Deep into a solo voyage in the Indian Ocean, an unnamed man (Redford) wakes to find his 39-foot yacht taking on water after a collision with a shipping container left floating on the high seas. With his navigation equipment and radio disabled, the man sails unknowingly into the path of a violent storm. Despite his success in patching the breached hull, his mariner's intuition and a strength that belies his age, the man barely survives the tempest. Using only a sextant and nautical maps to chart his progress, he is forced to rely on ocean currents to carry him into a shipping lane in hopes of hailing a passing vessel. But with the sun unrelenting, sharks circling and his meager supplies dwindling, the ever-resourceful sailor soon finds himself staring his mortality in the face.
Never Give Up