Uploaded January 2020 | Updated September 2026, 2 weeks ago

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We went through the derivations of the normal velocity geometric integral (Iij) and the tangential geometric integral (Jij). The Iij term is used in the expression to solve for the source panel strengths. The Jij term is used in the expression to solve for the velocity of the flow on each panel. In order to compute the flowfield around the airfoil (off the airfoil), we need to know the X and Y components of the velocity at arbitrary grid points (similar to a CFD solution).

In this video, we go through the derivation of the X and Y velocity geometric integrals (Mx(ij) and My(ij)). These will allow us to compute the flowfield pressure coefficients and the streamlines around the airfoil. Much of this derivation is exactly the same as the Iij derivation, so I will refer you to that video for those details.

===== 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

 ===== NOTES =====
- I'll 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
amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
amzn.to/2wvZyUt