In the previous section, the main wing airfoil and the horizontal stabilizer airfoil were simulated using Xflr5. The three coefficients, lift, drag and moment were then interpolated on charts in Excel using 4th and 5th order polynomials. This section shows a few tricks about how to easily introduce those 60 equations as spreadsheet formulas in Excel ranges. It also presents a simple linear interpolation method across the Reynolds… Read More... "Longitudinal Aircraft Dynamics #2 – 2D polynomial interpolation of parameters cl, cd and cm"
This section is dedicated to modeling science in Excel 2003 standard.
This is a tutorial about using a free aerodynamic modeling package (Xflr5) to simulate two airfoils in 2D (the main wing and the horizontal stabilizer) for ten different Reynolds numbers, then using Excel to extract the approximate polynomial equations of those curves (cl, cd and cm) and based on them, simulate a 2D aircraft as an animated model. This section deals with… Read More... "Longitudinal Aircraft Dynamics #1 – using Xflr5 to model the main wing, the horizontal stabilizer and extracting the polynomial trendlines for cl, cd and cm"
The previous section implemented and charted the ping-pong polar diagrams in a spreadsheet and showed a reasonable similarity, for moderate angles of attack, between these diagrams and the ones modeled using Xflr5, a virtual wind tunnel. This section introduce the concept Reynolds number and it also contains a very brief introduction to Xflr5, the free virtual wind tunnel software. Aerodynamics… Read More... "Aerodynamics Naive #3 – a brief introduction to Xflr5, a virtual wind tunnel"
This section of the tutorial implements the lift and drag formulas in a worksheet, creating and charting the polar diagrams for an ultra simplified ping-pong model of an airfoil. Comparing these diagrams with ones obtained by using a virtual wind tunnel (XFLR5) we can see a decent resemblance for moderate angles of attack (smaller than about 8 degrees in absolute value).… Read More... "Aerodynamics Naive #2 – spreadsheet implementation of the Ping-Pong polar diagrams"
This is the ping-pong aerodynamic analogy. The wing is a ping pong bat and the air is a bunch of evenly spaced array of ping pong balls. It is a naive model but, as we will see in a later post, the polar diagrams derived from this analogy (between -12 to +12 degrees of angle of attack) are surprisingly close shape wise to the real diagrams of a thin,… Read More... "Aerodynamics Naive #1 – deriving the Ping-Pong airfoil polar diagrams"
Have you ever wondered why the flight attendants of a half empty airliner talk people into moving to the front half of the plane? Have you ever wondered why a flying wing can fly without a tail or why the stability of some of these flying wing can be controlled only by computer? Or why a 12 pack stored in at… Read More... "How Do They Fly? – an intuitive look into lift generation and flight stability"
This is another basic demo investigating the feasibility of using anaglyph wireframes to plot scientiffic data. Open the attached worksheet and with your 3D glasses on, watch the chart. The data is a dynamic temperature map obtained from a 2D heat transfer model in a metal plate. The heat model is complete and you can run it with various parameters. You can… Read More... "Anaglyph Charts Demo #2- an animated heat transfer model using a red-cyan wireframe chart"
This is a basic demo investigating the feasibility of using anaglyph sprites to plot scientiffic data. Open the attached worksheet and with your 3D glasses on, watch the chart. The data results are various temperature maps obtained from a 2D heat transfer model in a metal plate. You have 4 different selectable mapps there but you can also invert the pattern using the “Flip” button. I… Read More... "Anaglyph Charts Demo #1- creating 3D effects on charts using red-cyan elementary chips (sprites)"
In this section, a joystick is added to the model which controlls the yaw rate and the pitch rate (not the angles!) of the stereoscopic cube. This joystick was used before in a dedicated tutorial and in the flight simulator tutorial. Its importance in future models can not be underestimated, hence I decided to cover this virtual device again. Use your 3D glasses while… Read More... "Introduction to Anaglyph Stereoscopy in Excel – part #5: adding a joystick to control the yaw and pitch rates of the 3D cube"
Reach out for your 3D goggles because this is a representation of the Cosmos through the eyes of a 5-year old. The model displays a few objects at various depths and move two of them back and forth on a chart to demonstrate the stereoscopic effect. Though very simplistic it is an excellent example of anaglyph stereoscopy in action showing you… Read More... "Cosmos Naive – a very basic demo of anaglyph stereoscopy with sprites in Excel"
This is the final part of the anaglyph stereoscopy tutorial. This part deals with the prectical implementation of the concepts and formulas discussed before to create a 3D cube. You need 3D glasses to notice the stereoscopic effect. The PDF erroneously claims this is part #3 of the tutorial, whereas this is actually part #4 (it’s a typo in the… Read More... "Introduction to Anaglyph Stereoscopy in Excel – part #4: worksheet implementation of a stereoscopic cube"
This section of the tutorial gives few more real life applications of the stereoscopic vision and also derives the stereoscopic 3D-2D perspective conversion formulas. These formulas are based on the approximation that the that both right and left eyes observe the same v-coordinate. Excel anaglyph stereoscopy #3 – 3D-2D perspective conversion formulas by George Lungu – While the previous section introduced the… Read More... "Introduction to Anaglyph Stereoscopy in Excel – part #3: a few analogies and the derivation of the stereoscopic 3D-2D perspective conversion formulas"
This tutorial explains the basic principles of creating and displaying anaglyph pictures. Excel anaglyph stereoscopy #2 – how to split the image by George Lungu – The previous section showed an improvement in the practical implementation of spreadsheet multiplication, namely based on the associativity of matrix multiplication the three elementary rotation matrices were combined in a composite rotation matrix which… Read More... "Introduction to Anaglyph Stereoscopy in Excel – part #2: the principles of creating and viewing 3D pictures"
This is a demonstrative model for 2D spherical mirror ray tracing in Excel displaying both the real reflected rays and the virtual reflected rays. You you have the option of turning the visibility of the virtual rays off if you wish. It works in Excel 2003 at about 40 frames per second and in Excel 2007 at about 4 frames per second.… Read More... "A 2D Demo for Spherical Mirrors in Excel – with virtual reflected rays"