THORACIC INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 213

of the exponential e − t/α is measured by α and, hence, this exponential
decays rather slowly for large α . The characteristic time of decay of the
exponential e − kαt is measured by 1 /(kα) and, therefore, this term decays
very rapidly. As a result, the control force very quickly [during the time
∼ 1 /(kα) ] reaches the nominal value ( u ≈− 1) and remains virtually on

this level for an extended time. If α 1, the object to be protected will be

decelerated with the nearly constant force u 1 until it comes to a stop.

The implementation of the control law of Eq. (6.20) is not associated
with the solution of a system of differential equations if the current tensile
force of the spring can be measured. The velocity of the attachment point
to be provided by the control system to compensate for the deviation of the
actual control force from the desired value u =−

≈−

1 can be calculated when

the measured value of u is known.

6.3 LIMITING PERFORMANCE ANALYSIS
FOR THE PREVENTION OF THORACIC INJURIES
IN A FRONTAL CAR CRASH

6.3.1 Thoracic Injury Model and Criteria

The dynamics of the human thorax under impact can be described using the
mechanical model shown in Fig. 6.1 (Lobdell et al., 1973). In the model,
mass m 1 represents the effective mass of the sternum and a portion of the rib
structure and thoracic contents. Mass m 2 represents the remaining portion of

f ( x 2 x 1 )

m 1 m 2

u ( t )

h ( x 2 x 1 )

c 2

k 2

x v

x 1

x 3

x 2

FIGURE 6.1 Frontal crash model for thoracic injury.