• Title/Summary/Keyword: Relative Velocity method

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OPTIMAL DEELECTION OF EARTH-CROSSING OBJECT USING A THREE-DIMENSIONAL SINGLE IMPULSE (3차원에서의 순간적인 속도변화에 의한 ECO의 최적궤도변경)

  • Mihn, Byeong-Hee;Park, Sang-Young;Roh, Kyoung-Min;Choi, Kyu-Hong;Moon, Hong-Kyu
    • Journal of Astronomy and Space Sciences
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    • v.22 no.3
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    • pp.249-262
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    • 2005
  • Optimization problems are formulated to calculate optimal impulses for deflecting Earth-Crossing Objects using a Nonlinear Programming. This formulation allows us to analyze the velocity changes in normal direction to the celestial body's orbital plane, which is neglected in many previous studies. The constrained optimization in the three-dimensional space is based on a patched conic method including the Earth's gravitational effects, and yields impulsive ${\Delta}V$ to deflect the target's orbit. The optimal solution is dependent on relative positions and velocities between the Earth and the Earth-crossing objects, and can be represented by optimal magnitude and angle of ${\Delta}V $ as a functions of a impulse time. The perpendicular component of ${\Delta}V $ to the orbit plane can sometimes play un-negligible role as the impulse time approaches the impact time. The optimal ${\Delta}V $ is increased when the original orbit of Earth-crossing object is more similar to the Earth's orbit, and is also exponentially increased as the impulse time reaches to the impact time. The analyses performed in present paper can be used to the deflection missions in the future.

Pull-out Test of Steel Pipe Pile Reinforced with Hollow Steel Plate Shear Connectors (유공강판 전단연결재로 보강된 강관말뚝 머리의 인발실험)

  • Lee, Kyoung-Hun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.17 no.12
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    • pp.285-291
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    • 2016
  • The purpose of this study was to evaluate the structural capacity of steel pipe pile specimens reinforced with hollow steel plate shear connectors by pull-out test. Compressive strength testing of concrete was conducted and yield forces, tensile strengths and elongation ratios of re-bars and hollow steel plate were investigated. A 2,000kN capacity UTM was used for the pull-out test with 0.01mm/sec velocity by displacement control method. Strain gauges were installed at the center of re-bars and hollow steel plates and LVDTs were also installed to measure the relative displacement between the loading plate and in-filled concrete pile specimens. The yield forces of the steel pipe pile specimens reinforced with hollow steel plate shear connectors were increased 1.44-fold and 1.53-fold compared to that of a control specimen, respectively. Limited state forces of steel pipe pile specimens reinforced with hollow steel plate shear connectors were increased 1.23-fold and 1.29-fold compared to that of a control specimen, respectively. Yield state displacement and limited state displacement of steel pipe pile specimens reinforced with hollow steel plate shear connector were decreased 0.61-fold and 0.42-fold compared to that of a control specimen, respectively.

A Study of the Method for Estimating the Missing Data from Weather Measurement Instruments (인공신경망을 이용한 기상관측장비 결측 보완 기술에 관한 연구)

  • Min, Jae-Sik;Lee, Moo-Hun;Jee, Joon-Bum;Jang, Min
    • Journal of Digital Convergence
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    • v.14 no.8
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    • pp.245-252
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    • 2016
  • The purpose of this study is to make up for missing of weather informations from ASOS and AWS using artificial neural networks. We collected temperature, relative humidity and wind velocity for August during 5-yr (2011-2015) and sample designed artificial neural networks, assuming the Seoul weather station was missing. The result of sensitivity study on number of epoch shows that early stopping appeared at 2,000 epochs. Correlation between observation and prediction was higher than 0.6, especially temperature and humidity was higher than 0.9, 0.8 respectively. RMSE decreased gradually and training time increased exponentially with respect to increase of number of epochs. The predictability at 40 epoch was more than 80% effect on of improved results by the time the early stopping. It is expected to make it possible to use more detailed weather information via the rapid missing complemented by quick learning time within 2 seconds.

Fundamental Experiment on the Flow Characteristics inside the Exhaust Duct of Cone Calorimeter (콘 칼로리미터의 배기 덕트 내부 유동 특성 기초 실험)

  • Shin, Yeon Je;You, Woo Jun
    • Fire Science and Engineering
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    • v.33 no.4
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    • pp.35-40
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    • 2019
  • In this study, the mass flow rate of the heat release rate equation, which is the major factor of the oxygen consumption method, was analyzed for the fundamental investigation of the cone-calorimeter (5 m length and 0.3 m diameter). The shapes of a completely empty inside, 3 mm pore diameter mesh and pore diameter 10 mm honeycomb with 0.76 porosity were constructed using the cone-calorimeter. To calculate the mass flow rate, four bi-directional probes and thermocouples were installed in a uniform position in the vertical direction of flow. The velocity gradient and flow perturbation were measured from the increase in Reynolds number. As the flow capacity increased, the speed gradient increased in all three shapes relative to the turbulence intensity. In addition, the deviation of extended uncertainty to the mass flow was completely low in the order of empty space, mesh (dp = 3 mm) and honeycomb (dp = 10 mm and 𝜖 = 0.76) at the 95% confidence level. The results can be used in designs to improve the flow stability of the cone calorimeter.

Estimation of Duck House Litter Evaporation Rate Using Machine Learning (기계학습을 활용한 오리사 바닥재 수분 발생량 분석)

  • Kim, Dain;Lee, In-bok;Yeo, Uk-hyeon;Lee, Sang-yeon;Park, Sejun;Decano, Cristina;Kim, Jun-gyu;Choi, Young-bae;Cho, Jeong-hwa;Jeong, Hyo-hyeog;Kang, Solmoe
    • Journal of The Korean Society of Agricultural Engineers
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    • v.63 no.6
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    • pp.77-88
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    • 2021
  • Duck industry had a rapid growth in recent years. Nevertheless, researches to improve duck house environment are still not sufficient enough. Moisture generation of duck house litter is an important factor because it may cause severe illness and low productivity. However, the measuring process is difficult because it could be disturbed with animal excrements and other factors. Therefore, it has to be calculated according to the environmental data around the duck house litter. To cut through all these procedures, we built several machine learning regression model forecasting moisture generation of litter by measured environment data (air temperature, relative humidity, wind velocity and water contents). 5 models (Multi Linear Regression, k-Nearest Neighbors, Support Vector Regression, Random Forest and Deep Neural Network). have been selected for regression. By using R-Square, RMSE and MAE as evaluation metrics, the best accurate model was estimated according to the variables for each machine learning model. In addition, to address the small amount of data acquired through lab experiments, bootstrapping method, a technique utilized in statistics, was used. As a result, the most accurate model selected was Random Forest, with parameters of n-estimator 200 by bootstrapping the original data nine times.

Study on the Evaluation of Ship Collision Risk based on the Dempster-Shafer Theory (Dempster-Shafer 이론 기반의 선박충돌위험성 평가에 관한 연구)

  • Jinwan Park;Jung Sik Jeong
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.29 no.5
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    • pp.462-469
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    • 2023
  • In this study, we propose a method for evaluating the risk of collision between ships to support determination on the risk of collision in a situation in which ships encounter each other and to prevent collision accidents. Because several uncertainties are involved in the navigation of a ship, must be considered when evaluating the risk of collision. We apply the Dempster-Shafer theory to manage this uncertainty and evaluate the collision risk of each target vessel in real time. The distance at the closest point approach (DCPA), time to the closest point approach (TCPA), distance from another vessel, relative bearing, and velocity ratio are used as evaluation factors for ship collision risk. The basic probability assignments (BPAs) calculated by membership functions for each evaluation factor are fused through the combination rule of the Dempster-Shafer theory. As a result of the experiment using automatic identification system (AIS) data collected in situations where ships actually encounter each other, the suitability of evaluation was verified. By evaluating the risk of collision in real time in encounter situations between ships, collision accidents caused by human errora can be prevented. This is expected to be used for vessel traffic service systems and collision avoidance systems for autonomous ships.

Red Pepper (Capsicum annum) Drying Using Flat-Plate Solar Collectors (평판집열기(平板集熱機)를 이용(利用)한 고추 건조(乾燥)에 관(關)한 연구(硏究))

  • Kim, Dong-Man;Kim, Man-Soo;Chang, Kyu-Seob
    • Korean Journal of Agricultural Science
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    • v.6 no.1
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    • pp.56-64
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    • 1979
  • Two types of fiat-plate collector were designed and constructed for utilizing the solar energy as heating source of red pepper drying. It was performed to investigate the basic factors on using the collectors and the drying effect on various types of red pepper, and the results obtained are summarized as follows. 1. The optimum tilted angles of the collector in Daejeon area were ${\phi}-15^{\circ}$ in summer season and ${\phi}+15^{\circ}$ in winter season when it was adjusted two times per a year: 2. In the conditions during experiment period, average atmospheric temperature and relative humidity were $25.6^{\circ}C$ and 52.6%, respectively, and $42.0^{\circ}C$, 74.2% in the control chamber. The temperature in the drying chamber connected to the water heater was the highest but relative humidity in the chamber connected to the air heater was the lowest among the chambers. 3. The drying velocity of whole red pepper in the chamber connected to the water heater was the fastest as 2.3 times as compared to the whole type on the mat drying followed by air heater and control in decreasing order. The horizontally cut red pepper in the chamber connected to the water heater was dried exceedingly fast among twelve plots. 4. The content of capsaicine as pungent principle and of capsanthine as red pigment in the red pepper were reduced during drying but there were no differences significantly on the drying method, and it could not affect much on the quality of dried product.

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Studies on Relations between Various Coeffcients of Evapo-Transpiration and Quantities of Dry Matters for Tall-and Short Statured Varieties of Paddy Rice (논벼 장.단간품종의 증발산제계수와 건물량과의 관계에 대한 연구(I))

  • 류한열;김철기
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.16 no.2
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    • pp.3361-3394
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    • 1974
  • The purpose of this thesis is to disclose some characteristics of water consumption in relation to the quantities of dry matters through the growing period for two statured varieties of paddy rice which are a tall statured variety and a short one, including the water consumption during seedling period, and to find out the various coefficients of evapotranspiration that are applicable for the water use of an expected yield of the two varieties. PAL-TAL, a tall statured variety, and TONG-lL, a short statured variety were chosen for this investigation. Experiments were performed in two consecutive periods, a seedling period and a paddy field period, In the investigation of seedling period, rectangular galvanized iron evapotranspirometers (91cm${\times}$85cm${\times}$65cm) were set up in a way of two levels (PAL-TAL and TONG-lL varieties) with two replications. A standard fertilization method was applied to all plots. In the experiment of paddy field period, evapotanspiration and evaporation were measured separately. For PAL-TAL variety, the evapotranspiration measurements of 43 plots of rectangular galvanized iron evapotranspirometer (91cm${\times}$85cm${\times}$65cm) and the evaporation measurements of 25 plots of rectangular galvanized iron evaporimeter (91cm${\times}$85cm${\times}$15cm) have been taken for seven years (1966 through 1972), and for TONG-IL variety, the evapotranspiration measurements of 19 plots and the evaporation measurements of 12 plots have been collected for two years (1971 through 1972) with five different fertilization levels. The results obtained from this investigation are summarized as follows: 1. Seedling period 1) The pan evaporation and evapotranspiration during seedling period were proved to have a highly significant correlation to solar radiation, sun shine hours and relative humidity. But they had no significant correlation to average temperature, wind velocity and atmospheric pressure, and were appeared to be negatively correlative to average temperature and wind velocity, and positively correlative to the atmospheric pressure, in a certain period. There was the highest significant correlation between the evapotranspiration and the pan evaporation, beyond all other meteorological factors considered. 2) The evapotranpiration and its coefficient for PAL-TAL variety were 194.5mm and 0.94∼1.21(1.05 in average) respectively, while those for TONG-lL variety were 182.8mm and 0.90∼1.10(0.99 in average) respectively. This indicates that the evapotranspiration for TONG-IL variety was 6.2% less than that for PAL-TAL variety during a seedling period. 3) The evapotranspiration ratio (the ratio of the evapotranspiration to the weight of dry matters) during the seedling period was 599 in average for PAL-TAL variety and 643 for TONG-IL variety. Therefore the ratio for TONG-IL was larger by 44 than that for PAL-TAL variety. 4) The K-values of Blaney and Criddle formula for PAL-TAL variety were 0.78∼1.06 (0.92 in average) and for TONG-lL variety 0.75∼0.97 (0.86 in average). 5) The evapotranspiration coefficient and the K-value of B1aney and Criddle formular for both PAL-TAL and TONG-lL varieties showed a tendency to be increasing, but the evapotranspiration ratio decreasing, with the increase in the weight of dry matters. 2. Paddy field period 1) Correlation between the pan evaporation and the meteorological factors and that between the evapotranspiration and the meteorological factors during paddy field period were almost same as that in case of the seedling period (Ref. to table IV-4 and table IV-5). 2) The plant height, in the same level of the weight of dry matters, for PAL-TAL variety was much larger than that for TONG-IL variety, and also the number of tillers per hill for PAL-TAL variety showed a trend to be larger than that for TONG-IL variety from about 40 days after transplanting. 3) Although there was a tendency that peak of leaf-area-index for TONG-IL variety was a little retarded than that for PAL-TAL variety, it appeared about 60∼80 days after transplanting. The peaks of the evapotranspiration coefficient and the weight of dry matters at each growth stage were overlapped at about the same time and especially in the later stage of growth, the leaf-area-index, the evapotranspiration coefficient and the weight of dry matters for TONG-IL variety showed a tendency to be larger then those for PAL-TAL variety. 4) The evaporation coefficient at each growth stage for TONG-IL and PAL-TALvarieties was decreased and increased with the increase and decrease in the leaf-area-index, and the evaporation coefficient of TONG-IL variety had a little larger value than that of PAL-TAL variety. 5) Meteorological factors (especially pan evaporation) had a considerable influence to the evapotranspiration, the evaporation and the transpiration. Under the same meteorological conditions, the evapotranspiration (ET) showed a increasing logarithmic function of the weight of dry matters (x), while the evaporation (EV) a decreasing logarithmic function of the weight of dry matters; 800kg/10a x 2000kg/10a, ET=al+bl logl0x (bl>0) EV=a2+b2 log10x (a2>0 b2<0) At the base of the weight of total dry matters, the evapotranspiration and the evaporation for TONG-IL variety were larger as much as 0.3∼2.5% and 7.5∼8.3% respectively than those of PAL-TAL variety, while the transpiration for PAL-TAL variety was larger as much as 1.9∼2.4% than that for TONG-IL variety on the contrary. At the base of the weight of rough rices the evapotranspiration and the transpiration for TONG-IL variety were less as much as 3.5% and 8.l∼16.9% respectively than those for PAL-TAL variety and the evaporation for TONG-IL was much larger by 11.6∼14.8% than that for PAL-TAL variety. 6) The evapotranspiration coefficient, the evaporation coefficient and the transpiration coefficient and the transpiration coefficient were affected by the weight of dry matters much more than by the meteorological conditions. The evapotranspiratioa coefficient (ETC) and the evaporation coefficient (EVC) can be related to the weight of dry matters (x) by the following equations: 800kg/10a x 2000kg/10a, ETC=a3+b3 logl0x (b3>0) EVC=a4+b4 log10x (a4>0, b4>0) At the base of the weights of dry matters, 800kg/10a∼2000kg/10a, the evapotranspiration coefficients for TONG-IL variety were 0.968∼1.474 and those for PAL-TAL variety, 0.939∼1.470, the evaporation coefficients for TONG-IL variety were 0.504∼0.331 and those for PAL-TAL variety, 0.469∼0.308, and the transpiration coefficients for TONG-IL variety were 0.464∼1.143 and those for PAL-TAL variety, 0.470∼1.162. 7) The evapotranspiration ratio, the evaporation ratio (the ratio of the evaporation to the weight of dry matters) and the transpiration ratio were highly affected by the meteorological conditions. And under the same meteorological condition, both the evapotranspiration ratio (ETR) and the evaporation ratio (EVR) showed to be a decreasing logarithmic function of the weight of dry matters (x) as follows: 800kg/10a x 2000kg/10a, ETR=a5+b5 logl0x (a5>0, b5<0) EVR=a6+b6 log10x (a6>0 b6<0) In comparison between TONG-IL and PAL-TAL varieties, at the base of the pan evaporation of 343mm and the weight of dry matters of 800∼2000kg/10a, the evapotranspiration ratios for TONG-IL variety were 413∼247, while those for PAL-TAL variety, 404∼250, the evaporation ratios for TONG-IL variety were 197∼38 while those for PAL-TAL variety, 182∼34, and the transpiration ratios for TONG-IL variety were 216∼209 while those for PAL-TAL variety, 222∼216 (Ref. to table IV-23, table IV-25 and table IV-26) 8) The accumulative values of evapotranspiration intensity and transpiration intensity for both PAL-TAL and TONG-IL varieties were almost constant in every climatic year without the affection of the weight of dry matters. Furthermore the evapotranspiration intensity appeared to have more stable at each growth stage. The peaks of the evapotranspiration intensity and transpiration intensity, for both TONG-IL and PAL-TAL varieties, appeared about 60∼70 days after transplanting, and the peak value of the former was 128.8${\pm}$0.7, for TONG-IL variety while that for PAL-TAL variety, 122.8${\pm}$0.3, and the peak value of the latter was 152.2${\pm}$1.0 for TONG-IL variety while that for PAL-TAL variety, 152.7${\pm}$1.9 (Ref.to table IV-27 and table IV-28) 9) The K-value in Blaney & Criddle formula was changed considerably by the meteorological condition (pan evaporation) and related to be a increasing logarithmic function of the weight of dry matters (x) for both PAL-TAL and TONG-L varieties as follows; 800kg/10a x 2000kg/10a, K=a7+b7 logl0x (b7>0) The K-value for TONG-IL variety was a little larger than that for PAL-TAL variety. 10) The peak values of the evapotranspiration coefficient and k-value at each growth stage for both TONG-IL and PAL-TAL varieties showed up about 60∼70 days after transplanting. The peak values of the former at the base of the weights of total dry matters, 800∼2000kg/10a, were 1.14∼1.82 for TONG-IL variety and 1.12∼1.80, for PAL-TAL variety, and at the base of the weights of rough rices, 400∼1000 kg/10a, were 1.11∼1.79 for TONG-IL variety and 1.17∼1.85 for PAL-TAL variety. The peak values of the latter, at the base of the weights of total dry matters, 800∼2000kg/10a, were 0.83∼1.39 for TONG-IL variety and 0.86∼1.36 for PAL-TAL variety and at the base of the weights of rough rices, 400∼1000kg/10a, 0.85∼1.38 for TONG-IL variety and 0.87∼1.40 for PAL-TAL variety (Ref. to table IV-18 and table IV-32) 11) The reasonable and practicable methods that are applicable for calculating the evapotranspiration of paddy rice in our country are to be followed the following priority a) Using the evapotranspiration coefficients based on an expected yield (Ref. to table IV-13 and table IV-18 or Fig. IV-13). b) Making use of the combination method of seasonal evapotranspiration coefficient and evapotranspiration intensity (Ref. to table IV-13 and table IV-27) c) Adopting the combination method of evapotranspiration ratio and evapotranspiration intensity, under the conditions of paddy field having a higher level of expected yield (Ref. to table IV-23 and table IV-27). d) Applying the k-values calculated by Blaney-Criddle formula. only within the limits of the drought year having the pan evaporation of about 450mm during paddy field period as the design year (Ref. to table IV-32 or Fig. IV-22).

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Analysis of Greenhouse Thermal Environment by Model Simulation (시뮬레이션 모형에 의한 온실의 열환경 분석)

  • 서원명;윤용철
    • Journal of Bio-Environment Control
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    • v.5 no.2
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    • pp.215-235
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    • 1996
  • The thermal analysis by mathematical model simulation makes it possible to reasonably predict heating and/or cooling requirements of certain greenhouses located under various geographical and climatic environment. It is another advantages of model simulation technique to be able to make it possible to select appropriate heating system, to set up energy utilization strategy, to schedule seasonal crop pattern, as well as to determine new greenhouse ranges. In this study, the control pattern for greenhouse microclimate is categorized as cooling and heating. Dynamic model was adopted to simulate heating requirements and/or energy conservation effectiveness such as energy saving by night-time thermal curtain, estimation of Heating Degree-Hours(HDH), long time prediction of greenhouse thermal behavior, etc. On the other hand, the cooling effects of ventilation, shading, and pad ||||&|||| fan system were partly analyzed by static model. By the experimental work with small size model greenhouse of 1.2m$\times$2.4m, it was found that cooling the greenhouse by spraying cold water directly on greenhouse cover surface or by recirculating cold water through heat exchangers would be effective in greenhouse summer cooling. The mathematical model developed for greenhouse model simulation is highly applicable because it can reflects various climatic factors like temperature, humidity, beam and diffuse solar radiation, wind velocity, etc. This model was closely verified by various weather data obtained through long period greenhouse experiment. Most of the materials relating with greenhouse heating or cooling components were obtained from model greenhouse simulated mathematically by using typical year(1987) data of Jinju Gyeongnam. But some of the materials relating with greenhouse cooling was obtained by performing model experiments which include analyzing cooling effect of water sprayed directly on greenhouse roof surface. The results are summarized as follows : 1. The heating requirements of model greenhouse were highly related with the minimum temperature set for given greenhouse. The setting temperature at night-time is much more influential on heating energy requirement than that at day-time. Therefore It is highly recommended that night- time setting temperature should be carefully determined and controlled. 2. The HDH data obtained by conventional method were estimated on the basis of considerably long term average weather temperature together with the standard base temperature(usually 18.3$^{\circ}C$). This kind of data can merely be used as a relative comparison criteria about heating load, but is not applicable in the calculation of greenhouse heating requirements because of the limited consideration of climatic factors and inappropriate base temperature. By comparing the HDM data with the results of simulation, it is found that the heating system design by HDH data will probably overshoot the actual heating requirement. 3. The energy saving effect of night-time thermal curtain as well as estimated heating requirement is found to be sensitively related with weather condition: Thermal curtain adopted for simulation showed high effectiveness in energy saving which amounts to more than 50% of annual heating requirement. 4. The ventilation performances doting warm seasons are mainly influenced by air exchange rate even though there are some variations depending on greenhouse structural difference, weather and cropping conditions. For air exchanges above 1 volume per minute, the reduction rate of temperature rise on both types of considered greenhouse becomes modest with the additional increase of ventilation capacity. Therefore the desirable ventilation capacity is assumed to be 1 air change per minute, which is the recommended ventilation rate in common greenhouse. 5. In glass covered greenhouse with full production, under clear weather of 50% RH, and continuous 1 air change per minute, the temperature drop in 50% shaded greenhouse and pad & fan systemed greenhouse is 2.6$^{\circ}C$ and.6.1$^{\circ}C$ respectively. The temperature in control greenhouse under continuous air change at this time was 36.6$^{\circ}C$ which was 5.3$^{\circ}C$ above ambient temperature. As a result the greenhouse temperature can be maintained 3$^{\circ}C$ below ambient temperature. But when RH is 80%, it was impossible to drop greenhouse temperature below ambient temperature because possible temperature reduction by pad ||||&|||| fan system at this time is not more than 2.4$^{\circ}C$. 6. During 3 months of hot summer season if the greenhouse is assumed to be cooled only when greenhouse temperature rise above 27$^{\circ}C$, the relationship between RH of ambient air and greenhouse temperature drop($\Delta$T) was formulated as follows : $\Delta$T= -0.077RH+7.7 7. Time dependent cooling effects performed by operation of each or combination of ventilation, 50% shading, pad & fan of 80% efficiency, were continuously predicted for one typical summer day long. When the greenhouse was cooled only by 1 air change per minute, greenhouse air temperature was 5$^{\circ}C$ above outdoor temperature. Either method alone can not drop greenhouse air temperature below outdoor temperature even under the fully cropped situations. But when both systems were operated together, greenhouse air temperature can be controlled to about 2.0-2.3$^{\circ}C$ below ambient temperature. 8. When the cool water of 6.5-8.5$^{\circ}C$ was sprayed on greenhouse roof surface with the water flow rate of 1.3 liter/min per unit greenhouse floor area, greenhouse air temperature could be dropped down to 16.5-18.$0^{\circ}C$, whlch is about 1$0^{\circ}C$ below the ambient temperature of 26.5-28.$0^{\circ}C$ at that time. The most important thing in cooling greenhouse air effectively with water spray may be obtaining plenty of cool water source like ground water itself or cold water produced by heat-pump. Future work is focused on not only analyzing the feasibility of heat pump operation but also finding the relationships between greenhouse air temperature(T$_{g}$ ), spraying water temperature(T$_{w}$ ), water flow rate(Q), and ambient temperature(T$_{o}$).

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