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@@ВадимСавенков-з2ю not fully sure but it does fit the the shape of wake curve that best fits experimental data. So in the 2D it pretty much flows off at the trailing edge angle, but as it continues down stream into the far field it then asymptomatically returns to uniform flow angle to that of the incoming stream. Find a online pdf copy of the international version of Low Speed Aerodynamics by Katz and go to chapter 9, figure 9.6. Should have a 2D wing with wake angles/curves. It talks about that shape being the best. It sadly doesn't go in to how to find these and each airfoil at each AOA would be different so not easy to find these curves but you maybe onto something with that being a good starting point.

@@Tidepodious Thank you, I'll try to do it

@@misterx8934 Thanks! And I actually have another video going over that method on this channel. Mind was blown when I animated it and realized there was actually no flow within the airfoil. At first a kinda assumed it would be like a doublet in uniform flow modeling a cylinder snd how there is an internal flow but yeah VPM, nothing, was nice to see clearly.

I would say start with Jos Stam's paper Stable Fluids, as it is alot of the basis of this process especially the advection. For the CFD part either John Anderson Computational Fluid Dynamics or Computational Fluid Dynamics for Engineers by Hoffman and Chiang their first volume covers these processes such as the Jacobi iterative method for elliptic PDEs. Good luck snd hope you enjoy the topic further!

@@Tidepodious I think I need more basic education since I'm in tenth grade rn

@@Tidepodious I discovered ur channel while learning how to solve depressed cubics

@@i_like_ft. I'm a UK student, so my curriculum modules won't be exactly the same as yours. But for fluid dynamics you'll need to have knowledge of vector and multivariable calculus - which I don't believe you'll learn in academia for a couple of years at least. Unless, by all means, have a go at learning them yourself (granted you already have basic calculus knowledge)

@jimmelton hlw im from Bangladesh so we also dont learn calculus till 11th grade. ik a little bit of calculus but i havent learned multivariable calculus yet.can u suggest from where i should learn ?

@@anthonysu1712 that's a good point. Me watching it there isn't an issue but I also have the knowledge of exactly what is about to happen and rewatching while trying to imagine that wasn't the case makes is super obvious this is annoying to a viewer lol thanks for pointing this out!

That is a good idea, and thanks!

Watch Veritasium channel #solve for depressed cubic !! You will get the Idea how quadric as well as cubic equation works in visual representation!!!

Search :How imaginary numbers were invented

If you mean make them based on the NACA design you can go to the Desmos link in the description and I have an interactive airfoil to play with, in there is the equations for the 4-series. If you mean make your own I would suggest reading that NACA document in the description, they outline how they came up with the equations they settled on and it may give insight on how you could create your own.

@@Tidepodious Thanks, I want to make the equations for the surfaces. I want to upload this to computational software where I can plot the equation of the two. Afterwards, I want to find the area between the curves. But I have no idea how to get the topic and bottom curves.

@@Tidepodious Hey, could you explain line 22, 24, 25 on desmos. I dont understand how a function is being drawn from that

These are parametric equations, so they are in form (x,y). The first half of the expression says where the x point should be and second the y. I prefer to compartmentalize equations but if you were to start with say line 23, and find all of it's variables and plug them in, then do it again for the new unknowns and fully collapse all equations down you should have 4 total parametric equations. (Top first half, top second half, bottom first half, bottom second half). The equations in this form are rather long so be careful not to get lost in the variables.

@@Tidepodious would it be possible if you may make a video tutorial or rundown of the desmos lines? especially the 22, 24, 25. I really appreciate this as a hobbyist

I use DaVinci Resolve 18, make the manim soundless video frist then in Resolve add the sounds. And the music is just pulled from royalty free website that I liked.

Thanks! I do need to get around to playing with blender lol

Oh and the camber line is just the midpoint between the top surface and bottom surface going along the chord.

Here is the core code but since I write over it each time to render each animation this is more like a template than the code itself. github.com/leeb2221/Parametric-Curves/blob/main/ParaCurveButterfly

It's just a habit, since I am only using the x-component of velocity (V) I use little u. Alot of textbooks use V=ui+vj+wk for the vector components.

Finally got around to making a GitHub, here is the code I was using. It is not all three since I was reusing for each one but the structure is there. github.com/leeb2221/Parametric-Curves.git

docs.manim.community/en/stable/reference/manim.mobject.vector_field.VectorField.html Under nudging. The vector field is not entirely accurate for real fluid flow using the Faulkner Skans Equations but is a parabolic approximation. Looks the same at this level so no reason to complicate the calculations.