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How many passengers are in planes in the air at any given time in the U.S.A.?
+2 votes
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in Estimation by (717 points) | 3.2k views

4 Answers

+3 votes

The key here is to think about what information you have (or can estimate) which can help you get to the answer. You need to be clear about your logic and assumptions, and be clear-minded enough to be able to sense-check the ultimate answer you arrive at.

First, I clarify the question – what is meant by “airplanes”? All planes, private jets, commercial flights only, military, fly-overs? And what is meant by “right now” – literally right this second? What is meant by “over the US”? Landmass only? Does this include ocean territory? What about Alaska and Hawaii?

I will assume that “airplanes” can be divided into four categories: commercial passenger, freight, small private and military. There will be other types (like charters and crop-dusters) but to simplify things I will leave them aside.

I assume that these flights are only those flying domestically or to an international destination (but still over the US). I will exclude planes flying over the US from one country to another.

I assume that “right this second” means 6.45pm.

I assume that “over the US” means over the landmass of the contiguous 48 states.

Then I look at each type of plane to look for drivers of the ultimate number.

For commercial passenger planes, I assume a good driver would be the number of airports in the USA. I assume there are:

10 giant airports
20 major airports
50 medium airports
100 small airports

Giant airports would have about 20 flights per hour taking off, 18 hours per day. So, about 360 flights per day. At any one time, perhaps 15 per cent of these flights would be in the air. I would assume that the average plane would contain 250 people. So, that’s 360 x 15% x 250 x 10 airports = 135 000 people.

Major airports would have about 10 flights per hour, 18 hours per day. Fifteen per cent would be in the air at any one time, with an average of 200 people on board. That’s 108 000 people.

Medium-sized airports would have about 10 flights per hour, 15 hours per day. Fifteen per cent would be in the air at any one time, with an average of 100 people on board. That’s 112 500 people.

Small airports would have about five flights per hour, 12 hours per day. Fifteen per cent would be in the air, with an average of 50 people on board. That’s 45 000 people.

Freight is trickier to estimate. I would estimate that there are an average of 100 cargo flights per major city in the US per day, and I’d estimate there are 200 major cities. Fifteen per cent of these flights would be in the air at any one time. They would have an average crew of five. That’s 15 000 people.

For small private planes, I’d say there is one private plane for every 500 head of population (300 million people), and that one per cent of these planes might be in the air at any one time, with an average of four people on board. That’s 600 000 x 1% x 4 = 24 000 people.

For military I am less sure. Let’s assume there are 10 000 military planes in the US (big and small). Let’s say five per cent are airborne at any one time with an average of 10 people aboard. That’s 5000 people.

Now I can add up all the people. The total equals 444 500 people in the air right now over the US.

To sense-check this, let me just divide by 200 (the average number on board a commercial airliner). That’s 2222 planes in the air, or 46 over each of the 48 states.

Hmm, this seems a bit on the high side, so I may have over-estimated somewhere. I can go back through my assumptions and calculations to see if I can trim the number a bit. However, I don’t think I’m far off.

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Great answer. Thank you.
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Nimesh, very good answer indeed. I have a question for both you and Bijan, what is the basis of estimating the # of airports inside the US? It does not seem to correlate to any other facts.

Also how did you come up with the assumption that 15% of the planes are in the air at any time? Thanks a lot!
0 votes

This will be variable based on the time of day, the day, and other factors. So let’s use some guesstimates.A flight from a major hub leaves every 2 minutes. Lets say each flight is in the air for an aver…See more

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+1
I was thinking of taking a similar approach but my concern was there are two uneducated assumptions I have to make:
1- Number of airports in the US
2- Average time between each departure
3- Average time of flights
I’m also not considering the impact of foreign flights.
Is there a better way to make this estimate?
0 votes

We are talking about the planes in the air. What different things do you see flying in the sky? ;)You see passenger planes international flight with destination/origin in USAnational flights in USA&n…See more

by (94 points)
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Hi Pegah,
I really like the structure of the answer and your ability to break it down to multiple segments based on some meaningful logic. Here are some feedback :
- Given there are different hours during the day and air traffic at 3am is very different than air traffic at 3pm, I suggest you pick a specific time of the day to do your calculations. The question does suggest "at any given time" but given the variety of time during the day, it's reasonable to make this adjustment. This will make it easier for you to determine which planes are in the air. For example, if you’re looking at all plans in the air at 3pm and average time of flights is 2 hours, you just need to look at # of planes that took off from 1pm to 3pm and multiple that number by # of passengers per plan (of course, adjust for the variation in size and international flights as well). You can apply the same model described above for other segments of the airline industry. If the interviewer insisted on "any given time", you can calculate the average number by using average number of planes that depart at any time of the day.
- I would count for empty seats by multiplying your number for passenger planes by something such as 80% (assume 20%of seats are empty
- For international flights, if average time in the US air for them is 15 minutes, then the number of international planes during a 2 hours divided by 8 gives you number of international planes in the air at a particular time
0 votes

Assumption 1: Only passenger planes are in the air. (Its not a war time). And, ignoring personal, jet planes, helicopters.Use cases: Domestic planes, International planes.Case 1: Domestic planes: Assuming…See more

by (46 points)
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