1. DOE Free Fall Time of Paper Cones Jiankun SUN, Nan CHEN, Donghui LI, Quan YUAN, Tianyang XU

2. DOE Contents Pre-experiment 2 Conclusion 4 Introduction 31 Formal Experiment 33

3. Introduction Literature Review  《浅探纸锥下落快慢与纸锥大小的关系》, 陆文彬  Only study free fall time of paper cones with same radius and different angles  Derive a complicated equation to describe the relationship between acceleration and velocity and the impacts from paper cone properties

4. Introduction Factor Decomposition  Response variable: free fall time  Input variables: paper thickness, cone radius, central angle,  Control variable: height  Nuisance factor: operator performance, recording error

5. Pre- experiment Pre-experiment Design  Purpose  Check the repeatability and reproducibility  Get a general idea of the degree of factors’ influence  Design  3 replications for each level and each operator Variables CodeRadiusThicknessAngle of cone 5 cmThin150° 110 cmThick270°

6. Formal Experiment Experiment Process  At platform of stairs in the hall of Shunde Building  The operator stretch out the arm horizontally and hold the paper cone with two fingers, and then release the cone without initial velocity  A camera is used to record the process for time analysis

7. Pre- experiment Analysis: Reproducibility  Check whether there is significant difference between results of different operators  Cannot claim significant difference

8. Pre- experiment Analysis: Influence Degree  Check which variables have influence and how much the influence is  Influence from certain variables and interaction

9. Formal Experiment Formal Experiment Design  Full Factorial Design  Level setting radiusthicknessangle 1 1continuous variable 5cm10cm70g/m2200g/m290+20k(k=0,1,2…9)

10. Formal Experiment Data Collection 大小厚薄锥角 时间 12704.734.404.53 12504.204.173.90 12303.904.003.73 12103.573.47 11903.273.203.10 11703.002.902.93 11502.702.60 11302.432.302.47 11102.672.472.37 1902.00 2.70

11. Formal Experiment Data analysis  Descriptive analysis:  Thickness may have influence while radius may not

12. Formal Experiment Data Analysis  Scatter Plot:  There seems to be a linear relationship between time and angel.

13. Formal Experiment Data Analysis  Main effects plot

14. Formal Experiment Data Analysis  Interaction plot  No significant interaction between radius and thickness or between angle and radius.  Interaction between thickness and angle.

15. Formal Experiment General Linear Model (GLM)

16. Formal Experiment Residual Plots  The residual versus is a bowl-like curve  May be due to interaction

17. Formal Experiment Conclusion from GLM  Free fall time of paper cones have strong linear relationship with central angle and paper thickness  At 95% confidence level, the correlation between free fall time and cone radius is not significant

18. Formal Experiment GLM adding interaction

19. Formal Experiment Residual Plots

20. Formal Experiment Conclusion from 2 nd GLM

21. Formal Experiment Conclusion from 2 nd GLM

22. Conclusion Conclusion & Explanation  Equations  thin paper: Time = 0.461408 + 0.0143581 Angle  thick paper: Time = 0.461408 + 0.00927134 Angle  Explanation  Air resistance increases with central angle.  For different paper thickness, different mass of paper contributes to different change in fall time as the central angle changes.  Wrong sign of coefficient of thickness: not significant

23. DOE