Uploaded May 2015 | Updated September 2026, 2 weeks ago
This is the eighth 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 radio button for showing the camber line of the airfoil. We also code the Exit button.
Radio Button Video:
goo.gl/E4Owva
Exit Button Video:
goo.gl/aarwmW
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 eighth 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 radio button for showing the camber line of the airfoil. We also code the Exit button.
Radio Button Video:
goo.gl/E4Owva
Exit Button Video:
goo.gl/aarwmW
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
![Source Panel Method: System of Equations
After solving for the geometric integral from the previous video (Iij), we have the expression for the normal velocity on a panels control point in terms of variables we know. Since we have N unknowns (where N is the number of panels approximating the airfoil surface), we need N equations to solve the system.
This video goes through how to set up the system of equations that needs to be solved in order to obtain each panels source strength.
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 [I(ij)]
https://www.youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
https://www.youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
https://www.youtube.com/watch?v=BnPZjGCatcg
NOTES
→ To solve the system of equations, Im using the programmatic function (x = Ab). This takes care of the solution method for you, but you can also use your own Gaussian elimination solver, for instance. Here is a link to the MATLAB documentation for the solver:
https://www.mathworks.com/help/matlab/ref/mldivide.html
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: System of Equations](https://i.ytimg.com/vi/ep7vPzGYsbw/mqdefault.jpg)
![Explained: Populate a Listbox [MATLAB]
This video explains how to select files from a folder and make those file names visible in a listbox. Explained: Populate a Listbox [MATLAB]](https://i.ytimg.com/vi/esZVttsTQ9I/mqdefault.jpg)

![Explained: Continuity Equation for Axisymmetric Conical Flow [Taylor-Maccoll]
The continuity (conservation of mass) equation was derived in a previous video. Since the Taylor-Maccoll problem is formulated in spherical coordinates, the conservation equation needs to be recast in terms of spherical coordinates. A few of the assumptions discussed in the previous assumptions video are used to simplify the equation to a useful form for this problem.
The links to relevant videos can be found here.
Continuity Equation
http://www.youtube.com/watch?v=uXPRyYAHvZk
Taylor-Maccoll Assumptions
http://www.youtube.com/watch?v=HIDeIZO0z-8 Explained: Continuity Equation for Axisymmetric Conical Flow [Taylor-Maccoll]](https://i.ytimg.com/vi/f79k_ZWtCdc/mqdefault.jpg)
![Explained: Sound Suppression Water System [Space Shuttle]
The acoustic waves generated from the space shuttle as it lifts off have the potential to damage both the launch structure as well as the shuttle itself. Water is used to absorb some of this energy to ensure a safe launch.
After seeing a different view in a video, it appears that the SSME exhaust hole water nozzles shoot water horizontally across the hole from the sides. The nozzles look like theyre located towards the top of the exhaust hole.
A couple videos that have excellent footage of the structure can be seen below. Note: I would turn down your volume a little before clicking the links because youve probably turned it up to watch my videos.
http://www.youtube.com/watch?v=ezVOSfbKNJ0
http://www.youtube.com/watch?v=dTAjGiZvI9k
This video is pretty spectacular too.
https://www.youtube.com/watch?v=mjrpuG2HOuI Explained: Sound Suppression Water System [Space Shuttle]](https://i.ytimg.com/vi/fc1WokD1A1c/mqdefault.jpg)
![Source Panel Method: Airfoil
Flows over a circular cylinder are a bit boring, so here we apply the same code (with a couple minor tweaks) to the flow over an airfoil. In this video, we add two code blocks: the first is for loading and creating the airfoil, and the second is to compute the circulation around an ellipse that encompasses the airfoil. Everything else from the previous video (Source Panel Method: Circular Cylinder) is the same. The results we get in this video motivate the need for the vortex panel method.
WHERE ARE WE GOING?
→ I will need to go through the derivations for the geometric integrals for the VPM (which are similar to the SPM derivations).
→ We will then implement the VPM and see some of its limitations. These limitations will 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/2020/03/05/source-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 [I(ij)]
https://www.youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
https://www.youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
https://www.youtube.com/watch?v=BnPZjGCatcg
► Solving the System of Equations
https://www.youtube.com/watch?v=ep7vPzGYsbw
► Source Panel Method: Circular Cylinder
https://www.youtube.com/watch?v=zIrDfEz-5mc
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: Airfoil](https://i.ytimg.com/vi/fdNOYdwY9Bw/mqdefault.jpg)
![Explained: Irrotational Condition [Taylor-Maccoll]
Croccos equation (under our given assumptions) led to an expression regarding the irrotationality of the flow. That is, the flow is free from rotation. Expanding the expression that the curl of the velocity field is zero, another expression relating the velocities flow can be obtained. Explained: Irrotational Condition [Taylor-Maccoll]](https://i.ytimg.com/vi/g4vnuSHBokU/mqdefault.jpg)



![Explained: Aligning Torque Simulation
Where does the plot of aligning torque versus slip angle come from? In this video, Ill describe the steps I took to simulate this curve using a simplified theory of tire forces and moments. Code can be found at the links below.
CODE
https://github.com/jte0419/Tire_Aligning_Torque
NOTES
► Im not including any mechanical trail in this description.
► The tire has no inclination angle/camber.
RELATED VIDEOS
→ Integral: U-Substitution
https://goo.gl/VmUzbA
→ Integral: Trig-Substitution
https://goo.gl/hNVVfz
→ Centroid of a Triangle
https://goo.gl/qqWBvY
→ Centroid of a Circular Segment
https://goo.gl/URd9Pj
→ Explained: Aligning Torque
https://goo.gl/pMfq1s
THUMBNAIL IMAGE
By J.H. Sohn from Melbourne, Australia (2014 Australian F1 Grand Prix) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons Explained: Aligning Torque Simulation](https://i.ytimg.com/vi/hfMoiC6JWWY/mqdefault.jpg)