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Tham khảo tài liệu 'intro to naval architecture 3e episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 20 SHIP FORM CALCULATIONS Figure 3. Ỉ situation is illustrated in Figure 3.1. The area of the shaded trapezium is n 2 n jVn JVn 1 Any area can be divided into two each with part of its boundary a straight line. Such a line can be chosen as the axis about which moments are taken. This simplifies the representation of the problem as in Figure 3.2 which also uses equally spaced lines called ordinates. The device is very apt for ships since they are symmeưical about their Figure 3.2 SHIP FORM CALCULATIONS middle line planes and areas such as waterplanes can be treated as two halves. Referring to Figure 3.2 the curve ABC has been replaced by two straight lines AB and BC with ordinates y0 y l and y2 distance h apart. The area is the sum of the two trapezia so formed A h y0 1 2 h yo 2yi y2 Area - ------- ------- - ----------------- 2 2 2 The accuracy with which the area under the actual curve is calculated will depend upon how closely the straight lines mimic the curve. The accuracy of representation can be increased by using a smaller interval h. Generalizing for n 1 ordinates the area will be given by h yQ 2yi 2y2 2yn_ yn Area ---------------------------------- 2 In many cases of ships waterplanes it is sufficiently accurate to use ten divisions with eleven ordinates but it is worth checking by eye whether the straight lines follow the actual curves reasonably accurately. Because warship hulls tend to have greater curvature they are usually represented by twenty divisions with twenty-one ordinates. To calculate the volume of a three dimensional shape the areas of its cross sectional areas at equally spaced intervals can be calculated as above. These areas can then be used as the new ordinates in a curve of areas to obtain the volume. SIMPSON S RULES The trapezoidal rule using straight lines to replace the actual ship curves has limitations as to the accuracy achieved. Many naval architectural calculations are carried out using what are known as Simpson s rules. In .