Guesstimation, or The City in the Sky

by on May 5, 2008 at 7:31 am in Books | Permalink

On average, how many people are airborne over the US at any given moment?

That’s a typical question from the new Princeton University Press book by Lawrence Weinstein and John Adam.  The title is Guesstimation and the subtitle is: Solving the World’s Problems on the Back of a Cocktail Napkin.

What’s your guess and why; let us know in the comments and I’ll post their answer later today.  The book also tackles such hoary chestnuts as "How many piano tuners are there in Los Angeles," although for mysterious reasons (are they mostly part-timers?) they fall far short of the actual number in the L.A. Yellow Pages.

This book isn’t for everyone but if you think you might like it you probably will.

Addendum: I post the authors’ answer at about comment #31.

1 greg May 5, 2008 at 7:58 am

How about 200,000

2 David Rotor May 5, 2008 at 8:23 am

My back of the napkin says 500,000-1,000,000, if you only include a 12 hour “daylight” period. Halve that if you want to average over 24 horus. Here’s my approach:

New York’s airports serves as the destination or origination for about 20% of the flights in the US. This is just a wild-assed guess, but seems reasonable given that the population surrounding NYC is about 30M giving just under 10% of the population being served by those airports, and that NYC serves as a hub for many other destinations … so I doubled the estimate.

There are four major airports in the NYC area. If I recall correctly there are about 10 active runways (LGA-3, EWR-3, JFK-3, HPN-1) at the four airports. Flights land/depart about 90 seconds apart on each runway. In a 12 hour day that gives us:

1 hour of runway time = 40 flights per hour
12 hours = 400 flights
400 flights X 10 runways = 4,000 flights
4000 flights X 5 (NYC is only 20% of total) = 20,000 flights

I estimate 25-50 people per flight on average:

25 people X 20,000 flights = 500,000
50 people X 20,000 flights = 1,000,000

Am I close?

Cheers,

David Rotor

3 KipEsquire May 5, 2008 at 8:35 am

You can fashion a sort of “Drake Equation” for this:

Number of planes
x average capacity
x average load factor
x fraction of day that the average aircraft flies over the U.S.

I’ll try 25,000 x 250 x 80% x 20% = 1,000,000

Note that this does not include crew.

4 burger flipper May 5, 2008 at 8:49 am

And I’d go with around 500,000 based on the assumption that I am a typical American and probably spend about 12 (miserable) hours in flight each year.

That same 500,000 number would also be my extrapoguess for yearly US Xanax consumption based on the same numbers, though I guess that is probably further off since some people take them while on the ground.

5 Consulting Applicant May 5, 2008 at 9:15 am

Would this be a good book for someone who has to prepare for the notoriously hard interviews in the consulting industry? One of the notorious questsion is “come up with a size for this market”…

Of course, shipping it to Europe with priority mail costs 3 times as much as the book 🙁

6 Andy May 5, 2008 at 11:05 am

My guess is 10,000. I’m a non expert, and I maintained my independence by not looking at any of the other guesses (I covered my eyes while I scrolled). Cheers.

7 Yancey Ward May 5, 2008 at 11:17 am

I don’t remember where I read it, but I once read there are two billion airline passengers/year globally. On any given day, assume an even distribution to give 5.47 million per day. If they are evenly distributed over the course of a day in flights that average 2 hours each, there may 456,000 in the air at any one time, world wide. Let’s just assume that Americans make up 40% of the volume which gives 183,000 overhead right now.

8 The other Eric May 5, 2008 at 11:28 am

Using no calculation method known… 220,000 people at any given moment.

9 vikram pathania May 5, 2008 at 11:50 am

My guess is 200,000 or so.

There are probably about 5000 commercial aircrafts – the big carriers have fleet sizes of between 300-600. Maybe about 2500 are the large jets and the rest are the small turboprops. A jet can seat about 200 (with crew) while a typical turboprop around 30. So the representative aircraft seats about 100. With 80% occupancy, around 80. How many aircrafts are in flight at a given time? The jets are mostly long haul, so with maintenance and turnaround time at airports, they might be in the air for about 50% of the time. The turboprops are short hauls and but turnaround may be faster – so they might be in the air for about 50% of the time as well. That makes 2500 in the air with 80 people on average = 200,000.

10 Anonymous May 5, 2008 at 12:37 pm

Suppose everyone in the US spends 3.65 hours per year in flight (exact
number chosen for ease of arithmetic). This may seem small, but remember
hat lots of people don’t fly at all. That’s a fraction of 3.65/(24*356)
= 1/2400 of their time. There are roughly 240 million Americans (a bit low,
but close enough, and the arithmetic is easier). Dividing, we get 100,000
in flight at any given time, averaging over day and night (there are obviously
some systematic time of day effects).

11 8 May 5, 2008 at 12:42 pm

I would guess about 250,000 to 300,000 during the daytime. I don’t know the number of flights, the number of airports, etc. Out of 300 million people, I doubt 1% travel by air each day, which would be 3 million passengers, but given international travel, it’s definitely more than 1 million. Assuming the average flight time over U.S. airspace is 2 hours, there would be about 1.8 million passengers between 8am and 8pm if it’s 300,000.

12 mpkomara May 5, 2008 at 2:00 pm

Average number of people per plane is too high. Also, the phrase “above the US” reduces the final answer, for many of these people on planes are somewhere over an ocean the minute they leave Logan, Dulles or JFK. “At any given moment” reduces the focus of the question. I’m already disappointed and I haven’t started my estimation.

13 Trey May 5, 2008 at 2:09 pm

Back of the napkin:

Say each American makes one round trip flight a year that’s 2.5 hours each way (total of 5 hours in the air per year). 5 hours: 9,000 hours in a year as x people : 360M.

So i get about 200,000

14 dave May 5, 2008 at 2:46 pm

I think at peak time, there are about 7,000-8,000 craft in the air over the U.S. Now, for a decent chunk of the day, there aren’t many planes in the sky (late night/early morning). So let’s say there are 4,000 in the sky on average. Not all of them are enormous airliners. I’d bet many of them are smaller regional jets. So 200 people per plane is probably an over estimate. Let’s say 100 people per flight. 4,000 times 100 = 400,000 people.

15 David Wright May 5, 2008 at 4:58 pm

There is an older book on this topic: “Consider a spherical cow”. I recommend it.

16 Tyler Cowen May 5, 2008 at 5:28 pm

The authors estimate about 300,000, based on the idea that the average American takes two to four flights per year, figuring out what percentage of their time that is, and then converting that into the percentage of the population that is airborne at any point in time.

I was very interested to read all your contributions and of course you don’t have to agree with their estimate!

17 John Dewey May 5, 2008 at 6:18 pm

The authors’ method is crude and probably incorrect. They seemed to only include American revenue passengers, excluding foreign passengers, passenger airline crews, military aircraft flight crews and passengers, and private aircraft pilots and passengers. But assuming that such exclusions do not significantly alter the number, we can use 2007 passenger airline data from the Bureau of Transportation Statistics to determine if the 300,000 figure is reasonable:

1. Annual passengers flown on domestic non-stop flights: 698 million
2. Total minutes flown by domestic passenger carriers: 966 million
3. Total annual commercial passenger carrier departures: 10.5 million
4. Average length per flight: 92 minutes (2 divided by 3)
5. Total annual airline passenger minutes: 64.1 billion (1 divided by 4)
6. Total minutes in one year: 525,600
7. Average revenue passengers per minute: 121,900 (5 divided by 6)

It seems unlikely to me that the exclusions I listed would increase my 121,900 figure to 300,000. My guess would be that those exclusions would increase the total by less than 20 percent. So I think their estimate of 300,000 is pretty high.

Note that the BTS data includes only airborne minutes and not taxi time before and after a flight. I don’t know how the authors estimated flight time, but they probably included the significant amount of taxi time in their crude estimation of flight time per American.

18 David May 5, 2008 at 8:13 pm

I’m an Australian reader and funnily enough my guess was exactly 300,000 based on some very crude, fast and loose reasoning starting from knowledge of my own town and working out:
1. Flights take off from Sydney airport at about one every 2 minutes = 30 an hour
2. Average plane would have about 100 passengers (some jumbos, some small, some cargo) = 3000 an hour taking off
3. Flights in Oz would be an average of about 2 hours over Oz airspace, so assume two hours worth airborne at any one time (= 6,000 in the air)
4. Guess that 20% of Oz flights originate from Sydney (= 30,000)
5. Multiply by 10 for the US! (= 300,000)

19 T. May 5, 2008 at 11:44 pm

(Sum of commenters’ answers)/(# of commenters)= 409,000

20 john b May 6, 2008 at 3:35 am

my guess was:
300 million * 1.5 hours in the air * 3 flights per year/365 days per year/ 24 hours per day = 154,109 passengers in the air

21 jvance May 6, 2008 at 4:05 pm

the animation at this site is fantastic and awe inspiring.

22 Yancey Ward May 6, 2008 at 4:31 pm

For the trash question, I just assume that we will have Black Hole Trash Company- the volume of the landfill will be less than that of a single proton.

23 Nathan Myers May 7, 2008 at 3:01 pm

The number is actually well known within the airline industry. Most estimates posted here are way too low. It’s close to a million, mid-day.

24 batage May 14, 2009 at 4:20 am

Every success is based on continuous efforts. It is not possible be done over nigh.
you are so clever

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