Upload
john
View
270
Download
2
Embed Size (px)
Citation preview
Soda Straw Rocket ScienceSoda Straw Rocket Science
Aerospace Engineering Projects forAerospace Engineering Projects forGrades K – 12+Grades K – 12+
4/13/2009 ELF 1
For permission to copy or republish, contact Eugene L. Fleeman, 4472 Anne Arundel Court, Lilburn, GA 30047, [email protected] , http://genefleeman.home.mindspring.com
List of ProjectsList of ProjectsProject Title Grade
1 History of Rockets K+2 How to Make a Soda Straw Rocket K+3 How to First Check Out of a Soda Straw Rocket K+4 How to Demonstrate Galileo’s Hypothesis and Newton’s 2nd Law K+5 Why Do Soda Straw Rockets Fly Differently? 5+6 What is the Scientific Method? 6+6 What is the Scientific Method? 6+7 How Does Newton’s 2nd Law Apply to a Soda Straw Rocket? 7+8 Example of Scientific Method Hypothesis Test 8+9 Design, Build and Fly Competition 9+9 Design, Build and Fly Competition 910 Structure Failure Prediction and Test 9+ 11 Thrust Prediction and Test 9+12 How to Measure Accuracy of Test Data 9+13 Flight Trajectory Analysis Using a Digital Camcorder 9+14 Technical Description of a Soda Straw Rocket 12+15 House of Quality for a Soda Straw Rocket 12+16 Design of Experiments for a Soda Straw Rocket 12+
4/13/2009 ELF 2
16 Design of Experiments for a Soda Straw Rocket 12+Appendix Syllabus N/A
Project # 1: Grades K+Project # 1: Grades K+
History of RocketsHistory of Rockets
4/13/2009 ELF 3
Who Invented Rockets?Who Invented Rockets?
Year 1232. Chinese Invent Fire Arrow Rocket …………………
Year 1926. Dr. Goddard Invents Liquid Propellant Rocket …………………………………
Year 1944. Dr. von Braun Invents V-2 Guided Rocket ……………..
Year 1957. Mr. Korolev Invents R-7 Sputnik Satellite Rocket ……………………………………..
Year 1967. Dr. von Braun Invents Saturn Moon Rocket …………
4/13/2009 ELF 4
Who Developed the Theory of Gravity and the Equations of Motion?
Who Developed the Theory of Gravity and the Equations of Motion?
Year ~ 340 BC. Aristotle’s Theory: Heavy Objects Fall Faster Than Lighter Objects ( Not True )
( Not True ) ………………………………………………………………………………
Year 1630 AD. Galileo’s Theory and Experiment: Objects Fall at about the Same Velocity, Due to Gravity……………………………………………………………….
Year 1687 AD. Newton Develops 2nd Law and Equation of Motion ( F = ma ) .….
4/13/2009 ELF 5
How Far Do Rockets Fly?How Far Do Rockets Fly?Chinese Fire Arrow Rocket: 1,000 Feet ………………
G dd d’ Li id P ll t R k t 3 Mil Goddard’s Liquid Propellant Rocket: 3 Miles ……………………………………………….
Gvon Braun’s V-2 Guided Rocket: 200 Miles ………………………….
Korolev’s R-7 Soyuz Rocket ( Sputnik Satellite ): 25,000 Miles ………….…………………………..
von Braun’s Saturn Moon Rocket: 240,000 Miles ……………………
4/13/2009 ELF 6
Soda Straw Rocket: 90+ Feet ……………………………………………………………………
A Soda Straw Rocket Has Thrust, Gravity, and Drag Forces, Like the Bigger Rockets
A Soda Straw Rocket Has Thrust, Gravity, and Drag Forces, Like the Bigger Rocketsg ggg gg
Saturn V Moon Rocket Video Space Shuttle Video Sounding Rocket Video
4/13/2009 ELF 7
Hellfire Missile Video LOSAT Missile Video Soda Straw Rocket Video
ProblemsProblems1. The first rocket was invented in the year 1232 by the C______.2. In the year 1630, G______ demonstrated that the force of
it i th f b th li ht bj t d h bj tgravity is the same for both light objects and heavy objects.3. The rocket equation F = ma is the 2nd Law / equation of motion
that was invented in the year 1687 by Sir Isaac N_____.4. In the year 1944, Dr. von Braun’s V-_ rocket flew from France
to England, a distance of 200 miles.5 In the year 1967 Dr von Braun’s Saturn rocket flew from the 5. In the year 1967, Dr. von Braun s Saturn rocket flew from the
earth to the m___, a distance of 240,000 miles.6. Your soda straw rocket follows the same rocket equation as
bi k t It h th th f f th t d d bigger rockets. It has the three forces of thrust, drag, and g______.
4/13/2009 ELF 8
Project # 2: Grades K+Project # 2: Grades K+
How to Make a Soda Straw RocketHow to Make a Soda Straw Rocket
4/13/2009 ELF 9
It Is Easy to Make a Soda Straw RocketIt Is Easy to Make a Soda Straw Rocket
1. Cut Large Diameter “Giant” Soda Straw to Desired Length
3 Slide Twisted / Squeezed Ear Plug Inside
2. Twist and Squeeze Foam Ear Plug to Fit Inside Soda Straw
3. Slide Twisted / Squeezed Ear Plug Inside Soda Straw
4. Trim Nose to Desired Shape
7 Cut Adhesive Tab(s) to Desired Height and
5. Select Adhesive Tab(s) with Desired Number of Tail, Wing, and Canard Surfaces ( 2, 3, 4 ) and Fold Adhesive Tab(s) Around Soda Straw
7. Cut Adhesive Tab(s) to Desired Height and Geometry of Surfaces
9. Slide Giant Soda Straw Rocket Over Smaller Di t “S J b ” S d St L h T b
8. Overwrap Front of Ear Plug and Straw with Tape
4/13/2009 ELF 10
Diameter “Super Jumbo” Soda Straw Launch Tube
ProblemsProblems1. We need to wrap the front of the ear plug and soda straw with
t___ to keep it from leaking air.Th d t k t h ld lid th l h t b 2. The soda straw rocket should slide o___ the launch tube straw.
4/13/2009 ELF 11
Project # 3: Grades K+Project # 3: Grades K+
How to First Check Out a Soda Straw How to First Check Out a Soda Straw Rocket
4/13/2009 ELF 12
First Check Out the Strength and Accuracy of Your Soda Straw Rocket
First Check Out the Strength and Accuracy of Your Soda Straw Rocket
Blow air into soda straw rocket. Check to see if nose section is air tight and has see if nose section is air tight and has structural integrity.
A Slide soda straw rocket over soda straw launch tube. Blow air into soda straw launch tube to launch rocket at accuracy scoreboard. Check flight accuracy of rocket.
Accuracy Scoreboard
rocket.
Soda straw rocket
4/13/2009 ELF 13
Launch tube
Soda Straw Rocket Accuracy Scoreboard for First Check Out Test
Soda Straw Rocket Accuracy Scoreboard for First Check Out Test
1Yellow
2White
3Green
2White
1Yellow
2White
3Green
4Blue
3Green
2WhiteWhite Green Blue Green White
3Green
4Blue
5Purple
4Blue
3GreenGreen Blue Purple Blue Green
2 3 4 3 2White Green Blue Green White
1 2 3 2 1
4/13/2009 ELF 14
Yellow White Green White Yellow
ProblemsProblems1. We need to blow air into the soda star rocket to check out the
strength of the n___ section.W d t h t th d t k t t b d t 2. We need to shoot the soda straw rocket at a scoreboard to check out its a_______.
4/13/2009 ELF 15
Project # 4: Grades K+Project # 4: Grades K+
How to Demonstrate Galileo’s Force of How to Demonstrate Galileo’s Force of Gravity Hypothesis
andNewton’s 2nd Law / Equation of MotionNewton s 2 Law / Equation of Motion
4/13/2009 ELF 16
How to Demonstrate Galileo’s Force of Gravity Hypothesis Using Soda Straw Rockets
How to Demonstrate Galileo’s Force of Gravity Hypothesis Using Soda Straw Rocketsyp gyp g
1 From the Same Height Simultaneously 1. From the Same Height, Simultaneously Drop a Rocket and Horizontally Launch Another RocketAnother Rocket
2. According to Galileo, Both Rockets Should Hit th G d t th S TiHit the Ground at the Same Time
4/13/2009 ELF 17
How to Demonstrate Galileo’s Gravity Hypothesis Using a Rocket Drop and a Horizontal Launch
How to Demonstrate Galileo’s Gravity Hypothesis Using a Rocket Drop and a Horizontal Launch
4/13/2009 ELF 18
Galileo Experiment Video Using Digital Blue Camcorder
How to Demonstrate Newton’s 2nd Law and Equation of Motion Using Soda Straw Rockets
How to Demonstrate Newton’s 2nd Law and Equation of Motion Using Soda Straw Rocketsq gq g
According to Newton the Force of Gravity According to Newton, the Force of Gravity Will Cause a Rocket Launched at an Angle of 45 degrees to Fly the Farthest Distanceof 45 degrees to Fly the Farthest DistanceAlso, According to Newton, the Force of G it Will C R k t L h d t Gravity Will Cause a Rocket Launched at a Vertical Angle / 90 Degrees to Fly the L t TiLongest Time
4/13/2009 ELF 19
How to Demonstrate Newton’s 2nd Law Using a Rocket Launched at a 45 Degree Angle
How to Demonstrate Newton’s 2nd Law Using a Rocket Launched at a 45 Degree Angleg gg g
4/13/2009 ELF 20
Newton Experiment Video Using Digital Blue Camcorder
How to Demonstrate Newton’s 2nd Law Using a Rocket with a Vertical Launch
How to Demonstrate Newton’s 2nd Law Using a Rocket with a Vertical Launch
4/13/2009 ELF 21
Newton Experiment Video Using Digital Blue Camcorder
Soda Straw Rocket LauncherSoda Straw Rocket Launcher
8. Inclinometer7. Rocket on Launcher6. Launch Tube5. Solenoid Valve4. Pressure Gauge3 Air Hose3. Air Hose
2. Pressure Tank
1. Air Compressor
4/13/2009 ELF 22
9. Rockets with Various Length and Geometry10. Measuring Wheel11. Launch Button
What Is the Test Process for a Compressor Launcher?
What Is the Test Process for a Compressor Launcher?
1. Wrap Tape 1” from End of Launch Straw
2. Insert Taped End of pLaunch Straw 1” into Launcher Bushing
3. Elevate Launcher to Desired Launch AngleDesired Launch Angle
4. Lock Friction Lid Support
5. Connect Air Supply Socket to Launcher PlugSocket to Launcher Plug
6. Turn Valve to Off
7. Turn on Compressor
8. Regulate Air Pressure to Desired Setting
9. Turn Valve to Launch Rocket
4/13/2009 ELF 23
Rocket
10. Record Flight Time / Distance
How Do You Conduct a Rocket 45 Degree Launch with a Compressor Launcher?
How Do You Conduct a Rocket 45 Degree Launch with a Compressor Launcher?
4/13/2009 ELF 24
Newton Experiment Video Using Digital Blue Camcorder
How Do You Conduct a Rocket Vertical Trajectory with a Compressor Launcher?How Do You Conduct a Rocket Vertical
Trajectory with a Compressor Launcher?j yj y
4/13/2009 ELF 25
Newton Experiment Video Using Digital Blue Camcorder
ProblemsProblems1. According to Galileo, if you simultaneously launch a rocket
horizontally and drop another rocket, the force of gravity will cause them to hit the ground at the s timecause them to hit the ground at the s___ time.
2. According to Newton, the force of gravity will cause a rocket that is launched at an angle of 45 deg to fly the f_______ di tdistance.
3. According to Newton, the force of gravity will cause a rocket that is launched vertically to fly the l______ time.y y
4/13/2009 ELF 26
Project # 5: Grades 5+Project # 5: Grades 5+
Why Do Soda Straw Rockets Fly Why Do Soda Straw Rockets Fly Differently?
4/13/2009 ELF 27
Why Do Soda Straw Rockets Fly Differently?Why Do Soda Straw Rockets Fly Differently?
Tails and WingsFront Tails ( Canards )Wi ith T ilWings with TailsLarge Tails: 3 or 4No Wings or TailsS ll T il 3 4 L t d M t A t Fli htSmall Tails: 3 or 4
Chamber Length
Longest and Most Accurate Flight
Shorter Than Launch Tube: 4 inLonger Than Tube: 7.5 inEqual to Launch Tube: 6 inq
WeightHeavy: 2 gram
4/13/2009 ELF 28
Heavy: 2 gramLight: 1 gram
Why Do Soda Straw Rockets Fly Differently ?( cont )
Why Do Soda Straw Rockets Fly Differently ?( cont )
Launch AngleLow Launch Angle: 20 Deg
( )( )
High Launch Angle: 60 Deg
Medium Launch Angle: 40 Deg
Launch PressureLow: 15 psi
4/13/2009 ELF 29
High: 60 psi
ProblemsProblems1. Your soda straw rocket will fly more accurately and farther if it
has no wings and 3 or _ small tail fins.Y d t k t ill fl f th if th h b l th i 2. Your soda straw rocket will fly farther if the chamber length is e____ to the launch tube length.
3. Your soda straw rocket will fly farther if it is l____ weight.4. Your soda straw rocket will fly farther if has a m_____ launch
angle.5 Your soda straw rocket will fly farther if it has a h launch 5. Your soda straw rocket will fly farther if it has a h___ launch
pressure.
4/13/2009 ELF 30
Project # 6: Grades 6+Project # 6: Grades 6+
Scientific MethodScientific Method
4/13/2009 ELF 31
What Is the Scientific Method?What Is the Scientific Method?1. State a Question of Something That Might Be True ( e.g., Galileo’s
Question of Gravity )Do All Objects Feel the Same Force of Gravity?j y
2. Form a HypothesisHeavy Objects Fall at about the Same Velocity As Light Objects, Due to the Same Force of Gravity.
3. Test the Hypothesis in a Controlled Experiment.Drop 1 lb Ball and 10 lb Ball from the Leaning Tower of PisaMeasure Time of Ground Impact
th H th i i T4. Present Results on Whether the Hypothesis is True.
4/13/2009 ELF 32
You Can Demonstrate Galileo’s Hypothesis Using a Heavy Ball / Light Ball Drop Test
You Can Demonstrate Galileo’s Hypothesis Using a Heavy Ball / Light Ball Drop Testg y g pg y g p
4/13/2009 ELF 33
Galileo Experiment Video Using Digital Blue Camcorder
ProblemsProblems1. The scientific method uses a c_________ experiment to test a
hypothesis.G lil d hi h th i f it b d d li ht 2. Galileo proved his hypothesis of gravity by dropped a light ball and a heavy ball from the Leaning Tower of P___.
3. According to Galileo, if you drop a a heavy ball and a light ball they will hit the ground at the s___ time.
4/13/2009 ELF 34
Project # 7: Grades 7+Project # 7: Grades 7+
How Does Newton’s 2nd Law Apply to a How Does Newton’s 2nd Law Apply to a Soda Straw Rocket?
4/13/2009 ELF 35
Newton’s 2nd Law Equation F = ma Applies to a Soda Straw Rocket
Newton’s 2nd Law Equation F = ma Applies to a Soda Straw Rocket
During launch, the force on the soda straw rocket is primarily due to the thrust from the air pressure launcher. Example for 1.5 gram rocket at 15 psi launch pressure:
F = Gravity = 0.015 Newton
After launch the force on the soda straw rocket is primarily due to the force of After launch, the force on the soda straw rocket is primarily due to the force of gravity. It follows a ballistic trajectory. Example for launch 50 ft / sec velocity:
F = Gravity = 0.015 Newton
4/13/2009 ELF 36
What Are Newton’s Equations of Motion Due to the Force of Gravity?
What Are Newton’s Equations of Motion Due to the Force of Gravity?yy
1. Vertical Acceleration Is -32.2 ft / sec2 ( Toward Center of Earth )a = a = g = -32 2 ft / sec2az = a = g = -32.2 ft / sec
2. Vertical Velocity Due to Force of GravityVz = a t + VzInitial
V ti l Di t D t F f G it3. Vertical Distance Due to Force of Gravityh = ½ a t2 + VzInitial t + hInitial
4. Horizontal Velocity ( Constant )y ( )Vx = VxInitial
5. Horizontal DistanceX = V t + xX = VxInitial t + xinitial
6. Launch Angle for Maximum Rangeθ = 45 dg
4/13/2009 ELF 37
7. Maximum RangeX = R = V2 / a
ProblemsProblems1. After launch the primary force on your soda straw rocket is
the gravity force. It follows a b________ trajectory.Y d t k t ill fl f th if th l h l i 2. Your soda straw rocket will fly farther if the launch angle is about __ degrees.
3. After launch, your soda straw rocket has nearly constant horizontal v_______ ( small drag force )
4. After launch, your soda straw rocket has nearly constant vertical a of -32.2 ft / sec2. vertical a___________ of 32.2 ft / sec .
4/13/2009 ELF 38
Project # 8: Grades 8+Project # 8: Grades 8+
Example of Scientific Method Hypothesis Example of Scientific Method Hypothesis Test
4/13/2009 ELF 39
What Is the Scientific Method?What Is the Scientific Method?
1. State a Question of Something That Might Be True.Example: Does the flight distance of the soda straw rocket depend upon the p g p p
chamber length?2. Form a Hypothesis.
Example: The longest flight distance occurs when the chamber length parameter i l t l h t b l this equal to launch tube length.
3. Test the Hypothesis in a Controlled Experiment.Example: Build and test soda straw rockets of different chamber lengths.
4 Present Results on Whether the Hypothesis is True4. Present Results on Whether the Hypothesis is True.Example: Give presentation on the results from the experiment.
4/13/2009 ELF 40
Example of Hypothesis PosterExample of Hypothesis Poster
Hypothesis: Longest Flight Is When Chamber Length Equals Launch Tube LengthEquals Launch Tube Length
80
100
d on
40
60
80
ange
Bas
edst
Dat
a, ft
0
20
40
Flig
ht R
aTe
s
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Chamber Length / Launch Tube Length, in
4/13/2009 ELF 41
Chamber Length = 4, 6, 7.5 in
Note: Flight range at 10 psi launch pressure and 40 deg launch angle.
Example of Hypothesis Poster ( cont )Example of Hypothesis Poster ( cont )
Hypothesis: Longest Flight Is When Launch Angle Equals 40 DegreesEquals 40 Degrees
80
Test
40
60
Bas
ed o
n T
ta, f
t
20
40
ight
Ran
ge
Dat
00 10 20 30 40 50 60
Launch Angle Deg
Fl
4/13/2009 ELF 42
Launch Angle, Deg
Note: Flight range at 10 psi launch pressure and 6 in chamber length.
Hypothesis Test DataHypothesis Test Data
Test Launch Launch Tube Hypothesis Chamber Launch Distance ( ft )Pressure ( psi ) Length ( in ) Length Angle ( deg )
1 Chamber Length1. Chamber Length2. “3. “4. Launch Angle5 “5. “6. “
4/13/2009 ELF 43
Project # 9: Grades 9+Project # 9: Grades 9+
Design Build and Fly CompetitionDesign, Build and Fly Competition
4/13/2009 ELF 44
Example of Customer Requirements –Design, Build, and Fly
Example of Customer Requirements –Design, Build, and Fly
Objective – Design, Build, and Fly Soda Straw Rocket with:Flight Range Greater Than 90 ft, 3σWeight Less Than 2 gramsWeight Less Than 2 gramsUnit Production Cost Less Than $0.50
Furnished Property / MaterialLaunch SystemLaunch SystemLaunch Tube ( “Super Jumbo” Soda Straw: 0.25 in Diameter by 7.75 in Length )Power / Power CordDistance Measuring WheelDistance Measuring WheelWeight ScaleMicrometer ScaleEngineer’s ScaleEngineer s ScaleScissorsTape Dispenser“Giant” Soda Straw: 0 28 in Diameter x 7 75 in Length
4/13/2009 ELF 45
Giant Soda Straw: 0.28 in Diameter x 7.75 in LengthAdhesive Strip TabbingFoam Ear Plug: 0.33-0.45 in Diameter x 0.9 in Length
Example of Design, Build, and Fly Customer Requirements ( cont )
Example of Design, Build, and Fly Customer Requirements ( cont )
Specified Launch Constraints / ConditionsL h T b Di t 0 25 iLaunch Tube Diameter: 0.25 inLaunch Tube Length: 6 inLaunch Pressure: 30 psiL h El ti A l 30 d Launch Elevation Angle: 30 deg
Compare Predictions with Test Data
4/13/2009 ELF 46
Test ScoresTest ScoresName Team Launch Distance ( ft ) Dispersal Integrity
Pressure ( psi ) Angle ( deg ) ( ft ) ( deg ) at 30 psi?
11.2.3.4.5.6.7.8.8.9.10.11.1212.13.14.15.
4/13/2009 ELF 47
16.
Example of Team Score PosterExample of Team Score Poster
Name Rocket Name Range* Dispersal* Integrity*
1. Gene Buzz 80 feet 5.1 degrees Yesg
2. Isaac Stinger 55 8.2 Yes
3. Robert Speedy 90 4.7 Yes
4. Wernher Bad Bee 85 4.9 YesTotal 310 22.9
Average 77 5.7
4/13/2009 ELF 48
*Note: Flight range and dispersal at 15 psi launch pressure and 25 deg launch angle respectively. Structural integrity at 30 psi launch pressure.
Project # 10: Grades 9+Project # 10: Grades 9+
Structure Failure Prediction and Structure Failure Prediction and Comparison with Test
4/13/2009 ELF 49
Soda Straw Rocket Side Wall Structure Failure Prediction
Soda Straw Rocket Side Wall Structure Failure Prediction
σFailure = pmax r / t
pr t
Predicted Side Wall Failure Gage Pressure for Soda Straw Rocket:
σFailure = 4600 psi
t = 0.04 in
r = 0 14 inr 0.14 in
pmax = σFailure t / r = 4600 psi x 0.004 in / 0.14 in = 131 psi
4/13/2009 ELF 50
Test Process for Structure Failure TestTest Process for Structure Failure Test1. Wrap Tape 1” from End of
Launch Straw
2. Insert Taped End of Launch 2. Insert Taped End of Launch Straw 1” into Launcher Bushing
3. Slide Soda Straw Rocket Over Launch Straw
4. Place Finger in Front of Soda Straw Rocket to Restrain It
5. Connect Air Supply Socket to L hLauncher
6. Turn on Compressor
7. Regulate Air Pressure to an Initial ( 30 i ) S tti( e.g., 30 psi ) Setting
8. Turn Valve on and Observe if There Is a Structure Failure
If N St t F il R t t
4/13/2009 ELF 51
9. If No Structure Failure, Repeat at Increasing Pressure Until Structure Failure Occurs
Example Structure Failure Test Data SheetExample Structure Failure Test Data SheetName Measured Failure Gage Pressure ( psi ) Predicted Failure Gage Pressure ( psi )*1. Isaac______________________________75____________________________131____________________2. Robert ____________________________80____________________________131____________________
4/13/2009 ELF 52
* Hypothesis: Predicted side wall failure gage pressure = Soda straw ultimate stress x thickness / radius = 4600 psi x 0.004 in / 0.14 in = 131 psi
ProblemsProblems
1. What could cause a difference between the prediction failure pressure and the actual test failure pressure?
2. How do we prevent the soda straw rocket nose plug from blowing out under pressure? blowing out under pressure?
4/13/2009 ELF 53
Project # 11: Grades 9+Project # 11: Grades 9+
Thrust Prediction and TestThrust Prediction and Test
4/13/2009 ELF 54
Soda Straw Rocket Thrust PredictionSoda Straw Rocket Thrust PredictionT = p A
T
Predicted Thrust for Soda Straw Rocket:
A = Launch Straw Cross Sectional Area = r2 = ( 0 125 )2 = 0 0491 in2A = Launch Straw Cross Sectional Area = π r2 = π ( 0.125 )2 = 0.0491 in2
P = Gage Pressure
T = 0.0491 p
4/13/2009 ELF 55
Test Process for Thrust StandTest Process for Thrust Stand1. Wrap Tape 1” from End of
Launch Straw
2. Insert Taped End of Launch 2. Insert Taped End of Launch Straw 1” into Bushing
3. Slide Soda Straw Rocket Over Launch Straw
4. Place Scale under Soda Straw Rocket
5. Connect Air Supply Socket t Th t St dto Thrust Stand
6. Turn Valve to Off
7. Turn on Compressor
8. Regulate Air Pressure to Desired Setting
9. Turn Valve on and Measure Th t F
4/13/2009 ELF 56
Thrust Force
10. Compare Calculated Thrust with Measurement
Example Thrust Test Data SheetExample Thrust Test Data SheetName Gauge Pressure ( psi ) Measured Thrust Data ( lb ) Predicted Thrust ( lb )*1. Isaac______________________________60____________________2.4____________________2.94____2. Robert ____________________________60____________________2.6____________________2.94____
4/13/2009 ELF 57
* Hypothesis: Predicted thrust = Launch straw cross sectional area x gauge pressure = 0.0491 x gauge pressure.
ProblemProblem
1. What could cause a difference between the prediction thrust and the actual test thrust?
4/13/2009 ELF 58
Project # 12: Grades 9+Project # 12: Grades 9+
Vertical Wind Tunnel TestVertical Wind Tunnel Test
4/13/2009 ELF 59
Test Process for Vertical Wind TunnelTest Process for Vertical Wind Tunnel
1. Insert Soda Straw Rocket Nose Down into Center of Pipe and Rest on FinsRest on Fins
2. Connect Air Supply Socket to Vertical Wind Tunnel
3 Turn Valve to Off3. Turn Valve to Off
4. Turn on Compressor
5. Turn Valve on
R l t Ai P t “Lift 6. Regulate Air Pressure to a “Lift Off” Pressure ( drag = weight )
7. Record the “Lift Off” Pressure
C l l t D i P 8. Calculate Dynamic Pressure and Drag Coefficient
4/13/2009 ELF 60
Example Vertical Wind Tunnel Test Data SheetExample Vertical Wind Tunnel Test Data SheetName Weight ( gm ) Gauge Pressure @ Liftoff ( psi ) Dynamic Pressure ( psf )* Drag Coefficient**1. Isaac_______________1.6___________________25________________________16.6_________________0.5____2. Robert______________1.4___________________29________________________18.2_________________0.4____
*Note: Throat Area = ( π / 4 ) x Minimum Diameter2 = 0.785 x 0.252 = 0.0491 in2( )
Exit Area = ( π / 4 ) x Exit Diameter2 = 0.785 x 0.752 = 0.442 in2
Velocity = 646 x Throat Area / Exit Area = 71.8 ft / sec
Density = Ambient density x ( gauge pressure + 14.7 ) / 14.7 = 0.0001617 x ( gauge pressure +14.7 )
4/13/2009 ELF 61
y y ( g g ) ( g g )
Dynamic pressure = ½ x density x velocity2 = 0.417 x ( gauge pressure + 14.7 )
**Note: Drag coefficient = Weight / dynamic pressure / soda straw cross sectional area = 5.15 x weight / dynamic pressure.
Project # 13: Grades 9+Project # 13: Grades 9+
How to Measure Accuracy of Test DataHow to Measure Accuracy of Test Data
4/13/2009 ELF 62
How Do You Measure Accuracy of Experimental Data?
How Do You Measure Accuracy of Experimental Data?
Repeat a Controlled Experiment More Than Once to ComputeAverage of the DataStandard Deviation of the Data
Equation for the AverageAverage = ( Data1 + Data2 + + DataN ) / NAverage = ( Data1 + Data2 + … + DataN ) / N
– Example: Flight Distance of First Test = 80 ft and Flight Distance of Second Test = 100 ft
– Average Flight Distance = ( 80 + 100 ) / 2 = 90 ftAverage Flight Distance ( 80 + 100 ) / 2 90 ft
Equation for the Standard DeviationStandard Deviation = {[( Data1 – Average)2 + ( Data2 – Average )2 + … + ( D t N A )2 ] / ( N 1 )}1/2DataN – Average )2 ] / ( N – 1 )}1/2
– Example: Flight Distance of First Test = 80 ft and Flight Distance of Second Test = 100 ftStandard Deviation of Flight Distance = {[( 80 90 )2 + ( 100 90 )2 ] / ( 2 1 )}1/2 =
4/13/2009 ELF 63
– Standard Deviation of Flight Distance = {[( 80 – 90 )2 + ( 100 – 90 )2 ] / ( 2 – 1 )}1/2 = {[( -10 )2 + ( 10 )2 ] / ( 2 – 1 )}1/2 = {[ 100 + 100 ] / 1 }1/2 = [ 200 ]1/2 = 14 ft
Example Slide of Student Team Test ResultsExample Slide of Student Team Test Results
N R k t L th W i ht Th t D C ff M iName Rocket Length Weight Thrust Drag Coeff MaximumTime Range
I B 6 i 1 6 2 4 lb 0 4 2 120 fIsaac Buzz 6 in 1.6 gm 2.4 lb 0.5 4.2 sec 120 ftRobert Stinger 5 1.4 2.6 0.4 4.0 110
Average = 5.5 in 1.5 gm 2.5 lb 0.45 4.1 115 ftStandard Deviation = 0 7 in 0 1 gm 0 1 lb 0 07 0 1 sec 7 ft Standard Deviation = 0.7 in 0.1 gm 0.1 lb 0.07 0.1 sec 7 ft
*Note:
Maximum time at 40 psi gauge pressure and 90 deg launch
4/13/2009 ELF 64
Maximum time at 40 psi gauge pressure and 90 deg launch
Maximum range at 40 psi gauge pressure and 45 deg angle of launch.
Measured thrust data at 40 psi gauge pressure.
Project # 14: Grades 9+Project # 14: Grades 9+
Flight Trajectory Analysis Using a Digital Flight Trajectory Analysis Using a Digital Camcorder
4/13/2009 ELF 65
How Do You Conduct Flight Trajectory Analysis Using a Digital Camcorder?
How Do You Conduct Flight Trajectory Analysis Using a Digital Camcorder?g gg g
Frame 21_12: t = 0.00 sec, h = 4.3 ft, x = 0 ft Frame 22_01: t = 0.27 sec, h = 3.5 ft, x = 2.1 ft
Frame 22 03: t = 0 40 sec h = 2 3 ft x = 3 3 ft Frame 22 05: t = 0 53 sec h = 0 ft x = 4 5 ftFrame 22_03: t = 0.40 sec, h = 2.3 ft, x = 3.3 ft Frame 22_05: t = 0.53 sec, h = 0 ft, x = 4.5 ft
4/13/2009 ELF 66Available Software Sources to Extract Frames from Video Include Microsoft Movie Maker ( free ) and Roxio Easy Media Creator .
How Do You Measure Flight Trajectory Velocity Using a Camcorder?
How Do You Measure Flight Trajectory Velocity Using a Camcorder?
t, Time, sec x, Horiz0ntal Distance, ft Δ X, ft Vx = Δ x / Δ t, ft / sec
0 00 0 00.00 0 0 -
0.07 0.3 0.3 4
0.13 0.9 0.6 100.13 0.9 0.6 10
0.20 1.5 0.6 9
0.27 2.1 0.6 9
0.33 2.7 0.6 10
0.40 3.3 0.6 9
0.47 3.9 0.6 9
0.53 4.5 0.6 10
4/13/2009 ELF 67
How Do You Measure Flight Trajectory Acceleration Using a Camcorder?
How Do You Measure Flight Trajectory Acceleration Using a Camcorder?gg
t, Timesec
h, Height
x, Horiz Distance
Δh Vz = Δ h / Δ t
Δ Vz az = Δ Vh/ Δ t
Δ Xft
Vx = Δ x / Δ t
Δ Vx ax = Δ Vx/ Δ t
ft ft ft / sec ft / sec2 ft / sec ft / sec2
0.00 4.3 0 - - - - 0 - - -
0.07 4.3 0.3 0 0 - - 0.3 4 4 57
0.13 4.2 0.9 -0.1 -2 -2 -33 0.6 10 6 86
0.20 3.9 1.5 -0.3 -4 -2 -57 0.6 9 -1 -14
0.27 3.5 2.1 -0.4 -6 -2 -29 0.6 9 0 0
0.33 3.0 2.7 -0.5 -8 -2 -33 0.6 10 1 14
0.40 2.3 3.3 -0.7 -10 -2 -29 0.6 9 -1 -14
0.47 1.3 3.9 -1.0 -14 -4 -57 0.6 9 0 0
4/13/2009 ELF 68
0.53 0 4.5 -1.3 -17 -3 -50 0.6 10 1 14
Example Drop Test or Rocket Horizontal Launch Test Data Sheet
Example Drop Test or Rocket Horizontal Launch Test Data Sheet
Name Height ( ft ) Launch Velocity ( ft / sec ) Impact Time ( sec ) Isaac 5.0 0 0.56Robert 5.5 0 0.59
• Hypothesis: Predicted time of ground impact = ( 2 x height / a )1/2 = 0.249 height1/2
• Note: Digital camcorder can be used to measure the launch location, time of impact, and impact location. It can also be used to derive the launch velocity.
4/13/2009 ELF 69
Example Rocket 45 Deg Launch Test Data SheetExample Rocket 45 Deg Launch Test Data Sheet
Name Gauge Pressure ( psi ) Launch Velocity ( ft / sec ) Launch Angle ( deg ) Time ( sec ) Max Range ( ft )1. Isaac____________40___________________75__________________45_____________3.2__________120_2 R b t 40 70 45 3 1 1102. Robert___________40___________________70__________________45_____________3.1__________110__
• Hypothesis: Predicted maximum range
• = 0.707 x Launch Velocity x Time of Flight
• = Launch Velocity2 / a = Launch Velocity2 / 32.2.
4/13/2009 ELF 70
Example Rocket Vertical Launch Test Data SheetExample Rocket Vertical Launch Test Data Sheet
Name Gauge Pressure ( psi ) Launch Velocity ( ft / sec ) Launch Angle ( deg ) Max Time ( sec )1. Isaac____________40___________________75_____________________90______________4.2_______2 Robert 40 70 90 4 02. Robert___________40___________________70_____________________90______________4.0________
• Hypothesis: Predicted maximum time of ground impact for vertical launch = 2 x Launch Velocity / a = 0.0621 x Launch Velocity
4/13/2009 ELF 71
Project # 15: Grades 12+Project # 15: Grades 12+
Develop a Technical Description of a Soda Develop a Technical Description of a Soda Straw Rocket
4/13/2009 ELF 72
Soda Straw Rocket Initial Baseline ConfigurationSoda Straw Rocket Initial Baseline Configuration
Foam Ear Plug “ Giant” Soda Straw Adhesive Strip Tabbing
0.28 in0.25 in
0.5 inllcc = 6.0 in= 6.0 in
l = 7.0 inl = 7.0 in
0.5 in
4/13/2009 ELF 73
Soda Straw Rocket Initial BaselineCost, Weight and Balance
Soda Straw Rocket Initial BaselineCost, Weight and Balance
Component Cost $ Weight g cg Station inComponent Cost, $ Weight, g cg Station, inNose ( Plug ) 0.10 0.6 0.5Body ( Soda Straw ) 0.01 0.5 3.5Fins ( Four ) 0.23 0.5 6.75 Total 0.34 1.6 3.39
4/13/2009 ELF 74
Soda Straw Rocket Initial Baseline DefinitionSoda Straw Rocket Initial Baseline DefinitionBody
Material type HDPE PlasticMaterial density, lbm / in3 0.043y,Material strength, psi 4,600Thickness, in 0.004Length, in 7.0Diameter, in 0.28Diameter, in 0.28Fineness ratio 25.0Nose fineness ratio 0.5
FinsM t i l Pl tiMaterial PlasticPlanform area, in2 ( 2 panels exposed ) 0.25Wetted area, in2 ( 4 panels ) 1.00Aspect ratio ( 2 panels exposed ) 1.00Taper ratio 1.0Chord, in 0.5Span ( exposed ), in 0.5Span ( total including body ), in 0.78
4/13/2009 ELF 75
Leading edge sweep, deg 0xmac, in 6.625
Soda Straw Rocket Initial Baseline Definition( cont )
Soda Straw Rocket Initial Baseline Definition( cont )
NoseMaterial type FoamMaterial type FoamMaterial density, lbm / in3 0.012Average diameter 0.39 inLength 0.90 in
Reference ValuesReference ValuesReference area, in2 0.0616Reference length, in 0.28
Thrust PerformanceInside cavity length, in 6.0Typical pressure, psi 30Maximum thrust @ 30 psi pressure, lb 1.47Time constant, s ( standard temperature ) 0.025, ( p )
4/13/2009 ELF 76
Soda Straw Rocket Initial Baseline HasExcess Static Margin
Soda Straw Rocket Initial Baseline HasExcess Static Margingg
( xAC )B
xxCGCG
d
( ( xxAC )Tl
xxACAC
xxCGCG
For body-tail geometry, static margin given by( xAC – xCG ) / d = - {( CN α )B {[ xCG – ( xAC )B ] / d } + ( CNα )T {[ xCG – ( xAC )T ] / d }( ST / SRef )} / [( CNα )B+ ( CNα )T ST / SRef ]
For baseline soda stra config ration ( 3 39 in d 0 28 in l 7 0 in S 0 25 in2 SFor baseline soda straw configuration ( xCG = 3.39 in, d = 0.28 in, l = 7.0 in, ST = 0.25 in2, SRef= 0.0616 in2 ) @ α = 0 deg )
( CNα )B = 2 per rad( xAC )B = [( xAC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in( xAC )B [( xAC )B / lN ] lN 0.63 ( 0.14 ) 0.09 in( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57( xAC )T = 6.5 + 0.25 ( cmac )T = 6.63
Substituting
4/13/2009 ELF 77
( xAC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [( 0.25 ) / 0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( excess static stability )xAC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose
Soda Straw Rocket HasHigh Acceleration Boost Performance
Soda Straw Rocket HasHigh Acceleration Boost Performancegg
100
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) Aa ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dt Thrust ( T ) from Pressurized Tube of Area A
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) AA = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time
80
s
Example:Assume pgauge = 30 psi, lc = 6 in, W = 1.6 g = 0.00352 lb, τ = 0.025 s ( Average for Solenoid Valve ), s = lc = 6 in
Thrust Equation Is:T 30 ( 1 t / 0 025 ) ( 0 0491 ) 1 4726 ( 1 40 00 t )
40
60
V, V
elocit
y, fp
s T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t )Note: Actual Boost Thrust Lower ( Pressure Loss,
Boundary Layer, Launch Tube Leakage, Launch Tube Friction )
Equations for Acceleration ( a ), Velocity ( V ), and Note: Time Tics Every 0.01 s
20
q ( ), y ( ),Distance ( s ) During Boost Are:
a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352 = 13471.1 ( 1 - e – 40.00 t )
V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78s = ∫ V dt = 6735 57 t2 8 419 e – 40 00 t 336 78 t + 8 419
00 2 4 6 8 10
s, Distance Traveled During Launch, Inches
s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t + 8.419End of Boost Conditions Are:s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 sa = 7123 ft / s2 = 221 gV = 75 2 ft / s
4/13/2009 ELF 78
pgauge = 15 psi pgauge = 30 psipgauge = 60 psi
V = 75.2 ft / sq = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psfM = V / c = 75.2 / 1116 = 0.0674
Most of the Soda Straw Rocket Drag Coefficient Is from Skin Friction
Most of the Soda Straw Rocket Drag Coefficient Is from Skin Friction
1.5
CD0 = ( CD0 )Body,Friction + ( CD0 )Base,Coast + ( CD0 )Tail,Friction
= 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )
1fficie
nt
Example for Initial Baseline Soda Straw Rocket:V = 75.2 fps, ST = 0.00174 ft2, SRef = 0.000428 ft2 ⇒ ST
/ SRef = 4.07Compute:1
-Lift
Dra
g Co
e Compute:CD0 = 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 +
0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]}0.2 }[ 2 ( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86
Note:0.5
CD0,
Zero • Above Drag Coefficient Based on Assumption (
Incorrect ) of Turbulent Boundary Layer• Soda Straw Rocket Small Size and Low Velocity ⇒
Laminar Boundary Layer ⇒ Large Boundary Layer
00 2 4 6 8 10
ST / SRef, Tail Planform Area / Reference Area
Thickness on Aft Body at TailsCompute Drag Force:Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) =
0.00247 lb
4/13/2009 ELF 79
ST / SRef, Tail Planform Area / Reference Area
V = 40 fps V = 80 fpsCompare Drag Force to Weight:Dmax / W = 0.00247 / 0.00352 = 0.70Note: Drag Force Smaller Than Weight
Soda Straw Rocket Initial Baseline Deterministic Ballistic Flight Range Is Greater Than 90 Feet
Soda Straw Rocket Initial Baseline Deterministic Ballistic Flight Range Is Greater Than 90 Feetg gg g
Rx = { 2 W cos γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2
W / [ gc ρ SRef CD0Vi ]}}
h = { 2 W sin γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2
Example, Assume lc = 6 in, pgauge = 30 psi, γi = 30 deg, τ = 0.025 sec, soda straw rocket initial baseline, h = sea level, t = timpact = 1.8 s
40
unch
{ γi [ gc ρ Ref D0]} { {
W / [ gc ρ SRef CD0 Vi ]}} + hi - gc t2 / 2
Note: Time Tics
Horizontal Range At Impact = Rx = { 2 ( 0.00352 ) cos γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 ( 0 00352 ) / [ 32 2 ( 0 002378 ) ( 0 000428
20
30
ove I
nitia
l Lau
ght,
ft
every 0.5 s 0.00352 ) / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}}
= 249.8 cos γi ln ( 1 + 0.301 t )= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] =
10
20
hi, H
eight
abo
Heig 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )]
93.7 ftHeight At Impact = h = { 2 ( 0.00352 ) sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )} ln { 1 + t / { 2 ( 0 00352 ) / [ 32 2 (
00 20 40 60 80 100
Rx Horizontal Range ft
h - )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2 (
0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}} + hi – 32.2 t2 / 2
= 249.8 sin γi ln ( 1 + 0.301 t ) + hi – 32.2 t2 / 2 = 249 8 ( 0 5 ) ln [ 1 + 0 301 ( 1 8 )]
4/13/2009 ELF 80
Rx, Horizontal Range, ft
Gamma = 10 Deg Gamma = 30 Deg Gamma = 50 Deg
t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 ( 1.8 )] + hi – 32.2 ( 1.2 )2 / 2
= hi + 1.9 ft
Pareto Analysis: Soda Straw Rocket Range Is Driven by Length and Launch Angle
Pareto Analysis: Soda Straw Rocket Range Is Driven by Length and Launch Angle
Note: Decreased chamber length ⇒shorter duration thrust ( decreased total impulse ) ⇒ decreased end-of-boost velocityExample: 10% decrease in velocitySoda Straw Rocket Initial Baseline:
W = Weight = 1 6 g = 0 00352 lb
inside chamber length ⇒7.7% decrease in range at t = 1.8 s. Note: Result is nonlinear because inside chamber length = launcher W = Weight = 1.6 g = 0.00352 lb
lc = inside chamber length = 6 inτ = Time constant to open solenoid valve = 0.025 s
chamber length launcher length. Increase in lc also leads to decrease in range.
pgauge = gauge ( launch ) pressure = 30 psiγi = Initial / launch angle = 30 deglt = 7 inV = Launch velocity = 75.2 fpsCD0 = Zero-lift drag coefficient = 0.86Sea level launch with no wind ( still air )
4/13/2009 ELF 81
timpact = Time from launch to impact = 1.8 sRx = Deterministic range = 94 ft
Because of Range Uncertainty ( +/- 2.4%, 1 σ ), Initial Baseline Does not Meet Range Requirement
Because of Range Uncertainty ( +/- 2.4%, 1 σ ), Initial Baseline Does not Meet Range Requirement
Parameter Baseline Value Uncertainty in Parameter
ΔR / R Due to Uncertainty
1. Inside Chamber Length 6 in +/- 2%, 1 σ +/- 1.5%, 1σ1. Inside Chamber Length 6 in / 2%, 1 σ / 1.5%, 1σ
2. Launch Angle 30 deg +/- 3%, 1σ +/- 1.7%, 1σ3. Gauge Pressure 30 psi +/- 3%, 1σ +/- 0.5%, 1σ4 Weight 1 6 g +/ 6% 1σ +/ 0 4% 1σ4. Weight 1.6 g +/- 6%, 1σ +/- 0.4%, 1σ5. Solenoid Time Constant 0.025 s +/- 20%, 1σ +/- 0.2%, 1σ
6. Zero-Lift Drag Coefficient 0.86 +/- 20%, 1σ +/- 0.2%, 1σ
Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based onWind tunnel testThrust static testWeight measurementStructure static testPrediction methods
T t l Fli ht R U t i t f 30 i L h t 30 d t S L l St d d At h i Still Ai
4/13/2009 ELF 82
Total Flight Range Uncertainty for 30 psi Launch at 30 deg at Sea Level Standard Atmosphere in Still AirΔR / R = [ (ΔR / R )1
2 + (ΔR / R )22 + (ΔR / R )3
2 + (ΔR / R )42 + (ΔR / R )5
2 + (ΔR / R )62 ]1/2 = +/- 2.4%, 1σ
R = 94 ft +/- 2.3 ft, 1σ 87 ft < R3σ < 101 ft
Revised Baseline Meets Range Requirement with Lighter Weight and Lower Cost
Revised Baseline Meets Range Requirement with Lighter Weight and Lower Cost
Concept Tail Planform
Length Weight Unit Cost
Drag Coefficient
Static Margin
3σ RangePlanformArea
Cost Coefficient @ 75 ft / s
Margin
Initial Baseline 0.250 in2 7.0 in 1.6 g $0.34 0.86 6.00 diam
87 to 101 ft
Revised Baseline 0.0784 in2 7.0 in 1.2 g $0.13 0.75 0.00 diam
93 to 107 ft
4/13/2009 ELF 83
Project # 16: Grades 12+Project # 16: Grades 12+
House of Quality for a Soda Straw RocketHouse of Quality for a Soda Straw Rocket
4/13/2009 ELF 84
House of Quality Translates Customer Requirements into Engineering Emphasis
House of Quality Translates Customer Requirements into Engineering Emphasisq g g pq g g p
-
0
-
Flight Range 5 7 2 1
Body ( Material, Chamber Length )
Tail ( Material, Number, Area, Geometry )
Nose Plug ( Material, Length )
Flight RangeWeightCost
523
7 2 14 1 5
1 2 7
46 5 7 2 4 3 1 18 5 2 2 1 3 2 36 5 1 2 5 3 746 = 5 x 7 + 2 x 4 + 3 x 1 18 = 5 x 2 + 2 x 1 + 3 x 2 36 = 5 x 1 + 2 x 5 + 3 x 7
1 3 2Note: Based on House of Quality, inside chamber length most important design parameter.
1 - Customer Requirements2 – Customer Importance Rating ( Total = 10 )3 – Design Characteristics4 – Design Characteristics Importance Rating ( Total = 10 )
Note on Design Characteristics Sensitivity Matrix: ( Room 5 ):++ Strong Synergy+ Synergy
4/13/2009 ELF 85
es g C a acte st cs po ta ce at g ( ota 0 )5 – Design Characteristics Sensitivity Matrix 6 – Design Characteristics Weighted Importance7 – Design Characteristics Relative Importance
0 Near Neutral SynergyAnti-Synergy- - Strong Anti-Synergy
Project # 17: Grades 12+Project # 17: Grades 12+
Design of Experiments for a Soda Straw Design of Experiments for a Soda Straw Rocket
4/13/2009 ELF 86
DOE Approaches Are a Trade-off of Time Required for DOE Study vs Confidence in Result
DOE Approaches Are a Trade-off of Time Required for DOE Study vs Confidence in Resultq yq y
DOE Approach Number R i d
Designs R i d f
Designs R i d f
Time R i d
Interactions / C fid i Required
DesignsRequired for
Simple Pareto ( 2
Parameters ), 2 L l
Required for Complex Pareto ( 5
Parameters ), 2 L l
Required for Each Design
Confidence in Predicted Optimum
2 Levels 2 LevelsParametric
Study 1 + k ( l – 1) ☺ ( 3 ) ☺ ( 6 ) ☺ ( None )
Adaptive One-Factor-at-a-
Time
1 + k ( l – 1 ) ☺ ( 3 ) ☺ ( 6 ) ☺ to ( Some )
Full Factorial lk ( 4 ) ( 32 ) ☺ ( Excellent )
☺ S i A B l A
4/13/2009 ELF 87
☺ Superior Average Below Average
Reference: Montgomery, D.G., Design and Analysis of Experiments, John Wiley & Sons, 2001
A DOE Parametric Study Changes One Factor at a Time, with All Others Held at Base Level
A DOE Parametric Study Changes One Factor at a Time, with All Others Held at Base Level
DesignNumber
Parameter( x1 )
Parameter( x2 )
Parameter( x3 )
Parameter ( x4 )
Result( y )
Example of Parametric Study: 4 parameters, 2 Levels 1 + k ( l – 1 ) 1 + 4 ( 2 – 1 ) = 5 DOE Designs
1 Low Low Low Low y1
2 High Low Low Low y2
3 Low High Low Low y3g y3
4 Low Low High Low y4
5 Low Low Low High y5Process:1 Specify levels for each parameter1. Specify levels for each parameter2. Change one parameter at a time, with all others at baseline ( e.g., low ) level3. DOE “Best” design is best row result yBest )
1. Compare y1, y2 ( x1 )Besty1 y2 ( 1 )Best
2. Compare y1, y3 ( x2 )Best
3. Compare y1, y4 ( x3 )Best
4. Compare y1, y5 ( x4 )Best
4/13/2009 ELF 88
5. Compare y1, y6 ( x5 )best
6. Assume ybest is row with ( ( x1 )Best , ( x2 )Best , ( x3 )Best , ( x4 )Best , ( x5 )best )7. Compare yBest with baseline to determine optimum design
A DOE Adaptive One-Factor-at-a-Time Study Sequentially Selects Parameters, Based on Result
A DOE Adaptive One-Factor-at-a-Time Study Sequentially Selects Parameters, Based on Result
DesignNumber
Parameter( x1 )
Parameter( x2 )
Parameter( x3 )
Parameter( x4 )
Result( y )
Example of OFAT Study with 4 parameters, 2 Levels 1 + k ( l – 1 ) 1 + 4 ( 2 – 1 ) = 5 DOE Designs
1 Low Low Low Low y1
2 High Low Low Low y2
3 Best High Low Low y3g y3
4 Best Best High Low y4
5 Best Best Best High y5
Process:Process:1. Specify levels for first parameter x1
2. Compare results for first parameter x1
3. Set new level for x1 based on row that gives best result4. Move on to next parameter and repeat until all rows evaluated5. Assume row that provides best y is yBest
6. Compare yBest with baseline to determine optimum design
4/13/2009 ELF 89
A DOE Full Factorial Study Evaluates All Combinations of Parameters, but Takes Longer
A DOE Full Factorial Study Evaluates All Combinations of Parameters, but Takes Longer
DesignNumber
Parameter( x1 )
Parameter( x2 )
Parameter( x3 )
Parameter( x4 )
Result( y )
Example of Full Factorial Study with 4 parameters, 2 Levels lk = 24 = 16 Designs
1 Low Low Low Low y1
2 High Low Low Low y2
3 Low High Low Low y3
4 High High Low Low y4 High High Low Low y4
5 Low Low High Low y5
6 High Low High Low y6
7 Low High High Low y77 Low High High Low y7
8 High High High Low y8
9 Low Low Low High y9
10 High Low Low High y10
11 Low High Low High y11
12 High High Low High y12
13 Low Low High High y13
4/13/2009 ELF 90
14 High Low High High y14
15 Low High High High y15
16 High high High High y16
A DOE Study Should Search the Broad Possible Design Space
A DOE Study Should Search the Broad Possible Design Space
Example: DOE Geometric Design Space for Soda Straw Rocket
No tail Statically unstableNo tail2 Tails3 tails
Statically unstable
Probably unstable
4 TailsMono-wingCruciform Wing
Adds unnecessary drag and weight
Adds unnecessary drag and weightCruciform WingCanardsShort Length ( < 7 in )
Adds unnecessary drag and weight
Adds unnecessary drag and weight
Lighter weight and lower drag does not compensate for lower launch velocity
Long Length ( > 7 in ) Adds unnecessary drag and weight because lower launch velocity for launch tube limit
compensate for lower launch velocity
Selection Filter
4/13/2009 ELF 91
Note: Required tail area / geometry will be dealt with in DOE study
Selection Filter
A DOE Study Should Search the Broad Possible Design Space
A DOE Study Should Search the Broad Possible Design Space
Engineering n Number of Tails S Tail Planform Area in2
Example: Geometric Design Space for Soda Straw Rocket
Engineering Characteristics Envelope
nTails, Number of Tails ST, Tail Planform Area, in2
Lower Value 3 0.0392Upper Value 4 0.25Upper Value 4 0.25
Note:Lower value of ST, based on ½ revised baseline tails area. It is considered a lower reasonable value because it is
statically unstable.
4/13/2009 ELF 92
Upper value of ST, based on 2x revised baseline tails area. It is considered an upper reasonable value because it has excess static stability.
Engineering Experience Should GuideDOE Study and Design
Engineering Experience Should GuideDOE Study and Design
As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational Rocket with Near-Neutral Static Stability ( e.g., Hydra70 )
Concept Sketch l / d,Total Length /
Diameter
b / d,Total Tail Span /
Diameter
c / d,Tail Chord /
DiameterRevised Baseline 25 2.00 1
Hydra 70 15.1 2.66 1
Note: For a subsonic rocket with the center of gravity in the center of the rocket slender body theory and slender
4/13/2009 ELF 93
Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender surface theory give total tail span and chord for neutral stability of bNeutralStability ≈ 2 d and cNeutralStability ≈ d respectively.
A DOE Parametric Study Provides aQuick Evaluation of Soda Straw Rocket
A DOE Parametric Study Provides aQuick Evaluation of Soda Straw Rocket
Design Number of Tails Tail Planform Area Notional Range
DOE Parametric Study Example with 1 + k ( l – 1 ) = 1 + 2 ( 2 – 1 ) = 3 Designs
DesignNumber
Number of Tails( x1 )
Tail Planform Area( x2 )
Notional Range( y )
1 3 0.0392 in2 TBD
2 3 0.25 in2 TBD2 3 0.25 in TBD
3 4 0.25 in2 TBD
ProcessProcess1. Compare y1, y2 ( x1 )Best
2. Compare y1, y3 ( x2 )Best
3. Compare DOE best design range with revised baseline design range to determine optimum design
4/13/2009 ELF 94
A DOE Adaptive One Factor at a Time Study Provides a Quick Evaluation
A DOE Adaptive One Factor at a Time Study Provides a Quick Evaluation
Design Number of Tails Tail Planform Area Notional Range
DOE OFAT Study Example with 1 + k ( l – 1 ) = 1 + 2 ( 2 – 1 ) = 3 Designs
DesignNumber
Number of Tails( x1 )
Tail Planform Area( x2 )
Notional Range( y )
1 3 0.0392 in2 TBD
2 4 0.0392 in2 TBD2 4 0.0392 in TBD
3 ( x1 )3 = ( x1 )2 = ( x1 )Best 0.25 in2 TBD
Process1. Compare y1, y2 ( x1 )Best
2. Set level for ( x1 )3 = ( x1 )2 = ( x1 )Best
3. Compare y2, y3 ( x2 )Best
4. Compare DOE best design range with revised baseline design range to determine optimum design
4/13/2009 ELF 95
A Full Factorial DOE Study ProvidesEnhanced Confidence in the Best Design
A Full Factorial DOE Study ProvidesEnhanced Confidence in the Best Design
Design Number of Tails Tail Planform Area Notional Range
DOE Full factorial Study Example with lk = 22 = 4 Designs
DesignNumber
Number of Tails( x1 )
Tail Planform Area( x2 )
Notional Range( y )
1 3 0.0392 in2 TBD
2 4 0.0392 in2 TBD2 4 0.0392 in TBD
3 3 0.25 in2 TBD
4 4 0.25 in2 TBD
Process:1. Assume y = β0 + β1 x1 + β2 x2 + β12 x1 x2
2. Find values of β0, β1, β2, β12,by solving equations from results of 4 designs3. Max / min occurs if
Δ y / Δ x1 = 0Δ y / Δ x2 = 0
4 Compare DOE best design range with revised baseline design range to determine optimum design
4/13/2009 ELF 96
4. Compare DOE best design range with revised baseline design range to determine optimum design
AppendixAppendix
SyllabusSyllabus
4/13/2009 ELF 97
Soda Straw Rocket Science BenefitsSoda Straw Rocket Science Benefits
For University Aerospace Engineering: Provides Education That Complements Typical University AcademicsThat Complements Typical University Academics
Translate Customer Requirements to Engineering Design EmphasisConduct Design Synthesis ProcessCompare System Prediction with TestCompare System Prediction with TestEvaluate Robustness and Uncertainty
For K - 12 Aerospace Outreach: Young Students and Teachers A I t d d t A E i tAre Introduced to an Aerospace Environment
Design, Build, and Test ProcessTeamworkCompetitionExciting / Fun
4/13/2009 ELF 98
Soda Straw Rocket Science Explores Boundary Limits – See the Forest, not Just the Trees
Soda Straw Rocket Science Explores Boundary Limits – See the Forest, not Just the Trees
4/13/2009 ELF 99
Soda Straw Rocket Science Is a Balance of Analytical Versus Experimental
Soda Straw Rocket Science Is a Balance of Analytical Versus Experimentalyy
Thomas Edison: "Genius is one percent inspiration and ninety-
i t i ti "Albert Einstein: "The only real
nine percent perspiration."valuable thing is intuition."
4/13/2009 ELF 100
Students Use Design, Build, and Fly Process, for Feedback That Leads to Broader Knowledge
Students Use Design, Build, and Fly Process, for Feedback That Leads to Broader Knowledge
Design Wisdom Where is the wisdom we have lost in knowledge? Where is the knowledge
Prediction Satisfies Customer
Requirements?Understanding
Nog g
we have lost in information?--T. S. Eliot ( The Rock )Knowledge comes by taking things apart: analysis. But wisdom comes by putting things together.--John A.
Build
I it P d ibl ?No
putting things together. John A. MorrisonWe are drowning in information but starved for knowledge.--John Naisbitt ( Megatrends: Ten New Directions Transforming Our Lives )
Knowledge
Fly ( Test )
Is it Producible?
Failure / Success
Information Transforming Our Lives )We learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a
Test Results Satisfy Customer Requirements
and Consistent with
No Data
Success never made a mistake never made a discovery.--Samuel Smiles ( Self Help )
4/13/2009 ELF 101
and Consistent with Prediction?
Yes
Why Use a Small Air Rocket?Why Use a Small Air Rocket?
Low CostFast Setup and Test in ClassroomFast Setup and Test in ClassroomAllows Comparison of Predicted Physics with Flight / Ground Test DataFlight / Ground Test Data
Controlled Chamber Pressure / ThrustControlled Total ImpulseControlled Total Impulse
SafeAdvantage Over Estes-type Hot Exhaust Rocketg yp
No CleanupAdvantage Over Water Rocket
4/13/2009 ELF 102
g
Example of a University Aerospace Engineering Education Program
Example of a University Aerospace Engineering Education Programgg
Provide Information to Students to Initiate Design, Build, and Fly ProcessCustomer RequirementsFurnished Launcher / MaterialsFurnished Launcher / MaterialsHow to Make a Soda Straw RocketPrediction MethodsBaseline Rocket DescriptionBaseline Rocket Description
DesignTranslate Customer Requirements to Engineering Design EmphasisC d A f Al iConduct Assessment of AlternativesSelect Preferred Design
Build RocketFly ( Conduct Flight Test )Document
Design Selection Process
4/13/2009 ELF 103
gDesign CharacteristicsComparison of Prediction with Test
Example of K - 12 Aerospace Outreach ProgramExample of K - 12 Aerospace Outreach Program
Pre-school ( ≈ 1 Hour )Vid f R k tVideos of RocketsHow to Make Soda Straw RocketQuestionsBuild and Fly Rockets
Elementary School ( ≈ 1 Hour )Above + History of Rockets Video of my grandsons – Nick ( 7 ) and Above + History of Rockets
Middle School Science Camp ( 4 Hours )Day 1 ( 2 Hours )
y g ( )Chris ( 4 )
– History of Rockets– Videos of Rockets– Galileo’s Hypothesis of Gravity
4/13/2009 ELF 104
– Newton’s 2nd Law– Soda Straw Rocket Design Parameters
Example of K - 12 Aerospace Outreach Program( cont )
Example of K - 12 Aerospace Outreach Program( cont )( )( )
Middle School Science Camp ( cont )Day 1 ( cont )Day 1 ( cont )
– Scientific Method– How to Build Soda Straw Rocket and Launcher / Ground Test Stand – Questions on PresentationQuestions on Presentation– Build Soda Straw Rockets– Teams Build Launchers / Ground Test Stands– Teams Conduct Thrust Ground Tests– Teams Conduct Thrust Ground Tests– Teams Conduct Drag Coefficient Ground Tests
Day 2 ( 2 Hours )Conduct Flight Tests– Conduct Flight Tests
– Predict Thrust, Drag Coefficient, Boost Velocity, Vertical Terminal Velocity and Maximum Range Using Simplified Physics
– Compare Prediction Ground Test and Flight Test
4/13/2009 ELF 105
– Compare Prediction, Ground Test, and Flight Test– Develop Team Posters and Present Results
Summary – Soda Straw Rocket Science Program Has Good Value
Summary – Soda Straw Rocket Science Program Has Good Value
University Aerospace Engineering EducationIncludes Elements of Aerospace System Development ProcessFast and Easy to ConductFast and Easy to ConductLow Cost
K - 12 Aerospace OutreachK - 12 Aerospace OutreachEducationalFunFunLow Cost
4/13/2009 ELF 106
Recommendations for Soda Straw Rocket Science Program
Recommendations for Soda Straw Rocket Science Programgg
Include in University Aerospace Engineering C i lCurriculum
Undergraduate Capstone Design ClassGraduate System Design ClassGraduate System Design Class
Include in AIAA Aerospace Outreach Program for K – 12 SchoolsK – 12 Schools
Sponsor Visits to Elementary, Middle, and High SchoolsSponsor “How To” Book on Soda Straw Rocket SciencepSponsor Computer Spreadsheet for Design of Soda Straw Rockets
4/13/2009 ELF 107