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维修烟囱时,首先要确定维修部位的实际外径,有时还需知道烟囱圆心的坐标。过去,人们一般是测量烟囱同一横截面上3个点(图1)A、B、C的坐标x_A、y_a,x_B、y_B,x_c、y_c将它们代入二元一次方程组 (x-x_A)~2+(y-y_A)~2=(x-x_B)~2+(y-y_B)~2(1)(x-x_B)~2+(y-y_B)~2=(x-x_C)~2+(y-y_C)~2解(1)式得圆心坐标x、y,再将x、y和上述3个测点中任意一个测点的坐标xi、yi一起代入下式R=(x-xi)~2+(y-yi)~2 (2)得到该截面的半径R。上述算法的特点是计算简便,但由于缺乏校核条件,不仅精度低,而且容易发生错误。要想避免错误和提高精度,就需要在烟囱同一横截面上观测4个以上测点。
When the chimney is being repaired, the actual outer diameter of the repair site must first be determined, and sometimes the coordinates of the center of the chimney must be known. In the past, people generally measured the coordinates of x, A, B, and C of the three points on the same cross section of the chimney (Fig. 1) (x_A, y_a, x_B, y_B, x_c, y_c) and substituted them into a binary equation (x-x_A)~ 2+(y-y_A)~2=(x-x_B)~2+(y-y_B)~2(1)(x-x_B)~2+(y-y_B)~2=(x-x_C)~ The 2+(y-y_C)~2 solution (1) obtains the center coordinates x and y, and substitutes the coordinates xi and yi of any one of the above three measurement points into the following formula: R=(x). -xi)~2+(y-yi)~2 (2) The radius R of this section is obtained. The above algorithm is characterized by simple calculation, but due to the lack of checking conditions, not only the accuracy is low, but also prone to errors. To avoid errors and improve accuracy, it is necessary to observe more than 4 points on the same cross-section of the chimney.