Biomechanics is the combination of two sciences – biology and physics. It’s the study of biological organisms from a mechanical perspective. Mechanics is the study of objects’ motion and is based on Newton’s three laws of motion.

Those three laws are:

• Objects in motion tend to stay in motion unless a force acts on them; objects not in motion tend to stay not in motion unless a force acts on them.
• There is a relationship between the forces (F) that act on an object and the object’s mass (m) and acceleration (a): F = ma.
• When a force acts on an object, the object exerts an equal force in the opposite direction.

If we want to understand how a bird flies or how a tree fails (birds and trees are biological organisms, obviously), we need to study their mechanics.

Understanding the likelihood of failure

From an arborist’s point of view, biomechanics is mostly related to understanding the likelihood of tree failure. For example, a client may ask you to assess tree risk. This involves assessing likelihood of failure, likelihood of impact and severity of consequences. Another example is a tree worker inspecting a tree before climbing and working in it. The likelihood of failure depends on two factors: the loads a tree experiences and the tree’s load-bearing capacity. When the loads exceed the load-bearing capacity, the tree – or part of it – will fail.

The concept of failure applies to more than just trees. It’s the same for climbing lines, carabiners or cellphones. If the applied load(s) exceeds the load-bearing capacity, the tree, climbing line, carabiner or cellphone will fail. When engineers design a structure (like a bridge) or device (like a laptop), they use more complicated and sophisticated approaches than arborists use to assess likelihood of tree failure. However, the basic process is the same. Engineers estimate the loads that the structure or device will experience over its predicted lifespan. They then design the structure or device to have a load-bearing capacity that is greater than the maximum estimated load.

Degree of accuracy

Engineers can use more sophisticated techniques to estimate the likelihood of failure for two reasons. First, there is typically less uncertainty associated with things they need to know to predict load-bearing capacity. Factors such as the material a structure is made of and its size and shape are known. The size and shape of components of a bridge – let’s assume they’re mostly steel beams and columns – are known with a high degree of accuracy. This is because they’re carefully fabricated for consistency. For the same reason, the strength and stiffness of steel also are known to a high degree of accuracy.

But the same degree of accuracy is not possible with trees, because trees are biological organisms. Many factors influence the size and shape of tree stems as well as wood stiffness and strength. Trees grow differently depending on the local growing conditions and the tree’s genetics. The size, shape and wood properties can change as the tree ages. Engineered structures and devices, in general, do not have these variations.

The second reason engineers can use more sophisticated techniques to estimate the likelihood of failure is that they have carefully studied both the loads on, and the load-bearing capacity of, structures. Such experiments also reduce uncertainty. The more experimental results there are, the easier it is to compute things such as wood stiffness and strength. This information is necessary to estimate load-bearing capacity.

Measuring uncertainty

With more data, it’s also possible to measure the uncertainty itself. For example, there are many experiments that have measured the stiffness and strength of steel I-beams. The results give an engineer the average stiffness and strength of a certain I-beam. They also give a measure of the variability of the measurements. This is something like the standard deviation or standard error of the average. This explains why engineers can say a certain steel I-beam is rated for a certain load, plus or minus a known amount of uncertainty. It’s also how rope manufacturers can carefully estimate the minimum breaking strength (MBS) of a climbing or rigging line.

Arborists do not have access to the same comprehensive test results for trees. This makes it much harder to estimate the load-bearing capacity of a stem. It’s even more difficult because of the uncertainty associated with changes as the tree grows and ages. As a result, when arborists estimate likelihood of tree failure, they must use experience – their own as well as the collective experience of others – more than the sophisticated approaches used by engineers. Nevertheless, it’s important for arborists to understand basic mechanics, because it will help complement their experience.

Next, I’ll introduce and define mechanics concepts that are relevant to understanding the likelihood of tree failure. The concepts relate to loads or load-bearing capacity.

Load

Load is a catchall term that refers to forces and moments that act on an object. A load is a push or pull on the object. Gravity pulls down on a tree, and the ground pushes on it in the opposite direction to hold it in place. The pair of forces (gravity and the ground) act on the tree equally (in this case, it’s the tree’s weight), but they act in opposite directions. This is why the tree doesn’t move relative to the ground. If the forces weren’t equal, the tree would sink into the ground or lift away from the soil! The two forces also line up with one another, which means they share the same line of action.

To visualize this, draw a straight line from the crown of the tree, through the trunk, into the ground. The forces of gravity pulling down and the ground pushing up both act along this line. (Photo 1) When you pick a tree or part of it with a crane, you can imagine the same straight vertical line drawn through the cable, the sling and the tree. Gravity is pulling down on the cut tree (or piece) along that line, and the cable is pulling upward along the same line.

Bending moment

Wind is another force that acts on trees. It pushes on the crown, and the ground pushes back in the opposite direction to hold the tree in place. If the forces weren’t equal, the tree would slide horizontally through the soil or tip over. But unlike in the previous example, the force of the wind (which is called drag) and the force that the ground applies to hold the tree in place against the wind do not act along the same imaginary line. Instead, there’s a distance between the forces, and you can imagine a vertical line that is perpendicular to both of them. The perpendicular distance is known as a lever, and you need to know that to calculate the second type of load, which is called a bending moment. (Photo 2)

To calculate a bending moment, multiply the applied force (for example, the drag from the wind) by the length of the lever. If the center of a tree’s crown is 50 feet above the ground, you can assume that the lever is 50 feet. If the drag from the wind is 1,000 pounds, the bending moment that it causes is 50,000 foot-pounds. In reality, drag acts on the entire tree crown, not just a single point in the center of the crown. But very careful measurements would be needed to calculate the total bending moment as the sum of all the individual bending moments on every leaf and twig. Given the uncertainty associated with the calculations, the extra effort wouldn’t necessarily give you a more accurate answer.

Load-bearing capacity

The load-bearing capacity of a structure (like a tree) or part of a structure (like a tree branch) depends on two main factors. The first is the size and shape of the cross section of the tree stem. The second is the strength of the wood in the cross section. The size and shape are more important than the wood strength. Imagine trying to break two branches, one from a tree with very weak wood and one from a tree with very strong wood. If the branches are the same diameter, it will be easier to break the branch with weaker wood. But if the weak-wooded branch is twice the diameter of the strong-wooded branch, it will be easier to break the smaller branch.

The load-bearing capacity is proportional to the cube of diameter. This means if one branch has twice the diameter of another, say, 1 inch vs. 2 inches, the load-bearing capacity increases eight times: 2 x 2 x 2, or 2³. If one branch has triple the diameter of another branch (1 inch vs. 3 inches), the load-bearing capacity increases 27 times: 3 x 3 x 3, or 3³. Most stems are circular in cross section, but some are elliptical. If the cross section is more elliptical than circular, then it will have a different load-bearing capacity depending on which way a bending moment acts on it.

Arborists often assess defects as part of assessing the likelihood of failure. Therefore, it’s worth describing how defects reduce load-bearing capacity. The easiest example is decay, which is a common defect in many trees. Decay increases the likelihood of failure because it reduces the load-bearing capacity in one of two ways. Decayed wood is much weaker than sound wood. Secondly, if the decay process has hollowed out a stem, there isn’t as much wood in the cross section to bear the applied load(s).

Some of the basic mechanics we’ve reviewed in this article include those related to how arboricultural practices influence the likelihood of failure. For example, pruning a tree can reduce the drag, because there’s less leaf area in the crown. But if pruning increases the length of the lever by removing only lower branches in the crown, the longer lever might compensate for the lower drag. This means the bending moment that results from the wind won’t be that much less than before the tree was pruned.

Another example is when setting an anchor for rigging or climbing. If the location of the anchor creates a lever between it and a branch union, the force exerted as you climb or lower pieces from the tree will be multiplied by the length of the lever. This increases the likelihood of failure. In general, it’s better to avoid bending moments to reduce the likelihood of failure.

There’s much more to learn about biomechanics. A greater understanding of mechanical concepts can help you plan work and assess likelihood of tree failure with more confidence. Even though arborists can’t use some of the more sophisticated approaches that engineers use, knowing the basics can help avoid dangerous practices.

Brian Kane, Ph.D., is the Massachusetts Arborists Association Professor in the Department of Environmental Conservation at the University of Massachusetts in Amherst, Massachusetts.

This article was based on his presentation on the same subject during TCI EXPO ’22 in Charlotte, North Carolina. To listen to an audio recording created for that presentation, go to this page in the digital version of this issue of TCI Magazine online at tcimag.tcia.org and, under the Resources tab, click Audio. Or, under the Current Issue tab, click View Digimag, then go to this page and click here.