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High collision rates on horizontal curves compared with other roadway elements make them one of the most critical elements in a transportation network and thus good candidates for new studies, especially of the stability of a vehicle driving on a horizontal curve. In this regard, spiral transition curves as facilities to enter horizontal alignments are very important. While the superelevation changes in these curves have always been linear, the aim of this study was to evaluate non-linearity in the superelevation attainment function (SAF). Various scenarios were used in order to cover different situations. As a simulation tool, the CarSim software package was used to model three kinds of passenger cars (sport utility vehicle, utility truck and sedan). In addition, 16 types of spiral–curve–spiral road plans for three different conditions of road slope, six types of warping in the SAF and two types of functional speed were examined (a total of 1728 scenarios). The results showed that non-linearity might produce better results than other proposed methods; for example, it was found that a parabolic function reduced the lateral acceleration rate by over 50% for high superelevation and design speed.

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