Explanations of tree-felling mechanics

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Logging is very dangerous. Usually, logging and off-shore fishing vie for the title of most dangerous occupation. Logging, most often, wins. See, for example, 59 Fed. Reg. 51,672, 80 (1994).

The method of cutting is chosen so that the tree will have maximum resistance to coming back over the stump at you and maximum strength to prevent the tree from going sideways away from the path you have chosen.

The tree pushes on the stump for the first 50^o of its fall; then pulls away from the stump. (See: Guimier, D. Y., Tree Falling Mechanics, Technical Report No. TR-42, Forest Engineering Research Institute of Canada, May 1980)

The tendency for the tree to move backward over the stump is resisted by the strength of the hinge wood until the hinge breaks, and by the butt off the log being "hooked" into the step that is left by the backcut being placed higher than the hinge point.

The distance the backcut is above the hinge is an important part of controlling the backward motion of the tree. The step means that the tree can fall a considerable way --- even after the hinge breaks --- without the tree slipping back over the stump. As a rough rule, a 1" step on a 10" tree (or a 2" step on a 20" tree, etc.) will let the tree fall 15^o and still be restrained.

How can we calculate how much higher the backcut should be than the undercut?

If, as the OSHA site implies, the problem is that the hinge on a tree being felled closes too soon and that's why the step is needed (I agree), then we can calculate the height of the step needed (which they don't seem to be able to):

One way to determine how much higher the backcut should be than the hinge point is to build on the idea that the force the tree exerts on the stump varies as the tree falls --- from pushing on the stump (and moving toward the logger) to pulling away from the stump (and, hence, away from the logger). The change from push to pull occurs at about 50 degrees (from FERIC). Therefore, we wish to have the stump, by some method, restrain the tree from moving back toward the logger until it has fallen through, say, at least 60 degrees.

The "open-face" method relies solely on the hinge not breaking while the tree falls through an angle of 70 degrees or more, whereupon the notch closes and the hinge then breaks. This method will work if the tree has perfect wood ---no rot, brashy grain nor a knot nor any other problem the logger may not be able to see until it's too late --- and the logger doesn't inadvertently cut too far nor too low. Presumably he'll never get distracted by bugs nor heat nor cold nor a lack of sleep nor an argument with his spouse that morning!

In the traditional methods, the hinge will, hopefully, remain intact through a fall of about 45 degrees before the notch closes and the hinge breaks. But even if it does break or is cut through, the step on the stump will also hold the tree from the beginning and will continue to restrain the tree until the angle has increased to where the broken hinge raises above the step. The angle for that can be calculated by simple trigonometry. The tangent of the angle will be equal to the step height divided by depth of the notch.

If we want a minimum of 60 degrees of fall before the restraint of the tree by the stump ends, then we need 15 degrees after the 45 degree notch closes. OSHA (on their web site) discusses whether the step should be 1" or, as in some states, 2"; and has decided to approve 1". On the face of it, this seems rather strange, as if 1" is enough for a 12" tree, it's not likely to have the same effect on a large redwood tree. In fact, if the tangent of 15 degrees is equal to 1" divided by the depth of the notch, then the depth must be equal to 3.7". If the notch is one-third of the diameter of the tree, the tree must be about 11" in diameter. Proportionally, a 2" step would be suitable for a 22" diameter tree, etc. If the notch is made not quite so deep, the tree may be larger.

This suggests a rule-of-thumb for step height: Make the step one-inch high for each 10" of the tree's diameter. This should be a safe rule, as it ensures some extra height --- thus protection --- over a greater angle.

But... If you cut the backcut higher, down where the root fibers are slanted, won't you cut through hinge fibers because they're at an angle? No.

The depth of the undercut can be calculated on the basis of the amount of the force required by the wedges to tip the tree. If the tree is perfectly symmetrical, then the center of the tree is over the center of the stump. If you cut the undercut in to the center of such a tree, no wedging force would be required to get the tree to fall. As the undercut is made less deep, more wedging force will be required. Since few trees are perfectly symmetrical, this is usually not an important consideration --- either the tree has a lean toward the direction of fall (or heavier branches, or a wind, or snow or ice on that side) and no wedging is required, or else it will require wedges or breaker bar. However, for a perfect tree, the graph of wedging force vs. undercut depth looks like this.

A tree that is leaning sideways can only be controlled by the strength of the hinge. When engineer designs a beam, he calculates the strength of the beam based on the total of the strength of the material and the thickness of the beam. The thickness is critical, because the material on the outside of the beam does almost all of the work. For example, if the beam is made of wood, we could calculate its strength by taking the strength of each fiber and multiplying each by their distance from the center of the beam cubed. Because the distance of a fiber in the center to the center is zero, that fiber adds no strength to the beam (which is why conduit, plumbing, etc., going thru a floor beam goes through holes drilled through the center of the beam).

The hinge on a tree being felled is acting like a beam, resisting the tendency of the tree to fall in the direction of a side lean. The wood in the center of the hinge can by cut away with no appreciable loss of strength. (Cutting the center out allows cutting larger trees with smaller bars.) The outside edges, though, are extremely important. Any cuts on the outside of the hinge make very large reductions in the hinge's strength.

As you cut a notch farther into a tree, the hinge gets wider. (But it's obvious that when you get halfway through the tree, the hinge will start to get smaller!) However, the strength of the hinge is going to be proportional to the cube of the width of the hinge, so the effects will vary. When you put the two effects together, you get a graph like this, showing that at first, a small increase in depth gets you greater and greater increase in strength, though the effect does taper off a bit toward the center. (The strength still increases the deeper you go toward the half-way point, but you don't get the increase as fast.) A notch one-quarter to one-third the diameter of the tree usually provides a wide enough hinge, but with a heavy side lean, a deeper notch will provide more strength.

Two other important factors are splinter pull and the volume of fiber lost in the wedge of wood cut out in the undercut.

The Shape of the undercut may vary. It doesn't really matter, except in terms of wood wasted. Originally, the notch was chopped into the wood (Waist-high, because it was easier to get the cut straight across ---and there were plenty of trees!) With the coming of the crosscut saw, the notch was either chopped in, sawed horizontal and then chopped down to, or two parallel cuts were sawed in and the wood between chipped out with a Pulaski or similar tool. The latter method was used with the early chain saws because they could only cut vertically or horizontally. (The McCulloch 12-55 was the first gas chain saw that I'm aware of that could cut at an angle.) The "Upside-down" or "Humboldt" cut may save wood on very large trees, but wastes wood on small trees. Here's some more info.

If using wedges, always use two wedges, and drive them alternately. Especially in frozen wood, wedges sometimes want to "squirt" back out. If you have two wedges in the tree, one should hold enough that you can get the other wedge back in. If you use only one wedge and it is squeezed out, you then have the problem of getting a wedge back into a cut that has closed up. You may be able to cut with your saw just to one side of center (leaving the other wood to hold the cut open), or, if you have an axe, you may be able to chip in enough to get the wedge started again. But if you had used two wedges, you wouldn't have had to worry about it.

Kickback is when a chain saw stops acting like a chain saw and starts acting like a crawler tractor. That is, with a chain saw, you expect the saw to stay where it is and the chain to move over whatever it's resting on (cutting into it); with a crawler, you don't want the chain to slip over whatever it's sitting on, you want it to dig in and pull the rest of the machine along.
But the cutters of a saw can also dig in and pull the saw along. (This is more likely on a sharp saw than on a dull one, unfortunately.) The cutters on the bottom of the saw tend to pull the saw forward, until the engine comes up against the wood --- usually harmless enough. Contact with the bottom part of the nose will tend to swing the bar up, but as soon as the bar moves it'll lose contact and the process will stop.
But --- if the upper part of the nose contacts something, look out! The bar will start to pivot upward, and this action will cause the teeth to be pressed more firmly into the wood. causing the bar to pivot upward, and this action will cause the teeth to be pressed more firmly into the wood. causing the bar to pivot up more strongly, which will cause the teeth to be pressed more firmly into the wood. causing the bar to pivot up more strongly, which --- well, you get the idea.
When the top of the bar contacts something, the tendency is for the saw to be pushed backward. Not all that bad, unless you let it move out to where only the tip is left to touch the wood --- at which point you are where you were at the previous sentence!
With modern, direct-drive saws, using low-kickback chain and bars the push of a kickback is not terribly strong. You can control it pretty well IF you're ready for it. The danger is that it happens very fast: With most saws today, the chain speed is over 50 feet per second. If a normal person's reaction time is one-tenth of a second, the saw can move through an arc such that the tip moves over five feet during the time it takes you to react --- and the saw is seldom more than five feet away from some part of you!

Here's what to do:

• On homeowner saws, use "low-kick" chain and bars. (These come on saws of less than 62 cc (3.8 cu. in.) displacement. Note that smaller, lighter saws kick faster --- and speed, after all, is the problem.) If you need to replace the bar or chain, replace with a bar or chain of the same type.
• Keep both hands on the saw.
• Don't use the "monkey grip" --- keep your thumb wrapped around and under the front grip.
• Don't stand directly in back of the bar. When bucking, for example, don't stand directly behind the saw. When clearing branches from the lower part of a tree, prior to felling, the saw can be held so that it is crosswise to your body --- if it kicks, it will go away from you.
• Don't over-reach and be off-balance when cutting.
• Wear pants or chaps with kevlar and/or ballistic nylon pads that are loose enough to give and absorb the momentum of the engine and chain, lessening the injuries if you are struck. (You can also get jackets, boots, and gloves with kevlar or nylon in them.)
• Make sure that the chain brake on your saw works correctly. A saw with an "inertia-type" brake (one that is triggered by the rapid movement of the saw) is better because your hand does not have to touch any control for it to work.)