Someone asked about head space needed above a roost several pages back. I never saw an answer to this question. I would also like to know.
Second question. So far, everyone has shown nests on the floor. Would a turkey hen use a nest three feet up?
I free range my turkeys over an acre, and each of 5 hens has created her own nest. One dug a hole in the ground behind a pile of wood, which she covers with dry leaves every day (smart little girl). Three have created soft round bowls of leaf litter that are well hidden underneath three different bushes, with very little head space. The last one alternated among the other hen's nests for a few months, then created her own nest about 3 feet off the ground, in the very center of a huge multitrunked maple tree. The main trunk of the tree is about 5 feet across, and rises out of the ground about 3 feet before dividing into five separate trunks, which are arranged somewhat in a circle around the periphery, with the central area vacant. Over the years that central area has become filled with leaf litter that has decomposed into wonderful soft organic material, and being elevated off the ground and surrounded by large tree trunks it is nicely hidden. There's about a 2X3 foot space available, so it's absolutely perfect for a turkey nest.
Now realize, that's a self-selected nest. There's no guarantee that a hen will use any nest that you want her to use. Before they each created their own nests, there was a large cardboard box, about 1.5'W X 1.5'H X 3'L that I put on its side, on a shelf that was about 8-10" off the ground. I put some padding in it, and had the opening facing the wall, with only about 8 inches between the wall and the box to get in. Four out of the five birds loved that box (all except the one that dug the hole and covers her nest daily). It was darkish inside, it was small enough to be enclosed, but large enough to fit two comfortably, it was long enough for their tail to stretch out, it was softish on the bottom, and it was easy to defend if a nosy rooster decided to peek inside. But they later decided to go with natural nesting, which is fine as long as they keep their nests where I can find them.
Regarding head space above a roost, that depends on the circumstances. Obviously, a tom is larger and needs more room. Birds that need to fly up on a roost need more headspace to accommodate flapping wings than birds that hop up to their roost. I have one roost that is 6 foot off the ground with a 3.5 foot headspace, and I wish I'd left another 6-8 inches up top. My large tom flies up to it off a 3 foot step, and he sometimes rubs a wing on the ceiling. Rarely, he even bumps his head when he stretches up. But those are minor issues that don't cause problems, so it's less than ideal but it works. I have another roost that is only 3 feet off the ground and has about 2 feet of headspace. That is perfect for the most of the hens, but way too tight for the toms. I have another roost that only has 1.5 feet of headspace, and the hens can fit but don't like it. The chickens prefer that roost. Those are the favorite roosts, although others are available. I wish that my toms would use a lower roost, as there are some with plenty of headspace, but they like being up as high as possible. Unfortunately, the jump down is worrisome for the largest one, as he refuses to use steps and just flies to the floor, where he chest flops in daily. At least there's lots of padding on the floor.