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. AerodynamicsContinue Reading

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).Continue Reading

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,Continue Reading

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 atContinue Reading

This part of the tutorial demonstrates the Fourier transform operation in a few cases of periodic and non-periodic signals, such as an AM signal, an FM signal, a rectangular non repetitive signal and a cardinal sine signal. The last slide contains an application to the scaling property of the Fourier transform on a non-repetitive time signal. It actually shows thatContinue Reading

The previous sections explains the creation of a discrete Fourier transform model in Excel. This section and the following one will use the model to calculate and chart the Fourier transform in several cases of periodic and non-periodic signals. [sociallocker][/sociallocker] A Fourier Transform Model in Excel, part #4 by George Lungu – This is a tutorial about the implementation ofContinue Reading

The previous sections of the tutorial handled the basic formulas behind building a Fourier model and creating a set of input functions. This section deals with formula implementation on the spreadsheet, the brief VBA code and the charting of the Fourier transform components. [sociallocker][/sociallocker] A Fourier Transform Model in Excel #3 by George Lungu – This is a tutorial aboutContinue Reading

In this tutorial the Excel implementation of a Fourier transform is discussed. Seven input signals are created among which sinusoidal, rectangular and combinations of them. A Dirac impulse, an amplitude modulated (AM) signal and a frequency modulated (FM) signal are also added among the input signal options. [sociallocker][/sociallocker] A Fourier Transform Model in Excel #2 by George Lungu – This isContinue Reading

This is a basic tutorial about implementation of a standard Fourier transform model in Excel. It is not an introduction to Fourier analysis. You could choose to familiarize yourself with the subject before proceeding with this tutorial. Solving a few Fourier transform excersises would be of help too. Essentially, this part shows you how to adapt the general Fourier formula for a continuous realContinue Reading

In this tutorial, most of the calculations for the numerical simulation a SMD (spring-mas-damper) system will be consolidated into a single formula, the coordinate formula. In this case, in order to calculate the coordinate at the end of a any time step, we will need just the coordinates from the previous two time steps and of course the input parameters (constants). TheseContinue Reading

This tutorial explains the principles to generating animation for the spring-mass-damper system analyzed in the previous presentations. [sociallocker][/sociallocker] A casual approach to numerical modeling – part #4 – a Spring-Mass-Damper-System – creating the animation by George Lungu – We are trying to generate animation for the system sketched above knowing the deviation from the equilibrium function of time. This deviation isContinue Reading

In the this tutorial, after we got most of the trajectory calculation concentrated in just two columns, we will write a custom VBA function (dual output) to replace the spreadsheet computations used. This process of  starting with very simple models, then refining the calculations and then learning how to write custom functions for those calculations will be extremely useful later for developing more complex models. [sociallocker][/sociallocker]Continue Reading

This tutorial simplifies the previous model and manages to describe the (x,y) flight coordinates using just two formulas placed on columns D and E. A custom VBA trajectory function will be introduced in the next section which preserves the effects of gravity and aerodynamic drag. [sociallocker][/sociallocker] Projectile Motion Tutorial #5 by George Lungu – a 2D projectile motion model of projectile dynamics includingContinue Reading

This is the next in a series of projectile motion tutorials for creating 2D trajectory models using numerical analysis of projectile dynamics (including aerodynamic drag). The trajectory formulas were derived in the previous tutorial. This post describes the Excel implementation (spreadsheet formulas, VBA code, buttons and charts). [sociallocker][/sociallocker] Projectile Motion Tutorial #5 – a 2D projectile motion model using numerical analysis of projectile dynamics (including aerodynamic drag)Continue Reading

This tutorial derives the formulas of a projectile model taking into account the aerodynamic drag. A finite differences numerical method is used. Though fairly easy to apply and understand, this type of methods can solve much more complex problems than the high-school type approach shown in the previous tutorials. An Excel model will be implemented in the next section. Projectile MotionContinue Reading