Trees break at around 42 m/s

[thorbiorn]

A new study based on the evidence provided by the storm that passed over Southern France in 2009 has revealed that all trees break at about the same windspeed:

Critical wind speed at which trees break
E. Virot, A. Ponomarenko, É. Dehandschoewercker, D. Quéré, and C. Clanet
Phys. Rev. E 93, 023001 – Published 2 February 2016
Abstract
Data from storms suggest that the critical wind speed at which trees break is constant (≃42m/s), regardless of tree characteristics. We question the physical origin of this observation both experimentally and theoretically. By combining Hooke's law, Griffith's criterion, and tree allometry, we show that the critical wind speed indeed hardly depends on the height, diameter, and elastic properties of trees.
DOI:http://dx.doi.org/10.1103/PhysRevE.93.023001

Here is the synopsis of the article:

Trees Crumbling in the Wind Cyclone Klaus struck a large swath of Western Europe in 2009, damaging millions of trees of all types and sizes, from towering oaks to bushy pines. Observations of the aftermath revealed the greatest damage (more than 60% of trees knocked down) occurred in regions where the winds topped 90 miles per hour (40 m/s). A new analysis shows that this critical wind speed is derivable from a few simple scaling laws.

A tall thick tree should be just as strong as a short thin tree. Many scientists, including Leonardo da Vinci and Galileo, have shown this to be true for wooden beams, but they haven’t agreed on how the force needed to snap a beam scales with its length and diameter. To better characterize wood strength, Emmanuel Virot of the École Polytechnique, France, and his colleagues performed simple experiments on horizontally held rods made from beech. Fixing one end, the researchers applied increasing weight at the other, recording the curvature of the rod as it bent and eventually snapped.

The data showed that wood breaks at a critical curvature radius, which depends on the diameter D
and length L of the rod. Using this relation and a model of wind force, the researchers arrived at a scaling law for the wind speed at which a tree breaks (V∼D0.75∕L). Previous studies have shown that trees nearly triple in diameter for a doubling in their height (D∼L1.5) which means the critical wind speed only weakly depends on tree height (V∼L1∕8

). The speed does not depend on the elastic modulus of the wood, which is consistent with data showing that hardwoods (e.g., oaks) are just as wind susceptible as softwoods (e.g., pines).

This research is published in Physical Review E.

–Michael Schirber

42 m/s is probably the average. I have seen many forest areas devastated storms, but often notice that a couple of trees may remain standing all alone. This is of course puzzling. How do they do it?

 

[monotonic]

There always seem to be some "hero trees" in the neighborhood that are always in good shape. A good question for a tree surgeon?

 

[zak]

Why do some trees fall during storms and others don't?
Here some but not all answers:
http://blogs.scientificamerican.com/guest-blog/why-do-trees-topple-in-a-storm/
And BLOWING IN THE WIND: STORM-RESISTING. FEATURES OF THE DESIGN OF TREES by Steven Vogel
https://www.google.fr/search?q=vogel,tree+in+storm&ie=utf-8&oe=utf-8&gws_rd=cr&ei=SGe6Vq3tBsKRaKDCl6gM

A videos compilation of falling trees:
https://www.youtube.com/watch?v=cYTJAXdYlAM
Some tips after the storm:
https://www.kansasforests.org/community_forestry/community_docs/Tree%20Care%20After%20Storms.pdf
To go further:
https://www.youtube.com/watch?v=1HMe3FGovD4

 

[Dylan]

Well, this here's right up my alley, as I spent the better part of the day dismantling 2 medium sized poplars each with about a 20 degree lean...not ideal but alls well that falls well.

There are so many variables, but what I can decipher from the article is that they've decided that there is a threshold at which the engineering of a tree is overcome by wind speeds greater than 40 m/s. Which is useful, if one is in the business of determining what kind of funds might be needed after a great wind event, but I think that's where the usefulness ends.

It seems that they've also inferred that there is a reliable metric to determine exactly where the tree might fail given the loading from wind speed at or above 40 m/s as well. Again, kind of useful, but no two trees live in exactly the same environment as each other.

So, if we assume all trees are equal (which they are not) and that all trees would experience the same loading in a wind event (which they wouldn't) then perhaps this threshold is useful in determining...well what exactly I'm not sure to be honest. It is kind of a luxury of retrospect situation, but perhaps I'm not imaginative enough to determine exactly what usefulness this information yields. One cannot assume that a 20m pine tree which has had windfirming work performed on it would react the same as a 20 m pine that had never been pruned, so I have a theoretical problem with the hypothesis. And it seems to suggest that lever length does not matter as much as the wind speed...well that seems mildly retarded from the point of view of someone who works on trees for a living. Simple physics would suggest that the longer the lever, the greater the force applied to the fulcrum area on the lever. And this is where it gets really complicated, as trees don't always break at some midpoint nor are the properties of all tree trunks the same, which the article seems to discount. A tree which has an old wound at a location on the trunk which is not too high off the ground, and in the case of severe wind loading, one would generally observe that it would be at this point, rather than some mathematically predetermined point, that the tree would fail. I've seen it thousands of times but of course this is anecdotal and I have no peers to review my observations. Any tree, free of defects, might then be expected to fail at a mathematically derived location given consistent loading at or above the 40m/s wind speed.

But what about the quality of the canopy? Does this article suggest that a thin crowned, upright tree like a Mediterranean cypress or upright oak would experience the same loading as a wide spreading canopied tree like a beech or a maple? I suppose it does, and infers that both would experience failure at or above 40m/s regardless of height. But, as you folks have pointed out, observation of trees in environments in which these wind events occur reveals that some trees do not, in fact, fail even though the majority of their dendritic friends have. Specie and growth habit seem to be entirely irrelevant to the search for a constant here, which again, makes me dubious of the usefulness of this information.

To the question of why do some trees withstand these wind events that are equal to or greater than the enumerated threshold, the only answer I would give is that the devil is in the details. Perhaps the tree was more sheltered and therefore not experiencing the same loads as trees less sheltered, perhaps these trees had been serviced by a technician who reduced the endweight consistently across the canopy, perhaps the type of wood actually does make a difference, which the article or some previous data set seems to discount. There are soooo many variable as to why a tree will fail, but I do understand the value of having a predetermined wind speed at which people can expect a great deal of tree wreckage in a severe weather event.

One question I have is regarding the type of failure the article indicates. It seems to indicate that trees experiencing this 40m/s loading will fail at a point on the main trunk determined by an equation. But, in severe wind loading events, especially hurricanes or cyclones which generally carry heavy amounts of precipitation along with high winds, we often see a great deal of partial failures in the crowns of trees rather than whole tree failure at a point along the trunk. So, were these simply induced by high winds or was there a greater saturation of water in the woody tissues of the tree? Indeed, partial failure of branches are far more likely than a catastrophic failure of the entire tree at a point on the trunk. And many times we'll find that there are failures in the root system of trees, whether it is because of a reduction in root friction with the soil in a saturated condition or a failure due to preexisting decay.

Trees are wonderful, complicated organisms and no two are the same. The article seems to posit that all trees will fail at or above a wind speed of 40m/s, but observation simply does not bear this out. Maybe, if all trees are left completely vulnerable to such loading, then this metric might be true. But, the centre of a forest does not experience the same wind loading, and in urban settings, buildings and all sorts of other things including other trees will yield completely different wind loading patterns. As to whether this information would affect management practice I am keen to see if it does. But, as a metric for emergency planning, I can see the usefulness.

I'm not sure this helps at all, but I enjoyed writing it!

 

[Voyageur]

Was interested in what you posted, thorbiorn, especially as it relates to an old and perhaps outdated interest of mine on studies of forest windthrow. Now the question in the paper, under what wind speed force will structure (fiber) become unstable and break (with consideration of other factors cited), focusing on the breaking strength limits, and it's an interesting limit which might be spot on as far as how they measure breaking rods. Unfortunately, the link is only to an abstract, so not sure what their full study involved. I'm trying to keep in mind that it is the physical wind force on fiber that has a limit (42m/s)

Nonetheless, here is what I was considering, as it also seems the factors discussed in the paper - other factors of trees; "height, diameter, and elastic properties" described as not being factors, may not be so easily reconciled; or perhaps they can be? It seems of these factors, such as general species select, stem-tapper; its conical shape, including tree fiber alignments, densities, geoclimatic zones that produce weaker or stronger fiber (and elasticity) which relates to its overall wind-firmenss, hopefully would be addressed in more detail. From observations, wind-firm veterans and their particular crowns and general stand crown-closure characteristics, a trees cambium layers, moisture content and even bark etc, might also have some bearing. There is also the canopy itself and the adjoining stands characteristics (its known defects/pathogens and overall neighbors as described in windthrow studies). These additional factors (and there are others) seem pivotal over just wind speed alone at determining breaking or windthrow, with a very important part, the root systems themselves (so what gives first). The limit, as it pertains to structural failure vs. root failure, is important and this is more applicable when root systems are frozen causing the tree to break before any windthrow effects can take place (via torsion). So I indeed see this 42m/s as a pure breaking value that may be a good general average for structural failure in some respects and yet am a little skeptical.

This paper, 'Introduction to Tree Statics & Static Assessment by Petr Horácek http://www.treeworks.co.uk/downloads/6%20-%20Petr%20Horacek_Tree%20Statics%20Seminar%20Presentation.pdf offers some other data. As a Pdf, it does not lend itself well to copy/paste functions, yet you can see many examples between species, crown and taper etc, such as page 36, 37, 38 'Resistance to Breakage'

"

The most unfavourable case is to be considered, which means that wind flows in such a direction that compressive stresses due to wind add to the compressive stresses due to crown eccentricity."

The study originally cited by Ponomarenko et al from the initial link said "that the critical wind speed indeed hardly depends on the height, diameter, and elastic properties of trees.", yet in the abstract it does not really mention crown eccentricity and other factors? It does not say that the 60% just broke (in the wind event cited), it instead says they were "knocked down", so not sure, this seems to infer that there was general windthrow involved also?

In terms of height, the second cited paper further referenced;

As trees grow taller they can become increasingly prone to failure. For example, a force of 100 N applied at a height of I0 m creates a moment of 1000 Nm, but the same force at the 30 m height generates three times as much torque.

In this reference, it seems to be discussing structural failure, although failure can be either breakage or root failure.

On 'Tree Biomechanics':

...as wind speed increases, the canopy tends to bend and deflect and become more streamlined. Drag coefficients have been found to vary considerably between species.

In the paper, it summarizes both aspects of failure (P.60):

The factors that affect windthrow and breakage of trees are those that influence the effectiveness of root anchorage, the strength and aerodynamic properties of the tree, and the direction and characteristics of the wind within and above the stand.

Anyway, one thing noticed was that this event happened in relation to Cyclone Klaus, and that was January 2009. In France, Spain and Italy at that time, how much of the forests would have had frozen root structures being wintertime, and if some did, than that may account for the breakage under these wind limit forces? Also, was there snow loading in the canopy in some regions coupled with the winds (this would add to the tension)? In other parts that were not influenced by frozen ground, was the tendency to windthrow over breakage? Just curious about this, the link does not provide much data and as said, can't access anything beyond the abstract.

Dylan hits on some valid points, too.

 

[Yupo]

We lost a lot of trees here (Eastern NC) in hurricane Fran about 20 years ago. Studies on the fallen were done. It was determined that most of them had sustained internal fracturing from hurricane Hazel (1950s). Interesting.
We usually see uprooted trees more than fractured trees. Lately our storms have been coming in packs, so the ground gets pretty saturated.

 

[zak]

We lost a lot of trees here (Eastern NC) in hurricane Fran about 20 years ago. Studies on the fallen were done. It was determined that most of them had sustained internal fracturing from hurricane Hazel (1950s). Interesting.
We usually see uprooted trees more than fractured trees. Lately our storms have been coming in packs, so the ground gets pretty saturated.

Cracks are the Achilles' heel of tree, so be on alert for large cracks on opposite sides of a tree.
Cracks are signs of problems for trees and property and people near trees.
Take a careful look in planting. Wounds to the young trunks or to the small
woody roots could start cracks that could persist for years in the tree.
Also be on alert for cracks on recently planted trees.
Look at the base where roots come together, not the root ridges, but in the depressions.
Cut off injured roots. They generate (not regenerate) new roots.
If large cracks are seen on young trees, remove the tree when it is still small.

Cracks that have fruit bodies of fungi indicates advanced decay. On mature trees such signs
are indicators of high risks hazard trees.
Remember: Symptom, function is altered; sign, visual manifestation of an agent that causes a problem.

Cracks can be prevented by preventing wounds and by pruning properly.

Some advices of the mother and the father of the arboriculture Alex Shigo.

 

[Dylan]

A beam made from wood is so much different than a tree. A tree dances in the wind, it oscillates in an irregular elliptical pattern, and so does every little branch on the tree, helping to diffuse the wind load and prevent catastrophic failure. And while a beam may be secured to the ground with a static anchor, tree roots are much more dynamic. Using beams may help as a launching point to understanding the different strengths of different species of wood, but I feel it is theoretically impossible to use beams as an analog for understanding tree strength or reaction to wind loading. Wind is also not often consistent, coming in gusts rather than at a consistent speed, but of course it does happen. Beams and trees cannot be compared as analogs to each other, a beam has no root system nor a canopy, and the wood is dead! Live tissue tends to be more elastic, but elasticity increases with moisture content and decreases when temperatures are below freezing.

Characteristics like water saturation or even temperature are important variables when analyzing tree failure. When temperatures are below freezing, I generally secure my climbing system lower in the canopy because I know wood elasticity is reduced when the wood is frozen.

Decay is also an important consideration when analyzing tree failure. Two similar sized trees of the same species, one with significant root crown decay and one without, would not be expected to fail at the same force as each other. The one with strength loss from decay would fail much sooner.

Fractures can affect the strength of a tree as well, it creates a shear plane (an engineering term used to identify weak points in wood) and effectively the wood of the tree would be considered as 2 distinct beams rather than one. I removed a tree a few weeks ago which fractured, at a very early age, right at the base and the crack was large and all the way through the base of the tree and extended several metres up the trunk. Thankfully, there were several sound trees to tie into so I didn't have to rely upon the obviously compromised target tree.

In all honesty, though, I'd never seen a tree like that before. And if it were solitary, I would have expected it to have failed many years ago. Which brings me to the point that the particular environmental niche in which it was growing sheltered it from loading and allowed it, to an extent, to compensate for strength loss.

The edge trees in a forest experience greater wind loading than those in the middle of a forest, which is why windfirming is performed on trees which are left from forestry or Arboricultural projects but are near enough or high risk enough to humans or their property. The root systems, and canopies are different, unused to high wind speeds, and are a greater risk for windthrow than their forest edge counterparts.

We have a measure of risk called a 'live crown ratio,' (LCR) in tree risk assessment. It is the ratio of the proportion of the trees canopy compared to the height of the tree. Simply, if a tree has no limbs until the top 30% of the height of the tree, it is much more prone to wind throw than a tree with limbs that start at 50% of the tree's height. This is because the canopy will catch more wind, and the loading on the tree with a 30% LCR will be higher on the lever. If a tree has a high crown ratio, then it is usually uncommon to see it fail from a wind gust hitch come from the prevailing wind direction in that area.

Which brings me to yet another very important variable. Prevailing wind direction. Most regions have a prevailing wind from which the typical wind events generally blow. In my area, the prevailing wind comes from the NW. In a valley close by, the prevailing wind comes from the west, and almost all the trees in the area show a physiological response to it; they all lean east to some degree and their canopies are far more dense on the west side. High wind events which come from directions that are different from the typical prevailing wind tend to cause more failures in trees than high winds from the prevailing direction. It might even be safe to assume that the threshold trees fail at from high winds which blow from different directions than the prevailing wind would be lower than the threshold they fail at from a prevailing wind. IME, these events tend to cause failure of the root system rather than failure of the tree trunk.

I love talking trees!