• Title/Summary/Keyword: Trapezoid

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Lateral Earth Pressures Acting on Anchored Diaphragm Walls and Deformation Behavior of Walls during Excavation (지하굴착시 앵커지지 지중연속벽에 작용하는 측방토압 및 벽체의 변형거동)

  • Hong, Won-Pyo;Lee, Moon-Ku;Lee, Jae-Ho;Yun, Jung-Mann
    • Journal of the Korean Geotechnical Society
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    • v.23 no.5
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    • pp.77-88
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    • 2007
  • Lateral earth pressure and horizontal displacement of the diaphragm walls constructed in multi-soil layers were analyzed by the field instrumentation from six building construction sites in urban area. The distribution of the developed earth pressure of the anchored diaphragm walls during excavation shows approximately a trapezoid diagram. The maximum earth pressure of anchored diaphragm walls corresponds to $0.45{\gamma}H$ and the earth pressure acts at the upper part of the walls. The maximum earth pressure is two times larger than the empirical earth pressure of flexible walls in sands suggested by Terzaghi and Peck(1967), Tschebotarioff(1973), and Hong and Yun(1995a). The horizontal displacement of diaphragm walls is closely related with supporting systems such as struts, anchors, and so on. The horizontal displacement of anchored walls shows less than 0.1 percent of the excavated depth, and the horizontal displacement of strutted walls shows less than 0.25 percent of the excavated depth. Therefore, the restraining effect of horizontal displacement to the anchored diaphragm walls is larger than the strutted diaphragm walls. In addition, since the horizontal displacement of the diaphragm walls is lower than the criterion, $\delta=0.25%H$, used for control the anchored retention wall using soilder piles, the safety of excavation sites applied with the diaphragm walls is pretty excellent.

An analysis on concept definition and concept image on quadrangle of middle and high school students (중·고등학생의 사각형에 대한 개념 정의 이해와 개념 이미지 분석)

  • Chang, Hyun Suk;Kim, Myung Chang;Lee, Bongju
    • The Mathematical Education
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    • v.61 no.2
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    • pp.323-338
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    • 2022
  • The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9th graders and 65 10th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.

A study of Improvement of Stiffness for Plastic PET bottle with Different Geometries and Numbers of Rib (리브 형상 및 개수에 따른 사각플라스틱 페트병의 강성보강에 관한 연구)

  • Young-Hoon Lee;Bum-Jin Park;Eui-Chul Jung;Jung-Gil Oh;Seok-Guwan Hong
    • Design & Manufacturing
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    • v.17 no.4
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    • pp.33-41
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    • 2023
  • Excessive use of plastic bottles contributes to a significant environmental issue due to the high volume of plastic waste generated. To address this, efforts are needed to reduce the weight of plastic bottles. However, indiscriminate weight reduction may compromise the essential rigidity required for plastic bottles. Extensive research on rib shape for pressure vessels are exists, but there is a few research of rib shapes to enhance the stiffness of plastic bottles. The following results were obtained from the analyses conducted in this study. 1) Among the rib cross-sections of square, trapezoid, and triangle, the buckling critical load of PET bottles with square-shaped ribs is improved by about 14% compared to the buckling critical load of PET bottles without ribs. 2) The buckling critical load is improved by about 18% when a square-shaped rib with an aspect ratio of 0.2 is applied, compared to the buckling critical load of the bottle without the rib. 3) When longitudinal and transverse square ribs were applied to the axial direction of the PET bottle, the buckling critical load was improved by about 32% and 58% compared to the buckling critical load of the PET bottle without ribs, respectively, indicating that applying longitudinal ribs is effective in reinforcing the stiffness of PET bottles. 4) When 14 transverse ribs were applied, the maximum improvement was about 48% compared to the buckling critical load of the plastic bottle without ribs. 5) When 3 longitudinal ribs were applied on each side, the maximum improvement was about 76% compared to the buckling critical load of the bottle without ribs. Therefore, it was concluded that for effective stiffness reinforcement of a 500ml square bottle with a thickness of 0.5mm, 3 square-shaped ribs with an aspect ratio of 0.2 should be applied in the longitudinal direction relative to the axial direction of the bottle.

쌍끌이 중층트롤어법의 연구 ( 1 ) - 모형어구의 망구형상에 관하여 - ( A Study on the Pair Midwater Trawling ( 1 ) - Mouth Performance of the Model Net - )

  • 이병기
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.31 no.1
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    • pp.29-44
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    • 1995
  • A model experiment on the pair midwater trawl net applicable to 800 PS class Korean pair bottom trawlers was carried out in the special-prepared experimental thank. the tank was prepared as a reverse trapezoid shape in its vertical section by digging out flat soil. The dimension of the tank showed the 9.6 W$\times$43.0 L(m) of the upper fringe and the 4.8 W$\times$38.0 L(m) of the bottom with 3.0m in depth. The depth of water was maintained 2.7m during experiment. The model net was prepared based on the Tauti's similarity law of fishing gear in 1/30 scale considering the dimension of the experimental tank. Mouth performance of the model net during towing were determined by the photographs taken in front of the net mouth with the combinations of towing velocity, warp length and distance between paired boats. The results obtained can be summarized as follows: 1. Vertical opening of the model nets A and B was varied in the range of 0.18~0.88 m and 0.21~0.78 m (which can be converted into 5.4~26.4m and 6.3~23.4 m in the full-scale net) respectively, and was varied predominantly by towing speed. Vertical opening (H which is appendixed m for the model net. f for the full-scale net. A and B for the types of the model net) can be expressed as the function of towing velocity$V_t$as in the model net $V_t$ : m/ sec)$H_{mA}$=1.67$e^{-1.65V_t}$ $H_{mB}$=1.15$e^{-1.13V_t}$, in the full-scale net ($V_t$ : k't) $H_{fA}$=50.27$e^-0.37V_t$ $H_{fB}$=34.46$e^{-0.26Vt}$. 2. Horizontal opening of the model nets An and b was varied in the range of 1.03~1.54m and 1.04~1.55 m (which can be converted into 30.9~46.2 m and 31.2~46.5m in the full-scale net) respectively, and was varied predominantly by distance between paired boats. Horizontal opening (W, appendixes are as same as the former) an be expressed as the function of distance between paired boats $D_b$as in the model net $W_{mA}$=0.69+0.09$D_b$ $W{mB}$=0.73+0.09$D_b$, in the full-scale net $W_{fA}$=20.81+0.09$D_b$ $W_{fB}$=22.11+0.09$D_b$ 3. Net opening area of the model net A and B was varied in the range of 0.28~1.04 $m^2$ and 0.33~0.94$m^2$(which can be converted into 252~936$m^2$ and 297~846$m^2$ in the full-scale net) respectively, and was varied predominantly by towing velocity. Net opening area ($S$, appendixes are as same as the former) van be expressed as the function of towing velocity$V_t$ as in the model net $v_t$ : m/sec) $S_{Ma}$=2.01$e^{-1.54V_T}$ $S_{mA}$=1.40$e^{-1.65V_t}$, in the full-scale net ($V_t$ : k't) $S_{fA}$=1.807$e^-0.35V_t$ $S_{fA}$=1.265$e^{-0.24V_t}$. 4. Filtering volume of the model nets A and B was varied in the range of 0.32~0.55 $m^3$ and 0.37~0.55$m^3$(which can be converted into 8.640~14.850 $m^3$ and 9.990~14.850$m3$in the full~scale net) respectively, and was predominantly varied by towing speed. filtering volume of the model net-A showed the maximum at the towing speed 0.69 m/sec(3 k't in the full-scale net), compared with that of the model net B showed at 0.92 m/sec(4 k't in the full-scale net).

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Hypoglycemic Effects of Fruits and Vegetables in Hyperglycemic Rats for Prevention of Type-2 Diabetes (고혈압쥐의 과일과 야채의 섭취에 따른 저혈당 효과)

  • Survay, Nazneen Shaik;Ko, Eun-Young;Upadhyay, Chandrama Prakash;Jang, Mi;Park, Se-Won;Lee, Dong-Ha;Jung, Yi-Sook;Yoon, Do-Young;Hong, Sae-Jin
    • Horticultural Science & Technology
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    • v.28 no.5
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    • pp.850-856
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    • 2010
  • An in vivo oral glucose tolerance test (OGTT) was performed on hyperglycemic male Sprague-Dawley rats to assess the effect of fruits and vegetables ($1g{\cdot}kg^{-1}$ body weight) on blood glucose levels (${\Delta}BGLs$) at different time intervals of 0, 5, 15, 30, 60, 90 and 120 min. The areas under glucose curve (${\Delta}AUCs$) were calculated at 120 min of OGTT by trapezoid method. Total phenolic content (TPC) and anti-oxidant activity (AOA) of fruits and vegetables were assayed in vitro by Folin Ciocalteu and DPPH (2, 2-diphenyl-1-picrylhydrazyl) methods, respectively. At the end of the experiment the correlations among the parameters TPC, AOA and ${\Delta}AUC$ was estimated by Pearson's correlations. Among fruit crops, tangerine, plum, grape and pear and among vegetables, blue leaf mustard, cabbage, chicory, broccoli and others exhibited significant hypoglycemic effects by reducing ${\Delta}BGLs$ with significant ${\Delta}AUC$. The effective ${\Delta}AUC$ ranged from $5548.2{\pm}462.1$ to $3823.3{\pm}282.0mg-min{\cdot}dL^{-1}$. The TPC and AOA ranged from $0.063{\pm}0.00$ to $0.913{\pm}0.14mg{\cdot}g^{-1}$ GAE and $01.05{\pm}0.08$ to $75.46{\pm}0.06%$, respectively. Overall, six fruits and fifteen vegetables exhibited higher TPC and one fruit and four vegetables exhibited higher AOA. There was a better correlation among TPC, AOA and ${\Delta}AUC$ of fruits and TPC & AOA of vegetables. We report that hypoglycemically significant fruits and vegetables investigated in this study have pharmacological importance which reduced ${\Delta}BGLs$ through insulin like activity and AOA in prevention of type-2 diabetes.

Comparative Assessment on Indicating Factor for Biomineralization by Bacillus Species (Bacillus종의 생광물화에 미치는 영향 인자의 비교 평가)

  • Seok, Hee-Jeong;Kim, Chang-Gyun
    • Journal of Korean Society of Environmental Engineers
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    • v.35 no.3
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    • pp.179-191
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    • 2013
  • This study was conducted to comparatively assess quantitative indicating factor for biomineralization characterizing $CO_2$ mineralization on three type of minerals (i.e., $CaCl_2$, $MgCl_2$, $CaCl_2-MgCl_2$) in an aqueous solution amended with Bacillus pasteurii or indigenous microorganisms for a S landfill cover soil. For given three types of minerals, $NH_4{^+}$ (urease activity) was released at the highest of 88 mg/L for $MgCl_2$, then 85 mg/L for $CaCl_2$, and the lowest of 42 mg/L for $CaCl_2-MgCl_2$. $CO_2$ gas in the head space was completely removed after 12, 12, and 24 hr for $CaCl_2$, $MgCl_2$ and $CaCl_2-MgCl_2$, respectively. $Ca^{2+}$ concentration in $CaCl_2$ solution was the quickest and the greatest decreased 92% for 12 hr whereas that in $CaCl_2-MgCl_2$ solution was lower at 85% for 36 hr. $Mg^{2+}$ concentration in $MgCl_2$ was more efficiently decreased at 46% for 48 hr than that of $CaCl_2-MgCl_2$ solution of 38.5% for 72 hr. Regardless of types of minerals or their concentration, pH was changed from 5.5 to 9 by biomineralization being progressed. Microbial activity ($OD_{600}$) was also changed from 0 to 0.6. SEM images indicated that spheroidal and trapezoid shape crystal were formed, which were identified as of $CaCO_3$ (Calcite) and $MgCO_3$ (Magnesite) by X-ray diffraction. In the long run, $NH_4{^+}$ (urease activity), $CO_2$ gas, $OD_{600}$, pH, $Ca^{2+}$ and $Mg^{2+}$ would be suitable for reasonable indicating factor in order to assess the degree of biomineralization efficiency.

A STUDY ON THE JUJEON OF AUTOMATIC CLEPSYDRA IN EARLY JOSEON DYNASTY (조선 전기 자동물시계의 주전(籌箭) 연구)

  • YUN, YONG-HYUN;KIM, SANG HYUK;MIHN, BYEONG-HEE;OH, KYONG TAEK
    • Publications of The Korean Astronomical Society
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    • v.36 no.3
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    • pp.65-78
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    • 2021
  • Jagyeokru, an automatic striking water clock described in the Sejong Sillok (Veritable Records of King Sejong) is essentially composed of a water quantity control device and a time-signal device, with the former controlling the amount or the flow rate of water and the latter automatically informing the time based on the former. What connects these two parts is a signal generating device or a power transmission device called the 'Jujeon' system, which includes a copper rod on the float and ball-racked scheduled plates. The copper products excavated under Gongpyeong-dong in Seoul include a lot of broken plate pieces and cylinder-like devices. If some plate pieces are put together, a large square plate with circular holes located in a zigzag can be completed, and at the upper right of it is carved 'the first scheduled plate (一箭).' Cylinder-like devices generally 3.8 cm in diameter are able to release a ball, and have a ginkgo leaf-like screen fixed on the inner axis and a bird-shaped hook of which the leg fixes another axis and the beak attaches to the leaf side. The lateral view of this cylinder-like device appears like a trapezoid and mounts an iron ball. The function of releasing a ball agrees with the description of Borugak Pavilion, where Jagyeokru was installed, written by Kim Don (1385 ~ 1440). The other accounts of Borugak Pavilion's and Heumgyeonggak Pavilion's water clocks describe these copper plates and ball releasing devices as the 'Jujeon' system. According to the description of Borugak Pavilion, a square wooden column has copper plates on the left and right sides the same height as the column, and the left copper plate has 12 drilled holes to keep the time of a 12 double-hours. Meanwhile, the right plate has 25 holes which represent seasonal night 5-hours (Kyeong) and their 5-subhours (Jeom), not 12 hours. There are 11 scheduled plates for seasonal night 5-hours made with copper, which are made to be attached or detached as the season. In accordance with Nujutongui (manual for the operation of the yardstick for the clepsydra), the first scheduled plate for the night is used from the winter solstice (冬至) to 2 days after Daehan (大寒), and from 4 days before Soseol (小雪) to a day before the winter solstice. Besides the first scheduled plate, we confirm discovering a third scheduled plate and a sixth scheduled plate among the excavated copper materials based on the spacing between holes. On the other hand, the width of the scheduled plate is different for these artifacts, measured as 144 mm compared to the description of the Borugak Pavilion, which is recorded as 51 mm. From this perspective, they may be the scheduled plates for the Heumgyeonggak Ongru made in 1438 (or 1554) or for the new Fortress Pavilion installed in Changdeokgung palace completed in 1536 (the 31st year of the reign of King Jungjong) in the early Joseon dynasty. This study presents the concept of the scheduled plates described in the literature, including their new operating mechanism. In addition, a detailed model of 11 scheduled plates is designed from the records and on the excavated relics. It is expected that this study will aid in efforts to restore and reconstruct the automatic water clocks of the early Joseon dynasty.

The Development and Originality of Wind Chimes of the Goryeo Dynasty (고려시대 풍탁(風鐸)의 전개와 독창성)

  • Lee, Young-sun
    • Korean Journal of Heritage: History & Science
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    • v.52 no.2
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    • pp.292-307
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    • 2019
  • Buddhists have always tended to adorn and embellish Buddhist statues and their surrounding spaces in order to exhibit the grandeur and sublime nature of the Buddha. The various kinds of splendid instruments and implements used in such ornamentation are collectively called jangeomgu in Korean. Thus, the term jangeomgu encompasses articles used to decorate Buddhist statues, halos, and baldachin, as well as Buddhist banners and wind chimes, which are generally hung outside a building. Wind chimes are still widely used at Buddhist temples. In China, judging from various structures such as the Wooden Stupa of Yongningsi in Luoyang and the Dunhuang Caves, wind chimes began to be used around the sixth century. As for Korea, Buddhism was first introduced from China during the Three Kingdoms Period, and Koreans accordingly began to build Buddhist temples and buildings. It would appear that wind chimes came to be used around the time that the first temples were built. The oldest extant wind chime in Korea is the gilt-bronze wind chime of Baekje, discovered at the Mireuksa Temple Site in Iksan. In general, Korean wind chimes dating from the Three Kingdoms Period are classified into two general types according to their shape and elevation, i.e., those shaped like a Buddhist bell and those shaped like a trapezoid. As these two forms of wind chimes have influenced each other over time, those made during the Goryeo dynasty, having inherited the style, structure, and design of the preceding period, display such features. At the same time, the artisans who produced wind chimes pursued technical development and adopted free, yet not extravagant, designs. In particular, Goryeo wind chimes are characterized by original designs created through exchanges with other Buddhist art forms of the same period, such as the embossed lotus design band of Goryeo bells; the bullmun design, which served to display the grandeur of the royal family; the samhwanmun design, which consisted of decorating the interior of a Goryeo incense burner with three holes; Sanskrit designs; and designs inspired by the windows and doors of stone pagodas. In this way, the production of Goryeo wind chimes developed with a focus on purpose while being free of formal constraints. This study started out from the fact that the largest number of Korean wind chimes were produced during the Goryeo dynasty. Therefore, research on wind chimes should be based on those of the Goryeo dynasty, especially since fewer relevant studies have been conducted compared to studies on other forms of Buddhist art. For the purposes of this study, the reasons for the production of wind chimes will be examined first, followed by an examination of the various styles of Korean wind chimes. Then, based on the findings of this investigation, the development and characteristics of the wind chimes produced during the Goryeo dynasty will be explored for each period.

The hydrodynamic characteristics of the canvas kite - 2. The characteristics of the triangular canvas kite - (캔버스 카이트의 유체역학적 특성에 관한 연구 - 2. 삼각형 캔버스 카이트의 특성 -)

  • Bae, Bong-Seong;Bae, Jae-Hyun;An, Heui-Chun;Lee, Ju-Hee;Shin, Jung-Wook
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.40 no.3
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    • pp.206-213
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    • 2004
  • As far as an opening device of fishing gears is concerned, applications of a kite are under development around the world. The typical examples are found in the opening device of the stow net on anchor and the buoyancy material of the trawl. While the stow net on anchor has proved its capability for the past 20 years, the trawl has not been wildly used since it has been first introduced for the commercial use only without sufficient studies and thus has revealed many drawbacks. Therefore, the fundamental hydrodynamics of the kite itself need to ne studied further. Models of plate and canvas kite were deployed in the circulating water tank for the mechanical test. For this situation lift and drag tests were performed considering a change in the shape of objects, which resulted in a different aspect ratio of rectangle and trapezoid. The results obtained from the above approaches are summarized as follows, where aspect ratio, attack angle, lift coefficient and maximum lift coefficient are denoted as A, B, $C_L$ and $C_{Lmax}$ respectively : 1. Given the triangular plate, $C_{Lmax}$ was produced as 1.26${\sim}$1.32 with A${\leq}$1 and 38$^{\circ}$B${\leq}$42$^{\circ}$. And when A${\geq}$1.5 and 20$^{\circ}$${\leq}$B${\leq}$50$^{\circ}$, $C_L$ was around 0.85. Given the inverted triangular plate, $C_{Lmax}$ was 1.46${\sim}$1.56 with A${\leq}$1 and 36$^{\circ}$B${\leq}$38$^{\circ}$. And When A${\geq}$1.5 and 22$^{\circ}$B${\leq}$26$^{\circ}$, $C_{Lmax}$ was 1.05${\sim}$1.21. Given the triangular kite, $C_{Lmax}$ was produced as 1.67${\sim}$1.77 with A${\leq}$1 and 46$^{\circ}$B${\leq}$48$^{\circ}$. And when A${\geq}$1.5 and 20$^{\circ}$B${\leq}$50$^{\circ}$, $C_L$ was around 1.10. Given the inverted triangular kite, $C_{Lmax}$ was 1.44${\sim}$1.68 with A${\leq}$1 and 28$^{\circ}$B${\leq}$32$^{\circ}$. And when A${\geq}$1.5 and 18$^{\circ}$B${\leq}$24$^{\circ}$, $C_{Lmax}$ was 1.03${\sim}$1.18. 2. For a model with A=1/2, an increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. Then there was a tendency of a very gradual decrease or no change in the value of $C_L$. For a model with A=2/3, the tendency of $C_L$ was similar to the case of a model with A=1/2. For a model with A=1, an increase in B caused an increase in $C_L$ until $C_L$ has reached the maximum. And the tendency of $C_L$ didn't change dramatically. For a model with A=1.5, the tendency of $C_L$ as a function of B was changed very small as 0.75${\sim}$1.22 with 20$^{\circ}$B${\leq}$50$^{\circ}$. For a model with A=2, the tendency of $C_L$ as a function of B was almost the same in the triangular model. There was no considerable change in the models with 20$^{\circ}$B${\leq}$50$^{\circ}$. 3. The inverted model's $C_L$ as a function of increase of B reached the maximum rapidly, then decreased gradually compared to the non-inverted models. Others were decreased dramatically. 4. The action point of dynamic pressure in accordance with the attack angle was close to the rear area of the model with small attack angle, and with large attack angle, the action point was close to the front part of the model. 5. There was camber vertex in the position in which the fluid pressure was generated, and the triangular canvas had large value of camber vertex when the aspect ratio was high, while the inverted triangular canvas was versa. 6. All canvas kite had larger camber ratio when the aspect ratio was high, and the triangular canvas had larger one when the attack angle was high, while the inverted triangluar canvas was versa.

A Study on the Excavated Sab(a funeral fan) from Lime-filled Tomb and Lime-layered Tomb during the Joseon Dynasty (조선시대 회격·회곽묘 출토 삽(翣)에 대한 고찰)

  • Yi, Seung Hae;An, Bo Yeon
    • Korean Journal of Heritage: History & Science
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    • v.41 no.2
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    • pp.43-59
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    • 2008
  • Sap(?, a funeral fan) is a funeral ceremonial object used in association with a Confucian ceremonial custom, which was crafted by making a wooden frame, attaching a white cloth or a thick paper onto it, drawing pictures on it, and making a holder for a handle. According to Liji(Records of Rites), Sap was used since the Zhou Dynasty, and these Chinese Sap examples are no big different than the Korean Sap examples, which were described in Joseon Wangjo Sillok(Annals of the Joseon Dynasty), Gukjo Oryeui(the Five Rites of the State), and Sarye Pyeollam(Handbook on Four Rituals). This study explored Sap excavated in lime-filled tombs and lime-layered tombs of aristocrats dating back to Joseon, as well as their historical records to examine Sap's characteristics according to their examples, manufacturing methods, and use time. The number and designs of Sap varied according to the deceased' social status aristocrats used mainly one pair of 亞-shaped Bulsap, and a pair of Hwasap with a cloud design depicted on it. A Sap was wrapped twice with Chojuji paper or Jeojuji paper, and for the third time with Yeonchangji paper. Then, it was covered with a white ramie, a hemp, a cotton, a silk satin, etc. Bobul(an axe shape and 亞-shape design) was drawn on both sides of Sap, and a rising current of cloud was drawn at the peripheral area mainly with red or scarlet pigments. Sap, which were excavated from aristocrats'lime-filled and lime-layered tombs, are the type of Sap which were separated from its handle. These excavated Sap are those whose long handles were burnt during the death carriage procession, leaving Sap, which later were erected on both sides of the coffin. The manufacturing process of excavated relics can be inferred by examining them. The excavated relics are classified into those with three points and those with two points according to the number of point. Of the three-point type(Type I), there is the kind of relic that was woven into something like a basket by using a whole wood plate or cutting bamboo into flat shapes. The three-point Sap was concentrated comparatively in the early half of Joseon, and was manufactured with various methods compared with its rather unified overall shape. In the meantime, the two-point Sap was manufactured with a relatively formatted method; its body was manufactured in the form of a rectangle or a reverse trapezoid, and then its upper parts with two points hanging from them were connected, and the top surface was made into a curve(Type II) or a straight line(Type III) differentiating it from the three-point type. This manufacturing method, compared with that of the three-point type, is simple, but is not greatly different from the three-point type manufacturing method. In particular, the method of crafting the top surface into a straight line has been used until today. Of the examined 30 Sap examples, those whose production years were made known from the buried persons'death years inscribed on the tomb stones, were reexamined, indicating that type I was concentrated in the first half of the $16^{th}$ century. Type II spanned from the second half of the $16^{th}$ century to the second half of the $17^{th}$ century, and type III spanned from the first half of the $17^{th}$ century to the first half of the $18^{th}$ century. The shape of Sap is deemed to have changed from type I to type II and again from type II to type III In the $17^{th}$ century, which was a time of change, types II and III coexisted. Of the three types of Sap, types II and III re similar because they have two points; thus a noteworthy transit time is thought to have been the middle of the $16^{th}$ century. Type I compared with types II and III is thought to have required more efforts and skills in the production process, and as time passed, the shape and manufacturing methods of Sap are presumed to have been further simplified according to the principle of economy. The simplification of funeral ceremonies is presumed to have been furthered after Imjinwaeran(Japanese invasion of Joseon, 1592~1598), given that as shown in the Annals of King Seonjo, state funerals were suspended several times. In the case of Sap, simplification began from the second half of the $16^{th}$ century, and even in the $18^{th}$ century, rather than separately crafting Sap, Sap was directly drawn on the coffin cover and the coffin. However, in this simplification of form, regulations on the use of Sap specified in Liji were observed, and thus the ceremony was rationally simplified.