## 1 Introduction  
When a vehicle turns, particularly trucks or other long wheelbase vehicles, the rear wheels deviate inside the path traced by the front wheels. The trailing axles of a turning vehicle increasingly deviate towards the curve center, until the rear axle wheels finally reach the maximum steady-state offset from the steering alignment path. This phenomenon is well known in transportation engineering as low-speed offtracking [1; 2; 3]. In contrast to this phenomenon, high-speed offtracking introduces movements of trailing vehicle axels outward the curve center due to the lateral acceleration of the vehicle as it traverses a horizontal curve at high speeds [4; 5]. In addition to the vehicle wheelbase length, road geometry parameters, such as the turn radius and turn angle, dominantly influence offloading intensity [6]. In general, two different states of low-speed offtracking exist: steady-state offtracking and active transient state offtracking. According to the authors of [7], steady-state offtracking is not normally reached before covering turn angle of 270\({}^{\circ}\). This means that particular vehicle will reach steady-state offtracking only after covering a constant radius curve with a turn angle greater than 270\({}^{\circ}\). The most widely accepted procedure for steady-state offtracking calculation is the traditional \"sum of squares\" method originally developed by the Western Highway Institute (WHI), and published in 1970 [8], and the letter repeatedly revised by the Society of Automobile Engineers--SAE International [9; 10]. Since roadway edges, especially in intersection zones, are usually designed with relatively small radii and with turn angles in the order of 90\({}^{\circ}\), the potential application of steady-state offtracking calculation methods is quite limited, if not questionable, in practice. When a vehicle performs a sharp turn like this one, it remains in an active transient offtracking state. Hence, the question how to accurately calculate the maximum offtracking value for a vehicle if an active transient offtracking state arises. Perhaps the most acute problem related to the lack of accurate transient offtracking calculation comes from the field of airport design. The official ICAO procedure for taxiway fillet design [11] assumes that the maximum offtracking is reached when the aircraft datum point (usually the cockpit) reaches the end of the taxiway lead arc, which is incorrect. The consequence is an insufficient pavement width in taxiway turns. Even in standard cases (turn angle of 90\({}^{\circ}\) and radii of 50 m), the magnitude of error is in the range of 0.30-0.75 m. In less common dispositions, when larger aircrafts, i.e., the Airbus A380, negotiate sharp turns, the error exceeds an enormous 4.3 m! Also, the lateral positioning of autonomous vehicles in relation to the geometry of roadway edges demands efficient transient offtracking assessment in order to safely guide vehicle through the crossroad [12; 13; 14]. This is especially critical in the case of an articulated autonomous vehicle such as a semi-tractor trailer [15; 16]. In past decades, numerous mathematical and numerical models for setting vehicles' movement trajectories, while negotiating different steering path alignment configurations, have been developed and tested in the field [17; 18; 19; 20; 21; 22; 23]. Additionally, commercial computer programs for the simulation of vehicle movements and vehicle swept path analysis, such as the Auto CAD Vehicle Tracking 2024 and Transport AutoTURN 12.0.0, have become indispensable tools for civil engineers and other specialists involved in intersection and roundabout design [24; 25]. Recently, extensive analyses, addressing the accuracy of the available numerical models and commercial software applications for setting vehicle movement trajectories, were conducted in a Ph.D. thesis [26].