You know I don’t really do much political stuff—but I sure do love a good estimation problem. And that’s just what we have with the following statement from Donald Trump:

“You could have 650 million people pour in and we do nothing about it. Think of it. That’s what could happen. You triple the size of our country in a week.”

OK, this is The Donald so I’m not sure if he’s being serious or using hyperbole. I don’t think he mentioned the 650 million number by mistake, since he also adds that it would triple the US population (approximately true).

Since I like to do estimations and analysis of fake things like Star Wars and super heroes, let me also explore this 650 million immigrants in just one week. Is it even possible? How would you make it work? For this calculation, I will treat it as a “back of the envelope” problem, making rough estimates for most quantities without looking up exact figures. This type of estimation problem gives you a rough idea if it’s even feasible to pursue better values.

Here are my starting assumptions (other than 650 million in one week—that was from Trump).

- All of these immigrants arrive by airplane. Why? Well, why not? If you need to get 650 million people into the country fast, you pretty much need to use airplanes. I’m not going to look it up, but I don’t think the population of Canada and Mexico is enough to achieve this number with people driving across the border. We only have
*one week*people! - There are lots of different kinds of aircraft that fly into airports. I am going to assume that the average airliner carries 300 passengers.
- These planes are going to have to come from all over the world. How long will it take for a plane to fly to the USA, drop off its people and return (including fueling and maintenance stuff)? I’m going to go with 20 hours. Sure, there are lots of places that would take longer to get there and back but there are also places that are close.
- I will assume there are 50 international airports in the USA (again, just a guess here). Yes, there are probably more than this, but one per state seems reasonable.

Now for the first calculation. How many flights would this 650 million immigrants require? If each plane carries and average of 300 passengers, that’s a straightforward calculation.

That’s 2.2 million flights in just one week. Yes, I rounded the number—it’s an estimate after all, so this is fine. But how many flights for each airport? Simply take the total flights and divide by the number of airports.

If these airports are open 24/7 for one week, then I can calculate the flight landing frequency. This is just the total number of flights divided by the total time. Note that I am using the unit “fpa” as flights per airport.

Over four flights a minute doesn’t seem very reasonable. But what if there were twice as many airports to fly to *and* twice the aircraft capacity*?* This would still be over one flight landing every minute. Maybe that’s possible, but not very likely.

How many aircraft would you need for this epic immigration? Well, there are a total of 2.2 million flights. Each flight takes an average of 20 hours (there and back). One aircraft can make 168 hours/20 hours = 8.4 flights per week. With this, I can calculate the total number of aircraft needed.

I don’t know how many total aircraft there are in the world, but 262,000 seems like a lot.

Now you can see the value of a “back of the envelope” calculation. It’s something that you could sit down and work out without too much trouble. Is it correct? That doesn’t matter—well, it doesn’t matter if it is exactly correct. Sure, I made some very rough estimates for some of these values but you can see that even if you increase some of the values you still get unreasonable results. In the end, it seems clear that the United States is not going to have 650 million immigrants arrive in just one week. It’s not really possible.