by Jake Dickerman
Title: Determining Optimal Launch Angles for Paper Pressure Rockets
Principle(s) Investigated: Pressure, Force, energy, engineering
NGSS Science and Engineering Standards
RST.6-8.3 Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks. (MS-PS1-6)
RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table). (MS-PS1-1),(MS-PS1-2),(MS-PS1-4),(MS-PS1-5)
WHST.6-8.7 Conduct short research projects to answer a question (including a self-generated question), drawing on several sources and generating additional related, focused questions that allow for multiple avenues of exploration. (MS-PS1-6)
MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.
MS-PS3-1. Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.
MS-PS3-5. Construct, use, and present arguments to support the claim that when the kinetic energy of an object changes, energy is transferred to or from the object.
ETS1.A: Defining and Delimiting an Engineering Problem
MS-ETS1-1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.
MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.
MS-ETS1-3. Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success.
MS-ETS1-4. Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved.
There are multiple ways to run this particular lab. The version I am doing in class will be day two in a four day activity, with day one being the day where students will design, build, and iterate on their own rockets, creating one of their own design and one using the Pop Rockets designs linked to above.
For this particular demo, we will be iterating on the launch angle necessary for greatest horizontal flight.
Procedure for each individual flight is relatively simple. Students will slide their paper rocket onto the launcher, make sure that no one is in the path of their shot, stomp on the 2-liter bottle, and then measure and record the distance from the rocket launcher to the place where the rocket landed. They will use a stop watch to record the flight time for each trial.
Students will begin by measuring 20, 30, 40, 50, 60, and 70 degree angles. Students will record their angles on the following data sheet.
In order to minimize variables, for this lab students should attempt to step on the plastic bottle in the same place for each launch and attempt to equalize the force of their step. This would be difficult, but multiple trials could be used to find an average launch.
Students can also use this projectile lab to calculate approximate amount of energy created by their stomp. By weighing their rocket beforehand and using the average horizontal velocity they calculated during their trials they could find an approximate horizontal kinetic energy. Students could also record the maximum height their rocket achieved on each flight and calculate the potential energy of the rocket at that moment by multiplying the mass of their rocket by the acceleration of gravity by the height off the ground. By adding that maximum potential energy (at a moment when all of the vertical kinetic energy should have been converted into potential energy) to that average kinetic energy, students would be able to find approximately the amount of energy that was given to their rocket when they stomped on the bottle.
Student prior knowledge:
In order to calculate the velocity of their rocket, students must understand that they can calculate average velocity by dividing the distance traveled by the time traveled.
It would be helpful if students also understood the basics of vectors, that firing something at an angle gives it both horizontal and vertical momentum, but they do not necessarily have to understand how to calculate what those vectors would be.
Students should understand the basic principles behind acceleration and be able to connect those ideas to the fact that the rocket falls and its basic path through space.
If a teacher wanted to also use the addition of calculating the energy the students were able to transfer to the rocket by stepping on the bottle, students would also have to know how to calculate kinetic energy (1/2 mv^2), potential energy (mgh), and understand that the total energy of the rocket throughout its flight should remain roughly constant.
When the student steps on the bottle, they vastly increase the pressure inside the bottle, which forces air through the vinyl tubing, pushing all of that air onto the paper rocket.
The paper rocket's low mass means the force that air exerts on the rocket will be translated into a large acceleration.
From a Newtonian perspective, the flight of the paper rocket can be seen as a consequence of Newton's first law, since the air exerts an applied force against the rocket, causing the rocket to be accelerated forward.
Questions & Answers:
1 - Shouldn't you be able to just calculate the best launch angle?
Yes! Well... kind of. There are easier and more difficult ways to calculate the ideal launch angle, some basic calculus can tell us that the ideal launch angle is forty five degrees, but the problem is that calculation ignores a vast number of variables. It's a calculation that would work really well if only the planet didn't have all that pesky air getting in the way of the rocket. Unfortunately, that would also make it pretty difficult to launch an air-powered rocket. There are more calculation intensive ways to get at the launch angle which take into account air resistance, the terminal velocity of the rocket, buoyancy, and if you can really calculate it, any movement in the air, but even these are approximations. There are always variables in the real world, it gets fairly difficult to account for all of them mathematically, especially with just a piece of paper and a pencil.
2 - If we can't get it right, why even try?
Maybe the world is full of variables and maybe we can't account for absolutely every one of them, but what we've learned throughout the years of doing science is that if we try really hard to just look at one variable, we can start to understand how that variable really works. The history of science is chock-full of scientists who have had to understand a big idea without being able to fully test that idea and eventually being proved pretty darn close to correct. Eratosthenes calculating the circumference of the earth, Galileo figuring out that objects should fall with the same accelerations even if he didn't have access to a vacuum to drop them in, Newton comprehending that the planets were pulled with the same force as the objects on planet earth -- physicists and mathematicians have largely proven, if you're careful with your fudge factors your math comes out pretty close to being right.
3 - Why isn't the US government launching space missions anymore?
That's a really good question. I don't know why they aren't. We should write them a letter about it.
Applications to Everyday Life: Projectile motion has thousands of applications, from rocketry
Having a basic understanding of projectile motion allows students to understand how objects can move in two dimensions and how masses only accelerate in the direction that force is exerted in.
This lesson also helps students get an idea of how powerful pressure can be and how energy is transferred through a system, moving from their weight moving down (mass times the acceleration of gravity plus the force from the contracting muscle all multiplied by the distance the foot moves through) transfers to the increased pressure on the bottle, transfers to increased air pressure in the tube, transfers to the acceleration of the paper rocket.