For this rocket project, students were asked to build functional rockets with safe launch and descents out of everyday items. The goal was to learn how to analyze a rocket’s flight in terms of the laws of physics and the quadratic formula; while also exploring the engineering and design process (EDP) which consists of a series of steps that an engineer takes when creating a final design and product by refining a product. The purpose of the EDP is to give an individual a way to define a problem and then find solutions to the problem through brainstorming, refinement, testing, and improvement. In order to prepare for our final project, we spent multiple weeks learning about linear motion and the quadratic formula and how they relate to rocketry, while also becoming experts on Newton’s laws of motion and different scientific equations to find things like force, mass, acceleration, and velocity.
The basic quadratic equation is written in the form of ax²+bx+c where a, b, and c represent known numbers, and x represents the unknown. When analyzing the flight path of a rocket, we can plug the data into this formula. In terms of quadratic expressions, the reason that we can use them to find the height and time of a rocket’s flight is because graphically, a quadratic equation follows a parabola, which is similar to a rocket’s flight or any projectile. The formula represents a predictable path of projectile motion in terms of height from the ground at a given time due to gravity and acceleration. Acceleration is the change in velocity of an object. This is represented by the changing slope throughout the graph. During freefall, an object is only being acted upon by the force of gravity which is about 9.8 meters per second squared and nothing else. The object can still experience acceleration at this time. The reason that the path of a projectile creates a parabola is because the velocity of the object is constantly changing. We use a frame of reference off of which we base our data collection by translating data from our graph into the real-world scenario. By analyzing things such as points on the graph, we can determine the position of our rocket during its flight. The slope at each point represents the rocket’s velocity.
Linear motion describes the one-dimensional path of an object’s displacement or motion. Linear motion can be in the form of an object moving with constant velocity or changing velocity. Velocity describes the direction of movement and speed of an object. Acceleration describes the rate of change in velocity of the object. Gs are used to measure acceleration. One G equals the acceleration experienced due to gravity, which on Earth is about 9.806 meters per second squared (m/s^2) which we can round up to 10 m/s^2.
Throughout this course, we studied Newton’s laws and how they act upon different objects. Variables such as friction, drag, mass, and weight, all affect a rocket’s flight. In addition, identifying the forces acting upon a rocket helped us to build a design that is efficient and functional in its environment. Newton’s first law of motion discusses inertia. It states that “An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line unless acted on by an unbalanced force.” This is basically saying that an object will continue to move or stay still unless something causes its motion to change. We can see this relative to the net force of an object. Net force is the sum of all forces acting upon an object. If two forces acting on an object are equal, they will cancel each other out and create a net force equilibrium. Solid objects on a solid surface exert normal force, which is a force that supports the weight of the object and pushes back against it. This is why the objects remain at rest rather than accelerating through the surface. So if an object is in motion at a constant velocity, it’s net force is zero, like this train moving at a constant speed:
Newton’s second law is most commonly presented in the form of F=ma, meaning that force is equal to an object’s mass multiplied by its acceleration. The other force-mass equation takes the shape of a=F/m, meaning that the acceleration of an object equals the force necessary to move the object divided by the mass of the object. In other words, the force required to move an object is dependent on the mass of the object. For example, it would take much less force to kick a beach ball 100 feet than it would to kick a bowling ball 100 feet. Force is a vector quantity that is the applied pressure on an object to change its velocity. Force is measured in Newtons (N). One Newton is equal to the force required to move a kilogram of mass at 1 meter per second squared. There is however a difference between mass and weight. Mass is the measurement of matter in an object, while weight is the measurement of how gravity acts on an object. Mass does often affect weight. There are also other things to consider, like friction and drag which both affect the force necessary to move an object. Friction occurs between two or more objects on a molecular scale, and it is a force that resists motion between objects when surfaces come in contact. Drag occurs between the object and its environment and it is a force acting opposite of the object in motion.
Finally Newton’s third law of motion states that every action has an equal and opposite reaction. An example of this would be a bouncing ball. When the ball hits the ground, the ground pushes back on the ball with the equal amount of force as the ball is applying to the ground, causing it to bounce back up. It’s also the reason why it hurts to punch a wall; the wall is basically punching right back. When two or more bodies, or objects, interact with each other it is referred to as a system of bodies. An example of a system of bodies would be a basket tied to a helium balloon. The helium balloon would have different forces acting upon it than the basket, but the two bodies would be connected and affect each other. While the helium balloon is pulling up on the basket, the basket is pulling down on the balloon with an equal and opposite force. The two bodies are doing so simultaneously.
Analysis of a Rocket's Flight
What is a free body diagram? A free body diagram is a simple illustration used to assist the visualization of forces acting on an object
Pre-Launch: During pre-launch, the only forces acting on the rocket are normal force and gravitational force. Both forces are applying about 11.4482N. The forces cancel each other out creating a net force of zero. This means that the rocket is not changing position or motion. The rocket is experiencing Newton’s first law of motion, which states that an object at rest or in motion will stay in that state of motion unless acted upon by a nonzero net force. The rocket is at rest, and it is experiencing a net force of zero. If the net force equilibrium is suddenly disrupted, the rocket will experience a change in motion.
Takeoff: During takeoff, the forces acting on the rocket are thrust and gravity. At this point, the net force is not zero because the thrust is greater than the gravity. The force of gravity acting on the full rocket is approximately 11.4482N, and the force of thrust is about 155.732N. We found this number by adding the force of gravity to the net force acting on the rocket during takeoff. This is why the rocket moves upwards rather than staying in place. Newton’s third law of motion states that for every action there is an equal and opposite reaction. We can see this law in action during takeoff. As the water is pushed out of the pressure chamber of the rocket, The water pushes back with the same amount of force. In other words, the rocket pushes the water, the water pushes the rocket. Additionally, Newton’s second law discusses that the amount of force required to change an object’s motion is proportional to the object’s mass and acceleration, or that the object’s accellerion is dependent on the net force acting on the object and the mass of the object. The amount of force required to accelerate the rocket is dependent on its mass, and the amount of acceleration that the rocket experiences depends on the amount of force acting on it relative to the mass.
Rising Flight: During rising flight, the rocket is experiencing only gravity. All of the water has already been pushed out. According to Newton’s first law, due to inertia, the rocket wants to stay in motion until another force acts upon it. This is why the rocket continues to travel upwards. It is also decelerating as gravity slows it down. We can see this on our h(t) graph as the rocket travels up, then curves back downwards.
Controlled Descent: During controlled descent, the rocket is experiencing approximately 2.374N (Fg empty) of force of drag and 2.374N of force of gravity. The deployment of a parachute or utilization of a backslider creates drag because the frontal surface of the rocket increases, and allows the rocket to descend at a constant velocity. It experiences a net force of zero, meaning that its forces are balanced and its velocity is constant. This is a demonstration of Newton's third law: for every action there is an equal and opposite reaction. As gravity pulls the rocket back towards earth, the force of drag is pulling up in the opposite direction with the same amount of force.
Blueprint
Reflection
Overall, our rocket was very successful. I felt as though we were able to implement our learning and background knowledge well when building and designing our rocket. I feel satisfied with the journey of building our rocket. Our rocket ended up very similar to our initial design, with a few additional tweaks and refinements that we made along the way in order to improve our final product. Our final launch went very smoothly. All components of our rocket functioned as they were supposed to and the flight and descent was spectacular. One thing that was slightly disappointing was that our altimeter kept failing. We had to fly our rocket three times in order to come up with any sort of results; and by that time the rocket lost some of its structural soundness. That resulted in a less successful flight in comparison with the first two and ultimately a lower max height. Our biggest success in this project was our rocket as a whole. I found that researching and implementing the most aerodynamic designs allowed us to build a rocket that could reach its maximum potential.
What were your successes in this project and how would you relay those successes to next year’s sophomores? A piece of advice that I would give to future sophomores would be to think ahead and plan out each and every component of your rocket so that you can easily assemble and make refinements to it. I found that by doing so, it is much easier to refine the individual components of the rocket.
If you were to do this project again, what would you do differently and why? If I were to do this project again, I would take more lecture notes throughout the unit to use for this writeup and my rocket calculations. I initially took a lot of notes for every lecture at the start, but then got lazy and stopped doing them as much when they weren’t required. I would also take my notes digitally so that I could stay more organized and easily access my learning.
What challenges did you encounter in this project and how did you navigate those challenges? A challenge that we encountered during the actual process of building the rocket was splicing our Smart Water bottles. This was a challenge because Julian and Ande had never spliced Smart Water bottles before and were unsure if it would even be possible. This resulted in my team spending two full class periods trying to make a male part of the splice. We were on the verge of giving up, but we persisted. It ended up working at the last minute and our splice held well! The biggest challenge of the entire project for me was the writeup. I felt as though I did not have time to translate the calculations and finish my writeup on time while also making it thorough and refined. I overcame this fear by working hard on my writeup and cover letter at home, and utilizing my class time for calculations and refinements.