Source Panel Method: Normal Velocity Geometric Integral [I(ij)]

In the previous video (Flow Around an Airfoil), we ended with an expression that still needed some simplification before we could use it to solve for the source panel strengths. In this video, we go through the solution process of that term, called the geometric integral (or at least that's what I'm calling it).
Don't worry, we're almost ready to code our panel method. The next video is about creating the system of equations and solving it.
===== 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...
===== 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

[@abhisheksabnis5065]

Thank you for this video. Was stuck on this problem for a long time.

[@JoshTheEngineer]

Glad I could help!

[@phleau6264]

This was fantastic! was reviewing numerical solutions to panel methods and going over this was everything i needed. You rock.

[@JoshTheEngineer]

Awesome, thanks!

[@zhujiang6299]

Good ! This video solves my puzzle , Look forward to your next video , Surface vortex method

[@JoshTheEngineer]

Thanks! Working on filming now.

[@RekhaSharma-eh2lp]

Thank you so much.

[@williamsworkshop8624]

At 21:22 for clarification. is (x_i, y_i) the coordinate of the control point for the i-th panel? or the starting boundary point for the i-th panel, like (X_j, Y_j) is for the j-th panel?

[@JoshTheEngineer]

Good question. Since we are solving for the normal velocity at the control point of the i^th panel, the (x_i, y_i) coordinates are always the control point coordinates. Since we are integrating over the j^th panel, we will be using the boundary point coordinates for the (X_j, Y_j) values.
When I post my final video (and code), you'll be able to see that every (x_i, y_i) gets replaced with values I call XC(i) and YC(i), and every (X_j, Y_j) gets replaced with values I call XB(j) and YB(j). As you might guess, the C stands for "control" and the B stands for "boundary".

[@williamsworkshop8624]

@@JoshTheEngineer Great, looking forward to seeing your implementation. I've got my own nearly finished and working.

[@JoshTheEngineer]

@@williamsworkshop8624 That's awesome. I'll be filming these final videos soon, and I'll post that code when I do.

[@Dani-ox6yw]

Great video. Thank you Sir

[@JoshTheEngineer]

You're welcome!

[@SoyoCraft]

fantastic!

[@JoshTheEngineer]

Thanks!

[@chickyapoo1913]

Perfect 👌

[@JoshTheEngineer]

Thanks!

[@MesbahSalekeen]

Just saying......God bless You.

[@JoshTheEngineer]

Thanks!

[@user-ip7ls2cx2d]

Thank you for the video! But why do we have to choose a control panel i instead of a control point?

[@nebulousjam8795]

Great😁👍

[@honneycookie1865]

Wish I could have sexy professor like you in my college😂😂😂 I wouldn't be looking here and there so desperately to understand the topics.

[@abdelhakimoussamabelmekki9139]

hi , can you please help , how to calculate the cartesian velocity fron the normal velocity and how to program this integral , thank you

[@ajitkumar3237]

at 7 min 56 sec you say del = 90-phi why is this so

[@JoshTheEngineer]

In the video (and on the board), I say that del is equal to phi plus 90. If you want to know why, please watch my "Panel Method Geometry" video (you can skip to 7:28 where I talk about it): ruclips.net/video/kIqxbd937PI/видео.html

[@ssllhh100]

how often do you check your email ?

[@JoshTheEngineer]

Probably once every few days. It depends on how busy I am.

[@elifvarol9913]

hııım nıce bıke

[@elifvarol9913]

CAN YOU TELL ME HOW CAN I EVALUATE THE LAMBDA FOR AİRFOİL. THANK YOU SO MUCH amk mühendisi

[@JoshTheEngineer]

If you go to my Panel Method playlist, you'll find all my videos on this topic. This video shows you how to solve the system of equations: ruclips.net/video/ep7vPzGYsbw/видео.html