Tag Archives: Computational modeling

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.

Screen Shot 2018-12-22 at 9.27.05 AM

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:

Screen Shot 2018-12-22 at 10.22.21 AM

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:

rocket_v_graph

velocity data from altimeter – imported into LoggerPro

rocket_y_graph

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.

 

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.

projectile-motion-600

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.  


phymod1

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:

cvpm_canvas_6

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:

settings

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:

graph

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.”

goals

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!