## 4 Evaluation of the Adopted Regression Model and Discussion
In contrast to this, the observed error in the \"lateral sense\" is far smaller, as can be seen in Figure 10.  
To more practically explain the minor importance of errors in the \"longitudinal sense\" when determining \(F_{OT_{max}}\) distances on the overall accuracy of the maximum transient offftracking calculation, one of the situations with an unfavorable (critical) combination of input parameters (\(R\), \(d\), and \(\theta_{S}\)) is presented in Figure 10. The selected vehicle with a datum length \(d=5.00\) m negotiates a circular curve with a turn angle of \(30^{\circ}\) and a radius \(R=20\) m. The required parameters \(F_{OT_{max}}\) and \(\beta_{d}\), determining the maximum transient offftracking position of the vehicle, are calculated numerically. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{6}{c}{**Input Parameters**} & \multicolumn{3}{c}{**Numerical Solution**} & \multicolumn{3}{c}{**Regression Model**} & \multicolumn{3}{c}{**Abs. Differences**} \\ \hline
**No \({}^{\star}\)** & \(\theta_{S}\) [\({}^{\circ}\)] & \(RId\) & \(\beta_{max}\) [\({}^{\circ}\)] & \(t_{N}\) & \(\beta_{d,N}\) [\({}^{\circ}\)]  
Figure 10: The influence of the magnitude of error in the “longitudinal sense” (when calculating \(F_{OT_{max}}\)) on the accuracy of the maximum transient offtracking vehicle position. Figure 10 proves that the lateral offset (transient offfracking) varies slightly whether the vehicles datum point is moved back or forth along the exit tangent, in relation to the point where the actual maximum transient offfracking is reached. Of course, the movement of the point concerned should stay within reasonable limits (1.0 m in Figure 10). Negligible differences between the pairs of lengths \(OT_{max}\) and \(OT^{\prime}\), and \(OT_{max}\) and \(OT^{\prime\prime}\), confirm that. From the presented example, it is clear that the maximum error of \(\Delta F_{OT_{max}}=0.203\) m when calculating \(F_{OT_{max}}\) distances using the derived polynomial regression function, in terms of practical engineering applications, has a negligible impact on the overall computation accuracy of the maximum transient offfracking position. Now, it is important to notice that the difference between the maximum transient offfracking value \(OT_{max}\) and the offfracking \(OT_{\beta max}\), calculated in the position where the maximum steering angle \(\beta_{max}\) is reached (the exact end of the arc) is 0.04 m. Though some safety margins must always be observed, the typical accuracy of construction works in plan projection must be within 1 cm. And as for aircraft negotiating taxiway turns, the error becomes much higher, compromising not specific ICAO formulas but the entire calculation procedure. The formulas recommended by the ICAO are absolutely correct, but the assumption that the maximum offfracking is reached when the aircraft datum point reaches the end of an arc is absolutely incorrect. In the common taxiway filled case, when a Boeing 747-100 negotiates a \(\theta_{S}=90^{\circ}\), \(R=50.00\) m curve, the error increases up to 0.30 m. In the same turn, the Airbus A380 produces a 0.75 m error. In a less common situation, the A380 negotiating a \(\theta_{S}=45^{\circ}\), \(R=50.00\) m turn, the error is 2.79 m. With \(\theta_{S}\) decreasing to \(30^{\circ}\), the error exceeds 4.3 m! There are even some rare \(\theta_{S}\), \(R\) combinations producing errors exceeding 6.0 m!