# drag

#### Longitudinal Aircraft Dynamics #6 – worksheet implementation of the dynamics equations (a)

In this section, the parameters cl, cd and cm are scaled back to the force of lift, drag and the pitching moment of the aircraft. After that, the numerical modeling scheme is described together with the macros behind it. At the end, the formulas for the angles of attack of the wing and the horizontal stabilizer are introduced.

#### 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…

#### 2D Projectile Motion Model #1 – a virtual tactical shooting range

Hi Folks, As a kid was fascinated with high power rifles, sniper rifles, cannons and in general, fast projectiles. As a kid I’ve been brainwashed with all sorts of urban legends about how far an AK 47 or a pistol can shoot or how thick a steel metal plate a bullet can penetrate at various distances. I’ve also watched some documentary about snipers and there were talking about highly bent trajectories, how…