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 don't make this video longer than it needs to be.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
• How To: Run XFoil from...
► Panel Method Geometry
• Panel Method Geometry
► Building More Complex Flows
• Building More Complex ...
► Flow Around an Airfoil
• Flow Around an Airfoil...
► Normal Velocity Geometric Integral, Iij
• Source Panel Method: N...
===== 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

[@williamsworkshop8624]

Perfect timing! Just finished the last video.

[@JoshTheEngineer]

Awesome!

[@joejoyce853]

If you're not already you should be a professor. Better than most at my university. Thank you for this series of videos.

[@JoshTheEngineer]

Thanks, you're very kind!

[@abdoulkarimboussari1119]

Amazing.