Search Results

Total station equipment, triangulation, or some other mapping technique can generate x-y coordinates describing curved tire marks on the pavement. These marks may result from a critical speed maneuver. Traditionally, these marks are assumed to follow a circular arc and a radius can be determined for use in the critical speed yaw formula. However, critical speed yaw marks typically have a decreasing radius in the direction of travel and a spiral is a more precise fit to the data. In this paper, a total least squares fitting approach is presented to fit the parameters of three types of spiral curves to coordinate data. These are a clothoid spiral, a logarithmic spiral, and an Archimedean spiral which are evaluated and compared for usability in a critical speed yaw analysis. A spreadsheet implementation is presented that makes use of the Microsoft Excel Solver Add-in to perform the minimization of the total least squares fit for the spirals.