PHYSICAL PROPERTIES OF POTATO TUBERS CV. ANALYTIC ...

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

_____________________________________________________________________________________________________

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)



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




variable

friction coefficient

surface area (mm2)

M.J. DALVAND – PHYSICAL PROPERTIES OF POTATO … 119

_____________________________________________________________________________________________________

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.


_____________________________________________________________________________________________________

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-


_____________________________________________________________________________________________________

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


_____________________________________________________________________________________________________

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


_____________________________________________________________________________________________________

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


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


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


Coefficient of rolling friction for unpeeled potato


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


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-


_____________________________________________________________________________________________________

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


_____________________________________________________________________________________________________

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


_____________________________________________________________________________________________________

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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[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.

PHYSICAL PROPERTIES OF POTATO TUBERS CV. ANALYTIC ...

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