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 USA
- national flights in USA
- flights crossing USA but not stopping there

- military planes
- private planes
- spaceships
- birds

Lets concentrate on passenger planes with a destination/origin in USA

Which cities can be an origin/destination? Those that have an airport. Which cities have an airport? Those that are big enough. Very few small cities have airports, except for very cheap airports which are in the middle of nowher, near a very small city.

So I will formulate the estimation for number (2) into this:

#flights with origin/dest in USA = #arrivals per airport * #airports + #departures per airport * #airport

I will break the problem into estimating for big cities and middle cities. Big cities have more than 3 million population. middle cities have an average of 400k population.

**Big cities**

**Assumptions**

- I will assume USA has 5 big cities with avg 2 airports.
- I assume each airport has 10 departure every 5 minutes, which makes 120 flights an hour. The same I assume for arrivals.
- I assume 60% of arrivals are from US airports, so they are already counted in departures. 40% are coming outside US. We assume that the distribution of departures/arrivals is the same, although possibly between midnight to 5 am there are less flights in certain cities, due to noise restrictions for example. Some airports do not have flights also 24hours.
- There are many flights with big planes, because there are more destinations, more passengers and the airport has the capacities and facilities for big planes. I assume 40% of flights are in big planes with 400 passengers, 20% middle planes with 200 passengers, 30% with 100 passengers, and 10% with 50 passengers.

#total flight in 1 airport in 1 big city = 120 departure + 120*40% arrival = 160 flights an hour

#passengers in one hour one airport= #passengers in big planes + #passengers in middle planes + #passengers in small planes + #passengers in very small planes

= 160 ( 40% * 400 +20% * 200 + 30% * 100 + 10% * 100)=

= 160 X (160 + 40+ 30 + 10) ~160*600 = 40k passengers /hour

#passengers in 1 day in all big cities = #big cities * #airports * #passengers/day = 5 * 2 * 40k = 400k

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**Middle cities**

**Assumptions**

- I assume there are 50 cities with more than 400k people, and 1 airport each.
- I assume each airport has 1 departure every 5minute, which makes 12 flights an hour. The same I assume for arrivals. 40% of arrivals are from outside US, the rest is from USA, which is counted in departures. We assume that the distribution is the same, although possibly between midnight to 5 am there are less flights in certain cities, due to noise restrictions for example.
- There are
**NOT** many flights with big planes, because there are less destinations, less passengers and the airport has less space for big planes. I assume 20% of flights are in big planes with 400 passengers, 30% middle planes with 200 passengers, and 20% with 100 passengers and 20% with 50 passengers.

#total flight in 1 airport in 1 big city = 12 departure + 12 * 40% arrival = 17 ~ 20 flights an hour

#passengers in one hour one airport= #passengers in big planes + #passengers in middle planes + #passengers in small planes

= 20 * 20% * 400 + 20 * 30% * 200 + 20 * 20% * 100 + 20 * 20% * 50 =

= 20 X (80 + 60 + 20 + 10) ~ 3.4k passengers /hour

#passengers in 1 hour in all middle cities = #middle cities * #airports * #passengers/hour = 50 * 1 * 3.4k =170k

====>

Total passengers in with origin/dest in USA in 1 hour = #passengers in 1 day in all middle cities + #passengers in 1 hour in all big cities

= 400k + 170k = 570k

I assume one average flight is for 2 hours over the USA air space

International flights that land on very east or very west coast, are very briefly in the air of USA, e.g. 15 minutes. I assume 10% of flights can be ignored because of this. I assume 40% of flights are 1 hour, 30% of them are 2 hours, and 20% are than 2 hours.

However, I don't know how to adjust my calculations, so I skip this.

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**Military planes**

I assume there are 20 cities with military airports. There are 5 flights an hour. Each flight has 10 passengers.

#passengers on military planes in 1 hour = 5 * 20 * 10 = 1000 passengers

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**private planes **

I assume 1 out of 50k person has 1 private plane. USA has 300mio people.

#private planes = 300mio/50k = 6k

avg #capacity/private plane = 10

total capacity of private planes = 6kX10 = 60k

In every hour there are 5% private planes in the air.

===> total number of passengers in air in private plane = 60k * 5% = 3k

-------------------

total #passengers in the air = passenger in private plane + passengers in military planes + passengers in flights in USA

= 3k + 1k + 570k = 570k

Considering that some flights take more than one hour, I add 20% to this number.

===> total passengers = 570k*1.2 = 680 k passengers

**According to Google, "At any given moment there are about 5,000 commercial airplanes in the sky over the United States"**

Does 680k make sense?

If middle plane has 200 seats, that makes 680k/200 = 3400 planes in air

#planes over each state = 3400/50 = 70

which makes sense I think.