Full disclosure: I do not believe the Earth is flat. However, a guy recently posted a YouTube video that purports to prove that the Earth is flat due to there having been no changes in the position bubble in a spirit level (possibly better known as carpenters level) that would have accounted for the plane's nose dipping to compensate for the earth's curvature.

Naturally, this led to attacks from commenters saying how stupid he is. What was interesting is that, despite it being more rational to believe that that the earth is indeed round from observations such as looking at the curvature of the horizon through a plane window or noticing the differences flight times (for those who have travelled internationally) for, say, flying to China from Europe (heading eastward, which I have done) or flying to China heading westward from the US (which I also have done), there was a lack of scientific rigor in these observations (and in the comments refuting his claim).

Could someone explain, in as plain of language as physics permits, the flaws of the spirit level experiment (and if the flaw is in the instrument itself, what would occur if a different leveling instrument were used)?

I see that there are a lot of questions about Flat-earth theory already on stackexchange so, once again, I want to emphasize that I am only concerned with the flaws of this particular experiment and am not looking to impugn Flat-earth theory altogether. As an aside, while I am not convinced that the Earth is flat, there is something respectable about an individual performing an experiment to determine something on his own rather than just accepting what books/teachers tell him.

  • $\begingroup$ There is possibly an answer to your question (aviation.stackexchange.com/questions/27603/…) in the aviation stack exchange which actually shows that planes do not have to angle down as long as they stay in a (relatively) dense part of the atmosphere. While referring to mathematics of curvature in his video he fails to examine the underlying physics of flying. $\endgroup$ – Jaywalker May 19 '17 at 23:34
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    $\begingroup$ I actually spend a fair amount of time on utube debunking flat-earth (as nicely as I can), and this airplane question comes up regularly. (I only bother because it has socio-political implications, believe it or not.) What people generally don't get is that an airplane is not a projectile or a laser beam. It just follows a pressure level in the atmosphere, parallel to the surface mostly (the ideal surface), and gravity is perpendicular to that surface. So the airplane follows that curved surface, and "up" is always up. $\endgroup$ – Mike Dunlavey May 22 '17 at 20:21
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    $\begingroup$ "changes in the position bubble in the spirit level?????" Do I have to go to a youtube video to find out what this means? As it stands, this post is incomprehensible. $\endgroup$ – WillO Aug 6 '17 at 16:49
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    $\begingroup$ @WillO: I suppose you have never done any amount of construction in your life? A spirit level is a very common tool. $\endgroup$ – Kyle Kanos Aug 7 '17 at 10:55
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    $\begingroup$ @kylekanos : apparently this was a case of ignorance on my part. Apologies to the OP. (Though I still think the reference to "the plane" (what plane?) is incomprehensible on its own.) $\endgroup$ – WillO Aug 7 '17 at 15:16

You would have to use a sensitive gyroscope, not a spirit level, to notice if the pilot was "dipping" the nose of the plane to follow the curvature of the earth. You don't "point below the horizon" to get to your destination!

The thing he is describing can be captured in this cartoon:

enter image description here

The distance from North Carolina to Seattle is about 4000 km (1/10th of the circumference of the earth), and it takes about 6 hours. So assuming that the earth is a stationary ball, you would have to "dip" by a total of 36 degrees over the course of 6 hours, 6 degrees per hour, or 0.1 degree per minute. Of course, if you are on a spinning earth, you are moving 360 degrees in 24 hours, and move 15 degrees per hour. Assuming that you move in a straight line for 10 minutes, then make an adjustment - then you would see the plane "dip" by 1 degree, and slowly pull up again. But if you did that, your altitude would keep changing. The pilot keeps the altitude constant, so the "dipping" of the plane happens so gradually that there is NO WAY you could see it with your spirit level. If he flew in a "truly straight line" for a minute, then adjusted by 0.1 degree - would you see it? Of course not.

There are other, more sensitive instruments you could use. There's something called a gyrocompass. In this, you mount a gyroscope so its axis is spinning horizontally, but it is free to change its axis of rotation in the horizontal plane. If you take such a gyroscope and leave it spinning with its axis pointing in an arbitrary direction, then as the earth rotates (15 degrees per hour) the axis of the gyroscope would try to lift out of the horizontal plane. If you prevent this (with the gimbal holding the gyro) then the only thing that the gyro can do is rotate towards the North pole - and that's exactly what happens. After 6 hours, it will be pointing to the true (rotational) North, and stay there. If you move it, it will come right back.

That can only happen because the earth is rotating. There are variations of this experiment you could attempt in a plane, to prove that the nose is "dipping" (you would have to account for the rotation of the earth). In fact - this is one of the navigation aids they use on most planes - because it is more accurate than a magnetic compass (and doesn't change with local magnetic fields). The plane also uses GPS - which again wouldn't work very well if the earth turned out to be flat (how do they keep those pesky satellites in orbit?)

Doing an experiment to verify a theory is great; but you have to make sure you understand the limits of your instruments and the accuracy required, before you make any claims.

Incidentally - when the author claims the bubble is "nice and flat", take a look at a couple of frames from the video and ask yourself - if this is "flat", what would a dip look like?

enter image description hereenter image description here

  • $\begingroup$ I actually think the guy in the video is a just a troll who wants views, but anyway, even not considering how stupid is to think that such effect of earth curvature isn't completely hidden under other millions of vibration, path changes etc. I think that you don't actually need to make the correction. The vertical force air apply on the wings depends on air density, air density diminish with altitude so if the plane maintain the same speed in straight line density would decrease and so the effect of gravity would be no more compensated leading the plane to naturally curve with earth . $\endgroup$ – Claudio P May 19 '17 at 22:32
  • $\begingroup$ @claudio - with your argument the plane would land with its nose pointing 30 degrees into the air... $\endgroup$ – Floris May 19 '17 at 22:39
  • $\begingroup$ For what reason? $\endgroup$ – Claudio P May 19 '17 at 22:41
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    $\begingroup$ If you maintain altitude without changing the direction the plane is pointing then when the angle of the earth surface changes by 30 degrees you appear to point "up" by that same amount $\endgroup$ – Floris May 19 '17 at 23:18
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    $\begingroup$ pilots follow the curviture of the earth because simply maintaining a constant altitude makes the plane follow the curviture. the pilot makes pitch and throttle adjustments almost uncociously to do this much like no one is very aware of what they are doing with a car steering wheel to follow a curve in the road. $\endgroup$ – scm May 20 '17 at 1:35

1) If you are trying to measure the downward angle a plane takes and that is 8 inches per mile.

That means it's 8 inches out of 5280 feet or 8 inches every 63,360 inches.

That comes out to a downward angle of 0.00723 degrees. That would be impossible to tell on a standard level.

2) Just like driving people make minor adjustments. It is the combination of ALL these minor adjustments that add up to that 8 inches per mile.

That is not something that can be measured by a level.

If a black box had all those adjustments recorded, then maybe we could interpret the 8 inches per mile down angle from that.

It's just too slight to notice. The world really is too big to sense with our eyes alone!

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    $\begingroup$ Where does the 8 in/mi value come from? $\endgroup$ – Kyle Kanos Aug 6 '17 at 16:33
  • $\begingroup$ @KyleKanos: I get about 16 inches a mile, which is suspiciously close to a factor of 2 error either by me or the original person (this is just from doing the obvious trigonometry for a 1-mile chunk of circumference of the earth with the radius being about 3960 miles). Not to mention a spirit level measures gravity so will not work for this, even in principle! $\endgroup$ – user107153 Aug 7 '17 at 12:41

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