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Several people have independently mentioned to me that all trees break at the same wind speed. This phenomenon is independent of type and size of the tree. Supposedly, Galileo already had described this phenomenon in one of his books. I think the wind speed was something like 150 km/h. I just do not understand what can cause such behavior to be valid for all size and types of trees.

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    $\begingroup$ Some examples of this claim: google.com/… $\endgroup$ – Keith McClary Feb 8 at 5:06
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    $\begingroup$ @KeithMcClary And of course Quora gets it wrong, as usual. $\endgroup$ – David Hammen Feb 8 at 7:10
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    $\begingroup$ The broader concept here is : Scale Invariance $\endgroup$ – J... Feb 8 at 17:55
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    $\begingroup$ @blacksmith37 The claim is about trees being snapped off above ground rather than falling over from a weakened root system or being in saturated soil. $\endgroup$ – David Hammen Feb 8 at 18:52
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    $\begingroup$ When there is a group of trees they protect each other from the wind. As soon as some trees start breaking, other trees are exposed directly to the wind. $\endgroup$ – Ian Ringrose Feb 9 at 9:55
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Why do trees break at the same wind speed?

Damage caused by storm Klaus on the Landes forest
Image source: Wikimedia Commons

Note that in the above image, that almost all of the trees had their tops snapped off. This claim is about tree's being snapped in two and is not about trees falling over or being uprooted.

This claim is approximately valid for many species of trees. Apparently oaks can withstand slightly higher wind speeds than can pines. This claim does not apply to non-woody trees such as palms. It also is not true for species of woody trees that have evolved to live in areas where winds occasionally exceed 42 m/s (the equivalent of a category two hurricane).

I just do not understand what can cause such behavior to be valid for all size and types of trees.

The authors of a recent paper on this subject attribute it to evolution. While winds frequently exceed 30 m/s (126 km/h), they very rarely exceed 50 m/s (180 km/h) in most places. The sweet spot in a tree's ability to sustain winds is between these limits. A tree that is too flimsy will be snapped by a heavy gale, won't live to maturity, and won't spawn offspring. A tree that is too sturdy is wasting precious energy building unneeded structure.

As for why and how, it's a matter of allometry. Trees grow in girth as the age and add to their canopy. Tree allometry investigates the relationship between tree girth at chest height and other features of trees such as height and canopy area. The relationship between girth and canopy area is close to linear.

Another factor is defects, which are places where a tree is most likely to snap in two. The extent of these defects also scales with size. Young trees lose tiny branches; the young tree eventually grows around these, leaving the small defect buried deep inside the tree as it ages. Older trees lose larger branches, leaving behind a potentially larger defect.

References:

Critical wind speed at which trees break.

Trees, regardless of size, all break at the same wind speed. Here’s why.

Urban Tree Database and Allometric Equations.

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    $\begingroup$ I don't see how this could be true. If it were, then when the wind exceeded that speed, all trees should break, no? But that is not what happens: instead, only a few break in any given windstorm. $\endgroup$ – jamesqf Feb 8 at 17:32
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    $\begingroup$ @jamesqf I suspect the question is trying to compare species. For example, that an average oak tree can survive similar wind-speed to a pine tree. I don't think this is talking about specific trees, since a tree that's rotting will generally be much less stable. $\endgroup$ – Patrick M Feb 8 at 18:18
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    $\begingroup$ @jamesqf I was skeptical at first, too - after all, it's not like an entire forest falls over when the wind gets high enough. The claim might be a little overstated in the question, as some trees certainly fall over before others, but I think the underlying phenomenon is that there's no systematic difference in windspeed required to knock over a tree that varies by tree age, height, thickness or species. I'd expect there's some bell curve of tree-breaking windspeeds that's invariant when looking at only young/old/big/small trees. On average, different types of trees break at the same speed. $\endgroup$ – Nuclear Hoagie Feb 8 at 18:23
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    $\begingroup$ @DavidHammen So all trees break at the same speed except for the ones that don't? $\endgroup$ – JimmyJames Feb 8 at 21:33
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    $\begingroup$ @JimmyJames Please. I wrote that it is approximately correct, not absolutely correct. $\endgroup$ – David Hammen Feb 8 at 21:45
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As the other answer points out, this is very likely an evolutionary adaptation that balances sturdiness with unnecessary overengineering. From a physics perspective, the relatively constant breaking strength of a tree is related to allometry, which is the relationship among the tree's proportions as it grows. A young tree is short and thin, with relatively little breaking strength, but it does not need to withstand very large wind shear due to its small size. As the tree's canopy grows larger, it must withstand greater forces from high winds, but is able to do so because of its thicker trunk/limbs. Because a tree's strength grows with the magnitude of forces it needs to withstand, it turns out that the windspeed required to break a tree is more or less constant across trees of different sizes/types. A tree that's twice as large might feel twice the wind shear, but it's also twice as strong.

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  • $\begingroup$ This is what I was thinking of. It's the fractal relationship between limb length and thickness. $\endgroup$ – Barmar Feb 8 at 15:38
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    $\begingroup$ The problem is that all wood is not the same strength. If you haven't had a chance, you should get a close look at live oaks. Their branches can extend out horizontally for distances that seem impossible. It was actually specifically harvested for that reason to build "old ironsides" $\endgroup$ – JimmyJames Feb 8 at 21:32
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    $\begingroup$ @JimmyJames, Live oak may be stronger than something like pine, but the branches are either longer in proportion or thinner in proportion, so that the overall resistance to wind damage is the same. $\endgroup$ – Mark Feb 9 at 22:01
  • $\begingroup$ @Mark Except they survive winds that are much faster than the rate at which it is claimed 'all trees snap'. There is ample documentation of this fact. $\endgroup$ – JimmyJames Feb 10 at 15:52
  • $\begingroup$ @JimmyJames "There is ample documentation of this fact." You'd convince me, an onlooker, far more if you provided said documentation rather than just saying "I'm right". $\endgroup$ – user20631 Feb 10 at 17:03
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The general claim seems to be incorrect:

This phenomenon is independent of type and size of the tree.

Based on other answers, the claims around this appear to be that the scale of the tree doesn't matter. For example the sciencemag.org article referenced in David Hammon's answer talks about experiments around different thicknesses of wood:

As one might intuit, they found that for a fixed length, increasing the diameter made the rods stronger ... which explain the relationship of tree size parameters such as diameter and height

So the size of the tree tends to not matter. However, that article says nothing about the composition of the wood which would require a different type of experiment altogether. In addition the main claim is this:

Trees, regardless of their diameter, height, or elastic properties, don’t tend to break until wind speeds reach about 42 m/s (94 mph).

Note that this doesn't say there are no trees that can tolerate speeds above that without snapping, just that this is the lower bound.

This landscaping website for a company based in Palm Beach Florida has an extensive list of tree species and their tolerance to high winds. It has an long list of references but mentions this particular study frequently: WIND AND TREES: A SURVEY OF HOMEOWNERS AFTER HURRICANE ANDREW

In this there are a number of confirmed cases of trees that survived wind speeds above 94MPH. Some are documented to have survived wind speeds as high as 150MPH. Note that while survival is different than having the trunk snapped, I think we can safely assume that if a tree survived, its trunk was not snapped. Unless someone can produce evidence that this university study was somehow flawed, I think we can pretty well say that different species of trees have different snapping tolerances for wind.

It may be true that in temperate regions where high wind speeds are very rare that all trees can tolerate roughly the same speed and that the size of the tree doesn't really matter. But if you look to regions where hurricane-level winds are more common and the native plants that have adapted to those storms, this claim seems to fall apart in the face of evidence.

Here are specific excerpts of the study mentioned above that explicitly contradict the claim that all species of trees have their trunks snapped by winds of 94MPH:

Trees along streets, in parks, in backyards were stripped of branches, uprooted or broken off by the 145 mph sustained winds

[emphasis mine]

I think we can all agree that a sustained wind speed of 145MPH is not approximately 94MPH. It's not even remotely close.

Native Trees. Native tree species survived the hurricane better than exotics; chi-square analysis showed that 34% of exotic trees were still standing after the hurricane while 66% of native trees were standing (n21/1 p<0.0001)

The paper also qualifies what standing/fallen means:

How Did Trees Fall? When trees fell, they were either uprooted, broken at he trunk or both (Table 2).

From which I conclude 'standing' means 'not broken at the trunk'. This seems to be confirmed by following note about live oaks in particular:

Live oak was placed at the top of wind-resistance lists developed after hurricanes such as Camille (1969) and Frederick (1979) (1,6). Live oaks are well known to have exceedingly strong and resilient wood (1). In our study the few live oaks that failed we[r]e uprooted and not broken at the stem.

[emphasis mine]

It even calls into question the assertion that size is not a factor and notes this has been found in other studies:

Larger trees within a species were more likely to fall than samller trees. For example, the average height of fallen royal Palms was 15 m while the height of standing royal palms was 10 m. Fallen slash pines averaged 20 m high and 53 cm in diameter while standing pines were 17m and 45 cm. Few exceptions to this size failure relationship we[r]e live oak and pink trumpet. Other studies in forests have shown that three with larger diameters and heights were more likely to be damaged by hurricane winds

Lastly the paper gives an hypothesis for why some trees can tolerated higher wind speeds:

Native dicots were more tolerant of high winds than exotics. This is not surprising since South Florida native trees have long been subjected to hurricanes, providing a natural selection for wind resistance.

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  • $\begingroup$ Trees do survive having their trunks snapped. I can see one out my window right now. A pine tree, it snapped ~20 ft above ground, where the trunk was ~15 inches thick. That was about 20 years ago. One of the upper branches became the new trunk, and it has about doubled in height since. This isn't at all uncommon, at least conifers (pretty much all that grows naturally hereabouts). I can find many examples in the local mountains. Also trees that were limber enough to bend into a hoop (presumably from snow load) then grow up from the tip. $\endgroup$ – jamesqf Feb 10 at 17:23
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    $\begingroup$ @jamesqf I don't doubt what you are saying but I don't think that's what was meant in the referenced study. From my reading, not surviving included much less extensive damage, such as losing too many limbs. In some of the examples, the live oaks were noted to have minimal damage after being subjected to high winds well about 100MPH. $\endgroup$ – JimmyJames Feb 10 at 17:30
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    $\begingroup$ @jamesqf "well above 100MPH" My fingers are idiotic sometimes. $\endgroup$ – JimmyJames Feb 10 at 17:54
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Some excellent answers are already available, but they are all examining a single tree in isolation, as if putting a tree to a wind tunnel to see whether it snaps or not. That's not how every trees species handles winds.

At the latitudes I'm used to, which is the temperate climate of Europe, the fastest winds blow over elevated terrain which is often continuously forested. And the trees in the forest protect each other against the effects of the wind; massive clearings or other unnatural edges of the forest can act as vulnerabilities.

The impact of the wind certainly depends not just on wind speed, but also on wind direction relative to terrain features and to various vulnerabilities including clearings, unsuitable tree varieties man-planted to higher elevations than where they evolved, or perhaps some calamitous diseases. The exceptionally fast winds that can snap any trees aren't steady at all and I'm not aware of any meaningful research into the gust speeds which actually start the snapping within a forest; we just know the general wind speeds during the area in the hours during which a forest was destroyed.

My point is: once many trees start snapping for any reason, other nearby trees, and also any downwind trees, start losing their usual physical protection from the wind. This means locally faster wind gusts, gradually extending to destruction of a large forest area. Some exceptionally strong trees may survive, but if the tree species is well adapted to dense forests, it will rarely survive destruction of the said forest through a 100-years strong gale.

There are differences between tree species. Scrub pines can survive wind speeds that are unthinkable for any uprights.

Some of you can perform an experiment. Plant a line of apple trees and a line of spruces on a more or less exposed garden and count the snapped trees over the next 100 years. Replace any trees that die from age or disease as you go. (Spruces prefer the protection of a forest. Apple trees prefer a lot of sunlight. The suggested experiment is biased against spruces from the start; but spruces will also quickly outgrow the apple trees, gaining more exposition to the wind, biasing the experiment even further.) Preliminary results that I have, although I haven't completed the first 100 years yet, nor reached any level of statistical significance, suggest that exposed spruces seem to snap more often than exposed apple trees.

And the unnaturalness of this experiment brings me to this conclusion. Trees develop in conditions where they are generally able to withstand the winds throughout their lifetime. If that takes a forest, fine, they will thrive in forests. If an occasional exceptional wind takes down the entire forest, the tree species can eventually repopulate the area, but only as long as their competitors have been taken down as well, so it pays off to stay within some proximity to the durability of those competitors.

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One important additional factor is that the stress (and damage) isn't linear. A very basic idea is that energy is velocity squared. But Prahl et. al. 2008 included some review of the theories on damage from winds and the two typical theories:

  1. wind loads, which are approximately proportional to the exerted pressure and, hence, to the square of the wind speed (e.g. Simiu and Scanlan, 1996);
  2. the concept of proportionality between structural damage and the dissipation rate of the wind kinetic energy that scales with the third power of wind speed (recently: Emanuel, 2005; Powell and Reinhold, 2007; Kantha, 2008).

Then added that:

In particular, the notion of a cubic relationship is backed by empirical analysis of insurance records, which appear to exhibit cubic or quartic behaviour depending on the storms under scrutiny (Munich Re, 1993, 2001). However, recent literature provides evidence for a much stronger increase of insured storm loss with wind gust speed (Huang et al., 2001; Heneka and Ruck, 2008). For the insurance data set that we employ here, Prahl et al. (2012) found a power law with regionally varying exponents that approximately range between 8 and 12.

So whatever the exact relationship, there clearly are fundamental physical reasons that the impact ramps up so much more rapidly than the direct numbers themselves hint at, and so thinking of 150 kph (93 mph) vs 140 kph (85 mph) as the same as 100 kph (62 mph) vs 90 kph (56 mph) is a flaw we often face... and it makes more sense there'd be a relatively narrow tipping point, much like there is, for example, with a disease outbreak, as we've seen with COVID infection comparisons from different regions\countries.

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  • $\begingroup$ If I'm not mistaken, air resistance actually has more like a cubic relationship to speed. In other words I think you make a good point but you might be understating it. $\endgroup$ – JimmyJames Feb 8 at 21:50
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    $\begingroup$ @JimmyJames: Unless your trees are being subjected to transonic-or-greater winds, aerodynamic drag (the force trying to make the trees, or parts thereof, move with the wind) is proportional to the square of the wind speed (and also to the air's density, the cross-sectional area the trees present to the wind, and the trees' drag coefficient) - en.wikipedia.org/wiki/Drag_equation $\endgroup$ – Vikki - formerly Sean Feb 9 at 0:49
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    $\begingroup$ (The reason for the qualifier about transonic winds is that an object's drag coefficient rises sharply in the vicinity of mach 1 due to shock-wave formation; above mach 1, it decreases again, but not all the way down to its subsonic value.) $\endgroup$ – Vikki - formerly Sean Feb 9 at 0:51
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    $\begingroup$ @Sean I stand corrected. Probably should have looked that up before commenting. Thanks. $\endgroup$ – JimmyJames Feb 9 at 14:43
  • $\begingroup$ @Sean Doesn't the "constant" factor depend on the Reynolds number, hence again on wind speed (though I have no idea if or when the dependecy on Re is linear)? And after all, multiplying the wind speed with -1 will multiply the force with -1, not +1 $\endgroup$ – Hagen von Eitzen Feb 10 at 16:52

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