The Neptune-class starship was a class of United Earth survey ships that were in service with Starfleet around 2141.
Neptune-class ships were limited in speed to warp factor 2. This class of ships utilized the same model of captain's chair that would be initially used on NX-class, a newer and more advanced design of starships. In 2152, Trip Tucker mentioned this fact as justification for his plans to create a new custom-fitted captain's chair for Jonathan Archer. (ENT: "Singularity")
"First Flight" established that warp 2 was not achieved by Humans until 2143, so the Neptune-class must have either entered service after that year, or was originally constrained to lower warp speeds before being upgraded prior to 2152.