SPINAL INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 202

segment over which the behavior of this force and the absolute acceleration
of the seat pan is more uniform. Such a behavior of the control function
provides a more uniform time history for the spinal compressive force,
which enables the minimization of the peak magnitude of this force. The
constant-force control and the control with constant absolute deceleration
of the seat pan, even optimized, are substantially inferior to the optimal
control. This is accounted for by the dynamic properties of the object to
be protected. The human vertebral column has a high compressive/tensile
stiffness and a relatively low damping ratio. The constant deceleration of
the seat pan excites a vibration in the upper torso relative to the lower
torso, which is attached to the seat pan. The period of this vibration is
less than the time required for the seat pan to come to a complete stop,
and the upper torso performs several oscillations relative to the lower torso
during that time. On some intervals, the absolute acceleration of the seat
pan and the relative acceleration of the upper torso coincide in direction.
Since the absolute acceleration of the upper torso is the sum of the absolute
acceleration of the seat pan and the relative acceleration of the upper torso,
the absolute acceleration of the upper torso at some instant substantially
exceeds the absolute acceleration of the seat pan. Accordingly, the spinal
compressive force substantially exceeds the force that would have occurred
if there had been no vibration of the upper torso relative to the seat pan.
The optimal control does not allow this vibration to be excited. It adjusts
the acceleration of the seat pan so as to keep the spine compression force
at an approximately constant level.
The development history of shock isolation (energy-absorbing) systems
used in crashworthy helicopter seats has been traced by Desjardins
(2003) in his paper presented at the American Helicopter Society's
59th Annual Forum, which shows that most isolators are designed to
provide a near-constant absolute deceleration of the occupant, beginning
from the instant when the deceleration pulse of the airframe exceeds an
acceleration tolerable to the occupant. Until this time instant, the seat and
the occupant's lower torso do not move relative to the airframe. A number
of design schematics of such isolators are presented. On the other hand,
a “notched” deceleration pulse of the occupant is noticed. At the initial
time interval of the response of the isolator to a crash deceleration pulse,
a transient high deceleration spike is applied to the seat that compresses
the spine rapidly, and then a lower deceleration is used that keeps the
spinal compressive force close to a constant. This idea was reported by
Desjardins et al. (1989). However, no rigorous mathematical methods were
used to prove it. The results of Chapters 4 and 5 of the topic validate
this idea using the concept of the limiting performance analysis for shock
isolators and the optimal control technique.