Direct Solution Of The Deflection Angle Problem Of Horizontal Highway Circular Curves (Asian Journal of Current Engineering and Maths, 2016)
Determination of the five elements of highway horizontal circular curve, which are tangent distance, T, external distance, E, middle ordinate, M, chord length C, and length of curve, L, is directly established in terms of the given radius R and deflection angle ∆.Field features may cause the infeasibility of the intersection point PI. Consequently, the deflection angle ∆ and the radius R cannot be measured which means the arising of non-linear problem.This paper presents a simple and direct solution for the problem by remodeling the non-linear problem as a rational function in terms of the deflection angle. The model’s function has been designated due to the similarity of the graphs of both non-linear function and the rational function.Such function has three coefficients and two asymptotes, x= π/2 as a vertical asymptote and y = a, the first coefficient, as a horizontal asymptote.Coefficients of the model were determined addressing the least squares technique employing different values of the deflection angle along the entire 0 < Δ < π/2 interval. Such model has been verified through adopting different random locations along the interval of J, and the output has proven an almost 100% accuracy.Also, the applicapility of the model for generating deflection angle and curve radius with fair accuracy was investigated numerically adopting designated values of L and T. The results exhibited fair accuracy in comparative to the previous methods in the favour of the iterative techniques of such methods which lack necessary initial guess.The highly precised output, dirct applicability and simplicity of the proposed model recommend such model for manipulation in practical purposes as well in analytical analysis of the highway engineering problems. Also, it may be considered as a preferable than iterative approaches as such approached involving absence of the initial guess.