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Make sure the tire is relatively clean and be sure it's still in good enough condition to not split under the weight of people . The bigger the tire, the better, up to a point. While you want plenty of room for kids to sit in the tire, a really huge tire will be especially heavy and may weight too much for a standard tree branch. Use your good judgement about the perfect balance between size and weight for your specific branch. Give your tire a good wash down with heavy duty detergent, scrubbing all of the exterior surface and rinsing the inside as well. If a dirty tire cleans up well, then it should be okay to use. Use WD40 or a tire cleaning product to remove stubborn grease spots. People will be sitting on this tire, so the more gunk you remove, the better. Be sure to get any cleaner residue off as well! The tree branch itself should be thick and sturdy, around 10 inches (25cm) diameter minimum. Be sure the tree is large and healthy, with no signs of weaknesses that might indicate the tree is unstable. An isolated Maple or Oak tree usually works best.  The branch you choose will impact the length of rope you'll need. Good dimensions for a tire swing branch are about 9 feet (2.7 meters) from the solid tree branch to the ground. The branch should stick out away from the tree far enough that when you hang your tire swing off of it, the swing will not immediately hit the trunk of the tree. While you don't want to place your tire swing out at the very end of a branch, you can't attach it within a few feet of the trunk. The higher the tree branch, the higher the tire swing will swing. So, if you are making a tire swing for a small child, you may want to chose a branch that is lower to the ground. Obtain about 50 feet (15.2 meters) of rope. It should be quality rope that won't fray or break when weight is applied to it.  There are a variety of ropes you can use for your tire swing, such as heavy duty climbing ropes or utility rope, but you can also use chain if you like. On a simple tire swing galvanized chain will last longer but rope is easier to handle, will potentially do less damage to the tree branch, and is easier to hold onto for kids. As well as quality rope, fraying can be prevented by the application of tubing down the length of the rope where fraying is most likely (wherever it comes into contact with the tree, the tire, and hands). Since this will be left in the rain, water will accumulate inside the tire if left solid. To avoid any accumulated water, drill three holes in the tire at what will become its base. Be careful when drilling through your tire. There may be metal strands on the inside of the tire, which you may hit with your drill bit. Just be prepared that you may hit a different layer while drilling through. Be sure to position the ladder safely so that you don't topple off it. Having a friend hold it steady as you climb is a wise precaution. If you don't have a ladder, you will need to find another way of getting the rope over the branch. Find a roll of duct tape or something of equivalent weight and tie it too the end of the rope. Then throw the duct tape over the branch, so that the rope is now looped over the branch. Once the rope is looped over the branch, untie the duct tape or whatever you used as weight for the end of the rope. Position the rope so that it won't be rubbed by knots or imperfections on the branch. You may want to wrap the rope around the branch a few times, just to make sure it stays in place. If you bought tubing, this part of the rope should have anti-fray tubing at either side of it (where it rests on the branch). (Do not use a square knot. Square knots were designed as a first-aid knot. If you pull backwards on either lose end, it will fall apart.) Make sure that the knot is solid. If you can't figure out how to make one, find someone who can. If you have looped the rope over the branch from the ground, you will have to tie a slip knot from the ground and then tighten it up, so that it cinches up at the branch. Again, use a square knot to secure the rope around the top of the tire.  Before you make your knot, judge how far you would like the tire to be off the ground. The tire should clear any obstacles on the ground and should be high enough so that your child's legs don't drag on the ground, so it should be at least a foot off the ground. On the other hand, it shouldn't be so high that your child can't get into it on their own. Be sure that the tire is at this height when you secure the knot. Remember to keep the drainage holes at the bottom, with the top of the tire opposite the side with the holes. Tie the tail of the rope up, so that it will not accidentally get in the way or come undone. Add mulch or dig over the ground to make it a softer surface for landing when jumping (or falling) off the tire swing. Check that the swing is sitting well for swinging. Before allowing others on the swing, test your handiwork with a spotter nearby in case anything goes wrong. If it works well, you, and your kids, are ready to start swinging.

Summary:
Find a suitable old, unwanted tire. Clean the tire. Find a suitable branch where you can hang your tire swing. Purchase the rope. Drill some drainage holes into the tire. Use a ladder to get up to the branch. Place the rope over the tree branch. Secure this end of the rope to the tree branch using a bowline or a fisherman's bend. Tie the other end of the rope around the top part of the tire. Trim off any excess rope. Fix the ground beneath the swing if you like. Test the swing.