Physicist Calculates Trajectory of Tiger At SF Zoo

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."

35mph sure - but not uphill!

[jbb1003]

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.

Re:Never mind the physics

[ScentCone]

A shotgun? Very unlikely to kill it, almost guaranteed to enrage it.

Actually, I believe they DID kill it with a shotgun - just not loaded with birdshot. Slugs. You don't use a high powered rifle in a setting like that, or bet your life on a handgun. A 12-gauge with slugs will definitely kill something that sized, no problem.

Re:Hmm

[somersault]

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:Call in the lawyers

[Goobermunch]

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 enclosure and taunting that tiger. We're going to split the fault between them. And his total economic worth (over the rest of his life) was $800,000 (since he clearly wasn't that bright)."

Then the judge comes along and says--"okay, the award is $800,000.00. But the moron was 50% at fault. Therefore, his family gets $400,000.00."*

* Actually, in some states, he gets nothing, because his fault was not less than that of the other idiot.

But you can't argue that the zoo's not at least partially at fault. It clearly had an enclosure that wasn't adequately designed to keep the tigers in. The fact that the person who got hurt provoked the tiger doesn't lessen the fact that the enclosure failed to do what it was supposed to do.

--AC

A high school physics problem, good for an olimpic

[Anonymous Coward]

The authors formulate a high school physics problem, good, for example for an olimpic competition. Nothing wrong with that, it proves thast something can be done with high school knowledge. However I expected more from a professional paper, which should go further. The tiger is not a material point, but a body with a variable geometry. A more detailed biomechanical description shoud be used, in order to describe the way the jump is initiated, etc. Nevertheless the elementary, high school style analysis of the authors is a good starting point.

However, in its present form the paper is not publishable in a scientific journal, much more should be done.

Re:Lateral velocity != jumping velocity

[BigGar']

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 inclined is called jumping perhaps you've heard of it. Also at 35 mi/hr the tiger wouldn't need as steep an angle as it could leap from farther away.

My cats at home don't seem to have a problem with going from a near full run to near straight up if they want to, enough so that I can easily imagine a large cat going from full run to only 55 degrees.

Not exactly...

[absurdist]

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 the scene.

What a load of crap.

[pavon]

This enclosure was built in the thirties. It was just as dangerous during the ~60 years that it was a public zoo, as it was the last ~15 years as a private zoo. The Association of Zoos & Aquariums, which sets standards for zoo design, first started it's formal accreditation program in 1974. So they should have been aware of the problem for a good 20 years before it was privatized.

There does appear to be problems with the way the SF zoo is being operated now, but this particular case is a long standing condition that neither the public caretakers, private owners, nor the AZA made any effort to fix.

Re:A word on tiger behavior

[Debello]

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)

Re:Never mind the physics

[Rick Bentley]

Wait, a high powered rifle is EXACTLY what you want to use to bring down a big animal. A shotgun slug won't penetrate well at all (it's a subsonic round and has a high cross sectional area). A high powered rifle moves at over 3,000 fps (several times the speed of sound), has a small cross sectional area, and will penetrate deep into a fleshy mass.

Hunters in Africa (whom I think are total losers for shooting animals instead of just shooting pictures of animals) don't carry shotguns, with or without slugs. They carry high powered rifles. The term "elephant gun" refers to just such a gun.

Usually the only other gun a cop will have with him, besides his semi-auto pistol sidearm, would be a shot-gun. Shot-guns are nice in Urban settings as they don't over-penetrate walls and accidentally kill bystanders who might be standing a ways away or in another room/house/building. In any case, if they did use a shot gun to kill the Tiger it was only because they didn't have a high powered rifle with them.

...of course, I like to get the BFG and the quad-damage power up and get a good killing spree going but I doubt the cops had either of those in the zoo map...

Re:Hmm

[Fred_A]

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 :)

Projectile motion

[AlpineR]

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.

We had a long discussion about this in torts..

[ChePibe]

We talked about this problem at length a while back in torts.

Basically, the subject here is one of civil liability. The kids - all under the age of 18 - all had alcohol and marijuana in their bloodstream at the time of the incident (according to police reports). Their alleged taunting could be used against them, not to completely excuse the zoo from guilt (although they'll try), but to reduce the damages. Generally speaking as to torts, a jury can find a defendant partially liable for their own injuries.

I don't think there's too much question here as to the zoo's liability - they failed to build a wall capable of keeping the tiger in, and failed to keep their team of snipers (as per their own emergency plan) on the zoo during all times it was open. But, the zoo will pen its hopes on the theory above, arguing that the kids are at least partially liable. They do have a point - this tiger has certainly faced taunting in the past, and no results like this occurred. But the case for the kids, I think, is a much better. one.

The zoo knows it's trying to shoot the moon by removing full liability from itself, but they could have a reasonable shot at reducing the damages if it goes to court.

Re:Hmm

[EdwinBoyd]

Not to be a pedant but Polar Bears in their natural habitat will actively hunt humans.

Re:Absolutely not surprising

[ceoyoyo]

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.

Re:A lot

[Anonymous Coward]

Well sure, if it's your own kids being evil. However, if someone raped your wife or daughter, I doubt you would be so quick to rationalize the evil in human nature. We regularly punish people for being evil in our society. The tiger did the same thing the only way it could. In fact, I would go further than the GP and say that the only fault of the zoo was in not sufficiently protecting its animals from human abuse.

I assume anyone who has been bullied can sympathize with the tiger. "Tragically," for the idiots, they were not dealing with a peer, but an efficient killing machine whose only limitation was imprisonment - an obstacle that the tiger was finally pushed to overcome (for the first time in how many decades?).

I think what's most interesting in this case is that the tiger only attacked the three people tormenting it. The cops were forced to shoot, not when the tiger turned on them, but when it continued to attack its previous victim. That tiger wanted justice on three specific people.

They DID NOT have slingshots.

[statemachine]

The zoo director has been making false statements from the beginning, and using his influence to get the city of SF involved.

1) This is the same tiger (Tatiana) that attacked and seriously injured a zookeeper [sfgate.com] (Lori Komejan) who was only doing her job just one year ago. The zoo initially blamed the attack on the zoo keeper.
From a later article [sfgate.com]:

On Dec. 22 of last year, 300-pound Tatiana severely injured keeper Lori Komejan inside the Lion House, "degloving" her arm, as the state's workplace safety report put it. That agency, Cal/OSHA blamed the zoo, citing defects that the zoo knew about but hadn't fixed, and imposed an $18,000 penalty.

2) Zoo director Manuel Mollinedo is incompetent and demoralizing [sfgate.com]:

"It would appear that his management style - which downplays the value of staff and the welfare of animals - remains in place," said a former worker from the Los Angeles Zoo.

A departed San Francisco Zoo manager concurred.

"It's a top-down mentality that the zoo has adopted," he said. "And I think it's very dangerous."

Since Mollinedo took over, there has been a steady exodus of employees, including the deputy director, education director, two successive public relations managers, development director, curator of birds, marketing manager, events director, human resources manager, general manager of concessions and a number of veteran keepers.

3) The zookeepers knew the wall was too low [sfgate.com]:

But escaping from an enclosure at the zoo is not beyond the ability of a Siberian tiger, according to a retired longtime keeper and other zoo veterans interviewed by The Chronicle. And many people who worked at the zoo knew it, the keeper said.

4) The police didn't find any slingshots in the cars or on the brothers, anything unusual on their cellphones, foreign objects in the enclosure, or any witnesses to back up any suggestion of taunting, and suspended the investigation [sfgate.com].

You can find more articles in the special section that SFGate has just for the tiger mauling [sfgate.com].

But people will believe whatever they want to believe, right?

Re:Never mind the physics

[djtack]

Wrong, police used .40 caliber handguns. [sfgate.com]

THERE WAS NO TAUNTING

[ClioCJS]

Every follow-up article (which people don't usually bother to read) has said that the investigation concluded THERE WAS NO TAUNTING. That was just FUD on the zoo's part. And you fell for it hook, line, and sinker. http://www.cnn.com/2008/US/01/07/tiger.attack/index.html#cnnSTCText [cnn.com]

Re:the tiger had superior knowledge of the situati

[Grishnakh]

Humans have pathetic jumping ability, even the basketball stars, compared to cats (or most animals for that matter). Humans' advantage is their bipedal nature and the flexibility that offers for things like climbing, carrying large objects, etc. For things like running and jumping, we simply suck. My housecats could outrun me.

House cats can easily jump a 6-foot wall. I see it all the time here in Phoenix, where all our back yards are separated by 6-foot block walls, and it's common to see cats running around on top of them. This is for a cat which stands less than 12" at the shoulder and weighs 10 pounds or less. A Siberian tiger weighs 300-450 pounds. These animals are huge, and they're at least as well-muscled as a housecat. It makes perfect sense that they could jump over the wall at this zoo, given sufficient motivation.

If you've ever had the privilege of being very close to a large cat, you'd have a better appreciation of their size and musculature. I got to sit next to a cage with a mountain lion at a zoo once (one of the zookeepers let me in the back to see it); mountain lions aren't anywhere near as large as tigers, maybe about the size of a large dog, except that they have FAR more muscle than any dog of that height and length. I wouldn't ever want to tangle with a mountain lion; it's possible to fight one off if you have to, but many people have been killed by them in the wild, and many others severely injured. Tigers are much bigger than this; fighting with a tiger is like fighting with a bear. You're probably going to lose.

Re:They DID NOT have slingshots.

[statemachine]

Did you just read that one line line and stop? Cal/OSHA found the zoo at fault, not the zookeeper.

That agency, Cal/OSHA blamed the zoo, citing defects that the zoo knew about but hadn't fixed, and imposed an $18,000 penalty.

Here's from the initial article. If the cage was built properly, Tatiana would not have been able to stick her paws through the bars and grab the zookeeper.

Once the keeper puts the meat in the device, the door on the keeper's side closes, and another on the tiger's side opens. That way, there is no danger of the big cat touching the keeper.

All went well during the feeding, Jenkins said. However, a few minutes after Tatiana was fed, she somehow managed to get her paws on Komejan's forearms. It's not clear whether Tatiana thrust her paws through the bars, which are a few inches apart, or whether the feeder's hands were close enough to the bars for Tatiana to grab them.

From an article last month [sfgate.info] (emphasis mine):

Louis Dorfman, an animal behaviorist with the International Exotic Feline Sanctuary in Boyd, Texas, agreed that Tatiana posed no greater danger than she had before Dec. 22, 2006 - when she reached under the bars of her cage and seized the arms of zoo employee Lori Komejan as dozens of people watched.

The feeding enclosure was not designed and/or built properly. This was not Lori Komejan's fault. Lori was properly doing her job.

Design Problem was known for 40 years

[billstewart]

According to an article in the San Francisco Bay Guardian [sfbg.com], the design problems were known 40 years ago. As you say, it wasn't "fine when it was built" - it's not like tigers have gotten bigger in the last century, though perhaps Siberian tigers are bigger than whatever species of tiger they originally put in it. And the moat was never deep or wide enough, and tigers are even better at leaping across than jumping straight up.

The real reason the wall worked that long is that none of the tigers had previously felt motivated enough to jump at it. Apparently Siberians are more aggressive than Bengals, and maybe the two drunk kids pissed her off or just acted enough like prey or cat toys that she went for them. My cats sit on the couch looking out the window at Bird TV, and when one of them sees a laser pointer red dot he has to jump for it without thinking about it first (the other one says "Hey, stop wavin' that thing around".) And I've seen zoo leopards looking at the crowds, intensely tracking the smaller ones that get separated a bit from their herds; I'd feel much safer around tigers.