Thanks for answers and votes so far, and keep them coming. I wanted to let this run a day and see what people's responses and experiences were in principle before telling y'all the actual situation.
I'm not the one organizing a festival, my band is playing in one, and the actual answer to the question is... ELEVEN. We will be last in an eleven-act lineup over a ten-hour day. Most of the acts are getting 25-30 minutes to play and there are generally 30-minute transitions between acts. The organizers are renting a PA but there's no other backline, so I'm particularly concerned about drums getting set up and torn down. The venue is a fairground building that's pretty rudimentary, there is a backstage space of sorts; last time I was there, there was no separate access to that backstage, you had to go across the stage itself, but I'm told the facilities guy at the grounds was going to open a door that was blocked before. I have heard there are volunteers to help with setup and teardown, I'm not sure how efficient or experienced they are.
From the bulk of responses so far, it looks to me like it really would have been better if they'd planned it as a six-to-eight act day. On the other hand, it sounds like the consensus that half-hour turnarounds between acts isn't unreasonable. I know I can get onstage and set up my own gear in fifteen minutes, though I'm concerned about things needing troubleshooting and getting a sound dialed in. I'm hoping that the 25-minute acts really can play 25 minutes and be done without running over; my concern is that just a few minutes' overrun with each act and by the time the ten before us have gone, we're hours behind.