Use a level to test the Earth's curvature?

[davee123]

So, I'm sure many of you have seen the experiment recently by a flat-Earth member who brought a level on a plane with him in order to determine whether or not the Earth is flat or round. And yeah, my immediate thought was similarly "how silly!" But it did make me wonder: Could you do it that way?

In addition to acting as a "level" to tell if surfaces are perpendicular to the pull of gravity, a level can (I believe) also be used as a makeshift accelerometer. If you're accelerating forwards, the liquid in the vial should move backwards, pushing the bubble forwards-- and then it should even out when you reach a constant velocity.

But since (when traveling in a circle around the Earth), you'd be changing your acceleration constantly, what would the effect be on the bubble?

Hence, the "correct" way (I think) to conduct the experiment would be to make sure the level was flat before takeoff and keep it in that position for the duration of the flight. Then, when the plane evens out at its cruising altitude and speed (presuming it maintains both constantly), if the bubble is positioned forwards, then there's centripetal force (and a curved Earth), and if the bubble's in the exact same place as before, there's no centripetal force (a flat Earth). (Obviously, you'd want to account for turbulence, perhaps averaging the bubble's position over the course of 10 minutes, say)

Of course, the particulars are where I think this method (as currently described) is useless. My rough guess is that at 500mph, and a mass of about 1g for the liquid, you'd get on the order of 0.000007841 Newtons of force on the liquid in the level, which (I'm guessing?) is way too small to detect. At that scale, would the liquid's viscosity or the effects of surface tension against the tube cancel out any change at all? Would you need laser precision to detect the difference in the position of the bubble? Could you use a longer (or straighter) tube or a more dense liquid to make the difference detectable to the human eye? Could this experiment be used to prove the Earth's curvature?

Other considerations I'm missing?

DaveE

 

[jbriggs444]

But since (when traveling in a circle around the Earth), you'd be changing your acceleration constantly, what would the effect be on the bubble?

"Changing your acceleration" and "accelerating" are two different things. A spirit level compares the direction of the current acceleration to the direction of the level. It is insensitive to a slow rotation of the acceleration direction coupled with a slow rotation of the level.

Hence, the "correct" way (I think) to conduct the experiment would be to make sure the level was flat before takeoff and keep it in that position for the duration of the flight. Then, when the plane evens out at its cruising altitude and speed (presuming it maintains both constantly), if the bubble is positioned forwards, then there's centripetal force (and a curved Earth), and if the bubble's in the exact same place as before, there's no centripetal force (a flat Earth). (Obviously, you'd want to account for turbulence, perhaps averaging the bubble's position over the course of 10 minutes, say)

Centripetal force is irrelevant since it acts in the same direction as gravity. The vector sum of the two will be in the same direction as both.

If you had a way to keep the level in a constant orientation (say with a good gyro) then one could see the bubble move to one end or the other as the force of gravity ceased to be aligned with the level.

Of course, simply holding the level in your hands and striving to keep it "level" is hopeless without an independent way to measure "level". Keeping it aligned with the horizon does not help since both flat Earth and round Earth theories predict that the bubble will stay centered.

 

[davee123]

Centripetal force is irrelevant since it acts in the same direction as gravity. The vector sum of the two will be in the same direction as both.

Ahh, ok-- I was thinking there was going to be a minor force perpendicular to gravity due to the acceleration, but yes, that makes sense, I guess that it would be along the same vector.

DaveE

 

[Tenebris]

I think the perpendicular force your thinking of is the instantaneous acceleration of the plane... or the inertia of the plane in that instant.

(i am not the happiest about this picture, centripetal force is non-existent)

 

[XZ923]

I hope you'll forgive an impertinent question, but why are you taking seriously anything coming from someone who claims the Earth is flat? According to the Flat Earth Society's webpage, they not only consider the Earth to be flat, they also believe it has an "infinite edge" and never ends (although their depiction of what they believe the Earth is does have an edge and ends at Antarctica). My point is that it's not even pseudoscience, it's even beyond that in terms of ridiculousness.

 

[davee123]

I hope you'll forgive an impertinent question, but why are you taking seriously anything coming from someone who claims the Earth is flat?

It was really just a thought experiment-- BUT, I will say this: If it did turn out that you COULD conceivably measure the Earth's curvature using a level on a plane (just not doing what that guy did), it would be hilarious to see them prove themselves wrong.

If you listen to them, they've got all kinds of excuses for why physics as described doesn't work. They're constantly saying "why can't any so-called scientists prove us wrong?" But will instantly dispute any proof provided. But if they're willing to believe a do-it-yourself experiment with a level (which they wouldn't if it worked against them, of course), then it'd be funny to actually give them something that they really COULD test with, that they really ought to supposedly believe.

DaveE

 

[berkeman]

Just a gentle reminder to stick with the science part of this thread. We don't allow debunking of pseudoscience here at the PF. Thanks.

 

[russ_watters]

It was really just a thought experiment-- BUT, I will say this: If it did turn out that you COULD conceivably measure the Earth's curvature using a level on a plane (just not doing what that guy did), it would be hilarious to see them prove themselves wrong.

If we're set on using an airplane, why not just ask them how long it takes to fly to China and what direction the plane flies to get there?

 

[XZ923]

If we're using an airplane, why not just take off and (using the runway as a reference and fuel considerations aside) fly in a straight line and see where you end up?

 

[russ_watters]

If we're using an airplane, why not just take off and (using the runway as a reference and fuel considerations aside) fly in a straight line and see where you end up?

How do you guide a plane to fly in a straight line?

 

[XZ923]

How do you guide a plane to fly in a straight line?

My thinking on it was that if you have a hypothetical runway sitting on the Earth's equator, then draw a straight line from one end of the runway to the other, and if the plane is programmed to simply fly along this line no matter what then it will take off, travel ~25,000 miles, and end up back where it started.

EDIT:
Just to add, the mechanism for how it maintains course is something I don't have an answer to. I know nothing about aeronautics. My assumption is that it's possible to program an autopilot system to simply maintain a straight line but I freely admit I don't know this for a fact. In any event, the main thrust is "an airplane that takes off and flies a direct circumference around the globe will end up back where it started"

 

[jbriggs444]

My thinking on it was that if you have a hypothetical runway sitting on the Earth's equator, then draw a straight line from one end of the runway to the other, and if the plane is programmed to simply fly along this line no matter what then it will take off, travel ~25,000 miles, and end up back where it started.

The devil is in the details, of course. There is no line of sight all the way down the runway. So you face a technical challenge making sure that the runway traces out a great circle on a sphere rather than a 25,000 mile circumference circle on a flat surface. The challenge is heightened because most of the equator is on water.

 

[russ_watters]

mechanism for how it maintains course is something I don't have an answer to. I know nothing about aeronautics. My assumption is that it's possible to program an autopilot system to simply maintain a straight line but I freely admit I don't know this for a fact.

That is indeed the issue I was referring to. Any automated directional control device needs to be able to detect its course and make adjustements to maintain that course. There are two basic ways for a plane (or boat):
1. Use a compass (referenced to the magnetic or "true" pole).
2. Use a mathematical model of the globe and GPS.

#1 will cause you to spiral toward one of the poles. #2 presupposes a round earth, so I'm not sure if it satisfies the intent or not. I'm not going to speculate on what a flat Earth map looks like or how their thought process works...