
0.337
0.275
0.209
0.150
0.081
0.012
-0.056
-0.124
-0.194
NA520 Final Project Report
0.057
0.062
0.067
0.072
0.077
0.083
0.089
0.095
0.101
0.108
0.115
0.123
0.131
0.139
0.147
0.156
0.165
0.175
0.185
0.195
0.206
0.217
0.229
0.241
0.253
0.265
0.278
0.292
0.305
0.319
0.334
0.348
0.363
0.378
0.393
0.408
0.424
0.440
0.455
0.471
0.487
0.503
0.519
0.535
0.551
0.566
-0.119
-0.186
-0.236
-0.288
-0.350
-0.398
-0.447
-0.502
-0.550
-0.597
-0.646
-0.692
-0.729
-0.781
-0.823
-0.856
-0.898
-0.935
-0.969
-1.002
-1.037
-1.062
-1.095
-1.120
-1.147
-1.170
-1.192
-1.210
-1.228
-1.246
-1.259
-1.274
-1.285
-1.295
-1.304
-1.306
-1.315
-1.318
-1.316
-1.316
-1.313
-1.310
-1.302
-1.295
-1.285
-1.272
0.062
0.067
0.073
0.078
0.084
0.090
0.096
0.103
0.110
0.117
0.124
0.132
0.140
0.149
0.158
0.167
0.176
0.186
0.197
0.207
0.218
0.230
0.241
0.253
0.266
0.278
0.291
0.305
0.318
0.332
0.346
0.361
0.376
0.390
0.405
0.421
0.436
0.451
0.467
0.483
0.498
0.514
0.529
0.545
0.560
0.576
-0.158
-0.214
-0.268
-0.326
-0.390
-0.446
-0.496
-0.556
-0.608
-0.661
-0.712
-0.761
-0.812
-0.858
-0.905
-0.950
-0.986
-1.032
-1.068
-1.106
-1.141
-1.175
-1.207
-1.240
-1.261
-1.292
-1.314
-1.337
-1.356
-1.376
-1.389
-1.407
-1.417
-1.426
-1.434
-1.441
-1.442
-1.446
-1.444
-1.441
-1.436
-1.427
-1.418
-1.407
-1.391
-1.374
0.068
0.073
0.079
0.085
0.091
0.097
0.104
0.111
0.118
0.126
0.134
0.142
0.150
0.159
0.168
0.178
0.188
0.198
0.208
0.219
0.230
0.242
0.254
0.266
0.278
0.291
0.304
0.317
0.331
0.344
0.358
0.373
0.387
0.402
0.417
0.431
0.446
0.462
0.477
0.492
0.507
0.522
0.538
0.553
0.568
0.583
-0.185
-0.247
-0.311
-0.373
-0.437
-0.490
-0.556
-0.613
-0.672
-0.726
-0.784
-0.838
-0.891
-0.943
-0.992
-1.041
-1.084
-1.130
-1.172
-1.214
-1.253
-1.288
-1.323
-1.359
-1.385
-1.417
-1.440
-1.465
-1.485
-1.506
-1.523
-1.537
-1.548
-1.559
-1.566
-1.570
-1.573
-1.571
-1.569
-1.564
-1.554
-1.543
-1.529
-1.513
-1.491
-1.471
23
0.074
0.079
0.085
0.092
0.098
0.105
0.112
0.119
0.127
0.135
0.143
0.152
0.160
0.170
0.179
0.189
0.199
0.209
0.220
0.231
0.242
0.254
0.265
0.277
0.290
0.303
0.315
0.329
0.342
0.356
0.369
0.383
0.398
0.412
0.426
0.441
0.456
0.470
0.485
0.500
0.514
0.529
0.544
0.559
0.573
0.588
-0.220
-0.285
-0.359
-0.417
-0.485
-0.550
-0.615
-0.676
-0.739
-0.797
-0.862
-0.919
-0.974
-1.032
-1.084
-1.134
-1.185
-1.236
-1.281
-1.324
-1.366
-1.406
-1.443
-1.481
-1.508
-1.544
-1.571
-1.594
-1.616
-1.639
-1.655
-1.668
-1.683
-1.689
-1.697
-1.697
-1.700
-1.698
-1.688
-1.681
-1.669
-1.652
-1.634
-1.612
-1.586
-1.559
0.080
0.086
0.092
0.099
0.106
0.113
0.120
0.128
0.136
0.144
0.153
0.161
0.171
0.180
0.190
0.199
0.210
0.220
0.231
0.242
0.253
0.265
0.277
0.289
0.301
0.314
0.326
0.339
0.353
0.366
0.379
0.393
0.407
0.421
0.435
0.449
0.463
0.477
0.492
0.506
0.520
0.534
0.549
0.563
0.577
0.591
-0.263
-0.333
-0.406
-0.474
-0.541
-0.609
-0.679
-0.750
-0.809
-0.881
-0.940
-1.005
-1.065
-1.126
-1.182
-1.238
-1.293
-1.345
-1.393
-1.442
-1.487
-1.529
-1.571
-1.606
-1.643
-1.672
-1.704
-1.730
-1.754
-1.775
-1.790
-1.808
-1.817
-1.827
-1.830
-1.833
-1.828
-1.825
-1.815
-1.802
-1.785
-1.765
-1.741
-1.714
-1.685
-1.654
NA520 Final Project Report
0.582
0.598
0.613
0.628
0.643
0.658
0.672
0.686
0.700
0.714
0.727
0.740
0.752
0.765
0.776
0.788
0.799
0.810
0.820
0.830
0.840
0.849
0.858
0.867
0.875
0.883
0.891
0.898
0.905
0.912
0.918
0.925
0.931
0.936
0.942
0.947
0.952
0.957
0.961
0.966
0.970
0.974
0.978
0.981
0.985
0.988
-1.259
-1.242
-1.224
-1.204
-1.183
-1.162
-1.143
-1.126
-1.112
-1.075
-0.943
-0.895
-0.855
-0.808
-0.754
-0.690
-0.619
-0.538
-0.446
-0.340
-0.218
-0.089
0.024
0.087
0.088
0.092
0.096
0.100
0.105
0.109
0.112
0.116
0.120
0.123
0.127
0.130
0.133
0.136
0.139
0.141
0.144
0.147
0.149
0.151
0.154
0.156
0.591
0.606
0.621
0.636
0.650
0.665
0.679
0.692
0.706
0.719
0.732
0.744
0.756
0.768
0.780
0.791
0.802
0.812
0.822
0.832
0.841
0.851
0.859
0.868
0.876
0.884
0.891
0.899
0.906
0.912
0.919
0.925
0.931
0.936
0.942
0.947
0.952
0.957
0.961
0.966
0.970
0.974
0.978
0.981
0.985
0.988
-1.354
-1.333
-1.310
-1.287
-1.264
-1.245
-1.229
-1.203
-1.045
-0.995
-0.953
-0.901
-0.840
-0.771
-0.694
-0.605
-0.504
-0.386
-0.253
-0.114
0.000
0.053
0.050
0.054
0.060
0.065
0.069
0.074
0.078
0.083
0.087
0.091
0.095
0.098
0.102
0.105
0.108
0.111
0.114
0.116
0.119
0.121
0.124
0.126
0.128
0.130
0.597
0.612
0.627
0.641
0.655
0.669
0.682
0.696
0.709
0.721
0.734
0.746
0.758
0.770
0.781
0.792
0.802
0.813
0.822
0.832
0.841
0.850
0.859
0.867
0.876
0.883
0.891
0.898
0.905
0.912
0.918
0.924
0.930
0.936
0.941
0.947
0.952
0.957
0.961
0.966
0.970
0.974
0.977
0.981
0.984
0.988
-1.445
-1.419
-1.394
-1.372
-1.353
-1.337
-1.208
-1.116
-1.065
-1.012
-0.949
-0.876
-0.795
-0.701
-0.597
-0.474
-0.334
-0.183
-0.052
0.013
0.011
0.017
0.023
0.029
0.034
0.039
0.045
0.049
0.054
0.059
0.063
0.067
0.071
0.074
0.078
0.081
0.084
0.087
0.090
0.092
0.095
0.097
0.100
0.102
0.104
0.106
24
0.602
0.616
0.630
0.644
0.657
0.671
0.684
0.697
0.710
0.722
0.734
0.746
0.758
0.769
0.780
0.791
0.801
0.811
0.821
0.831
0.840
0.849
0.858
0.866
0.874
0.882
0.889
0.897
0.904
0.910
0.917
0.923
0.929
0.935
0.941
0.946
0.951
0.956
0.960
0.965
0.969
0.973
0.977
0.981
0.984
0.987
-1.530
-1.504
-1.481
-1.463
-1.431
-1.244
-1.189
-1.136
-1.073
-0.999
-0.915
-0.821
-0.711
-0.586
-0.441
-0.280
-0.128
-0.037
-0.033
-0.028
-0.021
-0.014
-0.008
-0.002
0.004
0.010
0.015
0.020
0.025
0.030
0.034
0.038
0.042
0.046
0.049
0.052
0.055
0.058
0.061
0.063
0.066
0.068
0.070
0.072
0.075
0.077
0.605
0.618
0.632
0.645
0.659
0.672
0.684
0.697
0.709
0.721
0.733
0.745
0.756
0.768
0.778
0.789
0.799
0.809
0.819
0.829
0.838
0.847
0.855
0.864
0.872
0.880
0.887
0.895
0.902
0.909
0.915
0.922
0.928
0.934
0.939
0.945
0.950
0.955
0.960
0.964
0.968
0.973
0.977
0.980
0.984
0.987
-1.626
-1.602
-1.582
-1.527
-1.343
-1.283
-1.224
-1.153
-1.070
-0.978
-0.871
-0.751
-0.610
-0.448
-0.273
-0.127
-0.075
-0.074
-0.066
-0.059
-0.051
-0.044
-0.038
-0.031
-0.025
-0.019
-0.013
-0.008
-0.003
0.001
0.006
0.010
0.014
0.017
0.020
0.024
0.026
0.029
0.032
0.034
0.037
0.039
0.042
0.044
0.046
0.048
NA520 Final Project Report
0.991
0.994
0.996
0.998
0.999
0.158
0.161
0.163
0.166
0.170
0.991
0.993
0.996
0.998
0.999
0.133
0.135
0.138
0.141
0.144
0.991
0.993
0.996
0.998
0.999
0.109
0.111
0.114
0.117
0.120
0.990
0.993
0.996
0.998
0.999
0.079
0.081
0.084
0.087
0.090
0.990
0.993
0.996
0.998
0.999
0.050
0.053
0.055
0.058
0.062
Table4. Cp along the cylinder by Xfoil (   0.8 1.0 )
x(0.8)
Cp
x(0.85)
Cp
x(0.9)
Cp
x(0.95)
Cp
x(1.0)
Cp
0.999
0.998
0.995
0.993
0.990
0.987
0.983
0.980
0.976
0.972
0.968
0.963
0.959
0.954
0.949
0.943
0.938
0.932
0.926
0.920
0.913
0.906
0.899
0.892
0.885
0.877
0.869
0.861
0.853
0.844
0.835
0.826
0.816
0.806
0.796
0.786
0.776
0.030
0.026
0.023
0.021
0.018
0.016
0.014
0.012
0.009
0.007
0.005
0.002
0.000
-0.003
-0.006
-0.009
-0.012
-0.015
-0.019
-0.022
-0.026
-0.031
-0.035
-0.040
-0.046
-0.051
-0.057
-0.064
-0.071
-0.078
-0.085
-0.093
-0.101
-0.110
-0.118
-0.124
-0.150
0.999
0.998
0.995
0.993
0.990
0.986
0.983
0.979
0.975
0.971
0.967
0.962
0.957
0.952
0.947
0.942
0.936
0.930
0.924
0.917
0.911
0.904
0.897
0.889
0.882
0.874
0.866
0.858
0.849
0.840
0.831
0.822
0.813
0.803
0.793
0.783
0.773
-0.003
-0.007
-0.010
-0.013
-0.015
-0.018
-0.020
-0.022
-0.024
-0.027
-0.029
-0.032
-0.034
-0.037
-0.040
-0.043
-0.046
-0.049
-0.053
-0.056
-0.060
-0.065
-0.069
-0.074
-0.079
-0.085
-0.091
-0.098
-0.105
-0.112
-0.120
-0.128
-0.137
-0.145
-0.154
-0.163
-0.170
0.999
0.998
0.995
0.992
0.989
0.986
0.982
0.979
0.974
0.970
0.966
0.961
0.956
0.951
0.945
0.940
0.934
0.928
0.921
0.915
0.908
0.901
0.894
0.886
0.879
0.871
0.863
0.854
0.846
0.837
0.828
0.818
0.809
0.799
0.789
0.779
0.769
-0.034
-0.037
-0.041
-0.043
-0.046
-0.048
-0.051
-0.053
-0.055
-0.058
-0.060
-0.063
-0.065
-0.068
-0.071
-0.074
-0.077
-0.080
-0.084
-0.088
-0.092
-0.096
-0.101
-0.106
-0.111
-0.117
-0.123
-0.130
-0.137
-0.145
-0.153
-0.162
-0.171
-0.180
-0.190
-0.200
-0.210
0.999
0.998
0.995
0.992
0.989
0.985
0.982
0.978
0.974
0.969
0.965
0.960
0.955
0.949
0.944
0.938
0.932
0.925
0.919
0.912
0.905
0.898
0.891
0.883
0.875
0.867
0.859
0.850
0.842
0.833
0.824
0.814
0.805
0.795
0.785
0.775
0.765
-0.066
-0.069
-0.073
-0.076
-0.078
-0.081
-0.083
-0.086
-0.088
-0.090
-0.093
-0.096
-0.098
-0.101
-0.104
-0.107
-0.110
-0.114
-0.117
-0.121
-0.125
-0.129
-0.134
-0.139
-0.144
-0.150
-0.157
-0.163
-0.171
-0.178
-0.187
-0.196
-0.205
-0.215
-0.224
-0.235
-0.245
0.999
0.998
0.995
0.992
0.989
0.985
0.981
0.977
0.973
0.968
0.963
0.958
0.953
0.947
0.942
0.936
0.929
0.923
0.916
0.909
0.902
0.895
0.887
0.880
0.872
0.863
0.855
0.846
0.838
0.829
0.819
0.810
0.801
0.791
0.781
0.771
0.761
-0.101
-0.105
-0.109
-0.112
-0.114
-0.117
-0.120
-0.122
-0.125
-0.127
-0.130
-0.132
-0.135
-0.138
-0.141
-0.144
-0.147
-0.151
-0.154
-0.158
-0.162
-0.167
-0.172
-0.177
-0.182
-0.188
-0.194
-0.201
-0.208
-0.216
-0.225
-0.234
-0.243
-0.254
-0.264
-0.275
-0.285
25
NA520 Final Project Report
0.765
0.754
0.743
0.731
0.720
0.708
0.696
0.684
0.671
0.658
0.646
0.633
0.620
0.606
0.593
0.579
0.566
0.552
0.539
0.525
0.511
0.497
0.483
0.470
0.456
0.442
0.429
0.415
0.402
0.388
0.375
0.362
0.349
0.336
0.324
0.312
0.299
0.287
0.276
0.264
0.253
0.242
0.231
0.220
0.210
0.200
-0.290
-0.477
-0.654
-0.809
-0.940
-1.056
-1.157
-1.245
-1.322
-1.386
-1.449
-1.654
-1.707
-1.728
-1.753
-1.784
-1.816
-1.848
-1.877
-1.902
-1.922
-1.940
-1.951
-1.963
-1.963
-1.968
-1.962
-1.957
-1.946
-1.932
-1.913
-1.895
-1.867
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26
0.755
0.744
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0.700
0.689
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-1.875
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-1.726
NA520 Final Project Report
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0.958
0.975
0.988
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1.000
1.000
0.995
0.987
0.975
27
0.219
0.209
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0.973
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1.000
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0.995
0.986
0.973
NA520 Final Project Report
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-1.919
28
0.003
0.004
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0.007
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-2.074
-2.134
-2.194
NA520 Final Project Report
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0.467
0.480
0.493
0.505
0.518
0.531
0.544
0.557
0.569
0.582
0.595
0.607
0.619
0.632
0.644
0.656
0.668
0.680
0.692
0.703
0.715
0.726
0.737
0.748
0.758
0.769
0.779
0.789
0.799
0.809
0.818
0.828
0.837
-1.969
-2.015
-2.050
-2.091
-2.124
-2.153
-2.180
-2.200
-2.218
-2.230
-2.241
-2.241
-2.243
-2.236
-2.228
-2.211
-2.190
-2.166
-2.136
-2.101
-2.065
-2.029
-1.999
-1.974
-1.952
-1.758
-1.632
-1.557
-1.477
-1.381
-1.269
-1.143
-1.000
-0.832
-0.637
-0.424
-0.255
-0.216
-0.210
-0.199
-0.189
-0.180
-0.171
-0.161
-0.153
-0.145
29
0.315
0.327
0.338
0.350
0.362
0.374
0.386
0.398
0.410
0.422
0.434
0.447
0.459
0.471
0.484
0.496
0.508
0.521
0.533
0.546
0.558
0.570
0.582
0.595
0.607
0.619
0.631
0.642
0.654
0.666
0.677
0.689
0.700
0.711
0.722
0.733
0.744
0.755
0.765
0.775
0.785
0.795
0.805
0.814
0.824
0.833
-2.106
-2.157
-2.192
-2.237
-2.264
-2.304
-2.321
-2.349
-2.363
-2.373
-2.383
-2.386
-2.382
-2.373
-2.360
-2.341
-2.316
-2.288
-2.253
-2.214
-2.176
-2.142
-2.115
-2.091
-1.997
-1.767
-1.692
-1.609
-1.513
-1.403
-1.273
-1.129
-0.961
-0.762
-0.540
-0.340
-0.258
-0.256
-0.245
-0.235
-0.225
-0.215
-0.205
-0.196
-0.187
-0.178
0.323
0.334
0.346
0.357
0.369
0.380
0.392
0.404
0.415
0.427
0.439
0.451
0.463
0.475
0.487
0.499
0.511
0.523
0.535
0.547
0.559
0.571
0.582
0.594
0.606
0.618
0.629
0.641
0.652
0.664
0.675
0.686
0.697
0.708
0.719
0.730
0.740
0.751
0.761
0.771
0.781
0.791
0.801
0.810
0.819
0.829
-2.244
-2.294
-2.337
-2.377
-2.411
-2.445
-2.472
-2.489
-2.505
-2.521
-2.523
-2.522
-2.519
-2.508
-2.491
-2.468
-2.442
-2.405
-2.367
-2.325
-2.287
-2.256
-2.231
-2.208
-1.920
-1.829
-1.749
-1.653
-1.536
-1.411
-1.259
-1.091
-0.890
-0.661
-0.440
-0.311
-0.308
-0.297
-0.285
-0.274
-0.264
-0.253
-0.243
-0.234
-0.225
-0.216
NA520 Final Project Report
0.853
0.861
0.869
0.877
0.885
0.892
0.899
0.906
0.913
0.920
0.926
0.932
0.938
0.943
0.949
0.954
0.959
0.963
0.968
0.972
0.976
0.980
0.983
0.987
0.990
0.993
0.995
0.998
0.999
-0.071
-0.064
-0.057
-0.051
-0.046
-0.040
-0.035
-0.031
-0.026
-0.022
-0.019
-0.015
-0.012
-0.009
-0.006
-0.003
0.000
0.002
0.005
0.007
0.009
0.012
0.014
0.016
0.018
0.021
0.023
0.026
0.030
0.849
0.858
0.866
0.874
0.882
0.889
0.897
0.904
0.911
0.917
0.924
0.930
0.936
0.942
0.947
0.952
0.957
0.962
0.967
0.971
0.975
0.979
0.983
0.986
0.990
0.993
0.995
0.998
0.999
-0.105
-0.098
-0.091
-0.085
-0.079
-0.074
-0.069
-0.065
-0.060
-0.056
-0.053
-0.049
-0.046
-0.043
-0.040
-0.037
-0.034
-0.032
-0.029
-0.027
-0.024
-0.022
-0.020
-0.018
-0.015
-0.013
-0.010
-0.007
-0.003
0.846
0.854
0.863
0.871
0.879
0.886
0.894
0.901
0.908
0.915
0.921
0.928
0.934
0.940
0.945
0.951
0.956
0.961
0.966
0.970
0.974
0.979
0.982
0.986
0.989
0.992
0.995
0.998
0.999
-0.137
-0.130
-0.123
-0.117
-0.111
-0.106
-0.101
-0.096
-0.092
-0.088
-0.084
-0.080
-0.077
-0.074
-0.071
-0.068
-0.065
-0.063
-0.060
-0.058
-0.055
-0.053
-0.051
-0.048
-0.046
-0.043
-0.041
-0.037
-0.034
0.842
0.850
0.859
0.867
0.875
0.883
0.891
0.898
0.905
0.912
0.919
0.925
0.932
0.938
0.944
0.949
0.955
0.960
0.965
0.969
0.974
0.978
0.982
0.985
0.989
0.992
0.995
0.998
0.999
-0.171
-0.163
-0.157
-0.150
-0.144
-0.139
-0.134
-0.129
-0.125
-0.121
-0.117
-0.114
-0.110
-0.107
-0.104
-0.101
-0.098
-0.096
-0.093
-0.090
-0.088
-0.086
-0.083
-0.081
-0.078
-0.076
-0.073
-0.069
-0.066
0.838
0.846
0.855
0.863
0.872
0.880
0.887
0.895
0.902
0.909
0.916
0.923
0.929
0.936
0.942
0.947
0.953
0.958
0.963
0.968
0.973
0.977
0.981
0.985
0.989
0.992
0.995
0.998
0.999
-0.208
-0.201
-0.194
-0.188
-0.182
-0.177
-0.172
-0.167
-0.162
-0.158
-0.154
-0.151
-0.147
-0.144
-0.141
-0.138
-0.135
-0.132
-0.130
-0.127
-0.125
-0.122
-0.120
-0.117
-0.114
-0.112
-0.109
-0.105
-0.101
Table5. Cp along the cylinder by Fluent (   0.1,0.2,0.5,0.7,1.0 )
x(0.1)
Cp
x(0.2)
Cp
x(0.5)
Cp
x(0.7)
Cp
x(1.0)
Cp
0.500
0.497
0.491
0.485
0.479
0.472
0.466
0.459
0.452
0.446
0.439
0.432
0.426
0.270
0.259
0.208
0.125
0.054
0.001
-0.040
-0.069
-0.093
-0.110
-0.124
-0.135
-0.144
0.500
0.499
0.496
0.491
0.486
0.481
0.475
0.469
0.462
0.456
0.450
0.443
0.437
0.271
0.269
0.268
0.268
0.265
0.244
0.201
0.143
0.080
0.019
-0.035
-0.081
-0.122
0.500
0.500
0.499
0.497
0.495
0.493
0.490
0.487
0.483
0.479
0.474
0.469
0.464
0.125
0.123
0.120
0.116
0.113
0.111
0.108
0.106
0.106
0.105
0.104
0.102
0.101
0.500
0.500
0.499
0.498
0.497
0.495
0.494
0.491
0.489
0.486
0.482
0.479
0.475
-0.037
-0.040
-0.045
-0.049
-0.054
-0.059
-0.064
-0.068
-0.073
-0.078
-0.082
-0.084
-0.085
0.500
0.500
0.500
0.499
0.498
0.497
0.496
0.494
0.492
0.490
0.488
0.485
0.483
-0.205
-0.207
-0.209
-0.210
-0.212
-0.214
-0.217
-0.220
-0.222
-0.225
-0.229
-0.236
-0.245
30
NA520 Final Project Report
0.419
0.412
0.406
0.399
0.392
0.385
0.379
0.372
0.365
0.359
0.352
0.345
0.338
0.332
0.325
0.318
0.311
0.305
0.298
0.291
0.284
0.278
0.271
0.264
0.257
0.250
0.244
0.237
0.230
0.223
0.217
0.210
0.203
0.196
0.190
0.183
0.176
0.169
0.163
0.156
0.149
0.142
0.135
0.129
0.122
0.115
-0.152
-0.158
-0.163
-0.168
-0.171
-0.175
-0.178
-0.180
-0.183
-0.185
-0.186
-0.189
-0.190
-0.191
-0.192
-0.194
-0.194
-0.195
-0.197
-0.197
-0.198
-0.199
-0.199
-0.199
-0.200
-0.201
-0.201
-0.202
-0.202
-0.202
-0.203
-0.202
-0.203
-0.203
-0.203
-0.204
-0.204
-0.204
-0.204
-0.204
-0.204
-0.205
-0.205
-0.205
-0.205
-0.205
0.430
0.423
0.417
0.410
0.403
0.396
0.390
0.383
0.376
0.369
0.362
0.355
0.349
0.342
0.335
0.328
0.321
0.314
0.307
0.300
0.293
0.286
0.279
0.272
0.266
0.259
0.252
0.245
0.238
0.231
0.224
0.217
0.210
0.203
0.196
0.189
0.182
0.175
0.168
0.161
0.154
0.147
0.140
0.133
0.126
0.119
-0.157
-0.186
-0.212
-0.233
-0.252
-0.269
-0.283
-0.296
-0.307
-0.317
-0.327
-0.334
-0.343
-0.349
-0.355
-0.360
-0.365
-0.370
-0.375
-0.378
-0.382
-0.386
-0.390
-0.391
-0.394
-0.398
-0.399
-0.402
-0.405
-0.406
-0.409
-0.411
-0.411
-0.414
-0.415
-0.416
-0.418
-0.419
-0.421
-0.422
-0.423
-0.425
-0.426
-0.427
-0.428
-0.429
0.459
0.453
0.447
0.441
0.435
0.428
0.422
0.415
0.408
0.401
0.394
0.387
0.379
0.372
0.365
0.357
0.350
0.342
0.334
0.326
0.319
0.311
0.303
0.295
0.287
0.279
0.271
0.263
0.255
0.247
0.238
0.230
0.222
0.214
0.205
0.197
0.189
0.181
0.172
0.164
0.156
0.147
0.139
0.130
0.122
0.114
0.099
0.096
0.093
0.089
0.083
0.075
0.064
0.050
0.032
0.010
-0.018
-0.049
-0.185
-0.234
-0.276
-0.320
-0.365
-0.410
-0.454
-0.497
-0.539
-0.578
-0.618
-0.653
-0.688
-0.721
-0.751
-0.782
-0.807
-0.835
-0.858
-0.883
-0.902
-0.925
-0.941
-0.962
-0.976
-0.994
-1.007
-1.023
-1.035
-1.047
-1.060
-1.069
-1.081
-1.089
31
0.471
0.466
0.462
0.457
0.452
0.446
0.441
0.435
0.429
0.423
0.416
0.410
0.403
0.396
0.389
0.382
0.374
0.367
0.359
0.352
0.344
0.336
0.328
0.320
0.312
0.303
0.295
0.287
0.278
0.270
0.261
0.252
0.244
0.235
0.226
0.217
0.208
0.199
0.190
0.181
0.172
0.163
0.153
0.144
0.135
0.126
-0.086
-0.085
-0.085
-0.086
-0.086
-0.088
-0.089
-0.091
-0.093
-0.095
-0.097
-0.099
-0.101
-0.104
-0.108
-0.113
-0.120
-0.129
-0.140
-0.155
-0.273
-0.295
-0.322
-0.354
-0.392
-0.434
-0.481
-0.531
-0.585
-0.641
-0.698
-0.756
-0.812
-0.869
-0.925
-0.977
-1.031
-1.078
-1.125
-1.171
-1.212
-1.255
-1.290
-1.327
-1.361
-1.391
0.480
0.476
0.473
0.469
0.465
0.461
0.457
0.452
0.448
0.443
0.437
0.432
0.426
0.421
0.415
0.409
0.403
0.396
0.389
0.382
0.375
0.368
0.360
0.352
0.345
0.337
0.328
0.320
0.311
0.303
0.294
0.285
0.276
0.267
0.257
0.248
0.238
0.228
0.219
0.209
0.199
0.188
0.178
0.168
0.157
0.147
-0.256
-0.267
-0.276
-0.282
-0.284
-0.284
-0.280
-0.274
-0.267
-0.259
-0.252
-0.246
-0.243
-0.242
-0.244
-0.247
-0.251
-0.255
-0.257
-0.259
-0.260
-0.261
-0.261
-0.261
-0.262
-0.263
-0.264
-0.253
-0.255
-0.257
-0.260
-0.264
-0.270
-0.279
-0.294
-0.320
-0.361
-0.428
-0.520
-0.632
-0.754
-0.878
-1.000
-1.116
-1.227
-1.331
NA520 Final Project Report
0.108
0.102
0.095
0.088
0.081
0.075
0.068
0.061
0.054
0.047
0.041
0.034
0.027
0.020
0.014
0.007
0.003
-0.003
-0.010
-0.017
-0.024
-0.030
-0.037
-0.044
-0.051
-0.058
-0.064
-0.071
-0.078
-0.085
-0.091
-0.098
-0.105
-0.112
-0.119
-0.125
-0.132
-0.139
-0.146
-0.152
-0.159
-0.166
-0.173
-0.179
-0.186
-0.193
-0.205
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.206
-0.205
-0.205
-0.206
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.204
-0.204
-0.204
-0.204
-0.204
-0.204
-0.204
-0.203
0.112
0.105
0.098
0.091
0.084
0.077
0.070
0.063
0.056
0.049
0.042
0.035
0.028
0.021
0.014
0.007
0.000
-0.007
-0.014
-0.021
-0.028
-0.035
-0.042
-0.049
-0.056
-0.063
-0.070
-0.077
-0.084
-0.091
-0.098
-0.105
-0.112
-0.119
-0.126
-0.133
-0.140
-0.147
-0.154
-0.161
-0.168
-0.175
-0.182
-0.189
-0.196
-0.203
-0.429
-0.430
-0.432
-0.432
-0.433
-0.433
-0.434
-0.434
-0.435
-0.436
-0.436
-0.436
-0.437
-0.437
-0.437
-0.437
-0.438
-0.438
-0.439
-0.439
-0.439
-0.439
-0.439
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.440
-0.439
-0.439
-0.438
-0.438
-0.437
-0.438
-0.437
-0.436
-0.436
-0.434
-0.434
0.105
0.097
0.088
0.080
0.071
0.063
0.054
0.046
0.038
0.029
0.021
0.012
0.004
-0.005
-0.013
-0.022
-0.030
-0.039
-0.047
-0.056
-0.064
-0.073
-0.081
-0.089
-0.098
-0.106
-0.115
-0.123
-0.132
-0.140
-0.148
-0.157
-0.165
-0.173
-0.182
-0.190
-0.198
-0.207
-0.215
-0.223
-0.231
-0.240
-0.248
-0.256
-0.264
-0.272
-1.099
-1.107
-1.113
-1.123
-1.127
-1.134
-1.140
-1.143
-1.150
-1.152
-1.156
-1.162
-1.161
-1.166
-1.167
-1.167
-1.172
-1.170
-1.171
-1.172
-1.169
-1.171
-1.168
-1.166
-1.166
-1.160
-1.161
-1.155
-1.152
-1.148
-1.141
-1.140
-1.129
-1.116
-1.106
-1.101
-1.091
-1.084
-1.073
-1.064
-1.052
-1.042
-1.028
-1.017
-1.000
-0.989
32
0.117
0.107
0.098
0.089
0.079
0.070
0.060
0.051
0.042
0.032
0.023
0.013
0.004
-0.004
-0.013
-0.023
-0.032
-0.042
-0.051
-0.060
-0.070
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-0.270
-0.278
-0.287
-0.295
-1.424
-1.448
-1.478
-1.498
-1.525
-1.542
-1.563
-1.580
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-1.623
-1.638
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-1.582
-1.571
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0.136
0.126
0.115
0.104
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0.083
0.072
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0.039
0.028
0.017
0.006
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-0.311
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-1.428
-1.519
-1.604
-1.682
-1.755
-1.822
-1.884
-1.940
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-2.037
-2.077
-2.113
-2.144
-2.169
-2.190
-2.206
-2.218
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-2.227
-2.225
-2.219
-2.208
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-2.174
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-1.981
-1.937
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-1.839
-1.785
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-1.610
-1.546
-1.471
-1.404
-1.335
-1.264
-1.191
-1.118
-1.043
-0.968
NA520 Final Project Report
-0.200
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-0.227
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0.110
0.247
0.413
0.610
0.824
0.928
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-0.935
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-0.742
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0.067
0.150
0.230
0.318
0.423
0.522
0.609
0.698
0.788
0.859
0.921
0.968
0.995
1.003
0.991
0.958
0.909
0.846
0.764
0.683
0.596
33
-0.303
-0.312
-0.320
-0.328
-0.336
-0.344
-0.352
-0.359
-0.367
-0.374
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-0.492
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-0.749
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0.051
0.127
0.203
0.279
0.354
0.429
0.503
0.575
0.643
0.707
0.767
0.820
0.868
0.909
0.943
0.970
0.989
1.001
1.004
1.001
0.988
0.968
0.940
0.906
0.864
0.817
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0.052
0.123
0.192
0.259
0.324
0.386
0.447
0.504
0.559
0.612
0.661
0.707
0.751
0.791
0.828
0.861
0.891
0.918
0.942
0.961
0.977
0.990
0.999
1.005
1.006
1.004
0.999
0.990
0.977
0.961
0.941
NA520 Final Project Report
-0.500
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0.749
0.514
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0.824
0.610
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0.110
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0.397
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0.134
0.043
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-1.068
-1.076
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-1.095
-1.106
-1.111
-1.122
-1.125
-1.124
-1.126
34
-0.489
-0.486
-0.483
-0.479
-0.476
-0.471
-0.467
-0.462
-0.458
-0.452
-0.447
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-0.236
-0.227
-0.218
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-0.182
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0.763
0.704
0.640
0.572
0.500
0.425
0.349
0.271
0.193
0.114
0.037
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0.918
0.891
0.861
0.827
0.791
0.751
0.708
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0.614
0.562
0.508
0.452
0.393
0.331
0.268
0.203
0.136
0.067
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-1.587
-1.656
-1.723
-1.797
-1.859
-1.919
-1.976
-2.030
-2.081
-2.129
NA520 Final Project Report
-0.196
-0.190
-0.183
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-0.169
-0.163
-0.156
-0.149
-0.142
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0.077
0.084
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0.074
0.082
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0.099
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0.116
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0.133
0.141
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0.166
0.175
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0.191
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0.208
0.216
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0.233
-1.133
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-0.991
-0.974
-0.960
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-0.924
-0.902
-0.883
-0.859
35
-0.164
-0.155
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-0.136
-0.127
-0.118
-0.109
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-0.090
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0.003
0.012
0.022
0.031
0.040
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0.059
0.069
0.078
0.087
0.097
0.106
0.115
0.124
0.134
0.143
0.152
0.161
0.171
0.180
0.189
0.198
0.207
0.216
0.225
0.233
0.242
0.251
-1.598
-1.612
-1.628
-1.633
-1.650
-1.652
-1.664
-1.667
-1.673
-1.676
-1.676
-1.681
-1.675
-1.680
-1.670
-1.671
-1.659
-1.657
-1.569
-1.564
-1.546
-1.538
-1.518
-1.506
-1.483
-1.467
-1.443
-1.421
-1.396
-1.368
-1.342
-1.307
-1.278
-1.240
-1.206
-1.166
-1.124
-1.082
-1.034
-0.988
-0.937
-0.885
-0.832
-0.776
-0.721
-0.664
-0.186
-0.175
-0.165
-0.155
-0.144
-0.133
-0.123
-0.112
-0.101
-0.091
-0.080
-0.069
-0.058
-0.047
-0.036
-0.025
-0.014
-0.003
0.008
0.019
0.030
0.041
0.052
0.063
0.074
0.084
0.095
0.106
0.117
0.127
0.138
0.149
0.159
0.169
0.180
0.190
0.200
0.210
0.220
0.230
0.239
0.249
0.259
0.268
0.277
0.286
-2.173
-2.215
-2.252
-2.286
-2.317
-2.343
-2.365
-2.384
-2.398
-2.408
-2.413
-2.414
-2.411
-2.403
-2.391
-2.374
-2.352
-2.325
-2.294
-2.258
-2.217
-2.171
-2.119
-2.063
-2.002
-1.935
-1.863
-1.786
-1.703
-1.614
-1.519
-1.418
-1.310
-1.195
-1.073
-0.945
-0.813
-0.682
-0.561
-0.463
-0.392
-0.350
-0.326
-0.309
-0.295
-0.285
NA520 Final Project Report
0.112
0.119
0.125
0.132
0.139
0.146
0.152
0.159
0.166
0.173
0.179
0.186
0.193
0.200
0.207
0.213
0.220
0.227
0.234
0.240
0.247
0.254
0.261
0.267
0.274
0.281
0.288
0.294
0.301
0.308
0.315
0.321
0.328
0.335
0.342
0.348
0.355
0.362
0.369
0.375
0.382
0.389
0.396
0.402
0.409
0.416
-0.205
-0.205
-0.205
-0.205
-0.205
-0.205
-0.204
-0.204
-0.204
-0.204
-0.204
-0.203
-0.204
-0.203
-0.203
-0.203
-0.202
-0.202
-0.201
-0.201
-0.201
-0.200
-0.200
-0.200
-0.198
-0.198
-0.198
-0.196
-0.196
-0.195
-0.194
-0.193
-0.192
-0.191
-0.189
-0.187
-0.186
-0.184
-0.181
-0.179
-0.176
-0.173
-0.170
-0.166
-0.161
-0.155
0.126
0.133
0.140
0.147
0.154
0.161
0.168
0.175
0.182
0.189
0.196
0.203
0.210
0.217
0.224
0.231
0.238
0.245
0.252
0.259
0.266
0.272
0.279
0.286
0.293
0.300
0.307
0.314
0.321
0.328
0.335
0.342
0.349
0.355
0.362
0.369
0.376
0.383
0.390
0.396
0.403
0.410
0.417
0.423
0.430
0.437
-0.428
-0.427
-0.426
-0.425
-0.423
-0.422
-0.421
-0.419
-0.419
-0.416
-0.415
-0.415
-0.411
-0.411
-0.409
-0.406
-0.405
-0.402
-0.399
-0.398
-0.394
-0.393
-0.389
-0.386
-0.382
-0.378
-0.375
-0.370
-0.365
-0.360
-0.355
-0.349
-0.343
-0.334
-0.327
-0.317
-0.307
-0.296
-0.284
-0.269
-0.252
-0.233
-0.211
-0.186
-0.157
-0.122
0.241
0.249
0.257
0.265
0.273
0.281
0.289
0.297
0.305
0.313
0.321
0.329
0.336
0.344
0.352
0.359
0.367
0.374
0.382
0.389
0.396
0.403
0.410
0.417
0.424
0.430
0.436
0.443
0.449
0.455
0.460
0.466
0.471
0.475
0.480
0.484
0.488
0.491
0.494
0.496
0.498
0.499
0.500
-
-0.838
-0.811
-0.786
-0.756
-0.728
-0.695
-0.663
-0.627
-0.590
-0.552
-0.511
-0.469
-0.427
-0.383
-0.338
-0.295
-0.253
-0.212
-0.183
-0.047
-0.016
0.012
0.034
0.052
0.066
0.076
0.084
0.090
0.094
0.097
0.099
0.101
0.102
0.104
0.105
0.106
0.108
0.110
0.113
0.117
0.120
0.124
0.125
36
0.260
0.268
0.277
0.285
0.294
0.302
0.310
0.319
0.327
0.335
0.343
0.351
0.358
0.366
0.373
0.381
0.388
0.395
0.402
0.409
0.415
0.422
0.428
0.434
0.440
0.445
0.451
0.456
0.461
0.466
0.470
0.474
0.478
0.482
0.485
0.488
0.491
0.493
0.495
0.497
0.498
0.499
0.500
-
-0.608
-0.554
-0.502
-0.452
-0.407
-0.365
-0.328
-0.297
-0.270
-0.147
-0.129
-0.114
-0.102
-0.093
-0.085
-0.079
-0.075
-0.072
-0.069
-0.067
-0.065
-0.064
-0.062
-0.060
-0.059
-0.058
-0.057
-0.058
-0.059
-0.060
-0.061
-0.062
-0.061
-0.058
-0.054
-0.050
-0.048
-0.047
-0.046
-0.043
-0.040
-0.038
-0.036
-
0.295
0.304
0.313
0.321
0.328
0.337
0.345
0.352
0.360
0.368
0.375
0.382
0.389
0.396
0.403
0.409
0.415
0.421
0.427
0.433
0.438
0.443
0.448
0.453
0.458
0.462
0.466
0.470
0.474
0.477
0.480
0.483
0.486
0.488
0.491
0.493
0.494
0.496
0.497
0.498
0.499
0.500
0.500
-
-0.277
-0.272
-0.268
-0.266
-0.252
-0.251
-0.250
-0.248
-0.247
-0.244
-0.242
-0.239
-0.237
-0.236
-0.236
-0.238
-0.240
-0.242
-0.243
-0.244
-0.243
-0.241
-0.238
-0.236
-0.234
-0.232
-0.231
-0.230
-0.229
-0.227
-0.224
-0.219
-0.215
-0.210
-0.206
-0.202
-0.199
-0.197
-0.196
-0.196
-0.197
-0.199
-0.202
-
NA520 Final Project Report
0.422
0.429
0.436
0.442
0.449
0.456
0.462
0.469
0.475
0.482
0.488
-0.148
-0.140
-0.130
-0.117
-0.102
-0.082
-0.056
-0.020
0.026
0.087
0.168
0.443
0.450
0.456
0.462
0.469
0.475
0.481
0.486
0.491
0.496
0.499
-0.082
-0.035
0.019
0.080
0.143
0.201
0.244
0.265
0.268
0.268
0.269
-
-
-
-
-
-
3. CD and CL along the cylinder
Table6. CD and CL along the cylinder by Xfoil and Fluent

CD (Xfoil)
CD (Fluent)
CL (Xfoil)
CL (Fluent)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1.0
0.00243
0.00398
0.00508
0.00644
0.00840
0.01142
0.01572
0.02111
0.02778
0.03572
0.04475
0.05509
0.06628
0.07910
0.09128
0.10357
0.11549
0.12612
0.13651
0.14717
0.00762
0.00741
0.04766
0.09203
0.15532
-0.00320
-0.00030
-0.00020
-0.00100
-0.00090
-0.00290
-0.00220
0.00150
0.00040
0.00110
0.00020
-0.00020
-0.00010
-0.00020
-0.00010
0.00000
-0.00010
0.00060
0.00020
0.00050
0.00000
0.00010
-0.00085
-0.00274
-0.00057
4. Separation locations along the cylinder
Table7. Separation locations along the cylinder by Xfoil and Fluent

 (Xfoil)
 (Fluent)
0.05
0.1
0.15
0.99948
0.99938
0.98283
0.992898
-
37
NA520 Final Project Report
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1.0
0.97442
0.96872
0.95217
0.94028
0.92796
0.91335
0.89584
0.87502
0.85936
0.84139
0.82128
0.79929
0.78623
0.77251
0.75836
0.74398
0.74011
38
0.978769
0.88824
0.80973
0.742049