## 5 Conclusions  
The calculation method presented herein offers a unique and practical solution for the calculation of the maximum transient offfracking of a single-unit vehicle when negotiating circular curves. It uses well-proven mathematical formulas from the ICAO mathematical model for the derivation of only one transcendental equation which precisely determines the maximum transient offfracking position of the vehicle. Complicated numerical methods for solving this type of equation were substituted by a relatively simple polynomial regression function capable to predict the maximum transient offfracking position with the desired level of accuracy. In this manner, computationally demanding numerical methods for transcendental equation solving are successfully compensated with a more practical and efficient calculation method. The accuracy of the presented regression model was assessed on the whole set of input data parameters, including all combinations of \(R/d\) ratios and \(\theta_{S}\) turn angles. The largest discrepancies in relation to the numerical calculations appear for turn angles \(\theta_{S}\) smaller than \(35^{\circ}\), but the magnitude of these discrepancies negligibly affects the reliability and overall accuracy of the developed regression model. Robustness analyses of the fourth-degree polynomial regression model revealed that the regression model has a negligibly lower prediction accuracy for the combination of input parameters covering turn angles \(\theta<75^{\circ}\) and \(R/d\) ratios in the range \(R/d<1.408451\). Though the polynomial regression function seems too long at first sight, its main advantage is the almost instant calculation of the maximum transient offfracking position. Minimal effort and an ordinary pocket calculator are enough to calculate maximum transient offfracking position for the specified input parameters \(R\), \(d\), and \(\theta_{S}\). All previously published mathematical models and, in particular, the currently available software tools for vehicle swept path analyses require more time and engineering skills to achieve the same results. Additionally, the method retrieves the maximum transient offfracking from the three input parameters (\(R\), \(d\), and \(\theta_{S}\)), skipping the need for CAD-like steering path construction (as an input) and swept path generation (as an output). It is demonstrated and proved that the maximum transient offftracking is not achieved when the vehicle's datum point reaches the end of circular arc (assumption in ICAO's design manual), but some distance beyond. What is more important, the error caused by this ICAO's assumption can significantly affect the accuracy of filled design at airports. By applying the regression model proposed herein, it is possible to calculate the maximum transient offftracking only when the vehicle negotiates simple circular curves. For other steering alignment configurations, which include more complex horizontal curve types, i.e., transition and revers curves, this method cannot be used. Currently, the proposed regression model can be applied for the maximum transient offftracking calculation of a single-unit vehicle and not for articulated or multi-unit vehicle combinations. These flaws have already been considered by the authors of the paper and new mathematical models which tackle these issues are already under development. Conceptualization, V.I. and D.G. ; formal analysis, M.L. ; investigation, S.F., F.T. and S.V. ; methodology, V.I. and D.G. ; software, M.L. ; supervision, V.I. and D.G. ; visualization, F.T., S.V. and N.M.; writing--original draft, V.I., D.G. and S.F. ; writing--review and editing, V.I. and M.L. All authors have read and agreed to the published version of the manuscript. This research was financed by the Ministry of Science, Technological Development, and Innovation of the Republic of Serbia through an agreement on institutional financing signed with the Faculty of Civil Engineering University of Belgrade, Grant No. 200092. Not applicable.