Journal of the Saudi Society of Agricultural Sciences xxx (2018) xxx–xxx
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Predicting header wheat loss in a combine harvester, a new approach
Reza Karmulla Chaab, Seyyed Hossein Karparvarfard ⇑, Hossein Rahmanian-Koushkaki, Alireza Mortezaei,
Mojtaba Mohammadi
Biosystems Engineering Department, College of Agriculture, Shiraz University, Shiraz, Iran
a r t i c l e
i n f o
Article history:
Received 10 May 2018
Revised 13 August 2018
Accepted 18 September 2018
Available online xxxx
Keywords:
Buckingham theorem
Dimensional analysis approach
Grain
Head loss
Reel index
a b s t r a c t
Header loss of wheat in a combine harvester was modelled and evaluated at Badjgah Research Station,
Shiraz University, Shiraz, Iran. The main objective was to develop a characteristics dimensionless model
to predict the header loss based on Buckingham pi theorem. A conventional New Holland TC5070 combine harvester was monitored in field studies. Parameters like rotational speed of reel (at 21, 25 and
35 rpm), forward speed (at 2, 3 and 4 km h1) and cutter bar height (at 15, 25 and 35 cm) were considered for field evaluation. Results showed that optimum values for reel index (ratio of forward speed to
rotational speed of reel), height of cutter bar, forward speed of combine harvester and rotational speed
of reel were 1.38, 15 cm, 4 km h1 and 21 rpm, respectively. Collected data were used to develop a model
for predicting header loss as a function of parameters studied. Results from F-test between predicted and
measured data were not significantly difference (p 0:05) which is a prominent result.
Ó 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction
Wheat (Triticum aestivum L.) is one of the most important and
strategic cereal crop in the world. According to the International
Food Policy Research Institute (IFPRI), the world request for wheat
will rise from 552 megatons in 1993 to 775 megaton by 2020
(Hossain et al., 2012).
Cereal grains are principally harvested with combine harvesters. The combine harvester, as we know it today, is a machine
used to harvest and thresh all kinds of grain in a variety of crop and
field conditions. Modern combines are available in a wide range of
types and sizes. To understand the operation of combine, look closely at each function of the machine. All combines perform the following five basic crops harvesting functions: cutting or windrow
pick- up and feeding, threshing, separating, cleaning and handling
(FMO, 1987).
One of the primary indicators of combine performance is the
amount of grain loss during harvesting operation (Siebenmorgen
et al., 1994). Combine harvesting can be profitable only if the oper⇑ Corresponding author at: Biosystems Engineering Department, College of
Agriculture, Shiraz University, Shiraz 71441-65186, Iran.
E-mail address: karparvr@shirazu.ac.ir (S.H. Karparvarfard).
Peer review under responsibility of King Saud University.
Production and hosting by Elsevier
ator knows how to adjust the combine properly and operate it efficiently with a minimum of losses. Recent studies have shown that
profit losses of nine percent or more can result if harvesting efficiency is not ideal (FMO, 1987).
Unless we know the source of grain losses, we cannot reduce
them. Some losses are caused by improper adjustments. One of
the sources of losses which must be identified is header loss that
includes lodging, shatter and cutter bar loss (Srivastava et al.,
2006). In other words, this loss occurs when the header is operated
improperly or when the crop tends to shatter easily. Each type of
header has operating characteristics which can cause losses.
Also usual causes of cutting platform losses are: grain missed by
cutter bar, grain missed because of improper reel speed, grain
thrown over in front of the reel by too low reel height and grain
shattered by too fast ground. A scientific report about combine harvesters in Iran states that 68% of harvest losses caused by platform
(Behroozi Lar et al., 1994).
No combine is 100 percent efficiency. If total losses are acceptable, no adjustments of the machine or operating procedures are
needed. Changing in moisture content level, field conditions;
how well the crop is standing and crop variety all affect the rate
of loss.
One of primary researches for determining harvesting loss in
grain was done by Andrews et al. (1992). They designed and constructed a combine test which installed on the commercial combine for measuring loss rates and quality reduction in rice. A
Case IH, model 1680, axial flow combine harvester was used to
evaluate the effects of forward speed, rotor speed and concave
https://doi.org/10.1016/j.jssas.2018.09.002
1658-077X/Ó 2018 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Please cite this article in press as: Chaab, R.K., et al. Predicting header wheat loss in a combine harvester, a new approach. Journal of the Saudi Society of
Agricultural Sciences (2018), https://doi.org/10.1016/j.jssas.2018.09.002
2
R.K. Chaab et al. / Journal of the Saudi Society of Agricultural Sciences xxx (2018) xxx–xxx
Nomenclature
Symbols
A
B
F
Hc
L
Lh
M
T
constant
exponent or the slop
function
height of cutter bar (m)
length (m)
length of header (m)
mass (kg)
time (s)
setting on harvesting losses. Finally, they proposed optimum settings for combine operating parameters when harvesting rice.
Sheikh Davoodi and Houshyar (2012) evaluated header losses in
New Holland TC56 combine harvester while wheat harvesting. The
results showed that best forward speed of machine and rotational
speed of thresher were 3 km h1 and 25 rpm, respectively.
For investigating grain loss monitoring, Mostofi Sarkari used
grain loss monitors to measure losses in different parts of a John
Deere 955 combine harvester. There was no difference between
measured and expected loss. In addition, the loss was about one
percent (Mostofi Sarkari, 2010).
Zhao et al. (2011) used piezo-electric polyvinylidene fluoride
(PVDF) film to design a grain flux sensor which can monitor the
separation loss real-time. Field trial results indicated that the
measurement errors of grain separation loss recorded by the monitoring system relative to the loss checked manually were less than
12%.
Paulsen et al. (2013) determined total harvest losses for a
sampling of combines harvesting corn and soybeans in Brazil. They
stated the combine’s losses separately including preharvest, gathering, threshing and separating losses. Finally, they suggested
some approaches for reducing these losses.
Dimensional analysis is defined as the mathematical theory of
functions that is characterized by a generalized type of homogeneity (Langhaar, 1980). The fundamental principle of this approach is
known as the Buckingham Pi theorem. This theorem states that the
number of Pi term (s) required to express a relationship between
variables is equal to the number of variables involved in the process minus the number of dimensions required to express those
variables. The power of the dimensional analysis resides in its ability to classify equations, convert equations from one system of
units to another, develop prediction equations, reduce the number
of variables to be investigated in an experiment, and provide the
basis for the theory of similitude (Murphy, 1950). The result of a
dimensional analysis of a problem is saving in both cost and labor
during the experimental determination of the function. It is; however, better than regression models in that the number of variables
that must be studied are reduced substantially (Srivastava et al.,
2006).
Karparvarfard and Rahmanian-Koushkaki (2015) used dimensional analysis approach to predict fuel consumption of a MF399 4WD (81 kW) tractor. The effects of blade width of chisel
plough, tillage depth and forward speed on fuel consumption were
investigated. The obtained fuel consumption model was a function
of tractor and implement dimensionless groups. Results predicted
by the model were compared to ASAE Standards (D497.4) and
show that the standard overestimates fuel consumption. Theses
researchers believed that the reason of this phenomenon were
resulted tractor size and experimental venue.
This research cannot be used as a guide to combine harvesting,
but it is an explanation of the principles of combine harvesting
Vc
Vf
Vr
cutter bar speed (cut min1 )
1
forward speed of combine harvester (km h )
rotational speed of reel (rpm)
Abbreviations
HG
mass of harvested grains (g)
HL
percentage of grain loss (%)
LG
mass of grain loss (g)
which are invaluable to any combine operator. To operate and
adjust the cutting platform properly, the following ground speed,
cutting height and reel adjustments were considered.
Many researches have used different approaches such as artificial neural network (Pishgar-Komleh et al., 2010; Jalali et al., 2013),
regression analysis (Zareei et al., 2012; Abdi and Jalali, 2013;
Bawatharani et al., 2014), and neuro-fuzzy approach (Zareei
et al., 2012) for predicting combine header loss, but little
information is available for using dimensional analysis method
on this issue. Considering advantageous of models by Buckingham
Pi Theorem, the overall aim of this research was to present a
method to predict header grain loss using dimensional analysis
approach.
2. Material and methods
2.1. Study site
This research was carried out at Agricultural Research Center,
Shiraz University, 15 km northwest of Shiraz, Fars Province, Iran
(29 320 N, latitude; 52 350 E, longitude; and 1810 m above sea
level) in summer 2016. The experiment was conducted on a field
measuring 1.4 ha. Plot size was 6 m wide and 100 m long. Number
of plots was 24.
2.2. Treatments and survey parameters
A randomized complete block design with three treatments and
three replications was constructed. The treatments consisted of
three levels of rotational speed of reel (21, 25 and 35 rpm), three
levels of forward speed (2, 3 and 4 km h1) and three levels of cutter bar height (15, 25 and 35 cm). It should be noted that length of
header and cutter bar speed were considered constant as mentioned in combine harvester manual (Table 1). In other words, 81
tests were done. The basis of choosing levels of treatments was
combine harvester manuals and driver’s experiences.
In this study, the Pishtaz wheat variety was used. During harvesting operation, moisture content of the wheat was 14% (d.b.).
Table 1
Some specifications of New Holland TC5070 combine harvester.
Characteristics
Values/Type
Unit
Engine power
Engine capacity
Transmission
Header length
Header height
Cutter bar speed
152
6.8
Hydrostatic
518
13–160
1150
kW
Liters
. . .. . ..
cm
cm
cut min
1
Please cite this article in press as: Chaab, R.K., et al. Predicting header wheat loss in a combine harvester, a new approach. Journal of the Saudi Society of
Agricultural Sciences (2018), https://doi.org/10.1016/j.jssas.2018.09.002
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R.K. Chaab et al. / Journal of the Saudi Society of Agricultural Sciences xxx (2018) xxx–xxx
P4 ¼
Hc
Lh
ð5Þ
Among the Pi terms above, P1 was dependent Pi term and the
others were independents. With respect to this manner, the nondimensional relation is:
HL ¼ f ð
V r V r Hc
;
; Þ
V c V f Lh
ð6Þ
Eq. (6) was revised as a product of three functions.
B
Vr
Vr
Hc
HL ¼ A f 1 ð Þ f 2 ð Þ f 3 ð Þ
Vc
Vf
Lh
Fig. 1. The New Holland combine harvester which used in field trials.
2.3. Combine harvester
The combine which was used in field evaluation was a New Holland TC5070, conventional type and self-propelled combine
(HEPCO, Iran) (Fig. 1). Some specifications of the combine were
listed in Table 1.
2.4. Combine loss measurement
Types of losses that considered in this research were preharvest
loss and header loss. Preharvest loss was assessed by putting a
frame with the dimensions of 50 50 cm on the unharvest rows
adjacent to the plots and far from the boarder, randomly. After cutting long obtainable crop heads the short crop heads and free
grains on the surface were gathered. In order to measuring the
header loss, the combine was driven in the field. After achieving
steady state condition, the combine was stopped. Then the combine was backed up a distance equal to the longitudinal distance
between the cutter bar and the discharge chute (Srivastava et al.,
2006). A sample area was marked off in front of the combine and
the losses collected from that area. Finally the collected losses
gained from the two steps were weighted by a digital balance
(GF-600, A&D Company, Japan, resolution ±0.01 g) and pre harvest
loss and header loss were calculated.
2.5. Development of dimensional analysis model
After the experimental tests have been done, the model for predicting header loss has been developed. Because of many effective
parameters on header loss and high calculation operations, we
decided to use dimensional analysis to investigate the experimental data. Accordingly, a model was proposed in which all the
parameters would be grouped in such a way as to produce sets
of independent dimensionless groups. It would be advisable, the
group forms which produce linear relationships with the dependent variable group. A general dimensional relation could be
expressed as Eq. (1). Since rank of dimensional matrix was 3 and
according to Buckingham Pi Theorem, the number of Pi terms
was the number of parameters (7) minus the rank of the dimensionless matrix. So the number of Pi terms was 4. The Pi terms
were defined as P1 to P4 .
f ðLG; HG; V r ; V c ; V f ; Hc ; Lh Þ ¼ 0
P1 ¼ HL ¼
LG
HG
ð7Þ
By taking logarithm of both sides of Eq. (7), the linear Eq. (8)
was obtained. It should be noted that the constants A and B were
not calculated until functions derived.
Vr
Vr
Hc
log ðHLÞ ¼ log A þ B log f 1 ð Þ þ log f 2 ð Þ þ log f 3 ð Þ
Vc
Vf
Lh
ð8Þ
In which log A is the vertical intercept and B the slope of the
straight line. At first all of functional relationships f 1 through f 3
were obtained. Then the two constants A and B were determined.
It can be stated that each of logarithmic functions in Eq. (8) has
special constants (A1 to A3 ) and special slops (B1 to B3 ) which
can be expressed as below (Karparvarfard and RahmanianKoushkaki, 2015):
log f 1 ð
Vr
Vr
Þ ¼ B1 logð Þ þ A1
Vc
Vc
ð9Þ
log f 2 ð
Vr
Vr
Þ ¼ B2 logð Þ þ A2
Vf
Vf
ð10Þ
log f 3 ð
Hc
Hc
Þ ¼ B3 logð Þ þ A3
Lh
Lh
ð11Þ
However, two constants were not determined until each functional relationship was found. The value of each constant A is different for different values of other functional groups. So for the
other functional groups, each one featuring a similar constant, all
of the constants could be combined into one value A for the final
correlation, containing all functional relations.
For the sake of the present discussion, then, the value of A could
be neglected as below:
log f 1 ð
Vr
Vr
Þ ¼ B1 logð Þ
Vc
Vc
ð12Þ
log f 2 ð
Vr
Vr
Þ ¼ B2 logð Þ
Vf
Vf
ð13Þ
log f 3 ð
Hc
Hc
Þ ¼ B3 logð Þ
Lh
Lh
ð14Þ
ð1Þ
Also it is necessary to define the following terminology for using
dimensional analysis.
ð2Þ
Vr
First Residual ¼ log ðHLÞ log f 1 ð Þ
Vc
ð15Þ
Vr
Þ
Vf
P2 ¼
Vr
Vc
ð3Þ
Second Residual ¼ First Residual log f 2 ð
P3 ¼
Vr
¼ ðreel indexÞ
Vf
ð4Þ
Third Residual ¼ Second Residual log f 3 ð
Hc
Þ
Lh
ð16Þ
ð17Þ
Please cite this article in press as: Chaab, R.K., et al. Predicting header wheat loss in a combine harvester, a new approach. Journal of the Saudi Society of
Agricultural Sciences (2018), https://doi.org/10.1016/j.jssas.2018.09.002
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R.K. Chaab et al. / Journal of the Saudi Society of Agricultural Sciences xxx (2018) xxx–xxx
2.5.1. Analysis of the group: log f 1 ðVV cr Þ
Explore in more detail at Eq. (6) indicates that the first and second pi-terms are both functions of the rotational speed of reel and
their effects could easily be separable if one could be held constant
while the other is varying. However, considering that the numbers
of experimental data points are quite large, it is possible to separate the effects of each group in the following way. In order to
determine the functional relationship for percentage of lossed
grain, let us use the data of the third replication as follows:
In the first, the values of the corresponding logðHLÞ plotted
against the values of log ðVVr Þ. Each point of Fig. 2 has a value for
However, the average slopes of all replications were used to
establish the following linear equation:
log f 1 ð
Vr
Vr
Þ ¼ 0:6705 logð Þ
Vc
Vc
ð19Þ
2.5.2. Analysis of the group: log f 2 ðVV r Þ
f
The values of the first residuals, as defined by Eq. (15), were calculated for plotting log f 2 ðVVr Þ against the corresponding values of
f
log ðVVr Þ. For this case, the following equation was found (Fig. 4):
f
f
Vr
Vr
Þ ¼ 0:8959 logð Þ
Vf
Vf
log ðVVcr Þ. Thus the points of fairly equal log ðVVcr Þ were connected
log f 2 ð
together (forming a number of parallel lines). The points which
identify on each line are the average of 81 raw data points. Then
a vertical shift line (m-n) to the 3 lines was drawn.
The vertical spacing of the lines is due to the effects of log ðVVcr Þ on
By averaging from the slopes of three replications, the fitted linear graph produced the following functional relationship:
the logðHLÞ, designated as the function of f 1 ðVVcr Þ (Fig. 3).
To find this function, the vertical spacing
ðlog f 1 ðVVcr ÞÞ
Vr
Vr
Þ ¼ 0:7519 logð Þ
Vf
Vf
ð21Þ
could be
found and plotted against the corresponding values of log ðVVcr Þ in
Fig. 3. It should be noted that each point on this plot corresponds
to one line of Fig. 3 or one value of log ðVVcr Þ. For this case, the following equation was found:
log f 1 ð
log f 2 ð
ð20Þ
2.5.3. Analysis of the group: log f 3 ðHL c Þ
h
For this analysis, the values of second residuals as defined by
Eq. (16), were found for log f 3 ðHL c Þ and plotted against the correh
sponding values of logðHL c Þ as shown in Fig. 5 for third replication.
Vr
Vr
Þ ¼ 0:5013 logð Þ
Vc
Vc
h
ð18Þ
This figure showed a linear graph with the following relationship:
log f 3 ð
Fig. 2. Relation between log ðHLÞ and log ðVV r Þ for third replication.
f
Hc
Hc
Þ ¼ 1:5813 logð Þ
Lh
Lh
ð22Þ
Fig. 4. Relation between log f 2 ðVVr Þ and log ðVVr Þ for third replication.
f
Fig. 3. Relation between log f 1 ðVVcr Þ and log ðVVcr Þ for third replication.
f
Fig. 5. Relation between log f 3 ðHL c Þ and log ðHL c Þ for third replication.
h
h
Please cite this article in press as: Chaab, R.K., et al. Predicting header wheat loss in a combine harvester, a new approach. Journal of the Saudi Society of
Agricultural Sciences (2018), https://doi.org/10.1016/j.jssas.2018.09.002
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R.K. Chaab et al. / Journal of the Saudi Society of Agricultural Sciences xxx (2018) xxx–xxx
Table 3
Results of F-test between predicted and measured header loss.
Sources of
Variation
Degree of
Freedom
Sum of
Squares
Mean of
Squares
F
Model
Residual
Total
1
4
5
62.740
22.052
84.791
62.740
5.513
–
11.381ns
–
–
ns: non-significant.
predicted and measured header loss showed that the resultant
slope for the header loss were not different from 1:1 line in a significant manner (P 0.05) (Table 3) (Karparvarfard and
Rahmanian-Koushkaki, 2015).
Fig. 6. Log (HL) versus log ðf 1 f 2 f 3 Þ for all experimental test runs.
4. Conclusion
However, the average slopes of three replications were used to
establish the following equation:
log f 3 ð
Hc
Hc
Þ ¼ 1:1993 logð Þ
Lh
Lh
ð23Þ
2.5.4. The overall head loss equation
At this step, it is time to find the final correlation of the data
using the model of equation Eq. (8). Accordingly, Eqs. (19), (21)
and (23) could be combined with Eq. (8) as follows:
log ðHLÞ ¼ log A
Vr
Vr
Hc
þ B 0:6705 logð Þ þ 0:7519 logð Þ þ 1:1993 logð Þ
Vc
Vf
Lh
ð24Þ
The values of the two constants or regression coefficients were
found to be: log A ¼ 3:5013 and B ¼ 1:4998 for 81 data points as
Fig. 6.
3. Results and discussion
If Eq. (24) is rearranged with the values of these constants, it
takes the following form as Eq. (25).
"
3:5013
HL ¼ 10
V r 0:6706
V r 0:7519
Hc 1:1993
ð Þ
ð Þ
ð Þ
Vc
Vf
Lh
#1:4998
By considering and comparing between all of data it indicated
that the minimum head loss obtained from Eq. (25) was 13.7%. This
value of loss occurred at 4 km h1 for forward speed, 1.38 for reel
index at 21 rpm for rotational speed of reel and 15 cm for height of
cutter bar. The interaction effects of identified treatments were the
mainly factor to values differences observed with another
researches. If the different variety of wheat accompanied by
changeable cutter bar speed, tine spacing, tine clearance over cutter bar, service life of cutter bar and different grain moisture content would be considered, the results would be different from
present study.
To minimize header losses, proper operation of the reel is very
important. As noted, one of factors affecting header loss is reel
index. It is recommended that the reel index be between 1.25
and 1.5. According to Table 2, this index is between 1.380 and
1.650. Although the range of variations of the index not in accordance with recommended conditions, but it is very close. This phenomenon could be due to any parameters such as field condition,
crop variety and type of combine harvester.
By using the dimensional analysis approach, it will be possible
to predict the header loss in all of the combine harvesters which
their characteristics arrangements confirm to range of dimensionless groups used in this research.
Acknowledgements
ð25Þ
Using the Eq. (25), care must be taken the limits imposed on the
values of the dimensional groups that are given in Table 2.
The authors would like to acknowledge Shiraz University for all
its support of this work.
References
3.1. Validation of the model
The developed model was tested against additional field data
for the validation purpose. In other words, 80 percent of data were
used to derive dimensional analysis models and 20 percent of data
were used for validation of the model. Results from F-test between
Table 2
Range of dimensionless groups used in this study.
Variable
groups
Definition
Range of
variation
HL
Percentage of loosed grain (%)
Ratio of Rotational speed of reel to
cutter bar speed
Ratio of Rotational speed of reel to
forward speed of combine harvester
Ratio of height of cutter bar to length of header
13.7–20
0.018–0.021
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Vf
Hc
Lh
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0.020–0.029
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Please cite this article in press as: Chaab, R.K., et al. Predicting header wheat loss in a combine harvester, a new approach. Journal of the Saudi Society of
Agricultural Sciences (2018), https://doi.org/10.1016/j.jssas.2018.09.002