為了瞭解自由落體下降時，由直線運動轉換為迴轉運動的現象，本文採用不同長寬比的紙製矩形葉片，改變葉片夾角，可觀察葉片長寬比和葉片夾角對矩形葉片下降時，受到之空氣阻力和能量轉換效率的影響。本文以長度比例為1.5：1，1.75：1，2.0：1，2.5：1和3.0：1搭配夾角為30度，60度和90度的矩形葉片，令其由2.5公尺高處靜止掉下，以觀察其運動轉換的現象。
實驗結果顯示，若取同一矩形葉片，改變角度逐次試驗，可以發現角度越大者轉速越慢，其所受到壓力差的阻力則越大，能量轉換的效率亦跟著變大。翼寬變大的矩形葉片，掉落運動距離的總時間較長，掉落速度也跟著變慢且摩擦阻力變大，能量轉換效率隨之降低。而翼長變大的矩形葉片，掉落運動距離的總時間較長，速度降低但是轉速卻較高，於是造成壓力差之阻力增加，導致能量轉換效率隨之上升。本文所採用之矩形葉片夾角90度且長寬比為2.5時，具有最大的能量轉換效率。

In order to investigate the phenomenon that liner motion will become rotational motion when subjects fall. We use rectangular blades with different aspect-ratios and vary the angles of the blades in the experiment. We observe the effect of air resistance and the efficiency of the energy transformation on the aspect-ratios and the angles of the wings when the blades fall. We let the vanes with the aspect-ratio of 1.5:1, 1.75:1, 2.0:1, 2.5:1 and 3.0:1 collocated with angles of 30˚, 60˚ and 90˚ fall from 2.5 meters and observe the changing phenomenon of the motion.
The result shows that, if we take the same blade and vary the angle gradually, the bigger the angle is, the slower the speed of rotation is. Besides, the resistance of the difference of the pressure to the blade goes greater, and the efficiency of the energy transformation increases. The blade with wider breadth of the wings takes much time to fall in a certain distance. Therefore, the falling speed slows down, the resistance increases, and the efficiency of the energy conversion goes down. Moreover, the rectangle blade with longer length of the wings takes much falling time. The falling speed goes slower, but the whirling speed is faster. So, the resistance causing the difference of the pressure increases and raises the efficiency of the energy transformation. It is found out the ninety angle between blades with aspect ratio of 2.5 has the highest energy conversion efficiency.

摘 要 I
Abstract III
目 錄 IV
圖 目 錄 VI
符 號 說 明 XII
第一章 緒論 1
1-1 文獻回顧 1
1-2 研究動機與目的 3
第二章 實驗設備與量測方法 4
2-1 實驗設備 4
2-2 實驗方法 7
第三章 矩形葉片運動原理與因次分析 11
2-1 矩形葉片運動之原理 11
2-2 實驗數據的演算 14
2-3 矩形葉片的因次分析 18
第四章 實驗結果與討論 22
4-1 矩型葉片落下時間的變化 23
4-2 矩形葉片落下速度的變化 28
4-3 矩形葉片於作用距離下的 值變化 35
4-4 矩形葉片落下時轉速的變化 39
4-5 矩形葉片落下時的效率變化與影響 42
4-6 無因次化 45
第五章 結論 57
參考文獻 59

1. D.J. Auld and K. Srimvas, “Analysis of Propellers”, Aerodynamics for Student, 2006.
2. T. Liu, “Comparative Scaling of Flapping-and Fixed-Wing Flyers”, AIAA Journal Vol 44, No.1, pp.24-33, Jan. 2006.
3. G. Sachs, “Aerodynamic Yawing Moment Characteristics of Bird Wings”, Journal of Theoretical Biology, pp.471-478, 2005.
4. P. Gerontakps and T. Lee, “Active Trailing-Edge Flap Control of Oscillating-Wing Tip Vortex”, AIAA Journal Vol 44, No.11, pp.2746-2754, Nov. 2006.
5. D.H. Wood, “Comment on Rotational Effects on the Boundary-Layer
Flow in Wind Turbines”, AIAA Journal Vol 43, No.10, pp.2268-2269, Oct. 2005.
6. P.R. Viswanath, R. Mukund, R. Narasimha and J.D. Crouch,
“Relaminarization on Swept Leading Edges under High-Lift
Conditions”, AIAA Journal Vol 44, No.11, pp.2621-2629, Nov. 2006.
7. A. Plotkin, “Thickness and Camber Effects in Slender Wing Theory”, AIAA Journal Vol 21, No.12, pp.1755-1757, 1983.
8. G. E. Torres and T. J. Mueller, “Low-Aspect-Ratio Wing
Aerodynamics at Low Reynolds Numbers”, AIAA Journal Vol 42,
No.5, pp. 865-873, 2006.
9. J. M. Young, H. J. Oh and J. H. Seo, “Aerodynamics
Investigation of Three-Dimensional Wings in Ground Effect for
Aero-Levitation electric Vehicle’, Aerospace Science and Technology, pp.485-494, 2005.
10. P. Gerontakps, T. Lee, “Managing Flap Vortices Via Separation
Control ”, AIAA Journal Vol 44, No.11, pp.2755-2764, Nov. 2006.
11. F. M. White, “Viscous Fluid Flow”, McGraw-Hill, Inc.,
P.311-322, 1911.
12. R. W. Fox, A. T. McDonald and P. J. Pritchard, “Introduction to fluid
mechanics”, John Wiley & Sons, Inc., P.409-464, 2004.
13. B. R. Munson, D. F. Young and T. H. Okishi, “Fundamentals of fluid
mechanics”, John Wiley & Sons, Inc., P.551-628, 1990.
14. M. V. Dyke, “An album of fluid motion”, The Parabolic Press,
P.24-41,1982.
15. S. Abrate, R. Dodey, R. Kaste, G. Thibault and W Millette,
“Nonlinear dynamic behavior of parachute static lines”,
Composite Structures, vol.61, P.3-12,2003.
16. J. Moon. Young, H. J. Oh and J. H. Seo, “Aerodynamic
investigation of three-dimensional wings in ground effect for
aero-levitation electric vehicle”, Aerospace Science and
Technology, vol.9, P.485-494, 2005.
17. J. H. Miao and M. H. Ho, “Effect of Flexure on Aerodynamic
propulsive efficiency of Flapping Flexible Airfoil”, Journal of Fluids
and Structyres 22, pp.401-419, 2006.
18. H. Huang and M. Sun, “Dragonfly Forewing-Hindwing Interaction at
Various Flight Speeds and Wing Phasing”, AIAA Journal Vol 45,
No.2, pp.508-511, Nov. 2005.
19. F. H. Gern, D. J. Inman and R. K. Kapania, ”Computation of
Actuation Power Requirements for Smart Wings with Morphing
Airfoils”, AIAA Journal Vol 43, No.12, pp.2481-2486, Dec. 2005.
20. D. F. Young, B. R. Munson and T. H. Okiishi, “A Brief Introduction to
Fluid Mechanics”, John Wiley & Sons, Inc. Second Edition.
21. R. W .Fox, A. T. McDonald, P. J. Pritchard, “Introduction to Fluid
Mechanics”, John Wiley & Sons, Inc. Sixth edition.
22. R. Wolfson and J. M. Pasachoff, “Physics with Modern Physics”,
An Imprint of Addison Wesley Longman,Inc. Third edition.
23. David Halliday, Robert Resnick, Jearl Walker, “Fundamentals of
Physics”, John Wiley & Sons, Inc. Seventh edition.
23. 張國標, 簡安男, “流體力學概論”, 台灣復文興業, 1994.
24. 都筑卓司, “物理趣談一百談”, 牛頓出版股份有限公司, 1992.