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在铁路設計,有时需要計算两錢間的距离(例如在作桥涵断面时)。尤其在复杂的地形条件下,桥涵往往要与綫路成一定角度且于曲綫地段穿过。这就使綫間距的計算工作复杂化。为了可以任意准确而普遍地解决线间距的计算問題,下面提出一个計算方法。一、公式推导: (一)一个圆心位于y軸上且切x軸于座标原点(O,0)的圓与直綫AC相交于B点,OA=P,求AB(=L)长度(如图1): 圓方程式 x~2+(y-R)~2=R~2或 x~2+y~2-2Ry=0 ①直线方程式 x=ycotα+ρ②∴ (1+cot~2α)y~2+2(ρcotα-R)y+ρ~2=0解之得:
In railway design, it is sometimes necessary to calculate the distance between the two funds (for example, in the case of bridges and culverts). In particular, under complex terrain conditions, bridges and culverts tend to be at an angle to the line and pass through the curve. This complicates the calculation of the line spacing. In order to solve the problem of calculating the line spacing arbitrarily and universally, a calculation method is presented below. First, the formula derivation: (A) a circle centered on the y-axis and cut x axis at the coordinate origin (O, 0) intersects the line AC at point B, OA = P, find AB (= L) length (such as Fig. 1): The circle equation x~2+(yR)~2=R~2 or x~2+y~2-2Ry=0 1 The linear equation x=ycot?+p2? (1+cot~2?)y~2 The solution of +2(ρcotα-R)y+ρ~2=0 is: