We've got a custom-built aluminum and carbon fiber rocket motor filled with water and compressed air. There is a target located a certain distance away along flat ground. You do the math.
|0||Jan 24||Project begins|
|1||Jan 31||Thrust brief due|
|2||Feb 7||Thrust challenge due|
|Feb 8||Team formation deadline (6:00 p.m.)|
|Feb 10||Nosecone selection deadline (6:00 p.m.)|
|3||Feb 14||Dynamic analysis due|
|4||Feb 21||Stability analysis due|
|Mar 14||Launch day!|
|Mar 21||Launch debrief due|
Understanding Water Rockets
Prepare a two-page-maximum technical brief to explain how thrust is produced by a typical water-propelled rocket motor. You should seek to generate and explain the relationships that you will need to solve the Thrust Challenge below (i.e. - How are the volume and pressure of the air related? Can you calculate how fast the water will exit the nozzle? How does the exiting water translate into thrust? Etc.). You must cite all sources. Submit a hardcopy of your brief at the beginning of lecture on Monday, January 31st.
We'll use thermodynamics. We'll use fluid dynamics. We'll use mechanical dynamics. We'll even use some aerodynamics! Yep. all dynamics, all the time!
Create a Matlab function to plot the thrust force (in Newtons) versus time (in seconds) from launch. Name your function "thrust.m", and pass in two arguments: air pressure (in kPa) and water volume (in milliliters). Your simulation can use either explicit timestepping or the ode45 function (preferred). The resulting plot should include 0.20 seconds of data, and include proper axis labels (please also include your name in the plot title)
You will need the following parameters that were measured from our actual rocket motor:
chamber diameter = 38.1 mm
nozzle exit diameter = 12.4 mm
empty motor mass = 148 g
To make things a bit easier, we have posted some known-good results here.
To submit, place your script(s) in a folder and change the name of the folder to match your PennKey. Zip the folder, and send it as an attachment to email@example.com with the title 247-thrust.
Add your name to a team of three here by 6:00 p.m on the above-stated deadline. Those not listed on the page by the deadline will be randomly assigned.
As a team, you will design and construct a rocket body to attach to the motor. While you can use any materials that you'd like, the following standard components will be available in M81:
- 1.8-inch ID x 18-inch long kraft fiber tubes
- 1.8-inch OD x 1.5-inch long tube couplers
- a selection of fin stock, including 4"x36" balsa sheets in 1/16", 3/32", and 1/8" thicknesses, as well as MDF and acrylic
To obtain a nosecone, examine the selection then send an email to firstname.lastname@example.org before 6:00 p.m. on Feb 10 entitled 247-nosecone with the part number for the one you want in the body of the email.
Note: to accommodate the motor, there must be an 11-inch long by 1.8-inch diameter open bore at the bottom of the rocket (this matches the inner diameter of the provided kraft fiber tubes).
This phase of the project should help you gain a more thorough understanding of the dynamics of our rocket. Your team will need to submit the results of this investigation in a brief report at the beginning of class on February 14th. The format of the report is up to you. Below you will find three technical components that you must include:
1 - Examine the system and list all of the parameters that you believe will have a significant influence on the rocket.
2 - Create a simulation that can plot the path of the rocket given a set of initial conditions. List the source and/or justification for values chosen, and briefly describe/show the effect that each variable has on the overall rocket performance. Include at least one plot of the rocket's path.
3 - Determine the minimum and maximum target distances that you believe are reasonably achievable, along with the parameters used to reach those distances.
1 To ensure stable flight, you must consider the effect of aerodynamic forces on your rocket. The method(s) you use to determine stability are up to you, but your team needs to submit a brief report at the beginning of class on the above-stated deadline showing that your rocket will remain stable throughout the duration of the flight. Two related papers can be found here and here.
At the launch event you will need to have a way to quickly set the primary control variables (water volume, air pressure, and launch angle) for a given target distance. We strongly recommend using Matlab to develop a method to quickly determine viable sets of parameters (this could take the form of a three-dimensional plot of the control variables, a custom function, or something more creative).
You will need to bring your rocket body and some method to determine the control parameters for a given target distance. Your team's target distance will be announced approximately 5 minutes before you will be due on the launch stand. When your turn arrives, you will go through the following steps:
- lock the motor to the launch pad
- fill the motor with your specified amount water
- cap the motor
- place your rocket body over the motor
- incline the rocket to the desired angle
- pump air into the motor to your pre-determined level (up to a maximum gauge pressure of 1200 kPa)
- pull the launch cable
- search for the O-ring
Each team will launch once, then we will take repeats. You will have a maximum of three attempts.
Prepare a brief document summarizing your work on this project. Describe the model used in your simulation, as well as how you determined the initial launch parameters for your given target distance. Also include a comparison between your target distance and actual results, and discuss what you believe caused any error between the two. Bring a printed copy to class for submission.