Uploaded June 2016 | Updated September 2026, 2 weeks ago
In this video I will derive both the angle sum and angle difference identities for tangent. We will use the angle sum identities for SIN and COS derived in this video:
goo.gl/Uzp7bM
For my derivation of the angle difference identities for SIN and COS, check out this video:
goo.gl/4hM5ae
In this video I will derive both the angle sum and angle difference identities for tangent. We will use the angle sum identities for SIN and COS derived in this video:
goo.gl/Uzp7bM
For my derivation of the angle difference identities for SIN and COS, check out this video:
goo.gl/4hM5ae
![Explained: Supercritical Airfoil [Airplanes]](https://i.ytimg.com/vi/HfW5YTjnp8k/mqdefault.jpg "Explained: Supercritical Airfoil [Airplanes]
At transonic speeds, shocks waves form on the wings of an aircraft. Wave drag due to the presence of shocks can become a large portion of the overall drag on the aircraft. A supercritical airfoil can be used to delay the onset of shocks, and thus enable faster cruising speeds.
If you would like some more background on the subject, feel free to watch the following videos.
http://goo.gl/hCKHgf
http://goo.gl/iFxmXs
There are a couple things I want to mention briefly regarding drag. I mentioned the critical Mach number in the video, but neglected to include the drag divergence Mach number. Nothing particularly special happens at the critical Mach number. The shock wave or pressure wave that is formed is actually fairly weak because the flow doesn’t need to slow down too much through the shock wave. There is, however, a freestream Mach number at which the drag starts to suddenly increase quite a bit. This Mach number is the drag divergence Mach number, and is actually more important than the critical Mach number when designing planes. Wave drag occurs due to the presence of shock waves, and as the Mach number increases, wave drag also increases. If you’d like to read some more about the drag divergence Mach number, here are some references to get you started.
Modern Compressible Flow, John D. Anderson, pg. 345
http://en.wikipedia.org/wiki/Drag_divergence_Mach_number
http://www.adl.gatech.edu/research/extrovert/classes/hispd/hispd_notes06.pdf
http://adg.stanford.edu/aa241/drag/cdcintro.html
http://naca.central.cranfield.ac.uk/reports/1947/naca-tn-1396.pdf (pg. 6 under Drag Characteristics)")
![Explained: ASCII Art Creator [MATLAB]](https://i.ytimg.com/vi/Hvz-M73xFt4/mqdefault.jpg "Explained: ASCII Art Creator [MATLAB]
This video details the steps in writing a code that creates an ASCII image from a picture of your choosing. The code is written in MATLAB. The pixel values (0-255) are used to determine the ASCII character to substitute in the picture. The image can be resized in the code for easier viewing.
I use the text editor Notepad++ because it allows me to zoom on the picture. The code also contains a line that resizes the image to make it more manageable.
Here are some things to keep in mind.
1. More ASCII characters can be added to the code, but the intensity variable must also be changed.
2. The characters in the symbols variable are in order of decreasing darkness. That is, the first symbol in the array is the one that appears darkest in the final image, and the last symbol is the one that appears lightest.
3. I chose the resizing values (60 by 200) based on how the final text file fit in Notepad++ when I scrolled to the extent of the window. These values can be played around with and may be different on your computer. Another way to resize the image is to replace the [x,y] part of the imresize function inputs by a single number, for example 0.5. This will scale the picture to 50% of its original size.")
![Explained: Waitbar Color Change [MATLAB]](https://i.ytimg.com/vi/IjkajdAE8vA/mqdefault.jpg "Explained: Waitbar Color Change [MATLAB]
This video shows how you can change the color of your waitbar (progress bar) in your MATLAB code.
Basic waitbar video: http://www.youtube.com/watch?v=k2wKPxRUPiE")
![Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]](https://i.ytimg.com/vi/IxWJzwIG_gY/mqdefault.jpg "Vortex Panel Method: Tangential Velocity Geometric Integral [L(ij)]
We just finished the video for the source panel method (SPM), and saw its inherent limitations as we looked at some results for an airfoil. Now, to be able to code up the vortex panel method (VPM), we need to compute geometric integrals similar to those for the SPM. These geometric integrals come from the expressions for the normal and tangential velocity.
In this video, we derive the geometric integral from the tangential velocity expression (Lij). In the next video, we will derive the X and Y velocity expression geometric integrals needed for the streamline calculations, after which we can construct a system of equations to solve for the vortex panel strengths.
RELEVANT VIDEOS
► Panel Methods Playlist
https://www.youtube.com/watch?v=bWjo3N9COz4&list=PLxT-itJ3HGuUDVMuWKBxyoY8Dm9O9qstP
NOTES
- Ill 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
https://amzn.to/3emVuXU
► Foundations of Aerodynamics, Kuethe and Chow
https://amzn.to/2yMg1Vi
► Theory of Wing Sections, Abbott and Doenhoff
https://amzn.to/2wvZyUt")
![Explained: NACA 4-Digit GUI Part 5/10 [MATLAB]](https://i.ytimg.com/vi/J0L7N7cvk80/mqdefault.jpg "Explained: NACA 4-Digit GUI Part 5/10 [MATLAB]
This is the fifth video in my 10-video series on coding a program in MATLAB to compute, display, and save a NACA 4-digit airfoil.
IN THIS VIDEO:
We code the input for the angle of attack and save file name edit text boxes. The angle of attack text box needs to be converted to a number, while the file name text box can remain a string.
IN THIS SERIES:
Part 1/10 : https://goo.gl/9UBgbo
Part 2/10 : https://goo.gl/jRRcYJ
Part 3/10 : https://goo.gl/rSVLHo
Part 4/10 : https://goo.gl/HwHB39
Part 5/10 : https://goo.gl/AlDne8
Part 6/10 : https://goo.gl/7n1QP7
Part 7/10 : https://goo.gl/nTGleR
Part 8/10 : https://goo.gl/ez247P
Part 9/10 : https://goo.gl/8mXYcc
Part 10/10: https://goo.gl/ovBlbW")
![Explained: Ghost Nodes [CFD]](https://i.ytimg.com/vi/JMP9aanQ5o0/mqdefault.jpg "Explained: Ghost Nodes [CFD]
In some finite difference/volume equations, you might need to use points that are outside of the actual grid domain. In these cases, ghost nodes can be calculated from the interior points and used for the differences (such as a central difference on a boundary node).")
