Don't really know of a set number, but can share what happened to us:
HEISMAN
Season 48 @ Buffalo W12 - L3 > Won Liberty Bowl...Rank #29
" 50 - 52 went back to 1AA
Season 53 @ Army W15 - L 0 > Won Fiesta Bowl...Rank #6
Season 54 Hired @ Minnesota
So we got there with 27 1A Wins
Don't know if that is an answer to your question, but we wish you good hunting.