# Computational Deployment: Simulating A Rocket

The model rocket project has long been a favorite at the Academy. For the past fifteen years, students have designed, fabricated and then launched model rockets as the first project of the program. Over the years, I have tweaked the project several times, each time finding new ways to introduce authentic analysis in the process.

This year I have taken a deep dive into computational modeling, and as part of the rocket project, students were asked to create a simulation of their rocket prior to launch. In this post I will discuss how I did this, and how it turned out.

## Simulating The Momentum Principle:

Prior to getting started on this, students investigated the causal relationship between forces and changes in motion. Using force sensors, carts, weights and elastic cords of different lengths, students began building a qualitative and quantitative model relating the momentum of a particle to the forces acting on the particle.

In previous years, I waited to introduce momentum until after a significant amount of time was spent on forces, balanced and unbalanced. This year I decided to go directly to momentum. This is a bit of a break from the established modeling instruction sequence, but I think its a good alternative that is also suggested by the great textbook Matter and Interactions. The momentum principle can easily be modeled computationally and I think the students are able to grasp it conceptually.

I have included a link to a Google Doc that is the introductory activity that I created. My approach here, as it has been with this entire unit is to give the students guided questions that allow the students to discover and investigate the code required to simulate the momentum principle. This is my first attempt, and I am sure it will undergo many revisions:

Simulating The Momentum Principle

## Introducing Conditional Behavior

One of the really great things about building a simulation of a rocket has three distinct phases of its trajectory – the thrust phase, the cruise phase and the descent phase. This gives the students three different phenomena to study and simulate: positive acceleration when two unbalanced forces are acting on the rocket during the thrust phase, free fall when the fuel runs out, and then constant velocity when the parachute has been deployed.

In order to simulate this, students needed a way to change the forces acting on the rocket at different time intervals. This is done using a conditional statement:

If This Then That

Conditional statements are very easy to create in Tychos – but they work a bit differently from other programming interfaces. Here is an example:

```# The thrust force - F (thrust, rocket, fuel)
Ftrf = if (t < 1.8, [0, 6], [0, 0])```

In this code snippet, a force is given a different value based on a condition, in this case whether the time in the simulation is less than 1.8 seconds. If it is, then the force is given a positive 6 value in the Y direction, and if the time is greater than 1.8 seconds, then the force becomes zero.

This allows the students to simulate the thrust phase of the rocket by having the thrust force disappear once the fuel has run out. We conducted tests on Estes C6-5 rocket engines in order to establish the time value. You can read more about how we did this here.

The students did the same thing to figure out when the parachute should deploy. Again this was established based on information from Estes as well as our own tests.

## Comparing Simulation Data to Real Data

The students could analyze the simulated rocket behavior by using the graphing tools in Tychos. The students graphed the vertical velocity as well as the vertical position of their simulated rockets. Here is an example of what those graphs look like:

The last step of the process was for the students to compare their simulated data to the real data that was captured by the altimeter that we use in the rocket’s payload. Below are two images of the graphs of the data they retrieved from the rocket’s altimeter:

velocity data from altimeter – imported into LoggerPro

altitude data from altimeter – imported into LoggerPro

The shapes of the graphs from the simulated data and the real data are very similar! That was certainly exciting to see that the simulations were at least giving results that qualitatively matched the real behavior of the rockets.

Two factors that certainly created significant discrepancies between the real rockets and the simulated rockets was the existence of air resistance on the real rocket, and the fact that the real rockets didn’t always go perfectly straight up! We plan on modifying the simulations, but that will have to wait for a future post.

# Simulating Circular Motion: An Inquiry Approach

This semester I have been very busy working on a new approach to teaching Physics. This has actually been part of an effort that has spanned more than three years, but this year I have really embraced this change and I have much to share.

This post is a preview of many to come. I am going to write several posts documenting my efforts and experiences throughout the school year. Hopefully these posts will help me capture what I have learned in the process, and perhaps will be a guide for anyone else who might be interested.

## Analytical Models Emerge From Computational Models

With the help and insights of others, I have been mapping out a new scope and sequence for teaching Physics that incorporates computational modeling as the primary method of modeling Physics. Rather than looking at computational modeling as an “add on”, I have been exploring the idea that analytical models are emergent. Computational models are more fundamental and analytical models emerge from those computational models.

The basic approach here has been to start with computational modeling, and then to allow the students to discover the analytical models that are revealed. This has been an exciting “unveiling” of physical patterns for the students. The other thing that I have witnessed is that students seem to intuit the principles of Calculus, even though my students are not at that level in mathematics training. More on this in a future post.

In future posts, I will report out on how this has been going and what I have learned in the process. For now, I simply want to share an example.

## The Inquiry Lessons: Discovering Centripetal Acceleration

One of the aspects of this project has been to re-invent many of my lessons. I have been creating inquiry based lessons based on an approach known as POGIL. I am not POGIL trained, so I wouldn’t say my activities are actual POGIL activities – they are POGIL “inspired”.

In the first lesson, students learned how to simulate an object moving in a circular path. I have attempted to incorporate an inquiry approach where students are guided using questions, as opposed to holding their hands. This approach can be messy, but I have found it has always lead to great conversations, unanticipated insights from the students and it gives the students a sense of discovery.

I have included a link to the lesson which you are free to copy, modify, etc. without any restrictions.

Lesson 1: Simulating Spinning Motion

Keep in mind that my students had already learned how to code movement, so if you are new to computational modeling, I will soon be writing some posts that introduce students to this approach and to computational modeling in general.

In the second lesson, students simulated circular motion using angular quantities. They then explored how they could represent the tangential velocity and then they explored what the acceleration was. This led them to discover that the simulation revealed that the acceleration vector pointed to the center of the circle. Through some guided inquiry, they discovered a number of interesting details, such as the acceleration increased when the radius declined, and that the tangential speed had a significant affect on the acceleration.

Here is a link to the lesson:

Lesson 2: Circular Motion

I do use a tool, that I am actually partly developing with some friends as the simulation software, called Tychos, but you can modify the lesson to use any coding platform you like (of course I like Tychos, but I am a bit biased!)

Please feel free to comment here to give me feedback on the lessons if you feel inclined. I am certainly on a learning path myself, and I am sure there are many improvements that could be made!

Thanks in advance,

Steve.

# Recruiting the Girls.

This post was written by Johnie Lee Fain, a recent graduate of San Rafael High School and the Academy. She is currently planning on studying computer science at Villanova University

I spent three years of my high school career in the engineering lab, and at most, there were six other girls beside me.

As a high school senior presented with the challenge of choosing an engineering project to research and produce as the focus of my third year in the Academy I turned to my own experience. I wanted more female students to discover an appreciation for not just STEM studies, but applying it to their own interests, whether that be art, fashion, literature, etc. Based on my opportunity to work with physics, fabrication and design, and computer science, my goal was to reach out to other girls, and facilitate a community of exposure and collaborative thinking for female students on campus and their varying degrees of interests in a STEM education. I then took this inspiration and used programming as my platform.

The graph below shows the enrollment ratio of male to female students From the 2013-14 academic year to 2016-17.

After initial research of the outstanding gender gap in science based fields, I focused my project development on the San Rafael High School campus specifically. Aside from my own opinions, I sought to learn and understand the experiences of my female peers in STEM as well as those who showed little enthusiasm about the subject. Thus, a discussion group was created to pair girls with little to no experience in STEM, with another eagerly involved student. This transition sought to introduce topics of discussion, and create a space for learning, project development and sharing of peer to peer experiences. Through this I sought to introduce Science, Technology, Math and engineering as an opportunity rather than an unknown.

SRHS Girls at the screening of CODE: Debugging the Gender Gap

There was a larger emphasis on social participation in my project than I had expected initially. I found myself talking to administrators, talking to younger students, and researching new ways to encourage young females than focusing on the technical aspects of my project. It is safe to say I underestimated my ability to create a recruiting website from scratch when I was still learning the basics of Computer Science. This deficit in what I thought was my only was to reach out to the community was in fact an example of the very work I was trying to emphasize. That while learning something new, I could share my thoughts, work and progress withe the girls around me.

Outside of San Rafael, I found mentorships and employment opportunities to help guide my project. Under the guidance of Ryan Robinett, a former partner at the software company Digital Foundry, I was able to visualize what I was attempting to accomplish in website design in the “real world.” This exposure not only broadened my understanding of the complexity of computing but as well as its team based nature. I felt somewhat vindicated in my struggle to produce something original when on a day to day basis software engineers are working in groups almost entirely. Additionally, my employment as a coding instructor at Mill Valley Code Club, a program designed to teach elementary through middle school students how to computer program, I was practicing how to explain and teach the vary programming fundamentals I was learning to a younger audience. Certainly solidifying the material I knew, and highlighting what I had yet to understand.

Ending the year I found I had not only exposed myself to programming in a variety of ways but had introduced the importance of collaborative thinking and communication amongst the female students and their envelopment in STEM education. Moving forward, the importance is consistency. Through deliberate action and communication, the next batch of San Rafael High School Engineering Academy graduates have an opportunity to continue to close the gender gap and inspire others.

SRHS girls meeting the film maker of She Started It

# Helping Students Create Their Own Mini Universes

For the past year, I have been helping a small software development team, headed up by my friend Winston Wolff, in the creation of a web based physics simulation tool. In this blog post, I am going to describe:

• Why we started this effort,
• What we hope to achieve,
• How far we have currently progressed towards our goals,
• And invite you to try it out.

## Simulations Can Be Helpful…

Many Physics teachers use computer simulations as a tool to help students learn physics. With a click of the mouse and a few keystrokes, students can quickly change the inputs to the simulation, producing different simulated behaviors of the system. This allows for quick exploration of the relationship between certain “physical” inputs and the governing dynamics of the system. Often, these explorations would be impossible to set up in the lab, or might take significant time and effort.

A great PHET simulation of projectile motion

## …But They Have Limitations.

Although these tools can be used with a high degree of success in the classroom, the students are interacting with a virtual universe created by another human. The rules of behavior and the underlying quantitative relationships have been defined by someone else who has already done the difficult work to model the physical universe. These relationships can be inferred and they can be explored by the student, but ultimately, they are hidden behind an impenetrable wall of software code. There is also a certain faith that the student must have in the simulation – there must exist an acceptance that the simulation creators did their job correctly.

## Students Coding Their Own Simulations is Awesome…

Some highly regarded physics educators have introduced the practice of teaching computer programming in the physics classroom. The advantage of engaging students directly in the construction of simulations, according to Ruth Chabay and Bruce Sherwood

is that there are no “black boxes”: students write all of the computational statements to model the physical system and to visualize the abstract quantities.”

Additionally, they argue that having students gain some experience and exposure to computational modeling

in the form of programming, even at the introductory level, can be an important component of a general education for living in today’s world.

Giving students the opportunity to write their own simulations gives them the ability to engage in computational physics directly and to give them vital experience in one of the aspects of being a scientist – namely writing some code.

## … But There Are Challenges For Teaching Coding.

Although there are great reasons for integrating computer science with Physics, and therefore developing students’ understanding and experience with computational Physics, there are some significant challenges for the teacher.

Teaching students to code their own physics simulations is not trivial. It requires significant instructional time, even given the fact that there are some amazing tools and frameworks for graphics programming (VPython, Processing). Chabay warns that time spent on teaching computer science principles and practices needs to be assessed against the time lost teaching and learning physics.

Due to the complexity and in many cases, the lack of exposure to computer science and “coding”, students can become lost in the syntax and specific computer science discourse, thus leading to confusion about the actual physics principles.

# A Hybrid Solution Is Needed: Tychos

Tychos (tychos.org) attempts to address the strengths presented by simulations and combine it with the value of computational modeling. It is a simulation tool that has been built to address the lack of transparency inherent in pre-constructed simulations while also simplifying and accelerating the acquisition of the skills needed to “code” the underlying physics.

We have never seen Tychos as a replacement for laboratory experiments. Quite the opposite, we see this as a way to enhance the laboratory experience. It gives students the ability to quickly define a hypothesis in code for anticipated behavior of a real experiment. Students can then run the real experiment and see if the simulation behavior that they defined matches or does not match the behavior defined by nature.

## No Black Boxes

The rules of the simulation are created and coded by the student. At its base, Tychos is really just a “drawing” and computational tool. There are no “virtual physics” built into the environment. Those rules must be defined and implemented by the student.

For example, if a student wants to simulate a particle moving in space with a constant velocity, they simply need to define the particle by using one of the few built in functions to place the particle at a position, set its visible size, and then optionally display with a given color, in this case the color red:

```p = Particle([0,0], 10, "red")
```

The “particle” is really just a graphic “dot” that appears on the screen. The simulator has no concept of movement, or mass, or energy, etc. The student must build in those rules. So for example, the student defines a numerical matrix to represent the particle’s velocity:

```p = Particle([0,0], 10, "red")
p.vel = [10, 0]
```

Then the student can use that variable to define how the particle will move in time. This is done by utilizing one of the few built in physical variables in the simulation software – “dt” which represents delta time:

```p = Particle([0,0], 10, "red")
p.vel = [10, 0]
p.pos = p.pos + p.vel*dt
```

With these three lines of code, a student can simulate a particle moving in space with a constant velocity. The student makes that happen and therefore the mechanics of the behavior are not hidden but rather fully exposed for the student to define.

## Built In Physics Analytical Tools

We have tried to create an environment where students have access to a suite of analytical tools that either do not require any coding, or very little.

### Visual Representations

As we develop Tychos, we are constantly looking at how we can make the tool easier to use for students. A few features that we have included are important visual representations that are commonly used to help represent motion. For example, we have made it very simple for students to see motion maps of their particles by simply clicking a button. We have also made it very easy to display vector arrows for any vector quantity, and to attach those vectors to a given particle:

This allows students to quickly assess the behavior of the simulation without needing to spend time learning how to implement complex tools.

### Easily Adjust Simulation Parameters

We have also tried to remove any coding that isn’t specifically targeted at modeling physics. For example, Tychos has a simple set of simulation parameters that can be changed with a few simple controls:

The above panel shows that a student can change the frame rate, the motion map strobe rate, set a simulation stop time, and change the extents of the viewing window – all without writing a line of code.

Coding of the GUI, rendering graphics, running the animation, etc are taken care of so there is less to program. The programs are much shorter and the code is more focused on the physics concepts, e.g calculating how force and momentum affect the position of a particle. There is no “boiler plate” code that needs to be used to get started which we have found to be cumbersome and confusing for students. Students spend less time learning programming and more time learning physics.

### Graphing

One of the great features that we are excited about and that I have found incredibly useful in class is the built in graphing tools in Tychos. With two simple lines of code, a student can graph any variables on a simple to read graph.

This allows for the student to graph the position, velocity,  and acceleration of a particle as a function of time (called motion graphs) but they can also graph energy, momentum, force, or any virtual quantity defined in the simulation code.

In the following example, the student has defined the kinetic energy of a particle and then has defined and displayed a graph for how the energy is changing with respect to time:

```KEgraph = Graph("KE vs Time")
KE = 0.5*p.mass*p.vel*p.vel
KEgraph.plot(t, KE)
```

The graph then looks like this:

This graph appears just under the simulation window, and the student can then easily connect the behavior of the simulated particle to the behavior of the graph.

## Integrated Formative Assessment:

Tychos has been built around the concept of a learning system. From the ground up, we have built in features that are designed to engage the student in the learning process. Tychos includes fast feedback in the form of instructor defined goals which are checked by the system such as “Your simulation should calculate position of particle at time 3 seconds.”

These goals keep students on track and allows for students to self assess. We have also noticed how these goals make the learning exciting. Students have expressed how much they enjoy watching the goals turn green as they accomplish them.

Teachers can also use the Goals as a quick and easy way to assess the learning progress of the entire class, and then focus on individuals that are having trouble. The teacher has the ability to peer into the individual student’s work and we are even building into the application the ability to see a “code history” of each student so that the teacher can track down the origin of a learning challenge and then direct the student to a specific solution.

## Our Roadmap

We think we are off to a great start with this app, but we also realize that there are a number of great potential features that we hope to add. This is a rough outline of our future goals:

### Tracking Student Progress

Soon the tool will show each student’s progress in realtime to the instructor so the instructor can maximize their time helping the students who need it. The tool will also allow instructors to see the work each student does, e.g. each attempt the student has made, the difference from the last attempt, and its outcome to help the instructor quickly deduce where the student’s thinking is and what is blocking her. Additionally, the instructor will be able to automatically export assessment data based on instructor’s defined criteria.

### Custom Defined Classes

We want to give the students the ability to define reusable components so that we can further reduce the amount of code that is needed to create a simulation. We are working on some strategies to build that into Tychos.

### Data Export/Import

To extend the connection between Tychos experiments and in class laboratory experiments, we intend to add the ability to export and import data to and from other data collection software like Logger Pro. This will allow more precise comparisons between simulated behavior and measured behavior from motion detectors or force sensors.

## Looking For Feedback

We are continuously looking for ways to improve our application, and we have no shortage of ideas. Our next challenge is finding the time and resources to make those future enhancements possible, but we are eager to have other Physics teachers try this tool out and let us know what else we should do to make this a better learning and teaching experience.

If you are interested in trying this application out, please visit our website: tychos.org. If you would like to give us feedback, or have questions, please feel free to post a comment on this blog post or contact me (stemple@srcs.org) or Winston (winston@nitidbit.com). We would love to hear from you!

# Our Goal – Make A Better Bridge Crusher!

This year Bob and I decided to upgrade our bridge project. We wanted to create an improved device for measuring the load on the model bridges created by the students. Specifically, we wanted to design a way for the students to collect meaningful performance data.

The problem with our old method (filling a bucket with sand until the bridge catastrophically failed) was that it didn’t allow for the students to collect evidence about where and why the bridge failed. In many cases, the bridge actually experienced a significant failure, but because the bridge collapsed around the loading plate, the loading plate actually acted as a support for the bridge.

We had seen other “bridge testers” from vendors (http://www.pitsco.com/Structures_Testing_Instrumenthttp://kelvin.com/kelvin-bridge-material-tester-w-cpad/http://www.vernier.com/products/sensors/vsmt/) but we had the idea that perhaps we could create one that might be better, or at least it might be fun to try. In this post, we are going to share with you what we created and why we think it actually turned out really well, but we also point out some room for improvement.

## The Frame

The frame of the entire device is really based on the Vernier Structures and Materials Tester. We thought this frame was probably the best, and we wanted to make our tester from extruded aluminum tubing as well. We went about designing the bridge tester in our favorite CAD program, Fusion360 by Autodesk. We sent our CAD file to the company 8020 and they precut all our t-slotted aluminum frame members to size. This was awesome because it made assembly super easy and it saved us on shipping too! Our experience with this company was amazing – they were super helpful and even gave us some really helpful advice. If you are thinking about making anything requiring t-slotted aluminum, definitely order from them.

## The Load Sensors

We wanted a a bridge tester that actually gave us data that allowed us to figure out how and why the student bridges failed. That meant that we needed more data and we needed data that could be connected to the design and fabrication of the bridge. We noticed that all the vendors’ designs had only one load sensor, and some also had a way to detect overall deflection. We suspected that we could get better data if we had four independent load sensors – one for each abutment where the bridges were supported. The four sensors would (theoretically) give the students a way to analyze how the load was being distributed, and thus tell us something about the torsional behavior of the bridge.

Sparkfun load sensor

I set out to learn a bit about load sensors and I came across a fantastic tutorial at Sparkfun (https://learn.sparkfun.com/tutorials/getting-started-with-load-cells). We ordered four load sensors (see picture above) from Sparkfun. Our design (shown below) has the four load sensors  fitted with 3D printed “shoes” as the bridge abutments.

The four load cells.

Two load cells with abutments.

The sensors are mounted on custom fabricated aluminum plates that can be moved laterally to accommodate slightly different bridge widths. The load sensors had to be connected to load amplifiers that were then connected to an Arduino (more on that below). The load sensors were mounted to the frame of the bridge tester on custom laser cut plates:

Load cell amplifiers for two load cells.

The load amplifiers have to be used with the load sensors in order to amplify the signal so that the Arduino can read the data correctly.

## The Loading Mechanism

Bob designed and fabricated the loading mechanism that was based on many of the designs we had seen online. It consists of a block that is free to move vertically up or down a threaded rod which is then connected to a spoked wheel.

Loading wheel.

When the wheel is turned, the block moves up or down the threaded rod. This bar is connected to a loading plate via a metal cable that hooks into the loading plate and the block:

Load plate from below – revealing loading wire attachment.

Loading wire attached to threaded block.

The loading plate is placed on the loading plane of the bridge (the “roadway”), and then the bridge is loaded by spinning the wheel, which lowers the block, which pulls the bridge downwards:

Loading plate on bridge.

## Collecting The Data: The Software

The software responsible for collecting the data is made up of two programs – one that runs on the Arduino micro-controller that is connected to the load sensors, and the other is a Processing sketch that runs on a computer/laptop connected to the Arduino via USB. The code is pretty simple, and it was mostly written using code from other sources and then modified for our specific purposes.

The Arduino code just collects the data from the four load sensors and then sends the data serially as a comma delimited package. The Processing code reads the serial port and then essentially dumps the data into a csv file. It does have some flourishes like a graphical display of the individual sensor loads as well as a display of the total load and whether or not the bridge has met the minimum load requirement set in the project descriptor.

You can view and download all the code here on GitHub.

## The Performance Report

When the data is displayed in a graphing program, it looks like this:

Sample bridge data

You can see that the four sensors do not read equal values, and that the bridge begins distributing the load unevenly. The blue and orange lines show that these two load sensors were equally loading and were taking on a larger load than the green and red values from the other two load sensors. Later inspection of the bridge showed that this bridge failed at the load sensors that were recording a higher load value. Also, these sensors were located diagonally from one another, and once again showed that the bridge was being twisted.

You can also see that around 80 seconds (the 800 data sample) that the bridge experienced a sudden decrease in load – this was the point of failure. The data clearly shows a point at which the bridge failed and thus gives us a clear metric for performance.

The student teams were each given the results and were asked to answer these questions:

1. What was the maximum load that your bridge sustained before failure?
2. Calculate the load to weight ratio of your bridge.
3. What were the individual maximum force values on each load sensor before failure?
4. Identify on your bridge where the bridge failed. Take a picture of this point of failure and note its location.
5. Based on the load data for the four sensors, describe why your bridge may have failed.
6. What could you have done to increase the performance of your bridge?

The data really allowed for some rich analysis and the students were able to make some really informed critiques of their design and fabrication quality. We have been very happy with the results!

## Future Improvements

For version 2.0 we hope to add these improvements:

• Add the ability to measure deflection. We think that this might be done by measuring the angular displacement of the loading wheel, but we aren’t sure just yet.
• Some way for the software to detect a failure – perhaps a way to detect a significant decrease in the load data. It would have to allow for some downward movement of the load data because there is some settling and deforming that can occur that might not be catastrophic.
• It would be nice to clean up the code – especially the Processing code. I’d like to add some fancy GUI elements too so that it is a bit more attractive.

If you would like to build your own advanced bridge tester for your classroom, we can send you all our CAD files, software files and even answer questions. Its not easy to build, but its fun, and we spent about \$350 dollars on this project as opposed to the \$1000 to \$1300 that the vendors are selling theirs for.