Tuesday, March 23, 2010

Pop History Moment: Taco Bell's Big Gamble

Since I am always looking for a bit of variety for my readers, here's what is definitely our (and may in fact be the world's) first-ever pop culture math word problem for you to ponder...

PhotobucketGiven that a) the Pacific Ocean has a surface area of 169.2 million square kilometers - give or take - and b) the Mir space station had a living volume of 350 cubic meters, and that c) on this day in 2001 the Taco Bell corporation placed a 144 square meter target in the ocean 15 km off the coast of Australia with the stated aim that if any part of Mir that didn't burn up on re-entry struck the target following its deorbit they would give every American a free taco, what was the chance of them actually having to pay out on their PR stunt?

The odds of this potential occurrence have been calculated by crack mathematicians (or were they mathematicians on crack?) at the Pop Culture Institute as being Not Bloody Likelyshitload*. Then again, math never was our strongest subject - obviously; William Ailor, director of The Aerospace Corporation's Centre for Orbital Re-entry Debris Studies, told the Associated Press at the time that the odds were 'slim to none'. Gee, for a smart guy that doesn't sound very scientific.

Still, as PR stunts go, it was pretty effective; even with a probability of 'Not Bloody Likely to the power of shitload' Taco Bell took out a pretty hefty insurance policy, just in case. After all, 280 million tacos costs a lot of money; not to mention what it would have done to the sales of Charmin. Had Mir hit the target, it would have gone down in the annals - not to mention the anals - of history.

Nevertheless, when Mir made it's run for the border of space it was the largest item in history to have been de-orbited; Skylab's mass was 77,088 kg compared to Mir's 124,340, and when it returned to Earth in July 1979 pieces of it rained down all over the town of Esperance, in Western Australia, the largest one the size of a washing machine. (The town fined NASA $400 for littering - a fine which has never been paid, I might add.) Had Mir struck land the possible fine could easily have bankrupted the Russian government, just as surely as it could have bankrupted Taco Bell's insurer had it struck the target.

*Kudos to regular commenter and Brain Trust member Sr. Mainar for providing some calculation of the possibility of Skylab hitting the target, which sounds pretty accurate to me; check it out in the comment section below.

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Anonymous said...

According US SPACECOM the odds of any given person being hit by Mir debris are 1 in 2 billion.

If a human occupies roughly two square feet when viewed from directly above then the target has 800 `human target sizes' in it (40x40=1600; 1600/2 = 800).

So, let's take 2 billion to one being the odds that a person will be hit, using the SPACECOM numbers. So, the odds that the target will be hit is:

Ptarget = Pperson * 800

Ptarget = 5 x 10-10 * 800 = 4 x 10-7

...or 1 in 2,500,000. So, using SPACECOM numbers, we get slightly crappy odds of getting a free taco (if we live in the U.S. or Canada).

Of course, let's check that over using some better numbers. This in no way takes into account such wonders as the fact that they're trying to steer Mir for a certain spot.

Earth's surface area is ~ 5*10^14 square meters. Assume that about 1000 different 1 square meter `plots' are hit with significant chunks. Assume these are independent (not true, but a start).

That gives 1 : 500,000,000,000 chance of any given square meter being hit, assuming a random reentry. If there are around 150 square meters of target (not exact, I know) then that means approximately 1 : 3.33 billion for the taco

Truly yours,


michael sean morris said...

There you go folks! All clear?