Head Injury Criteria
For instance, the Federal Motor Vehicle Safety Standards define the Head Injury Criteria as a moving window with the average acceleration (in Gs) raised to the 2.5th power. A Head Injury Criteria over a thousand is not good. The moving window is usually 15ms as the structural properties of the human head function like a low-pass filter. Jiggly acceleration signals in the 5ms range and shorter duration are noise.
The HIC (Head Injury Criteria) was developed for impacts that drive the human head rearward. There are significant structural differences in how the human head responds to frontal hit and to rear hits, but we will use the FMVSS HIC number as a starting point.
Said another way, the chart tells me that if I want to limit the HIC to 499, then I need to limit the maximum acceleration to 12 Gs. If I limit the acceleration to 12 Gs, then I need to find 30 inches of crush space and design a structure that will generate the proper force pulse to generate 12 G.
Magee and Thornton (1978)
As a convenience, rectangular sections are approximated using the formula for the square section by taking the average of the height and width of the section.
Magee and Thornton's approximation is:
Average axial crush force for a rectangular section = 17 * (metal thickness in millimeters)^1.8 * (Material's Ultimate Tensile Strength) * ((Height + Width)/2)^0.2
|2" by 2" and 4" and 6". Metal thickness in inches listed in second row from top. 60ksi ultimate tensile strength assumed.|
Assuming four fat men and two hundred pounds of seats and framing, we are looking at a max load of 1000 pounds. Assuming we have one longitudinal rail along each side of the buggy, the table shown above translates rectangular tubing dimensions into the accelerations in Gs for maximum ballast condition.
|Functionally, this would perform similar to a 2"-by-6" section if the flanges were one inch, each.|
The longitudinal rails for the occupant protection structure for the buggy would optimally be 16 gauge steel and 2" wide by 4" high in order to provide sufficient energy capacity for maximum ballast conditions.
Additional "crush distance" for less than maximum ballast conditions must be engineered into the individual seats to avoid excessive HIC numbers for the occupants.