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ToniG

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When reconstructing traffic accidents to obtain the collition velocities it is needed to obtain the "crush energy" which is the amount of kinetic energy transformed into permanent damage to the cars involved. From that kinetic energy we get the Energy Barrier Speed which is used with the momentum equations to determine the speed of the cars involved . The crush energy is based on measurements of the deformation of the cars involved in the collision.

When in a two car collision only one of the two cars "Crash energy" is known, the total Crash energy of the two cars can be obtained if the relationship between the masses of the two cars is known. That formula is shown in "SAE Technical Paper 920604: Wood, D., Collision Speed Estimation Using a Single Normalised Crush Depth-Impact Speed Characteristic".

I attach a snapshot of the paper showing the formula.

Et = E1*(1+ M1/M2)

Where Et is the total crush energy, E1 is the Crush energy of car 1, M1 is mass of car 1 and M2 is mass of car 2.

It is not intuitive to me how can the relationship of the energy dissipated into each body only depend on the relationship of masses. I thought that the "stiffness" of each car, or other properties should be involved but it seems not according to the paper.

Can you help understand where the above formula is derived from?

When in a two car collision only one of the two cars "Crash energy" is known, the total Crash energy of the two cars can be obtained if the relationship between the masses of the two cars is known. That formula is shown in "SAE Technical Paper 920604: Wood, D., Collision Speed Estimation Using a Single Normalised Crush Depth-Impact Speed Characteristic".

I attach a snapshot of the paper showing the formula.

Et = E1*(1+ M1/M2)

Where Et is the total crush energy, E1 is the Crush energy of car 1, M1 is mass of car 1 and M2 is mass of car 2.

It is not intuitive to me how can the relationship of the energy dissipated into each body only depend on the relationship of masses. I thought that the "stiffness" of each car, or other properties should be involved but it seems not according to the paper.

Can you help understand where the above formula is derived from?