## Tuesday, February 16, 2010

### Chris Moore and Vampire Hummingbirds

This question comes courtesy of the very funny and talented Christopher Moore, author of The Stupidest Angel, Fluke, Lamb, and many other hilarious books. Chris wants to know…

“If your body could be reduced to its pure sugar content (sure, you can use equivalent carb calories), how long would it take 1000 hummingbirds to drink you as nectar?”

There are many interesting hummingbird facts on the Web. According to one source:

“Hummingbirds feed on a variety of flower nectars with caloric values that may vary from 10 to 82 calories per meal (1/100 fluid ounces). We found that when using a relative rich sugar solution, a three-gram male Ruby-throated Hummingbird ate five meals an hour.”

Taking the mean, we’ll say that hummingbirds consume 46 Calories per meal or roughly 230 Calories per hour. There are 4.0 Calories per gram in a carbohydrate. From this we can compute the mass of carbohydrates consumed by a hummingbird in an hour,

mass eaten per hr = (Cal. eaten per hr) / (Cal. per g of carbs)
= (230 Cal. consumed per hour) / (4.0 Cal. per gram)
= 58 grams of carbs per hour per hummingbird

This means that 1000 hummingbirds would consume 58,000 grams of carbohydrates per hour.

Figuring out how many carbohydrates are in the human body is a trickier question. Many diet websites suggest getting anywhere from 40-65% of your daily calories from carbohydrates, but the human body doesn’t store anything close to this amount. According to at least one source, the human body is about 61.8% water, 16.6% protein and 14.9% fat, leaving at most 6.7% for carbohydrates. In general, humans store energy in glycogen, also called animal starch, instead of table sugar. I’ll assume this is what the hummingbirds are after. According to Wikipedia, glycogen makes up about 8% (~100-120 g) of our liver, but only about 1-2% or our muscles mass. Muscles make up about 42% of male human body, which can weigh about 82 kg (~180 lbs). From this we can estimate the total mass of glycogen in the human body,

total mass = (mass in liver) + (mass in muscles)
= (110 g) + (0.01)
-->· (0.42) · (82 kg)
= 450 g

Now we can compute the total time it takes for a hummingbird to devour all the carbohydrates in a human,

time = (g of carbs per human) / (g of carbs eaten per hour)
= (450 g per human) / (58,000 g per hour)
= 28 s

It would take only about 28 seconds for hummingbirds to suck all the nectar out of a human body.

This, of course, assumes we have normal hummingbirds rather than vampire chupacabra-eque hummingbirds, which would devour our entire body like a cartoon piranha. How long would it take for 1000 vampire chupacabra-eque hummingbirds to devour a human body? Assuming they eat just as fast as normal humming birds, we can use the same math above,

time = (g of total human) / (g eaten per hour)
= (81 kg) / (58,000 g per hour)
= 1.4 hours

It would take about one hour and twenty-three minutes to be eaten by vampire hummingbirds. Thanks so much to Chris Moore for taking the time to submit a Fermi problem. Check out his very funny books at www.chrismoore.com or follow him on Twitter @TheAuthorGuy.