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

#### Neil Obstat

##### Member
I think it would be a great idea if we all could start bringing torpedo levels on our plane trips and prop them up on our laps during the flight. Imagine being a stewardess walking down the aisle seeing all those torpedo levels on passengers' thighs! Wouldn't that just make your day at work!

#### Kevin McMillen

##### New Member

Wouldn't my cup of coffee, Coke or Sprite be good enough to prove the plane isn't dropping 67ft per second as FEers claim?

#### Neil Obstat

##### Member
Wouldn't my cup of coffee, Coke or Sprite be good enough to prove the plane isn't dropping 67ft per second as FEers claim?
I'm not sure. You never know what a flat-earther has up his/her/unID'd sleeve. They manage to come up with the most bizarre accusations!

But if you want to be really in the "loop" you ought to remember to bring your torpedo level to keep on your thigh, then you'll be sure to get plenty of attention.

#### Richard Aguirre

##### New Member
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.

Posting further support to this statement. The altitudes being flown in this experiment are in the Reduced Vertical Separation Minimim (or RVSM) airspace, which requires, according to 14 CFR Part 91, App 6 Section 21 the aircraft pressure altimeters maintain accuracy of +\- 65 feet in still air. Although the autopilot makes continuous tiny changes to maintain essentially 0 feet variation in Pressure Altitude, say for example the Altimeter tolerance was at its limit, and reached 65 feet error before correcting. If we also accept the 5 statute mile drop over 200 miles distance, the average angular change would be 1.43 degrees (-1tan a = 5/200). But a 65 foot change is one 406th of a 5mi drop (5x5280’ / 65’). So the aircraft would make 1.43/406=.0035 degree changes each time it corrected altitude (not realistically how an airplane flies but as a worst case approximation in favor of the experimenter we’ll use it). In that case, even the most sensitive spirit levels (https://www.leveldevelopments.com/sensitivity-explained/), ones with a tube radius of a 100m (most definitely not the one used) would register this .003 angular difference as a .06mm deflection of the ball. Clearly undetectable by the naked eye.

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#### Trailblazer

##### Moderator
Staff member
Posting further support to this statement. The altitudes being flown in this experiment are in the Reduced Vertical Separation Minimim (or RVSM) airspace, which requires, according to 14 CFR Part 91, App 6 Section 21 the aircraft pressure altimeters maintain accuracy of +\- 65 feet in still air. Although the autopilot makes continuous tiny changes to maintain essentially 0 feet variation in Pressure Altitude, say for example the Altimeter tolerance was at its limit, and reached 65 feet error before correcting. If we also accept the 5 statute mile drop over 200 miles distance, the average angular change would be 1.43 degrees (-1tan a = 5/200). But a 65 foot change is one 406th of a 5mi drop (5x5280’ / 65’). So the aircraft would make 1.43/406=.0035 degree changes each time it corrected altitude (not realistically how an airplane flies but as a worst case approximation in favor of the experimenter we’ll use it). In that case, even the most sensitive spirit levels (https://www.leveldevelopments.com/sensitivity-explained/), ones with a tube radius of a 100m (most definitely not the one used) would register this .003 angular difference as a .06mm deflection of the ball. Clearly undetectable by the naked eye.

I was flying back from holiday last weekend and had my Bluetooth GPS antenna connected to my phone so I could see where we were (it's a lot more accurate than the built-in GPS, especially since Apple ruined the GPS capabilities of iPhones, but I digress...). The GPS altitude - which of course is not the same as the pressure altitude, for a number of reasons - changed very little when we were in "level flight", maybe fluctuating by a metre or two (5ft or so) every few seconds. Certainly nothing as big as 65 feet.

Using GPS altitude has the complication that the aircraft is maintaining a constant pressure altitude, not a constant height above the surface (as Mick mentioned in post #77). So if for example you are flying from an area with low sea-level pressure to one with higher sea-level pressure, you will actually be slowly ascending in terms of GPS altitude, because the pressure at a given height (above sea level) will be higher. GPS altitude also isn't exactly the same as altitude above sea level, but that's not so important for this discussion.

I noticed this when flying from Iceland, where there was a deep low pressure system, towards the UK, which was still under high pressure. When the on-board screens indicated we were flying at 35,000 feet (for example, I can't remember the exact numbers), the GPS indicated we were at about 33,500 feet. After an hour or so, despite the indicated flight level being the same, the GPS showed we had ascended by few hundred feet. So while there were no big corrections in flight, the overall trend was a very gradual ascent above the ground. Of course, flying the other way a plane in level flight would be descending.

#### Richard Aguirre

##### New Member
Your observation is correct. There is also the effect that long range flights often use a stepped altitude profile to take advantage of greater engine efficiency and true air speed gained at higher altitude. As the aircraft burns fuel it loses weight, allowing better performance. The pilots can then periodically climb slightly to a more favorable altitude, depending upon winds and other traffic. This can account for a few thousand feet of change over a long flight.

GPS as you may know is also not a perfect measure of altitude, as it still relies upon line-of-sight radio signal reception and requires correction by ground stations which may not always be in range over water. GPS altitude is also referenced to a different geodetic datum than charted MSL altitude so there are variations in comparison. (Nevertheless GPS it is still very, very accurate, accounting for such things as transmission lag and Einstein’s relativistic effects, as well as variations in Earth’s gravitational field to define the actual datum). Here is a great article on GPS altimetry for those who are interested. https://www.esri.com/news/arcuser/0703/geoid1of3.html

#### JohnP

##### New Member
"Fuzzy Math" that is what a FEer uses to "prove" their point about airplane flight.

I'm using 600mph to simplify things.

A FE would correctly calculate the drop in 600 miles as 240,000ft. Now they go to fuzzy math. Since the plane is going 600 miles in an hour they divide 240,000 by 60 and get 4,000 ft drop per minute. Divide 4000 by 60 seconds and you get a drop per second of 66.7 ft per second.

Anyone would notice that right? a spirit level should show that. Right?

Let's now use correct math. 600 mph is 10 miles per minute. That would be 1 mile in 6 seconds.

Ok, now we have 1/6th of a mile per second. That 's .1667 x .1667 x 8 = tada .222 inches.

Yep, that's less than 1/4inch per second. Anyone going to notice that?
Kevin

Actually (1) I have no idea what you did there: where does the 8/(6x6) come from?
(2) I think this is all a red herring. The real reason the "change in altitude" is not perceptible is because it's not happening. Your argument would suggest that under the right circumstances, with the right equipment, it could be measured. I'd prefer to just say: level (horizontal) flight is perpendicular to the direction things fall.

#### Amber Robot

##### Active Member
Don’t airplanes fly at a fixed air pressure usually? And surfaces of equal pressure will mostly lie on gravitational equipotentials, so by definition they are always in level flight, since “level” means parallel to gravitational equipotentials.

#### Landru

##### Moderator
Staff member
Don’t airplanes fly at a fixed air pressure usually? And surfaces of equal pressure will mostly lie on gravitational equipotentials, so by definition they are always in level flight, since “level” means parallel to gravitational equipotentials.

https://en.m.wikipedia.org/wiki/Flight_level?wprov=sfla1

#### Trailblazer

##### Moderator
Staff member
Don’t airplanes fly at a fixed air pressure usually? And surfaces of equal pressure will mostly lie on gravitational equipotentials, so by definition they are always in level flight, since “level” means parallel to gravitational equipotentials.
In the absence of weather systems they would be, but there's up to a ~100mb range between the highest and lowest sea-level pressures encountered in the atmosphere, which means that a given flight level will vary in actual altitude above the ground by a couple of thousand feet or more depending on where the aircraft is flying in relation to those weather systems.

You can think of the high and low pressure systems as like "hills and valleys" that the aircraft will follow as it maintains a given pressure altitude, just like a car driving over hills and valleys while staying on the ground.

Weather maps often show the "geopotential height", eg on this chart the main colours indicate the height of the 500 millibar pressure level above sea level:

The scale at the bottom shows the geopotential height in decametres (tens of metres).

So for instance if a plane was following a flight level that corresponded to a pressure of 500 millibars, then it would be around 5,900 metres above sea level in north Africa, but only about 5,200 metres above sea level off the coast of Norway.

Generally these geopotential heights roughly correspond to the sea-level weather systems, but not always and not exactly, as the temperature of the air also affects the height. So for instance you can see that the highest and lowest sea-level pressures (shown by the white isobars labelled with black numbers) approximate but don't exactly match the highest and lowest 500mb heights.

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#### Richard Aguirre

##### New Member
Technically
Actually (1) I have no idea what you did there: where does the 8/(6x6) come from?
(2) I think this is all a red herring. The real reason the "change in altitude" is not perceptible is because it's not happening. Your argument would suggest that under the right circumstances, with the right equipment, it could be measured. I'd prefer to just say: level (horizontal) flight is perpendicular to the direction things fall.

I think it’s true there is no appreciable altitude change, because the aircraft adjusts to maintain level flight as oriented to a plane perpendicular to the force of gravity, and the force of gravity is balanced by the lift the plane generates, precluding a continual climb (or drop). But the orientation of the aircraft relative to the original plane it departed from (perdencicular to the gravitational force) has to change or else it would be slowly flipping over backward relative to the new “level plane” as it moves forward over time. It requires stabilization via a pitching moment, which is theoretically measurable, but not by the crude methods employed in the original example.

#### JohnP

##### New Member
Technically

I think it’s true there is no appreciable altitude change, because the aircraft adjusts to maintain level flight as oriented to a plane perpendicular to the force of gravity, and the force of gravity is balanced by the lift the plane generates, precluding a continual climb (or drop). But the orientation of the aircraft relative to the original plane it departed from (perdencicular to the gravitational force) has to change or else it would be slowly flipping over backward relative to the new “level plane” as it moves forward over time. It requires stabilization via a pitching moment, which is theoretically measurable, but not by the crude methods employed in the original example.

It would entail a comparison with the original orientation--so we're probably back to ring laser gyros.

#### Clouds Givemethewillies

##### Senior Member
In the absence of weather systems they would be, but there's up to a ~100mb range between the highest and lowest sea-level pressures encountered in the atmosphere, which means that a given flight level will vary in actual altitude above the ground by a couple of thousand feet or more depending on where the aircraft is flying in relation to those weather systems.

You can think of the high and low pressure systems as like "hills and valleys" that the aircraft will follow as it maintains a given pressure altitude, just like a car driving over hills and valleys while staying on the ground.

Weather maps often show the "geopotential height", eg on this chart the main colours indicate the height of the 500 millibar pressure level above sea level:

The scale at the bottom shows the geopotential height in decametres (tens of metres).

So for instance if a plane was following a flight level that corresponded to a pressure of 500 millibars, then it would be around 5,900 metres above sea level in north Africa, but only about 5,200 metres above sea level off the coast of Norway.

Generally these geopotential heights roughly correspond to the sea-level weather systems, but not always and not exactly, as the temperature of the air also affects the height. So for instance you can see that the highest and lowest sea-level pressures (shown by the white isobars labelled with black numbers) approximate but don't exactly match the highest and lowest 500mb heights.

It is only the weight of the density profile of the air above, in turn determined by temperature profile above, that determines the pressure at any level according to the hydrostatic equation, although if you know the temperature profile you can integrate up or down from a known pressure and altitude.

It is a chicken and egg thing..

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#### jtveg

##### New Member
Great explanation.
What some people don't understand is that planes (ie pilots) try to maintain a certain cruising altitude so the pilot / autopilot is constantly adjusting the plane's controls, usually the throttles to maintain that altitude.

Planes can only fly up to a certain altitude anyway. The thinning atmosphere means the wings cannot create enough lift nor can the engines get enough oxygen. So planes can't fly directly straight out towards space even if they wanted to. They would eventually begin to nose down regardless.

#### DavidB66

##### Active Member
Over the few years I've been following the flat earth 'debate', the question of how aircraft manage to follow the curvature of the earth has come up a lot. I recall seeing three broad classes of explanation:

1. The pilot (or autopilot) will need to adjust the controls from time to time to maintain a desired altitude, e.g. to allow for wind conditions and the changing weight of the plane as fuel is consumed. These adjustments are made by reference to an altimeter which measures the height of the plane above the ground, so they will automatically follow the curvature of the earth. There is no need for any separate allowance to be made for this.

2. Once the plane is at the desired altitude, the pilot will set the 'trim' of the plane to maintain the desired altitude as far as possible without further ad hoc adjustments. Since in level flight the ground is 'dropping' at a predicable way due to curvature, the setting will consciously or unconsciously allow for this. An analogy is often made with a car going round a circular track: the driver need only (in principle) keep the steering wheel in a set position once a steady rate of turn has been achieved. (As a variant on this explanation, it may be suggested that the necessary allowance for curvature is built into the design of the plane. To pursue the analogy of the car, if manufacturers and designers knew that the car was usually going to be going round a circular track of a given size, they might make this the default setting for the steering.)

3. Occasionally it is suggested that the plane follows the curvature of the earth automatically in accordance with the laws of physics, in response to the changing direction of gravity. I don't recall any convincing argument for this type of explanation, but it is not impossible. An analogy might be made with a pair of weighing scales. A pair of scales is usually designed to give a stable equilibrium, most often by ensuring that the centre of mass of the balance arm is below the pivot. If one side of the scales is depressed, the centre of mass will be displaced to the other side, so it will pull that side down and restore the balance. If a pair of scales of this kind were transported around the curvature of the earth, it would not be necessary to adjust the balance arm to keep it horizontal, as it would respond automatically to the changing direction of gravity. In the case of an aircraft, the balance of forces is much more complex, but it is conceivable that some such automatic process contributes to its stability.

Explanations of type 1 seem to be most common, and are sufficient without appealing to types 2 and 3. We know that adjustments of type 1 are in fact made, so any other explanation is not strictly necessary. Whether processes of types 2 and 3 make any contribution in practice is however an empirical question, and explanations of all three types are not mutually exclusive.

#### Mick West

Staff member
1. The pilot (or autopilot) will need to adjust the controls from time to time to maintain a desired altitude, e.g. to allow for wind conditions and the changing weight of the plane as fuel is consumed.

I feel the fundamental error they are making by even asking this question is to assume that a plane's natural inclination is to fly in a perfectly straight line. If they think this is true then ask them to drive a mile straight in their car without touching the steering wheel.

Really the answer is a combination of #1 (constant adjustments) and #2 (setting the trim for constant altitude) because what is often being constantly adjusted is the trim.

#3 (constant altitude as a result of curved gravity or atmosphere) is pretty much irrelevant. Just a meaningless thought experiment. If the plane is trimmed for level (constant altitude) flight then it will stay in level flight regardless of if the Earth is flat or round. If it's trimmed to descend then likewise it will descend, gaining speed, which might or might not result in a lower altitude equilibrium. Similar with trimmed to ascend, where it will lose speed, possibly settling down.

The bottom line, the plane has to be trimmed for level flight to stay in level flight. It's going to need frequent adjustments regardless.

#### Richard Aguirre

##### New Member
I feel the fundamental error they are making by even asking this question is to assume that a plane's natural inclination is to fly in a perfectly straight line. If they think this is true then ask them to drive a mile straight in their car without touching the steering wheel.

Really the answer is a combination of #1 (constant adjustments) and #2 (setting the trim for constant altitude) because what is often being constantly adjusted is the trim.

#3 (constant altitude as a result of curved gravity or atmosphere) is pretty much irrelevant. Just a meaningless thought experiment. If the plane is trimmed for level (constant altitude) flight then it will stay in level flight regardless of if the Earth is flat or round. If it's trimmed to descend then likewise it will descend, gaining speed, which might or might not result in a lower altitude equilibrium. Similar with trimmed to ascend, where it will lose speed, possibly settling down.

The bottom line, the plane has to be trimmed for level flight to stay in level flight. It's going to need frequent adjustments regardless.
Just a technicality here, but the aircraft are not actually trimmed for an altitude, but for a desired airspeed, which establishes a particular amount of lift in opposition to its current weight. At a given power setting, it may be either descending or climbing and still be “trimmed” at that constant speed. To achieve level flight then requires continual adjustments to power setting and pitch, and occasional adjustments to trim as fuel burn-off reduces the weight and center of gravity. All this means is that the aircraft is actively “flown” in level flight, either by the pilot or autoflight system. This is somewhat semantic but but more accurate than thinking of trim as simply being responsible for the apparent stability of the flight. This is where analogies to cars on roads fall short, and why explanation 1 (above) is most relevant. The aircraft follows the curve of the earth because it is “flown” to follow the curve of the earth. It’s inherent behavior is not really proof of anything.

#### Mick West

Staff member
Just a technicality here, but the aircraft are not actually trimmed for an altitude, but for a desired airspeed, which establishes a particular amount of lift in opposition to its current weight. At a given power setting, it may be either descending or climbing and still be “trimmed” at that constant speed. To achieve level flight then requires continual adjustments to power setting and pitch, and occasional adjustments to trim as fuel burn-off reduces the weight and center of gravity.

I wonder if it's overcomplicating things to focus so much on trim. The relevant trim here is just an adjustment made on the elevator so that you can hold at a particular pitch angle (nose up, level, or down) without having to maintain pressure on the controls.

Really the bottom line is that to maintain a constant altitude, you just adjust the controls (details irrelevant, but it's elevator/trim and throttle) until the vertical speed indicator is zero. Any adjustments made after that are nothing to do with the curve of the Earth.

#### Richard Aguirre

##### New Member
Really the bottom line is that to maintain a constant altitude, you just adjust the controls (details irrelevant, but it's elevator/trim and throttle) until the vertical speed indicator is zero. Any adjustments made after that are nothing to do with the curve of the Earth.

(Thumbs up) - clearly you understand it well.

Fascinating thread IMHO - especially to see how complicated the explanations for seemingly simple things can become, and the work it takes to distill an accurate, yet understandable explanation. Which, at risk of censure, I’ll suggest is one legitimate use for the FE movement... (ducking and covering)... if it at least generates more critical analysis. Too bad for some it still seems no explanation is good enough.

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