The NX-Delta was the third prototype vessel used in the NX Program in an effort to test and refine Henry Archer's warp 5 engine design.
In 2144, months after Commanders Jonathan Archer, Henry Archer's son, and A.G. Robinson's illegal flight in the NX-Beta, the NX-Delta, piloted by Duvall, became the first Human spacecraft to break the warp 3-barrier. (ENT: "First Flight")
Given the greek alphabet naming system, one would think that there should be an NX-Gamma, and that the NX-Delta would be the fourth prototype.
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