Copyright © Thomas Fetter
2014-2025
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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 work 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 papers here describing this work as I complete them.

To see a visualization of the model, go to the Flight Data Analysis page and scroll to the bottom of the page.


This paper on Rotational Dynamic Stability was first presented at the R&D event at NARCON-2024.  The paper addresses the question of why rockets are so stable, and examines the conventional wisdom of stability margin.

Click here to download the complete paper.


A video of the R&D presentations is available on YouTube at 
NARCON-2024 R&D Oral Presentations .   The Rotational Dynamic Stability presentation starts at time 1:04:40.

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 - ultimately to aid in designing an active vertical trajectory system (VTS), a project I started in 2022 and will document here as well.  I put all the pieces together to build a complete 6 degree-of-freedom flight trajectory model.  The  model covers both the trajectory of the rocket in three dimensions as well as the attitude (yaw, pitch, and roll) of the rocket.

Along the way, I ran into questions that have resulted in a number of side investigations    Topics have included rotational dynamic stability and why rockets are so stable, how far a rocket turns into the wind, and understanding the mechanisms of coning.  I have written papers to document some of this work, and they are available below.  I will continue to make these papers available here as I complete them.


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This paper on Linear Systems and Control Systems Overview is a short overview of the mathematical tools and methods that are used throughout the papers by this author on the topics of rocket rotational dynamic stability, rocket trajectory analysis, and vertical trajectory control systems.  This paper is intended as a brief introduction for someone new to these topics, or as a quick review for someone who has studied these topics.  By showing the context of how these concepts are useful in modeling real systems, the intension is to provide the motivation to study these topics further for someone not familiar with them. 

Click here to download the complete paper.


This paper on How Far Does a Rocket Turn Into the Wind looks at the magnitude of the angle of a rocket's rotation in response to the step in wind velocity as a rocket leaves the launch guide.  It also looks at whether being "overstable" is a significant factor in how far a rocket turns into the wind.  This paper was given as a presentation session at NARCON-2024.

Click here to download the complete paper.



You can hear my interview about why rockets turn into the wind on episode 131 of The Rocketry Show