A propulsion unit is provided for propelling a piece of equipment that is normally intended to be pushed by a pedestrian. The unit involves a way to support an upright rider that is sized to allow the rider to reach a handle of the hand-pushed mobile equipment; a plurality of ways to contact the ground and allowing the way to support a rider to move across a surface in a low-friction manner; a way to provide thrust in one or both of the forward and backward directions; and a way to couple the unit to the hand-pushed mobile equipment and allow the hand-pushed mobile equipment to yaw relative to the unit around a vertical axis that is approximately collinear with the vertical axis of the upright rider.