I have all different heavy breeds and a 3 1/2 to 4 foot fence works for me. If I see a chicken trying to get over (and usually it is only one or two), I clip their wings to be safe. Occasionally I have had birds get over the fence, young ones especially, clipped wings and all. They did this by jumping, flapping and clawing their way over, not by "flying" per se, but they got over nonetheless. Normally, they do this in one spot only, often at a certain time of day, making a routine of it. Once it was just one hen that did it. Conveniently, I culled her and that did the trick. Another time, several figured out this "squawk-flap-and-scramble" technique. I spent a few minutes attaching some chicken wire to the top, along the section of fence they were jumping over, in such a way that the netting was bent or flopped over ninety degrees or more towards the inside of the pasture. They weren't able to climb over it, so that fixed the problem. Since then, I haven't had one get out yet. Typically, they don't fly much, and are only interested in what's on the ground, and the only time they fly with any enthusiasm is to roost at night.
So the upshot is that a fence that size is certainly manageable for heavy breeds, but isn't a perfect guarantee. But it works fine for me, which is good, because at least here, chicken wire only comes in four-foot-wide rolls...
Good luck!
