# Consulting interview question #2520

A debate has ensued between myself and a friend, and I’m calling on the weblog community to help us solve it. So here it is:

Which is more probable: a meteor hitting a commercial airliner, or a meteor hitting a person?

There are quite a few variables in this debate, which I will list along with my approximation, usually pulled from thin air:

Number of people on planet earth: 6 billion

Average percentage of people standing outdoors at a given point in time: 0.1%

Surface area of an average person (from the top): 1 sq. foot

Surface area of “in risk” population: 6 million sq. feet

Average number of airliners in the air at any given point in time: 10,000?

Average surface area of a commercial airliner: 2500 sq. feet?

Surface area of “in risk” airplanes: 25 million sq. feet?

My money was on the demons in the sky, which is why my statistics probably favor that solution. If anyone has a better estimate on these numbers, or can find some motherf%@\$ing google query that turns up good statistics, please lend a hand. The fate of a job-seeking consultant may be in your hands.

## 11 thoughts on “Consulting interview question #2520”

1. pb says:

I’ve heard of meteorites hitting people in their houses. They’ve gone straight through roofs. So you may need to increase your percentage of potential human targets.

2. krispy - the friend says:

two complaints:

1) .1 percent is a very questionable figure. only one out of a thousand are outside at anytime? for 6 billion people, that equates to 6 million people outside. during the baseball season, there are on average 14 games a day. let’s say 10 of those games are in non-dome stadiums at half capacity of 25000 fans. thats 250k people… and thats simply from baseball in the US during the summer. and it’s always spring/summer somewhere in the world.

2) 2500 sq feet for an airplane? you are not accounting the high lateral velocity. when you computed 1 sq feet for humans, you assumed 2 things. they are standing still and meteors fall straight down. the former assumption is not true for airplanes in flight which changes the equivalent surface area of the airplane that an opject will see if its falling straight down. you need to figure out the terminal velocity of a small meteor in the earth’s atmosphere. you can then compute the angle at which the meteor is falling relative to the moving airplane, and then you can compute the equivalent surface area of the plane at that angle, which will be much smaller.

3. The first is a subset of the other. There are always people in commercial airliners.

Now if the question is about directly hitting people who are not containted within anything (vehicle or building,) I agree with krispy, I strongly doubt your very low proportion of people outdoors at a given point in time. In China alone there are approximately 700 million peasants. My childhood experience with traditional agriculture at my grandparents farm is that you spend a lot of time outdoors. These people are not sitting in their office calculating how much subsidies they’ll get from the government next year.

There’s another factor you forgot. Airliners are exposed to more meteors because they fly high in the sky. People on the ground have more atmosphere depth to protect them, i.e. more meteors burn before they reach the surface. You need to know how many meteors hit the outer atmosphere, how big they are, and at what rate they burn.

4. Oh, but those planes are so fast. A meteor would have to try really hard to nail one. People are slow.

The relative altitudes are important. If you abstract an airplane as a 2500 sq. ft. polygon, it’s taking up 2500 sq. ft. of surface area of a much larger sphere than just the surface of the earth. I guess what you need to do is get a handle on the trajectory of the meteor, and then based on that, project all people and airplanes onto a common sphere, and compare _those_ surface areas.

6. I’m just hoping that someone projects the two spheres (surface sphere, and cruising alititude sphere) and the ratio turns out so that a person on the ground covers the same amount of relative space as a plane in the sky. My money’s on the planes getting hit, but not for any rational reason except the extremely higher incidence of meteors vs. meteorites.

7. Some things I haven’t seen mentioned, but which seem important:

1. The speed of a meteor ( many Km/sec ) is so much greater than the speed of an airliner ( many m/sec ) that you can assume the airliner is not in motion.
2. There is no reason to factor out people indoors. The high speed of a meteor means it can easily penetrate most structures and smite those within.
3. The ten kilometers of atmosphere between airline cruising altitude and the ground may be enough to burn up some smaller meteorites before they hit the ground.
4. Airliners are more likely to be hit an an oblique angle ( not from directly overhead ) than are objects at ground level beccause of the aforementioned blanket of thick air hugging the ground. You are not likely to be hit in the chest by a meteor coming from just over the horizon because of the many kilometers of dense air it would have to cross without disintegrating.

8. francesco says:

i’m with the crowd who count *all* 6 billion people: if a meteor is aiming at someone on the ground, it’s going to be fairly immaterial whether that someone is in a building or not.

but i think there’s bigger factor at work here that no-one’s brought up: if over 60% of the earth’s surface is ocean, and assuming that airliners fly over oceans as much as they do over land, then we have to factor in that only 40% of meteor strikes have a chance of hitting a warm body, yet airliners are exposed to all 100% of strikes.

9. Shari says:

I don’t know about taking the airplane’s speed into account. A meteor would enter the atmosphere at a rate of speed of something like 11 km/sec so I would think the plane’s speed would be insignificant. And another thing, I wouldn’t trust any building for protection from a meteor hitting me. Would you have to factor in the average size of such a meteor. Assuming it was large enough to hit the earth, what would it’s average size be? I think we all need another good disaster movie so we can all learn more science. haha

10. sometimes , spooks are very corny like the Disater Movie ”