Modeling
A model is a set of equations or computer code that describes the flight of the rocket. The forces and torques in a rocket model come from gravity, thrust, lift, and drag. Models are classified as 1-D, 2-D, or 3-D models. A 1-D model assumes that the rocket flies straight up and falls under parachute straight down. A 2-D (or 3 DoF) model assumes that the rocket can travel vertically and horizontally, and rotate in the 2-D plane of motion. A 3-D (or 6 DoF) model assumes that the rocket can travel in 3-D space and rotate about any of its three principal axes. The required modeling in E178 is:
Develop or prove an analytic 1-D model with constant thrust during motor burning, and a constant coefficient of drag during the flight. Learn to use a 2-D (3 DoF) open source program called Open Rocket to model and predict rocket behavior. Use this code for all three rockets you will construct. Develop and/or use a 1-D code to permit calculation of 𝐶𝐷 and thrust curves from flight data.
1-D models
- Analytical with constant thrust and constant drag coefficient.
- Analytical with multiple constant thrusts and constant drag coefficient
- Runge-Kutta with thrust curve and constant drag coefficient
- Numerical integration of accelerometer data
There are two reasons for creating models of rocket flight
- Predict performance of a rocket with a given motor.
- Fit data from a flight to determine parameters such as \(C_D\) or thrust curve.
We have multiple packages that we’ll use for modeling. The general packages are:
- LibreOffice or other spreadsheet
- Python
The rocket-specific packages are:
Other packages we’ll use:
Analytical with Constant Thrust and Constant Drag Coefficient
This is the simplest model that does a good job of describing a rocket flight up to ejection and is useful for processing data to determine total impulse, total burn time, and an average C~D. This model assumes that the motor thrust is constant at the average level for the motor burn time. For example looking up the Estes C6 motor on ThrustCurve.org shows a total impulse of 8.8 Ns and a total burn time of 1.9 s. The motor would be modeled as generating a constant thrust of 8.8 Ns/1.9 s = 4.63 N for 1.9 s. Notice the listed average thrust is 4.7 N, which is close to the value we would specify, but not exactly the same. Which is correct? That would depend on what you think is correct.
3 3-D models