#### 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…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 7

Based on the formulas derived up to this point in the series, this section creates an improved custom VBA function which calculates the x-y Cartesian coordinates of three points: the incident point, the terminal point of the real reflected ray and the terminal point of the virtual reflected ray. The structure of the  function is fairly simple and it is very easy to use too. The model is upgraded using the…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 6

This section simplifies the formula for the Cartesian coordinates of the terminal point of the reflected ray and derives a very similar formula for a terminal point of the virtual reflected ray. In the next section all these new formulas together with some old formulas will be combined into a new user defined VBA function which will be used alone to trace the incident, the reflected and the virtual reflected…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 5

This brief section takes the two previously created custom VBA functions (Reflect() and Chart_Reflect()) and use them to create the data for both the incident and the reflected bundles of rays within the same table. The data is then plotted on the same chart with the mirror and the result is a preliminary model which you can experiment with.

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 4

This section begins by charting the incident rays on the same 2D acatter chart with the mirror and then explains how to derive the Cartesian coordinates for a “final” point which together with the point of incidence will define the reflected ray. A custom VBA function is created for this purpose.

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 3

This section explains explains how to implement the formulas that define the emergent (reflected) rays into a custom VBA function. Though geometrically the last two presentation might look a little  elaborate, just be patient and follow the presentation, or even better try to just sneak peek and do it yourself. All this derivation is done based on first principles and some Mickey Mouse geometry. Take all the time you need, a day, a week…

#### Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 2

This section explains the illumination setup by using an artificial star, derives the equations of the incident rays and also solves the system of equations for finding the exact coordinates of the points where the incident rays hit the mirror. Looking at the sign of the determinant of a quadratic equation involved in finding the intersection between an incoming ray and the mirror we can say if the ray hits…