Soda Straw Rocket Science

Soda Straw Rocket ScienceSoda Straw Rocket Science

Aerospace Engineering Projects forAerospace Engineering Projects forGrades K – 12+Grades K – 12+

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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+

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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

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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 …………

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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 )

qq

( 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 ) .….

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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 ……………………

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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

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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______.

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How to Make a Soda Straw RocketHow to Make a Soda Straw Rocket

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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

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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.

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How to First Check Out a Soda Straw How to First Check Out a Soda Straw Rocket

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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

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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

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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_______.

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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

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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

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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

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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

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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

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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

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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

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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

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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?

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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

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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

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Project # 5: Grades 5+Project # 5: Grades 5+

Why Do Soda Straw Rockets Fly Why Do Soda Straw Rockets Fly Differently?

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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

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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

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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.

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Scientific MethodScientific Method

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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.

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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

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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.

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How Does Newton’s 2nd Law Apply to a How Does Newton’s 2nd Law Apply to a Soda Straw Rocket?

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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

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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

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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 .

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Example of Scientific Method Hypothesis Example of Scientific Method Hypothesis Test

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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.

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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

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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

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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. “

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Design Build and Fly CompetitionDesign, Build and Fly Competition

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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

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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

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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.

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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

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*Note: Flight range and dispersal at 15 psi launch pressure and 25 deg launch angle respectively. Structural integrity at 30 psi launch pressure.


Structure Failure Prediction and Structure Failure Prediction and Comparison with Test

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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

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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


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

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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____________________

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* 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?

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Thrust Prediction and TestThrust Prediction and Test

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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

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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


8. Regulate Air Pressure to Desired Setting

9. Turn Valve on and Measure Th t F

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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____

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* 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?

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Vertical Wind Tunnel TestVertical Wind Tunnel Test

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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


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

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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 )

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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.


How to Measure Accuracy of Test DataHow to Measure Accuracy of Test Data

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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 =

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– 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

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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.


Flight Trajectory Analysis Using a Digital Flight Trajectory Analysis Using a Digital Camcorder

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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

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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


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


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


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



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



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



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


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 )



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



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


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


DOE OFAT Study Example with 1 + k ( l – 1 ) = 1 + 2 ( 2 – 1 ) = 3 Designs

DesignNumber



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



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


DOE Full factorial Study Example with lk = 22 = 4 Designs

DesignNumber



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


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

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– 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

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– 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

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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

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Soda Straw Rocket Science

Documents

Transcript of Soda Straw Rocket Science