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Security Science

Physicist Calculates Trajectory of Tiger At SF Zoo 713

KentuckyFC writes "Is it really possible for a 350-pound tiger to leap a 12.5-foot barrier from 33 feet away? (Said another way: a 159-kg tiger, a 3.8 m barrier, and 10 m away.) A physicist at Northeastern University has done the math, a straightforward problem in ballistics, and the answer turns out to be yes (abstract on the physics arXiv). But I guess we already knew that following the death of Carlos Souza at the paws of Tatiana, a Siberian Tiger he had allegedly been taunting at San Francisco zoo at the end of last year."
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Physicist Calculates Trajectory of Tiger At SF Zoo

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  • Someone should warn SF Zoo!
    • Re:Hmm (Score:5, Funny)

      by Smidge204 ( 605297 ) on Friday February 01, 2008 @10:47AM (#22260748) Journal
      Seriously, you'd think the people who designed the enclosure would know how to do that kind of math... or at least be smart enough to get a consult. I wonder how many aquarium designs they went through before they finally made one that held its contents properly...

      =Smidge=
      • Re:Hmm (Score:5, Informative)

        by somersault ( 912633 ) on Friday February 01, 2008 @11:03AM (#22261002) Homepage Journal
        Well TFA points out that the enclosure didn't meet the recommended height, but still passed a safety check by the same body that actually made the recommendations.. strange, and tragic.
      • Re:Hmm (Score:5, Insightful)

        by Megane ( 129182 ) on Friday February 01, 2008 @11:05AM (#22261054)

        The people who "designed the enclosure"? It was (IIRC) a WPA project from the 1930's. It wasn't designed, it was built.

        The crazy part was that the people who ran the zoo had no idea of its height, or lack thereof. And when inspectors came through the zoo a couple of years ago, nobody mentioned to the zoo that the height was below standard. In other words, it's not a design problem (the height was fine when it was built, back when nobody was stupid enough to taunt tigers like that), it's a maintenance problem, as in keeping up to standards, or even knowing that you aren't.

        • Distance (Score:4, Interesting)

          by simpl3x ( 238301 ) on Friday February 01, 2008 @01:06PM (#22263036)
          I worked at a zoo in Chicago, and the Siberian Tigers were a concern. The distance between the habitat and the rest of us, seemed fine, would probably stand up to calculations, but never quite seemed enough for an animal bent on escape. When the things arrived at the zoo, I was photographing them, and the shear power of the roar was simply amazing. Standing outside of a steel box with the things in them didn't diminish the fact that they were there.

          One night I was watching some European wolves pace around there cage, when one caught my eye. Eye contact bad! It walked slowly down the exhibit and launched at the wall hitting the top. I left quickly... The Mexican wolves were rumored to escape often.

          People want to see the animals, and like everything else in this world it is a balance of risks. It's bad enough that the animals appear so sedate, but compound that with a realistic safe distance, and it would be a recipe for disaster. There was a reason they used bars back in the day.
      • Re:Hmm (Score:4, Informative)

        by Fred_A ( 10934 ) <fred@NOspam.fredshome.org> on Friday February 01, 2008 @12:49PM (#22262706) Homepage

        I wonder how many aquarium designs they went through before they finally made one that held its contents properly...
        Silly as it seems, there are several documented cases where octupus would leave their aquarium at night for a snack in the neighbouring basins, only to return before morning. Leaving only baffled keepers.
        Until someone sets up a camera.
        And then some thin mesh wire.

        Don't assume that animals are dumb because they live in water :)
  • by ta bu shi da yu ( 687699 ) * on Friday February 01, 2008 @10:44AM (#22260708) Homepage
    Surely someone would have calculated how far away a tiger needed to be from the public? Or doesn't anyone know how far a tiger can leap at SF zoo?
    • by eln ( 21727 ) on Friday February 01, 2008 @11:00AM (#22260950)
      Unfortunately, the zoo made their initial estimates for the enclosure based on the ballistic characteristics of a Southern Asian tiger carrying a coconut, not an unladen Siberian tiger, so their calculations were off slightly.

    • by Jamu ( 852752 ) on Friday February 01, 2008 @11:09AM (#22261116)
      They did, unfortunately the calculations were only accurate for spherical tigers leaping in a vacuum.
  • by ScentCone ( 795499 ) on Friday February 01, 2008 @10:46AM (#22260728)
    It's just nice to see that the zoo's kharma system was working. Unfortunately, someone meta-modded the tiger with a shotgun.
  • Never taunt someone call Tatyana or god forbid Katusha... If you value your life that is...
  • So 26.7mph is fine - great, but I'd like to see a tiger run at 26.7mph uphill (at 55 degrees!). That would be vastly more impressive than 35mph on the flat.
  • by ackthpt ( 218170 ) on Friday February 01, 2008 @10:51AM (#22260826) Homepage Journal

    Is it really possible for a 350-pound tiger to leap a 12.5-foot barrier from 33 feet away?

    All prior researchers have not returned from the jungle. Information is incomplete.

  • by arkham6 ( 24514 ) on Friday February 01, 2008 @10:53AM (#22260850)
    Well, I guess this is enough for the lawsuits to start flying at the zoo. Surely there are enough lawyers out there that will take the case. "Your honor, the zoo was clearly negligent in designing a tiger cage that a tiger could jump out of. The fact that the victim was allegedly taunting the tiger does not factor into the fact that the tiger was able to escape due to the mistake of the zoo building the environment."
    • Re: (Score:3, Informative)

      by Goobermunch ( 771199 )
      This is stupid.

      Yes, the zoo was negligent. It should have known the safe parameters for a tiger enclosure.

      However, in the law, there's a doctrine called comparative (or contributory negligence). This means that where two people are negligent and one gets hurt, his or her recovery is reduced by his or her own proportion of the fault.

      F'rex: A jury looks at this situation and says "Boy, the zoo sure was negligent, they should have built a higher wall. But boy, did this guy act stupidly, entering the enclos
    • Not exactly... (Score:3, Informative)

      by absurdist ( 758409 )
      Unfortunately, it's not as simple as that. Inspectors from the AAZA (American Association of Zoos and Aquariums) were out two years ago and measured the walls of the enclosure, calling them adequate according to their standards. And they're the ones who write the book on these matters.

      Still, it's a damned shame. For the tiger, that is. Not for the drunken nimrod who was teasing her, going so far as to pass the barriers erected to keep the public back from the animals, according to the evidence found at
  • by imstanny ( 722685 ) on Friday February 01, 2008 @10:56AM (#22260874)
    Which begs the question; What kind of methods are used to determine the 'standards' for an inclosure?
  • by SharpFang ( 651121 ) on Friday February 01, 2008 @10:57AM (#22260902) Homepage Journal
    I did a similar calculation a while ago.

    An object of 750kg can accelerate to 60km/h in 5 impulses (rapid pushes).
    How far will an object of 75kg travel when one such impulse is applied at angle of 45 degrees upward?

    The 750kg object is a horse. About 5 pushes of hind hooves are enough to reach the full speed.
    The 75kg object is a human kicked by the horse (remaining motionless with a counter-push of front hooves).

    The result was something like 30 meters. The damage was equivalent to fall from 6th floor.

    And they tell us horses can't say "no" when they don't want sex.
  • by Schraegstrichpunkt ( 931443 ) on Friday February 01, 2008 @11:00AM (#22260932) Homepage

    "Is it really possible for a 350-pound tiger to leap a 12.5-foot barrier from 33 feet away? ... But I guess we already knew that following the death of Carlos Souza at the paws of Tatiana, a Siberian Tiger he had allegedly been taunting at San Francisco zoo at the end of last year."

    If we already know the answer, then the question really is, can we explain how a 350-pound tiger to leap a 12.5-foot barrier from 33 feet away, or do we need to do some more research?

  • Inaccuracies (Score:4, Interesting)

    by sifi ( 170630 ) on Friday February 01, 2008 @11:00AM (#22260946)
    Looking at this diagram: http://www.sfgate.com/c/pictures/2008/01/03/mn_grotto.jpg [sfgate.com] You can see that it is 33ft along and 2.5ft up for starters. (12ft is from the bottom of the moat, not from where the tiger jumped).

    Then the tiger's centre of mass is probably about 2.5ft up anyway so it more about being able to jump 33ft flat.

    Also speed doesn't translate into distance in this simplistic way either: if it did humans would be almost able to jump the distance (max speed = 26.25mph) which is close as damm it to the 26.7mph required.
  • The numbers don't tell the entire story. Just because something can go 27mph doesn't mean it can necessarily project itself over the fence at a given projectory. The worlds fastest humans can go 27mph, but I'll put money against their ability to jump over a 12.5' fence; the world high jump record is 8'. Tigers and people are built differently for sure, but I'm not sure how the math applied in this document applies to animals when so many other factors are at play.
    • Re: (Score:3, Insightful)

      by Sockatume ( 732728 )
      I think the point is that a trivial, back-of-the-envelope calculation would've told them that an idealised tiger could've jumped the fence. If you build a fence which can hold an idealised tiger, it's more than enough for the real thing. I'm sure our engineers, physicists and chemists will agree that a bit of head-scratching and guesstimation is advisable before you do something that could blow up in your face.
  • by sizzzzlerz ( 714878 ) on Friday February 01, 2008 @11:03AM (#22261012)
    before I finally decide.
  • by daffmeister ( 602502 ) on Friday February 01, 2008 @11:04AM (#22261030) Homepage
    From TFA:

    From our calculations it was shown that a tiger only needs a little over 26 mi/hr to cross the 33 ft moat and clear the 12.5 ft high wall. From the current data that is available, a tiger can attain a maximum speed of 35 mi/hr.

    35 mi/hr across the ground != 26 mi/hr at a 55 deg angle. I'd like to see how they propose converted that lateral velocity to the highly inclined one.

    This is high school physics done badly. Very poor analysis.

    • Re: (Score:3, Informative)

      by BigGar' ( 411008 )
      What they're saying is that the tiger would only need to get to 26 mi/hr at a launch angle of 55 degrees to clear the 12.5 ft wall 33 ft away, however, the maximum speed of a tiger is 35 mi/hr - 9 mi/hr faster than needed, thus the tiger could clear either a taller wall at 33 ft away or a 12.5 wall farther away.

      In any event given the maximum known speed of the tiger it should have been a simple matter to know that it was capable of jumping out of its "cage". Converting lateral velocity to highly incline
  • by GodfatherofSoul ( 174979 ) on Friday February 01, 2008 @11:12AM (#22261160)
    I took engineering physics in college, and from what I recall all formulas only worked on massless, frictionless systems and didn't account for air resistance. Now, how the hell did a physicist crunch these numbers?
  • by bluesangria ( 140909 ) on Friday February 01, 2008 @11:33AM (#22261490)
    I was watching a Discovery channel show on some guy who was raising two tigers in a park preserve to be eventually released in the wild. To avoid incurring any dependencies on humans in the tigers, he kept away from them as much as possible, only associating enough to feed them and care for any injuries. To train them to hunt, he would make the tigers chase a deer or goat carcass dragged behind a car. The tigers were rewarded with their "kill" once they managed to get a good bite on the carcass to hold it. Afterwards, to up their training, he simply released several live prey animals into the park (goats, gazelles, etc.) and let the tiger's instincts take over. One thing that impressed me, and that they did not know before studying these tigers, is that tigers tend to go on "killing frenzies". Without being hungry or being threatened, tigers will simply run from one prey animal to the next, slaughtering it, taking a bite or two, then rushing to find another. They are, quite simply, relishing their power as a predator. After the end of a frenzy, the two tigers had slaughtered almost 40 prey animals in a short while.
    I don't know whether or not those boys taunted the tiger, and honestly, I'm not sure it would have made a difference. But I'm fairly certain the tiger would not have "settled down" after only killing a couple of people, not when the place was filled with fearful, slow two-legged animals acting like "prey". Welcome to the world of wild animals.

    blue

    • by Debello ( 1030486 ) on Friday February 01, 2008 @12:31PM (#22262422)
      No, no, no, no and NO. You know nothing of tigers.

      1. Tigers have practically no natural instincts when it comes to being predators. Tigers in the wild have to be trained by their mothers how to do things like hunt, climb trees, eat properly, etc. These are things that a human cannot teach. Therefore, any tiger born in captivity cannot be released into the wild and survive. It simply does not have the skills necessary.

      2. Look at the way these tigers were trained. Just two bites, and then they get their kill. They can eat it whenever they want. Now observe the way that they killed the 40 animals released into the zoo. Killing frenzy? Yes. By all definitions, that's a killing frenzy. But was that killing frenzy a product of their instincts? No! If you've done any research or paid attention to anything about tigers, you would quickly learn that my first point is quite correct and proven. Tigers have no natural instincts when it comes to killing their prey. Again, observe how it was trained to hunt and how it slaughtered the wild animals: in the same fashion. This is because it knows no other way to kill animals. You say, 'welcome to the world of wild animals.' I say, 'welcome to the world of tigers not being properly trained by their human caretakers.' All tigers are in captivity are oversized house cats, and about just as aggressive. This means yes you need to be careful, but it means no they're not just going to kill you because they're hungry.

      3. Which leads me to my third point. where you say:

      But I'm fairly certain the tiger would not have "settled down" after only killing a couple of people, not when the place was filled with fearful, slow two-legged animals acting like "prey".
      Well, you put your certainty in the wrong place. Unless the tiger in TFA was trained to attack and kill humans for food, the chances of it deciding to just jump out of its cage and go on an eating frenzy is virtually zero. A tiger must be TRAINED to be a predator, and it must be TRAINED to attack humans for food or for pleasure. In the wild, this training is not done by instincts like you so ignorantly proposed, but by the tigers mother. And this leads me to my fourth point:

      4. You know nothing of tigers. (See opening sentence)

  • by KDN ( 3283 ) on Friday February 01, 2008 @11:35AM (#22261516)
    Is it really possible for a 350-pound tiger to leap a 12.5-foot barrier from 33 feet away?

    Coming up next on Mythbusters :-).

  • by Tanuki64 ( 989726 ) on Friday February 01, 2008 @11:40AM (#22261598)
    I once had a guided-tour through a German zoo. When we came to the tigers the guide told us that the tigers in theory were able to leap over the barriers. According to the guide many animals in that zoo were able to escape when they really wanted. However, animals are similar to most people in some aspects. Life is good in the zoo and within the known areas. What is outside is unknown, perhaps scary, so why bother? Looks like the taunting was enough reason to bother for that tiger.
    • Re: (Score:3, Informative)

      by ceoyoyo ( 59147 )
      I was at the zoo once when a vulture managed to fly out of her cage. It had been a little too long since her last wing clip. She was terrified and spent all her free minutes desperately trying to teleport back through the fence into her enclosure, until a keeper picked her up.
  • Who cares!? (Score:5, Insightful)

    by jav1231 ( 539129 ) on Friday February 01, 2008 @11:45AM (#22261682)
    I contend that the enclosure was just fine. The tiger was content until he was taunted. This story had less to do with "how to contain a tiger" than "don't taunt the potentially man-eating tiger!" Note, he only went after those who taunted him! I'm not saying it was justified, but given that the tiger could hardly go to the authorities and his predisposition to violence he did what a tiger does back home.

  • by penguin_dance ( 536599 ) on Friday February 01, 2008 @12:04PM (#22261978)

    The asian elephant in this is about 12' tall. Back story: A tiger escaped from a preserve in India (Kaziranga National Park) and had killed a couple of farm animals. She was training her cubs to hunt. Rangers had found the cubs and took them (which I find incredibly stupid because now she's stressed and looking for them). Riding elephants, they found the female in the brush and tried to tranquilize her, but the dart missed. What happened next [youtube.com] should give you and idea what the jerks in the SF zoo saw.

    The elephant trainer survived, but was badly wounded.

  • Projectile motion (Score:3, Informative)

    by AlpineR ( 32307 ) <wagnerr@umich.edu> on Friday February 01, 2008 @12:57PM (#22262854) Homepage

    Clearing a 12.5 ft barrier at 33 ft away just didn't feel intuitively possible, so I found a projectile physics toy to test it:

    Projectile Motion [virginia.edu]

    In SI, the values are 12 m/s at an angle of 55 degrees with a mass of 160 kg, clearing a 3.8 m barrier at 10 m away.

    I had some recollection that 45 degrees was the optimum launch angle, but apparently that maximizes distance, not height. Mass doesn't factor into the calculations unless you include air resistance, which the paper neglects.

    The surprisingly sensitive factor is launch velocity. Lose 1 m/s and you smack into the middle of the wall. Gain 1 m/s and clear a 16 ft barrier, landing 52 ft away. It still seems phenomenal to actually get a tiger's horizontal velocity redirected at 55 degrees.

  • by Guysmiley777 ( 880063 ) on Friday February 01, 2008 @01:43PM (#22263648)
    The autopsy done on the tiger showed shattered and broken claws from scrambling over the concrete. The tiger didn't just do some anime style super-leap, she got claws on the edge and pulled herself up, shattering claws in the process. This was not a happy tiger that these 3 douchebags happened to get caught by. She was pissed off and looking to confront her tormentors.
  • by LrdDimwit ( 1133419 ) on Friday February 01, 2008 @02:39PM (#22264572)
    Physicist conducts analysis, concludes that thing which already happened is theoretically possible.

Math is like love -- a simple idea but it can get complicated. -- R. Drabek

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