I don't recall having seen anything specific on times for limbering/unlimbering (as opposed, for example, to how often a well-drilled crew could fire in a minute). If somebody else has, that would be interesting. Regarding drill specifications, the 1861 Instruction for Field Artillery, "school of the piece", and Patton's simplified version of the Instruction, "school of the piece", are very precise regarding the steps for executing these actions. Keep in mind that the prescribed requirement was that after unlimbering, the limber was to be positioned in rear of the piece, team and limber behind it facing towards the front. That would necessarily add time for limbering. The first manual which was specifically based on the relatively new concept of "mounted" field artillery (adopted in 1838) was probably Ringgold's 1845 manual, which again had precise steps for limbering and unlimbering in its "school of the piece". Without going into detail, limbering would involve bringing the limber around so that the trail could be moved to it, the lunette and pintle joined, and the key used to lock it in place. In truly desperate circumstances, a crew might move the gun to the rear by prolonge until getting to a position where it could be properly limbered. Again, if somebody has information on average time required in practice under fire, that would be helpful.