"Sometimes a Great Notion" was the classic 1971 logger movie with Paul Newman and Henry Fonda. Our commercial arborist crew all went down to see it at the Cinerama Dome in Hollywood when it first came out. The story was written by storyteller Ken Kesey, who also wrote "One Flew Over the Cukoos' Nest", with Jack Nicholson. Kesey was the leader of the Merry Pranksters, a hippie group doing yoga alongside their psychedelic bus in the rock documentary, "Woodstock". His biography, by Tom Wolfe, "The Electric Koolaid Acid Test", chronicled the Haight-Ashbury days of 1967's 'Summer of Love'.
I identified with the character played by Michael Sarrazin, the younger brother of the family who wants to follow along in the logging dynasty caulk bootprints of the Stamper family. Old man Henry Fonda's favorite saying is "Never give an inch", an example of the gritty determination needed by the family to get thru the tough times of daily forest life, plus all those hassles injected by the need for conflict in a major studio/literary production.
The movie version wimped out on the origin of the incestuous conflict among the principals in the story. It also changed the type of logging accident central to the story from a skidding operation to a more visual felling incident, where the tree barberchaired, causing all kinds of mayhem, and tearing off ol Henry's arm.
15 years after that movie came out, I bought the biggest chainsaw I could find and packed up off to Oregon, to be a logger. I subscribed to "Timber Faller" and "Loggers World" (as well as the J of A) magazines to get the kind of versatile background needed to thrive in the big woods.
After arriving, I found there was a demand for piecing down logs off of trees near the rural dwellings on the forest interface. These logs must be in merchantable lengths(16', 20', 24', 32'), off the top of the most valuable butt log, which needs to be 32' tall. Getting them down off the top of this stick intact (amongst outbuildings and fences) without splintering them to smithereens became the order of the day.
So, here we are, talking about how to get a tree to go where it doesn't want to go. Fiddling with the face and all. Too much ambitiousness in this type of endeavor can lead to tragic accidents. That's why we have textbooks and standards and old timers to teach the young'ns. And stories of mayhem, too.
Thanks to those who made comments here about 'hangin in there', steering the work, while it's falling, right into the intended lay. As long as that chainsaw is in your hands, and the tree is not completely on the ground, you're still in the drivers' seat.
The height of the backcut above the floor of the face was the subject that was on the table, before this long ol harangue started. If it is higher on one side of the cut then the other, more holding power will result from the taller hinge.
This taller hinge is also thicker, leaving more wood extending out in front a bit more. The angle of the second face cut leaves more wood out in front of the upper portion of the face, the higher the backcut comes in.
This is right about where a coupla good diagrams would be handy. We're not inventing anything here, so it's merely a question of digging these drawings up (hint, hint). Luckily, we're climbers, so we can take it out in the field and try it out by starting to cut leaning limbs as if they're leaning trees. Get them to go in places other than where they'd like to.
Make the face of your choice (Humboldt or conventional) right where you want to lay the work. Place the angle of the backcut on the leaning (weak) side up to the hinge at the floor of the face. You won't need much holding power here. Angle this cut upwards to come in almost at the top of the face on the opposite side (away from the lean), where you do need all the strength.
But don't cut right up to the face. Leave a bunch of wood, and wait. Just be patient. If you have a tree with enough diameter to put wedges behind your bar (on the side opposite the lean), do so. The lean will take the tree over very slowly at first, then it will take off, after it has had a chance to get started over the center of gravity.
Vary the location, depth and tilt of the backcut to modify the strength of the hinge between trees with differing species, wood soundness, diameter, and headlean. Play with an assortment of these possibilities in non-critical areas, because someday, that stick may decide to barberchair on you, Henry.
Here's a pic of KC out of Poulsbo, WA, from the Madsens Power Equipment site.