JoshTheEngineer | Source Panel Method: System of Equations @JoshTheEngineer | Uploaded January 2020 | Updated October 2024, 3 hours ago.
After solving for the geometric integral from the previous video (Iij), we have the expression for the normal velocity on a panel's 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 panel's source strength.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
youtube.com/watch?v=BnPZjGCatcg
===== NOTES =====
→ To solve the system of equations, I'm using the programmatic function (x = A\b). 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:
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
amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
amzn.to/2wvZyUt
After solving for the geometric integral from the previous video (Iij), we have the expression for the normal velocity on a panel's 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 panel's source strength.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
► Panel Method Geometry
youtube.com/watch?v=kIqxbd937PI
► Building More Complex Flows
youtube.com/watch?v=EKzbwJvKcmw
► Flow Around an Airfoil
youtube.com/watch?v=cLdv1UfX1g8
► Normal Velocity Geometric Integral [I(ij)]
youtube.com/watch?v=76vPudNET6U
► Tangential Velocity Geometric Integral [J(ij)]
youtube.com/watch?v=JRHnOsueic8
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
youtube.com/watch?v=BnPZjGCatcg
===== NOTES =====
→ To solve the system of equations, I'm using the programmatic function (x = A\b). 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:
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
amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
amzn.to/2wvZyUt
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The links to relevant videos can be found here.
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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.
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