

Solving xkcd's raptor problem - dons
http://pgraycode.wordpress.com/2010/05/29/raptors/

======
allanmac
This looks like a variant of the "Lion and Man" problem which is also
described as a "bounded pursuit" problem in the operations research journals:

[http://www.google.com/search?q=lion+and+man+problem+&ie=...](http://www.google.com/search?q=lion+and+man+problem+&ie=utf-8)

-and-

<http://mathworld.wolfram.com/PursuitCurve.html>

-and-

<http://books.google.com/books?id=HeESjfM2geUC> (good!)

This problem may have had relevance in World War II all the way to the
present: dogfights between airplanes, battleships trying to sink each other,
etc.

~~~
Groxx
Wolfram is frightening in its completeness... I should really look into their
setup some time.

Anyone have any suggestions for starting it? From what I've gathered, it's a
bit different than other math texts / different conceptual basis.

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harpastum
I've created a quick graph [1] of the survival time running in a single fixed
direction. While this doesn't take acceleration into account, the results
agree with the article and common sense. No matter which direction you run,
one of the 25 m/s raptors will catch you, so your best bet is to run directly
toward the weakened one. The code's available here:
<http://gist.github.com/418783>

[1]
[http://chart.apis.google.com/chart?cht=s&chd=t:0.0,1.111...](http://chart.apis.google.com/chart?cht=s&chd=t:0.0,1.11111111111111,2.22222222222222,3.33333333333333,4.44444444444444,5.55555555555556,6.66666666666667,7.77777777777778,8.88888888888889,10.0,11.1111111111111,12.2222222222222,13.3333333333333,14.4444444444444,15.5555555555556,16.6666666666667,17.7777777777778,18.8888888888889,20.0,21.1111111111111,22.2222222222222,23.3333333333333,24.4444444444444,25.5555555555556,26.6666666666667,27.7777777777778,28.8888888888889,30.0,31.1111111111111,32.2222222222222,33.3333333333333,34.4444444444444,35.5555555555556,36.6666666666667,37.7777777777778,38.8888888888889,40.0,41.1111111111111,42.2222222222222,43.3333333333333,44.4444444444444,45.5555555555556,46.6666666666667,47.7777777777778,48.8888888888889,50.0,51.1111111111111,52.2222222222222,53.3333333333333,54.4444444444444,55.5555555555556,56.6666666666667,57.7777777777778,58.8888888888889,60.0,61.1111111111111,62.2222222222222,63.3333333333333,64.4444444444444,65.5555555555556,66.6666666666667,67.7777777777778,68.8888888888889,70.0,71.1111111111111,72.2222222222222,73.3333333333333,74.4444444444444,75.5555555555556,76.6666666666667,77.7777777777778,78.8888888888889,80.0,81.1111111111111,82.2222222222222,83.3333333333333,84.4444444444444,85.5555555555556,86.6666666666667,87.7777777777778,88.8888888888889,90.0,91.1111111111111,92.2222222222222,93.3333333333333,94.4444444444444,95.5555555555556,96.6666666666667,97.7777777777778,98.8888888888889,100.0|70.5,71.5,72.5,73.5,75.0,76.0,77.5,78.5,80.0,81.5,83.0,84.5,85.5,87.0,88.5,90.0,91.5,92.5,94.0,95.0,96.5,97.5,98.5,98.5,97.5,96.5,95.0,94.0,92.5,91.5,90.0,88.5,87.0,85.5,84.5,83.0,81.5,80.0,78.5,77.5,76.0,75.0,73.5,72.5,71.5,70.5,69.5,68.5,67.5,67.0,66.5,66.0,65.5,65.0,64.5,64.5,64.5,64.5,64.5,65.0,65.0,65.5,66.0,66.5,67.5,68.0,69.0,70.0,70.0,69.0,68.0,67.5,66.5,66.0,65.5,65.0,65.0,64.5,64.5,64.5,64.5,64.5,65.0,65.5,66.0,66.5,67.0,67.5,68.5,69.5,70.5|40&chxt=x,y&chs=700x400&chxr=0,0,360,45|1,0,1)

~~~
harpastum
I created an interactive version of the graph, so you can enter values and see
how long you would last: <http://news.ycombinator.com/item?id=1390136>

------
roschdal
What about problem #3 of <http://xkcd.com/135/> ? Will xkcd ever publish the
floor plan from the next page where you escape from the raptors?

~~~
dutchflyboy
About that, has anyone noticed the test isn't very consistent? In the first
exercise the speed of a raptor is 25 m/s, in the second exercise the wounded
raptor runs at 10 m/s. So far, so good. But in the third exercise the raptors
run at 10 m/s. Why, are they wounded? And of course, can the raptors chew
through walls?

~~~
orangecat
_in the third exercise the raptors run at 10 m/s. Why, are they wounded?_

The third exercise is inside a building, where obstructions and narrow paths
slow them down.

------
harpastum
Interesting. Haven't had time to fully create my own solution; I'll have to
work on it tonight. If anyone wants what I've got so far (ruby):
<http://codepad.org/qggAcIKy>

------
adharmad
An analytical solution would be nice in addition to the simulation one. Even
better if the number of sides of the polygon could be parametrized :)

~~~
merraksh
The optimal solution, i.e. the human's trajectory, is a function and therefore
has to be found through variational calculus. Not sure there is an analytical
one, but the optimum should be quite easy to find numerically.

------
mitko
Apparently, from the plot seems that if you are faster than the slow raptor,
your best direction is not straight at it, but nearby. This makes some sense
because if you you are close to the slow one and far of the fast ones you can
outrun go around the slow one.

------
kingkawn
i had to take an intro calc class recently, my professor put this problem on
the final exam.

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andrewljohnson
Why use we instead of I? There is just one author and the we convention used
for papers with multiple authors is inappropriate and misleading.

Just a small quibble... the article was otherwise fine if you like that sort
of thing.

~~~
sundarurfriend
A polite expression of opinion here has been downvoted, and a comment
elsewhere that just informs that this question appeared in someone's exam has
been upvoted _twice_!

