既有铁路曲线整正计算中的计划正矢计算方法的研究

Research on Calculation Method of Plan Versine in Existing Railway Curve Adjusting

分别利用绳正法、坐标法、偏角法各自的相关理论分析推导了曲线的计划正矢的计算公式,为现场计算各测点的计划正矢提供了一种程序化的新方法。坐标法计算出的计划正矢的结果是精确的,将偏角法和绳正法的计算结果和它进行对比,可分析出它们计算计划正矢的误差大小及其规律。分析结果表明:偏角法和绳正法计算计划正矢的结果是相同的,它们与坐标法之间的误差与半径的大小有关系,半径越小,误差越大,但即使在半径很小的情况下误差都不会超过0.06 mm,这对曲线整正的计算结果影响可以忽略不计。由于利用偏角法计算计划正矢的方法与绳正法比较起来,公式较为简单,故绳正法中计算计划正矢时利用偏角法的方法来计算,可简化计算。

Based on the theories about rope-rectification method,coordinate method and declination angle method,the calculation formula for the curve plan versine was analyzed and deduced.And a new procedural method was provided for calculating in site the plan versine of each survey point.The calculation result about the plan versine according to the coordinate method is precise.Then compared coordinate method with the rope-rectification method and declination angle method,the error magnitude and law of the plan versine calculated can be found out.The calculation results show that the results calculated by those two methods above are the same.The error is related to the radius.The smaller the radius is,the greater the error becomes.But even if the radius is very small,the error is always so small that it would not be more than 0.06 mm,so the influences of the radius on curve adjustment calculation can be ignored.The formula of the declination angle method is easier than that of the rope-rectification method,so declination angle method can be used for simplifying the calculation of plan versine in rope-rectification method.