At about 1130 Pacific time, the airplane lost the majority of its left side cockpit door during cruise flight. Separated door components impacted and dented the airplanes left stabilator, causing minor damage. Visual conditions prevailed. Neither the flight instructor (CFI) nor the private pilot was injured. According to the CFI, the airplane was cruising in level flight at about 4000 feet MSL when the left door “popped open” minutes after the airplane entered an area of moderate clear air turbulence. The door separated from the airplane and the CFI took control of the airplane. Despite full power, level flight could not be maintained. The pilots were able to land without further mishap. As the airplane taxied to parking, the local air traffic controller advised them that an airframe component dropped from the airplane onto the tarmac. The door was broken into several pieces. A Safety Board investigator noted the door is not rigid, and its frame can be torsionally twisted by application of force on either the doors lower front or lower rear.