# Study on Gage Widening Methods for Small-Radius Curves
## 3 Status of Gage Widening Standards
When the curve radius is in the range of 125 to 150 m, the minimum gage shall not be less than 1440 mm, and when the curve radius is in the range of 100 to 125 m, the minimum gage shall not be less than 1445 mm. Gage widening on the small-radius curves of Chinese railways can be divided into three stages. In 1954, China adopted the calculation methods and parameters of the Soviet Union to determine gage widening values. The wheelbase was 3.9 m, the wheel flange gap was 11 mm, and the corresponding gage widening values are listed in Table 9. The minimum radius to be widened was 651 m, and the maximum widening amount was 15 mm, divided into four levels. When the technical regulations were revised in 1972, the gage widening amount remained unchanged [20]. In 1976, [PERSON] from the Academy of Railway Sciences hypothesized that the parameters of China's vehicles had changed. The bogie wheelbase was now 2.7 m, and the wheel-rail gap was 18 mm. Based on the dynamically free inscribing theory, the correlation between the curve radius and gage widening value was calculated (Table 10). For all operating speeds, when the radius exceeded 300 m, the vehicles could pass the curve in dynamically free inscribing. Through many field tests, the revised values for gage widening were proposed (Table 11) [21]. The minimum curve radii that FD-type and forward-type locomotives could pass under the condition of no gage widening were 283 and 256 m, respectively (Table 12). Therefore, the gage widening standard specified in Table 11 can ensure the normal passage of locomotives. This standard was formally implemented in 1983. In 2010, because the curve gage widening value was still too large, which was inconvenient for maintenance and management, and the curve gage widening value lacked transition as the starting point, the geometrically free inscribing theory was adopted to calculate the correlation between the curve radius and the gage widening amount. As listed in Table 13, widening the gage was not necessary if the radius exceeded 300 m. According \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Superelevation (mm)**} & \multirow{2}{*}{**Curve Radius**} & \multicolumn{8}{c}{**Driving Speed (km/h)**} \\ \cline{3-10}  & & **5** & **20** & **30** & **40** & **50** & **60** & **70** & **80** & **90** & **100** \\ \hline \multirow{4}{*}{\(100\)} & 350 & \(-3.7\) & \(-4.4\) & \(-4.8\) & \(-5.2\) & \(-5.7\) & \(-6.1\) & \(-6.7\) & \(-7.5\) & \(-8.2\) & \(-9.4\) \\  & 300 & \(-1.6\) & \(-2.0\) & \(-2.5\) & \(-3.1\) & \(-3.7\) & \(-4.5\) & \(-5.4\) & \(-6.0\) & \(-7.5\) & \(-9.1\) \\  & 250 & 1.5 & 2 & 0.4 & \(-0.4\) & \(-1.2\) & \(-2.0\) & \(-2.9\) & \(-4.5\) & \(-7.2\) & \(-10.5\) \\  & 200 & 4.4 & 3.7 & 2.8 & 1.9 & 0.7 & \(-0.5\) & \(-2.4\) & & & \\ \hline \end{tabular}
\end{table} 
Table 10: Gage widening values in Chinese railways (1954) (mm). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Locomotive Type**} & \multirow{2}{*}{**Number of Axes**} & \multirow{2}{*}{**Wheelbase**} & \multirow{2}{*}{**Widening Amount (mm)**} & **0** & **5** & **10** & **15** \\ \hline FD-type & 5 & \(1625+1625+1625+1625\) & Minimum Curve Radius & 283 & 209 & 166 & 137 \\ Forward-type & 5 & \(1600+1600+1600+1600\) & (m) & 256 & 192 & 153 & 128 \\ \hline \end{tabular}
\end{table} 
Table 12: Gage widening values in Chinese railways (1983) (mm). \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Curve Radius (m)**} & \multirow{2}{*}{\(\geq\)651} & \multirow{2}{*}{650–451} & \multirow{2}{*}{450–351} & \multirow{2}{*}{\(\leq\)350} \\ \cline{3-3} \cline{5-7}  & & & & & & & \\ \hline Widening Value (mm) & 0 & 5 & 10 & 15 \\ \hline \end{tabular}
\end{table} 
Table 9: Gage widening values in Chinese railways (1954) (mm).