Kryptonian scientist Jor-El started developing a faster way of space travel than step-through (in part due to the permanent shut-down of the World-Gate network) when his research on a series of earthquakes in Krypton made him believe the planetary core would explode, destroying the planet. He eventually built a Trans-Warp prototype ship, which he tested with Krypto. The test was successful, but Krypto's ship was caught in a space rift and became lost in space for over thirty years.
Jor-El eventually built a second prototype, which he was forced to use to save his infant son, Kal-El, when Krypton exploded. The ship took a ten-year travel to reach planet Earth, and landed on Smallville, Kansas, where Kal-El was found and adopted by the Kents as their son, named Clark Kent.
Almost twenty years later, Clark Kent, who now had assumed the superhero identity of Superman, repaired and modified his old ship in order to use it for space travel himself, which he used to do some research on the nearby planets of the Sol system, Mars and Jupiter.
After Superman salvaged the old Swift-Justice Class Speeder belonging to Kon-Lir from the ocean depths, he installed a Trans-Warp drive on it. He was forced to test it when his friends were kidnapped by Supreme Kree Accuser Ronan, who tried to drag him into a trial to exact his revenge.
Both ships were eventually used by Superman and General Zod to reach the Kryptonian outposts in Cel'Mak IV and In'Ri III in order to acquire the access modules for Battlestation Sentrius, in the preface to the invasion of the Kree, Skrulls and Shi'ar.