It would have to be large, and would require the Orion propulsion system of nuclear impulses. The largest spacecraft theorized in the Orion project (a US space project circa 1960) was 400m x 400m and weighed approximately 8,000,000 tons. It could be large enough to be a city holding upwards of 100,000 people.
Assuming that we could launch this craft into space it would be large enough to be self-sufficient. The issue posed by such an ark is that humans might drastically change in the many generations that it would take to reach even our nearest neighboring star system, Alpha Centauri. Another important issue in judging the viability of such arks is the estimate of the minimum number of inhabitants required to maintain a self sufficient, isolated culture.
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