Provided is a target launching machine having a circular section portion. The machine includes a launching arm rotatable about an axis of rotation and a bearing surface that accommodates a circular section portion of the target and includes an offset portion that is configured so that a spacing between a trajectory of the launching arm and the offset portion increases in a direction of rotation of the launching arm. The offset portion includes a portion having a circular profile about a portion axis that is offset relative to the axis of rotation and parallel to the axis of rotation. The offset between the portion axis and the axis of rotation has a non-zero component in a primary direction defined in a vertical plane, with the non-zero component positioned relative to the axis of rotation opposite the portion.