Sensitivity Analysis
Varying Initial Velocity
From the diagram, we can see that the velocity at time zero starts from the peak of the initial velocities and is slowly damped. Furthermore, it can be seen that although the damping ratio is constant, the lower the velocity of the vehicle before impact, it will be easier for the vehicle to be halted since there is less kinetic energy being converted into another form as a result of dissipation. As you double the velocity of a vehicle on a highway, you double the force of impact.
Varying Mass
In a collision between a heavy vehicle and a barrier, and a lighter vehicle and a barrier, the
weight factor would favor the occupants of the heavier vehicle because of momentum conservation. Because of its greater mass, the heavier vehicle is likely to suffer a smaller change in velocity. This is an ideal or better situation because, during impact, energy needs to be dissipated at a slower rate to not affect the vehicle’s occupants.
Varying Damping Constant
Underdamped: Damping factor less than one. Allows for a longer stopping time. The gradual decrease in velocity implies less change in momentum of the vehicle per unit time hance less energy acting on the vehicle occupant.
Overdamped: Damping factor greater than one. The stopping time is very short as observed from the time it takes to get to a velocity of 0m/s.
Undamped: Damping factor of zero. The vehicle would oscillate back and forth forever! This is not the case since even if there was no other resistive mechanism, there would be air resistance.
Critically damped: Damping factor equal to one. A force is applied that aids in the stopping of the car. Although the stopping time is not as fast as that of an overdamped model, it is still too rapid and poses a great danger to the occupants.
Implications
Human beings in the passenger compartment of an automobile are capable of withstanding large
changes in momentum provided (1) they are properly restrained, (2) the change
in momentum of the passenger compartment does not occur too rapidly, and
(3) exterior objects to the passenger compartment do not penetrate to where
they could injure the passengers.