Built on Facts

Sole Survivor

CNN has a headline up: Fate or Fluke: Air crash sole survivors. ON the homepage itself the banner reads “Fate or Physics?”

(CNN) — Some will see it as divine intervention, others a simple quirk of fate, fortune or physics, but one boy’s cheating of death in an air crash in Libya this week adds another name to a small roll call of aviation disaster sole survivors.

The boy, identified as Ruben van Assouw, suffered multiple fractures in his lower limbs when the Afriqiyah Airways Airbus A330-200 crashed Tuesday at Tripoli International Airport killing 92 passengers and a crew of 11.

Statistically improbable, the fact of his survival is also unlikely to shed any light on the mysterious factors that increase the chances of escaping alive from a plane wreck.

It’s sort of a fluff piece about a tragedy, but I’m not going to rake it over the coals because honestly it’s not all that bad. Of course I don’t think it’s much of a mystery either – human bodies are all pretty similar in terms of what their structure can endure with regard to sudden deceleration. This is why airplane crashes usually have either many survivors or no survivors. Same thing with, say, car accidents, though the small number of passengers in most cars doesn’t highlight the “most survive or nobody survives” tendency to the same degree.

The list of sole survivors doesn’t appear to be comprehensive, but if it’s representative then it seems to highlight the possibility that the exceptions to the rule are often quite young. If this is a general trend, it may well mean that there is a physics principle behind the unlikely survival of these young passengers. During flight, each passenger is going to have an equal momentum per kilogram by virtue of their all sharing the velocity of the airplane. In a disaster, that momentum is going to be brought to zero by the forces of the crash. If the deceleration is similar for each passenger, then the forces per kilogram are going to be comparable. However, a person’s bone length scales with their height H and their skin surface area scales roughly with the square of their height H^2. But their total mass scales roughly with their volume, which is ~H^3. Thus the ratio of structural support (bones, skin) to vital organs is the highest for lower values of H.

Might this be an explanation for the possible advantage of the young in serious crashes? I couldn’t say for sure, and in any event the advantage may be an illusory effect of CNN’s selection of stories. For that matter I’m afraid it may be in terribly bad taste to discuss this only days after the accident. Still, it’s cold-eyed answers to the questions of physics in airplane tragedies that’s the reason there are so few of them. I hope the investigation into the science of this crash will make such tragedies that much less likely in the future.


  1. #1 Grad
    May 13, 2010

    I’m pretty sure that there is evidence (see the NHTSA maybe?) for youth being a factor in accident survivability. I suspect that your argument is at least part of it.

  2. #2 just some guy
    May 13, 2010

    Another factor to consider regarding youth and survivability, is the way children are treated/handled. I think more care is given to protecting children both from the manufacturers of safety devices and the behavior of parents and others. Kids get all the fancy safety harnesses and are put in the safest parts of vehicles where they are watched and cared for.

  3. #3 rob
    May 13, 2010

    unsubstaniated memory:

    you also have better chance of surviving if you are in the back of the plane, if the plane goes in nose first. passengers in the back have a longer distance to decelerate, so the max force can be lower.

  4. #4 dylet1
    May 13, 2010

    If the plane rotated when crashing, the momentum and (negative) acceleration were not the same for all passengers. I think. Also, if the interior of the plane ‘folded’ at different rates, the momentum and acceleration would be unequal.

  5. #5 Uncle Al
    May 13, 2010

    Hang tight! Marrow freed from broken long bones routinely clogs narrow blood vessels to cause ischemic retinas and blindness, cerebrovascular failures (strokes), pulmonary emboli, and renal damage. Yahweh is singularly disinterested in human suffering other than to inflict it.

  6. #6 Anonymous Coward
    May 13, 2010

    Your dimensional analysis is correct.

    This is why small animals can undergo great accelerations without ill effect.

    I can flick an ant off my wrist and it’ll be just fine, but put me through the same acceleration and I’d be a big mess. It’s not that the ant’s better built, it’s just smaller.

  7. #7 meichenl
    May 13, 2010

    It would be interesting to know how many crashes there are with just two survivors. I would expect this to be a smaller number than for sole survivors.

    If a plane crash has a 99.9% death rate, for example, then in a plane of 100 people there is a 90% chance of all passengers dying, a 9% chance of 1 passenger surviving, and a 0.4% chance of two passengers surviving.

    So assuming that plane crashes are very deadly, then we would expect there to be a sole survivor more often than two survivors or three.

  8. #8 Anonymous
    May 14, 2010

    One of major factors in surviving an airplane crash is the seat collapsing, absorbing energy, and lengthening the deceleration time and therefore rate. The seats are better able to do this for a smaller passengers such as children then for a large people such as an adults.

  9. #9 Eric Lund
    May 14, 2010

    I’d imagine that in a plane crash there will be a fair amount of flying debris that in some cases will do for passengers that otherwise would have survived. A small body means a smaller cross section for that debris to hit.

    Another factor which is probably irrelevant for plane crashes but more significant for things like building collapses is that the smaller the body, the more likely it will fit into some air pocket that happens to remain after the incident.

  10. #10 Alex
    May 16, 2010

    You would think occasionally two people would survive.

  11. #11 MPL
    May 18, 2010

    I would suspect children are both more likely to die and less likely to die—that is, I wouldn’t be surprised if children show greater variability in survival. If an accident had only one survivor or only one fatality, it might be likely to be the child involved.

    Children are just more varied than adults—mass, size, metabolism, sleep/wake patterns, all sorts of things that might have an impact on survivability.

  12. #12 MPL
    May 18, 2010

    Also, car crashes come in three kinds, not two: “everyone dies”, “everyone without a seatbelt dies”, “nobody dies”.

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