8th International DAAAM Baltic Conference
"INDUSTRIAL ENGINEERING”
19-21 April 2012, Tallinn, Estonia
DEVICE FOR BRANCH VOLUME DISTRIBUTION
MEASUREMENT
Aarnio, A.; Kananen, E.; Keltto, V.; Vartiainen, V-M; Laasasenaho, J.; Kiviluoma, P.
& Kuosmanen, P.
Abstract: The volume and crosssectional area of tree as a function of its
length can be estimated by mathematical
taper curve models which often exclude
branches. To include branches into new
whole tree volume models representative
measurement data is required. Currently
the data is acquired by manual
measurements.
This study presents an automated
measuring device based on Archimedes’
principle which will offer fast and accurate
method to measure the volume distribution
of irregular shaped objects such as
branches.
This study shows that measuring with this
device is faster than manual measuring
and the results are promising. The device
is a potential platform for diversity of
volume measurements and it could define
global standards for cross-sectional area
and volume measuring in forest research.
models. The amount and type of branches
affects to the distribution of tree’s biomass
and on the tree’s effect as a carbon sink.
The type, size, amount and placement of
branches affects also to the quality of the
saw timber and to the distribution of the
stem volume (known as taper curve).
The standard method so far to obtain
accurate branch volume information in
research work is manual measurement,
which is time-consuming and inaccurate.
Measuring a branch can take up to several
hours. In manual measurement branches
are divided into segments which are
limited between two branching points as
shown in Figure 1.
Key words: irregular volume measurement,
immersion,
cross-sectional
area,
Archimedes’ principle
1. INTRODUCTION
The dimensions and volume of a standing
tree can be estimated by mathematical
models [1,2]. These models are being used
for example to estimate the amount and
quality of the biomass in the forest and to
determine the optimal log length (bucking)
of the trees. Most of the current models
take into account only the stem volume and
diameters, but there is a growing interest to
include also the branch volume into the
Fig. 1. Branch segment and measuring
points.
From each segment, several measurements
are taken: segment length (L), maximum
and minimum diameter (D) as close as
possible to the beginning, the middle and
the end of the segment. From these values
the volume of the branch segment can be
estimated with Newton’s equation
1
𝑉 = 6 (𝑔𝑏 + 4𝑔𝑚 + 𝑔𝑒 )l
(1)
where gb is cross-sectional area in the
beginning of the segment, gm in the middle,
ge in the end and l is the length of the
segment.
Immersion in the water has been used to
estimate the total wood volume both in
forest industry [3] and in forest research
[4]. In this research also the distribution of
the volume is measured.
This study presents an automated
measuring device that speeds up the
measurement process, facilitates the data
gathering by instantaneously saving and
visualizing the branch volume distribution
and it also removes some of the possible
error sources of the manual measurements.
As a result, large amounts of representative
branch volume information can be
collected.
Combining this with other
information such as branch type and
distance from the ground a new, branchincluding tree model could be created.
The purpose of this study is to verify if the
manual measurement method can be
replaced with automated measuring device.
Determining factors are most importantly
precision and accuracy, but also
measurement speed and usability of the
device.
2. METHODS
2.1. Measuring device
The branch volume distribution measuring
device is shown in Figure 2. The main
structure of the device is a crane mounted
to a supporting frame. A winch is mounted
to the crane and winch cable runs through
two pulley wheels. The height and the
reach of the crane arm can be adjusted for
fluid containers of different sizes. A force
sensor is attached to the mounting bracket
which is attached to the winch cable. The
immersion depth is determined by the
distance sensor mounted to the crane arm.
It measures the distance between the crane
arm and the force sensor mounting bracket.
Support stand is attached to the force
sensor during measurement. It consists of a
threaded rod and a bottom plate of known
dimensions. Fluid tank is located under the
crane arm and it is positioned in a way that
the support stand is located at the centre of
the tank.
This first generation device is designed for
branches up to 1.4 m and 3.4 kg. Longer
and heavier branches can be measured in
pieces.
E
F
B
G
C
D
A
Fig. 2. Measurement device consisting of
frame (A), crane (B), winch (C), fluid
container (D), distance sensor (E), force
sensor mounting bracket (F) and support
stand (G).
2.2. Immersion method
When an object is immersed it displaces
fluid and causes an upwards force called
buoyancy. The force is defined by
Archimedes’ law
𝐹 = 𝑉𝜌𝑔
(2)
where V is the volume of displaced fluid, ρ
is the density of the fluid, g is standard
gravity and F is the buoyancy. When
measuring the volume as a function of
branch’s length, equation (2) becomes
𝐹(𝑥) = 𝑉(𝑥)𝜌𝑔
(3)
where V(x) is the volume of displaced fluid
as a function of immersion depth and F(x)
is the buoyancy caused by the displaced
fluid. Volume of the displaced fluid equals
the volume of immersed object. When the
density of fluid and the buoyancy is known
the volume of immersed object can be
calculated.
The device measures the objects according
to the functional model shown in Figure 3.
In the branch measurements, the base of
the measured branch was set on top of the
support stand’s bottom plate and sub
branches were folded to align with the
main branch. Branches were attached to the
support stand with a thin steel wire to keep
them stationary during the measurement
and to minimize the momentum caused by
buoyancy. Branch prepared for the
measurement is shown in Figure 4.
Fill the fluid
tank
Measure the
temperature
of the fluid
Fix the object
into machine
Lower the
object into
water
Measure the
position of
the object
Measure
weight of the
object
Physical
human
action
Physical
machine
action
Computer
action
Transferring
the data into
a computer
Computer
program saves
the data
Generate an
excel file
Redo?
Fig. 3. Functional model of the wood
volume distribution measuring device.
Fig. 4. Branch attached to the support stand
After fastening of the branch the support
stand was attached to the force sensor and
immersed into the fluid tank. While
immersing, the immersion depth and the
weight of the branch were measured using
20 Hz sample rate. Immersions were done
both by hand and by using the winch.
Total volumes of the branches were also
measured by a static immersion using a
precision scale. In this study this is
considered to be the most accurate method
to measure the total branch volumes.
2.3. Materials
Measurement
and
data
acquisition
components used in measurements are
shown in Table 1. In this study two aspen
(Populus tremula) specimens and a
reference object of known volume and
shape were measured. The reference object
is shown in Figure 5. Water was used as
the fluid into which the immersions were
made.
Force sensor
Tedea Hunleight 1022
(5 kg)
CLIP IG AE 301
Measurement data
4th order estimation
Manual method
450
Immersed volume (cm³)
Force sensor
amplifier
Distance sensor UniMeasure JX-PA-80
Measurement
National Instruments
card
NI USB-6009
Precision scale
Precisa XB 620M
Table 1. Data acquisition instruments.
branch weight in the beginning of the
immersion is determined by averaging
multiple points in the beginning of each
measurement repetition.
350
250
150
50
-50 0
Fig. 5. Reference object.
50
Immersion depth (cm)
3. RESULTS
Fig. 6. Branch #1.
Measurement data
4th order estimation
Manual method
250
Immersed volume (cm³)
As the viscosity of water creates a drag
force in vertically moving branch, the
measurement was done in both lowering
and lifting directions. In this way the
combined data of these two directions
cancel the effects of the additional,
opposite forces.
Volume of a steel wire which was used to
attach the branch was neglected. Volume
of the measurement platform was known
so its volume was compensated for the
final measurement data.
The measurement data from all repetitions
of each branch was placed in one table.
The processed data is presented in a
graphical from in Figures 6 and 7, the
volume of the immersed branch as a
function of immersing depth. A polynomial
fit of fourth order was determined. The
volumes of both branches measured in the
conventional way were also included in the
charts. As it is seen, the variation of values
is significant in a single point. The initial
200
150
100
50
0
0
-50
50
Immersion depth (cm)
Fig.7. Branch #2.
The total volumes of branches are
calculated from equations of the fourthorder polynomial fits shown in Figures 7
and 8. The volumes defined in three
different methods are shown in Table 2.
Method
Branch #1 Device
Manual
Precision scale
Volume
(cm³)
426
347
399
Branch #2 Device
Manual
Precision scale
Table 2. Total volume of branch
defined by different methods.
176
152
179
#1 and #2
In addition to the branches, the reference
object was measured and the data was
processed as with the branches. Measured
volume and accurate known volume of this
reference object is illustrated in Figure 8.
Lowering
Lifting
Accurate
Immersed volume (cm³)
400
350
300
250
200
150
100
50
0
-5 -50
5
Immersion depth (cm)
Fig. 8. Reference object.
15
The theoretical maximum error for the
measured weight due to the inaccuracies of
measurement system is 2 grams in force
transducer, 4.5 grams in force sensor
amplifier and 3.865 grams in measurement
card. Total error is 10.365 grams.
Theoretical maximum error in distance
measurement is 5 mm in distance sensor
and 4 mm in measurement card, being 9
mm in total. Observed deviation in static
measurement was 4 mm for distance and
11 grams for weight. In dynamic branch
measurement
the
observed
weight
deviation was 30 grams.
4. CONCLUSION
The device works as expected and the
results prove that the branch volume can be
measured by buoyancy. The automated
measurement process removes routine
work and is at least twice as fast as the
manual method. The device produces
results that are close to the accuracy scale
volume which is considered as the best
estimation of the total volume. Therefore
the results obtained by the device can be
considered more accurate than the ones
obtained by the manual method. Also the
reference object measurements prove that
valid data can be obtained.
With the branch specimens, difference
between manually and automatically
measured volumes is surprisingly large.
This may be caused by the fact that manual
measurement doesn’t take all of the branch
specialities into account. For example, in
each branching point there is a base
enlargement which is difficult to measure
and to predict (grey branch area in figure
1). Also the cross-sectional area and the
shape of the stem are difficult to estimate
with limited amount of measurements.
Furthermore, the length of the branch in
manual and automated measurement isn’t
exactly the same as can be seen in
Figure 8. This is because in manual
measurement the segment lengths are
added up instead of measuring the total
length of the branch. Also manual
measurement takes into account the
changes of directions in different sections
whereas the device measures the length
only in the direction of immersion.
The results are interesting, but they are
based on only two specimens of single tree
species. Larger amount of both manual and
automated measurements on many
different species would be required to have
statistically valid comparison of these two
methods.
There are two main reasons for the
variation in the measurement data. First is
the lack of signal filtering. Second and
greater reason for the variation is the
changes in the lowering speed and
mechanical vibrations of the lowering
system. This is supported by the fact that
the lowering done by hand produced a lot
less variation in the measurement data than
the lowering by winch.
Based on the results, several improvements
can be suggested in order to achieve better
measurement accuracy. These include the
stabilization of the lowering process,
improving sensor accuracy and the use of
signal filtering.
The device can also be used to determine
the cross-sectional area of a branch as a
function of the immersing depth as well as
the total density of the branch. By
combining data from several different
measurements the volume distribution of
other tree parts such as bark and leaves can
be distinguished. The device can be used
for various shapes and a wide range of
materials and it can be scaled to measure
different sizes of objects by changing the
force sensor to the suitable range.
http://www.idanmetsatieto.info/fi/documen
t.cfm?doc=show&doc_id=1277 (8.3.12).
4. Williamson, G, B & Wiemann, M, C.
Measuring
wood
specific
gravity…Correctly. American Journal of
Botany 97(3): 519–524. 2010.
CORRESPONDING ADDRESS
Panu Kiviluoma, D.Sc. (Tech.), Post-doc
researcher
Aalto University School of Engineering
Department of Engineering Design and
Production
P.O.Box 14100, 00076 Aalto, Finland
Phone: +358 9 470 23558,
E-mail: [email protected]
http://edp.aalto.fi/en/
6. ADDITIONAL
AUTHORS
DATA
ABOUT
Aarnio, Aleksi, B.Sc. (Tech)
Phone: +358 40 838 4856
E-mail: [email protected]
Keltto, Ville
Phone: +358 50 343 5721
E-mail: [email protected]
Vartiainen, Vesa, B.Sc. (Tech)
Phone: +358 44 364 1000
E-mail: [email protected]
5. REFERENCES
1. Laasasenaho, J. 1982. Taper curve and
volume functions for pine, spruce and
birch. Communicationes Instituti Forestalis
Fenniae
108.
74
p.
2. Zianis, D., Muukkonen, P., Mäkipää, R.
& Mencuccini, M. 2005. Biomass and stem
volume equations for tree species in
Europe. Silva Fennica Monographs 4. 63 p.
3.
Wood
logs
imported
to
Finland. Measuring Instruction.
Forest
Industries Association's standard, 2007, (in
Finnish) [WWW]
Kuosmanen, Petri, D.Sc. (Tech.), Professor
Phone:+358 9 470 23544
E-mail: [email protected]
Kananen, Eero, B.Sc.
Phone:+358 40 586 2850
E-mail: [email protected]
Laasasenaho, Jouko, D.Sc., Professor
Emeritus
Phone: +358 40 5066 055
E-mail: [email protected]
Department of Forest Sciences
University of Helsinki