Cryogenic cooling system for an aircraft

A method comprising:

• driving rotation of a plurality of components of a first air cycle machine through a gearbox operably coupled to a shaft of a gas turbine engine to produce a cooling air stream based on a first engine bleed source of the gas turbine engine;
• outputting a chilled air stream at a cryogenic temperature from a second air cycle machine based on a second engine bleed source cooled by the cooling air stream of the first air cycle machine;
• and
• condensing the chilled air stream into liquid air for an aircraft use.

A system for an aircraft, the system comprising:

• a gas turbine engine operable to produce thrust for the aircraft;
• a means for cryogenically cooling the aircraft;
• and
• a means for transferring energy from the gas turbine engine to the means for cryogenically cooling the aircraft.