以線元素移動方法應用於受約制豎曲線定位之研究

Abstract

在工程測量中，路線縱斷面對於既存或預留結構物之縱向距離需求，例如橫交道路，高壓電線或地下管線等位置條件（siteconditon）之約制，豎曲線可能需要通過其中若干個限制點，傳統求算受約制豎曲線長度（或曲率半經）之方法，乃基於切線坡度已知為前提，以試誤法或計算法解算，而未考慮坡度未知時之處置，及解算出之值是否符合設計規範規定等實務性問題，本文乃以解決此二點問題為出發點，以線元素移動的觀念，直接設定豎曲線經過之位置及其半經，求解符合設計規範規定之豎曲線線形，提供傳統解算方法之外，另一種改變思維方向之解法。 本文將豎曲線的基本型式分為12個測試模組及二個應用實例驗證，線元素計算法確能提昇受約制豎曲線通過一個及二個固定點定位之效率，尤其應用於反向豎曲線之設計上，效果更為顯著。

In engineering surveying, the vertical profiles are always constrained by existing conditions. Such as the vertical distances between highway and structures are often affected and constrained by the position of these structures. The traditional method for the calculation of vertical curve is based on the grade of the tangent and uses the trial-and-error method to find the solution. However, this method ignores the case in which the grade is unknown. In addition, whether the results can meet the design rules can not be assured immediately. This paper aims to examine the feasibility of using moveable linear element in vertical curve calculation. The solution is based on the method that linear elements are moveable and then check the positions and radius of the linear element movement.Compare to the traditional method, it is provided a different way in the concept of calculation and met the requirements in the specification. In the study, 12 modules based on different shapes of vertical curves and two real practice examples were used to examine the erriciency of position constrained vertical curves when passing one or two fixed points. Compare to the traditional method, It is found that this method is better than the traditional one, not only in efficiency, but also in meeting the requirements of design rules.