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20,000-lb. vs. Pedestrian - Analogy Sought

  1. Jul 28, 2004 #1

    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 linebacker's 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 and all input.
  2. jcsd
  3. Jul 28, 2004 #2


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    The momentum of the bus was (20,000 lb)(10 mph). The kinetic energy was 1,000,000 lb-(mph)². Given a linebacker of mass X lb, it would have to be going at a speed u of 200,000/X mph to have the same momentum and a speed of v = sqrt[2,000,000/X] mph to have the same kinetic energy. If you can find some X such that u = v, then a linebacker of mass X lb and speed v will be analogous to the bus. If no such X exists, then you'll have to decide whether you want to find a human analog in terms of momentum or kinetic energy.
  4. Jul 28, 2004 #3


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    How about getting the bus dropped on you from about 3 feet up instead?

    There are problems with square-cube relations involved here that make changing scales potentially misrepresentative. That said, it's probably not far from a grown man drop-kicking a rat, and the rat surviving.
  5. Jul 28, 2004 #4
    If the bus was only going 10 mph, how was the woman knocked up (heh) into the bus' windshield? Something's not right.
  6. Jul 28, 2004 #5


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    I agree. I think the woman would get knocked down and then subsequently run over by the bus. :eek:
  7. Jul 29, 2004 #6
    I, for one, would rather get hit by the bus than the linebacker. Shoot, a linebacker travelling at merely 200 mph would certainly kill the woman.
  8. Jul 29, 2004 #7
    By the way, these analogies are almost never accurate. I have seen collisions compared to dropping cars off buildings, and it is pretty obvious that the two situations are not really that similar. The Earth doesn't budge or buckle nearly as much as an opposing car.
  9. Jul 29, 2004 #8
    JohnDubya & Gza

    That's very telling that you both questioned the speed of the bus vis-a-vis the woman being launched up and into its windshield upon impact. In fact, the exact mph of the bus is unknown. The 10 mph speed is what was reported by the bus driver himself and may be an underestimation. Given the circumstances and injuries, what would you guys estimate the speed of the 20,000-lb. bus really was? (And BTW, the 10-ton weight of the bus is accurate per the manufacturer.)
  10. Jul 29, 2004 #9


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    Why do I have this nagging feeling that some lawyer somewhere is trying to get a free consultation on a personal injury case? :)

  11. Jul 29, 2004 #10


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    The key here is not total energy, but or energy transfer from the bus to the woman. The bus is so much more massive than the woman, you can ignore the woman's effect on the bus completely (technically, the impact will slow the bus down to just under 10mph, but the difference is so small you can ignore it). So the energy transfer is what it takes for the woman to go from 0-10mph.

    An analogy would be the same woman (assuming she is in decent shape) running into a brick wall at a full sprint.

    A football linebacker would need to be about twice her weight and an olympic sprinter to transfer the same energy (someone else can do the calculation).
    Last edited: Jul 29, 2004
  12. Jul 29, 2004 #11
    If I'm the bus company, I sue for damages to my bus. She stepped off the curb before it was safe to do so. Her fault.

    There, that ought to fix 'em. :)
  13. Jul 29, 2004 #12
    Scaled Example

    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?
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