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I often need to tension a rope between two trees, usually 20-30 ft apart. I am not skilled with knots so it is often sloppy and the tension doesn't hold even very modest weight (such as clothes or something like a target hanging).
What are some compromises between reliability and portability/simplicity when tensioning a rope between two trees, meaning using only rope (and not hardware like beeners or ratchets)?
At one end, I tie the rope any old how. It can be loose even. Then I go to the other tree and pull as hard as I can on the rope until it's really tight. Then, holding tight, I walk around the tree several times until the turns of the rope round the trunk are doing most of the work of holding it tight. Then I can tie it off. If things slipped a little while I was doing that, I can throw the free end over the rope and pull down so that it's tight again, though somewhat lower, and tie it off.
I have used this to hang wet laundry with minimal drooping.
Although you asked an outdoors question, I'm going to give you a physics answer that might shed some light (with an outdoors note at the end.) When you string an ideal rope (with zero stretch) horizontally between two ideal vertical trees (with zero give), and then hang an object from the center, the horizontal force pulling on the two trees is... infinitely large.
Of course, in reality it drops off immediately, as the rope stretches and the trees bend. At a sag of 1 degree from horizontal, the force on each tree will be 57 times the mass of the hanging weight. At 5 degrees of sag, it's about 11 times. (And even if your knots are perfect, it takes less than half a percent of rope stretch to get you 5 degrees of sag.)
Why the physics lesson? Just to point out that knots in this setup are taking a LOT more force than most people expect. It's unrealistic to want the rope to hang flat and level. The more sag you're prepared to allow, the easier this problem is. Tying the ends up higher might be easier than tying them tightly enough for your needs.
What about an actual answer to your question? The most basic knot for tensioning a rope in a setup like this is the tautline hitch: https://en.wikipedia.org/wiki/Taut-line_hitch . When tied properly, you can slide it along the rope AFTER tying it to increase the tension, and then it will stay in place. That won't get you the incredible amounts of tension you'll need to hang heavy objects with minimal sagging, but it will probably work for something like a clothesline.
If you need more tension than that, there's a cute trick called a "trucker's hitch": https://en.wikipedia.org/wiki/Trucker%27s_hitch . There are a number of variants, but the basic idea is to tie a loop in the rope, then run the end around the tree and through the loop. This acts like a pulley system, to give you mechanical advantage in pulling the rope tight before tying it off.
A final note of caution: Be careful of the health of the tree when doing this, especially the trucker's hitch or other approaches that create a huge amount of tension. Make sure the trees are solid enough to hold the amounts of force you're applying to them. And while this is ok for temporary usage, don't leave permanent supports tied directly around a tree for a long period of time (like years) -- as the tree grows this can damage or even kill the tree.
You can tie the rope to one tree using a knot of your choosing, depending on the application.
The other end you fit using a prusik knot, which is easy to tie. You can tie this knot while the rope is loose, then slide it along to make it as tight as you need it to be.
I use this for my hammock Ridgeline and with a bit of practice, it's extremely easy and you can make it very tight with no effort whatsoever.
