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Guesstimation, or The City in the Sky
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.
Posted by Tyler Cowen on May 5, 2008 at 07:31 AM in Books | Permalink
Comments
How about 200,000
Posted by: greg at May 5, 2008 7:58:09 AM
I recall on the morning of 9/11 there was some thing like 4000 planes aloft....commercial, transport and small private. So a very wild guess is 800,000
Posted by: outback at May 5, 2008 8:14:46 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
Posted by: David Rotor at May 5, 2008 8:23:10 AM
And apparently I can't do times tables over 10 ...
should be
12 hours = 480 not 400
changes my bottom line to 600,000 - 1,200,000
David Rotor
Posted by: David Rotor at May 5, 2008 8:26:35 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.
Posted by: KipEsquire at May 5, 2008 8:35:34 AM
I'm still shocked that there are thousands of flights daily and I don't think there has been an airliner crash in the US since the one in NY shortly after 9/11. Gut level, I'd expect one every 6 months or so.
I wonder how much a crash costs an airline in lost business and in settlements.
Posted by: burger flipper at May 5, 2008 8:35:55 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.
Posted by: burger flipper at May 5, 2008 8:49:27 AM
I believe there are about 1000 flights/day out of Logan, so at an average of 100/passengers per plane that's 100k out of Logan. Logan probably represents between about 2-4% of the national air travel giving a number of flyers/day of 2.5M-5M...which seems too high; at the high end that'd be over 2% of the population flying every day.
Most likely error is average per plane. Figure a lot more of those flights than I realize are 35 seater's and bring the average to about 60. Now we are looking at a range of roughly 1.5M - 3M and err towards the low side at 2M.
Average flight hours are from 6am EST to about 9pm PST so 15 hours calling the average 133k in the air at any moment. Peak though is probably 7-10EST when the number may reach as high as 200k.
So average ~130k and peak ~200k. Holy crap! That's unbelievable. City in the Sky indeed!
Posted by: Lou at May 5, 2008 9:01:59 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 :(
Posted by: Consulting Applicant at May 5, 2008 9:15:55 AM
Great estimates! You guys used two *very* different techniques:
1) Drake-equation type [number of runways * planes per runway * ...]
2) time-in-the-air [12 hours per year = about 0.1% of time => 0.1% of Americans = 300k airborne]
and got about the same results.
Here are two more questions from the book:
How big a landfill would we need to store all our trash for the next century? (And what fraction of the US landmass is that?)
Compare the waste generated per kilometer of horse-drawn carriages and of automobiles.
- Larry Weinstein (co-author of Guesstimation)
Posted by: Larry Weinstein at May 5, 2008 9:33:05 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.
Posted by: Andy at May 5, 2008 11:05:52 AM
My calculation:
120 people per plane
20 flights leave per hour per airport
100 airports in the country
= 240,000 people take off each hour
3 hours average airtime per flight
= 720,000 People in air at any given time
Posted by: Rob at May 5, 2008 11:15:05 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.
Posted by: Yancey Ward at May 5, 2008 11:17:13 AM
350,000 based on my idea of what percentage of time the average american spends flying over america in an airplane and the amount of that travel that is national.
Posted by: Michael Foody at May 5, 2008 11:25:32 AM
Using no calculation method known... 220,000 people at any given moment.
Posted by: The other Eric at May 5, 2008 11:28:49 AM
I'm struck by the evident importance of having a mind already well furnished with back-of-the-envelope estimates of other numbers that can be combined to arrive at a plausible estimate for an answer to a novel question. (I'd have started with "planes grounded on 9/11" too.)
Apart from the parlor game of making estimates just for the fun of it, there's the politically salient question of whether people are well equipped to judge whether the results claimed for a proposed policy are plausible.
Posted by: linda seebach at May 5, 2008 11:32:41 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.
Posted by: vikram pathania at May 5, 2008 11:50:47 AM
Assuming this is not a trick question, and the answer is not 300 million. I like Rob's numbers. 720,000/2 because I think the average plane has 60 people.
Posted by: brainwarped at May 5, 2008 12:11:49 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).
Posted by: at May 5, 2008 12:37:59 PM
I'll go with two statistics I vaguely recall reading somewhere, and two damn lies that I'm making up on the spot.
I vaguely recall reading somehere:
- there are around 30k commercial aircraft in the world
- a commercial aircraft spends around 60% of its time in the air ('cos I read after 9-11 that there was talk of grounding all the world's commercial planes, but there isn't room for them on the ground anywhere)
I guess wildly
- a third of the world's commercial aircraft are in the US
- a commercial aircraft carries an average of 150 passengers
Giving: (30,000 / 3) * 0.6 * 150 = 900,000
... which feels way too high. A third might be *owned* in the US but let's guess a third of those are flying internationally and aren't *over* the US for much of the time, any they're the bigger ones. So I'd happily halve my number.
Posted by: Alan Little at May 5, 2008 12:39:57 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.
Posted by: 8 at May 5, 2008 12:42:58 PM
I would say 500,000.
I recently saw a statistic that quoted how many airplanes, N, fly in a day in the US (I won't say the number to avoid spoilers).
I estimated that the average flight takes 2 hours (lots of shuttle flights).
So if you spread that evenly throughout the day (not a good assumption since most flights are not redeye but oh well), you get about N/12 flights in the air at one time.
I estimated about 150 people per flight, which gets me 600,000. That might be a bit too high, but then again it might not.
Posted by: mk at May 5, 2008 1:36:40 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.
Posted by: mpkomara at May 5, 2008 2:00:28 PM
300 Million Americans spend maybe an average of 1/50th of their year on vacation. Assuming vacation time is equally divided (not true but anyway) that's 6 million Americans on vacation at any one time. Of those 6 million Americans, say one third of them stay home, one third drive somewhere by car, and one third fly somewhere by plane. So that's 2 million Americans on vacation at any one time, that arrived at their location via plane.
If you take a vacation via plane in America, you are going probably going to fly between 2 and 10 hours total roundtrip over the course of your vacation. Some people will take two vacations per year, so that's 4 to 20 hours. Going in between these two for good measure, and we'll say a statistically typical person spends 3 to 15 hours in the air on their trip. The median time is 9 hours.
So that means, of the 2 million Americans who are on vacation at any given time, they spent nine hours of their vacation time on a plane.
The average vacation lasts 1/50th of a year.
9hours/(1/50 year x 365 days x 24 hours) percent of the vacation is spent on a plane. That simplifies to:
15/292, which we round to 15/300 = 5/100 = 1/20
So 2 million people, with 1/20th of them flying at any given time, is 100,000 people. Double it to account for business travellers and international visitors and you have:
200,000 people over the USA at any given time.
Posted by: Matt Clancy at May 5, 2008 2:04:20 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
Posted by: Trey at May 5, 2008 2:09:46 PM
This is a good example of a useless estimation problem. The number of people in the air fluctuates wildly across the day (at 4 AM EST = 1 AM PST, very few, all on red-eyes; at 4PM EST = 1 PM PST, a hell of a lot). Most of the interesting questions are about the peak load. Sometimes they're about sustained loads across a couple of hours. But nobody cares about averages across 24 hours.
Posted by: jim at May 5, 2008 2:38:28 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.
Posted by: dave at May 5, 2008 2:46:53 PM
180,000.
Peak maybe 400 - 500k.
Don't forget - you spend time waiting at both ends, so you are not "in the air". There is not much flight overnight.
Estimation method : None.
My first thought is usually pretty accurate when estimating Systems projects (and in that case usually 2 or 3X what other folk estimate).
Posted by: Rich at May 5, 2008 3:19:38 PM
There is an older book on this topic: "Consider a spherical cow". I recommend it.
Posted by: David Wright at May 5, 2008 4:58:42 PM
jim, I'd say that the responses here clearly disapprove your idea that nobody cares.
Personally, I find this fascinating and I'm eager to read more.
Posted by: Ian Deans at May 5, 2008 5:07:30 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!
Posted by: Tyler Cowen at May 5, 2008 5:28:42 PM
There is a pretty interesting site that tracks planes here. At the time I checked it was tracking 5,343 planes. So a rough guess would be that much by about a hundred, or 534,300 people in the air at any one time.
There is another cool graph of flights over the US here at www.visualcomplexity.com.
Posted by: Fabio Franco at May 5, 2008 6:12:13 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.
Posted by: John Dewey at May 5, 2008 6:18:39 PM
fabio franco,
That's an interesting way to estimate the peak airborne population, but not the average airborne population.
I think 100 passengers per aircraft is too high. A significant portion of the planes on those charts are cargo, military, and private aircraft. Many more are small regional jets and propeller planes operated by airlines. Though international and some transcontinental planes carry hundreds of passengers, the typical "large" domestic aircraft carries only about 100 passengers. My guess is that the average load of those peak period 5,343 aircraft would be about 60 passengers.
As the charts show, the number of aircraft in U.S. airspace drops off significantly after dark. An average for the full 24 hour period would be under 3,000 aircraft.
Using the aircraft data you linked to, I would estimate the average number of people airborne to be 3,000 aircraft times 60 persons per aircraft, or 180,000 in total.
Posted by: John Dewey at May 5, 2008 6:42:13 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)
Posted by: David at May 5, 2008 8:13:04 PM
Holy crap if you can write a book about this topic you can write one about anything.
Posted by: Paul N at May 5, 2008 10:05:03 PM
(Sum of commenters' answers)/(# of commenters)= 409,000
Posted by: T. at May 5, 2008 11:44:16 PM
This is some "cool-ass shit"; and I still want to know the answers re: the fraction of space for trash and automobile versus horse pollution
Posted by: enrique at May 6, 2008 12:27:37 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
Posted by: john b at May 6, 2008 3:35:51 AM
I was thinking that there seems to be, what 50 or so arriving flights on the screens at a medium sized (that is, average sized) airport. So, there must be 75 to 100 airports in the country.
Say, 85 passengers per flight....
85 * 50 * 85 = 361,250
Posted by: john doe #2 at May 6, 2008 11:41:28 AM
the animation at this site is fantastic and awe inspiring.
Posted by: jvance at May 6, 2008 4:05:00 PM
Trash: Averaga family of 3 produces <2.5 cu.ft. of uncompacted trash per week; compacted, that's less than 1 cu.ft./wk, or 50 cu.ft./yr, times 100,000,000 "families" is 5 billion cu.ft./year nationally, or 500 billion cu.ft. for 100 years.
Assume population will increase from 300 million to 400 million in 100 years; assuming parabolic shape for increase curve, average population will be 366 million, so multiply estimates by 11/9 (or add 22%). That brings estimate from 500 to 611 billion cu.ft.
Assume landfill can be piled 100 feet high, and that edge of landfill will be trivial compared to area in center, that's 6.11 billion square feet. That works out to 220 square miles, or a square slightly less than 15 miles on a side. Total land area of the U.S. is about 3.5 million square miles, so that's one part in 16,000.
Posted by: Anthony at May 6, 2008 4:08:23 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.
Posted by: Yancey Ward at May 6, 2008 4:31:50 PM
This is what we at the Dept. of Energy (descended from the Manhattan Project) call a "Fermi Problem." The great experimental physicist Enrico Fermi used to challenge his students at the University of Chicago with questions like "How many piano tuners are there in Chicago?"
Posted by: Ralph Hitchens at May 6, 2008 4:55:08 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.
Posted by: Nathan Myers at May 7, 2008 3:01:43 PM
