Biomedical Engineering Reference
In-Depth Information
v
5
/
0
/H
2
/
3
and change
to
H
2
/
3
/v
5
/
0
. In the dimensional variables,
T
decreases as
H
increases and/or
v
0
decreases. Expressions for
T
for
H
2
/
3
/v
5
/
3
0
≥
1 (which corresponds to
≥
1 in the dimensionless vari-
ables) and
H
2
/
3
/v
5
/
3
1(
1 in the dimensionless variables) are
0
v
5
/
3
if
H
2
/
3
v
5
/
3
0
H
2
/
3
T
=
≥
1
,
(7.53)
0
if
H
2
/
3
v
5
/
3
v
0
H
2
/
5
2
/
5
∼
T
1
.
(7.54)
0
As was the case for the expressions of Eqs. (7.50) and (7.51) for the optimal
deceleration distance, the expression of Eq. (7.53) for the deceleration time
is important for applications, since it corresponds to a broad range of the
parameters typical of car crash test conditions, whereas the expression of
Eq. (7.54), which characterizes the increase in the deceleration time as the
initial velocity,
v
0
, increases without limit or
H
tends to zero, can be of
interest only for theory.
7.3 MINIMIZATION OF HIC FOR CONSTRAINED
DECELERATION DISTANCE
Problem 7.2 Minimization of HIC for Constrained Displacement of
Headform
List of Variables for Problem 7.2
State variable
x
Displacement of the head relative
to the inertial reference frame
Control variable
u
Force of interaction of the head
with the impact surface
Functions and parameters of
the model
m
Mass of the head
v
0
Initial velocity of the head
The maximum length of the time
interval
t
1
≤
t
≤
t
2
occuring in the
definition of HIC
Performance index
J
2
Head injury criterion (HIC)
(continued)
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