Modeling and Simulation Learning Goals
- Methods: Translate the physics equations that describe particle motion into functional Matlab code
- Results and Discussion: Verify your simulation using measurements from your parachute prototype, with data collected using the Tracker software; if measurements do not match up to simulation, determine what went wrong and make adjustments accordingly
- Results and Discussion: Apply the simulation to predict future performance for an actual person using parachute, choosing appropriate parameters to produce a safe landing

Matlab learning goals
- Use arrays to collect data for y and Vy vs t
- Plot real and measured data on a single axis
- Understand use of while loop vs for loop
- Read data from spreadsheet into Matlab arrays

In my class, this assignment takes place 5 weeks into the semester in an introductory engineering class. There are no pre-requisites for the class and many students enter the class with no previous programming experience. Prior to this assignment, they completed the MATLAB Onramp and one other simulation assignment.

This is first presented to students in class, and then they work on it independently.

This is given as a homework assignment, and students have 2 weeks to complete it. In week 1, students obtain physical measurements that will be used to validate the simulation. In week two, students will develop the simulation, validate it by comparing simulation results to the measured data from week 1, and then determine the parameters for a real life parachute with a human connected to it.

This simulation requires the implementation of some principles of physics, but we provide students with the equations for determining velocity and acceleration of a falling object, including drag. When students work on this project, their prior programming experience ranges from virtually none to extensive.

Students submit their completed MATLAB live script (mlx file) and a report.

The goal for this assignment is to determine a "safe" terminal velocity for a skydiver so that they don't get hurt when landing on the ground. They need to choose a diameter that is large enough to produce a safe terminal velocity, but not so large that it would be unwieldy and heavy. It is up to the student to do some research and determine what is a safe velocity, and what is a reasonable size parachute.

In order to validate the model, students make a grocery bag parachute model: a plastic grocery bag (the parachute) with a binder clip (the person) hanging from it. Students take a video as they drop it from a height of 2-3m. They import this video into the open source Tracker program to obtain y-position and y-velocity data. The simulation results are then compared to these measurements. Once the model is validated, then students can use the model to simulate a skydiver with a realistic parachute.

Slides for classes #1-#3 (PowerPoint bytes Oct8 25)
Assignment and template for simulation report (Microsoft Word 2007 (.docx) 20kB Nov9 25) 
Matlab live script (MATLAB Live Script 199kB Nov9 25) 
Grading rubric (Microsoft Word 2007 (.docx) 19kB Oct8 25) 
Report instructions (Microsoft Word 2007 (.docx) 93kB Oct8 25)
Parachute worksheet.docx (Microsoft Word 2007 (.docx) 27kB Nov9 25)

Students have a ton of fun on the day when they make the grocery bag parachutes, take some measurements, and record a video of it dropping from a few meters high! It's a great activity. Because my class is up to 70 students, I have them do this in groups of 4. If you have a smaller class, this could be an individual activity. Aside from the plastic grocery bags and binder clips (1 for each group of students), you'll need to have some tape measures and at least one scale in the classroom. This activity takes about 30 minutes.

I'm always amazed that these measurements from the grocery bag parachutes are pretty accurate compared to the simulation! This is true even though the measurements are far from precise, and we make a number of approximations and assumptions in the simulation. It's a great example of a real-world problem.

The biggest challenges for the students are using arrays in MATLAB, especially for students who are new to programming. I give them time to work on this during class so that they can help each other and get feedback from myself and from TAs. There are also some challenges using the Tracker software. This is free software and sometimes it shows! There is little support or documentation online but some helpful tutorial videos. Also, I made a tutorial video of myself using the Tracker software and share it with students via our Canvas site.

The grade for this assignment is 50% based on the live script, and 50% based on the report. See attached rubric for more information.

Tracker software: https://opensourcephysics.github.io/tracker-website/