### Alex Wenjian Zhao

This project is my major in a nutshell. My major was originally called Theoretical and Applied Mechanics, which is also the title for this class, and now it is called Engineering Mechanics. We study mechanics by analyzing math and physics and build models to represent the real world. This is one of the reasons why I am choosing this major over Mechanical Engineering so that I can use my math and analytical skills.

At the start of this project, I did not really know anything about the bottle rocket and the knowledge taught in class was not related to it. So I had to do all the studying by myself. Luckily the university library has a lot of resources and our team managed to find a few helpful research papers. Fluid mechanics involves complicated math such as surface integral and differential equations. Our goal was to come up with a simple model, so we had to make assumptions and simplify the theories we found. This process helped me to understand what each variable in the equations stands for and how I can solve them in different conditions. There were also challenges our team encounter. Finding the drag acting on the rocket is difficult and minimizing it is even more difficult. To accurately calculate the drag coefficient of an object requires methods like computational fluid dynamics analysis, which is beyond the scope of this course. Therefore, in the model, we made an assumption that the rocket is a blunt cylinder so that the drag coefficient is already given.

With the experience of this project, I will be more competent to solve complex engineering problems. I have learned time management skills by delivering the expected result in a tight deadline. Our team started researching early and that gave us some extra time to polish our findings. I have also learned teamwork skills by collaborating with my three other teammates. We set weekly objectives, exchange knowledge, and solve each other’s problems. And last but not least, the analytical skills I learned from this process apply to any challenge I will face in the future. By breaking down complicated problems to many different aspects that could be solved with one equation, a problem will become easier to tackle. I am feeling much more prepared for my future career.

### Viola Yuqi Wang

I learned a lot from this mini project. I learned how to use the mass conservation equation. This can not only be used in calculating the force provided by thrust, but also explain the high velocity of water coming out of the bottle. In addition, we learned the Bernoulli equation by ourselves. This equation is very useful since it linked pressure and velocity. By combining the mass conservation equation and Bernoulli equation together, we can calculate the thrust force. Addition to the fluid mechanics, I also learned thermal mechanics in this project. Regarding this system as an adiabatic system, PV is a constant. In this way, the pressure of the air in the bottle can be calculated after knowing the initial pressure, initial and changing velocity.

When studying the method of reducing drag, I found that adding weight to the nose of the rockets will help a lot. When looking more into it, I figured out that it had the same principle as what we have learned about the buoyancy of ferry on the sea. I also learned that the less area means less drag force, so we would choose the thin and long bottles instead of fat and short ones.

However, we also met with some problems. At first, we found that the acceleration would not go down all the time. Instead, the acceleration would go down then go up. After communicating with other groups, I found that the infinity acceleration resulted from the small mass. So we cannot omit the weight of the bottle itself. From this mistake, I realized the importance of communication, because we always can learn something from others.

This process enhanced my ability of self-learning and organizing knowledge. In the future, if I need to learn new knowledge by myself, I will read lots of journal articles and learn to solve the problems from different perspectives.

### Angela Chan

I was hoping to build an actual rocket when given this project. It would be cool to test and try different things, then physically see the effect; however, building real models is dependent on many other factors of accessibility and knowledge that therefore affects the data. This project reminded me of all the other factors I can’t see that go into optimizing a system, and eventually you won’t be able to brute force a solution.

The bottle rocket taught me how to break a problem down into different pieces. It reflected how the complex situation can be modeled by a simple problem, in this case F=ma. While doing the analysis, I learned how different components of energy ties into a stream of flow with Bernoulli’s Equation. Through reading many different articles, it was interesting to see how each author parsed the process at varying complexities. Compared to class problems, there are many parts that you can you to plug into other equations as hard numbers as opposed to breaking down each variable. This process also helped me see how to figure out which variables are known, impractical to predict, and which are easiest to model. Framing the problem this way makes physical relationships clearer to understand, such as the air pressure directly affecting the water exit velocity.

This exercise was useful to see how mathematical theorems are applied to a real situation. It’s hard to determine when to stop drawing from every equation there is out there. However, the real world also has its own constraints, so it was interesting to see what assumptions people decided to make. While doing research, especially for the drag, I enjoyed reading the discussions of other rocket designs as I have been interested in the field of design. The application of analyzing center of pressure from drag was something I didn’t expect, as I mostly only knew of how shape would affect it. Additionally, it was fascinating to see how my understanding of the journal articles increased once I was able to dissect one method completely. I could recognize similar equations, but also acknowledge how other pieces of the system would change the model we decided to use.

The process of conducting this project is especially helpful in learning to work on technical projects with a team. Our group was very cohesive and communicative with objectives, struggles, and building on each other’s knowledge.

### Lucas Hopper

Before the start of this project, I only knew the basics of how bottle rockets worked: compressed air in one half, water in the other, and then unscrew the cap or nozzle to launch it. But through this lab, I finally learned the specifics. Thanks to the many research papers and articles dedicated to something as seemingly simple as a bottle rocket, I was able to learn how to effectively model the interactions taking place throughout the launching process. Or, more specifically, I learned from the papers what parts of the process can be reduced or at least assumed to be something much simpler to aid in the calculation of the launching process. One such assumption is treating the mass of air as constant throughout the launch because even though the force of the launch comes from the air being such a high pressure and pushing the water out of the bottle at high speed, once the water is gone and the air is able to leave the bottle there is such a small amount of thrust generated that it can be safely ignored. Such an assumption is something I never would have thought of on my own and now that I know something like this is a possibility, I can use it or similar assumptions in future situations.

What this project really accomplished though was allowing my teammates and myself to familiarize ourselves with a real-world application of the equations we have been using theoretically for years now through open ended problem solving. Through teamwork and research, we learned how to manipulate an important equation in fluid mechanics which we have rarely if ever used: Bernoulli’s equation. Because of the manipulations and subsequent implantation into excel, I gained a deeper understanding of how each part of the equation relates to every other part, as well as how and when to implement the equation. These skills will serve me well for the rest of the class, as well as the rest of my life as a nuclear engineer working with highly pressurized water pipes where mistakes absolutely cannot happen.