The Physics of Tatiana

i-ab222cf9ca9b8e8bb7322a8fb392a522-tatiana.jpgTatiana was the captive Siberian Tiger who, on Christmas Day, leaped out of her cave to attack teenage boys who were taunting her. She killed one of them. Zookeepers are investigating how she did it, considering the possibility that the wall of her enclosure was not high enough (technically, it was lower than recommended height by a short distance). Tatiana’s leap has, indeed, has rekindled a long term dialog regarding zoos, and big cats in zoos in particular.

Now, a physicist at Northeastern University in Boston, has produced an analysis indicating that what did happen was possible. However, I think there is a problem with the analysis.

The analysis, reported here and discussed here, investigates the necessary velocity to “350 pound object over a 12.5 foot barrier that is 33 feet away.” The answer is 26.7 miles per hour at an angle of about 55 degrees above horizontal.

I’ve looked over the paper and it seems fine. The analysis is approached using multiple techniques and all the techniques come up with the same result. I’m trusting their math.

There are three factors that are either not fully addressed or that may be problematic.

1) The tiger has to be going just under 30 miles per hour. How long of a distance does a tiger need to attain that speed, and was such a distance available? I suspect a tiger does not need too much distance. They are built as ambush hunters. In other words, they are designed to “spring,” but this is a factor that must be at least considered.

2) What is the air resistance factor in this equation? One of the methods used in this analysis presumes the object in question to be, essentially, a mortar or cannon ball. But Tatiana is a big floppy furry tiger. How does this play in?

I suspect that if these factors are worked into the equation, the result would be the same, but I’m just sayin…

3) A witness at the scene described hearing bushes rattling around then the tiger showed up. This is important evidence that may tell us something in more detail about where the tiger was coming from, or what part of the enclosure the tiger was passing through, during this great leap.

I have no problem believing that this is physically possible. This is for two reasons. One, I’ve seen some pretty amazing leaping in cats, including large cats, and I suspect the range of jumping capacities of the large cats is unmeasured but impressive. Two, it actually happened, so in my own naive way I assume it was possible.

Safety (of both gusts and animals) in the case of large carnivores in zoos is important. I hope that this physical analysis is brought to bear on the investigation.

Comments

  1. #1 Shaun
    February 2, 2008

    I’m no physicist, but I wouldn’t be surprised if a leaping tiger was just as or more aerodynamic than a cannonball. I suspect that a leaping tiger would flatten itself out, making for a fairly aerodynamic shape.

    Also, is it possible that the fur acts to improve aerodynamics like dimples on a golf-ball?

  2. #2 Greg Laden
    February 2, 2008

    Shaun,

    You may be right about the aerodynamics of cats. But there is another problem that has occurred to me. The model seeks an optimum speed against height allowing angle to adjust itself. But I’m certain that a cat cannot take off at an arbitrary angle. THAT would require a cannon ball coming from a cannon on a mount!

  3. #3 Joshua Zelinsky
    February 2, 2008

    Gregg, first “gusts” should be “guests” in the third to last line. Now, more substantially, I don’t think the angle matter will be that serious. Cats seem in general to be very good at figuring out what angels to jump from and seem to have a lot of flexibility to do so (maybe similar to how humans are very good at doing the non-trivial task of throwing or catching a ball?).

  4. #4 Gerry L
    February 2, 2008

    When the elk exhibit was built at our zoo some years back, I noticed that the fencing around the off-exhibit paddock was higher than the fencing around the yard. The keeper explained that elk will jump higher when they are in a tighter space. If this is true, it’s probably a behavior thing rather than physics, right?

  5. #5 Greg Laden
    February 3, 2008

    Josh:

    Thanks for the correction.

    That’s 2, no3 3, G’s in Greg, by the way… :)

    I think the angle matters. Cats seem quite able to do things in many different directions, etc. but you are right, they are actually “figuring it out” rather than having bones, muscles, and joints that are of fixed lengths and relationships. We know, for instance, that the large tail, which adds weight and wind resistance, offers balance while turning or jumping. This means that a cat pays a cost (in weight) to be able to adjust for the fact that a four legged animal … which initially evolved for cursorily running along the ground is now doing something somewhat different.

    A lion, a tiger, and a cheetah are different enough in their body shapes that they have differen abilities regarding climbing, running, and turning. There is simply no way that the angle does not matter.

    It may be that tigers are optimized to leap over the highest possible object (or more likely to leap as high as possibly onto a branch or something) given their quadrupedal body form, large tail, big head, etc. But if so, I doubt that is at this specific angle derived from the physics.

    I personally suspect that cats, including tigers, would jump at a higher angle with zero initial speed than most people would imagine possible (including experts). I also suspect they can spring while running (taking the energy from running, trapping it in their gait, and using it for leap) and thug gain some great height from a relatively slow speed. (Please seem my earlier post, linked to above, regarding leopards).

    Gerrry,

    That is interesting to hear that about Elk. I was wondering that just the other day.

    As a rule of thumb, there are certain categories of ungulate that jump very high from standing still, and others that jump typically on a run. A cow can go pretty high up from a standstill, while a horse does not do that.

    In either case, though, they have to follow the laws of physics. What this person was telling you is a bit strange. If the minimum space an Elk needs to jump high is zero, then they can do that in a small place or a large place, so both places need a large fence. If it is “behavioral” … i.e., they WANT to leap from the paddock but they DON’T want o leap from the exhibit, then we have “behavior.”

    We also have an exhibit designed so that if a bunch of drunk teenagers come along and taunt the elk, and instead of an elk it is a tiger, and the exhibit was designed with using this behavior, instead of physics, as a key variable, then the elk (tiger) eventually will leap out of the enclosure and eat the teenagers.

    (In real life, taunted elk do not attack so much as they get really upset, their metabolic rate raises, and they die younger. According to the Rangers at Yellowstone….)

  6. #6 Alan Kellogg
    February 3, 2008

    There’s another matter to be taken into consideration. How pissed is the cat. Adrenaline greatly improves performance, and from reports Tatiana was pissed.

  7. #7 Matt
    February 3, 2008

    Greg,

    My name is Matt and I am a high school biology student.
    I think there are most likely many more factors that played into the attack than the evidence says. Like Alan said we do not know if another animal or perhaps a trainer had upset the tiger ewarlier that day. The victims were also probably taunting the tiger. Are there any other factors you can think of?

  8. #8 KevinC
    February 3, 2008

    I remember reading a quote from the vet who performed the autopsy that included the fact that Tatiana’s claws were cracked and had cement in them. Thus she did not need the speed, the question is how far a large cat can climb up cement walls when pissed off.

  9. #9 D'oh!
    February 3, 2008

    Bound, rather than climb, I should think.

    My cats can jump up walls that are higher than they can jump in a single jump by inserting a vertical bound or two while their upwards momentum still holds. They use their back paws push off again–usually with extended claws to help with traction. This is consistent with the vet’s findings.

    (OTOH, I have to add that running on concrete when they are adrenalized can also shred my cats’ back claws. I think that they extend their back claws in an all-out run so that they work like cleats. Probably a good idea on soft soil–not so great on concrete.)

    It’s unclear to me how high the wall was from the bottom of the moat. But I personally wouldn’t be surprised if pissed off Tatiana leapt up the wall vertically with a bound or two.

    Which brings me to my next point: animals have different personalities and different athletic abilities. From what I’ve read, Tatiana was a more assertive, daring animal. It is quite possible that she attempted something most tigers would not. And succeeded, obviously.

  10. #10 carey
    February 3, 2008

    Well, the math was fine, but if a big tiger is approximately 8.5 feet in length (legs outstretched), it could stretch its claws to within 4 feet of the lip of the moat. Jumping four feet (just enough to give its claws some purchase on the lip of the moat) seems quite feasible for a pissed-off kitty.

  11. #11 natural cynic
    February 3, 2008

    The analogy with the type of calculations that go on subconsciously when we throw or catch an object successfully only occur with a lot of practice. IIRC Tatiana was captive bred and probably had little practice at the kind of bound she made. She may just have been unlucky enough to succeed.

  12. #12 Greg Laden
    February 3, 2008

    Natural cynic: Good point. The systems of learning motion may be different for cats vs. primates, though.

    On the other hand, do we know exactly how many people each day for the last several years entered the SF zoo but never returned? Maybe this time Tatiana merely screwed up and got caught…

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