View Factors
179
factor for radiation leaving object B and received by object A - FB-*. In
a simple conceptual model of outdoor radiation the sources would be the
sun, sky, and ground. For our purposes, a diffuse source of radiation like
the sky can be treated as a hemispherically-shaped object of exceedingly
large radius. In engineering, view factors are computed between objects;
whereas in environmental biophysics the interest is usually in view factors
between objects and sources of radiation. By considering the example of
a small sphere located inside of a large sphere, these two applications of
view factors can be related to each other. The view factor from the small
sphere to the large sphere is 1.0, because all the radiation leaving the
small sphere is received by the large sphere. Alternatively, all the view
of the small sphere is entirely occupied by the large sphere because the
small sphere cannot view any of itself. In contrast, the view factor from
the large sphere to the small sphere is given by the ratio of the sphere
areas (Asmll/Alarge) SO that all the radiation leaving the large sphere is
not received by the small sphere but some is received by the large sphere
itself. This fraction of radiation leaving the large sphere that impinges
on other areas of the same large sphere is the view factor between the
large sphere and itself (1 - Asmll/Alarge). AS the small sphere, which
is inside the large sphere, becomes smaller and smaller, the view factor
from the large sphere to the small sphere becomes small; but the view
factor between the small sphere and the large sphere remains 1.0. In
environmental biophysics we are usually interested in the view factor
between an object, such as the interior sphere in the example above which
might be a bird flying, and the imaginary sphere surrounding that object
representing the source of radiation, such as the sky and ground. Usually
the sphere of view surrounding the object has several sources of radiation
such as sky or ground, so the view of the object is divided up into the
various components that represent the various sources of radiation; but
the sum of all these view factors must always be 1 .O. If the exterior (large)
sphere in the example above is divided into two hemispheres, the view
factor between the interior (small) sphere and the exterior (large) upper
hemisphere is 0.5. Likewise the view factor between the interior (small)
sphere and the lower exterior (large) hemisphere is 0.5. If the interior
(small) sphere is replaced by an interior (small) cylinder or thin flat plate,
the view factor between this cylinder or thin flat plate and either exterior
hemisphere also is 0.5.
Frequently the thin flat plate case leads to the greatest confusion
because the area of thin flat plates is almost always specified by the
"one-sided" area or "silhouette" area by convention. You might normally
consider a 3 in. x 5 in. card to have an area of 15 in? because you tend to
use the convention of one-sided area. In this book, however, we consider
such a card to have an area of 30 in.2 because we always use the area of
the total surface (top and bottom). Because we generally are interested
in the view factor between an object and radiation originating from some
portion of a sphere, we omit the initial subscript denoting the object so
that a view factor between a leaf and the sky is given by Fsb not &f-sb.
179
factor for radiation leaving object B and received by object A - FB-*. In
a simple conceptual model of outdoor radiation the sources would be the
sun, sky, and ground. For our purposes, a diffuse source of radiation like
the sky can be treated as a hemispherically-shaped object of exceedingly
large radius. In engineering, view factors are computed between objects;
whereas in environmental biophysics the interest is usually in view factors
between objects and sources of radiation. By considering the example of
a small sphere located inside of a large sphere, these two applications of
view factors can be related to each other. The view factor from the small
sphere to the large sphere is 1.0, because all the radiation leaving the
small sphere is received by the large sphere. Alternatively, all the view
of the small sphere is entirely occupied by the large sphere because the
small sphere cannot view any of itself. In contrast, the view factor from
the large sphere to the small sphere is given by the ratio of the sphere
areas (Asmll/Alarge) SO that all the radiation leaving the large sphere is
not received by the small sphere but some is received by the large sphere
itself. This fraction of radiation leaving the large sphere that impinges
on other areas of the same large sphere is the view factor between the
large sphere and itself (1 - Asmll/Alarge). AS the small sphere, which
is inside the large sphere, becomes smaller and smaller, the view factor
from the large sphere to the small sphere becomes small; but the view
factor between the small sphere and the large sphere remains 1.0. In
environmental biophysics we are usually interested in the view factor
between an object, such as the interior sphere in the example above which
might be a bird flying, and the imaginary sphere surrounding that object
representing the source of radiation, such as the sky and ground. Usually
the sphere of view surrounding the object has several sources of radiation
such as sky or ground, so the view of the object is divided up into the
various components that represent the various sources of radiation; but
the sum of all these view factors must always be 1 .O. If the exterior (large)
sphere in the example above is divided into two hemispheres, the view
factor between the interior (small) sphere and the exterior (large) upper
hemisphere is 0.5. Likewise the view factor between the interior (small)
sphere and the lower exterior (large) hemisphere is 0.5. If the interior
(small) sphere is replaced by an interior (small) cylinder or thin flat plate,
the view factor between this cylinder or thin flat plate and either exterior
hemisphere also is 0.5.
Frequently the thin flat plate case leads to the greatest confusion
because the area of thin flat plates is almost always specified by the
"one-sided" area or "silhouette" area by convention. You might normally
consider a 3 in. x 5 in. card to have an area of 15 in? because you tend to
use the convention of one-sided area. In this book, however, we consider
such a card to have an area of 30 in.2 because we always use the area of
the total surface (top and bottom). Because we generally are interested
in the view factor between an object and radiation originating from some
portion of a sphere, we omit the initial subscript denoting the object so
that a view factor between a leaf and the sky is given by Fsb not &f-sb.