Dan Coby wrote, on Sun, 28 Sep 2014 20:32:48 -0700:

If you are tensioning the cables for very little sag
then the forces in the cable can be many time the weight
of the tree house.

We "tensioned" the cables, by hand.

What we literally did was put a broomstick through the 60 pound wooden
spool of 250 feet of 3/8" steel cable and we mounted that on two chairs
about 15 feet downhill of a big pine tree.

Then we went uphill to that pine tree at a point about 15 feet off the
ground and then back to the chairs with the spool of wire.

At that point, we tied a rope to the end of the wire, and we walked the
wire downhill a little less than about 100 feet to a big redwood.

At that redwood, we climbed up to the same height as the pine (which,
since it's downhill, is about 40 or so feet up in the air) and we pulled
the rope with the wire cable attached.

Then we pulled the rope which pulled the cable back up the hill back to
the point on the path 15 feet below the pine, where we pulled it tight by
hand, and then clamped the 8 clamps on.

Then, we simply slid the cable around the big redwood and slid it around
the pine, until the cable clamps were symmetric around the pine, as shown
in the last set of pictures.

I won't mention the fact that we accidentally crossed the cables because
we went around the big redwood the wrong way, as that's embarrassing to
mention. Nor will I mention how many times we got hung up in the branches
between trees, necessitating mid-air precarious surgery on the trees.

Given all that, I wouldn't call the tension all that tight. You can see
the sag in the photos. Maybe it sags, oh, I don't know, about 5 to 10
feet maybe?

I do not know what you are planning upon building. That was why I asked
you. If you are talking about the tree houses that we built as kids with
a plywood floor and a few boards and a tar paper roof then only a couple
of hundred pounds. If you are talking about some of the multi story
creations that I have seen on TV then many tons.

I think we're talking just a plywood box, with a deck. I should mention
that there will be anchors on the two little redwoods, so, the treehouse
won't actually be floating on all sides. The bridge *will* be floating
though. It should be fun once it's done and wired for Internet. It has a
great view once you're up in the redwoods.