This summer, a man wrecked into and totalled my husband’s car. We only owed $450 more on that car. Stupid chode.
Anyway, the scene was spectacular. The guy – heretofore referred to as Chode – was driving a white Jeep Cherokee which was smashed to oblivion. The woman in the car behind Chode said he didn’t even hit the brakes when he slammed into my husbands Honda Element, which was at a full stop waiting for the man driving the Mercedes Sprinter in front of him to turn left into the Burger King for a Whopper made his way. I drove up to see my husband’s car smashed in the front and the back like a sheet metal accordion, and my husband pacing back and forth with a freaked-out, confused look on his face. When he asked me if I thought “they” could repair it, I told him, “Oh no, I don’t think so honey. There are five kinds of fluid leaking from under the car.”
Chode wasn’t wearing a seat belt. So I didn’t get the liberty to tearing into him for his obvious distracted driving as the ambulance carted him directly to the ER. (At 6:30 pm, he could only remember leaving the house that morning.) His head left a spider mark (Figure 1) on the windshield that left me puzzled as to how the dude didn’t end up on a flying mission to the pavement. (Thank science for airbags, eh?) I mean, how hard does one have to hit the windshield before the windshield wins? Which got me thinking. I’ll betch my husband saved that man’s life. My husband wasn’t convinced. So I will use PHYSICS to prove I am right!
Figure 2 shows a diagram of what the accident conditions were just before impact. My husband was stopped behind a Mercedes Sprinter that was trying to make a left turn into a Burger King. Both the Sprinter and my husband were at a full stop.
I performed an evaluation to compare the force that Chode’s brain would experience if he had rear-ended the Sprinter cargo van head on, rather than encountering my husband’s car first. The key assumption is that, while the Honda Element has a rear crumple zone (see Figure 3), the Sprinter cargo van lacks a rear crumple zone. (The Sprinter and the damage it incurred can be seen in the backgroud of Figure 3.) I reason that incorporating a crumple zone on the cargo van would pose a danger to the passengers in the cargo van. If the rear of the cargo van crumpled, the crumpling could transfer crash forces to the payload inside, possibly flinging objects toward the passengers in the open cab at the front of the van. One would not want flying objects to injure the passengers. I posit it would be safer to design the Sprinter with a rigid cargo hold to prevent objects from being ejected from the cargo hold.
I had to make lots of assumptions based on insight alone. But as long as the assumptions are conservative and are equally applied in all cases, the results of my analysis should be reasonable. Figure 4 shows a snapshot of the results. I cannot be sure the forces encountered according to these calculations are entirely accurate without downloading the information from the data recorders from all the vehicles involved. But the values are not as important as the comparison of the actual accident to the hypothetical event.
Observing the equations for conservation of momentum, the initial and final velocities of the vehicles can be estimated. My husband said he let up on the brake when he saw the Jeep was about to hit him. I confirm that since the Honda left no skid marks on the road. Assuming that – after collision – two cars can be treated as a single mass, I calculated the velocity after collision. To be conservative, I assumed the Sprinter was carrying merely a third of its full capacity. Then, setting an arbitrary (but informed*) impulse time, I calculated the G forces Chode’s average sized** brain encountered. Since there was only one crumple zone in the hypothetical event (as compared to two in the actual event), I cut the impulse time in half for that event. I believe this is conservative, because crumple zones have been linked to a 400-500 percent increase in impulse time. So the effect of losing a crumple zone is most likely underestimated in my evaluation.
The G forces encountered by Chode’s brain in calculation of the hypothetical event are more than twice that of the actual event. I cannot definitively say that, had Chode hit the Sprinter head-on, he would have died. The relationship of force to traumatic brain injury are quite complex. However, I can with some confidence conclude that encountering my husband’s crumple zone-equipped Honda prior to hitting the Sprinter’s rigid body definitely saved Chode some hospital time.
However, it didn’t save me any money. Stupid Chode.
*Insight sources: German, A. and Comeau, J-L., et al; Event Data Recorders in the Analysis fo Frontal Impacts; Annu Proc Assoc Adv Automot Med. 2007; 51: 225–243.
**Do note, I cannot assume Chode’s average sized brain provided him average intellect.