缓和曲线要素公式的精度分析

Precision Analysis of Spiral Elements Formulae

现有的缓和曲线要素计算公式是取三角级数展开项中的前3项推导而得,国内公开出版的所有公路勘测设计书刊都是使用这些公式。由于各等级公路与高速公路主线的设计μ值一般较小,三角级数展开中忽略掉的第4项也比较小,可以忽略不计,但高速公路匝道的设计μ值通常较大,忽略三角级数展开项中的第4项将导致缓和曲线要素计算误差偏大。该文推导了取至三角级数展开项前4项的缓和曲线要素计算公式,分析了设计μ值对缓和曲线要素计算误差的影响,用几个典型案例验证了新公式的正确性。

The existing spiral elements formulae are from intercepting the front three item of a trigonal series extended,which have been used in all publishing books and periodicals in China about reconnaissance and design of road.For as much as the μ of main route of grading road and speedway is usually too small,the omitted fourth item on the trigonal series extended is also too small,but the μ of ramp of speedway is usually bigger,omitted the item will bring bigger errors in the spiral elements.This paper reduces new spiral elements formulae adding the fourth item on the existing formulae,and analyzes that computing errors of spiral elements are influenced by the their μ.which are accurate and effective.