Uploaded May 2015 | Updated September 2026, 2 weeks ago
This is the fifth video in my 10-video series on coding a program in MATLAB to compute, display, and save a NACA 4-digit airfoil.
IN THIS VIDEO:
We code the input for the angle of attack and save file name edit text boxes. The angle of attack text box needs to be converted to a number, while the file name text box can remain a string.
IN THIS SERIES:
Part 1/10 : goo.gl/9UBgbo
Part 2/10 : goo.gl/jRRcYJ
Part 3/10 : goo.gl/rSVLHo
Part 4/10 : goo.gl/HwHB39
Part 5/10 : goo.gl/AlDne8
Part 6/10 : goo.gl/7n1QP7
Part 7/10 : goo.gl/nTGleR
Part 8/10 : goo.gl/ez247P
Part 9/10 : goo.gl/8mXYcc
Part 10/10: goo.gl/ovBlbW
This is the fifth video in my 10-video series on coding a program in MATLAB to compute, display, and save a NACA 4-digit airfoil.
IN THIS VIDEO:
We code the input for the angle of attack and save file name edit text boxes. The angle of attack text box needs to be converted to a number, while the file name text box can remain a string.
IN THIS SERIES:
Part 1/10 : goo.gl/9UBgbo
Part 2/10 : goo.gl/jRRcYJ
Part 3/10 : goo.gl/rSVLHo
Part 4/10 : goo.gl/HwHB39
Part 5/10 : goo.gl/AlDne8
Part 6/10 : goo.gl/7n1QP7
Part 7/10 : goo.gl/nTGleR
Part 8/10 : goo.gl/ez247P
Part 9/10 : goo.gl/8mXYcc
Part 10/10: goo.gl/ovBlbW
![Explained: Oblique Shock Relations Derivation
In this video, we will derive the oblique shock (OS) relations. We will start from integral conservation equations, and derive expressions for the downstream Mach number, density ratio, velocity ratio, pressure ratio, and temperature ratio.
RELEVANT VIDEOS
→ Oblique Shock Example
https://goo.gl/77hjcb
→ Normal Shock Relations Derivation
https://goo.gl/Unvjey
→ Normal Shock Example
https://goo.gl/RBJtgV
RELEVANT LINKS
► Surface (Double) Integrals Explanation
http://www.joshtheengineer.com/2017/01/02/surface-double-integrals/
► VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
► MATLAB Functions
https://github.com/jte0419/Compressible_Flow_Relations
THUMBNAIL CREDIT
By Settles1 (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons Explained: Oblique Shock Relations Derivation](https://i.ytimg.com/vi/JBZtFhXRkVM/mqdefault.jpg)

![Vortex Panel Method: Airfoil
The vortex panel method code in this video is an adaptation of the source panel method code from a few videos ago. The only change weve made between the codes is the formulation of the matrix system of equations (including the addition of the Kutta condition equation).
Well look at a few examples of the code working like you would expect, and compare resulting lift and moment coefficients to the XFOIL results. Then well look at a few cases where the code seems to fall apart, which is the motivation for my next two videos, the combined source/vortex panel method.
WHERE ARE WE GOING?
→ The limitations in this video motivate the need for a more robust implementation of the VPM.
→ I will derive the combined SPM/VPM formulation and code it to show how good we can get the results for a pretty simple implementation.
→ We can finally extend the SPM/VPM formulation to multiple separate airfoil elements. This will be the last video in the series.
CODE
► My website
http://www.joshtheengineer.com/2020/06/21/vortex-panel-method-airfoil/
► GitHub
https://github.com/jte0419/Panel_Methods
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
https://www.youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
https://www.youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
https://www.youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [K(ij)]
https://www.youtube.com/watch?v=5lmIv2CUpoc
► Tangential Velocity Geometric Integral [L(ij)]
https://www.youtube.com/watch?v=IxWJzwIG_gY
► Streamline Geometric Integral VPM [Nx(ij) and Ny(ij)]
https://www.youtube.com/watch?v=TBwBnW87hso
► Solving the System of Equations: VPM
https://www.youtube.com/watch?v=j3ETHFBiYOg
► Source Panel Method: Airfoil
https://www.youtube.com/watch?v=fdNOYdwY9Bw
NOTES
→ Ill add notes here if I need to.
ERRORS
→ If you see an error in the video, please let me know and I will include it here.
REFERENCES
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt Vortex Panel Method: Airfoil](https://i.ytimg.com/vi/JL2fz-xTTT0/mqdefault.jpg)
![Explained: Ghost Nodes [CFD]
In some finite difference/volume equations, you might need to use points that are outside of the actual grid domain. In these cases, ghost nodes can be calculated from the interior points and used for the differences (such as a central difference on a boundary node). Explained: Ghost Nodes [CFD]](https://i.ytimg.com/vi/JMP9aanQ5o0/mqdefault.jpg)
![Source Panel Method: Tangential Velocity Geometric Integral [J(ij)]
In the previous video (Geometric Integral Iij), we went through the full derivation of the geometric integral for the normal partial derivative, which was needed to solve for the source panel strengths. In this video, we will go through the (very similar) derivation of the tangential partial derivative geometric integral, which is needed to solve for the panel velocities, and thus the panel pressure coefficients.
This derivation is almost exactly the same as the normal geometric integral derivation, but there are some slight differences. Where it is exactly the same, I will refer you back to my other video (Iij) so we dont make this video longer than it needs to be.
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
https://www.youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
https://www.youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
https://www.youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral, Iij
https://www.youtube.com/watch?v=76vPudNET6U
NOTES
- Ill add notes here if I need to.
ERRORS
- If you see an error in the video, please let me know and I will include it here.
REFERENCES
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt Source Panel Method: Tangential Velocity Geometric Integral [J(ij)]](https://i.ytimg.com/vi/JRHnOsueic8/mqdefault.jpg)

![Oblique Shock Example Problem
Lets work through an oblique shock (OS) example. In this video, we will go through four methods for solving OS problems.
1) Derived equations
2) Compressible flow tables (NACA 1135)
3) VT calculator
4) MATLAB functions
RELEVANT VIDEOS
→ Oblique Shock Derivation
https://goo.gl/xLYYYP
→ Normal Shock Relations Derivation
https://goo.gl/Unvjey
→ Normal Shock Example
https://goo.gl/RBJtgV
RELEVANT LINKS
► VT Calculator
http://www.dept.aoe.vt.edu/~devenpor/aoe3114/calc.html
► MATLAB Functions
https://github.com/jte0419/Compressible_Flow_Relations
THUMBNAIL CREDIT
By Settles1 (Own work) [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)], via Wikimedia Commons Oblique Shock Example Problem](https://i.ytimg.com/vi/JvrWmg8m5is/mqdefault.jpg)
![Explained: TI-83 Linear Interpolation Program [Math]
In this video I show you how to program a linear interpolation equation into your TI-83 graphing calculator.
If you would like to see how the equation is derived, click the link below to my other video.
https://goo.gl/7OA0UU
Here is the code if you already know how to input it into your calculator:
PROGRAM:INTERP
Input X1=,A
Input X2=,D
Input X= ,I
Input Y1=,N
Input Y2=,S
Disp (((S-N)/(D-A))(I-A)+N) Explained: TI-83 Linear Interpolation Program [Math]](https://i.ytimg.com/vi/KQzK5z9jkHE/mqdefault.jpg)
![Explained: Croccos Theorem [Taylor-Maccoll]
Croccos theorem is needed to obtain the irrotationality condition used later in the overall derivation. The equation is essentially a combination of the momentum and energy equations. The final resulting boxed equation states that the curl of the velocity field is zero, indication an irrotational flow.
The extra videos I mention in this video can be found below.
Momentum Equation: http://www.youtube.com/watch?v=ZH0fiaYGTYQ
Assumptions: http://www.youtube.com/watch?v=HIDeIZO0z-8
Total Derivative: http://www.youtube.com/watch?v=bgUDbntoXBY
TdS Equation: http://www.youtube.com/watch?v=N126SaEGuJA
Vector Identity: http://www.youtube.com/watch?v=0LO-ZcESYdE
Enthalpy: http://www.youtube.com/watch?v=yy5HQ9syrrI Explained: Croccos Theorem [Taylor-Maccoll]](https://i.ytimg.com/vi/KZYHjujYpFk/mqdefault.jpg)

