International Conference of Agricultural Engineering XXXVII Congresso Brasileiro de Engenharia Agrícola Brazil, August 31 to September 4, 2008 MATHEMATICAL MODELING AND SPARK MAPPING OF SHADE STRUCTURES FOR CORRAL SYSTEMS IN HOT CLIMATES MOHAMED SAMER 1 ; HARTMUT GRIMM 2 ; MOHAMED HATEM 3 ; REINER DOLUSCHITZ 4 ; THOMAS JUNGBLUTH 5 1 PhD Student, University of Hohenheim (440b), 70593 Stuttgart, Germany. E-mail: samer@uni-hohenheim.de 2 PhD, Scientific Staff, Livestock Systems Engineering, University of Hohenheim (440b), 70593 Stuttgart, Germany. 3 Professor, Agricultural Engineering Department, Faculty of Agriculture, Cairo University, Giza, Egypt. 4 Professor, Computer Applications and Business Management in Agriculture, University of Hohenheim (410c). 5 Professor, Livestock Systems Engineering, University of Hohenheim (440b), 70593 Stuttgart, Germany. Presented at CIGR INTERNATIONAL CONFERENCE OF AGRICULTURAL ENGINEERING XXXVII CONGRESSO BRASILEIRO DE ENGENHARIA AGRÍCOLA – CONBEA 2008 Brazil, August 31 to September 4, 2008 ABSTRACT: A tool is developed in order to assist in designing and planning dairy farms in hot climates. The tool is developed by integrating a mathematical model into an electronic spark map. The spark map (decision tree) assists the designer in making decisions to select the roof material and the roof type suitable for the selected corral system. Subsequently, the roof and the structure dimensions will be calculated automatically. Furthermore, it calculates the capital investment and the fixed, variable, and total costs of the shade structure and the roof material. However, the mathematical model of the spark map requires some input data. According to the inserted input data, the designer will be advised to implement one of the available roof types and roof materials. Afterwards, the spark map using the mathematical model will make the calculations which guide the designer to compare the output data of the different roof types and roof materials, and then to make the right decision. KEYWORDS: mathematical modeling, spark mapping, precision livestock farming, shade structures, roof materials, costs calculation, corral systems, hot climates, dairy cows INTRODUCTION: Lindley and Whitaker (1996) stated that yards or corral systems are best suited to dry, hot climate zones. Ikeguchi and Okushima (2001) investigated the relationship between roof type, roof slope angle, and wind direction and air movement inside and outside the house. Samer et al. (2007) developed a mathematical model to plan several corral systems. The objective of this study is to develop a tool to assist the designers of dairy farms in hot climates in designing and specifying the dimensions of the shade structure, selecting the suitable roof material, and calculating the costs. METHODOLOGY: The tool is developed by integrating a mathematical model into an electronic spark map. The mathematical model was developed using the designs, parameters, variables, and constant values of the different shade structures of corral systems available in the references. Subsequently, MS-Excel is used to develop the spark map of the mathematical model, and to show the results of the input settings automatically. RESULTS AND DISCUSSION: The spark map (Figure 1) assists the designer in making decisions to select the roof material (reed or straw mats, polished or isolated aluminum, or burnt-clay bricks) and the roof type (horizontal, mono-slope, open-ridge, or compound) suitable for the selected corral distribution (two sides of corrals, one side of corrals, or one corral); afterwards, the roof and structure dimensions will be specified. Moreover, it calculates the capital investment and the fixed, variable, and total costs of the shade structure and the roof material. However, the mathematical model (Tables 1 through 4) of the spark map requires some input data (Table 5) such as: shade dimensions, roof slope, cowshed height, corrals distribution, span between 2 posts, some other engineering parameters,