When the body is inverted, both the body and the sky board catches the relative wind. The asymmetrical foot position causes a spinning action, often referred to as a helicopter spin. While standing on the board, the board catches most of the relative wind. A similar effect can be experienced while standing on a partner's belly.
To bring the sky board under you from the inverted orientation, your goal is to "knife" the edge of the sky board into the wind. The sky board presents much less drag when its edge is presented into the windflow. (The sky board catches much more wind if one if its flat sides is presented to the windflow.) It is easier to knife the sky board under yourself with a sideways rotation. While trying to bring it forward or backward while knifing it into the wind, the sky surfer must accomedate the long length of the board. You will be fighting the tail of the sky board if you are bringing it under yourself from a rocking front loop action and you will be fighting the nose of the sky board if your are bringing it under yourself from a rocking back loop action. A cartwheel action is the best rotational movement for bringing the sky board back under yourself. If it is a left cartwheel with the left foot forward, your chest will twist to the right as you stand up again. Relaxing the legs as you pass side into the wind position will allow the sky board to find the optimum knife edge presentation to the wind.