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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 formula for calculating the curve elements is deduced from the first three terms of the triangle series expansion. All the formulas published in the domestic road survey and design publications are publicly available. Since the design μ values of the main roads of all grades of highways and expressways are generally small, the fourth item neglected in the trigonometric series expansion is negligible, but the design μ value of freeway ramps is usually large, ignoring the triangular grades The fourth item in the expansion item will result in a large error in the calculation of the easing curve elements. This paper derives the calculation formulas of the easing curves obtained from the first four items of the triangular series expansion, analyzes the influence of the design μ on the calculation error of the easing curves, and verifies the correctness of the new formula with several typical cases.