Copyright © Thomas Fetter
I use Mathcad, as shown here, to build the model, as because it is a very visual programming language for mathematical modeling. Equations are written as they would be written on paper, so they are easy to read and understand, and the result of working in Mathcad is nicely self-documented. Mathcad solves equations numerically including numerical analysis of simultaneous nonlinear differential equations, which forms the core of the flight simulation model. Mathcad also has a symbolic equation solver which often comes in handy.
My works actually consists of many Mathcad models, each focused on a specific study of a rockest dynamic behavior. Many of these are works in progress. I will be adding these models here in the future.
To see a visualization of the model, go to the Flight Data Analysis page and scroll to the bottom of the page.
To document my work, I am (slowly) writing a paper to put everything together in a logical flow, a kind of Advanced Topics in Model Rocketry - Book 2. I will be publishing the chapters here as I complete them.
In 1999, I started studying my copy of Topics in Advanced Model Rocketry while recovering from knee surgery. I particularly enjoyed Gordon Mandell's chapter in Topics in Advanced Model Rocketry on dynamic stability, in part because it used modeling methods similar to what I used in my work as an electrical engineer for designing rf circuits. Each chapter Topics in Advanced Model Rocketry covers a different part of the analysis of a rocket flight, but never puts all the pieces together to build a complete flight trajectory model. So I started working on building a rocket flight simulation model focused on helping to understand the dynamic stability. The purpose of the simulator was to understand the dynamics of a rocket's flight. I put all the pieces together to build a complete 6 degree-of-freedom flight trajectory model. The model models both the trajectory of the rocket in three dimensions as well as the attitude (yaw, pitch, and roll) of the rocket.
The purpose of the model is to help me explore specific elements of a model rocket's flight trajectory. Topics have included understanding how stable rockets are, how far a rocket weathercocks, or turns into an oncoming wind, and how a long rocket transitions into a stable backward glide on descent.