The height of the dispenser should take into account the length of the roll of paper. For example, the quick way to figure it is to multiply Pi (3.14159) with the diameter midway through the roll. That will let you know that the entire roll is x feet long unless you're in Canada where it would be x meters long. So, with that underconsideration, and if you intend to make full use of the roll, and say the whole roll is 125 meters long, don't hang the dispenser more than 124 meters from the floor. As you take say a meter of paper to wipe your unmentionables be sure to leave at least a foot in the US or a meter/3 in Canada so you can pull on the roll and get paper, else you'll be using your hand and no one will want to be your friend. I worked all this out earlier. A word of caution, I think this is a really stupid idea. And the fuckin' calculator fell in the bowl, blocked it when I flushed and there's about 1/2" of water on the floor if yer in the US or 2.54 cm/2 if yer in Canada and a perfectly good mathematical instrument has gone to its great reward in the sky.

FYI