Eighth International IBPSA Conference
Eindhoven, Netherlands
August 11-14, 2003
SHAPE FACTOR CALCULATION AND VISUALIZATION FOR THE
INFLUENCE OF THE THERMAL ENVIRONMENT ON THE HUMAN BODY
Masaki Manabe1, Hitoshi Yamazaki2, Koji Sakai1
Oita University, 700, Dan-no-haru, Oita, 870-1192, Japan
2
Kanto Gakuin University, kanazawa-ku, Yokohama, 236-8501, Japan
1
ABSTRACT
The purpose of this paper is to explain the indoor thermal
radiation environment of the human body in detail. Using a
3-D human body model, shape factor calculations between a
human body and surroundings are executed. First, the shape
factor between the human body and each surface of the room
is calculated. The human body is placed in the center of the
room. The shape factor results are visualized by VRML.
Generated VRML images indicate the influence of thermal
radiation, which the human body receives from the room
surfaces. Second, the shape factor between the human body
and surroundings (the room surfaces and some people) is
calculated. Some "people influence" on the subject's human
body is shown. And the shape factor variation with body
position in the room is shown in detail.
INTRODUCTION
The human body always receives thermal radiation from the
environment. Usually, however, each body part receives a
different amount of thermal radiation. In order to measure this
indoor thermal radiation, it is necessary to calculate shape
factors between each fraction of the human body and each
surrounding surface. In previous studies, shape factors for the
whole body were obtained by photography (Fanger, 1970), or
by numerical methods (Olsen, 1989, Tanabe, 2000, Manabe,
2002). In this paper we report the development of a program
for these shape factor calculations.
Figure 1 Virtual cube and calculation point
Since the number of grid cells decides the shape factor
accuracy, it is necessary to choose a suitable number of
divisions. We adopted 90000 divisions of each cubic face.
EFFECTIVE RADIATION AREA
The effective radiation area is calculated from the shape factor
between each fraction of the human body and each
surrounding surface. The human body is viewed as consisting
of n fractions, in an enclosure consisting of m surfaces. Fij is
the shape factor between surface i of the body with area Ai,
and surrounding surface j. A part of the body consists of
fractions n1 to n2. The following equations represent the
effective radiation area Aeff and part of the effective radiation
area PAeff.
SHAPE FACTOR CACULATION
BASIC CACULATION PROCEDURE
There are several calculation methods to obtain these shape
factors. The Hemi-Cube algorithm (Cohen, 1985) is one of
the typical methods of calculating shape factor. The algorithm
uses the hemi-cube, but we have adopted a calculation
method using a virtual cube (Manabe, 2001). The shape
factor calculation procedure is outlined as follows.
(1) Each face of the cube, except the bottom, is divided into
small grid cells. (2) Calculate the shape factor between a
fraction of the center of the bottom cube face and each cell
(Yamazaki, 1983). (3) Place a virtual cube on a calculation
point (Figure 1). (4) Execute a perspective projection of
human body on each cubic face (except for the bottom face).
(5) The total shape factor for each cell containing the drawn
perspective produces the shape factor of the human body.
SHAPE FACTOR OF WALLS
Shape factor Fhk between a body and a surrounding surface k
is calculated from the following equation using the effective
radiation area Aeff.
Therefore, the shape factor Fpk between a surrounding
surface and a human body part p is represented by the
following equation.
- 799
791 -
Table 1 Effective radiation area factor
(Upper: body area [m2], Lower: effective radiation area factor)
(1)Standing
Nude
(2)Standing
Clothed
(3)Seated
Nude
(4)Seated
Clothed
(5)
Walking1
Nude
Figure 2 Standing nude and clothed models
(6)
Walking2
Nude
(A)
Body
(B)
Head
(C)
Trunk
(front)
(D)
Trunk
(back)
(E)
Arm
(F)
Leg
1.71
0.80
2.13
0.76
1.72
0.75
2.18
0.71
1.71
0.82
0.13
0.96
0.13
0.95
0.13
0.96
0.13
0.94
0.13
0.96
0.29
0.82
0.35
0.79
0.26
0.75
0.30
0.71
0.29
0.85
0.28
0.82
0.33
0.80
0.32
0.84
0.39
0.85
0.28
0.84
0.27
0.56
0.36
0.51
0.27
0.56
0.36
0.50
0.73
0.84
0.95
0.80
0.74
0.74
1.00
0.71
(right)
(right)
0.14
0.65
0.37
0.85
(left)
(left)
0.14
0.65
0.37
0.82
(right)
(right)
0.14
0.65
0.37
0.87
(left)
(left)
0.14
0.65
0.37
0.87
1.71
0.83
0.13
0.96
0.29
0.85
0.28
0.85
FFECTIVE RADIATION AREA OF HUMAN BODY
Shape factor calculations between a human body and surfaces
of enclosure have been performed, and the effective radiation
area of a human body obtained. Figure 2 shows the standing
nude and clothed body model. Figure 3 shows the seated
nude and clothed body model. Figure 4 shows two walking
nude body models. These figures have colored corresponding
parts. Body parts are head, trunk, hands and legs.
Figure 3 Seated nude and clothed models
Table 1 summarizes the calculation results and shows the
effective radiation area and factor of the body and parts. Table
1 of (1) - (6) is the body model type and table 1 of (A) - (F) is
the body and body parts. Each cell of table 1 consists of two
values: body area (upper) and effective radiation area factor
(lower). In (1) - (4) line, cells of body parts (E) and (F) have
values for a hand or a leg, because of their symmetrical shape.
But In (5) - (6) line, cells of body parts (E) and (F) are right
and left.
Figure 4 Two walking nude models
EFFECTIVE RADIATION AREA
CALCULATION
HUMAN BODEY MODEL
The cross-sectional shape of a standing nude body (young
boy, height 167 cm, weight 60 kg) was measured. Generating
triangles between measurement sections, the 3D solid nude
human body model was created. Also, measuring the standing
body in a business suit, the 3D clothed human body model
was created. The 3D standing nude body model consists of
2972 triangles, and the 3D standing clothed body model has
the same number of triangles. Rotating joints of the 3D
standing body using the body data generation program, the
other 3D posture models were created. The created four
posture models are: standing nude, standing clothed, seated
nude and seated clothed. The other created two models are
walking body models: one model is beginning to walk
(moving leg) and the other model is walking (moving trunk).
These values of cells indicate that different postures have
different values. The effective radiation area factor of the nude
body is from large to small in the order of the seated body,
standing body and walking body. And clothed bodies are in
the same order. Because body posture has shifted to a more
open state from a more compact state, the body is more easily
influenced by thermal radiation.
SHAPE FACTOR DISTRIBUTION MAP OF
HUMAN BODY
Shape factor simulations between a human body and room
surfaces are executed and the results are visualized for the
purpose of understanding the details of the influence of the
thermal radiation environment on the human body. A human
body was placed at the center on the floor, and the shape
factor between the body and a room surface was calculated.
The subject human body is the standing nude, and the room
size (WDH) is 10x9x3 [m]. The simulation model is shown
in Figure 5.
- 800
792 -
Figure 5 Room and subject position
Shape factor simulation results are visualized using VRML
(Virtual Reality Modeling Language). Shape factor
calculations for each room surface are expressed with a gray
scale of the human body's triangles. The shape factor
distribution maps with smoothing representation are shown in
Figures 6 through 9. The shade on the human body indicates
the shape factor value.
Shape factor 0.0 - 1.0 corresponds to black - white in Figures
6 and 7, and in Figures 8 and 9, the shape factor 0.0 - 0.5
corresponds to black - white. Shade of these figures expresses
the strength of thermal radiation received from the room.
Figure 6 is the floor shape factor distribution map, Figure 7 is
the ceiling one, Figure 8 is the front wall one, and Figure 9 is
the right wall one. These figures clearly demonstrate that the
shape factor changes greatly with human body part.
Figure 6 Floor shape factor distribution map
Figure 7 Ceiling shape factor distribution map
CASE OF PEOPLE IN A ROOM
Consider a classroom with some people in the room. In this
case, people who exist in a subject's surroundings affect the
subject's thermal radiation environment. Moreover, thermal
radiation to the subject from each room surface is interrupted
by the surrounding bodies.
In order to analyze such a thermal environment, a simulation
is executed using a 3D human body model. A body model is
placed in the center of the floor, and some people are arranged
in the room around the subject. The shape factor between the
subject's human body model and the surroundings is
determined by simulation. The size of the room used for this
calculation is the same as in Figure 5.
Simulations are executed for 4 cases: a room occupied by 1
person, a room occupied by 9 people, a room occupied by 25
people, and a room occupied by 49 people. In all cases, the
number includes the subject. All human bodies are the same.
Figure 10 is the room plan occupied by the 9 people, and
Figure 11 is the generated VRML image in3D of the 9 people
standing in the room. Figures 12 13 are for the 25 person case,
and Figures 14 and 15 are for the 49 person case. In addition,
Figure 16 is the VRML image of the seated 49 person case.
The shape factor between the body of the subject placed in the
center of the room and each surface of the room is calculated
for these several cases.
- 801
793 -
Figure 8 Front wall shape factor distribution map
Figure 9 Right wall shape factor distribution map
Figure 10 Plan of room occupied by 9 people
Figure 11 Room occupied by 9 people
Figure 12 Plan of room occupied by 25 people
Figure 13 Room occupied by 25 people
Figure 14 Plan of room occupied by 49 people
Figure 15 Room occupied by 49 people
Simulations were executed for the standing nude body and
the seated nude body. These results are shown in Figures 17 24. Figure 17 is the case of the standing subject in the center
of the room. Figure 18 is the seated subject. These figures
show the shape factor between the body and each surface of
the room, and between each part of the body and each surface
of the room. The vertical axis is shape factor, and the
horizontal axis is body parts, wherein [Body] means whole
body, [Head] means head, [F-Trunk] means front trunk,
[B-Trunk] means back trunk, [R-arm] means right arm,
[L-arm] means left arm, [R-Leg] means right leg, and [L-Leg]
means left leg. For example, in Figure 17 the shape factor
between the right leg and the floor is 0.51.
Figure 16 Room occupied by 49 seated people
- 802
794 -
0.6
0.5
Floor
Shape Factor / Standing, Nude / 0
0.4
Celing
0.5
Front
0.4
Back
0.3
0.6
Floor
Shape Factor / Seated, Nude / 0
Celing
Front
Back
0.3
Right
Left
Right
0.2
0
0
Left
F-
Bo
dy
H
ea
d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0.1
Bo
dy
0.1
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0.2
Figure 17 Shape factor / Standing-01
Figure 18 Shape factor / Seated-01
0.6
0.6
Floor
Celing
0.4
Front
0.4
0.3
Back
0.3
Right
0.2
Left
0.1
Others
Shape Factor / Seated, Nude / 8
0.5
Celing
Front
Back
Right
0.2
Left
0.1
Others
0
Bo
dy
Bo
dy
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0
Figure 19 Shape factor / Standing-09
Figure 20 Shape factor / Seated-09
0.6
0.6
0.5
Floor
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0.5
Shape Factor / Standing, Nude / 8
Shape Factor / Standing, Nude / 24
Floor
Shape Factor / Seated, Nude / 24
0.5
Floor
Celing
Celing
Front
0.4
0.4
Front
0.3
Back
0.3
Right
0.2
Left
0.1
Others
0.2
Back
Right
Left
0.1
Others
0
Bo
dy
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
Bo
dy
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0
Figure 21 Shape factor / Standing-25
Figure 22 Shape factor / Seated-25
0.6
0.6
Shape Factor / Standing, Nude / 48
Celing
0.5
0.4
Front
0.4
0.3
Back
0.3
Right
0.2
Left
0.1
Others
Shape Factor / Seated, Nude / 48
Front
Back
Right
0.2
Left
0.1
Others
0
Bo
dy
Bo
dy
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0
Figure 24 Shape factor / Seated-49
Figure 23 Shape factor / Standing-49
- 803
795 -
Floor
Celing
H
ea
F- d
Tr
un
B- k
Tr
un
k
RA
rm
LA
rm
RLe
g
LLe
g
0.5
Floor
Figure 25 Shape factor distribution map of 48 others
Figure 27 Room and people positions
SHAPE FACTOR AND BODY POSITION
In order to understand the thermal radiation environment of
the room occupied by 49 people, the shape factor calculation
is performed. This simulation aims at obtaining the difference
in thermal radiation environment with body position. Figure
27 shows the room plan occupied by 49 people. Shape factors
between the subject and the surroundings that are the room
surfaces and the people, except for the subject, are calculated.
Each subject position is indicated by A-D and a-g. For
example, a body is placed at a-A of Figure 27, and the shape
factor between the body and floor is a-A in the3D graph of
Figure 28.
Figure 26 Shape factor distribution map of 48 others
These figures indicate the strength of thermal radiation from
each surface of the room to each part of the body. Comparing
the standing and the seated case, the seated body has
somewhat larger floor shape factor than the standing.
Figure 19 is the case of the room occupied by 9 people (0.1
persons/m2). The subject is standing in the center of the room.
In this figure, [others] in the introductory notes mean human
bodies except the subject. The shape factors between the body
and the other bodies are 0.03 (standing) and 0.02 (seated).
Figure 21 is the case of the room occupied by 25 people (0.28
persons/m2) and the shape factors between the body and the
other bodies are 0.12 (standing) and 0.11 (seated). This shape
factor is smaller than the shape fact or between the trunk or
the arm and the other bodies.
In Figures 28 and 29, in spite of body position, there is no
large difference in the shape factor between the body and the
floor. In the standing case, the range of values of shape factor
is about 0.29 to 0.33. In the seated case, as compared with the
standing case, shape factor is larger by about 0.03.
In Figures 30 and 31, the shape factor between the body and
the ceiling becomes small at the corner of the body. In the
standing case, it is about 0.08 smaller than the shape factor at
the center of room. There are few differences of shape factor
between the standing body and the seated body.
In Figures 32 and 33 the shape factor between the body and
the front wall decreases rapidly when the subject goes from
the front wall to the back wall. There are few differences in
shape factor between the standing body and the seated body.
The shape factor of the standing body is 0.03 at d-A (center)
and 0.19 at a-A. In Figures 34 and 35, the back wall case is
opposite the front wall case.
Figure 23 is the case of the room occupied by 49 people. As
the density of people rises (0.54 persons/m2), the shape factor
between the body and the other bodies increases. The body
shape factors are 0.3 (standing) and 0.27 (seated).
In Figures 36 and 37, the shape factor between the body and
the right wall is small, since the subject stays away the wall. In
Figures 38 and 39, the shape factor between the body and the
right wall is 0.26 (standing) and 0.25 (seated) at d-D.
Figure 25 is the shape factor distribution map of 48 other
people on the human body surface. Figure 26 is the same
shape factor distribution map for the seated subject. The color
of the surface, which has turned to the ceiling and the floor in
the human body portion, is dark. This indicates that this shape
factor is smaller than the other fractions.
In Figures 40 and 41, the shape factor between the subject and
the others is large at the center of the room, and small at the
corner of the room. These shaper factors (standing) are 0.11 at
d-A, 0.3 at a-D, 0.1 at d-A and 0.27 at a-D. The standing case
generally has a shape factor larger than the seated case.
- 804
796 -
shape
factor
0.4
0.4
0.35
0.35
0.3
shape
factor
0.35-0.4
0.25
0.3-0.35
0.2
0.15
0.1
0.05
0
0.25-0.3
0.2-0.25
0.15-0.2
g
e
D
d
0.15-0.2
0.1-0.15
b
a
D
e
0.05-0.1
d
Floor
Seated, Nude / 48
A
0.05-0.1
0-0.05
C
c
0-0.05
B
B
b
a
A
Figure 29 Floor shape factors in the room (Seated)
0.4
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.35
shape
factor
0.35-0.4
0.3-0.35
0.25-0.3
0.2-0.25
0.15-0.2
g
f
0.3
0.35-0.4
0.25
0.2
0.15
0.1
0.05
0
0.3-0.35
0.25-0.3
0.2-0.25
0.15-0.2
g
C
c
Ceiling
Standing, Nude / 48
a
d
0.4
0.4
0.35
0.3
shape
factor
0.35-0.4
0.3-0.35
0.3
0.2-0.25
0.15-0.2
D
d
C
c
Front wall
Standing, Nude / 48
b
a
0.25-0.3
0.2-0.25
0.15-0.2
0.1-0.15
f
e
0.05-0.1
D
d
A
C
c
Front wall
Seated, Nude / 48
0-0.05
B
0.3-0.35
g
0.1-0.15
e
0.35-0.4
0.25
0.2
0.15
0.1
0.05
0
0.25-0.3
f
A
Figure 31 Ceiling shape factors in the room (Seated)
0.35
g
a
0.05-0.1
0-0.05
B
b
Ceiling
Seated, Nude / 48
Figure 30 Ceiling shape factors in the room (Standing)
0.2
0.15
0.1
0.05
0
C
c
A
0.25
D
e
0.05-0.1
0-0.05
B
b
0.1-0.15
f
0.1-0.15
D
e
d
shape
factor
0.2-0.25
f
Figure 28 Floor shape factors in the room (Standing)
shape
factor
0.25-0.3
C
c
Floor
Standing, Nude / 48
0.3-0.35
g
0.1-0.15
f
0.35-0.4
0.3
0.25
0.2
0.15
0.1
0.05
0
b
a
0.05-0.1
0-0.05
B
A
Figure 33 Front wall shape factors in the room (Seated)
Figure 32 Front wall shape factors in the room (Standing)
0.4
0.4
0.35
0.35
0.3
shape
factor
0.35-0.4
0.25
shape
factor
0.3-0.35
0.2
0.15
0.1
0.05
0
0.2-0.25
0.15-0.2
0.1-0.15
f
e
D
d
C
c
Back wall
Standing, Nude / 48
B
b
a
0.35-0.4
0.3-0.35
0.2
0.15
0.1
0.05
0
0.25-0.3
g
0.3
0.25
0.25-0.3
0.2-0.25
0.15-0.2
g
0.1-0.15
f
0.05-0.1
e
D
d
0-0.05
Back wall
Seated, Nude / 48
A
C
c
B
b
a
0.05-0.1
0-0.05
A
Figure 35 Back wall shape factors in the room (Seated)
Figure 34 Back wall shape factors in the room (Standing)
- 805
797 -
shape
factor
0.4
0.4
0.35
0.35
0.3
0.35-0.4
0.25
0.3-0.35
0.2
0.15
0.1
0.05
0
shape
factor
0.2-0.25
0.15-0.2
0.1-0.15
f
e
Right wall
Standing, Nude / 48
0.15-0.2
0.1-0.15
f
e
D
d
Figure 36 Right wall shape factors in the room (Standing)
C
c
Right wall
Seated, Nude / 48
A
a
0.2-0.25
g
B
b
0.25-0.3
0-0.05
C
c
0.3-0.35
0.05-0.1
D
d
0.35-0.4
0.2
0.15
0.1
0.05
0
0.25-0.3
g
0.3
0.25
0-0.05
B
b
a
0.05-0.1
A
Figure 37 Right wall shape factors in the room (Seated)
0.4
0.4
0.35
0.3
shape
factor 0.25
0.2
0.15
0.1
0.05
0
shape
factor
0.35-0.4
0.3-0.35
0.25-0.3
0.2-0.25
0.15-0.2
g
e
D
d
0.3-0.35
0.25-0.3
0.2-0.25
0.15-0.2
g
a
d
0.05-0.1
C
c
Left wall
Seated, Nude / 48
b
a
0.05-0.1
0-0.05
B
A
A
Figure 38 Left wall shape factors in the room (Standing)
Figure 39 Left wall shape factors in the room (Seated)
0.4
0.4
0.35
0.35
0.3
0.35-0.4
0.25
0.3-0.35
0.2
0.15
0.1
0.05
0
shape
factor
0.2-0.25
0.15-0.2
0.1-0.15
g
0.3
0.35-0.4
0.25
0.3-0.35
0.2
0.15
0.1
0.05
0
0.25-0.3
0.25-0.3
0.2-0.25
0.15-0.2
g
D
e
d
C
c
e
0-0.05
Other persons
Seated, Nude / 48
B
b
0.1-0.15
f
0.05-0.1
f
a
D
e
0-0.05
B
b
0.1-0.15
f
C
c
Left wall
Standing, Nude / 48
Other persons
Standing, Nude / 48
0.35-0.4
0.1-0.15
f
shape
factor
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
D
d
C
c
B
b
a
A
Figure 40 Other persons shape factors in the room (Standing)
0.05-0.1
0-0.05
A
Figure 41 Other persons shape factors in the room (Seated)
CONCLUSION
REFERENCES
In order to understand the indoor thermal radiation
environment in detail, the shape factor simulation is executed.
Shape factors are calculated by the method shown in this
paper. The calculation result is visualized by VRML. The
shape factor distribution map, which indicates the influence of
thermal radiation from the surroundings to the human body, is
expressed as shading on the 3D human body model. The
simulation is executed for situations where the room is
occupied by various numbers of people, and the influence of
thermal radiation from the others on the subject is presented.
In the case of the room occupied by 49 people, the shape
factor between the subject in the center of the room and the
others is 0.3. Moreover, the simulation indicates the difference
in thermal radiation environment depending on body position
in the room.
Cohen,F and Greenberg,P, 1985. The Hemi-Cube A Radiosity
Solution for Complex Environments, SIGRAPH85.
Fanger, P.O.,et al., 1970. Radiation Data for the Human Body,
ASHARE Trans., Vol.76-II.
Manabe,M., et al. 2002. Shape Factor Simulation Between a
Human Body and a Room Using Scan Line, The 10th ICEE.
Manabe,M, et al., 2001. Daylighting Simulation of Japanese
Architecture Using All Sky Model, Building Simulation 2001.
Olsen,B.W, et al., 1989. Methods for Measuring and Evaluating
the Thermal Radiation in a Room, ASHARE Trans., Vol.95-II.
Tanabe,S., et al. 2000, Effective radiation area of human body
calculated by a numerical simulation, Energy and Buildings
32.
Yamazaki,H., 1983. Shape Factor Calculation and Computer
Graphics. The 4th International Symposium on the Use of
Computers for Environmental Engineering Related Buildings.
- 806
798 -