Casual Introduction to Numerical Methods – spring-mass-damper system model – part#5

February 22, 2011

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). These input parameters are: mass, damping ratio, spring constant and time…


2D Projectile Motion Tutorial #7

February 20, 2011

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.


2D Projectile Motion Tutorial #6

February 19, 2011

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.


Near-Exponential VBA Conversion

February 18, 2011

The macro in this tutorial creates a near exponential variable conversion to be used for very large dynamic range input data entry . If for instance, we have to adjust a parameter from 1 to 1 million we can either make a spin button which can go from 1 to 1 million in unity steps (which would take for ever), or implement an exponential scheme. We would like an exponential series of powers of…


2D Projectile Motion Tutorial #5

February 17, 2011

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).


Easy Zoom – Chart Axis Scaling Using VBA

February 15, 2011

In certain models we need to be able to change the scale of the chart axes function of the result of a simulation. Excel charts do have auto-scaling as a default option but sometimes the scaling values we get are not what we need. Another reason against using auto-scaling is that during the time the model runs, the scale self-adjusts and it gives an ever changing, distorted view of the results….


2D Projectile Motion Tutorial #4

February 14, 2011

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.


2D Projectile Motion Tutorial #3

February 13, 2011

Now that we have a simple animated projectile motion (previous tutorial) let’s try to add on the chart the three instantaneous speed vectors associated with the projectile. These speed vectors are: the horizontal speed, vertical speed and the total speed vector. The model works in all Excel versions but in 2007 it’s painfully slow.


2D Projectile Motion Tutorial #2

February 12, 2011

This part of the tutorial shows you how to animate the model created in the first part. Since it is addressed to beginners, this part of the tutorial will show you in detail how to create buttons and the associated macros for the input data interface and it will also show you how to animate the flight of the projectile and explain the VBA macro behind the animation.


Creating a Speedometer in Excel, Part #2 – tutorial

February 11, 2011

The previous tutorial (first half) explained how to download a speedometer picture from and how to alter it (delete the needle) using a freeware called Gimp (similar to Photoshop). – The model replaces the deleted needle from the picture with a moving one created from a chart line. – This second half of the tutorial explains the geometry, trigonometry and VBA code used to build a new rotating speedometer…


Creating a Speedometer in Excel, Part #1 – tutorial

February 10, 2011

This is the first half of a tutorial which shows how to create a speedometer in Excel. The model is essentially a 2D scatter chart having as background the picture of a speedometer dial downloaded from Before using the photograph you need to erase the arm of the speedometer from the picture using Photoshop or other photo editing software. In the model I replaced the deleted arm with a moving arm created from…


A Family of Speedometers in Excel

February 9, 2011

Hi guys, by popular demand, this is a file containing five different animated speedometers and a tachometer (rpm-meter). I can recognize two models: a Toyota Camry and a Ford Crown Victoria. They work great. The rest I am not sure what they are, I would appreciate if you tell me. Just leave a comment. The model works in all versions of Excel. Cheers, George


2D Projectile Motion Tutorial #1

February 7, 2011

This part of the tutorial will show you how to create the simplest possible projectile motion model using standard kinematic formulas from the first year of high school. The variable parameters of the model will be: initial height, initial speed and initial angle and time step. “g” – the gravitational constant will be set at 9.81 m/s^2. This model is a static one and it will be animated in the following…