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. [sociallocker][/sociallocker] Introduction to Geometrical Optics – a 2D ray… Read More... "Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 4"

This category hosts engineering animated models in MS Excel. Excel is particularly valuable in engineering being inexpensive and ubiquitous. In my career I managed to solve difficult engineering problems by building animated simulations where engineers using other, much more expensive software, failed. Unlike dedicated engineering software, excel is not a “black box”, which means that you develop your models from scratch using basic principles, calculations and charting. This leads to a much better understanding and control of the problem.

Excel is a great software for engineering calculations because it can combine data tables, charts and even engineering formulas under the same application.As far as civil engineering is concerned, Excel can do regular calculations such as cost estimates, schedule and cost control, and markup estimation, as well as structural calculations of reactions, stresses, strains, deflections, and slopes. Excel can deal with difficult problems, charting, and report generation.

## 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 basic… Read More... "Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 3"

## 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… Read More... "Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 2"

## Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 1

This is a first post of an introduction to optics series and it explain how to create a 2D ray tracing model for a spherical mirror. This section deals with the creation and charting of the mirror using a parametric equation for a circle. [sociallocker][/sociallocker] Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 1… Read More... "Introduction to Geometrical Optics – a 2D ray tracing Excel model for spherical mirrors – Part 1"

## Spectral Analysis – a Fourier transform tutorial – part #5

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 that… Read More... "Spectral Analysis – a Fourier transform tutorial – part #5"

## Spectral Analysis – a Fourier transform tutorial – part #4

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 of… Read More... "Spectral Analysis – a Fourier transform tutorial – part #4"

## Spectral Analysis – a Fourier transform tutorial – part #3

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 about… Read More... "Spectral Analysis – a Fourier transform tutorial – part #3"

## Spectral Analysis – a Fourier transform tutorial – part #2

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 is… Read More... "Spectral Analysis – a Fourier transform tutorial – part #2"

## Spectral Analysis – a Fourier transform tutorial – part #1

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 real… Read More... "Spectral Analysis – a Fourier transform tutorial – part #1"

## The Melting Snow Castle – a diffusion model application

This is an application to the previously derived 2D diffusion (heat transfer) model. The snow melting process is very similar to diffusion or heat transfer. Just open the model and hit “Start-Pause” to see for yourself. It is a 2003 model or earlier. I wasn’t able to run it in 2007 with animation but I’ve got some friends who managed to run… Read More... "The Melting Snow Castle – a diffusion model application"

## Building a Dynamic Two Dimensional Heat Transfer Model – part #2

This is the second half of the tutorial which shows how to build a basic animated 2D heat transfer model in Excel. [sociallocker][/sociallocker] Building a Dynamic Two Dimensional Heat Transfer Model – part #2 by George Lungu – This is the second half of a tutorial which shows how to build a basic dynamic heat conduction model of a square… Read More... "Building a Dynamic Two Dimensional Heat Transfer Model – part #2"

## Building a Dynamic Two Dimensional Heat Transfer Model – part #1

Here is the first part of a tutorial which shows how to build a two dimensional heat transfer model in Excel. The presentation shows how to partition a square plate in elementary elements on which the simplest form of the heat storage and heat transfer equations can be applied. The numerical form of the final temperature formula is derived . Building… Read More... "Building a Dynamic Two Dimensional Heat Transfer Model – part #1"

## A Basic 2D Animated Heat Transfer Model (a diffusion model too)

Here is a basic 2D heat transfer model. The first five worksheets model square plates of 30 x 30 elements. The last worksheet is the model of a 50 x 50 plate. You can modify the initial temperature by hand within the range C21:AF240. It is also a diffusion model. It uses the storage and transport equations derived in the previous tutorials.… Read More... "A Basic 2D Animated Heat Transfer Model (a diffusion model too)"

## Animated Heat Transfer Modeling for the Average Joe – part #4

This is the last tutorial of the series and it shows how to implement the previously derived formulas into a spreadsheet model. The spreadsheet formulas, the macros and charting of the dynamic data is explained. [sociallocker][/sociallocker] Animated heat transfer modeling for the average Joe – part #4 by George Lungu – This is the last section of the beginner series… Read More... "Animated Heat Transfer Modeling for the Average Joe – part #4"