For no real reason, it occurred to me on Friday to wonder what would have happened if Trump had never gotten off that escalator. If, instead of stepping off at the bottom in the lower level of the Trump Tower atrium, it were instead an infinite escalator that stretched on in the same direction to eternity, and Trump was still riding along. Where, I wondered, would he end up?
And then I answered my question.
To do so, though, I had to answer a number of other questions first. Namely, we have to know three things: How fast he was traveling, the direction he’s traveling in and how much time had elapsed.
1. How fast was Trump traveling?
This is trickier to determine than you might realize.
We have this video of Trump going down the elevator. But it’s hard, from that, to judge distances, and because speed is a function of distance and time, that’s a problem.
Happily, in October of 2015, I visited Trump Tower for an article exploring what there was to see and do in the building. Part of that involved recording my own trips up and down the escalator, filling in at least one variable for me.
For example, that video told me that it took 4.6 seconds to travel the length of one of the vertical panes of glass that makes up the side of the escalator. You can see those vertical lines in this version of the Trump video:
That video is important; we’ll come back to it.
In the GIF below, you can see the actual time that elapses as my thumb travels the length of one of those panes of glass.
Again: 4.6 seconds.
Now we need to know how big those panes of glass are. You may remember from high school that, given the lengths one side of a triangle and the angles within the triangle itself, you can figure out the lengths of other two sides. (If you didn’t take trig, you may not remember that.) We know one of the angles: By definition, one angle is a right angle, 90 degrees.
(In this and the ensuing diagrams, the diagonal line — the hypotenuse of the triangle — is the escalator itself.)
Matt Johnson of the Schindler elevator company informed me that escalators in the United States are mandated to be angled at 30 degrees, which gives us another angle. (And the third, because a triangle’s angles add up to 180 degrees.)
Now we just need the length of one of the sides.
From that video I shot in October 2015, we can see that my body descends from about the height of my glasses to the height of my belt as I travel down the escalator the length of that pane of glass.
That distance is about 31 inches.
And so we can use our trigonometry and learn that we traveled about 54 inches down the escalator in 4.6 seconds.
That’s a speed of about 0.3 meters per second.
How much time had elapsed?
That second video, above, tells us that Trump got on the escalator at about 11:05 a.m. and 46 seconds. You can see the time change shortly before the video ends. That means that, as of writing, about 63 million seconds had passed.
That means that, at 0.3 meters per second, Trump would have traveled a grand total of about 18,837 kilometers on that infinite escalator. But where would it have taken him?
In which direction was Trump traveling?
Trump Tower is located at the intersection of 57th Street and Fifth Avenue in Manhattan. 57th runs east-west, and the escalator runs parallel to the street. So, 18,837 kilometers due west of Trump Tower, right?
No, for two reasons.
First, Manhattan’s streets don’t run true east-west. Instead of pointing due west at 270 degrees, for example, Charles Petzold calculated that the streets run about 29 degrees off that mark. Meaning that 57th Street runs at about 299 degrees — as does our escalator.
Second, though, the Earth is roughly a sphere, not an endless flat plain. That means that the escalator would probably, at some point, stop going down and start coming back up, perhaps even emerging from under the surface of the Earth. And, in fact, at 18,837 meters, that’s precisely what it does.
That’s a complicated graphic, so let’s walk through it.
The large triangle that’s overlaid on Earth is our escalator triangle from above. Here, the escalator part is the solid line. It ends at a point somewhere above the Earth’s surface — but where?
We can draw a dashed line back to the center of the earth. Using trig, we can figure out the angle between Trump Tower and that endpoint, and then the distance from the center of the Earth to the endpoint. The diameter of the Earth is 12,742 kilometers, meaning that the radius is about 6,371 kilometers. And that tells us that our endpoint is about 10,224 kilometers above the surface of the Earth.
How high is that? It’s just past the approximate end of the exosphere, the last point at which there are still detectable remnants of Earth’s atmosphere.
Trump would need to be in a space suit, at this point.
Where on Earth would he be? This is actually fairly easy to calculate. Using more math, we learn that the distance along Earth’s surface we need to travel is about 11,200 kilometers. We know that we’re headed 299 degrees from Trump Tower, in a west-northwesterly direction. Plugging that into Google Earth, we learn that Trump is in space about 600 miles south of Wake Island in the South Pacific.
How much would such an escalator cost? Well, a 30-foot tall escalator can apparently cost about $200,000. Ours is 9,418 kilometers high. Setting aside the cost of supporting an escalator in midair, that’s a cost of about $206 billion.
More than even Trump could afford.
Update: Actually, it gets worse.
After this story published, a real-life math teacher pointed out that I’d made a mistake. The 54-inch distance is the bottom of the triangle, not the hypotenuse. Meaning that the length of one of the panes of glass is 62 inches. And that means that Trump would have traveled at 0.342 meters per second — and wound up 21,655 meters away from his starting point.
The rest of the math is straightforward from there. Trump would end up in outer space,about 13,000 kilometers above a point 40 miles north of Rongelap Atoll. (The atoll was evacuated in 1954 when residents were exposed to radioactive fallout from nearby nuclear testing.) The escalator will now cost $236.8 billion.
The Post regrets our initial miscalculation, and will accept a C-minus on this assignment.