A high thermal efficiency reciprocating hydrogen-fueled engine for ultra-high altitude long endurance flight and its method of operation are described. The engine is based on an opposed piston barrel design where long cylinders are employed to accommodate extraordinarily large compression and expansion strokes where the corresponding ratios are over 50:1, taking advantage of the very low ambient air pressures and temperatures at 60,000 ft and higher to reduce the overall weight and strength requirements of the inventive engine that would be a factor for operation at lower altitudes. The engine is designed to obtain more than 70% indicated thermal efficiency when operated at ultra-high altitudes of 60,000 ft and greater. A combination of large compression ratios combustion temperature optimization and management, instantaneous and complete combustion at TDC, followed by a rapid and long expansion stroke using tailored control of piston movement provide the means to achieve such high efficiencies.