#### Moment of Force and Torque Calculation

This is an addition to a previous post, introducing the reader to different ways of calculating the moment of a force and the torque of a couple. This information will be useful in aircraft dynamics models.

#### Longitudinal Aircraft Dynamics #5 – finishing the aircraft

This section finalizes the aircraft (glider) by inserting the wing, the horizontal stabilizer and a center of gravity (CG) sprite in the layout.

#### Newton Generalized Treatment

Most of people have heard of Newton’s second law, mass, moment of inertia or the definition of the acceleration both linear and angular. The stuff presented here is elementary (9th grade), yet it is generally not properly understood. What happens when one applies a bunch arbitrary forces on an arbirtarily shaped body?  The resultant force vector produces a linear acceleration while the resultant torque produces a resultant angular acceleration around…

#### Longitudinal Aircraft Dynamics #4 – virtual aircraft definition

This section of the tutorial explains how to create the  2D aircraft components for the animated longitudinal stability model. The first part deals with extracting the x-y coordinates for the fuselage, canopy, vertical stabilizer and rudder. The second part handles the main wing airfoil and the horizontal stabilizer airfoil. All thses parts will be put together in the next section.

#### Longitudinal Aircraft Dynamics #3 – layout parameters and wireframe fuselage generation

This section discusses the layout of the virtual plane and provides for the worksheet implementation of the plane dimensions as input parameters controlled by spin buttons and macros. In the final part a freeform is used to generate raw data for the fuselage.

#### Longitudinal Aircraft Dynamics #2 – 2D polynomial interpolation of parameters cl, cd and cm

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 number range. We need to do this since we simulated…

#### Longitudinal Aircraft Dynamics #1 – using Xflr5 to model the main wing, the horizontal stabilizer and extracting the polynomial trendlines for cl, cd and cm

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 the aero modeling and the 4th and 5th order polynomial extraction.

#### Aerodynamics Naive #3 – a brief introduction to Xflr5, a virtual wind tunnel

The previous section implemented and charted the ping-pong polar diagrams in a spreadsheet and showed a reasonble similarity, for moderate angles of attack, between these diagrams and the ones modeled using Xflr5, a virtual wind tunner. This section introduce the  concept Reynolds number and it also contains a very brief introduction to Xflr5, the free virtual wind tunnel software.

#### Aerodynamics Naive #2 – spreadsheet implementation of the Ping-Pong polar diagrams

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).

#### Aerodynamics Naive #1 – deriving the Ping-Pong airfoil 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, symmetric airfoil. The model of course cannot possibly calculate anything related…

#### How Do They Fly? – an intuitive look into lift generation and flight stability

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 the back of a Cessna can make the plane unstable……

#### VertX – a Very Useful Macro for Extracting the Vertex Coordinates of Freeforms – part #2

The first macro created in this section of the tutorial improves on the previously developed macro by correcting the up-down orientation of the shape, referencing the shape position to the coordinate of the first drawn point and closing the shape by repeating the coordinates of the first point at the end of the table. A last macro is then created which can retrieve multiple shape vertex coordinates, placing them in a table…

#### VertX – a Very Useful Macro for Extracting the Vertex Coordinates of Freeforms – part #1

Using autoshape freeforms is a very easy way to duplicate object outlines from pictures. It is convenient to create a freeform and once created, its vertices (points) can be edited with without difficulty.  Aditional points can be inserted and others can be deleted. This is a tutorial about a series of macros which allow the extraction of freeform vertex coordiantes to a worksheet range in Excel. These coordinates can be later employed to create 3D wireframe…

#### Excel Drawing – creating graphical object data

This tutorial will introduce the reader to creating simple drawings in Excel by using the “Freeform” auto shape. Later on, we will be able to convert this data in x-y-z vertex information for various models by using a macro.

#### Anaglyph Charts Demo #2- an animated heat transfer model using a red-cyan wireframe chart

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 hit “Start / Pause” and manually adjust the pitch and…

#### Anaglyph Charts Demo #1- creating 3D effects on charts using red-cyan elementary chips (sprites)

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 find the 3D effect to be decent but not good enough…

#### Introduction to Anaglyph Stereoscopy in Excel – part #5: adding a joystick to control the yaw and pitch rates of the 3D cube

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 running the mkodel.

#### Cosmos Naive – a very basic demo of anaglyph stereoscopy with sprites in Excel

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 excelent example of anaglyph stereoscopy in action showing you how it’s built. The farther the red and cyan (turquoise)…

#### Introduction to Anaglyph Stereoscopy in Excel – part #4: worksheet implementation of a stereoscopic cube

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. 0

#### Introduction to Anaglyph Stereoscopy in Excel – part #3: a few analogies and the derivation of the stereoscopic 3D-2D perspective conversion formulas

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.