Thank you all for reminding me of just how rusty I am with my physics. Here's a crude drawing that I'm going to use to illustrate an experiment that you could easily do:
(the white erased spots where numbers that I had drawn on but erased when I realized that they complicated the explanation)
In the left example, you're hoisting yourself into the tree. There's a snatch block attached to the tree branch and you're suspended in a bos'ns chair. You want to move one foot vertically, how much line are you going to have to pull? One foot. There's no mechanical advantage there. If there's 200 lbs that you're trying to move and a one foot pull moves you one foot (1:1), you're going to need more than 200 lbs of force to make the move.
In the right example, you're in the tree hoisting someone up. The person you're hoisting is holding onto the snatch block. In this scenario, in order to hoist the person one foot vertically, you'll need to pull two feet of line. If two feet of pull moves you one foot, that's a 2:1 advantage. Now, instead of pulling with 200 lbs, you only need to pull with more than 100lbs to move the person upwards. They won't move vertically as fast, but you only need half the force.
How does this apply to trucks? Let's say you're stuck on a muddy slope. In the left picture, replace the person's arms with your winch and the rest of the person with your truck. You have no mechanical advantage. Rigging a snatch block to a tree and running it back to your vehicle will be a 1:1 pull. It won't reduce the amount of work needed to get your truck up the hill. But, there may be an advantage to doing this. Let's say that you've got 100' of line on your winch, but the tree at the top of the hill is only 50' away. You run the line to the tree but now you've still got 50' of line on your winch drum. The rated pull power of the winch is based on having one layer of line on the spool of the winch. If you've still got 50' of line on the drum, you've probably got two or more layers of line, effectively reducing the amount of force that your winch can pull with. If you run the line to snatch block on the tree and then back to the truck you're basically getting more line off of the drum and moving closer to having one layer of line, which is where your winch is most effective.
If you're stuck on the slope and want to reduce the amount of force needed to pull your truck up, you'll need two snatch blocks. You'll have to run the line from the winch to a snatch block on the tree, then back to a snatch block on the truck, then back to the tree (or another fixed point). This will give you a 2:1 advantage.
Now, let's say that you get to the top of the muddy slope. Your buddy behind you gets stuck and doesn't have a winch of his own. You get yourself turned around at the top of the hill so that you can pull him up. You could do a straight line pull and use the brute strength of the winch to drag him up, or you could set up like in the right drawing. Now, your truck is the person in the tree. Again, the arms are the winch. You run the line from your truck to a snatch block attached to your buddy's rig and then back to yourself. You could attach it back to your truck which would put all of the force of the lift on your truck. It'd be better if you attached it to the tree you hoisted yourself up on if possible, since this would split the force of the pull over two different objects.
