從小玩意探討大問題-磁浮隔空旋轉器的轉動情形與磁場變化之研究
磁浮隔空旋轉器是由一個旋轉軸和底座構成,利用兩者間相互排斥的磁力, 產生隔空漂浮的效果。本研究首先對旋轉軸的結構加以分析,並設計啟動裝置, 探討啟動電壓、旋轉軸重量及底座磁力等因素對漂浮轉動的影響。 我們分析維持旋轉平衡的各種作用力,並探討旋轉軸重心位置與摩擦力的關 係,以驗證我們的分析結果。此外,我們也利用自行設計的啟動裝置,提供穩定 的初始轉速,探討旋轉軸重心位置不同時,持續轉動時間的變化,進一步驗證所 做的分析。 為了瞭解磁場在旋轉軸漂浮過程中發生的變化,我們設計了支架把空間座標 化,再以高斯計測量出各點的磁場,獲得各平面的磁場強度分佈圖。配合磁力線 分佈圖與所測得的磁場強度分佈圖,我們以一個嶄新的分析模式,將抽象的磁場 概念具體化,使我們對旋轉軸放置前後及磁力與重力平衡時的磁場變化,更深入 的了解,同時也發現磁場強度會隨距離的增加而減弱。 最後我們在旋轉器上裝置感應線圈,經由旋轉實驗測得感應電壓的存在,證 明旋轉器轉動時,磁場會產生變化。 經由對磁浮隔空旋轉器的探討,我們得以了解它的漂浮原理、磁力與摩擦力 間的平衡關係,以及旋轉前後磁場變化。The Magnetic Floating Spinner(MFS) is composed of one spinner with a magnetic base. The floating effect of the spinner is caused by the interaction between the two opposite magnetic fields. We first analyzed the detail structure of the MFS, and then designed a starter to rotate it. Later, we studied the effect of starting electric potential, the weight of the spinner and the magnetic force of the base on the floating movement. We presented an explanation for the forces that maintained the floating of the spinner and, to support that, we studied the friction force with the position change of the spinner gravity centre. We also used the starter designed by us to provide a stable initial rotating force and analyzed the relationship between the change of gravity centre position and the duration of rotation. In order to understand the magnetic field change during floating movement, we designed a spatial frame to coordinate the spinner that floated above the base. We measured the surrounding magnetic force with the Goth’s apparatus and conducted a magnetic force distribution diagram. According to this diagram and the line of magnetic force, we therefore provide a brand new analysis model , which bring the abstract concepts of the magnetic field into a concrete theory. This research not only brings us to understand the magnetic field change of the spinner before and after its placement over the base and the balance between the magnetic and the gravity force, but also reveals that the magnetic force will wane with the increase of distance. Finally, we placed an induction coil by the spinner to detect a voltage change during spinner movement. This is an evidence that the magnetic field will change during the spinner movement. Through the study of MFS, we can now understand why it floats, the balance between magnetic and friction force, and the change of the magnetic force before and after the spinner movement. MFS = Magnetic Floating Spinner
輸贏一線間-淘汰賽的相關探討
單淘汰賽是一種失敗一次即遭淘汰的賽制;在此假定每位選手都有一相對應的能力數值,本文主要探討在均高的單淘汰賽程表之下,若賽程安排完全依照種子安排原則(亦即最強的選手對最弱的選手、次強隊次弱….),則對於能力越強的選手越有保障,直觀上而言能力最強的選手應有最大的奪冠機率,探討此種賽程安排是否滿足能力較強的選手有較大的勝率?因發現在某些特殊的選手能力數值分佈之下會發生次強選手勝率大於最強選手的情況,令A、B代表最強與次強選手,P(A)、P(B)代表A、B奪冠的機率,故擬定P(B)/ P(A)為參考依據,尋求P(B)/ P(A)的最大值發生處作為最極端的狀況。發現四位選手的情況下,P(B) / P(A)最大值 = 1;八位選手的情況下,P(B) / P(A)最大值=(196+98) / 343=1.0938,當選手數為2n時,P(B)/ P(A)最大值隨n的增加而遞增。
Knockout Tournament is a highly competitive system in which any player losing a game can no longer play in the tournament. Here we suppose that every player has a numerical value that corresponds to his ability. We consider a totally-seeded knockout tournament with 2n players where in the first round, the strongest player matches the weakest player, the second strongest player matches the second weakest player, and so on. We examine whether a stronger player always has a greater probability of winning the tournament. The answer is in the affirmative for n = 2. For a tournament with eight players(n = 3), the situation is much more complicated. In certain cases, the second strongest player has the greatest probability of winning the tournament. Specifically, let A and B denote the strongest and second strongest players, P(A) and P(B) their respective probability of winning the tournament. We find that the maximum value of P(B)/P(A)equals (196+98) / 343 = 1.0938. For n > 3, we have not obtained the maximum value of P(B) / P(A) . However, it can be readily seen that the maximum value of P(B) / P(A) is non-decreasing as n increases.
松鶴土石流災害初步調查分析
The heavy rain fall brought by Typhoon Mindulle in 2004 caused debris flows in the mountains of Taiwan. The most serious debris flows took place in the areas along the East-West Expressway. The area from Mt. Li to Tien Leng, namely, from the upper course to the middle course of River Da Chia. There was plenty of debris flowing to the courses of the rivers from the hot spring area in Ku Kuan to the starting place of East-West Expressway, Tien Leng. This situation caused the sedimentation of the river courses. According to the data issued by The Soil and Water Conservation Bureau of the R.O.C, on July 2nd debris flows erupted in the First and the Second branches of the river in Sung Ho Village and caused 1 death and 2 injuries, besides, the disaster destroyed 8 major roads causing transportation breakdown. On August 24th, the Typhoon Aere caused the heavy flow of the river which destroyed Po I Elementary School and Chun Chin Bridge. The researchers employed research reviews and field investigations as the research methodology with the research scope of Sung HoVillage in middle Taiwan and disaster of debris flow. The First and the Second branches of Sung Ho River belong to the category of high potentiality of danger of debris flows. The Chichi Earthquake had accumulated sufficient sedimentation of soil and stone. 2004 年敏督利颱風豐沛的雨量,引起台灣山區發生土石流,中橫公路沿線尤其嚴重。從 大甲溪上游的梨山到中游的天冷都有災情;谷關溫泉區至新中橫起點的天冷,大量土石,流 入溪中,造成河道淤積。據水土保持局的資料顯示,7 月2 日松鶴一、二溪爆發土石流,傷 亡各1 人,2 人失蹤,對外聯絡道路台8 省道崩塌中斷。8 月24 日艾莉颱風來襲,溪水暴漲, 沖毀博愛國小、長青橋及民房7 戶【1】。 本文以松鶴為試區,土石流災害為對象,使用文獻探討及現場調查的方法,進行研究。 結果顯示,松鶴一、二溪,均屬於土石流高危險潛勢溪流;肇因於九二一地震的崩塌地,提 供充足的土石堆積物。