Dynamic Wind Loads on Trees by Ken James, ResearchEngineer, Burnley College, University of Melbourne, Australia. November, 2005 kenj@unimelb.edu.au Introduction This article reports on research being conducted at Burnley College, University of Melbourne, Australia. After several years of studying the dynamic loads in tree cables in high winds, further work has developed to measure the dynamic forces on trees during wind storms. Results indicate that trees are a complex dynamic system in which branches interact to prevent dangerous sway motion developing. To quote Shigo, A tree without branches is not a tree. Up till now, there have been many simplified models of trees, which often consider the tree as a single pole, and many of the studies have been computer simulations. The major focus of the present work is to find out how real trees behave in real wind storms. There is little published actual field data on the dynamic forces experienced by trees in real storms so new instruments have been designed to measure dynamic wind forces on trees. How big can trees grow and what are the forces on these trees? Trees are the largest living things ever to exist on earth. The world s tallest living tree is the Stratosphere Giant measuring 112.7m (370 ft) as of July 2004. This coast redwood ( Sequoia sempervirens ) was discovered in 2000 in the Rockerfeller Forest of the Humbroldt Redwoods State Park, California, USA. The tallest tree ever measured was an Australian Eucalyptus regnans at Watts River, Victoria, Australia, reported by forester William Ferguson. It was 132.6m (435 ft) tall and almost certainly measured over 150m (500 ft) originally. The most massive tree ever (by trunk size) was the Lindsey Creek tree, a coast redwood ( Sequoia sempervirens ) in Califormia, USA. It had a mass of 3,300 tonnes ( 3,248 tons) and blew over in a storm in 1905. (all data from www.guinessworldrecords.com). Trees have a limit to how big they can grow and this is essentially a structural limit. Wood is always wood, and cannot get stronger than its material properties allow. As size increases so do the forces until a limit is reached. Beyond this limit, structural failure occurs. The examples of tall trees above gives us an idea of where this limit is. The structure of trees is the focus of this discussion. Tree growth and development is a precise balance between biological growth and mechanical structure. No part of the tree is independent of another. The canopy provides energy to the roots which in turn provide nutrients and water to the canopy. Both the laws of nature and the laws of physics must be followed by a tree in order for it to survive. A tree cannot grow bigger than its strength can support. The largest forces on trees are dynamic wind forces. Wind storms can cause tree failure and wind throw, Figure 1, which may lead to property damage and loss of life in urban areas.
Figure 1. Storm damage from tree wind throw Top (Q macrocarpa).photo by Wayne Gebert Bottom (Catalpa bignonioides ) Photo by Kiah Martin
Knowledge about tree structures has improved dramatically over the past decades and has provided a better understanding of how trees respond to the structural loads that are placed upon them. These studies have led to the development of an Axiom of uniform stress (Mattheck and Breloer 1994) which states that the growth of a tree is in response to the loads at a specific point. This leads to a conclusion that trees are optimised structures, neither too thin in any part, which would result in failure, nor unnecessarily thick, that would waste the use of energy and nutrients by growing unnecessary wood. The analysis used to develop the axiom of uniform stress, is essentially a static analysis. The loads and forces considered are the static loads of the tree weight and other static loads such as ice and snow. Wind loads have also been considered but only as a static force pushing sideways on a tree. A static tree pull test is a technique originating in Germany and gaining wider use in Europe. It is a test to simulate wind forces and is used to evaluate the stability of trees. A rope is attached to a tree, about half way up and a load is applied. This is to simulate the wind forces and make some prediction of the structural integrity of a tree. Several tree failure studies have shown that using a static analysis may overestimate the wind load likely to cause tree failure. This test uses static forces to approximate the dynamic wind forces and conclusions from this test are difficult to evaluate because there is very little actual published field data on the wind loads experienced by trees during storms. Measuring dynamic wind loads on trees The dynamic wind forces on shade trees are being measured with new instruments, which have been successfully tested on trees under field conditions, during storms. These instruments are attached to the trunk (or a branch) of a tree, and measure the strain of the trunk as it bends in the wind. (Strain is defined by engineers as the change in length of an object.) As the wind blows a tree, the tree bends in the wind and the outer fibres of the trunk are stretched on the windward side and compressed on the leeward side. New instruments have been designed to measure this small movement at the outer fibres of a tree trunk Figure 2. Strain meter attached to a tree trunk, with data logger, and wind sensor
Instruments The strain meter has a very accurate probe inside a stainless steel case, which is attached to the tree using two small nails at each end. The sensitivity is enough to measure even small gusts of wind that cause the slightest movement on trees up to 2 m in diameter at breast height. Two strain meters are used on each trunk, to measure strain in the N/S and E/W directions. This ensures that the resultant motion of the tree in two dimensions is recorded. Each sensor is accurate to one micron and is read at 20Hz to record the dynamic motion of the tree in the wind. Wind speed, wind direction, and temperature are also recorded via a data logger and computer. The results indicate that trees sway in a complex looping manner, different from many of the computer model analyses. The complex sway motion measured in the field is different from the natural frequency models put forward by several authors. A comprehensive mathematical analysis of the dynamic motion is being undertaken to better understand how the tree actually sways. Field sites are being developed for monitoring trees in wind storms in Australia and USA, Massachusetts under a project supported by a 2003 Hylands John Grant of the Tree Fund. Calibrating a tree The Tree Pull Test (The tree becomes its own wind sensor) The method used to measure the wind load on the tree is to pull on the tree with a known load and record the strain meter readings. This effectively calibrates the tree so that the whole tree becomes the wind sensor. Later, when the wind blows, the strain meter reading can then be used to determine the wind load at the trunk. A rope is attached at a known height (meters m) on the tree as shown in Figure 3. When a pull (in kilo newtons kn) is applied the strain meters respond with a certain value. The overturning moment is the product of pull (kn) and distance (m) and is recorded in knm, which is a difficult unit, but nevertheless correct. By pulling at a few different values, a calibration curve is established for each tree. This is shown in Figure 3. Figure 3. Pulling on a tree to calibrate the strain meter The next step is to wait for a wind.
Wind storms and sample results When a wind blows, the tree bends in response to the wind loads and the strain meters record the movement. Using the calibration data from the above test, the overturning moment at the tree trunk caused by the wind can be measured. This is done 20 times each second so the full dynamic loads on the tree are accurately monitored. A hoop pine at Burnley College Araucaria cunninghamii was monitored during a wind storm and a sample of a 30 minute period is shown in Figure 4. Figure 4. Wind Forces on Hoop Pine (Araucaria cunninghamii) for a 30 min period In Figure 4, the diagram is split into three parts with tree on the left, showing the sensors attached to the base of the tree on the trunk, and the wind coming from the side. In the centre the circle represents a view looking down on the trunk of the tree, with the sensors (1 & 2) attached to the trunk, and the direction of the wind shown. It can be seen that the wind is coming from a direction between the two sensors so the output from both must be put together to see the resultant motion. The graph on the right is the resultant motion of the two sensors and looks like a ball of string. This graph represents the motion and the forces on the tree, and should be viewed as if one was looking down on the tree from above, in a similar manner to the middle view of the tree trunk shown as a circle. It should be noted that the motion is not backwards and forwards but rather it is a complex, looping pattern that responds to the changing wind gusts. The dynamic motion is difficult to show in a static diagram but all the motion is down wind from the rest point of the tree (ie the position when there is no wind). The tree does not sway back towards the wind. In very simple terms the tree does not do the Mexican wave. In order to see the complex sway motion more clearly, a short two minute sample of the motion after a large gust of wind is shown in Figure 5.
Figure 5 Wind Forces on Hoop Pine (Araucaria cunninghamii) for a 2 min period A tree without branches is not a tree - complex Sway motion The complex sway motion appears in all the measurements of both trees and branches under wind loading. It occurs because of the complex interaction of the branches, the sub-branches and so on. A mathematical analysis of the data shows that there is no dominating natural frequency. This means that under wind loading, the tree never gets a resonant oscillation up like a swing. An interesting comparison occurs when the tree is pulled with a rope and suddenly released. The sway motion is dramatically different from the motion under wind loading. The sway motion after pulling then releasing is shown in Figure 6. Figure 6 Sway response after pulling with a rope then releasing. An explanation for this response is that the energy is released from the tree pull, in a sudden manner and the tree sways backwards away from the pull then back towards the pull direction. This is definitely a back and forth motion. But the interactions of the branches causes the motion to begin looping into a circular pattern, then gradually this pattern reverses itself and goes in exactly the opposite direction. It is fascinating to see and very different to
the motion response in the wind. It also raises questions on the relevance of the static pull test in its representation of wind loads. Wind throw forces and Overturning moments Figure 7 Overturning moments on trees. The wind forces on tree canopies create an overturning moment that is measured in kilonewton meters. This is a difficult unit to understand, and is described and shown previously in Figure 3. A scale of wind overturning moments is shown in Figure 7 to give some understanding of what all these numbers mean. Beginning at the low end of the scale the numbers 45 and 60 knm are values from tree pull tests conducted at Burnley when a rope has been attached to a tree, and a pull applied. At 60 knm the arborists are yelling to stop Araucaria because they are nervous about causing some damage to the tree or pulling off a limb. 60 knm is approximately equivalent to pulling with a force of one tonne (1000 kgs) with the rope attached at a height of 6 meters. It is a big value. The next number of 180 knm is the wind force measured on the same Araucaria cunninghamii during a wind storm in February 2005. This is a very large moment value and was measured with the strain meter sensors attached to the tree and after calibration. The storm was of moderate force with some limbs on nearby trees coming down, but no trees were blown over in this windstorm. The tree survived quite well at this load, which is about three times higher than the static pull test. Some high measured values have been reported by Moore (2000) who pulled several hundred mature trees over in New Zealand and recorded a maximum moment before failure of around 400 knm. Some trees broke at the trunk and some trees overturned when the root/soil interface failed. This seems to be about the upper limit of measured values. The rest of the scale, above 500 knm are calculated values by various authors who have made some calculation to determine the maximum moment force from the wind on a tree. The highest value of 1219 knm is a calculation by Mattheck (2000) based on a theoretical analysis of a large tree, and the forces needed to break the outer fibres of the trunk.
Summary The application of dynamic measurement of forces will lead to a better understanding of how trees withstand winds. Knowledge of the actual wind forces will allow for a better understanding of tree stability and will be helpful to assess the likelihood of overturning. This information will provide a measure against which static tree pull tests can be compared. The stresses in the tree trunk and branches can be measured with these new instruments. An understanding of the dynamic forces within the tree has implications for evaluating tree stability and failure,pruning techniques, and understanding safe work practices during tree felling and dismantling operations. References BRUDI, E. 2002. Trees and Statics: An introduction. Arborist News: 28-33. MATTHECK, C., AND H. BRELOER. 1994. The body language of trees. HMSO, Dept of Environment. MATTHECK, C., AND K. BETHGE. 2000. Simple mathematical approaches to tree biomechanics. Arboricultural Journal 24: 307-326. MOORE, J. R. 2000. Differences in maximum resistive bending moments of Pinus radiata trees grown on a range of soil types. Forest Ecology and Management 135: 63-71. SHIGO, A. 1991. A New Tree Biology. Shigo and Tree Associates, Durham, NH., USA.