20,000-lb. Bus vs. 165-lb. Pedestrian -- Analogy Needed

[Jeekay]

Hi,

Here's a true scenario: A 50 year-old female of average height and weighing 160-lbs. steps off a curb and is hit square-on by a 20,000-lb. bus going a steady 10-mph. The bus impacts the woman at 10-mph, then stops. The woman is first knocked up into the windshield of the bus, then "bounces" off the windshield and lands in the street (an unknown distance from the front of the bus). She survives the accident, sustaining a fractured arm, rib and skull.

Here's my question: Can someone come up with a real-world, more human-sized physical analogy for this incident? In other words, in terms of impact force, can this pedestrian-vs-bus scenario be reasonably equated to, say, someone being hit by a football linebacker of X weight and running at X speed? If so, what would that weight be, and what would that speed be? Or perhaps there's a better, more illuminating physical analogy that someone could come up with. I realize the variables at play in the bus-vs-pedestrian situation are myriad, but I am just seeking a reasonable analogy.

My powers of forensic force analysis pretty much end at KE = 1/2 m v^2, so I'm looking for some help here.

Thanks in advance for any input.

 

[IRstuff]

This is a swag, I'd guess a linebacker hitting you at about 50 mph.

There basically is no good analogy, since a linebacker is still made of flesh and bones, albeit padded, while a bus is made from hard materials throughout, e.g., metal or plastic. So, I guess about a 5:1 difference in effective force. Bear in mind that a normal linebacker only does about 20 mph.

TTFN

 

[Jeekay]

Going with your 5:1 estimate of effective force, about how heavy would the linebacker have to be if he impacted the pedestrian at, say, 25 mph?

 

[IRstuff]

Since this is a swag, I'd venture that the weight needs to be proportional to the velocity ratio squared, e.g., 4 times as much.

TTFN

 

[Jeekay]

A friend suggested I conduct the following experiment as an apt "scaled analogy": Buy two 1.65-lb. tomatoes that are as similar in firmness as possible. Then (somehow) borrow a small car that weighs 2,000-lbs. Drive the 2000-lb. car at 10mph into the first 1.65-lb. tomato that's been suspended by a string at bumper level. Just after impact, grab the tomato by the string before it pendulums back into the car and see what kind of bruising it has sustained. Then take the other 1.65-lb. tomato and position it at bumper level atop some kind of narrow support stand. Drive into this tomato at 10-mph and let it hit the street. Now compare the two tomatoes to determine what damage was caused by the vehicle impact and what damage was caused by the ground impact. Anyone for ketchup?

 

[sreid]

How about being dropped on to concrete from about a meter?

 

[jabonet]

I could say its more like falling one meter and landing on top of the bus roof, a concrete slab is harder than the bus (I guess) and if the bus front bends it takes a lot of energy doing so.

the speed is not really high, the impact is pretty much the same as a marathon runner could suffer if he hits a standing still bus, running at cruise speed.

one question. are you sure the woman bounced from the bus, or was it just that the bus was stoping after the impact?

 

[adrianviorel]

Just want to remind all that, in this particular case, an important part of the impact energy serves to deform bus body, or to crack the windshield. Therefore, comparing it with dropping on a concrete surface seems a bit daring... and definitely a wrong model