Modeling and evaluating the relationship between the radius superelevation and comfort speed in horizontal curves

The paper presents a methodology for correlating the radius of horizontal curve (R) and the superelevation rate (e) when the radius is above the minimum and the superelevation is below its maximum (emin < e < emax). The proposed method, implements the radial utilization friction factor (fR) concept. The relationship between e and R was established by assuming linear or parabolic relationship between the superelevation rate and the radial friction coefficient and generating e-fR distribution factors (γL, γP) correspondingly. The proposed models are sensitive to the superelevation policy by applying the desired maximum superelevation rate that is appropriate with the design speed. The models were further evaluated by examining their impact on the comfort speed. The linear model generates stable or slight increase in the comfort speed as the horizontal curve radius increases and therefore maintains unconstrained (comfort) driving and reduces the potential of negative friction lateral acceleration. The results were compared to the e-R relationships recommended by the United States policy on geometric design of highways (AASHTO): method 5 (for high speed facilities) and method 1. Both models generated intermediate radii results between AASHTO's method 5 and method 1. The highest difference between AASHTO method 5 and the proposed models and between AASHTO method 1 and the linear model occurs when the radius reaches its maximum value for a minimum superelevation (emin = 2%). The linear model resulted in lower radii design values than the parabolic model and is therefore superior in terms of topography harmonization and right of way in addition to its preferable comfort speed pattern. The linear e-fR distribution model was further adjusted to the superelevation range: 0 to - emin (normal crown, NC) by controlling the radial utilization factor and maintaining the horizontal curve radii design values in a similar level. A graphical presentation and additional design radii values for e = 0 and for normal crown (NC) were supplemented.