# Explained: Why a Spirit Level on a Plane Does Not Show Curvature "Corrections"

Discussion in 'Flat Earth' started by Mick West, May 22, 2017.

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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.

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Last edited: Jun 7, 2017
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Getting into a little more detail: what does "level" actually mean, and how is a spirit level actually measuring it?

People who argue the earth is flat are quite strident in their argument that "level" means only a perfectly flat surface. They argue that since "water finds its own level", then the surface of any body of water must be level, and hence flat. On a small scale this is essentially true, as we see the curve of the earth is very slight, and on a small scale it looks very similar to a straight line.

But on a large a scale what "level" actually means is "perpendicular to the direction of gravity", which boils down to "perpendicular to down", where "down" is towards the center of the Earth. So if you fly along the curve of the earth then you are always level, because you (and hence the spirit level) remain at right angles to "down" the entire time.

In the above diagrams the planes and arrows are actually rotated, but because it's only 0.5° every 70 miles, it's hard to see.

However you DO see the bubble moving in the level in the video. That's probably not because the plane is tilting up and down, it's because the plane is speeding up and slowing down.

Spirit levels are just tubes with a slightly bulge in the middle, the tube is filled with liquid (originally alcohol, hence "spirit" level), and a bubble of air is left in there. The bubble rises to the top, which is in the center of the bulge when the level is level. (It rises because of buoyancy, which is a function of gravity)

A spirit level does not magically indicate "level", it actually indicates the sum of all the forces acting upon it. When the level is on the ground then the only significant force is the force of gravity, which acts straight down. When the plane accelerates there's an additional force acting on the liquid, so the apparent direction of "level" will change. However most of the time the plane is just cruising at a constant altitude, so the level remains still.

The GPS track includes altitude, and we can plot a graph of that:

The video was shot in the first half of the flight, at 32,000 feet. Halfway through the flight the plane climbed to 34,000 feet. The level would have shown this movement, but it would still have been pretty slight.

Last edited: May 22, 2017
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3. ### Spectrar GhostSenior Member

I think it's a mistake to imply that the pilot needs to nose down at all. Perhaps one of our pilots can clarify, but it was my understanding that aircraft need not 'correct for curvature' at all, because their altitude is determined by a dynamic equilibrium, in which their lift cancels out their weight.

If they were to climb away from earth due to curvature, the lower air pressure at higher altitude would mean less lift (because less mass of air would be forced down), causing the aircraft to sink until it reached equilibrium again at its original flight level. It requires no active control on the pilot's part to remain level so long as the thrust, attitude, and atmospheric conditions remain constant.

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4. ### TrailblazerModeratorStaff Member

Yes, I think this is misleading. You don't need to "make an adjustment" for the curvature, you just fly level. Imagine that the plane did fly the "straight" red line here.

What that would actually mean is that the plane would be climbing all the time (relative to the ground, which is how we measure altitude), and the rate of climb would be getting steeper over time.

Last edited: May 22, 2017
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I didn't really mean to imply that they need to "nose down".

From a practical perspective they don't think "I'll just put the nose down 0.01° to account for curvature" - they just trim the plane so altitude is constant. From my manual experience of flying small planes this requires frequent adjustments both up and down. There's a variety of factors at play here, none of which from the pilot's perspective are curvature.

If you are climbing the air gets thinner and gives less lift, so at some point (with constant throttle) you'd stabilize at a particular altitude. However you generally want to fly at a specific altitude, so you fly up to there, then reduce the throttle and adjust the trim to stay at that altitude.

Trim is an adjustment you can make to the control surfaces of a plane that stays adjusted. Normally if you let go of the yoke it would return to center. The trim adjustment might be a nose down thing, but it might equally be a nose up thing depending on airspeed and throttle.

Last edited: May 22, 2017
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6. ### TWCobraSenior Member

To complicate things slightly, aircraft at high altitude do not maintain an altitude above sea level or even follow the curvature of the Earth.

Climbing above what is called the "Transition Level" pilots set a standard setting of 1013.25 HPa or 29.92 Hg and fly a cruise altitude based on that setting. This is called a Pressure Altitude.

Because the atmosphere thickens towards the equator and has less depth towards the Poles, a pressure altitude can vary from the equivalent true height above sea level, called the Geometric Altitude, by a few thousand feet at any time. It's not unusual to see this discrepancy on the GPS altitude displays which are geometric readouts.

The system retains proper traffic separation because ALL aircraft flying above the Transition Level have the standard setting on their altimeters.

It is also not unusual to see the autopilot on an aircraft subtly adjusting the aircrafts altitude to account for changes in air pressure as it moves along the route. The aircraft never adjusts to maintain height above sea level when above the TL.

I'll do a time lapse of the Vertical Speed indicator next time I go flying, to illustrate the point

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I forgot about that, and of course that will apply in this instance, as he's at 32,000 feet. It's another factor that's way more significant than the slight curvature of the Earth.

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8. ### deirdreModeratorStaff Member

not really. the plane is initially going up to reach altitude. From a FEers perspective level means flat, but the plane isnt "flat" when it reaches cruise altitude. the plane is level but that means its nose is .01 degrees from flat.

9. ### andycroftsNew Member

There's gonna be some folks who'll say "Maybe the bubble glass wasn't exactly mounted in the spirit level! FAKE SCIENCE!"
Simple answer: After taking one measurement, turn the spirit level around, do another measurement then take average of the two measurements.
Doddle.

Last edited by a moderator: May 23, 2017
10. ### ChewSenior Member

@TWCobra how often does an autopilot read the altimeter? How large of an error between the altimeter and the ordered altitude can develop before the autopilot corrects for it?

11. ### Clouds GivemethewilliesActive Member

They do that to put FEers off the scent.

12. ### TWCobraSenior Member

The Pitot/Static system on an airliner reads the air pressure and the Air Data Computers constantly uses this information and other inputs to determine both correct airspeed and altitude. Typically there are three altimeters working off three independent pitot/static systems; The Captains, First officers and the Standby system and either two or three ADC's which can be switched should one fail.

The advent of Reduced Vertical Separation Minima (RVSM) where vertical separation was reduced from 2000 feet to 1000 feet placed a requirement for altitude computation to be more accurate than in the past. Altimeters have a error tolerance both on the ground and at altitude, and are checked during pre-flight and during cruise.

The tolerance gets larger as the aircraft climbs as the lowering of air pressure during the climb makes altimeters less accurate at altitude. Typically the Captains and First officers altimeters must read within 35 feet of each other on the ground and within 75ft of the airport elevation (with the same barometric pressure set). The maximum allowable difference in the air is 200 feet for RVSM. It is rare to see more than 50 feet however.

Chew, in practice when we engage an autopilot it will fly to the altitude information coming from its dedicated ADC. It will simply change the altitude when it senses a discrepancy to the altitude assigned. I can't tell you what the tolerance is but it isn't much. As I mentioned before, a time lapse taken of an altimeter readout next to a vertical speed readout will show graphically how sensitive it is.

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13. ### Bass In Your FaceActive Member

Doesn't that tray table jiggle, on a jiggly seat? It seems there would be too many variables using a tray table. If movement of the bubble was what he was looking for, I'm sure constant random vibrations would muddy his results (if the results were large enough to distinguish in the first place)

Well he's not getting any "curvature" result even if he was on an airship, as the level would remain level. But yes, there's a lot of additional noise there.

That would be great.

Using the Vertical Speed Indicator (VSI) might have been a better way (for me) of putting it. When pilots level off they are looking to maintain a fixed altitude - but they (as I remember my flying) don't do this so much be watching the Altimeter, they do it by adjusting until the VSI reads zero.

If you were to fly in an actual straight horizontal line you'd be climbing, and the VSI would gradually rise. So you adjust the throttle and trim so that it doesn't, and you are flying around the curve.

Again though, this isn't a correction for the curve, it's just maintaining level (constant altitude) flight.

16. ### IR240474New Member

Cool info guys...

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17. ### Scott OrshanNew Member

The experiment is flawed, because the pitch angle of the airplane is not representative of its direction of flight. An airplane can be in level flight with the nose pitched down slightly, or pitched fairly high, depending on speed and load. A level will not show you whether you are climbing or descending.

I'm sure that you've experience a nose-high attitude when landing, even though you are descending.

That's with a level facing front to rear. A level facing left right might not even show any tilt during a turn if the turn is coordinated, as you see in this video. A level just doesn't tell you much of anything in an airplane.

Another flaw to the argument is that if you're part way through your trip, you should have been pointing the airplane up, since the earth behind you is lower.

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18. ### TWCobraSenior Member

That reminds me. Water bottles can also be used to determine cloud tops. Looking out the front of an aircraft, objects at a distance from the aircraft at high altitude generally appear higher than they actually are. This is due to an optical illusion caused by the curvature of the Earth as it slopes away from the observer.

We generally get a bottle of water such as the one in that video, look through one end towards a cloud top and if it is below the level of the water, then the aircraft is above the cloud. Works like a charm.

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"5 miles "down" after traveling 200 miles" ? The horizon "drops" only 8 inches per each mile. So, if we multiply 200 x 8 inches we get just 1600 inches = 233 feet . The problem comes from a google search that takes you to a page that says the following "The Earth has a radius of approximately 3965 miles. Using the Pythagorean theorem, that calculates to an average curvature of 7.98 inches per mile or approximately 8 inches per mile (squared)." No square, please ! And as we know, it doesn't really "drop", it's a visual line of sight drop. All other arguments given in this thread apply.

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20. ### TrailblazerModeratorStaff Member

If the horizon dropped by 8 inches per mile then it would be a flat slope. Eight inches x (distance in miles squared) is a reasonable approximation for the "drop" figure: after 1 mile it is 8in, after 2 miles it is 8 x 22 = 32in, after three miles it is 8 x 32 = 72in, and so on.

Of course, this "drop" is compared to a tangent line taken at the original point. The actual drop is 8 inches over each mile, it doesn't get bigger the further you fly, because the curvature is (virtually) constant all around the globe.

Your figure of a 233ft drop after 200 miles is incorrect: the drop is just over 5 miles.

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The amount of drop over distance is one of those things that confuses people. The drop is indeed 8 inches over the first mile. It's also 8 inches over the second mile, and the third.

But over the first two miles it's about 32 inches, and over three miles it's about 72 inches, and over ten miles it's 800 inches.

And going the other way, over the first 1/10th of a mile (528 feet) the drop is 0.08 inches, which is 1/100th of the one mile drop.

All these numbers are very confusing to the average person. But maybe they could concentrate on how a 8" drop on both the first and second mile results in a 32 inch drop over the first two miles.

I'd illustrate this with two 1000 mile segments, as otherwise everything looks like straight lines. Note at this scale you can't use the 8"/miles^2 approximation and have to use the full equation

(To understand the following, every time I mention a letter, like B, look it up in the above diagram)

We start at B and fly around the curve to D, 1000 miles away, then continue another 1000 miles to F.

Over the first 1000 miles (B->D) the drop (i) is 128 miles from a line level at B.

Then over the the next 1000 miles (D->F) the drop (j) is again 128 miles from a line level at D

However if you consider the entire trip (B->F) the drop (j+l) from a line level at B is 542 miles (a bit over 4 times as much)

I would hope that the diagram would make it clear why this is the case.

Last edited: May 30, 2017
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22. ### Bass In Your FaceActive Member

If it helps with the explanation, angle CDE is 90 degrees (just like line BC is 90 degrees to the y-axis) and line DE is a tangent to the Earth (just like line BC).

If we wanted to compare on a graph the earth's curvature to the drop 'estimate', the earth would be expressed as a circle equation, and the "8 inches per mile squared" drop estimate would be expressed as a parabola.

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23. ### deirdreModeratorStaff Member

are you trying to explain why C-D and G-E-F dotted lines look "angled"?

24. ### Bass In Your FaceActive Member

?

Was just trying to clarify what's in the photo, for those who may not understand...............

........ it seems Flat Earth-ers asking these questions keep getting drop types confused.........

25. ### thehatNew Member

Don't neglect the effect of gravity while the plane is in flight. Since the plane is always essentially "level" with the ground below, in maintaining a set altitude, the gravity of earth will pull upon the passengers and the alcohol in the level as though the center of the earth were directly below, exerting an equal force along the airplane and basically showing it as level by the spirit bubble. Although mountains, basins, etc., may affect the force of gravity on the plane very slightly as it flies overhead, the force is still exerted on the plane pulling it straight down in opposition to the force of lift.

I stand corrected, sir ! You are absolutely right. The surface in one direction is a circle, and thus, the square term

27. ### gungustNew Member

My first language is not English, so maybe I´m missing some subtle wording, but shouldn´t the last B be D.

"Then over the the next 1000 miles (D->F) the drop (j) is again 128 miles from a line level at D"

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Oops, thanks, fixed!

29. ### mowgliNew Member

Good solid info again guys.

So what we are essentially saying is that use 8inch squared with a static starting/end point. Such as a situation when you want to measure line of sight distance or on a distance object. But when we talk about travel do not square the 8 inch drop as obviously we have a _moving_ starting point that is gobbling up your tangent sum as quickly as it is moving? . Essentially all the plane (or a train - we know how Flat Earthers love long train tracks) has to compensate for is that 8 drop directly in front of it for that mile, then it starts all over again. It is not an accumulative measurement.

Also i couldn't help but notice the bulge in the spirit level image. I am assuming like all tools it has a tolerance or a minimum accuracy quota? Is it a flight of fancy (pun intended) to suggest as part of an argument that if the curve in the top of that glass bubble is _greater_ than that of curve of the earth putting a spirit level on an angular incline that matches the above mentioned "first 1/10th of a mile (528 feet) the drop is 0.08 inches" - which works out to be fraction of a degree pitch that this is well below detection capability of the spirit level?

On a side note i am coming across another similar echoed argument among flat Earthers. "water always finds it's own level". Which as far as i can remember is actually an observation from Pascal concerning liquids always finding the same height in containers when/if connected by a pipe. I'm working on that one at the moment also. As to all Flat earthers it is a clear indication that water is therefore always flat and so oceans can not curve.

Last edited: May 30, 2017
30. ### TrailblazerModeratorStaff Member

No, it's not a cumulative measurement, but it's meaningless to say it has to "compensate" for 1 mile, or 0.1 miles, or 0.01 miles. Nobody is really compensating for anything. If you maintain level flight, you follow the curve automatically. If you drive along a road, or drive a train along tracks, you don't have to remember to push the nose of the vehicle down to stop it from floating off the ground as it would if it went in a "flat line". Gravity does it for you.

I think the degree of bulge is a bit of a red herring. Obviously it is many, many orders of magnitude more than the curve of the Earth. The bubble tube is curved so that the bubble rises to the top. The sharper the curve, the less the bubble will move for a given angle of tilt. If you had a very gentle curve, then the level would be more sensitive, but it would also be more prone to manufacturing error as the curve must be produced very precisely. If you have a sharper curve, then the bubble will move less for a given tilt, so the level will be less sensitive.

Flat Earthers generally have trouble differentiating between "flat" and "level". Water finds its own level; it doesn't find its own flat

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31. ### Clouds GivemethewilliesActive Member

The most sensitive levels have a radius of ~100 metres, which is pretty amazing.
https://www.leveldevelopments.com/sensitivity-explained/

32. ### Graham2001Active Member

Stuart Robbins over at the Exposing PseudoAstronomy podcast briefly touches on this one of his recent series of episodes on Flat Earth claims. His explanation is short and to-the-point:

http://podcast.sjrdesign.net/shownotes_149.php

The rest of the episode covers other aircraft related claims (No continent-to-continent flights in the Southern Hemisphere, radar coverage issues, flighttracker issues, etc...) this forum has touched on.

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33. ### Keith BeachyActive Member

Pilots can keep the level level and don't care if the earth is flat or round.

Some deck angles for airliners are not level during cruise. I assume the flat earth level man leveled his level parallel to the longitudinal axis of the aircraft on his tray some how to get a level reading. Then I was laughing as the bubble moved during the video, and laughed more as I remembered engineering work in aerodynamics assume a flat earth.

When engineers work on flight systems (not the navigation systems), we make an assumption of a flat earth for the flight dynamics.
An example of what I am talking about, see 1.1.2 Making assumptions.
http://aerostudents.com/files/flightDynamics/flightDynamicsFullVersion.pdf
If you don't make assumptions, the equations of motion will fill all the black boards in the lecture room and you end up with lots of terms which are essentially negligible anyway for flight in earth's atmosphere for conventional aircraft.

needle, ball and airspeed, or use the cat and duck method of instrument flying.
http://www.hsvwings.com/C&D_Flight.pdf
The cat and duck don't care if the earth is flat or round

The "level on a plane" kind of proves gravity is just like acceleration, yet the flat earth level guy denies gravity exists, and then says a stone is heavier than the air.

34. ### SinsiMember

With all the comments from such smart people. Not one person will conceded that the results of the experiment are consistent with living on a flat plane?

It's beyond amazing that the globe model needs this vigorous defending. It was fun reading all the replies in this thread. If you ever wonder why the FE movement is growing. Just read all the mental gymnastics and nonsense you guys have written in the thread. You guys sound like the church.

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I'll concede it. But it's also consistent with living on a globe. Marble's claim was that a globe would give different results.

Can you quote one bit of uncorrected "nonsense" in this thread

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36. ### Keith BeachyActive Member

The results are consistent with flying on a spherical earth, confirming how the bubble acts on a spherical earth. The bubble moved all over the place. The experiment was not evidence for a flat earth, because there is no science on how a level works on a flat earth. A level on a plane would act like it did because the aircraft in level flight is always tangential to the earth's center of mass. The guy doing the experiment denies gravity exists to make the bubble level, which is not true. To use a level, there has to be science to explain how a level works in a flat earth, along with gravity, and it would be neat if the sun was explained. (note: the author of the experiment denies the sun is 93,000,000 miles away, he says the sun is closer - it becomes a gish gallop based on no science)

welcome to the church of science, truth, logic and knowledge - reality

Last edited: Jun 3, 2017
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37. ### mcdoubleNew Member

I think this may be a point where people are dismissing the FE claim too easily. A car will keep it's nose on the ground as the earth curves because of gravity, but there doesn't seem to be any reason why gravity would pull an aircraft's nose down in the same way.

Let's say I design an aircraft that maintains exactly level flight in a wind tunnel at a specific air pressure and air speed. I lock the control surfaces in place and then attempt to fly that aircraft across the Earth at the corresponding pressure and speed (ignoring all the obvious complications like variations in wind, pressure, temperature etc). It seems as if some people are claiming that this craft would maintain level flight in this case as well, "automatically" pitching itself to follow the curve of the Earth. I don't see why that would be the case, as gravity would be pulling on all parts equally, not the nose in particular. So it should indeed seem to slowly pitch up, gaining altitude until it eventually stalls.

In that sense aircraft do compensate for the Earth's curvature, in that they must be trimmed to pitch ever so slightly down compared to what they would on a theoretical flat plane or in a wind tunnel in order to maintain a constant altitude. As has been said already, that compensation is so miniscule as to be lost as noise amongst all the other more significant factors, but it is still there. So, I think when people ask "why don't planes have to constantly pitch their nose down to account for curvature?" the answer should really be "they do", rather than just dismissing the idea as silly.

You are kind of asking what would happen if a plane was flying on a flat earth, and then suddenly was teleported to a round earth at the exact same altitude, pressure, etc. What would happen to the plane, if we ignore all the complications.

I'm not sure it would suddenly follow the curve, however it's orientation would be very slightly pointing uphill. Over the next mile you would (in theory) gain 8 inches in altitude.

However you'd ALSO lose airspeed, because now you are starting to rise, and the Vertical Speed Indicator would start to increase.

And reduced airspeed means reduced lift, meaning reduced vertical speed, meaning you'd lose altitude.

It's an interesting thought experiment, but really it's a combination of throttle and elevator setting that dictate changes in altitude. Pilots set them to maintain altitude, and adjust if altitude is changing. They usually adjust the throttle, not the angle of the plane.

Last edited: Jun 12, 2017
39. ### mcdoubleNew Member

Right, it's purely a thought experiment as in reality the other complications are far more powerful than the effect of curvature. But I think it's worthwhile to consider as it shows that you can't just assume that gravity will take care of everything. There is at least some validity in the idea of "having to constantly pitch down" that should be acknowledged.

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