Experiment on Farthest Throw of Catapult

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Experiment on Farthest Throw of Catapult

Course project of DOE, 2010 spring

By Group 11:沈坤，孙维，袁怡潇，于漠南，朱雯

Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG


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•Introduction

•Factor Analysis

•Experiment and Analyzing

•Summary

Agenda


Experimenting and AnalyzingFactor AnalysisIntroduction Summary

Background• Catapult in history

– Application of the principal of leverage– A tool for attack

How to make it have a launch on the largest distance?

• Catapult in experiment– Composed of a band, a ball, some

bolts and the basic wooden structure



Objectives

− A statistical model of significant factors in response to the cast distance of the catapult

− The optimal combination of the significant factors to maximize the cast distance

− An estimation of this “optimal distance”


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Related Chapters in Textbook

23 full factorial design

Response surface analysis --- The steepest ascent method

Fitting regression model

General linear model


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Related Papers

《利用响应曲面法确定竹叶中黄酮最佳提取条件》，冯涛、曹东旭、高辉、季光， 2003 年 6 月，《天津轻工业学院学报》。《试验设计与优化》，李波、徐泽民、李方、张新申， 2003年 1 月，《中国皮革》。《 Experiment of washing process 》，于航等。（五字班 DOE 课程小组大作业报告）《 An investigation on data entry effectiveness & efficiency 》，张重阳等。（五字班 DOE 课程小组大作业报告）


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•Introduction

•Factor Analysis


•Summary



Response variable

Cast distance of the catapult− Range

0.5 through 3.5 meters Measurement

− band tape + number of floor tires



Effect factorCatapult

The open angel of the cast armThe position of the apron

Tiredness

Concentration

Put the cast arm to the precise angel

Humidity

Air resistance

The right position of the ball

Temperature

Wind velocity

Put the cast arm to the precise angel

The height of the catapult

The radius of the ball

The precision of the band tape

The front fixture of the band

The back fixture of the band

OperatorMeasurement

CatapultEnvironment

Cast distance of the catapult



Constant Variables & Noise Variables

Constant Variables

•Humidity•Air resistance•Temperature•Radius of the ball•Height of the catapult •Back fixture of the band

Noise Variables

•Elasticity of the band•Precise angel of arm•Launch orientation•Wind velocity•Vibration•Human factor•Concentration•Tiredness•Accuracy of reading



Control the interference factor

The reading accuracy

• Two observers each read a value• Use the average to represent the result of that throw

The orientation and initial position of the throw

• Use hand to press the catapult on the ground to avoid vibration• Use the gap line of the tiles to align the catapult and the ruler

The precise angel of arm

• Pay a special attention on the scale mark• Release the arm decidedly and rapidly



Control VariablesReal factor Range Category Influence Level

Front fixture of the band

1,2,3,4 Discrete Tension of the band 1,3 (a)

Position of the apron

1,2,3,4,5,6 Discrete Angel of the ball 4,6 (b)

Open angel of the cast arm

0~180 degree

Continuous

Cast speed of the ball

160 and180 degree (c)

(a)

(b)

(c)



Real factor Variable name

Range Category Coded value

— +

Front fixture of the band

A 1,2,3,4 Discrete 1 3

Position of the apron

B 1,2,3,4,5,6 Discrete 4 6

Open angel of the cast arm

C 0~180 degree Continuous 160 180

The 23 factorial design

Replications: 5


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•Introduction

•Factor Analysis


•Summary



Factorial Design Qualitative Analysis

Quantitative Analysis

Estimating the Optimal Value

A Special Verification of

“factor B”

General Linear Model

Our experimenting and analyzing process



321

600

500

400

300

200

654

180170160A

Dist

ance

B C

Di stance 与 A, B, C 的矩阵图

ABC

316464

180160180160180160180160

600

500

400

300

200

Dist

ance

Di stance 的箱线图

31

500450400350300

64

180160

500450400350300

A

平均值

B

C

Di stance 主效应图数据平均值

64 180160

500

400

300

500

400

300

A

B

C

13

A

46

B

Di stance 交互作用图数据平均值B*A

3. 02. 52. 01. 51. 0

6. 0

5. 5

5. 0

4. 5

4. 0

C*A

3. 02. 52. 01. 51. 0

180

175

170

165

160

C*B

6. 05. 55. 04. 54. 0

180

175

170

165

160

A 1B 4C 160

保持值

> – – – – – – < 250

250 300300 350350 400400 450450 500500 550

550

Di stance

Di stance 的等值线图

B*A

3. 02. 52. 01. 51. 0

6. 0

5. 5

5. 0

4. 5

4. 0

C*A

3. 02. 52. 01. 51. 0

180

175

170

165

160

C*B

6. 05. 55. 04. 54. 0

180

175

170

165

160

A 3B 6C 180

保持值

> – – – – – – < 250

250 300300 350350 400400 450450 500500 550

550

Di stance

Di stance 的等值线图

The qualitative analysis of factors’ effects



The further analysis of response surface

We will show the process in Minitab.

Regression model:

When A=1, B=6, C=180 :

C)(B0.642500+ C)(A 1.59750 -C10.3300 +B106.450 -A214.550 +-1288.50=Distance

553.1=180)(60.642500+180)(1 1.59750 -18010.3300 +6106.450 -1214.550 +-1288.50=Distance



A GLM between distance and the significant factors and interactions− Resources: A, B, C, AC, BC

The function

The theoretical optimal solution:− Setting A at “1”, B at “6”, C at “180”

General Linear Model

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Special verification of “B”

Whether or not factor B is significant to Distance− Full factorial design: B is proved to have no significant

effect− General linear model: B’s effect seems to be significant

Advanced analysis: − Based on more data− 10 replications

A1 B5 C180A1 B6 C180A1 B4 C180



Data in detail:

Conclusion− B has a slight positive effect to the response variable

Distance Optimal style: A=1, B=6, C=180

Box-plot:

Special verification of “B”, cont



Under A=1, B=6, C=180 20 replications 95% confidence interval

Our estimation of the “Largest distance”: (544.98, 551.02)

Estimating the Optimal Value

565560555550545540535530

99

9590

80706050403020

105

1

Di stance

百分比

均值 548标准差 6. 448N 20AD 0. 315P 值 0. 517

Di stance 的概率图正态


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•Introduction

•Factor Analysis


•Summary


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Our methodology

1 •Design, and Experiment

2 •Analysis of significant factors•Model (Regression, GML)

3 •Verification of insignificant factor (B)

4 •Estimation of response variable


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Our final result

Optimal style: A=1, B=6, C=180

Optimal value: (544.98, 551.02)


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The End !Thank you!Q & A

Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG

Documents

Experiment on Farthest Throw of Catapult