Youtuber Darryle Marble, a believer in the "Flat Earth" theory, recently took a spirit level on a plane to attempt to demonstrate that the world was flat by showing the pilot never had to angle the plane down to compensate for the curve. Somehow the story went viral and the internet reacted as you would expect, with incredulity and mockery.
Unfortunately most of the reaction seemed to boil down to "what an idiot, of course the world isn't flat", when really the situation arose from a series of misconceptions and misunderstandings of flight and physics that are shared by many people. Very few people really think much about things like gravity, acceleration, or the curvature of the earth. Despite getting everything wrong, Marble is at least doing an experiment, so I think it's worth explaining a little more in depth why it went the way it did.
Basically Marble placed the level on his tray table while the plane was cruising and videoed it for 23 minutes.
Here is his description of the experiment.
The main mistake here is quite simple - he's assuming that five miles is a lot, and so there much be a lot of quite large corrections to the angle of the plane. However, when a plane is flying at cruise altitude the pilot makes only the most minor adjustments to maintain a constant altitude. Theoretically only one "adjustment" is needed. Practically the pilot will make several, but not related to curvature.
It's essentially the same as if you were in a car driving along a road that has a very slight curve to the right. All you would do is turn the steering wheel very slightly to the right until the car maintains a constant distance from the side of the road, and then you would leave it there. The car will simply drive around the very slight curve. In the same way the plane is flying around the very slight curve of the Earth simply by having the controls adjusted to maintain a constant altitude.
So no significant movement of the level would be expected, and that's what we see.
Delving a little deeper here, one aspect of the misunderstanding is the fact that the plane has to "drop" five miles. Now this figure is correct, that's how much the earth would drop away from a horizontal plane over 200 miles. That sounds like a lot, so the thinking goes that the pilot would have to make several major course corrections, maybe dropping half a mile every five minutes, something that would show up on the level (if it didn't just slam everyone against the ceiling).
However, as noted above, the pilot doesn't just keep flying along a perfectly straight line up towards space - he sets the controls to maintain a constant altitude. No additional correction are needed. But what of this initial correction? Wouldn't that be a big jolt as the pilot pushed the nose down? No, in fact it would barely be noticeable, for a variety of reasons.
Let's get a sense of scale here. How much of a curve are we talking about? We can draw a diagram of the Earth with its 3959 mile radius. I'll also put the 200 mile trip on there as a red line
Let's zoom in:
The red line is what you get if you theoretically fly in a perfectly straight line. (It's "theoretical" as gaining five miles above cruise altitude would not be possible for a passenger jet). Instead since the pilot has done the equivalent to slight turing the steering wheel the plane just flies along the black line, a constant altitude above the surface of the earth. There's no initial adjustment detectable with the level because it's such a slight turn. Similar to the curve of this road, ND-46 in North Dakota:
ND-46 was laid out along a line of latitude, so it's got curvature that is similar in scale to the curve of the Earth. No only does it curve with the surface of the Earth, but more importantly it also curves towards the North. When you are on it it looks like this:
So when you are driving along ND-46 it feels like you are going in a straight line when the road actually has a continuous curve to the North (left on the above image). It's a tiny factor, and realistically you are not actually going to set your steering wheel very slightly to the left and then leave it there - just like the autopilot you'll be making continuous small movement of the wheel, otherwise you'd drift off the side of the road. The curve is simply lost in the noise of everything else.
Similarly, you would probably not be able to detect the slightly curved motion of the plane even with the most sensitive of instruments, because there's a heck of a lot more going on with the plane on a far larger scale - the most significant part of which is the headwind. Variations in windspeed will mean the pilot (or more likely the autopilot) will have to make small correction (usually to the throttle) to maintain constant altitude. Those corrections will be hundreds of times more noticeable than the very slight force due to the plane's curved path. In fact we see that in the video the bubble is moving, possibly from those accelerations and decelerations. However this movement is partially obscured simply by people moving around in their seats.
The curve in the diagram above is an idealized version of the plane's flight, but we can actually look at GPS data from his probable flight on May 1 2017, AA1974 from Charlotte, NC to Seattle, WA. Takeoff was at 07:55 EDT. The video segment starts (according to the iPhone time) at 09:16 and ends at 09:39, and I'm assuming the phone was still on EDT. Here's the actual track of the entire flight as recorded by FlightAware.com.
The section from 9:16 to 9:39 is between the two pins near the center, this is a nice level portion of the flight, but still follows the curvature of the Earth. We can zoom in:
So that's the path the plane flew, a smooth curve maintaining a constant altitude of 32,000 feet above sea level. No "corrections" are needed, and so no movements of the level are expected.