## Finite Element Analysis

The image immediately below is a Pro-E Model of a bumper attached by two shafts to a plate. In a collision, the plate crushes an energy absorbing material behind the plate in a box. The simulation was run with two types of aluminum honeycomb material. One type has a crush strength of 245 psi, and the other had a crush strength of 120 psi. The simulation was done by the University of Dayton.

I currently propose to use polyurethane foam instead of aluminum honeycomb. the foam is lower in cost, and has equal properties in all directions. The simulation would give the same results for polyurethane foam.

In the graph at the bottom of the page, the blue line shows the case where 245 psi material is used to absorb the collision forces.
The height of the blue line shows the g forces felt by a passenger in a car, at rest, hit by a 3000 lb vehicle traveling at 30 mph.
The bottom of the graph is time.

The red line shows the case where 120 psi material is used.

The blue line requires more psi to start crushing, so the g forces start out at 40 g's and remain at 40 g's for the duration of the collision.
Note that the National Highway Transportation and Safety Administration (NHTSA) allows up to 82 g's on the thorax (abdomen) of a passenger in a side collision. Many cars are close to that number even with the use of side airbags and seatbelts.

The 40 g's supplied by my invention is much lower than 82 g's.

In a low speed collision, the 245 psi may not deform at all. That is because its crush point of 245 psi may not be reached.
In this case, the foam does not help reduce the g forces at all. This is the problem that Gordon Murray discusses.

In a low speed collision, the 120 psi material (the red line) will crush at a lower psi, and the initial g force will be around 20 g's.
Note that the red line goes up to 48 g's at the end of the collision. This happens because the 120 psi material was hit by a large vehicle going at 30 mph. The 120 psi material was "used up" and the end of the collision has no foam to compress.

My Adaptive Bumper invention matches the amount of  energy absorbing material to the quantity of the collision energy.

In a lower speed collision, the lesser area of foam will reach a high enough psi to crush the lesser area (volume) of foam.
In a higher speed collision, all of the available foam will be used to absorb as much as possible of the collision energy.

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