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ROCKET RECOVERY DESIGN CHALLENGE: DRAG AND TERMINAL VELOCITY
Submitted by: Timothy Couillard
James River High School, TARC Team 5308
[email protected]
This lab is designed as an enrichment lab for an 11th/12th grade physics course to
address the following National and State Science, Technology, Engineering, and
Mathematics (STEM) Standards:
National Science Education Standards (NSES):
NSES CONTENT STANDARD A: Science as Inquiry
As a result of activities in grades 9-12, all students should develop
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Abilities necessary to do scientific inquiry
Understandings about scientific inquiry
NSES CONTENT STANDARD B: Physical Science
As a result of their activities in grades 9-12, all students should develop an understanding of
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Motions and forces
NSES CONTENT STANDARD E: Science and Technology
As a result of activities in grades 9-12, all students should develop
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Abilities of technological design
Understandings about science and technology
Virginia Standards of Learning (SOL):
The student will plan and conduct investigations in which
a) the components of a system are defined;
b) instruments are selected and used to extend observations and measurements of mass,
volume, temperature, heat exchange, energy transformations, motion, fields, and electric
charge;
c) information is recorded and presented in an organized format;
d) metric units are used in all measurements and calculations;
e) the limitations of the experimental apparatus and design are recognized;
f) the limitations of measured quantities are recognized through the appropriate use of
significant figures or error ranges;
g) data gathered from non-SI instruments are incorporated through appropriate conversions;
and appropriate technology including computers, graphing calculators, and probeware, is
used for gathering and analyzing data and communicating results.
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PH.1
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PH.2
The student will investigate and understand how to analyze and interpret data. Key concepts
include
a) a description of a physical problem is translated into a mathematical statement in order to find
a solution;
b) relationships between physical quantities are determined using the shape of a curve passing
through experimentally obtained data;
c) the slope of a linear relationship is calculated and includes appropriate units;
d) interpolated, extrapolated, and analyzed trends are used to make predictions; and
analysis of systems employs vector quantities utilizing trigonometric and graphical methods.
PH.4
The student will investigate and understand how applications of physics affect the world. Key
concepts include
a) examples from the real world; and exploration of the roles and contributions of science and
technology.
PH.5
The student will investigate and understand the interrelationships among mass, distance, force,
and time through mathematical and experimental processes. Key concepts include
a) linear motion;
b) Newton’s laws of motion;
c) gravitation;
Topic/Concept
Drag Force, Drag Coefficient, Terminal (Constant) Velocity, Equilibrium
Materials
Parachute materials:
• String, Hole Punch, Scissors, and any other fabrication materials
• Plastic garbage bag/Nylon Fabric/Tyvek, etc. (Open inquiry: let each group select their parachute
material.)
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Mass Hangers and Slotted Masses (or Hanging masses)
Tape
Fishing lure connectors
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Stopwatch and Tape Measure/Meter Stick (Optional: or a Hot Wheels Toy Radar Gun or a
Vernier/PASCO Motion Sensor)
Vernier Wireless Dynamic Sensor System (WDSS) or PASCO PASPORT 3-Axis
Acceleration/Altimeter Sensor. Note: If you do not have a remote sensor package, you can use a
dummy payload to represent the sensor package and forgo the final data collection step.
Padding for sensor package.
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Safety Considerations
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Make sure the parachute payload is secure before dropping. If you include the Vernier WDSS in your
experimental payload, make sure it is properly padded. All payloads need to be inspected by the
instructor before dropping.
Mark the drop zone with cones or caution tape. There should be a 10’x10’ safe area zoned off for the
drops. Drops should not occur until the drop zone is clear.
Limit the mass of the payload to no more than 200 g. If you are dropping from a height of less than
twenty feet, consider reducing the size of your payload further. 50 g works well for small drop heights and
smaller parachutes.
Presentation
http://www.apogeerockets.com/images/Quest_parachute.jpg
http://www.soundingrocket.com/myrockets/video.shtml
The Challenge: Students are tasked to design a parachute that when deployed will safely transport a
sensor package (~50-200 g) to the ground at a speed of 15-20 ft/s. If the parachute can demonstrate the
ability to deliver that amount of mass to the ground at a safely, it will be attached to a sensor package
(Vernier WDSS or other) that will record the altitude, acceleration, and force of the fall.
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ROCKET RECOVERY DESIGN CHALLENGE-- DRAG AND TERMINAL VELOCITY
Challenge: Design a parachute to safely drop a 200 g sensors payload to the ground at a speed of 15-20 ft/s.
Background: The equation for the force of drag on an object is Fdrag = 1/2 (Cd) (ρ (A) (V2).,
where Cd is the drag constant determined by the shape of the object, and ρ (“rho”) is the density of the air, (ρ =
1.29 kg/m3), A is the cross-sectional area of the object, and V is linear velocity.
At terminal velocity, the drag force (Fdrag) is equal to the weight (Fg = (m) (g) ) of the object (Fdrag = Fg).
So, Fg = 1/2 (Cd) (ρ) (A) (V2).
mg = 1/2 (Cd) (ρ) (A) (V2)
Cd = 2mg / (ρ) (A) (V2).
Other background on parachutes:
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http://en.wikipedia.org/wiki/Parachute
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http://www.parachutehistory.com/eng/drs.html
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http://www.pcprg.com/rocketre.htm
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http://www.pcprg.com/rounddes.htm
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http://www.angelfire.com/co/m2rules/paracalc.html
Research questions (choose at least one to investigate):
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How does the size of the parachute affect the drop speed?
How does the shape of the parachute affect the drop speed?
How does the number of shroud lines affect the drop speed?
How does the shroud line cinch point location affect the drop speed?
How does the size of a spill hole in the parachute affect the drop speed?
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Can you think of any other factors that might be worth investigating?
Planning A (Experimental Design)
Include your problem(s), hypothesis, and experiment variables and constants. Make some predictions. What
outcomes do you foresee based on prior knowledge?
Planning B (Methods and Equipment Set-up)
Explain you method/ approach to this lab. Describe how you gather your data. Include a labeled diagram of the
equipment setup. Also, list everyone on your lab group and identify the jobs responsibilities of each.
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Experiment Tips
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Use a dummy mass (50-200g) to test your parachute design. Once you can demonstrate that your
parachute falls at a safe speed (Cite your data!), submit your design to the instructor for approval. You
will then be provided with the padded sensor payload to conduct the final collection of force, acceleration,
and altitude data.
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Use the toy radar gun (or a stop watch) to measure the terminal velocity. Take radar gun readings close
to the end of the fall.
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Modify and test one variable at a time. Make changes to your design in steps not all at once.
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Hold the parachute and payload, dropping them vertically at the same time.
Data Collection
Present the raw data information you gathered in the lab, be it qualitative, a table of numbers, or a graph. Don’t
forget to include units! Include error and uncertainties as needed.
Data Analysis: Process the data in a way that best allows for interpretation. This may be a graph or
identifying key results in a data table.
Use the equation for the force of drag to approximate the drag coefficient. Assume that the parachute falls at
a terminal velocity. Also, make some geometric estimates to determine the cross-sectional area of the
parachute.
Compare the drag coefficients for different design modifications to the terminal velocity as measured by radar
gun, motion sensor, or stop watch/meter stick.
If your design is successful, include your force, acceleration, and altitude data in an appropriate graph format.
Label key aspects of the graphs.
Conceptual Analysis and Conclusion:
1. Answer the following conceptual questions. (Be sure these are in complete sentences.)
a) Draw a force diagram for an object falling at terminal velocity.
b) What is the sum of the forces at terminal velocity?
c) Draw a sketch of a velocity vs. time graph that displays terminal velocity. What is the slope at
terminal velocity equal to?
d) Explain the relation between the sum of the forces and the slope of the v vs. t graph at terminal
velocity.
e) What factors influence the drag coefficient?
f) How did you keep your drop technique consistent?
2. Summarizes the findings of the lab in paragraph form. What was the point of this lab? What did you
find out? How do your findings compare to what we have learned previously? Revisit your
predictions and discuss how each of them turned out. Were your initial ideas correct? Or did your
results surprise you? .
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3. Identify the limitations, weaknesses, and errors in procedure, materials or in the data analysis.
Suggest ways to improve the investigation following the identification of weaknesses.
4. Include at least one thought-provoking question that might have occurred to your lab group while
doing the lab.
Teacher Tips Regarding Lab
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Teachers may want to assign different research questions to different groups.
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Treat this as a student inquiry. Present the materials available to the students but do not indicate a
specific course of action. Let the students figure out the best way to address their specific research
question.
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Approximate class time: Two or three 90-minute blocks depending on a) how many options for materials
used and how much time for testing and design modification.
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Choose a drop site that is manageable and can be secured safely. Make sur tou have enough height to
achieve terminal velocity for the weight you are using. Reduce the weight if necessary. Dropping from
the back off of the football bleachers or a stairwell that can be blocked off are some options.
Additional Notes
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By asking students to work in teams and assigning each student on a team a specific role, we work to
encourage a cooperative working atmosphere. Each student must be accountable to each other and all
students must sign off on a mutually agreed upon self-evaluation. Students much engage successfully in
cooperative learning in order to successfully. Like most team engineering challenges, students must go
through the engineering design process (brainstorm, design, create, test, modify, retest, etc.) together.
No one student can do this lab by himself or herself. In the post lab discussion, students are responsible
for a whiteboard presentation where the entire group must present their findings to the class and answer
questions. The preparation of this whiteboard requires students to work together in anticipation of making
their oral remarks.
All students regardless of ethnicity or gender are provided with equal opportunity. All are expected to
participate in this lab and present their findings. Females and minorities are encouraged by the instructor
addressing their questions seriously and to the fullest extent. By working in collaborative groups,
students are given a safe environment in which to ask their questions, test their ideas, and refine their
thinking. Each student is expected to show what he or she has learned from this activity. In this
environment, we hope to stimulate a positive, professional STEM experience and provide students every
opportunity to succeed.
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Sources & References
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Stine, B., (2004). Handbook of Model Rocketry. London: J. Wiley
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http://www.sciencebuddies.org/mentoring/project_ideas/Aero_p017.shtml?from=Home
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http://puzzling.caret.cam.ac.uk/game.php?game=parachute
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http://www.rocket-simulator.com/simulator.php
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http://www.esteseducator.com/Pdf_files/PhysicsCurr.pdf
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http://nasaexplores.com/show2_912a.php?id=03-035&gl=912
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http://nasaexplores.com/show_58_student_st.php?id=030509111221
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http://media.nasaexplores.com/lessons/03-035/5-8_1.pdf
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http://media.nasaexplores.com/lessons/02-081/9-12_2.pdf
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http://media.nasaexplores.com/lessons/03-035/9-12_1.pdf
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http://www.hazelwood.k12.mo.us/~grichert/sciweb/parachut.htm
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http://www.seed.slb.com/en/scictr/lab/parachute/index.htm
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http://www.seed.slb.com/en/scictr/lab/parachute/notes.htm
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http://www.parachutehistory.com/eng/drs.html
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http://www.pbs.org/teachers/mathline/lessonplans/pdf/msmp/awchute.pdf
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http://en.wikipedia.org/wiki/Parachute
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http://www.pcprg.com/rocketre.htm
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http://www.pcprg.com/rounddes.htm
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http://www.angelfire.com/co/m2rules/paracalc.html
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Appendix
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