Friday, May 18, 2012

Running Off With The Circus

Many people dream of dropping out of school and running off to join the circus.  Today's guest did just that (minus the dropping out of school part).  Tanya Burka is an MIT graduate and circus artist currently performing the aerial silk act in Cirque Du Soleil's Quidam.  Through her unique blend of science and athletic talent, Tanya has composed quite an impressive resume, one perhaps better-suited to an aspiring superhero or possibly a sexy James Bond villain.

Tanya Burka is the lone point of intersection in this Venn diagram.

Tanya writes, 

It's not a circus-related question (or if it is, only tangentially in that an elephant is referenced), but I've always wanted to know how many ants it would take to lift an elephant, and whether or not it would be possible in practical terms in having enough surface area on the elephant at some angle (lying down, for example) for the ants to all support his weight.

It's often said that ants can lift 50 times their own weight.  Even if we assume this is true, there's still some ambiguity about exactly how much weight they can lift.  There are over 12,000 species of ants spanning a wide range of sizes.  For simplicity, I'll assume ants weigh 20 mg so that they can each hold 1.0 gram of weight.  In contrast, an elephant can weigh anywhere from 100 kg (~200 lbs) as a newborn to 10,000 kg (~20,000 lbs) as a large adult.  If we take 1000 kg as an average, we can estimate that it would require about one-million (106) ants to lift an elephant.

To fit that many ants under an elephant, you'll need a wide area.  For this reason, it's better if we have the elephant lay on its side.  With a shoulder height of about 3 m, we can estimate that the side of an typical elephant would have an area of about 4.5 square meters.  This would mean each ant would need to fit in an area of about 4.5 square millimeters.

This result is a fair bit smaller than the ant we assumed originally, but it's closer than I would have guessed.  It's just as well.  Logistically, it would be a nightmare trying to lay the elephant down exactly evenly over all the one-million ants before they could get away.

Thanks for a great question, Tanya!

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions.   

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