I was recently cutting down a tree and, even though I'm ashamed to admit it, it fell in the wrong direction. It fell in the opposite direction as to what was intended. Well, lesson learned. Next time I will be more careful and use a rope if I want to be completely sure it falls in some specific direction.
So, let's investigate things. Not by cutting down more trees, but instead by simulating doing it!
So, what's happening?
To simulate this, i drew a very simple tree-like structure in 2D (to defend myself I'll have to say that the tree I cut down looked a lot more centered than the one above, where it looks quite obvious that the tree would fall to the left). The tree has a lot more branches on one side as compared to the other. The center of mass is shown to to the left of the trunk. The resulting average force will force the tree to tip over to the left as it's located to the left of the trunk, no matter how we cut the main trunk (if there is some magic trick I'm not aware of, please let me know).
After cutting a dent in the trunk with the purpose of allowing the tree to fall to the right, we can see that it starts to lean to the left. Whoops. This moves the centre of mass even further to the left. From the figure above, you can also see that the tiny narrow partition to the the left of the dent is carrying the whole tree; all the major forces (in red) are now centered around the dent.
As long as the centre of mass is located to the right of the tiny partition left after the dent, we should be fine. This is not always easy to see, especially if the tree has a lot of branches.
I used my solver in python with plane elements to calculate the figures above. The colors represent the von Mises stress.