強風下的樹木受力與截面積分析

Force and Cross-Section for Trees under Strong Wind

李信輝(Hsin-Huei Li)

指導教授 ： 洪在明

國立清華大學/理學院/物理學系/碩士(2020年)

摘要

2010年代，由於全球暖化，許多人開始關注起環保議題，對於樹林的保育是主要的議題之一，不管是因人為開發，或森林大火、風災等自然原因，都促成了一些以環保為核心發展的研究。
　　在一篇2016年發表的Physical Review E論文，研究者引用到一場2009年的颶風風災數據，宣稱樹木的年齡和高低並不影響樹木斷裂時的風速，亦即當風速達到某臨界值時，絕大部分的樹木都會應聲斷裂。
　　在上個世紀就有許多林業發達的國家，使用真實樹木進行風洞實驗，這些論文結論：樹木所受的風力與風速在一定風速下呈線性關係。另外，也有關於樹葉在強風下，會捲曲成圓錐狀，以及阻力係數隨風速下降的研究。
　　本研究針對樹木在風災中的影響，主要包括兩個部分：
一、 經由風洞實驗量測樹枝所受的風力與風速的關係，檢驗前人的研究結論。
二、 在風力增加的過程中，樹冠的截面積如何變化？
　　對於樹冠的截面積變化，我們也提出簡單的理論模型，成功解釋實驗觀察到的現象。

關鍵字

風阻力 ； 樹木 ； 截面積 ； 風速 ； 風洞

並列摘要

During the 2010s, many people began to pay attention to some environmental issues due to the global warming. One of their most concerned issues is how to protect the forests. Whether it was because of human development, forest fires, storms or some other natural disasters, it led to the beginning of research on environmental protection.
In an article that appeared in Physical Review E on 2016 that cited the data from a storm in 2009, a group of French researchers concluded that all trees break down when the wind speed exceeds a critical value.
During the last century, there have been many wind-tunnel experiments in countries where the forest industries were well developed. They concluded that the wind force acting on the plant is proportion to the wind velocity below a critical speed. There was also other research indicating that leaves tend to roll into a cone shape and the drag coefficient decreases with the increasing wind velocity.
In this thesis, we will focus on the effect of crown for the force trees endure in a storm. Our experiments consist of two parts:
(1) By use of the wind tunnel, we measure the wind force and the wind speed and check the validity of their relationship by previous researchers.
(2) How the cross section of branches and leaves decreases with the wind velocity?
Heuristic models and simple calculations are also proposed to successfully explain the change of the cross section with wind speed.

並列關鍵字

Drag_force ； Trees ； Cross-section_area ； Wind_velocity ； Wind_tunnel

參考文獻

[1] E. Virot, A. Ponomarenko, É. Dehandschoewercker, D. Quéré, and C. Clanet, Critical wind speed at which trees break, Phys. Rev. E 93, 023001 (2016).

[2] Mark Rudnicki, Stephen J. Mitchell, and Michael D. Novak, Wind tunnel measurements of crown streamlining and drag relationships for three conifer species, Can. J. For. Res. 34, 666 (2004).

[3] Stephan Vollsinger, Stephen J. Mitchell, Kenneth E. Byrne, Michael D. Novak, and Mark Rudnicki, Wind tunnel measurements of crown streamlining and drag relationships for several hardwood species, Can. J. For. Res. 35, 1238 (2005).

[4] Scott Cullen, Trees and Wind: a Practical Consideration of the Drag Equation Velocity Exponment for Urban Tree Risk Management, J. Arbor. 31, 101 (2005).

[5] Steven Vogel, Drag and Reconfiguration of Broad Leaves in High Winds, J. Exper. Bot. 40, 941 (1989).