Formulation of Elastic Loading Parameters for Studies of Closed-Circuit Underwater Breathing Systems

Peak-to-peak mouth or oro-nasal pressure is used as an indicator of flow resistance during unmanned testing of Underwater Breathing Apparatus (UBA). This interpretation can be confounded by UBA elastance. In modern UBA's elastic pressures can be greater that resistive pressures at low flow rates, resulting in a miscalculation of the work of breathing. Not only must elastance be properly accounted for in UBA testing, but an understanding of elastic loads in general must be acquired. To the latter end, this work provides a rigorous description of elastic loads encountered in the use of breathing systems underwater. Elastance equations were derived from first principles, and compared with experimental measurements. The pressure-volume characteristics of boxes, cylinders, pyramids, and various breathing bags were examined, as was a U.S. Navy MK-15 closed-circuit UBA. The major determinant of elastance underwater was the geometry of the deformable gas volume, with elastic pressures generated by the movement of the air-water interfaces. Both the behavior of various elastances, and the errors involved in common assumptions about elastance were detailed. For simple geometries, theory and measurement agreed closely. In spite of the complex geometry of the MK-15 breathing bag, the MK-15 elastance approximated that of a cylindrical water column. A submerged MK-15 oriented vertically and horizontally, yielded elastances of 4 and 1.8 cm H20/1, respectively.