Computer and Mathematical Modelling of the Female Human Body:
Determination of Mass-inertial Characteristics
in Basic Body Positions
Gergana Stefanova Nikolova, Vladimir Konstantinov Kotev and Daniel Marinov Dantchev
Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Building 4, Sofia 1113, Bulgaria
Keywords: Human Body Modelling, Mass-inertial Parameters, Anthropometry, CAD Design.
Abstract: The aim of the current article is: 1) to present 16-segmental biomechanical model of the female human body
generated within a SolidWorks medium. 2) to determine the mass-inertial characteristics of the human body
of the average Bulgarian female on the basis of the model. These parameters are needed in order to design
wearable or rehabilitation robots and devices properly; 3) to verify the model via comparing its results for the
segments of the body with analytical results from our previous investigation of these segments; 4) to predict
the inertial properties of a human body in various body positions. The comparison performed between our
model results and data reported in literature gives us confidence that this model could be reliably used to
calculate these characteristics at random postures of the body.
1 INTRODUCTION
The knowledge of the geometric and mass-inertial
characteristics (volume, mass, center of mass,
moments of inertia) of human body segments, as well
as those of the total body, is needed for analyses of
the human motion – of the specific segments of it, or
of a given person. This topic has been subject of
intensive simulations and mathematical modeling,
see,e.g., classical positions on a system theory (Zadeh
and Desoer, 1963); human gait analysis (Jensen,
2009); theory-based simulation applied to the
physical objects (Respondek, 2010); modeling of the
dynamics and energetics of impact in crutch walking
(Carpentier et al., 2010); biomechanical optimization
to interpret dancers’ pose selection (Allen et al.,
2011); studies of vibration response of idiopathic
scoliosis patients via investigating a proper 3-
dimentional finite-element model (Li et al., 2011); the
investigation of inertial properties of athletes
performing pure somersaults (Mikl, 2014).
Obviously, the knowledge of the geometric and mass-
inertial characteristics is equally important for the
both genders – for males as well as for females.
Unfortunately, the overwhelming amount of data
available in literature, due to a variety of different
reason, concerns males. Next, even when such
measurements have been performed, almost all
available data is about the different segments, not for
the body as a whole. Therefore, an approach aiming
to fill in that gap is highly desirable. A 3D model of
the female body and its computer realization within
the SolidWorks media is presented is the current
work. The model allows, in principal, the
determination of the mass-inertial parameters of the
female body in any posture of the body that is of
interest. In order to make some systematization in
studying of the mass-inertial parameters of the
humans in position related to their everyday
activities, leisure, sport, work, etc., the basic positions
have been classified long ago (Santschi et al. 1963;
Chandler et al., 1975; Hanavan, 1964). In the current
article we will present data for these characteristics
for the average Bulgarian women in four of these
basic positions.
As far as antropometric and mass inertial data for
females are concerned, initially, using
stereophotogrammetry, the regression equations on
the base of a sample of 46 adult women were
developed (Young, 1983). Then, on the basis of
gamma-scanner method, the mass-inertial parameters
of 15 female athletes have been investigated
(Zatsiorsky and Seluyanov, 1983). Over that period
of time based on the so-called elliptical zone method,
the body segment parameters of 15 college-age
females have been estimated and classified into endo,
416
Nikolova, G., Kotev, V. and Dantchev, D.
Computer and Mathematical Modelling of the Female Human Body: Determination of Mass-inertial Characteristics in Basic Body Positions.
DOI: 10.5220/0006480304160421
In Proceedings of the 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2017), pages 416-421
ISBN: 978-989-758-265-3
Copyright © 2017 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

meso- and ecto-morphs (Finch, 1985). The mass-
inertial charchterstics of 80 Japanese women have
been investiagted and the diff erence in segment mass
proportions with the sample of 215 men has been
discussed (Ae et al., 1991). On the basis of
measurements of 25 young German females, the
regression equations for estimating length, mass and
moments of inertia of the segments have been derived
(Shan and Bohn, 2003). One of the most
contemporary used method is the one dual energy x-
ray absorptiometry. Based on it, the differences in
estimation of mass, center of mass location and radius
of gyration of 5 segments between 4 human
populations were estimated (Durkin and Dowling,
2003). Finally, in Yordanov et al., 2006 the
anthropometrical data from a detailed representative
anthropological investigation of the Bulgarian
population have been gathered. The study contains
data of total of 2854 females at the age 31-40 years.
This study will be our major source of anthropometric
data when modeling the body of the average
Bulgarian female.
Certainly, the generation of 3D model of the
human body in a CAD media needs knowledge of
anthropometry and biomechanics. One should,
effectively resolve specific problems related to: a)
correct body decomposition; b) the selection of
necessary anthropometric landmarks; c) the choice of
the geometrical bodies with which the corresponding
segments of the body shall be modeled; d) the genuine
model generation within a proper CAD system (e.g.
SolidWorks); e) The verification of the so generated
model via comparison with analytical results in order
to show that computer generated model provides
reliable data quantities.
Let us emphasize, that understanding the mass-
inertial parameters of the body is of importance for
proper design of vehicles, wheelchairs, exoskeletons,
rehabilitation devices, ergonomics, sports, orthotics
and prosthetics design, etc. We hope that our model
will be helpful in these areas.
The aim of this study is to develop a mathematical
model of woman able to predict the inertial properties
of the human body in any fixed body position and to
use this model to develop a design guide for some of
the problems mentioned above. For the specific
realization of the model in the current study we will
rely on data for the Bulgariam women. However, our
approach is, of course general and can be applied to
any other set of data for other women. In the current
study we will perform a comparsions of our results
for the average Bulgarian women with data available
in literature for other Caucasian women.
2 MODEL AND METHOD
We utilize a mathematical model of the human body
initially proposed in (Nikolova and Toshev, 2007).
Out there, this model has been used to determine the
geometric and mass-inertial parameters of the
different segments of the body. Here, in order to avoid
any repetition of these details, we refer the interested
reader for further specifics to (Nikolova and Toshev,
2007). We are going to present only some brief
comments in order to introduce the very basic facts
for the model used in the current study - see Fig. 1.
Figure 1: 16-segemental model of the female human body
and the corresponding dimensions [cm].
In the current work the model consists of 16
segments: head + neck, upper, middle and lower part
of torso, thigh, shank, foot, upper arm, forearm and
hand, assumed to be relatively simple geometrical
bodies. We accepted full body symmetry with respect
to the sagittal plane, i.e., complete ‘‘left–right’’
symmetry. The decomposition of the body segments
is made according to anthropometric points used in
(Zatsiorsky, 2002).
The anthropometrical data needed is taken from
the detailed representative anthropological
investigation of the Bulgarian population (Yordanov
et al., 2006). We recall that 2854 females at the age
31-40 years have been measured. For any segment
and any quantity measured, we take the average
values established in this investigation and design a
model that represents the so defined "average"
Bulgarian woman. As it illustrated in Fig. 1, the
segments are modeled by means of geometrical
bodies similar to those in (Hanavan, 1964), but with
the following modifications:
(1) the torso is decomposed in three instead of two
parts;
(2) the upper part of the torso is approximated by
means of a right reverted elliptical cone, while it is an
elliptical cylinder in (Hanavan, 1964);
Computer and Mathematical Modelling of the Female Human Body: Determination of Mass-inertial Characteristics in Basic Body Positions
417

(3) we specify both middle and lower torso
according to (Zatsiorsky, 2002), modeled as an
elliptical cylinder and an elliptical cylinder + reverted
elliptical cone, respectively. Let us recall that in
(Hanavan, 1964), these two segments are grouped
together and modelled as an elliptical cylinder.
All segments of both the lower and upper
extremities are assumed to be cone frustums and the
hand is modeled as a sphere.
After determining the geometrical parameters of
the segments, one can analytically obtain all the other
characteristics of interest, such as volume, mass and
moments of inertia.
Once the mass-inertial parameters of the segments
are determined, one can also study the corresponding
characteristics of the total body assuming the body to
be in a given position of interest. To realize this goal,
we have performed a generation of the model in CAD
system – SolidWorks. We have verified the computer
realization by comparing the results it achieved for
the mass -inertial parameters of the segments of the
body with the ones reported in (Nikolova and Toshev,
2007).
The basic positions of the body have been
classified long ago in the literature – see, e.g.,
(Santschi et al. 1963; Chandler et al., 1975; Hanavan,
1964; NASA, 2000). One usually considers eight
principal body positions. Unfortunately, the data from
the above studies is only for men while for women
they are either missing or are very few and not enough
for reasonable statistically verifiable estimations. In
the following sections we will try to enrich the
literature with data for four of these positions for the
female human body:
1) the so-called standing position – see Fig. 2,
which will provide us a basis of comparison,
2) the sitting with forearms down position – see
Fig. 3,
3) the standing with arms over head – see Fig. 4,
and
4) the standing position with maximal horizontal
span of upper extremities – see Fig. 5.
3 DETERMINATION OF
MASS-INERTIAL
CHARACTERISTICS IN
DIFFERENT BODY POSITIONS
As stated above, we consider the “standing position”,
“sitting position”, “standing with arms over head
position” and the “standing position with maximal
horizontal span of upper extremities”. For each
position, a system of axes with an origin at the center
of mass is defined. The axes coincide with the
approximate body axes: the frontal (y), the sagittal
(z), and the longitudinal (x) ones.
3.1 Standing Position
Data for males in such a position are well known –
see, e.g., (Santschi et al. 1963; Chandler et al., 1975;
Hanavan, 1964; NASA, 2000). In the “standing
position” the individual stands erect with head
oriented in the so-called Frankfort plane and with
arms hanging naturally at the sides. Data for the mass-
inertial parameters of the female human body in
standing positions we are aware of is presented in
Table 1. This table contain data for the center of mass
in the corresponding posture of the body measured
from the anthropometric point vertex of the head (the
“x” coordinate) and from the sagittal plane through
the middle of the body when in standing position.
Figure 2: Standing position.
Table 1 also provides a comparison with the data we
have obtained for the average Bulgarian female in this
position with the corresponding data taken from the
literature. Table 1 contains the data for the average
height and mass of person in the corresponding study
compared with the investigations of (Abraham et al.,
1979) and (Young, 1983).
The inspection shows a reasonably good
agreement between our results and those previously
reported in the literature.
X
0
Y
0
Z
0
SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
418

Table 1: Standing position.
Young
Abraham et
al.
Our
data
Min
Max
Mean
I
XX
[kg.cm
2
]
5.8
24.0
11.6
-
6.7
I
YY
[kg.cm
2
]
49.1
135.0
85.0
78.3
I
ZZ
[kg.cm
2
]
53.0
135.0
91.9
-
81.9
Stature
[cm]
161.20
162.60
160.51
Mass [kg]
63.90
64.64
60.65
Center of
mass
[cm]
-
-
67.3
3.2 Sitting, with Forearms Down
In the “sitting, with forearms down” position the
segments of the body are as in “standing position”,
except that the forearms are parallel to X-axis and the
wrist axes are also parallel to X-axis, see. Fig. 3.
Figure 3: Sitting, forearms down.
Table 2: Sitting, forearms down.
Characteristic
Our data
I
XX
[kg.cm
2
]
13.0
I
YY
[kg.cm
2
]
56.8
I
ZZ
[kg.cm
2
]
59.5
Center of mass [cm]
60.7
Table 2 contains data for moments of inertia and
center of mass [cm] of model of the body in the
corresponding position.
3.3 Standing, Arms over Head Position
In the “Standing, arms over head” position, legs,
torso, and head same as “Standing position”; upper
extremities raised over head, parallel to X axis; wrist
axes parallel to Y-axis; hands slightly clenched (see.
Fig. 4). Table 3 contains data for moments of inertia
and center of mass of model of the body in the
corresponding position.
Figure 4: Standing, arms over head.
Table 3: Standing, arms over head.
Characteristic
Our data
I
XX
[kg.cm
2
]
67.1
I
YY
[kg.cm
2
]
99.8
I
ZZ
[kg.cm
2
]
103.3
Center of mass [cm]
63.0
3.4 Standing Position with Maximal
Horizontal Span of Upper
Extremities
The position shown on Fig. 5 is not one of the basic
ones described in (Santschi et al. 1963; Chandler et
al., 1975; Hanavan, 1964; NASA, 2000). It has been
studied from (Hanavan, 1964), but only for men.
Figure 5: Standing position with maximal horizontal span
of upper extremities.
X
0
Y
0
Z
0
Z
0
X
0
Y
0
Computer and Mathematical Modelling of the Female Human Body: Determination of Mass-inertial Characteristics in Basic Body Positions
419

We investigate it and think it would be useful in
sports like figure skating etc. Table 4 contains data
for moments of inertia and center of mass of model of
the body in the corresponding position. The
comparison of this data with the data from Table 1
shows that Ixx increases 10 times in position with
maximal horizontal span of upper extremities in
comparison with the standard standing position. The
last implies that when skater suddenly contracts his
upper limbs towards the body the angular speed of
rotation will diminish also about 10 times from the
initial angular speed. This is the scientific foundation
for the effect, which the skaters are customarily using
in figure skating nowadays and one enjoys on TV.
Table 4: Standing position with maximal horizontal span of
upper extremities.
Characteristic
Our data
I
XX
[kg.cm
2
]
67.1
I
YY
[kg.cm
2
]
99.8
I
ZZ
[kg.cm
2
]
103.3
Center of mass [cm]
65.6
4 CONCLUSIONS
In the current paper a 16-segment biomechanical
model of the human body of women is proposed and
its 3D model realization in SolidWorks environment
is performed. The specific geometrical realization
reflects the “average” Bulgarian woman. Using the
model, data for the mass-inertial characteristics of the
body in its four basic positions have been obtained
and compared, wherever possible, with those reported
in the literature. Let us note that the model is suitable
for the performance of static, kinematic and dynamic
analysis. A modification of the model so that it can
represent a specific individual is easily achievable by
using the individual anthropometric dimensions for
that particular person. The comparison performed
between our model results and data reported in
literature gives us confidence that this model could be
reliably used to calculate the mass inertial
characteristics at any specific posture of the body.
The model is applicable in rehabilitation robotics,
computer simulations, medicine, sports, ergonomics,
criminology and other areas.
ACKNOWLEDGEMENTS
Support via Bulgarian National Science Fund:
Contract DN-07/5 “Study of anthropometric and
mass-inertial characteristics of the Bulgarian men and
women via mathematical models of the human body”
is gratefully acknowledged.
REFERENCES
Abraham, S. et al., 1979. Weight and height of adults 18 -
74 Years of Age. US1971-74, (PHS) 79-1659, HANES.
Ae, M., Tang, H., Yokoi, T., 1991. Body segment
parameters of Japanese adults. Proceedings of 12th
Annual Meeting of SOBIM Japan, pp. 191–202.
Carpentier, C., Font-Llagunes, JM., Kövecses, J. 2010.
Dynamics and energetics of impacts in crutch walking,
Journal of Applied Biomechanics, 26, pp. 473-483.
Chandler, R., Clauser, C., McConville, J., Reynolds, H.,
Young, J., 1975. Investigation of inertial properties of
the human body. Technical Report AMRL-TR-74-137,
Wright-Patterson Air Force Base, Ohio.
Durkin J., Dowling J., 2003. Analysis of body segment
parameter differences between four human populations
and the estimation errors of four popular mathematical
models. Journal of Biomechanical Engineering, 125,
pp. 515-522.
Finch, C., 1985. Estimation of body segment parameters of
college age females using a mathematical model. MHK
Thesis, University of Windsor, Ontario.
Hanavan, E., 1964. A mathematical model of the human
body. AMRLTR-64-102, Aerospace Medical Research
Laboratories, Wright-Patterson Air Force Base, Ohio.
Jensen, R., Paulsen, R., Larsen, R., 2009. Analyzing gait
using a time-of-flight camera. In: Salberg AB.,
Hardeberg J.Y., Jenssen R. (eds) Image Analysis. SCIA
2009. Lecture Notes in Computer Science, vol 5575.
Springer, Berlin, Heidelberg.Li, X.F. et al., 2011.
Dynamic response of the idiopathic scoliotic spine to
axial cyclic loads. Spine, 36, pp. 521-528.
Mikl, J. 2014. Do some athlete’s inertial properties give
them a natural advantage when performing pure
somersaults? Proceedings of 32 International
Conference of Biomechanics in Sports, July 12 - 16,
2014, Johnson City, TN. USA, pp. 717-720.
NASA-STD-3000, 2000. The Man-System Integration
Standards, Volume I, Section 3. Anthropometry and
Biomechanics. Available at:
https://msis.jsc.nasa.gov/sections/section03.htm#3.2.1.
Nikolova, G., Toshev. Y., 2007. Estimation of male and
female body segment parameters of the Bulgarian
population using a 16-segmental mathematical model.
Journal of Biomechanics, 40, pp. 3700-3707.
Respondek, J., 2010. Numerical simulation in the partial
differential equation controllability analysis with
physically meaningful constraints. Mathematics and
Computers in Simulation, 81, pp. 120–132.
Santschi, W. et al., 1963. Moments of Inertia and Centers
of Gravity of the Living Human Body. AMRL TR 63-
36. Wright-Patterson Air Force Base, Ohio: 6570th
Aerospace Medical Research Laboratories.
SIMULTECH 2017 - 7th International Conference on Simulation and Modeling Methodologies, Technologies and Applications
420

Selbach-Allen, ME., McIlhany, K., Gentry, S., 2011.
Optimization and pose selection for a lindy hop
partnered spin, Proceedings of 2011 American Control
Conference on O'Farrell Street, San Francisco, CA,
USA, pp. 3831-3836.
Shan, G., Bohn, C., 2003. Anthropometrical data and
coefficients of regression related to gender and race.
Applied Ergonomics, 34, pp. 327–337.
Yordanov, Y., Nacheva, A., Tornjova, S., Kondova, N.,
Dimitrova, B., Topalova, D., 2006. Anthropology of the
Bulgarian population at the end of the 20th century
(30–40 years old persons). Professor Marin Drinov
Academic Publishing House, Sofia, Bulgaria.
Young, R., 1983. Anthropometric and mass distribution
characteristics of the adult female. FAA-AM-83-16,
Oklahoma City.
Zadeh, A., Desoer, C., 1963. Linear system theory.
McGraw Hill, New York.
Zatsiorsky, V., 2002. Kinetics of human motion. Human
Kinetics, Champaign, IL.
Zatsiorsky, V., Seluyanov, V., 1983. The mass and inertia
characteristics of the main segments of the human body.
In: Matsui, H., Kobayashi, K. (Eds.), Biomechanics
VIII-B. Human Kinetics, IL, pp. 1152–1159.
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