My new bed

I got a large hand woven Mayan hammock to use as a bed from now on. I’m going to hang it between wall studs. I’ll be able to make my bed by just unhooking the end of it from the wall and hooking it up with its other end. Then it will be just a net full of pillows, stuffed animals, and a quilt. I’ll have all the space in my room for my own use during the day, and will never have to worry about cleaning under the bed, or losing things under it.

I’ve decided I want to figure out how high I can hang this from the floor and still get in and out, while being able to hang it on one wall without it hitting the floor. I’ve gotten it down to this equation. I was told that given base b and height h, the length of a special segment on a parabola can be computed as follows:

But I already have the length (13.5) and the base (10-12), so I need someone told solve this for height. If I hang it lower than half its length, it will drag on the floor when I double it over to one wall. So I need to hang it at 6.75′ up on the wall. But when it dips down from being hung across only 10-12 feet, will it dip down far enough to get in and out of? The math will say for sure, but I’m thinking it won’t.

Hey I know! I can put in a third hook. It will be on the same wall as the first, but over far enough to keep the hammock from dragging. It will look like a big smile on the wall.