A wheel apparatus for a self-propelled irrigation system has a center portion, a rim assembly, and a support structure disposed between the center portion and the rim assembly. The rim assembly has a plurality of rigid members spaced apart from each other with longitudinal axes that are parallel with each other and equidistant from the axis of rotation. The rigid members are cylindrical with unsupported ends, and a mounting portion between the ends is connected to an outer periphery of the support structure. The rigid members are held in a fixed position relative to the center portion by the support structure. The rigid members are arranged to contact the ground surface to support the irrigation system with spaces between the rigid members allowing mud and debris to pass freely between the rigid members during operation to enhance traction while minimizing mud from being forced out of a wheel track.
