Modern military aircraft and weapon systems generate extremely high gravitational acceleration and deceleration forces that impair the physiological functions required by pilots for safe operation. These forces, by shifting blood from upper extremities of the body, including the brain, to the legs and feet cause impaired vision, impaired breathing, and loss of consciousness that could be fatal in combat operations. As countermeasures to the acceleration forces, pneumatic anti-G suits and anti-G straining maneuvers were used to prevent the on-rush of blood to the lower part of the body; however, the pneumatic systems consisting of valves, pumps and switches are complex and add undesirable weight to the aircraft; and the straining maneuvers cause physiological fatigue in pilots. As a better system for protection against acceleration forces, a liquid-filled protective garment called ?Libelle anti-G suit? is being tested at various global air force establishments. In the present paper a theoretical investigation based on large elastic deformation theory of submerged liquidfilled membranes is reported laying the mathematical foundation to explain how the anti-G effect is generated by the external hydrostatic pressure. Assuming a neo- Hookean strain energy function of rubberlike materials, a mathematical model of a liquid-filled axi-symmetric closed membrane subjected to various depths of submergence is derived in the form of nonlinear, ordinary differential?integral type of equations. These nonlinear equations were solved numerically using digital computers. Considering the inflating medium and the surrounding liquid medium to be different, the deformed shapes of the membrane were calculated. The membrane profiles illustrate the lifting of the internal fluid by increasing levels of hydrostatic pressure of the external fluid, thus verifying the concept of nullification of gravitational effects on blood pooling in the lower extremities of the body by pressurized external flexible chambers. This study provides the mathematical and computational support to anti-G principles that may influence the design of future anti- G suits for combat pilots.
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