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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Over the last decade, wireless devices have decreased in size and power requirements. These devices generally use batteries as a power source but can employ additional means of power, such as solar, thermal or wind energy. However, sensor networks are often deployed in conditions of minimal lighting and thermal gradient such as densely wooded environments, where even normal wind energy harvesting is limited. In these cases a possible source of energy is from the motion of the trees themselves. We investigated the amount of energy and power available from the motion of a tree in a sheltered position, during Beaufort 4 winds. We measured the work performed by the tree to lift a mass, we measured horizontal acceleration of free movement, and we determined the angular deflection of the movement of the tree trunk, to determine the energy and power available to various types of harvesting devices. We found that the amount of power available from the tree, as demonstrated by lifting a mass, compares favourably with the power required to run a wireless sensor node.

The use of sensor networks for remote monitoring within forests is becoming widespread. Use of these networks in forests is occurring for detection and monitoring of forest fires [

We conceived the idea of harvesting energy from tree movement due to the problem of energy supply that currently affects users of remote wireless sensors nodes located under the canopies of trees in forests [

Within densely wooded forest, access to wind power is also limited. Wind speeds under the canopies are far lower than those above the canopy; as much as 1/10 to 1/100 the velocity at 1.3 m above ground compared to above the canopy [

It appears that little investigation into converting the mechanical energy of tree movement to electrical energy has been previously performed. No published articles on such research exist to the authors’ knowledge, although a number of patents and patent applications for machines to convert “natural forces”, including tree movement, do [

Some work has been performed to harvest energy from trees using other methods, including the Voltree Bioenergy Harvester [

A number of other mechanisms exist [

The thermoelectric based systems are currently characterised by low efficiency, particularly at the 1–5 K thermal difference offered across the internal to external structure of a tree. Piezoelectric based vibration harvesting, which is effectively a higher frequency version of the mechanisms discussed in this paper, typically need frequencies in the range of 100+ Hz to be efficient. Wind driven micro turbines, of the sort noted in the references, have start up speeds of over 3 m/s, which are rare under dense tree coverage.

We offer a number of possible methods by which energy may be extracted from tree movement, and the investigation into the amount of energy available for energy harvesting from tree movement, to power a wireless sensor node. These methods include energy harvesting via the horizontal acceleration of the tree, the lean angle of the tree and the force/displacement of the tree, as demonstrated by having the tree lift a mass. Device design methodologies to extract energy from these different aspects of tree movement are explained. We found that energy harvesting using a device that could exploit the force/displacement of the tree showed a greater potential than the other proposed methods. We also present a simple model of a tree with the goal to estimate power dissipation by any tree, and energy available at a given point on the tree trunk.

To capture movement energy from trees, a number of possible methods of operation for a device have been conceived. These methods can be broadly categorised into ‘inertial mass’ and ‘tethered’ approaches. Either of these approaches may ultimately employ the use of electromagnetic or Piezo transducers.

The inertial mass method of movement energy harvesting requires a mass to be suspended and connected to a transducer, which then attaches to the tree, as shown in

As the tree sways, the mass may move relatively to the tree due to either relative acceleration, change in orientation with respect to gravity, or possibly resonant oscillation. The transducer will operate as a result of the relative movement between the inertial mass and the tree. The shaker style flashlight and the Seiko Kinetic™ range of watches are both examples of inertial mass movement energy harvesting.

Inertial mass movement harvesters may be arranged in a number of ways, such that the inertial mass has at least one degree of freedom of movement with respect to the tree. It may also require some form of restoring force to return the mass to the starting position after movement.

The methods by which this may be accomplished include a pendulum that swings about a horizontal axis, which is restored to vertical (or near vertical) by gravity after side to side movement has ceased; a pendulum arranged to swing about a vertical axis, possibly with a spring to return to a known starting position; a mass allowed to travel back and forth linearly along an axis (say in a tube) arranged horizontally or perhaps another orientation.

To drive a linear inertial mass harvester requires some amount of acceleration. That is, to provide a

Thus, the net force applied to the transducer, if linear in action, is a product of the magnitude of the inertial mass (

Further, an inertial mass energy harvester may be driven not by the acceleration of the tree but by

Having provided a force to the transducer, the combination of the magnitude of the displacement or distance moved (Δ_{NET}_{MOV}

For a constant acceleration, and therefore constant force, the above equation can be simplified for any period of time to:

For a pendulum based harvester, and assuming small horizontal tree displacement, the energy input into the system can be determined as a function of the rise/fall (

That is, if a pendulum device is actuated purely via the lean angle, _{PEND}

It can be seen from the above equations that the greater the inertial mass (_{MOV}

The ‘tethered’ method of operation requires a transducer to be attached at two points. These points can be one of a number of combinations e.g., a tree and the ground, two neighbouring trees, or two points within the same tree (between branches or from a branch to the trunk). See

A tethered transducer is acted upon directly by two opposing forces; between a point on a tree and some other. Therefore the reaction force (_{TRAN}_{TRAN}

It should be noted that if the resistance force offered by the transducer is greater, the distance the tree can displace will be minimised due to the force acting against it. That is for a small reaction force, a greater displacement can occur because little is acting to stop the tree from moving, and for a large reaction force little displacement can occur. Again, to maximise energy input into the harvester, at a given point on a tree, there will be an optimum level of resistance force compared to movement, as the tree sways.

Methods to determine how much energy at a given point on a tree trunk were investigated and are described. A model of a tree is presented to provide a basis for further calculations.

As a starting point to determining how much power and energy might be dissipated by a tree, a simple aerodynamic model of a tree has been devised and analysed. The modelling was based on conventional aerodynamic and mechanical/material science theory. See

The intention was that the model, if verified by experimentation, would allow predictions to be made about energy dissipation by any tree at its trunk (or branch if developed further) given known wind conditions and various dimensions of the tree.

The study of fluid dynamics has shown that the force acting on an object due to laminar fluid flow can be given by:

_{D}

From the above equation, the force acting on the tree can be determined for any given wind speed, if the projected area of the foliage (

From the force acting on a tree, the distance through which the tree sways can be determined from the mechanical properties of the tree trunk. That is, if the properties of the tree trunk are known, and the force applied is known, the elastic deflection of the tree trunk can be determined. Once the deflection is known

Further, if the force acting on the tree is known, the magnitude of wind power can be determined from the following:
_{W}_{D}

To find the deflection of the model tree trunk, the ‘spring rate’ (

By definition, the spring rate (

_{D}

Further, the value

The value for Young’s Modulus (

_{G}^{−9}) = Young’s Modulus (measured in GPa rather than standard units of Pa).

To verify the model, a local, easily accessible tree was chosen for experimentation.

A eucalypt tree (

The tree used for experimentation was chosen due to its proximity to an office building and opening windows. This position was not considered ideal, but offered a number of critical advantages. These include:

Safe access to the tree for attachment of instruments and measuring equipment, including sensitive electronics, which would have been difficult to otherwise achieve.

Ability to mount a video recorder and a computer next to the experiment.

The equipment was out of the weather in a secure location with power.

This position was not considered ideal for determining accurate wind speed measurements due to the wind shading and wind vortices resulting from the nearby building. Importantly, the experimental tree was considered representative of trees expected to be candidates for this style of energy harvesting; including that likely trees chosen would be subject to turbulent conditions.

To be able to verify all results from the model, a number of data were required. These included the difficult to obtain values for _{MAX}_{MIN}

The projected area for this tree (

The value for the drag coefficient of the tree is unknown. Little information exists with reference to drag coefficients of trees, however Munson

To obtain the specific gravity (^{3} to 1,200 kg/m^{3}. As such, it was decided to use 1,100 kg/m^{3} for calculations, or a specific gravity (

To be able to predict the lean angle of any tree due to a given applied force using simple constant section beam analysis, the mean effective trunk diameter (_{MIN}

From the above,

A test was conducted which involved attaching, and hanging, a known mass to an inelastic cord, which was then passed over a roller to attach horizontally to a clamp rigidly attached to the tree trunk. See

The cord was marked with tape above the mass (of 5.0 kg), and a graduated placard placed behind the weight and marked cord. A video recorder was then set up to record the position of the marker in relation to the graduated placard, to record the positional change over a period of 15 min (900 s). The video recorder sampled at a rate of 10 Hz (10 frames per second). The mass was not allowed to touch the floor during the experiment, and was, therefore, always applying a 49 N force to the tree trunk. The video data was analysed with video processing software to plot the motion of the mass on the cord against time. From this, the magnitude of the energy required to raise the mass for each sway of the tree was determined, and the subsequent power output over time calculated. The data obtained from this experiment is shown in

At the time of the experiment, the wind conditions were observably windier than average for this site (Beaufort 2). This corresponded to an estimated wind of 4 on the Beaufort scale of wind force (5.5 m/s to 7.9 m/s).Unfortunately, no correlating wind data for the time of the experiment exist. It was noted at the time of the experiment that the roller was not frictionless, and that a small amount of energy was required to overcome the friction of the roller on its bearing shaft. This was not considered to be of concern in determining ‘ballpark’ values for preliminary calculations.

This experiment was able to measure energy from movement in one axis,

As explained in Section 3.1.1, an inertial mass harvester requires acceleration or effective acceleration (due to gravity) to operate. To determine the potential for such a device to operate in a tree, a further experiment was conducted, and further analysis of existing data performed.

The experiment involved placing a 3 axis accelerometer in the tree, attached to the same clamp in the same position as the first experiment (as shown in

Data was collected from the accelerometer over a period of 9 h at 2 Hz sampling frequency, of which the first 273 s were sampled at 32.636 Hz (or 0.0306 s intervals). The experiment was started on an afternoon that was observably not as windy as the day of the displacement experiment, but still determined to be represented by a 4 on the Beaufort scale of wind force.

Using basic trigonometry, the raw data were transformed into 3 orthogonal axes, labelled HA, HB and Vnet. Axes HA and HB were both arranged horizontally relative to gravity, and Vnet arranged vertically. It should also be noted that Vnet was the difference between the magnitude of acceleration in the vertical direction and acceleration due to gravity, ^{2}, and, as a result, was not considered worthy of evaluation. The following figure,

It should be noted that a second analysis using the displacement data, as obtained by methods described in Section 3.3, was undertaken. This data was differentiated to find acceleration and thus energy. In the interests of brevity this analysis is not included as it provided a lower bound for the predicted power and energy available to be harvested and is of academic interest only for a prediction of maximum output.

An inertial mass based movement energy harvesting device has the potential to operate due to the lean angle of the tree, and therefore due to a force due to gravity. That is, rather than relying on the acceleration of the tree in relation to an inertial mass to impart a force (or torque), the force can be applied directly by gravity due to the reorientation of the attachment point (tree) with respect to the earth.

To determine the magnitude of the lean angle of the experimental tree, the data gathered as outlined above, and displayed in

It has been previously shown that the tree trunk could be modelled as a vertically arranged cylindrical beam, and an equivalent ‘mean effective diameter’ found. Using some of this information (namely beam length) the angle of the beam, at the point where the displacement measurements were obtained, was calculated. Beam theory was again used to perform the calculations. It can be shown that the slope (

Substitution of

To determine the angle of lean (

The displacement data, shown in

From a given lean angle, the component of the force due to gravity can be determined, again using simple trigonometry. Further, this component of gravity can be described as an acceleration, rather than as a force, to allow comparison to the horizontal acceleration plot (from Section 3.4.1). That is, the component of acceleration due to gravity (_{g}

Again, refer to right side axis in

The breakdown of the energy or power imparted by wind upon a tree is shown in

To that end, as a first step, total wind power for an average wind speed past the experimental tree has been determined. Further, elastic energy and maximum elastic power input have been estimated.

To determine the wind power dissipated by a tree for a given wind speed, the value for density of air (^{3}) and values stated in

This value is the total power dissipated by the tree. This value includes not only the movement of the tree which would be lost as heat within the tree structure, but also any vortices created in the passing air. The proportion of the power dissipated as heat from the tree

To determine the amount of elastic energy in the tree trunk due to one gust of wind of a given speed, _{D}

Further, for a linear spring of rate

_{D}

Substituting values into

The data shown graphically in _{NET}

Within the 15 minute period, the total value of energy required to lift the mass, by the tree, was determined to be 52 Joules, from the raw data. For individual rises of greater than 0.7 mm, the total value of energy required to lift the mass, by the tree, was determined to be 40.2 Joules, as shown in

Using data gathered by the experiment explained in Section 3.4.1, the lean angle of the tree was determined at each peak and trough. From each change in angle between the peaks and troughs, the energy required swinging a pendulum of mass _{PEND}

As the data used were gathered via a 5 kg mass attached to the tree, it was considered prudent to use 5 kg as the value for _{MOV}_{PEND}_{PEND}

The running total of energy, as plotted above, results in 0.034 J after 900 s of tree sway. This equates to an average power output of about 38 μW. It should be emphasised that this figure was calculated using a pendulum length (_{PEND}

Determination of power and energy from those data recorded by the accelerometer ultimately proved impossible to verify as correct. A process was followed with the aim of finding an upper bound figure of energy. That is, the initial aim of the experiment was to integrate the accelerometer data to find velocity, and integrate velocity to find displacement. Upon undertaking this process, a significant amount of ‘drift’ resulted. From the accelerometer data, step integration resulted in significant (unrealistic) velocities, which contributed to extreme displacements (not possible for an object fixed to ground). To counter the drift, a number of techniques were considered and implemented. Of those techniques, the process deemed to be most successful was as follows:

take an average, over the period of time used for analysis, of the acceleration data,

use the average to offset the data such that it cycles around an average of 0 m/s^{2},

integrate the acceleration data to find velocity,

produce a Fast Fourier Transformation (FFT) of velocity plot to find significance of low frequencies,

eliminate drift in the velocity data by filtering via a ‘high pass’ filter developed by Murphy and Robertson [

integrate filtered velocity data to find step change displacement and absolute displacement, and

use the step change displacement (Δs) to determine work and energy via use of

_{MOV}

Σ

It was found, however, that the abovementioned process would produce results for velocities and displacement that were highly dependent upon the cut off frequency of the high pass filter. That is, the high pass filter was used to eliminate the slow build up (drift) of velocity, as integrated from acceleration. The elimination of this build up (or drift) was directly proportional to the cut-off frequency, as was the resulting integrated displacement. It was found that the cut off frequency could be altered to give ‘realistic’ peak displacements for the tree sway, from which calculation of energy could be made. Analysis was performed on the data recorded between times 15 and 273 s (

As stated, a Fast Fourier Transformation (FFT) was performed on the velocity data, and a number of cut-off frequencies were experimented with, to view the effect on velocity and subsequent displacement (

To put the results shown above into context, examples of the energy consumption of a typical wireless sensor node are provided. The energy required to power a wireless sensor node is dependent upon a number of factors. These factors include such aspects as the electrical requirements of the various brands and types of nodes, any associated sensor power requirements, data sampling rate, radio communications quality and reliability, battery voltage, as well as any loss due to battery self-discharge.

From the three methods of movement energy harvesting considered, it is clear that one of those methods stands out as clearly superior in terms accessing the energy available,

However, the calculated Beaufort 4 wind gust tree sway energy of 9.2 J compares well to the 40.2 J of energy collected in the 900 s of sampling, where wind speeds were estimated to be as high as Beaufort 4. Further, from

It was difficult to correlate the wind dissipation by the tree to power available for harvesting, as it appeared to the observers of the experiment that the vast majority of the work performed by the tree on lifting the mass, was

As discussed in Section 4.4, above, the energy available to an inertial energy harvester was not able to be accurately found from these experiments due to the drift in the displacement data determined from double integration of acceleration data. This resulted in no firm values for step displacement, from which energy calculations would have been derived. Data logging of trunk acceleration and displacement at the same time, would allow determination of energy available for an inertial mass harvester simpler. However, the simple analysis in this document reveals that despite some estimation problems, the energy captured from an inertial system is much less than for a tethered system. Additionally, the reported experimentation did not take into account any relationship between known wind speed and power output, simply an estimate for the wind speed (using the Beaufort scale). To more accurately estimate the energy available for a movement energy harvester, wind data will be required, for correlation.

The effect on energy output due to the size of a tree was not specifically investigated in the above work; however, verification of some of the modelling techniques used may be required. This would allow known tree properties for any tree to be used to determine an estimate of average power available.

Lastly, the point on the tree trunk used for the experiments outlined was determined somewhat arbitrarily,

The use of sensor nodes in forests is expanding for a variety of research end uses. In most outdoor areas solar panels offer a good energy source for a sensor node. However, as discussed in this paper, the under canopy area of a forest has a much lower solar resource and this has lead to research into a variety of non-solar energy sources. The process discussed in this report is energy from tree movement.

While wind power is a good resource its direct access under trees is also limited, however, indirect access via tree movement can be exploited. This resource has been studied in terms of a number of possible methods by which energy may be extracted from tree movement, and the investigation into the amount of energy available for energy harvesting from tree movement.

The extraction methods include energy harvesting via the horizontal acceleration of the tree, the lean angle of the tree and the force/displacement of the tree, and was demonstrated by having the tree lift a mass. Device design methodologies to extract this energy was explained and it was found that energy harvesting using a force/displacement methodology showed a greater potential than the other proposed methods, as outlined in

This paper also presented a simple model of a tree that was able to determine the power dissipation by any tree, and energy available at a given point on the tree trunk.

The authors acknowledge the work of Matthew Ingram-Gavin, and thank him for the initial background research into harvesting energy from trees, the hardware setup and data collection, initial data analysis and experimentation. The authors also acknowledge the work of Michael Collins, and thank him for his assistance with photographic and video analysis, setup and control of laboratory equipment. The authors give special thanks to Camilla Myers and Mark Goldsworthy for their review of this work, and helpful suggestions. This work is fully funded by the CSIRO Transformational Capability Program—Sensor and Sensor Networks.

‘Tethered’ and ‘Inertial Mass’ general arrangements.

‘Lollipop’ model of a tree.

Photograph of the experimental tree.

Tethered harvester experimental arrangement.

Displacement of suspended mass,

Inertial harvester experimental arrangement.

HA Axis Acceleration, as recorded by an accelerometer.

Calculated Lean Angle and resultant effective acceleration.

Wind power/energy dissipation breakdown.

Accumulated Energy, E_{MOV} from lifting suspended mass.

Theoretical arrangement of inertial harvester used for tree lean angle analysis.

Accumulated Energy, E_{MOV}, from tree lean, for inertial mass 5 kg on 4 m long pendulum arm.

Theoretical arrangement of inertial harvester used for tree acceleration analysis.

Acceleration in horizontal axis, HA (time 15 to 273 s).

Derived, high-pass filtered velocity in horizontal axis HA (cut off 0.3 Hz).

Derived displacement in horizontal axis, HA.

Accumulated Energy (E_{MOV}) from acceleration in axis HA, for inertial mass = 5 kg.

Data for experimental tree.

D_{MIN} |
0.055 m | G | 1.1 | E | 14.8 GPa |

D_{MAX} |
0.111 m | Cd | 0.43 | D | 0.056 m |

L | 4.16 m | k | 289 N/m | ||

A | 6.4 m^{2} |
I | 482 × 10^{−9} m^{4} | ||

P (to find k) | 61 N | ||||

y (to find k) | 0.21 m |

Fleck 3B energy and power consumption at 3.3 volts. Energy requirements for different regimes given; sleeping except to sample and transmit once every 1 min, sleeping except to sample and transmit once every 60 min, and as a permanent receiver.

Sleep | Transmit | Receive | 1 min Tx | 60 min Tx | Constant Rx |
---|---|---|---|---|---|

0.142/0.470 | 22/73 | 12/40 | 50 | 41 | 3,456 |

Summary table of results, from analysis of tree movement energy harvesting methods.

| |
---|---|

Pendulum style inertial harvesting via tree lean | 38 μW |

Pendulum style inertial harvesting via tree acceleration (upper bound) | 14 mW |

Tethered harvesting via tree pull force/displacement | 44.7 mW |

Total wind power dissipated by tree | 496 W |