無尾翼飛行器之穩定與控制
無尾翼飛行器(Tailless Aircraft)在軍事上的價值極大，且對於目前正在起步的微飛行載具(Micro Air Vehicle)而言，亦是值得嘗試與投資的。然而，由於無尾翼飛行器缺乏用以平衡的水平尾翼，造成其靜態的不穩定，即使設法提高靜態穩定特性，但其氣動力阻尼低、穩定性仍舊不佳。操縱上更是困難，在飛行穩定性與控制系統設計上極其挑戰性。本研究目的在探討無尾翼飛行器之穩定性與控制技術，改善其先天之不穩定特性，考慮之項目有縱向靜態穩定性、動態穩定性、控制面與組件配置等因素等進行詳細之探討。首先，找出了適用於無尾翼飛行器之Reflex翼形，接著建立無尾翼飛行器之非線性縱向動態模式，然後針對一翼展8Ocm之小型飛行器進行外型設計，並觀察分析其實際飛行狀態，再以理論與經驗公式估算無尾翼飛行器之氣動力導數，探討其飛行穩定與操控性能。此外，並運用古典控制PID控制法則，設計控制器進行非線性受控系統之動態響應模擬。由模擬結果可看出，經由翼剖面改變與控制系統的輔助下，大幅提高了其性能，使得無尾翼飛行器克服了先天的不穩定特性，更提高了其發展空間 The tailless aircraft has a great value on the military use. Meanwhile, it is worthwhile to try and to invest in it for the investigation of MAV(Micro Air Vehicle), which is being developed now. However, because of lacking horizontal tail which is used for balance, the tailless aircraft is static unstable. Even with the attempt to enhance its characteristics of static stability, the stability of the tailless aircraft is still poor for the sake of it's low damping in aerodynamics. Therefore, it is a challenge to flight stability and control system designing. The purposes of this research are to study the stability and the control technique of the tailless aircraft. To improve its congenital lacking of stability, thought over the longitudinal static stability, dynamic stability and control system. First, find the "Reflex" airfoil is suitable for the tailless aircraft. Second, set up a non-linear and longitudinal dynamic model of the tailless aircraft. Third, design an 80cm span small airplane. Hence, observe and analyze its flying condition. Finally, utilize the theoretical and experiential equations to estimate the aerodynamic derivatives and investigate its stability and controllability. Besides, use the PID controller to proceeded the time-response simulation of the non-linear system. The result of simulation shows that the performance is improved through the change of the airfoil and with the auxiliary of the control system. With this improvement, the tailless aircraft overcome the congenital lacking of stability to broaden its utilization potential.
明察秋毫-金屬的熱膨脹
Thermal expansion exists in our daily life. However, thermal expansion is generally too slight to be seen by naked eyes. Therefore, in the present project, a dilatometer was assembled to enhance better sensitivity toward thermal expansion. Hopefully the self-assembled dilatometer could contribute to teaching purpose.The structure of our 4th generation dilatometer is showed below. Using an ‘L’ square to hang up the metal stick and a rolling needle with a mirror to reflect the laser light are the critical parts of this equipment. By using this special reflection mechanism, the slight expansion of a metal stick caused by heat can be enlarged to a large scale. This special mechanism is where our creativity laid. Measuring in millimeter (mm), the measurement precision of the equipment can be extended to 0.0001 decimal. Our dilatometer was used to measure the expansion of various metal sticks caused by the temperature changes. Results were drawn from analysis of the data: 1) The average relative deflection was within 1.0~1.8%; 2) The relative deviation of linear thermal expansion coefficient was within –1.2~-4.4%.
物質熱漲冷縮的特性普遍存在於我們的生活環境中，但因其變化量相對微小，一般並不容易直接觀察，爲了進一步研究這課題，我們組裝偵測熱膨脹的儀器，並希望儀器的靈敏度高，能推廣為教學器材，經過我們不斷努力與改良，終於有了令人愉悅的成果。
自製第四代熱膨脹儀的結構如圖，設計「角尺懸吊金屬棒」與「滾針及鏡面反射」是儀器的重要部份，利用滾針旋轉及鏡面反射雷射光，加乘放大熱膨脹的微量變化，這是我們主要的創意，以公厘（mm）為單位，儀器的精確值到小數第四位。
利用自製的熱膨脹儀，探討金屬熱膨脹的影響因素。分析實驗所得數據，平均相對偏差在1.0~1.8﹪，而線膨脹係數的相對誤差約-1.2~-4.4﹪。
聽音辨位--聲波的測量應用
本實驗設計主要是以波的傳送速度(特別是聲波)，以及接收收到的時間值來做實驗、運算、討論。而其特點是為了應用於實際生活中，做了許多異於平常測量方法的設計。主要是使用時間差(｜t1–t2｜V=發聲器到兩感應器的距離差 )來消彌掉一般測量時，需要採取同步的條件，說明如下：
1. 由以上的圖中，t1’ = T + t1 為實際由感應器開始感應到感應器#1 接收到訊號的時間；同理，t2’ = T + t2 為實際由開始感應到感應器#2 接收到訊號的時間。而T 為感應器開始感應到發聲器開始發聲的的時間(之後的 T 皆為如此)。由以下式子得知：
｜t1’ - t2’｜=｜( T + t1 ) - ( T + t2 ) ｜=｜t1 - t2｜及為本實驗所需的時間差。利用減法將T 消除，便及為發聲器與感應器不必採取同步，此為本實驗目標以及優點之一。
2. 之後的公式推導中，實際由感應器開始感應到感應器接收到訊號的時間中，表示為t1、t2、t3……以此類推。
像是市面上販售的反射式測距器由於其直線性的限制，在我們可負擔的情況下，就只能做一維的測量，而在本實驗中，我們使用多個感應器，而可測量至二、三維空間，並使測出的物體由相對位置轉為絕對位置。再加上正在計劃中的測量儀器改良與自製，例如利用電腦的音效卡接上麥克風或是其他感測器，以及電子零件、電路的組合與設計。而在於一般的實際應用面上可配合工業的破壞性檢測，甚至是橋樑的斷裂處、各種振源的測量，亦或是人員的搶救，都應有不錯的效果與利用價值。
1.The major design of experiment is to spot the location of an object by experiment, calculating and discussing of such figures like the transmission speed of the waver (especially sound wave), plus time value of the receptor and so on to get the result. 2.In practice, the ordinary measuring method has to be implemented under the circumstance of synchrony: however, the distinguishing characteristic in the experiment is to overcome such restriction with the use of the “time lapse” concept. 3.The reflecting measuring instrument on the market is limited by its “straight-line characteristic.” Instead, we use multiple sensors to spot the absolute location of an object in its 1-D, 2-D, 3-D form. 4.We have now been working on the improvements of the measuring instruments, for instance, using sound cards to connect to the microphone to make a new sensor; also, the redesign and combination of other electric parts and circuits are also under construction. 5. We plan to apply the experiment not only in spotting the location of an object but also in further spotting the location of vibration coming from various objects (e.g. in the use of rescue).
直接乙醇燃料電池之觸媒層研究
直接乙醇燃料電池以酒精與氧氣透過氧化還原反應產生電能，但化學反應緩慢，需利用觸媒以增加其速率。本實驗目的在於盡可能找出一個表現最佳的觸媒。本實驗利用活性碳粉作為觸媒（鉑、錫）的載體，以酸性（HNO3）與鹼性（NaOH）環境分別處理碳粉，再以含浸法與多元醇含浸法將觸媒還原。我們得到以HNO3 處理的碳粉無法保有原碳粉的型態，較利用NaOH 處理為差。在觸媒製備方面，多元醇含浸法還原效果比含浸法可得到較小的觸媒尺寸，在本實驗中，溶液中鉑與加入的碳粉重量比為3:7 時，可得到最大的反應面積。此外，當鉑與錫原子數比為4:1 時，可得到最大的乙醇氧化電流。Direct ethanol fuel cell is a kind of power source which generates electrical power by a redox reaction involving ethanol fuel and oxygen. However, this reaction takes place slowly; therefore, catalyst is needed to improve its activity. The goal of this project is to get an optimize catalysts ratio to obtain the best catalyst activity. Activated carbon is used as the support of catalyst (platinum and tin) particles in this project, which is pre-treated in acid (HNO3) and alkaline (NaOH) solutions respectively. Then, the precursor is reduced by impregnation and EG-impregnation. We learned that activated carbon pre-treated with NaOH activates better than which pre-treated with HNO3 because the latter bear less resemblance than the former. As for the catalyst, the results of EG-impregnation show smaller size of catalyst particles than those of impregnation. In this project, when the ratio of the weight of platinum and activated carbon added into the solution is 3:7, we can get the largest surface area. In addition, when the ratio of the amount of platinum and tin atoms is 4:1, we can get the largest current of ethanol oxidation.
繪身繪影-正三角形磁磚設計方法與碎形密舖之研究
本研究主要以正三角形作為基本單元，透過窮舉討論得到正三角形邊的作用方式只有五種，再經由排列組合歸納出11 種正三角形密鋪磁磚設計方法。進一步，運用我們的研究結果，配合數學簡報系統製圖，創作新圖樣，也彌補了Escher 在手繪時所造成的誤差，達到完全密鋪的效果。碎形磁磚的部份，我們也依據其背後的數學理論創作幾套結構圖，利用結構解析，碎形密鋪磁磚將變得十分容易，學習者將可輕鬆製作富有創意的新圖樣。 ;This research mainly takes the regular triangle as the basic unit. Through the enumeration, we obtain that there are only five operations for edge of the regular triangle, and then 11 kinds of regular triangle design methods are induced. Even more, utilizing our findings and Mathematical Presentation System (Math PS), we created the new pattern which makes up Escher’s errors and achieves the tiling. As to Fractal Tiling, we create several sets of structure drawings according to its mathematics theory. Using structure analysis, the Fractal Tiling will become extremely simple, and the learner can make the rich creative new pattern easily.
溫度與光週期對淡黃蝶的影響
為了了解淡黃蝶Catopsilia pomona無紋型crocale-like及銀紋型pomona-like中間受到環境因子的差異。先比對兩型的粒線體ＤＮＡ，之後模擬夏季和冬季自然環境進行實驗。得知兩型為同種。另一方面進行溫度和光週期的實驗，顯示淡黃蝶幼蟲和成蟲雌雄個體各部位會受到此兩環境因子的影響。In order to realize if Catopsilia Pomona and Catosilia crocale are the same species, we analyzed and compared the DNA sequences of Mitochondria, and the result revealed they are indeed the same species. Then we observed the developmental process of the butterfly, and inspected the effects of different factors: photoperiod and temperature were shown to affect the phenotype of the butterfly; lower temperature and shorter day resulted in phenotypic shift from crocale-like to pomona-like, and vice versa. Also, the conflicting factors produced intermediated form. (e.g. lower temperature with longer day) Not only changed the phenotypes of adult with photoperiod and temperature, those of larvae also did. However, the mechanism how photoperiod and temperature affect the phenotype of the butterfly is unknown.
Double Pedal Curve
設Γ為一平面曲線而 P 為一定點 , 自P 向Γ所有的切線作對稱點，則所有對稱點所成的圖形Γ1 稱為曲線Γ對定點P 的double pedal curve , Γ1 對定點P 的double pedal curve Γ2 稱為曲線Γ對定點P 的2-th double pedal curve , Γ2 對定點P 的double pedal curve Γ3 稱為曲線 Γ對定點P 的3-th double pedal curve ,…… 。以下是本文主要的結果：結論A：當Γ為一圓形而P 為圓上一點時 , 計算其n−th double pedal curve 的方程式。結論B：當Γ為任意平滑的參數曲線而P 為任意一點時 , Γ的 double pedal curve 的切線性質。結論C：當Γ為任意平滑的參數曲線而P 為(0,0)時, 計算其n−th double pedal curve 的方程式。
Given a plane curve Γand a fixed point P ,the locus of the reflection of P about the tangent to the curveΓis called the double pedal curve of Γwith respect to P.We denote Γ1 as the double pedal curve of Γwith respect to P, Γ2 as the double pedal curve of Γ1 with respect to P , Γ3 as the double pedal curve of Γ2 with respect to P ,and so on , we call Γn the n-th double pedal curve of Γwith respect to P. If Γ is a circle, and P is a point on the circle, we got the parametric equation of the n−th double pedal curve of Γ with respect to P. And, for any parametric plane curve Γ; we got the method to draw the tangent of the double pedal curve of Γ.
倒車攝影機影像之變形校正
與傳統的鏡頭比較起來，廣角鏡頭可取得較大範圍的影像，所以廣泛地運用在很多地方，例如倒車攝影機、內視鏡、防盜警眼等，但是其影像會有很大的變形失真，容易造成人類眼睛的錯覺與誤判。本篇研究以倒車攝影機為例，使用了多項式函數來校正其影像的變形與失真，從程式實作的校正結果看來，我們的方法之效果還不錯，相信同樣的模式可用來校正其他使用廣角鏡頭的儀器設備之變形影像。 Compared with the traditional lens, wide-angle lens can make images of larger range, so they are widely used in a lot of places, such as move backward cine-cameras, laparoscopes, and burglarproof eyes. The drawback is that the images distort a lot and may cause the illusion to human eyes and lead to erroneous judgments. This reserch takes the backward cine-camera as example and utilizes multinomial function to correct the deformation and distortion of the image. The results show that the method we use are quite effective and the model can be applied to other equipment with wide-angle lens.