2011 vol. 74, 117-128
DOI: 10.2478/v10032-011-0010-x ________________________________________________________________________________________
Corresponding author:
e-mail: [email protected]
© Copyright by RIVC
PHYSICAL PROPERTIES OF POTATO TUBERS
CV. ANALYTIC CULTIVATED IN IRAN
Mohammad Jafar DALVAND
Department of Agricultural Machinery,
Faculty of Agricultural Engineering and Technology,
University of Tehran, Karaj, Iran
Received: March 10, 2011; Accepted: June 13, 2011
Summary
The objective of the experiments was to study some physical properties of
potato tubers, such as dimensions, weight, projected area, sliding and rolling
friction properties, in order to determine the best post-harvest options. Mean
values of weight, length, width, thickness and CPA were 136.69 g, 78.99 mm,
57.12 mm, 50.44 mm, and 33.12 cm2, respectively. The lowest values of the
coefficients of rolling and sliding friction were obtained for sheet glass. Tuber
mass was predicted based on the dimensions, projected area and volume. Linear
models and nonlinear models were investigated. The results indicated that best
model for predicting tuber mass was based on projected area with R2= 0.99.
key word: potato, mass, physical properties, friction properties, projected area
INTRODUCTION
In most industrial, developed and
developing countries, potato has par-
ticular importance in the food chain
among agricultural products. The
amount of energy in this product is
830 calories per kg. Quantitative and
quality developments in the produc-
tion of potato have been especially
important in Iran. In the 130 counties
where about 75% of the world’s popu-
lation lives the area of potato cultiva-
tion is 20 million hectares. The annual
production of potato is 280 million
tons, which makes it the fourth ma-
jor crop plant in the world after wheat,
rice and corn (Ahangarnezhad 2009).
Physical characteristics of agri-
cultural products are the most im-
portant parameters for the designing
of grading, conveying, processing,
and packaging systems. Among these
physical characteristics, mass, vol-
ume, projected area, and center of
gravity are the most important in siz-
ing systems (Malcolm et al. 1986).
Other important parameters are width,
length, and thickness (Mohsenin
1986). The frictional properties (an-
gles of repose and coefficients of fric-
tion) are important in designing
equipment and machines for harvest-
ing, conveying, separating, sorting,
handling, processing, storage, etc. The
coefficient of static friction is used
118 VEGETABLE CROPS RESEARCH BULLETIN 74
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to determine the angle at which chutes
must be positioned in order to achieve
consistent flow of material through
the chute. In addition, this coefficient
is important in the designing of con-
veyors because friction is necessary to
hold the potato tuber to the conveying
surface without slipping or sliding
backward (Razavi et al. 2007).
The quality of food materials can
be assessed by measuring their densi-
ties. Density data of foods are re-
quired in separation processes, such as
centrifugation and sedimentation, and
in pneumatic and hydraulic transport
of powders and particulates (Sahin &
Gülüm Sumnu 2006, Gorji
Chakespari et al. 2010).
There are some situations in
which it is desirable to determine
relationships among physical charac-
teristics; for example, fruits are often
graded by size, but it may be more
economical to develop a machine
which grades by weight. Therefore,
the relationship between weight and
the major, minor and intermediate
diameters is needed (Stroshine &
Hamannd 1994).
Determining a relationship be-
tween mass, dimensions and projected
areas is useful and applicable in sizing
by weight (Marvin et al. 1987). The
physical properties of different fruits
and vegetables have been determined
by other researcher; caper fruit (Sessiz
et al. 2007), potato (Tabatabaeefar
2002), apple (Meisami-asl et al. 2009).
Safa and Khazaei (2003) studied the
physical properties of pomegranate and
found models of predicting fruit mass
based on the dimensions, volume and
surface area. Taheri-Garavand et al.
(2010) studied hydro-sorting of potato
and tomato based on some physical
characteristics.
The objective of this study was
to investigate some physical proper-
ties of the potato tuber, namely the
linear dimensions, unit mass and vol-
ume, sphericity, densities, porosity,
projected area, as well as the coeffi-
cients of rolling and sliding friction
against three structural surfaces. The
mass of tubers was then predicted
based on the dimensions, projected
area and volume. This information
will be used in the design and devel-
opment of sizing systems.
Nomenclature
L
W
T
CPA
PAL
PAW
PAT
Dg
R2
V
Vsp
Vosp
F
length (mm)
width (mm)
thickness (mm)
criteria projected area (cm2)
projected area (cm2)
projected area (cm2)
projected area (cm2)
geometric mean diameter (mm)
coefficient of determination
volume (cm3)
volume of ellipsoid (cm3)
volume of oblate spheroid (cm3)
force
ρb
ρt
λ
Sp
M
a
b
c
d
k
μ
S
bulk density (kg·cm-3
)
density (kg·cm-3
)
porosity
sphericity
mass (g)
parameter of equation
parameter of equation
parameter of equation
parameter of equation
variable
friction coefficient
surface area (mm2)
M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 119
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Materials and methods
1. Materials
Potato tubers (cv. Analytic) were used
for all the experiments in this study.
The tubers were obtained from the
Seed and Plant Breeding and Im-
provement Institute, Karaj, Iran (Lon-
gitude: 51o21'N, Latitude: 36
o12'E).
The initial moisture content of the
potato tubers was determined using
the oven method (ASAE Standard
1998) and obtained as 82% w.b. Some
of the samples for frictional tests were
manually peeled.
2. Methods
2.1 Physical properties
The physical properties of potato tu-
bers, such as mass, volume, bulk den-
sity, density, dimensions, projected
area, porosity and surface area, were
measured. The mass (M) of each pota-
to was measured to 0.01 g accuracy
with a digital balance.
To determine the average size of
the potato tubers, one hundred sam-
ples were randomly selected. Meas-
urements of the three major perpen-
dicular dimensions of the tubers,
namely, the length (L), width (W) and
thickness (T), were carried out with a
micrometer with an accuracy of 0.01
mm. Potato tuber volume (V) was
obtained with the water displacement
method (Mohsenin 1986, Stroshine &
Hamannd 1994); then the density of
each sample was calculated.
Density is calculated by dividing
the weight of samples by the volume
obtained with the water displacement
method (Stroshine & Hamannd 1994).
Bulk density was determined using
the mass-volume relationship by fill-
ing an empty plastic container of pre-
determined volume with samples and
weighing it; then the bulk density was
determined by dividing the weight of
the samples by the container volume
(Fraser et al. 1978, Ghabel et al.
2010). Geometric mean diameter (Dg)
and surface area (S) were determined
by using the following formula, re-
spectively (Mohsenin 1986):
(1)
(2)
Density was obtained as follows:
(3)
where: ρt is true density (kg·cm-3
), M is
tuber mass (g), V is tuber volume (cm3)
(Mohsenin 1986).
Bulk density was obtained as follows:
(4)
where: ρb is apparent density (kg·cm-3
),
Mt is mass of tubers (g), Vc is container
volume (cm3) (Mohsenin 1986).
The porosity (λ) of a bulk sample
was computed from the values of true
density and bulk density using the
relationship given by Mohsenin
(1986) as follows:
(5)
where: pb is the bulk density and pt is the
true density.
Projected areas were determined
with the image processing method. In
order to obtain projected areas, WinA-
rea_UT_06 system (Keramat Jahromi
et al. 2007) was used (Fig. 1). The
WinArea_UT_06 system comprises
the following components:
1. Sony still camera, model CCD-
TRV225E,
2. Device for preparing media for
picture taking,
3. Capture Card named Winfast,
model DV2000,
4. Computer software programmed in
Visual Basic.
120 VEGETABLE CROPS RESEARCH BULLETIN 74
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Fig. 1. Apparatus used for determining
projected areas
Three mutually perpendicular ar-
eas, PAL, PAW, PAT, were measured
with an area meter. Total error for
those objects was less than 2%. This
method has been used and reported by
several researchers (Khoshnam et al.
2007). The average projected area as a
criterion for the sizing machine was
proposed by Mohsenin. The average
projected area (known as criteria area,
CPA) was determined from
(Mohsenin 1986):
(6)
The sphericity, Sp (%), defined as the
ratio of surface area of a sphere hav-
ing the same volume as that of fruit to
the surface area of the fruit, was de-
termined using the following formula:
(7)
Other parameters were calculated
from the following equations
(Mohsenin 1986):
(8)
(9)
Where Vsp is the volume of an ellipsoid
and Vosp is the volume of an oblate sphe-
roid.
2.2 Frictional properties
2.2.1 Method for coefficient of static
friction
The coefficients of static friction on
three different frictional surfaces,
namely galvanized iron, wood, and
glass were measured for potato tubers
using the inclined plate method (Al-
Maiman & Ahmad 2002). The friction
tests were replicated three times for
each surface. The coefficient of static
friction was calculated from the fol-
lowing equation:
μs = tan(α) (10) where: α is the angle of inclination at
which samples start to slide down.
2.2.2 Method for coefficient of dy-
namic friction
The coefficient of dynamic friction
was determined with the same tubers
in a topless and bottomless plywood
box with dimensions of 250 × 250 ×
90 mm3. The box placed on the test
surface was filled with a known quan-
tity of potato tubers and force was
applied to it until it moved uniformly
with a gentle pull. The friction tests
were replicated three times for each
surface. For each replication, the box
was emptied and refilled with a dif-
ferent sample. The coefficient of dy-
namic friction was calculated as fol-
lows (Amin et al. 2004, Puchalski et
al. 2003):
(11)
The friction force was measured using
a digital pull force gauge (Model
DS2-100N, IMADA).
2.3 Mass modelling
Many spreadsheet programs can per-
form multiple regressions. Spread-
sheet software, Microsoft EXCEL and
SPSS, were used to analyze the data
and determine regression models be-
M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 121
_____________________________________________________________________________________________________
tween the parameters of either linear
or polynomial form. When evaluating
the usefulness of such regression
analyses, it is necessary to know how
the data fit the model. In order to es-
timate tuber mass from the measured
dimensions (length, projected area,
and volume), the following two cate-
gories of models were suggested.
1. Regression models with linear vari-
ables for potato tubers.
This category was divided into three
classifications as follows:
1.1. Single or multiple variable re-
gressions of potato tuber dimensional
characteristics: length (L), width (W)
and thickness (T).
1.2. Single or multiple variable re-
gressions of potato tuber projected
areas.
1.3. Single regression of potato tu-
ber mass based on the measured (ac-
tual) volume and volumes of the
shapes assumed (oblate spheroid and
ellipsoid).
In the case of the first classification,
mass modelling was accomplished
with respect to the length, width and
thickness as follows:
M= aL + bW + cT +d
In the second classification model,
mass modelling of potato tubers was
based on mutually perpendicular pro-
jected areas as follows:
M= aPAL + bPAW + cPAT + d
In the third classification, the mass
and surface area can be estimated as
either a function of volume of the
supposed shape or the measured vol-
umes, as represented by the following
expressions:
M= aV + b
M= aVsp + b
M= aVosp + b
2. Regression models with nonlinear
variables for potato tubers
Three classifications were considered
similar to those in the previous cate-
gory and then, in each classification,
mass modelling of potato tuber was
estimated based on single variable
regressions with the following models:
M= a+b(k)+c(k)2
M= a(k)b
M= a(e)b×k
where: M is mass (g), k is the value of a
parameter that we want to find its rela-
tionship with mass (independent parame-
ter), a, b, and c are curve-fitting parame-
ters, which are different in each equation.
2.4 Surface area modelling
In order to estimate surface area from
the measured volume, volume of an
ellipsoid and volume of an oblate
spheroid the following models were
suggested.
S= aV+ b
S= aVsp + b
S= aVosp + b
where: S is the surface area of sample,
a and b are curve-fitting parameters
which are different in each equation
RESULTS AND DISCUSSION
1. Physical properties
A summary of the physical properties
of potato tubers (cv. Analytic) is
shown in Table 1. These properties
were found at a specific tuber mois-
ture level (82%, w.b.).
In a study conducted by Ja-
natizadeh et al. (2008), sphericity
values of Iranian apricot differed sig-
nificantly among the tested cultivars;
the mean values were 0.971, 0.917,
0.973, 0.925, 0.923, and 0.875 for
Shams, Nakhjavan, Djahangiri, Sefide
122 VEGETABLE CROPS RESEARCH BULLETIN 74
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damavand, Shahroud-8, and Gheysi-2
cultivars, respectively.
Kheiralipour et al. (2008) report-
ed the length, width, and thickness of
apple fruit (cv. Redspar) as 57.13,
66.98, and 62.60 mm, respectively.
Table 1. Physical attributes of potato tuber
Minimum Maximum Mean Std. Deviation
M (g) 85.11 191.44 136.69 32.05
L (mm) 61.38 92.26 78.99 8.38
W (mm) 48.15 67.00 57.12 5.38
T (mm) 41.50 62.86 50.44 5.65
Dg (mm) 56.16 73.10 66.13 5.19
PAL (cm2) 26.07 52.62 39.64 6.97
PAW (cm2) 25.51 45.48 34.17 5.77
PAT (cm2) 19.04 32.18 25.55 4.01
CPA (cm2) 23.95 43.08 33.12 5.43
ρt (kg·cm-3
) 1030 1090 1060 10
ρb (kg·cm-3
) 620 750 680 30
Vsp (cm3) 73.15 158.84 120.29 26.59
Vosp (cm3) 76.25 198.30 137.41 34.59
V (cm3) 80.00 180.00 128.69 29.70
porosity 29.45 41.15 35.64 2.92
Sphericity 0.76 0.95 0.84 0.05
S (cm2) 99.04 167.81 138.16 21.23
As seen in Table 1, the mean
values of bulk density and density
were reported as 680 and 1060 kg·cm-
3, respectively. In a study conducted
by Kheiralipour et al. (2008), the
mean values of fruit density for Red-
spar and Delbarstival apple cultivars
were 811.49 and 759.02, respectively.
2. Frictional properties
The experimental data for the coeffi-
cient of sliding friction for potato
tubers in two states (peeled and un-
peeled) on frictional surfaces of glass,
galvanized iron sheet, and wood are
reported in Table 2. As presented in
Table 2, the coefficient of sliding fric-
tion on the glass surface (0.27-0.35)
was the lowest, while the greatest val-
ue was obtained on the wooden surface
(0.52-0.58) for unpeeled potatoes.
In a similar research, Janatizadeh
et al. (2008) studied frictional proper-
ties of Iranian apricot. They reported
that on a galvanized iron sheet the
highest coefficient of static friction
was obtained for Gheysi-2 fruit with a
mean of 0.308, while the correspond-
ing value was 0.141 for Shahroud-8 as
the lowest coefficient (Janatizadeh et
al. 2008). Also, static friction coeffi-
cients on sheet iron, galvanized sheet
iron, and rubber surfaces were report-
ed as 0.201, 0.181, 0.281 for the culti-
var Zerdali (Hacisefrogullari et al.
2007).
The variance analysis of the data
indicated that the difference in the
coefficient of sliding friction for un-
peeled and peeled potato tubers was
significant at a 1% probability level.
The coefficient of sliding friction on
M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 123
_____________________________________________________________________________________________________
glass, galvanized iron and wood sur-
faces for peeled potato tubers was
greater than the corresponding values
for unpeeled potatoes.
Table 2. Sliding friction properties
Minimum Maximum Mean Std. Deviation
Coefficient of sliding friction for unpeeled potato
Galvanized iron 0.42 0.49 0.45 0.03
Glass 0.27 0.35 0.31 0.03
Wood 0.52 0.58 0.55 0.02
Coefficient of sliding friction for peeled potato
Galvanized iron 0.49 0.55 0.52 0.02
Glass 0.34 0.40 0.37 0.02
Wood 0.60 0.64 0.61 0.02
As seen in Table 3, the mean
values of the coefficient of rolling
friction for unpeeled potatoes on gal-
vanized iron, glass and wood was
0.25, 0.18 and 0.35, respectively. The
values for peeled potatoes were 0.31,
0.23 and 0.42, respectively.
The variance analysis of the data
indicated that the difference in the
coefficient of rolling friction for un-
peeled and peeled potato tubers was
significant at a 1% probability level.
The coefficient of rolling friction on
glass, galvanized iron and wood sur-
faces for peeled potato tubers was
greater than the corresponding values
for unpeeled potatoes.
Table 3. Rolling friction properties
Minimum Maximum Mean Std. Deviation
Coefficient of rolling friction for unpeeled potato
Galvanized iron 0.23 0.28 0.25 0.02
Glass 0.16 0.20 0.18 0.01
Wood 0.32 0.36 0.35 0.01
Coefficient of rolling friction for peeled potato
Galvanized iron 0.28 0.33 0.31 0.01
Glass 0.20 0.27 0.23 0.02
Wood 0.38 0.43 0.42 0.01
According to the experimental
data in Tables 2 and 3, when potato
tubers are put on an inclined surface,
they will roll down rather than slide
down.
Sessiz et al. (2007) studied coef-
ficients of static and dynamic friction
on four different surfaces, namely,
galvanized steel, plywood, rubber,
and metal steel for caper fruit. On all
of these surfaces, the values of the
coefficient of static friction were
higher than those of the coefficient of
dynamic friction.
3. Mass modelling
3.1 Linear models
The results of the linear models in the
three classifications for predicting
mass of potato tubers based on geo-
124 VEGETABLE CROPS RESEARCH BULLETIN 74
_____________________________________________________________________________________________________
metrical attributes (dimensions, pro-
jected area and volume) are shown in
Table 4.
For potato tubers, in the case of
mass modelling based on dimensional
characteristics including length, width
and thickness, the best option was
based on all of them and the model
was as follows:
M=-265.98+1.74L+2.56W+2.36T,
R2=0.95
However, measurement of three di-
ameters is needed for this model,
which makes the sizing mechanism
more complex and expensive. Mono-
chromatic current is used in on-line
sorting systems, which are cheap.
The results indicated that the
best model in the second classification
for predicting mass of potato tubers
was based on the criteria projected
areas (CPA) with this equation:
M= -57.77+5.87CPA, R2=0.99
As shown in Table 4, the best
model in the third classification for
predicting mass of potatoes was based
on the measured volume, with this
equation:
M= -2.04+1.08V, R2=0.98
Khanali et al. (2007) used this
classifications for mass and volume
modelling of tangerine fruit. They
reported that, based on their results,
mass and volume modelling on the
basis of the intermediate diameter,
any projected area, and the measured
volume are the best models.
Among all of the linear models
in these classifications, the best model
was based on the criteria projected
area (CPA), as shown in Fig 2.
Table 4. Linear models for predicting the mass of potato tubers
Independent
variable Model Regression R2
dimensions
L M=a+bL M= -111.29+3.13L 0.82
W M=a+bW M= -107.65+4.28W 0.72
T M=a+bT M= -39.76+3.50T 0.68
L,W M=a+bL+cW M= -182.45+2.34L+2.35W 0.80
T,W M=a+bT+cW M= -241.40+3.91W+3.08T 0.84
L,T M=a+bL+cT M= -182.92+2. 65L+2.19T 0.81
L,T,W M=a+bL+cW+dT M= -265.98+1.74L+2.56W+2.36T 0.95
projected
area
PAL M= a+bPAL M= -40.71+4.47 PAL 0.95
PAW M= a+bPAW M= -49.11+5.43 PAW 0.97
PAT M= a+bPAT M= -54.34+7.47 PAT 0.92
CPA M=a+b(CPA) M= -57.77+5.87CPA 0.99
PAL, PAW M= a+bPAL+cPAW M= -49.36+1.99 PAL+3.13PAw 0.98
PAL, PAT M=a+bPAL+ cPAT M= -56.75+3.04 PAL+2.85PAT 0.98
PAW, PAT M=a+bPAW+cPAT M= -59.93+3.92 PAw +2.44PAT 0.98
PAL,PAW,PAT M=a+bPAL+cPAw+
dPAT
M=-58.78+1.66PAL+2.19PAw+
2.14PAT 0.98
volume
V M=a+bV M= -2.04+1.08V 0.98
Vsp M=a+bVsp M= -5.09+1.18 Vsp 0.96
Vosp M=a+bVosp M= 27.94+0.72 Vosp 0.81
M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 125
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Fig. 2. Potato mass model based on crite-
ria projected area
Fig. 3. Potato mass model based on meas-
ured volume
3.2 Nonlinear models
The best model in the first classifica-
tion was the exponential model based
on the major diameter (L), with the
following equation:
M= 0.08(L)1.84
, R2 =0.71.
The best model in the second
classification was the quadratic model
based on the first projected area
(PAL), with the following equation:
M= -118.07+9.52(PAL) -0.06(PAL)2,
R2 =0.96
In a study conducted by Khanali
et al. (2007), the recommended equa-
tion for mass modelling of tangerine
fruit based on projected area was
based on the second projected area,
with the following equation:
M=0.64 (PA2)1.47
, R2 = 0.89
The best model in the first classi-
fication was the exponential model
based on the measured volume (V),
with the following equation: M=
1.01(V)1.01
, R2 =0.97
In a study conducted by Khanali
et al. (2007), the best model for pre-
dicting fruit mass was based on the
actual volume, with the following
equation:
M = 0.99 V - 5.52, R2 = 0.96
Among all of the nonlinear mod-
els, the recommended model was the
exponential model based on the
measured volume (V) shown in Fig. 3.
Khoshnam et al. (2007) reported that,
from an economic and agronomical
point of view, a suitable grading sys-
tem of pomegranate mass was ascer-
tained based on fruit thickness as a
nonlinear relationship:
M = 0.06T2- 4.11T + 143.56, R
2 = 0.91.
According to the analytical data
in Table 4, the linear models applied
to the data in this study generally had
higher R2 in comparison with the
nonlinear models.
4. Surface area modelling
As seen in Table 5, the best model for
surface area modelling based on di-
mensional characteristics including
the measured volume, volume of an
ellipsoid and an oblate spheroid, the
best attribute was the volume of an
ellipsoid, with the following equation:
S= 42.20+0.80 Vsp, R2= 0.99
126 VEGETABLE CROPS RESEARCH BULLETIN 74
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Table 5. Linear models for predicting the surface area of potato tubers
Independent
variable Model Regression R
2
V S=a+bV S= 48.31+0.70V 0.96
volume Vsp S=a+bVsp S= 42.20+0.80 Vsp 0.99
Vosp M=a+bVosp S= 66.50+0.52 Vosp 0.79
This indicated that the surface
area of a potato tuber was more like
the surface area of an ellipsoid. Meas-
uring the actual volume is a time-
consuming task, therefore, surface
area modelling based on it is not rea-
sonable; consequently, it seems ap-
propriate that the surface area model-
ling of potato tubers be accomplished
based on the volume of the assumed
ellipsoid.
CONCLUSIONS
A number of physical attributes and
their relationship with the mass of
potato tubers were examined in this
study. On the basis of the results it
can be concluded that:
1. The difference between the coeffi-
cient of sliding friction and rolling
friction for unpeeled and peeled
potato was significant at a 1%
probability level.
2. The coefficient of sliding friction
on glass, galvanized iron and wood
surfaces for peeled potatoes was
greater than the value obtained for
unpeeled potatoes, which may be
due to the fact that a peeled potato
tuber has a wet surface.
3. The coefficient of rolling friction
with respect to glass, galvanized
iron and wood surfaces for peeled
potatoes was greater than the value
obtained for unpeeled potatoes,
which may be due to the fact that a
peeled potato tuber has a wet sur-
face.
4. From an economic point of view, a
suitable grading system for potato
tuber mass was ascertained based
on the length, expressed as the lin-
ear relation:
M= -111.29+3.13L, R2= 0.82
5. The mass model recommended for
sizing potatoes based on a project-
ed area had a linear form:
M= -49.11+5.43 PAW, R2= 0.97
6. The mass model recommended for
sizing potatoes based on the vol-
ume of an ellipsoid was a linear
model:
M= -5.09+1.18 Vsp, R2= 0.96
7. The recommended equation for
calculating the surface area of po-
tato tubers based on the volume of
an ellipsoid was in the following
form:
S= 42.20+0.80 Vsp, R2= 0.99
8. which can be used in the peeling
process for estimating the amount
of the skin to be peeled.
Acknowledgments
The author wishes to thank the University
of Tehran for the support in this project.
The author is also grateful to Zahra Sa-
mari for their help.
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M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 127
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[DOI: 10.2478/v10032-010-0026-7]
WŁAŚCIWOŚCI FIZYCZNE BULW ZIEMNIAKA (odm. ‘ANALYTIC’)
UPRAWIANEGO W IRANIE
Streszczenie
Celem niniejszej pracy było zbadanie niektórych właściwości fizycznych bulw
ziemniaka, takich jak wymiary, masa, pole powierzchni rzutu, właściwości tarcia śli-
zgowego i tocznego, w celu scharakteryzowania najlepszych opcji pozbiorczych. Śred-
nie wartości masy, długości, szerokości, grubości i powierzchni rzutu wynosiły odpo-
wiednio 136,69 g, 78,99 mm, 57,12 mm, 50,44 mm i 33,12 cm2. Najniższą wartość
tocznego i ślizgowego współczynnika tarcia stwierdzono dla szklanej tafli. Następnie
określano masę na podstawie wymiarów, powierzchni rzutu i objętości. Badano modele
liniowe i nieliniowe. Wyniki wykazały, że najlepszy model do przewidywania masy jest
oparty na polu powierzchni rzutu przy R2= 0.99.
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