Feline ballistics

tiger-leap

Here’s a straightforward question in ballistics:

What velocity do you need to launch a 350 pound object over a 12.5 foot barrier that is 33 feet away?

The answer, thanks to Raza Syed, a physicist at Northeastern University in Boston, and a pal is: 26.7 miles per hour at an angle of about 55 degrees.

Now let’s make a few substitutions. Replace 350 pound object with a female Siberian Tiger called Tatiana. And for 12.5 foot barrier 33 feet away substitute the dimensions of the tiger enclosure at San Francisco zoo.

Is this kind of speed possible for a tiger? Apparently yes. Syed says tigers can reach speeds of 35 miles per hour with a run up of only a few feet so this enclosure was clearly no barrier to Tatiana.

After her leap for freedom, Tatiana killed 17-year old Carlos Souza and was shot dead after mauling two other victims.

Ref: arxiv.org/abs/0801.4407: Tiger Tales: A Critical Examination of the Tiger’s Enclosure at the San Francisco Zoo

104 Responses to “Feline ballistics”

  1. Jesse says:

    Neat physics! As for the nutjobs that say the humans should be killed or bitten, or eaten…do the rest of us ‘human vermin’ a favour and kill yourself.

    A canadian.

  2. Taco Sauce says:

    Don’t drink vodka and tease tigers.

  3. Kjellander says:

    Great physics behind this, but I think it is a bit flawed.

    From doing extensive studies on trying to keep our cat in a back yard at my grandparents place hours before going back in the car (preferably with our cat), I can say, with confidence, that the center of mass does not have to get all the way to the edge of said fence/zoo pit in order for the feline to get out.

    All it needs is to get it’s paws over the edge, and then they can do what climbers call “mantle the edge”, heaving themselves up. The reach of our cat var probably 35-40 cm over the center of mass so a 175 cm wooden fence was no match for our cat. It just pulled itself up, balanced perfectly on the top of the fence, looked back at me with a “You can’t contain me”-look and jump to the other side.

    So recalculating everything with the reach of a tiger, probably 1-1.5 m over center of mass, is probably a better estimate.

    So in conclusion, the tiger probably needs even less speed to get out of it’s pit.

  4. Marie says:

    To inform those commenting…the tiger was killed because she was mid-attack when they (police) found her. And there was not enough time for anyone to rationalize that the tiger only wished to hurt those who harrased her or for police officers to arm with tranquilizers opposed to guns which are already on their person while on duty. It is a shame truly, but I can’t blame the officers seeking to protect themselves from a potential attack. As for the boys who were injured and killed- I cannot say I feel as sorry for them as I do for the tiger.

  5. Richard says:

    And how, exactly, do you know what God looks like? Oh, because it says so in some old book, somewhere in there with other great fairy stories like the world’s being created in 7 days and “Thou shalt not suffer a witch to live.”

    “Seriously, humans are flawed, sure– we’re all in need of redemption because of our sin, but we’re also created in the image of God”

  6. Kjellander says:

    Gunnar: It’s not silly, there is nothing wrong with the physics behind the ballistic path, but as both you and I have pointed out, the center of mass does not have to go from the ground all the way to the edge.

    I even forgot that the center of mass of a tiger is quite some distance from the ground, and then of course it doesn’t have to get all the way to the edge.

    To correct the equations; how far above the ground is the center of mass of a tiger, how long is the reach of a tiger beyond its center of mass and how much energy is lost into rotational momentum getting the tiger more upright to reach the edge?

  7. Kjellander says:

    flug’s link tells it all. It’s a lot easier for the tigers to jump that distance, so redo all calculations according to the new data.

  8. Scott says:

    “Human lives are inherently worth less than those of any other large animal on the planet, by virtue of numbers. There are 6 billion of us, and not nearly that many of anything else.”

    Penguin — Please tell me you are not serious with this statement. This is quite possibly the most asinine thing I have ever seen anyone say.

  9. Dan says:

    “Americans ARM our police, so thankfully no further harm to the highest life form on the planet took place.”

    I had no idea that any dolphins were hurt in the attack!

  10. Scott says:

    “Humans Suck, we are a blight, killing two more of us wouldnt have mattered in the long run.”

    Gregory — You may have topped Penguin in the most asinine statement I’ve ever seen. If people who say this crap really believe it, there is one thing that they can do to reduce the population by one.

  11. Alex says:

    “I wish to God the tiger had killed the other two. Shooting the tiger was absolutely inexcusable. They should shoot the other two humans.” -Dan

    “Humans Suck, we are a blight, killing two more of us wouldnt have mattered in the long run.”-Gregory

    people that say this have got to be the most selfish jackasses on earth. How about you two pick up the slack and offer yourselves up for slaughter? I’d be happy to blow your brains out to satisfy you. Or would you prefer to be wounded first, then start being eaten like a tiger’s meal? Let me know how I can make you happy over this whole ordeal by killing you the way you desire. Just as long as it’s somebody else that dies, it’s cool w/ you guys to act all high and mighty on the top of the food chain, right? IMHO, you two are excellent substitutes.

    DIAF.

  12. Eddie Haskel says:

    For all you crack smokers out there:

    1) don’t deny what the Tiger did. IT CLEARED THE FENCE… duh. Doesn’t matter if it cleared the WHOLE fence, or clawed the rest of the way to the top…. so stop arguing about it.

    2) don’t think the Tiger can’t fend for itself in the wild and would starve to death… He did pretty good in SF didn’t he? 1 Meal down, working on 2 more…

  13. Wayne says:

    I believe Vietnam was a disaster the French left behind for the US to clean up.

  14. Area 51 says:

    Vietnam didn’t happen. It was all made up by a consortium of rightwing Hollywood producers and the trilateral commission to divert attention away from secret and illegal human testing being conducted by the military in area 51 – the real reason there is a fenced desert!

  15. Jesse says:

    but now the question is…can a tiger get OVER the fence in the desert…..LOL

  16. Tim says:

    The mauling is enough. And I would not have shed a tear if it killed the other two.

    I am so sick of the current population of youth expecting everything to be handed to them and how amazed they are when they are forced to accept responsibility for their decisions. In this case they taunted a living creature. In 17 years even around people you think they would have learned that taunting things tends to cause a reaction that is not positive. They got what they deserved.

    As for the Tiger, It is sad they had to kill it. But I agree once an animal kills a human it cannot be trusted not to do it again. Is the zoo at fault? Yes, the tiger should not have been able to get out. They should have security monitoring high profile/dangerous animals and those “kids” should have been arrested long before it escalated this far.

    Good riddance to that trash.

  17. Lisa says:

    Too bad she didn’t kill the other two. Her death would have been more meaningful.

    +1

  18. sanity check says:

    I wasn’t there. However, police in this country has a long tradition of “shoot first, ask questions later”. I doubt that the tiger put other people in danger after taking care of the idiots who harassed her (if it did, perhaps the killing was justified). And it’s a pity she didn’t finish her job…
    I think that the tiger should have been tranquilized first AND NOT KILLED ON THE SPOT, regardless of what the decision would have been on her ultimate fate.

  19. Spinner says:

    A standard housecat can make 30+mph over the ground. I’ve seen one (my own) blast across a yard at warp 9, go airborne (with no perceptable loss of velocity, the vertical is added to the horizontal, not ‘converted from”) and clear a 4 foot fenct by 10 feet on each side. It took him another 30 feet to stop on the far side. That was a 16 lb house cat. Scale appropriately for one each tiger. Big cats are house cats writ large, and every bit as powerful and agile per cubic inch. You seldom see a cat at 100% effort, and are very likely not going to see a wild one. They trade speed and violence for stamina .. they can only be on game for a few seconds but in their world thats all that matters.

  20. Jub Jub says:

    The authors of the paper did not consider air resistance. Was the tiger jumping on the moon? Why does a generation of teachers teach this vacuum equation on a planet that continues to have at atmosphere. Shame on you, Sir. Shame on you all.

  21. verge says:

    “Human lives are inherently worth less than those of any other large animal on the planet, by virtue of numbers. There are 6 billion of us, and not nearly that many of anything else. The solution is to cut back in reproduction, but until that happens on a large scale, the large number of humans is the biggest problem we know of in the universe.”

    Please then, feel free to remove yourself from the problem. Use a knife as gunpowder releases greenhouse gases when burned.

  22. Spinner says:

    Reply to jub jub

    Air resistance at 25 mph on something as dense and, yes, streamlined, as an elongated tiger is not zero but it is negligible in the uncertainies of the other part of the equations … a pound or five on the size of a cat.

    Look at a mid-flight cat head on.. all you see is head and front paws, they are rather smooth and have a ridiculously efficent moment of inertia for jumping on food from a distance. It just amazing what a few million years of darwininan guess and hope does for aerodynamics.

  23. chmod says:

    Wow. I live in the Bay Area. I didn’t witness this incident. I had no idea so many others did and can therefore state, without hesitation, that the three guys provoked the animal.

    As I did not witness this I cannot assert why the cat scaled the wall. It seems reasonable to speculate something provoked it. But come on folks, a human being died as a result of this.

    And again, since you all appear to have all of the facts, I’m sure you realize the one guy who died was not the one with any manner of police record or dope in his car or blood alcohol levels above legal. He was, regrettably, a friend of the two brothers where were cut up, but not derived from the same mold in terms of his track record.

    If the three were indeed doing something lame, then they should have been immediately escorted out of the zoo. There is an ongoing investigation, far from over, which continues to probe for details. The zoo is completely at fault and has admitted so publicly. There were witnesses quoted in the news, but oddly enough there has been nothing put forth to indicate any of them will stand up and assert what they saw.

    There is no excuse for having an enclosure which cannot contain a beast which is by nature, designed to kill to survive. It makes me want to puke to think of the death of the guy and the animal which never should have come close to happening.

    But reading many of these comments makes me realize what a savage and reactionary group of people can devise from the confines of their network connected spaces without anything more than thrice removed data from which to form conclusions. Sleep well fair people.

    I can only hope you are never requested to judge me or my actions.

    chmod

  24. mean kids says:

    I have a neighbor with some Rottweilers and there are neighborhood kids that taunt them and poke them with sticks through the fence almost every day. It drives the dogs dangerously crazy-mad. I hope someday one of them gets out and shows the little bastards how stupid they are. Of course, the dog would be put down, and that would be a shame, but kids don’t seem to have respect. There should be some kind of law that you get what you ask for in circumstances like this. GO TATIANA! We will miss you!

  25. sflocal says:

    For all the non-SF-natives that are just picking up on this story:

    1. The tiger was loose in the zoo, after dark, with an unknown number of zoo employees trapped in place; it was stalking the two young men, one of whom was leaking blood. Tranquilizers would take upwards of 30 minutes to affect an animal that large. In that situation, the police had no choice but to use lethal force — and would have done so against a human murderer as well. Tatiana wasn’t a murderer, she was just a predator doing what predators do — but if the policy has left her free to kill again, they would be in gross violation of their commitment to the public’s safety.

    2. The young man who died did so after distracting the tiger from the original victim; it appears from the evidence we’ve been given so far that he was not the one who taunted or provoked the animal and is an innocent victim. So a little F’ing humanity for the death of a young man with a long life ahead of him and a loving family, if you please.

    3. Every zoo professional would agree that you should be able to walk through the zoo covered in raw meat, screaming at the top of your lungs and jumping in front of every predator, and be perfectly safe. The zoo is certainly at fault in this case, both for the death of the young man and the death of the tiger, and has been in full liability-limitation mode since day one.

  26. billnvd says:

    Many posters here are using human strength as the measure for the ability of a cat to leap and run. Felids have radically different muscle fibre than humans.

    The muscles in these animals are adapted to sudden and short term high energy use.

    They can haul themselves and an equal weight prey animal 20 feet up a tree in just a few seconds. They can reach a decent top speed from a stand still in just a few strides. They can unleash a massive amount of raw power for a very limited time.

    If you want to feel superior to a cat, challenge one to a 10k marathon.

    Just don’t try to estimate a cats power/speed/endurance based on a human equivilant.

    Pound for pound, cats are just about as bad ass a predator as you get.

  27. Personally I think it came across the moat quickly, jumped and stretched out reaching high and clawed up the wall with all fours a bit, assuming the concrete wasn’t perfectly flat, it got just enough traction to keep some upward momentum and get it claws to the top. Once claws got there, it was game over. Who knows, maybe it tried that repeatedly as it was being taunted failing each time, and finally made it on the last try. The 33ft leap is dramatic, but not really realistic. Plus for those who think it just needed claws over the wall in that scenario, that meant the 350lb tiger hit a concrete wall at 26MPH+, which would sort of hurt and make it hard to hold on, even for a tiger.

  28. writing without reading says:

    “that is what Americans do to animals who present a danger to humans”

    and I will show you what Americans do to ignorant twits who define entire cultures by the actions of two men.

  29. writing without reading says:

    sflocal, I am not a zoologist but I honestly can’t believe that the zoo doesn’t have tranqs that work nearly instantly. Where did your information come from? 30 minutes seems like a VERY long time for blood to circulate.

  30. Gavin says:

    Surely the police could have just put their phasers on “stun” :P

    I’m sorry, but I don’t think there’s any “tranquilizer” drug and delivery system out there that will stop an angry 350 pound tiger (without killing it) in less than a minute, probably longer. The tiger was standing next to a wounded victim when the police arrived, so there’s no way they were going to do anything other than employ massive lethal force at that point.

    Anyone who thinks otherwise has likely been watching too much TV full of instant-sleep ninja-dart-weapons.

    G.

  31. Robert says:

    It’s amazing how many people don’t understand the concept of a ballistic problem. Yes it’s harder to run up an incline than in a straight line, but with a ballistic problem you don’t need to run at the incline or keep your speed, in fact it’s understood that you would loose speed otherwise you would never land. So, the tigger didn’t need to run up a 55% incline at 26 miles per hour, it only need to be going 26 MPH when it started going up 55%.

  32. I am surprised because even if the animals could jump, they are loath to take the risk unlles it is to save their own life; there is initial hitch. There could not be threat to life in zoo.

  33. asdf says:

    “a human being died as a result of this”

    wtf? are you this obtuse? how about they should have thought twice about putting the human near a dangerous animal.tigers don’t want to live in zoos for your amusement and certainly don’t warrant killing because someone was stupid enough to bring the cat and humans into close enough proximity that the human could be killed. what they should consider is shooting those responsible for running the zoo who deluded the humans into thinking they were in a safe environment.

    at least the tiger got one.

  34. dan says:

    From the condition of the animal’s claws, it has been suggested that the tiger scaled the wall rather than leapt it. I’m not sure if mantling the edge would have left the claws in the condition they were in as I have no first hand knowledge of the condition of those claws.

  35. ross says:

    Informal poll: How many of us here have been at the zoo, drunk(!), and thought hey, lets stick our feet in the tiger cage and piss off a tiger(!). Lets hear someone try and defend that CHOICE that they made!

  36. nhac says:

    asdf: are you drunk? put yourself in the place of a zookeeper or police officer. a tiger has leapt from its cage and is in the process of killing people. you have a firearm.

    do you:

    a) leave it to roam free and KILL MORE PEOPLE
    b) or, b, shoot it before it KILLS YOU

    to suggest that they had any other option is just ludicrous.

  37. PETASUCKS says:

    I would kill a million tigers to let one human survive. YOU HIPPIES SUCK

  38. stephen says:

    I think the moral of the story is it’s not nice to torment animals. Intelligent social animals (even invertibrates) including herbivors will bite back when you tease them. Most anamals are armed and capable of attacking or defending themselves in some way when provoked dont tease the pirana’s :-)
    – These idiot kids should have know better well the ones who survived learnt a valuable lesson,
    Their parents should keep their kids under control at zoos – i once saw a kid purposly teasing some little monkies come within seconds of being visciously mauled by their parents who were watching him, his parents rescued him just in time he was shit scared.
    Its a pity the police resorted to lethal fource to stop the tiger mauling the 2 surviving the attack.
    Guess in the circumstances it seemed the quick way to solve the problem – tiger eating someone – i have gun hmm.

  39. Ben says:

    The real question about why the tiger was killed is, “Why don’t police have trank guns when the respond to loose animal calls at a zoo?”.

  40. Susan says:

    For all those folks who think Europeans are inherently “better and kinder” to their animals, look here:

    Chimpanzee escapes the Whipsnade Zoo, does no harm, attacks no one – they kill it.
    http://www.usatoday.com/news/world/2007-10-01-3923286721_x.htm

    I doubt those who denigrate Americans will even think about their views, but I can try. Sure we have our faults, and I admit many Americans are fat and look silly because of it, but I do not know of a people more generous.

  41. David says:

    Unfortunately this is a freshman physics calculation done and published well before it should have been. I would warmly suggest to the authors that they withdraw the paper, redo their analysis based on what they’ve learned from the various observations that have come in, and then run their results by some colleagues before republishing it. I’d be happy to help….

  42. ClockCat says:

    I hope the surviving pricks get lifetime in prison for what they did to the tiger.

    They were yelling at it, and throwing things at it, intentionally trying to piss it off, while it is in a contained environment. What did they expect?

    Even humans when feeling trapped and threatened will get an adrenaline rush and do things extraordinary.

  43. mahrsart says:

    The general comment goes something like this “The tiger should have killed those boys. They shouldn’t have killed the tiger.”

    Idiots. Two human lives ARE more valuable than a tiger.

  44. The Vagabond Astronomer says:

    “Idiots. Two human lives ARE more valuable than a tiger.”
    That’s pound per pound, right? Haven’t checked the price of late…

  45. George Bell says:

    Regarding the paper, they have the geometry of the leap totally wrong. See the diagram at

    http://66.35.240.8/cgi-bin/object/article?o=1&f=/c/a/2007/12/28/MNSKU5OFE.DTL

  46. [...] איפה צריך להעסיק פיזיקאים? בג

  47. HappyPanda says:

    By Wayne on Feb 1, 2008 | Reply
    “I believe Vietnam was a disaster the French left behind for the US to clean up.”

    Is that the new history-as-it-best-suits-us lesson here in the US? We got our asses kicked there, and again in Afghanistan and again in Iraq.

  48. what?? says:

    We got our asses kicked in Afghanistan and Iraq? Here I thought it was just the control of the countries that was the problem.

  49. [...] they see and you’ll never guess how I stumbled across it.

  50. Deli says:

    In China panda attacked man in zoo. Man had fell into pandapit. Because panda is a national treasure man didn’t fight back. This was third time this panda bit a human. They still won’t shoot it.
    http://us.cnn.com/2009/WORLD/asiapcf/01/09/panda.attack/index.html