Here I will discuss one of the most common ways to remove a tree, and what tree felling means.
Felling a tree in plain English is essentially "Cutting a tree down so it goes where you want it to."
Face Notch: This is a triangle shape piece of wood cut out to allow the tree to fall towards the ground.
Hinge: Another term for this is holding wood. This is the wood that directs the fall of the tree.
*Warning* Cutting through hinge wood before the tree falls may cause the tree to fall sideways, or even backward towards you!
Back Cut: The cut behind the Face Notch, used to fell tree.
Back Lean: This is the term used to describe a tree when it is leaning away from the intended felling direction.
Throw Rope: A small rope connected to a throw bag used to get a larger line up in the tree.
Throw Bag: A small weight connected to the throw line used to get the rope up into the tree and back onto the ground.
Pull Line: A rope or wire used to pull the tree in the desired felling direction. A strong rope must be used or it may fail (break) causing unexpected damage or injury.
Barber Chair: A barber chair occurs when a tree splits and pushes back towards the back cut.
*Warning* A barber chair can seriously injure or kill someone. That is one of the reasons why it is advised to stand on the side of the tree and not behind it while performing the back cut.
Widow Maker: A widow maker is any loose overhead debris such as limbs or tree tops that may fall at any time.
Before you make a cut you need to make sure that you are safe. Danger can be hidden in the tree such as a widow maker, dead limbs, trunk rot, a back lean, or even a barber chair. You will need to inspect the tree to make sure you can anticipate as many problems as possible.
Make sure you have a clear path to safety. Typically you want to have an escape path at a 45 degree angle from the direction of felling. Cut any small brush or debris and move it out of the way so you will not trip. It is important to have an escape path because it is dangerous to stay close to the tree.
Before you make the face notch, make sure you have the ability to get the tree on the ground safely with the tools you have. One of the most common ways to overcome a back lean and help the tree fall in the correct direction is a pull rope. The easiest way to get a pull rope in a tree is to use a throw rope. Use the throw rope and get the pull line as high as you can around the trunk. The higher it is, the more leverage you have.
Caution, pushing a tree takes more skill and understanding than pulling a tree. Do not push a tree over unless you know what you are doing. People have been know to push over trees with a skid steer, bulldozer, or excavator. Check youtube for "tree cutting fails" there are numerous videos of people pushing with a machine while it falls backward onto them. I do not want this to happen to you, be careful.
A face notch is necessary in order to allow the tree to fall in the correct direction. Here are a couple examples of face notches Humboldt, open face, conventional. Each one will cause the falling tree to react differently. Currently my favorite is the open face notch because it allows the tree to fall further before the hinge breaks. Most people use the conventional notch without even thinking about it which has a 45 degree cut. The Humboldt is common among loggers because it can save more of the wood as the wedge is cut from below. Check out an animation of those three notches.
The back cut is what releases the tree to fall in the correction. The act of making a face notch & back cut does not automatically cause the tree to fall where necessary. Make sure you have the right tools to cause the tree to fall down before you make the back cut. The most common tool is a wedge and an axe. Also, the most important thing while performing the back cut is not to cut through the hinge. Cutting the hinge is one of the most common mistakes and most costly mistakes when cutting a tree down. The tree will fall towards the way it is leaning when the hinge has been cut, which defeats the whole purpose of the notch.
While you are cutting the back cut place some wedges in to keep the tree from pinching your bar or falling the wrong way. *Warning* if you pinch your bar while performing the back cut this means the tree is leaning towards you. Make sure to pay attention to the amount of pressure on the wedges as this can also indicate how much weight is leaning away from the notch.
Make sure to place your back cut above the horizontal face cut to prevent the butt of the tree from sliding backwards to