## Wednesday, February 17, 2010

### Can you pass the Phil please?

Q: A plane crashes at the U.S.-Canada border. Where do you bury the survivors?
A: You don’t bury survivors.

But if you were the only survivor, how long could you survive by eating the other passengers?

We’re going to assume it’s winter and the bodies stay frozen so they don’t decay. A Boeing 747 can carry 416 passengers, meaning there are 415 potential menu choices. Assuming our cannibal doesn’t eat the bone, he’ll be getting all of his calories from the rest of the tissue. A normal-sized person is about 68 kg (~150 lbs). Skeletons weigh about 14% of the total body weight, leaving about 59 kg of edible other stuff. Since protein is 4.0 Calories per gram and fat is 9.0 Calories per gram, we’ll assume that the average caloric density is 6.0 Calories per gram. From this we can compute the total Calories in each person,

Cal. per person = (edible mass of person) · (Cal. per g)
= (59 kg) · (6.0 Cal per g)
= 3.5×105 Cal. per person.

Multiplying by 415 people, we can compute the total number of Calories,

total Cal. = (Cal. per person) (# of people)
= (3.5×105 Cal. per person) · (415 people)
= 1.5×108 Cal.

Assuming a 2000 Calorie per day diet, we can compute just how long it would take to eat and successfully digest all the other passengers,

time = (total # of Cal.) / (# Cal. per day)
= (1.5×108 Cal.) / (2000 Cal. per day)
= 200 years.

It would take 200 years to eat all the passengers. So, if you’re the only survivor in a plane crash, look on the bright side. At least you wouldn’t starve to death.

1. You can't possibly use every last gram of food you eat. If you poop 1 lb every day on a 2500 Calorie diet you can get the equation

t = (m - p*t)*Crho/2500 = (59 - 0.454*t)*6000/2500

Solving for time you can find that 1 person will last for about 68 days and 415 people would feed you for 77 years. That number still seems too high.

2. Love your site! Hate your background (sorry)! It hurts my eyes, yesss, it does...

3. I did it a different way and got similar results to Thomas, who correctly points out that not all of a human besides bones is useful calories.

Cows, pigs, sheep, deer, typically yield less than 60% of usable meat, sometimes as low as 30% of total weight is turned into meat and edible offal during the slaughter process. (57% of human body is water with zero calories).

So lets use 50% as a slightly more conservative number for useful meat from a human. Therefore we have 39kg/person. Meat from fatty pigs averages 3000-4500 calories/kg, so let's assume the plane is filled with fat French-Canadiens from Montreal providing 4000cal/kg.

(39kg/person) * (4000cal/kg) * (1 day/2000 calories) = 68 days/person

As Thomas pointed out 68 days/person * 415 persons *(1 year/365 days) = 77.3 years.

4. Plus you'll start dealing with nutrient deficiencies at some point. Scurvy seems like a likely problem.

5. "Plus you'll start dealing with nutrient deficiencies at some point. Scurvy seems like a likely problem."

Actually the first problem will be constipation. According to 'Alive:The Story of the Andes Survivors'. I won't go into detail but you will not have to worry about malnutrition. You will die in a much more gruesome way.