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On a non-scheduled flight, would an interstellar space ship need an active crew consisting of a captain, several officers and a number of technicians, similar to the bridge of the Enterprise, or would one pilot, with maybe a replacement for emergencies, be enough, similar to yachtspeople navigating earth's lakes and oceans alone?
This question only pertains to the flying of the ship, not catering to the passengers, maintenance etc.
Zero.
Voyager 1 has left the solar system, and is therefore an interstellar spacecraft. I'm not sure what qualifies a ship, but there is no reason why it would take any humans. Nor do yachts (or cars) need humans for navigation, for that matter.
Interstellar space is particularly dull. You'll be travelling for many years with absolutely nothing happening. To employ a human to fly a ship would quite literally mean letting him or her sit there from birth to death with no events happening for his or her entire life. You can't do that to people. That's what computers are for.
The comment by Mike Adler is a good addition, and I will quote it here in its entirety:
Autonomy is always with respect to a time scale. By necessity, spacecraft have always been autonomous on the minutes time scale. Modern spacecraft are autonomous on the days to weeks time scale. Rosetta took care of itself for more than two years. I would expect an interstellar ship would be designed to be autonomous over much longer periods, but would be designed for Earth to check in once every decade or so to see how things are going, and reprogram around any issues uncovered. The "crew" may very well be frozen embryos, awaiting blastulation upon arrival.
If defining a ship as having a minimum of one human crewman...
In the absence of FTL drives, a minimum for an active human crew is however many are required to perform the maintenance tasks on the life support, drives, and power systems.
Since this is extremely variable based upon automation and durability, what can be said is merely "you need engineering crew."
Given human need to interact, this sets a further minimum crew standard. The military has had a number of small outposts for years. Minimum crew size for these correlates directly to maximum duration of assignment. A 4-5 person crew tends to start experiencing issues between 2 and 6 months deployed in isolation, even with routine work contact via radio with outside persons. A 20-30 person crew can go for 4-6 months before similar issues. After this initial period of troubles, many crews are able to work things out, and a stable long term status quo evolves; but when it doesn't, the results are often tragic. NASA long term missions have typically been 3-5 person crews, and the crews have been put in isolation for the requisite several months during training; those who can't handle it have been weeded before flight.
In looking at small communities, the smallest psychologically stable communities appear to be in the range of 20-30 people; smaller communities (such as McGrath, Alaska) tend to be stable until some stress, then violence happens; usually a new stable evolves shortly thereafter. The problem being that a spacecraft can not afford such violence.
So, for an STL ship, you'll want at least 20 active persons, rotating which 20 if practical, in order to maintain the hamlet level of community which seems the minimum for long term psychological stability.
Since any mission to another star system in an STL craft is likely to be one-way, the overall mission crewing needs to be considered as well. And the limit there is the genetic viability of the colony. If completely unrelated individuals and absolute breeding authority can be presumed, as low as 30 individuals may be viable. Long term, the lowest genetically stable populations in isolation seem to be about 100 individuals - a small village level, or several hamlets. At about 200, consanguinity selection for the colonists sent is a low priority.
Assuming Dr. White's assumption of 10C capability is correct, this puts many nearby stars under a year away. Within a year, the technical needs of the hardware trump the psychology of the crew. Keep them busy, and each with private space, and a crew of 3-5 should be functional long term. Even up to 2 years, to allow for a round trip, a Warp Drive at 10C can reach any of a dozen stars, specifically, any of 9 systems.
We can't yet estimate the requisite engineering/maintenance times.
We can note that, unlike STL ships, not all are one-way trips. Therefore, the colonial need is also able to be ignored.
There is no other FTL drive thought feasible at this time. Therefore, no practical considerations can be made.
Technically, no human presence is required, as elucidated by the previous answer. However, if one considers the subset of manned interstellar missions:
Assuming Sonny White doesn't figure out FTL in the next couple of years, current and near-term technology in propulsion systems dictate an extremely long duration for any interstellar flight. Even the Icarus Interstellar team, the folks redesigning the Daedalus probe, assume a flight time to Alpha Centauri of 100 years. Thus the question of crew size for a manned interstellar mission is either determined by progress in suspended animation (sleeper ship), or minimum population size for genetic viability after a given number of generations (world ship).
Some light on the second option can be found here: What is the smallest number of humans required for colonization?
