Sunday, April 29, 2012

Rockstars and Cat Ladies and Pterodactyls, Oh my!

Today's question comes from special guest Sarah Donner.  Sarah is a very talented indie folkpop singer/songwriter whose lovely voice can be heard in various places around the interwebs.  Recently, she's been found singing the praises of pterodactyls on The Oatmeal.1 

Sarah would like to know, "How many lightening bugs could a pterodactyl eat?"

According to at least one source, Lampyridae, commonly called lightening bugs or fireflies, have only been around since the Eocene epoch about 56 million years ago.2  In contrast, pterosaurs died off at the end of the Cretaceous Period 65.5 million years ago.  Pterodactyls in particular existed about 150 million years ago, so it seems like they missed each other by about 100 million years.  Still, if they crossed paths, I'm sure the glow bug would have made a tasty treat. 

"No!!!  Don't eat me!!!"

Adult pterodactyls have an estimated wing span of about 1.5 m.  That's about the same wingspan as a fruit bat.  Assuming they have similar weights, that would put the pterodactyl at about 1.5 kg.  He probably eats about 10% of his weight each day, meaning he'd consume 150 grams of food.  Assuming lightening bugs weigh roughly 10 mg, a pterodactyl could consume about 15,000 lightening bugs over the course of one day.3  According to the song, the pterodactyl "ate 10,000 lightening bugs", a very good estimate indeed.  Well done, Sarah!

To find out more about Sarah, you can visit her website or follow her on Twitter.

[1] Just a warning, the lyrics are not safe for work.
[2] We know this because you can find fossils of insects trapped in amber.
[3] I suppose one could instead consider the maximum number of lightening bugs a pterodactyl could eat if he kept going non-stop.  According to Donald R. Griffin's Echos of Bats and Men, bats can catch a mosquito once every 6 seconds.  Assuming pterodactyl have a similar catch rate (unlikely since they probably don't have a bat's echolocation abilities) and a lifespan of 20 years, a pterodactyl could have eaten 100 million lightening bugs.

Monday, April 23, 2012

Ballparking Contest!!!

In case you haven't heard, I HAVE A NEW BOOK!!!!!  To celebrate the publication of Ballparking: Practical Math for Impractical Sports Questions, we're going to have another estimation contest.   

Here's how it works. I’m posting a Fermi question below. To enter, estimate an answer and send it to “aaron at aaronsantos period com.” If your answer is closest to mine, I'll mail you a free signed copy of Ballparking.1 Second prize receives a signed copy of my other book, How Many Licks? Or How to Estimate Damn Near Anything. Submit your entry on or before June 1, 2012.  Don't worry…I won't spam you or share your email with any third parties.  Here's the question:

When I was a teen, my cousin Nick (who makes a brief appearance in Ballparking) and I used to play home run derby at a baseball field on Sconticut Neck.  Being two years older, I had quite the height/strength advantage and would typically crush him into a metaphorical bloody pulp.  However, once we hit our early 20's, I noticed a striking change.  All of a sudden, the pulp into which I was beating him was dramatically less bloody.  In fact, it was not even much of a pulp:

Me: Why am I sweating?  And what the hell's wrong with the score board?  It says I'm losing!!!"

Here's the field we played on.
Being a teen has a way of disillusioning you into thinking you'll always have a 32-inch waist and be stronger than people that are younger than you.  This is, of course, not the case.   Now that I'm in my 30's my match-ups with Nick have become decidedly one-sided in the opposite direction, and now the vast majority of blood in the pulp is my own.  Fortunately, I still have cognitive dissonance and a healthy dose of wind blowing in from right field.  You see, being on The Neck, the winds tend to blow in off the water.  As a left-handed hitter, I'm at somewhat of a disadvantage to my right-handed cousin.  I've seen (or at least convinced myself that I've seen) some of the tennis balls that I hit go over the fence only to be blown back onto the field.  How fast (in mph) must the wind be to blow a ball back onto the field after it's gone over the fence?

[1] NOTE: I make no pretenses that my answer is correct or even close. Your answer may very well be a better estimate than mine. In fact, your estimate may even be exactly right and you still may not win the contest if somebody else's answer is closer to mine. Sorry about that. This is the best way I could come up with to pick a winner and I'm not changing it now. Like any good game, there's an element of luck required even if you do have great skill. With that disclaimer out of the way, good luck and happy calculatings!

Thursday, April 19, 2012

My Book Has Shipped

My book is now officially available!  Every time you buy a copy, your favorite sports team gets a win.  Also your rival sports team gets mauled by bears. 

Daddy Loves Froggy

To the outside observer, it may seem that scientists hate frogs.  Perhaps it's true.  After all, they're green, slimy, and with a little salt they can enter zombie mode.  That's probably not enough to justify dissection, but perhaps it's enough to justify this:

Now, I know what you're thinking.  It's a frog.  Levitating.  In a magnetic field.  WTF?!?! 

Frogs aren't normally magnetic.   However, frogs (and other living creatures) contain water, which is a diamagnetic material.1  Diamagnetic materials have this weird property that when you place them in a magnetic field, they turn into a magnet themselves.  The new magnet points in the opposite direction of the first magnet.  In this way, a diamagnetic material is like a magnet that always repels.  Normally, this effect is very weak, but NASA scientists have shown that if you have a very big magnetic field, you can generate a magnetic force that is large enough to lift everyday objects like frogs.2  Now you might wonder why NASA cares about levitating frogs...!!!

In truth, they've levitated more than just frogs.  Their goal seems to be eventually levitating a human.  This, of course, would be one way to mimic the effects of zero gravity.  How large of a magnetic field would it take to lift a human?

According to Wikipedia, it takes about 16 Tesla of magnetic field to levitate a frog.  For comparison, an MRI machine, which can erase all your credit cards if they're in the same room, has a magnetic field of 3 Tesla.

Now the magnetic field serves two purposes.  First, it magnetizes our prospective astronaut.  The amount he gets magnetized will be roughly proportional to the magnitude of the magnetic field.  After magnetizing the astronaut, the magnetic field will then push him up with a force that depends on both its own value and the value of the astronaut's magnetization.  Since the field appears twice in the force we can say that the force is proportional to the field squared:

Force ~ (magnetic field)2.

A small frog might weigh 50 grams, which is roughly 1000 times smaller than a human.  To get 1000 times the upward force, you'd need a field that's 32 times bigger.  (You can see this by squaring 32 to get roughly 1000 times the force.)  For this reason, you'd need a field that's about 500 Tesla, which is like having 170 MRI machines.

[1] Other diamagnetic materials include gold, silver, copper, carbon dioxide, and bismuth.
[2] For more info, click here