How Can a Logger Fell a Tree in a Chosen Direction?
― The Uncut "Hinge" Does the Steering
Foresters bring down trees 20 metres tall and weighing several tonnes in exactly the direction they choose. The secret lies less in cutting than in leaving wood uncut. A strip about as wide as a finger, left on purpose at the base, works like a door hinge and decides which way the tree turns.
On a mountain slope, a person in a helmet holds a chainsaw. First they make two cuts into one side of the tree's base, one slanted and one horizontal, and pull out a wedge-shaped piece of wood.
Then they walk round to the other side and start cutting straight in, a little higher up. But just before the blade reaches the first cut, they stop dead.
Before long the tree leans slowly and falls almost perfectly straight toward the side where the wedge was removed. It would be quicker to cut all the way through, so why did they stop?
Only two things let you fell a tree on target
When you remove a wedge from the base on the side you want the tree to fall, it gains room to lean that way only. The other side is still solid wood, so the tree cannot fall backward.
The thin strip left at the end holds the trunk to the stump. The tree has no choice but to turn about this strip, so it falls in one direction, at right angles to the hinge.
In forestry, the wedge-shaped cut is called the "notch" (ukeguchi), the cut from the opposite side is the "back cut" (oiguchi), and the strip left uncut is the "hinge" (tsuru). Let's take them in turn.
The wedge cut opens a "path" for the tree to fall
Figure 1 shows the base seen from the side. The wedge on the right is the notch, and its depth is usually put at about a quarter of the trunk's diameter. The back cut, made from the left, goes in a little above the bottom of the notch.
Once the notch is cut, the only place left to hold up the tree's weight is the remaining part on the left. As the back cut severs the left side, the support shifts steadily to the right, until only the hinge is left. The tree can only lean toward the side that has lost its support, that is, to the right.
Making the back cut higher than the bottom of the notch also has a purpose. It leaves a small step in the cut, and this is explained as stopping the base of the trunk from sliding back toward the person doing the cutting once the tree starts to fall.
The uncut strip works just like a door hinge
A door can only turn about the edge that carries the hinges. It cannot move up, down or sideways. The hinge in a tree is the same: it fixes the axis the tree can turn about as a single line. The tree falls at right angles to that line, straight out from the front of the notch.
The hinge works because wood fibres are very strong when pulled along their length. As the tree tips, the fibres on the back side of the hinge are stretched and those on the front are squashed. Even so, they do not snap at once, and they bend while still holding the trunk to the stump.
If the back cut goes all the way through the hinge, the axis is lost. The trunk is left floating on the stump, and a slight lean or a puff of wind can send it either way. That is why foresters always stop the blade short of the hinge.
To get a feel for the fall, try the slider in Figure 2. As the tree turns about the hinge, its top sweeps along a circle toward the ground. That top reaches the ground faster than a stone dropped from the same height. The tree's centre of mass is around the middle of the trunk, and the swing from its fall is magnified in the parts farthest from the axis, so the top is whirled around the hardest.
If the hinge is made thicker on one side than the other, the tree is said to be drawn toward the thicker side as it falls. Fibres on the thick side are harder to tear, so that side stays as a pivot for longer. Skilled loggers say they use this to cancel out the lopsided weight of an uneven crown of branches.
The base of a fallen tree can sometimes spring up off the stump and kick backward. So the basic rule is to choose a retreat path diagonally behind the felling direction. Others nearby must stay at least twice the tree's height away. As Figure 2 shows, the top of a tree hits the ground much faster than you would expect.
Summary
A tree can be felled in a chosen direction because the notch opens a path on the falling side, and the uncut hinge fixes the turning axis as a single line. Tough wood fibres hold the trunk to the stump to the very end and guide its direction. Knowing when not to cut is the most important skill.
It is not the part that is cut that brings the tree down.
It is the finger-wide strip left uncut that decides where it goes.
You can read why trees are cut in certain seasons in "Why Are Trees Felled in Autumn and Winter?", and how wood warps in a set direction in "Why Do Wooden Boards Always Warp the Same Way?".
- Take one toilet-paper tube. About 2 cm up from the bottom edge, snip a V-shaped cut into one side with scissors and remove the small wedge (the notch).
- From the opposite side, cut horizontally a little above the bottom of the V, and stop short of the V to leave a thin strip (the back cut and hinge). Tape the bottom edge to a desk.
- Gently push the top edge of the tube with a fingertip from various directions. Compare it with a tube where you cut through the strip as well.
The tube with the strip left should fold about the strip whichever way you push, and tend to fall toward the V side. The tube with the strip cut will flop in whatever direction you push. ※Be careful when using scissors. Cutting down real trees is a job for people who have had proper training.
For those who want to know more ― terms, formulas and links to textbooksWe label which level each part belongs to, from junior high science to university specialist courses
- Junior highCovered in junior high school science
- High schoolCovered in high school "Physics"
- High school+Advanced high school material, or textbook sidebars
- UniversityUniversity specialist courses (mechanics, strength of materials, forest engineering) not taught in high school
- ResearchNot yet taught as settled fact even at university; being studied by researchers right now
Junior highTerms: this phenomenon has names
- Felling: the work of cutting down a standing tree. Cutting so that it falls in a chosen direction is called "directional felling".
- Notch and back cut: the wedge-shaped cut made on the falling side is the notch, and the cut made from the opposite side is the back cut.
- Hinge: the strip left uncut between the notch and the back cut. It becomes the axis the tree turns about.
- Moment of force (torque): how strongly a force tries to turn an object. It is the size of the force multiplied by its distance from the axis.
Junior highHigh schoolChecking with a formula: how fast is the top of a falling tree?
Treat the tree as a single rod of uniform thickness turning about the hinge at its base. It starts to fall gently from upright, and we find the speed of the top just before it lies flat on the ground.
| In symbols | v ＝ √( 3 × g × L ) |
| In words | Speed of the top ＝ the square root of (3 × gravitational acceleration × tree height) |
| Where it comes from | Conservation of mechanical energy. The potential energy lost as the centre of mass drops by L/2, m × g × L/2, turns into the rotational energy about the axis, (1/2) × I × ω². For a uniform rod the moment of inertia is I ＝ m × L² / 3, and the speed of the top is v ＝ L × ω. Compared with √( 2 × g × L ) for a dropped stone, the 2 becomes a 3 |
| Symbol | Meaning and unit |
|---|---|
| v | Speed of the treetop just before it reaches the ground (m/s) |
| g | Gravitational acceleration (m/s²) |
| L | Height of the tree (m). The distance from the axis to the top |
| I | Moment of inertia about the axis (kg・m²). A measure of how hard it is to set turning |
| ω | Angular velocity of the turning tree (angle turned per second, rad/s) |
| Gravitational acceleration | 9.8 m/s² |
| Tree height (example of a mature cedar or cypress) | 20 m |
| Square root of 588 | about 24.2 |
| Square root of 392 | about 19.8 |
| 3 × gravitational acceleration | 3 × 9.8 ＝ 29.4 |
| Multiply by the tree height | 29.4 × 20 ＝ 588 |
| Take the square root: speed of the top (per second) | about 24.2 m/s |
| Convert to km per hour | 24.2 × 3.6 ≒ 87 km/h |
| For comparison: a stone dropped from 20 m (2 × 9.8 × 20) | 19.6 × 20 ＝ 392 |
| Its square root is the stone's speed (per second) | about 19.8 m/s |
| How many times faster the top is than the stone | 24.2 ÷ 19.8 ≒ 1.22 |
The top of a 20 m tree hits the ground at about 87 kilometres per hour, close to the speed of a car on a motorway. That is about 20% faster than a stone dropped from the same height, and the taller the tree, the greater this speed. This is also why others stay at least twice the tree's height away.
High schoolHigh school+Why is the top faster than a stone?
High schoolWhen a stone falls, all the potential energy it loses goes into the stone's own speed. In a tree, the centre of mass only drops by half the height, so the energy lost is half that of the stone. But that energy is not shared out to the base near the axis. More of it goes to the upper parts, far from the axis. The base hardly moves while the top is swung around hardest, so the top's speed ends up higher than the stone's.
High school+As the tilt grows, there are moments when the acceleration of the top exceeds gravitational acceleration. A falling chimney snapping partway down is thought to work the same way, and this is known as the "falling rod problem". The calculation assumes that the hinge holds the axis fixed at one point. If the hinge tears and the base slides, the tree loses its axis, and both how it turns and where it falls will change.
UniversityRotation of a rigid body, and bending failure of wood
A falling tree can be treated as what university mechanics calls rotation of a rigid body about a fixed axis. The equation of motion is "moment of inertia × angular acceleration ＝ moment of force due to gravity", and for a uniform rod the moment of inertia is m × L² / 3. What happens inside the hinge, on the other hand, is bending in the strength of materials. The anisotropy of wood, strong when pulled along the fibres and somewhat weaker when squashed, is what makes the hinge a "hard-to-tear axis". In forest engineering, researchers study how hinge width and thickness, tree species and moisture content relate to how well the hinge holds.
📖 Derivations and further reading: Moment of inertia (Wikipedia, in Japanese) ／ Conservation of mechanical energy (Wikipedia, in Japanese)
ResearchWhat is still not well understood
- When exactly the hinge will tear. How well a hinge holds is said to vary greatly with species, moisture content, whether the wood is frozen and where the knots are, and most on-site rules of thumb come from experience. Models that predict it mechanically are still being developed.
- How rotten trees fall. Hidden rot or hollows can stop the hinge working as expected. Methods that probe the inside with sound or electricity are being studied, but how to use them in felling decisions has not been settled.
- Branch shape and wind. For trees with lopsided branches, or when the wind is blowing, how far hinge adjustments can correct the fall has not been worked out quantitatively.
So the content of this article is also "an explanation of what is known at present". The numbers in forestry working standards were likewise built up from a great deal of experience and lessons from accidents.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Junior high | Science: "Action of forces", "Energy" | Potential energy turning into kinetic energy |
| High school | Physics: "Equilibrium of a rigid body", "Moment of force" | A tree turning about the hinge, the centre of mass |
| High school+ | Physics (advanced): "Rotational motion of a rigid body" | Why the top becomes faster than a stone |
| University | Mechanics, strength of materials, forest engineering | Moment of inertia, anisotropy and bending of wood |
| Research | Forest engineering, tree diagnosis | Predicting hinge holding strength, assessing rotten trees |
| ― | Links to daily life | Why garden trees and fallen trees are left to professionals |
- Ministry of Health, Labour and Welfare (厚生労働省), "Guidelines on the Safety of Tree Felling Work Using Chainsaws" (revised 2020)
- Forestry and Wood Manufacturing Industry Occupational Accident Prevention Association (林業・木材製造業労働災害防止協会), Textbook for Safety and Health Education of Workers Engaged in Felling with Chainsaws
- National Forestry Extension Association (全国林業改良普及協会), Ringyō Genbajin: Dōgu to Waza series (Forestry Field Workers: Tools and Skills)
- Logging (Wikipedia, in Japanese)
- High school physics textbooks, chapter on "rigid bodies" (various publishers)
※This article is a general-audience science explanation. The numbers given are guidelines and rough estimates meant to help you understand the mechanism. Felling standing trees is dangerous work and legally requires special training. For real work, take a course and follow the working standards and the instructions of the site supervisor, local authorities and so on.