Small-radius wheels are gradually introduced on special rail vehicles, such as double-decker coaches and piggyback wagons. It allows for a low-floor design and further increases the loading capacity of vehicles. From the perspective of vehicle dynamics, small-radius wheels have lower unsprung mass than the nominal wheels with a radius of 460 mm, and it could mitigate the wheel-rail dynamic interaction. Also, the contact patch size is reduced due to the increased curvature of the rolling contact circle, and they are more sensitive to changes in the track geometry than nominal wheels, especially in turnouts with discontinuous rail profiles. To investigate the dynamic response of small-radius wheels in a turnout, the Manchester Benchmark passenger coach with variable radius wheels and a left-hand turnout with a radius of 245 m are introduced in this work. The influence of wheel radii on the running performance, including the wheel-rail interaction and wheel damage behaviour, is investigated by numerical simulations. In addition, a sensitivity study is executed to evaluate the influence of unsprung mass and wheel flange friction on the performance of a vehicle whose wheel radius is 275 mm, and the potential remedy to mitigate high wheel wear is proposed.