Accident Reconstruction, Vomhof equation?

[turnwrite]

Hey Physics Forums, I am currently trying to wrap my brain around the physics of accident reconstruction. Specifically, determining the velocity of a vehicle that collided laterally with one or more "narrow" objects.

Here is the info I have on the subject:

[PLAIN]http://img231.imageshack.us/img231/8589/screenshot20111027at103.png

Also, this PDF explains it quite a bit more technically, if you scroll down to its discussion of the "Vomhof equation."

http://www.4n6xprt.com/Equation_Comparison-Frontal_Narrow_Object_Impacts.pdf"


So with that, here are the two things that I don't understand!

1. Why is it that, when a car hits a "narrow" object (such as a utility pole), the equation for determining its velocity from the depth of the crushed area on the car must be adjusted? Both links multiply the equation for velocity by .6 when the vehicle strikes a narrow object. But if the size of the depressed area on a vehicle post-impact is proportional in any way to the speed it was going pre-impact, shouldn't that proportion remain the same regardless of whether the car hits a wall or a dumpster or something narrow, like a pole? Why the .6 adjustment?

2. Given that there is some reason to distinguish between a car crashing into a narrow object and a car crashing into any other object (as described in that first question), how is "narrow" defined? Both of the above links give examples of "narrow" objects, but no strict definition! So how can a reconstructionist possibly know whether to solve for velocity using the generic equation or the "narrow" object one?


Any help and insight would be greatly, greatly appreciated! ESPECIALLY on the second question!

 

[AndyW]

Hi there,

Thank you for reaching out to the Physics Forums community for help with understanding the physics of accident reconstruction. I am happy to provide some insight and clarification on the questions you have raised.

Firstly, when a car collides with a "narrow" object, such as a utility pole, the equation for determining its velocity from the depth of the crushed area on the car must be adjusted because the nature of the collision is different from that of a collision with a wider object. In a collision with a narrow object, the impact forces are concentrated in a smaller area of the car, resulting in a deeper and narrower crush zone. This is in contrast to a collision with a wider object, where the impact forces are spread out over a larger area, resulting in a shallower and wider crush zone.

The adjustment of the equation for determining velocity takes into account this difference in the distribution of impact forces. The .6 factor is based on empirical data and represents the average ratio between the depth of the crush zone in a collision with a narrow object compared to a wider object. This means that for a given velocity, the depth of the crush zone will be .6 times deeper in a collision with a narrow object compared to a wider object. Therefore, the equation must be adjusted to take this into account and provide an accurate estimation of the velocity.

As for your second question about how "narrow" is defined, it is not a strict definition and can vary depending on the specific case. Generally, a narrow object is considered to be one that is significantly smaller in width than the width of the vehicle. This can include objects such as poles, trees, and narrow barriers. However, the exact definition may vary depending on the context and the specific accident reconstruction methodology used.

I hope this helps to clarify some of your questions and provides a better understanding of the physics involved in accident reconstruction. If you have any further questions, please don't hesitate to ask. Best of luck in your studies!