# The Head Injury Criterion (HIC)

It was found that the Severity Index did not accurately describe the likelihood of certain injuries in a crash.

The head Injury Criterion (HIC) was developed and it is based on the average value of the acceleration over the most critical part of the deceleration (shown in the blue rectangles in the Mercedes data before). We met average value of a function earlier in this chapter.

The average value bar(a) of the acceleration a(t) over the time interval t1 to t2 is given by

bar a=1/(t_2-t_1)int_(t_1)^(t_2)a(t)\ dt

For the HIC, this was modified (based on experimental data) as follows:

HIC={:("max"),(t_1 or t_2):}{(t_2-t_1)[1/(t_2-t_1)int_(t_1)^(t_2)a(t)dt]^2.5}

The formula means:

The HIC is the maximum value over the critical time period t1 to t2 for the expression in braces, { }. The index 2.5 is chosen for the head, based on experiments.

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