at the expansion start stage, and expands gradually at the stage in which the body of the rider receives protection power from the air bag. Especially, it is desirable for the air bag shrink at that time. Such an air bag apparatus for side crash is described in Japanese Laid Open Patent Application (JP-A-Heisei 8-268213: a first conventional example). In the first conventional example, holes are opened on the middle portion of the air bag. However, because there is fear that the holes receive any damage when expanding, a perimeter of the hole is reinforced. Thus, the reinforcement effect around the hole is excellent. In the first conventional example, the reinforcement effect is achieved by the formation of the protrusion. Such a protrusion is folded and the protrusionis pushed into the inner space of the air bag. In the first conventional example, the expansion is rapid at the expansion start stage and contraction is carried out at the expansion end stage. Also, it is important that the air bag apparatus for side crash expands to a predetermined final shape at a moment in the narrow space between the rider and the side body of the car.
Another air bag apparatus is known in the Japanese Laid Open Patent Application (JP-P2000-85517A: a second conventional example) in which the proximal end of an air bag is formed with a hard member to extend and expand smoothly in a front direction. The 3-dimensional final shape of the air bag in the expansion is determined through sewing a combination of