Physical Characteristics
Dr. Muanmai Apintanapong
Physical Characteristics
 Considering either bulk or individual units
of material.
– Shape, size, volume, specific gravity
surface area, bulk density and etc.
Size
Shape
Weight
Volume
Shape and size
 Inseparable in a physical object
 =  (sh, s)

=
Index
sh
=
shape
s
=
size
 Other applications
 =  (sh, s, o, p, f,…)
Y = b1X1+b2X2+b3X3+b4X4+b5X5
Irregular in shape
 Seeds, grains, fruits and vegetables are
irregular in shape
 important to know what criterion should
be used to decide when adequate number
of measurements has been made to define
the form of object.
 Griffith (1964) : related volume (V) to their
axial dimension (a)
V = a1b1 a2b2 a3b3 … anbn
log V = b1 log a1 + b2 log a2 +….+ bn log an
Criteria for describing shape and size
 Size : a representative dimension
 In fruit and cereal: 3 main projected area
– a = length
– b = width
– c = thickness
Average dimension
 Arithmatic mean size
length  width  thickness

3
 Geometric mean size
 (length width thickness)1 3
 Size based on volume
V   De  De  (6V  )1 3
6
3
Average dimension
 Size based on surface area
S A  Ds  Ds  (S A  )1 2
2
 Size based on projected area
Ap  Dp / 4  Dp  (4 Ap  )
2
12
Measuring Grain Dimension
Grain Type
very long
long
medium
short
Length (mm)
> 7.5
> 6.5 < 7.5
>5.5 < 6.5
< 5.5
Physical Properties>>shape
 The concept of shape
factor
– Geometric
dimensions (L,W,T)
of various objects
are plotted against
their volumes,
surface areas or
projected areas
– The slope of
regression line
yields shape factor
(α)
V
αv
LWT
SA
αSA
(LWT)2/3
Ap
αAp
(LWT)2/3
Example
Axial dimension (cm)
Weight
(g)
Volume
(cm3)
a
b
c
apples
7.0
6.76
5.64
145.5
180.3
potatoes
8.2
7.2
5.3
204.0
184.0
tomatoes
6.45
5.92
4.72
127.3
126.2
 Determine: v, density, equivalent diameter of
sphere, average diameter, geometric mean
diameter
Charted standards
 Compare longitudinal and lateral cross section
with the shapes listed on a charted standard
Roundness
 Measure of sharpness of the corners of the solid
 Ap = largest projected area in natural rest position
 Ac = area of smallest circumscribing circle
Roundness
r
Roundness 
NR
 r = radius of curvature as defined in figure
 R = radius of maximum inscribed circle
 N = total number of corners summed in
numerator
Roundness
r
Roundness 
R
 r = radius of curvature of the shapest
corner
 R = mean radius of object
Sphericity
di
Sphericity
dc
 di = diameter of the largest inscribed circle
 dc = diameter of the smallest
circumscribed circle
Sphericity
de
Sphericity
dc
dc
 de = diameter of a sphere of same volume of
object
 dc = diameter of the smallest circumscribed
sphere (usually the longest diameter of
object)
Sphericity


Vol of solid

Sphericity 
 Vol of circum scribed sphere


Sphericity 




abc 
6

 3 
a 
6

1
1
3
3
 bc 
 2 
a 
1
3


abc 

geom etricm eandiam eter

Sphericity
 6
m ajordiam eter
  a3 


 6

a = longest intercept
b = longest intercept normal to a
c = longest intercept normal to a and b
1
3

abc 3

1
a
Shape factor ()
 SAof spherehavingsam evolum e

Shape factor( )  
SAof object


Measurement of axial dimension
 Use photographics enlarger to determine
a, b, c
 Use shadowgraph
Resemblance to geometric bodies
 Shape can be approximated by one of the
following standard geometric shapes:
– Prolate spheroid
– Oblate spheroid
– Right circular cone or cylinder
Resemblance to geometric bodies
 Prolate spheroid
– Volume
V=
– Surface area
S=
A prolate spheroid is a
spheroid in which the polar
diameter is longer than the
equatorial diameter.
a, b = major & minor semi-axes of ellipse of rotation
1
e = eccentricity
2
 b  2
e  1    
V = volume
 a 


S = surface area
Resemblance to geometric bodies
 Oblate spheroid
– Volume
V=
– Surface area
S=
An oblate spheroid is a
rotationally symmetric ellipsoid
having a polar axis shorter than
the diameter of the equatorial
circle whose plane bisects it.
a, b = major & minor semi-axes of ellipse of rotation
1
e = eccentricity
2
 b  2
e  1    
V = volume
 a 


S = surface area
Resemblance to geometric bodies
 Frustum of right cone
– Volume
V=
– Surface area
S=
r1 & r2 = radii of base & top
h = altitude
A cone that has its apex aligned
directly above the center of its
base.
Right Circular Cylinder
 A right cylinder with bases that are circles.
Resemblance to geometric bodies
 Estimation of V and S in this manner
should be corrected.
 Correction factor is determined by finding
actual
volume
and
surface
area
experimentally and establish correction
factor for the typical shape of each variety
of product.
Average projected area
 Camera set up for recording the criterion
area (above left) of fruits and vegetables
for several orientations.
Average projected area
 Based on Theory of Convex body (Bannesen
and Fenchel, 1948)
– Sphere:
V

6
D 3 , S  D 2

2
3
 D 
V
6
  1
 3 
3
S
36
D 2
2


– Nonsphere:
V2
1

3
S
36
Polya & Szega (1951)
 Assume averaged projected area of convex
body = ¼ of surface area
For sphere:
V2
1

, S  4 Ap
3
S
36
2
V
1

3
36
4 Ap
Ap  1.21V
2
3
1
 9  3
K 
  1.21
 16 
For nonsphere: K  1.21
Volume and Density
 Platform balance method: for large objects
such as fruits and vegetables
wt. of displacedwater
V
wt. densityof water
wt. in air  sp. gr. of water
specific gravity 
wt. of displacedwater
Example
 Assuming a specific gravity of 1.0 and a weight
density of 62.4 lb/ft3 for water, using a platform
scale method, the volume and specific gravity of
an apple was determined as follows:
– Weight of apple in air = 0.292 lb
– Weight of container+water = 2.24 lb
– Weight of container+water+apple submerged =
2.61 lb
– Weight of displaced water = 2.61-2.24 = 0.37
lb
Specific gravity balance
 For smaller objects such as small fruits,
peas and beans, kernels of corn, etc.
Specific gravity balance
 If solid is heavier than water:
V
wt. in air  wt in water
wt. densityof water


wt. in air
SG of water
specific gravity  
wt
.
in
air

wt
in
water


 If solid is lighter than water (attach another
solid as sinker)


Wa object
SG of water
specific gravity  




W

W
both

W

W
sin
ker
w
a
w
 a

 Wa = wt. in air
 Ww = wt. in water
Specific gravity gradient tube
 Fast and accurate
 Ex: toluene & CCl4
(sp. gr. 0.87-1.59)
 Measure the height
after object reaches
equilibrium and
calculated and
compared with
calibration curve.
Air comparison pycnometer
The density of a solid in any form can be
measured at room temperature with the gas
comparison pycnometer. The volume of a
substance is measured in air or in an inert
gas in a cylinder of variable calibrated
volume. For the calculation of density one
mass measurement is taken after
concluding the volume measurement.
Air comparison pycnometer
Pycnometer method
 Specific gravity bottle and toluene
 Toluene (C6H5CH3) has the advantages of:
– Little tendency to soak into the kernel
– Low surface tension, enabling it to flow smoothly
over kernel
– Little solvent action on constituents of kernel
especially fats and oils
– High boiling point
– Not changing its specific gravity and viscosity on
exposure to atmosphere
– Having low specific gravity
Pycnometer method
 sg . gr. of tolueneat 20C  wt. of grain 

specific gravity  
 wt. of toluenedisplacedby grain 
Example
 Consider the volume measurement for a
sample of 16 corn kernels coated with
Pliabond
– Weight of sample = 4.4598 g
– Weight of pycnometer = 55.6468 g
– Weight of pycnometer+toluene = 78.2399 g
– Weight of pycnometer+toluene+sample =
79.6226 g
– Weight of pycnometer+water = 81.7709 g
Porosity
 Void volume or pore volume (empty space)
relative to total volume
volum eof void
porosity 
total volum e
volum eof void
void ratio 
volum eof solid
void ratio  porosity
porosity  f (m oisturecontent, particlesize)
Porosity tank
V2
void volum e
V1
Example
 To determine the porosity of dry shelled
corn, tank 2 of the apparatus is filled with a
sample of this corn to a bulk density of 47
lb/ft3. The pressure readings were P1 =
15.2 and P2 = 10.4 in Hg
Porosity
 Porosity is also referred to as packing
factor (PF):
solid densityof particles densityof packing
PF 
solid densityof particles
Porosity and bulk density
Weight and surface area
 W
V
 SA  KW
23
Surface area




Leaf and stalk surface area
Light planimeter
Indirect estimation (projected area)
Surface coating method
– Estimated by the weight of coating material
– Material is coated on grains and glass beads of
known surface area (control).
Surfaceareasample 
surfaceareaglass beads
Wglassbeads
 Air permeability method
Wsample
Shape, Size and Area
 Using image analysis
– The image analysis setup consists of a color CCD
camera and a circular lighting chamber connected to
a host Pentium II 400 MHz computer.
Top view of the Image Analysis Set up
CCD Camera
Illumination Chamber
Image Analysis Software
 Two image analysis software are available for extracting the
dimensional feature of rice kernels
 1. Image Tool 2: This program was developed at the
University of Texas Health Science center at San Antonio,
Texas and available from the internet
(http://ddsdx.uthscsa.edu/dig/download.html).
 2. Particle Image Analysis: This program was developed
by Procure Vision AB Ltd., Stockholm, Sweden and the
evaluation version is available from the internet
(http://www.acoutronic.com).