I was wondering If there is a correlation between the size of your face cut and the force it puts on the tree when it comes off. Sometimes on a really dead tree I get nervous then I take a top or big chunk because it really shakes the sh_t out of the stick. If its narrow and comes off early does it push the stick back less the a 45deg or more cut would?
Correlation to force against the tree? Well, sort of, but not really. It does in small ways.
How wide open the face cut is made is will determine when the falling log/branch separates from the tree.
How much it shakes the tree is more determined by how much rotational inertia the branch has, how stable the spar is to oscillations, and what is the relative weight of the two separate parts of the tree.
When a tall section is cut away from a trunk, it pushes sideways against the spar as it is accelerated away from the tree. A short section of the same weight will not be accelerated as far to the side, so it will shake the tree less.
If you can cut a section away from the trunk and reduce the time that the removed section is pushing sideways on the spar, you will get shaken less. Salami cuts are very good for that, but you loose control of the top. Narrow face cuts, perhaps with a Humbolt-style face will cause the branch to separate from the spar sooner, thereby shaking the tree less. What really counts is how much rotation occurs before separation, and how much energy is transferred to the tree.
Also a factor: the speed of the release from the tree. A tall heavy dead section will have a lot of inertia during rotation, and will release and fall quickly. The same branch with all the leaves still attached has a lot more wind resistance, and rotates slower and releases from the tree slower. Less shaking.
Oops. Now you have to stop that falling section on the end of your bull rope. Lots more factors to weigh in here, mostly a reverse of all of the momentum incurred from cutting the section off. If the falling section is stopped in resonance with the oscillating spar, you get shaken off the tree. If it bangs back into the side of the tree as it is rebounding back from the push of the cut, it can stop the movement cold, leaving you with a big thump and not much motion.
Nobody ever talks about harmonic resonance in tree work here at AS, but it becomes terribly important on tall spars with no branches left on the tree to provide damping of motion.