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Experiment on Farthest Throw of Catapult

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. Agenda. Introduction Factor Analysis Experiment and Analyzing Summary. Background. Catapult in history

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Experiment on Farthest Throw of Catapult

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  1. 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

  2. Agenda • Introduction • Factor Analysis • Experiment and Analyzing • Summary

  3. Background • Catapult in history • Application of the principal of leverage • A tool for attack • Catapult in experiment • Composed of a band, a ball, some bolts and the basic wooden structure • How to make it have a launch on the largest distance?

  4. 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”

  5. Related Chapters in Textbook • 23 full factorial design • Response surface analysis --- The steepest ascent method • Fitting regression model • General linear model

  6. 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）

  7. Introduction • Factor Analysis • Experiment and Analyzing • Summary

  8. Response variable • Cast distance of the catapult • Range 0.5 through 3.5 meters • Measurement • band tape + number of floor tires

  9. Catapult Humidity Effect factor The position of the apron Temperature Catapult The open angel of the cast arm Environment Air resistance The front fixture of the band The radius of the ball Wind velocity The back fixture of the band Put the cast arm to the precise angel Cast distance of the catapult The right position of the ball Tiredness Concentration Put the cast arm to the precise angel The height of the catapult The precision of the band tape Measurement Operator

  10. Constant Variables & Noise Variables

  11. Control the interference factor

  12. Control Variables (a) (b) (c)

  13. The 23 factorial design • Replications: 5

  14. Introduction • Factor Analysis • Experiment and Analyzing • Summary

  15. Our experimenting and analyzing process

  16. The qualitative analysis of factors’ effects

  17. The further analysis of response surface We will show the process in Minitab. Regression model: When A=1, B=6, C=180 :

  18. General Linear Model • 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”

  19. 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

  20. Special verification of “B”, cont • Box-plot: • Data in detail: • Conclusion • B has a slight positive effect to the response variable Distance • Optimal style: A=1, B=6, C=180

  21. Estimating the Optimal Value • Under A=1, B=6, C=180 • 20 replications • 95% confidence interval • Our estimation of the “Largest distance”: (544.98, 551.02)

  22. Introduction • Factor Analysis • Experiment and Analyzing • Summary

  23. Our methodology

  24. Our final result Optimal style: A=1, B=6, C=180 Optimal value: (544.98, 551.02)

  25. The End !Thank you! Q & A Photo art courtesy: smart_katalog_fortwo_2007.pdf, Daimler AG

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