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Why is the pitch measured with respect to the horizon and not the ground? How different are the angles between the ground and the horizon? Would it be possible to fly with an attitude indicator that indicated pitch with respect to ground rather than horizon? What does it mean when you have a 0 degree pitch with respect to the horizon? What, exactly, are you flying towards in that case?

I've always had a hard time understanding this. Thanks for your time.

Dargscisyhp
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    If you were flying over steeply sloped ground, what would you want the pitch angle to show? Pitch is related to the aircraft's passage through the air, not to the ground. Think of it this way. Pitch is related to angle of attack which is related to lift. Lift counters gravity which always acts vertically downwards, perpendicular to the horizontal (the horizon) and not to the ground underneath which could be doing anything. – Simon Feb 04 '16 at 15:36
  • So if the Earth were perfectly spherical pitch with respect to the horizon and ground would be the same thing? – Dargscisyhp Feb 04 '16 at 15:39
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    At the microscopic level of an aircraft flying over it, yes. It assumes that the world is flat. If the world was a perfect sphere, then the pitch would be constantly changing but by such a tiny amount, that the changes would just be "noise" in everything else that affects pitch. – Simon Feb 04 '16 at 15:40
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    I should have phrased that better. I mean in the perfectly spherical Earth sense of the word. If that was the case would the angle between the velocity vector of the plane and the horizon be the same as the angle between the velocity vector of the plane and the ground? – Dargscisyhp Feb 04 '16 at 16:00
  • Take a line directly down to the center of the earth from the aircraft. where the aircraft is on this line, construct a plane that is perpendicular to this line. That plane (no pun intended) is the "horizon". – Steve Feb 04 '16 at 16:04
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    @Simon - that sounds like a very simple, yet valid answer, to me! – FreeMan Feb 04 '16 at 16:31
  • @Simon It's important to properly differentiate between pitch and angle of attack, though. Pitch is defined as the angle between body axis and horizontal, it is thus the angle between local gravity vector and body axis minus 90 degrees. Angle of attack is the angle between body axis and air flow. This is the same as pitch angle only in steady level flight without wind.Consider a modern airliner on approach. Often their pitch is nearly level, while the angle of attack is greater; as they are descending, the air flow "hits them from below". – Cpt Reynolds Feb 06 '16 at 11:49
  • @CptReynolds I'm a pilot! I am fully aware of the difference between pitch and angle of attack but for a simple explanation, where I say that they are related, it will suffice. – Simon Feb 06 '16 at 20:20
  • @Simon My apologies, I didn't mean to be patronising. It's an easy mistake which many people make (not meaning you!), and all I was trying to do is to ensure this thread helps to dispel the common misconception. No offence! – Cpt Reynolds Feb 07 '16 at 01:17

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Pitch is measured with respect to a plane orthogonal to the local weight¹ force, which is properly called the horizontal.

That is used because:

  • It is equipotential plane of the gravitational field. Moving around it won't change your potential energy.
  • Is always well defined.
  • Is smooth and locally flat (it is still a spherical surface globally, of course).
  • Can be measured by averaging inertial forces on board without external reference.

It is called simply horizon, presumably because looking at the horizon is the easiest way to find that plane by human senses.

Using ground, which is not flat, as reference wouldn't work. Aircraft need to fly mostly along the equipotential plane, because climbing to a higher one requires adding more energy by the engines and descending below means the aircraft accelerates and needs to dissipate (= waste) the energy. So following terrain would require quite a bit more energy than flying horizontal. Plus it would be very complicated.

¹ By weight I mean the sum of gravity and centrifugal force in the reference frame rotating with Earth.

Jan Hudec
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  • Follow up question: how does a plane stay on that equipotential plane? If the lift force and gravity force cancel, then Newton's second law would seem to imply that the plane will move in the same direction it was previously moving, meaning the Earth would curve away from it and the plane would seem to ascend. Is there a constant correction for this, or is the lift on the plane made just right that the plane is constantly "falling," keeping it in circular motion? – Dargscisyhp Feb 04 '16 at 15:58
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    @Dargscisyhp See this question over at Physics.SE. In short, they don't cancel. But really, your altitude will vary a lot more due to local winds and non-perfect control inputs - the curvature of the earth is negligible compared to that. – Sanchises Feb 04 '16 at 16:02
  • Heh, I actually asked that question. I'm not sure I got a consensus there and a couple of people suggested that physics.se was not the right place to ask. – Dargscisyhp Feb 04 '16 at 16:04
  • @sanchises, That question is about including the centrifugal force due to Earth rotation and I intentionally said weight, not gravity, to include it. – Jan Hudec Feb 04 '16 at 16:24
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    @Dargscisyhp, If you perfectly balanced the plane to make it fly straight (in the reference frame rotating with Earth; we are including the centrifugal force by referring to weight), the lift would initially cancel each other, but the weight would slowly rotate, so after a bit the forces would no longer cancel perfectly, but instead add up to a small aft force. And that would slow the plane, exactly as expected from conservation of energy. The pilots (or autopilot) need to maintain the correct level by rotating the lift correspondingly. – Jan Hudec Feb 04 '16 at 16:31
  • @sanchises, No, weight is correct. General relativity says that "effect of homogeneous gravitational field is indistinguishable from effect of accelerating reference frame", so there is no way to distinguish the forces by local measurement. Yes, weight does not point to the centre of Earth, but it is what defines the equipotential surface followed by water level, and also ground, because rock is soft enough to behave pretty much as liquid on the planetary scale. I.e. Earth is not a sphere, it is slightly flattened and the centrifugal force is the reason. – Jan Hudec Feb 04 '16 at 16:42
  • "It is equipotential plane of the gravitational field. Moving around it won't change your potential energy". At a simplified level yes, but actually the equipotential surface is the geoid. – mins Feb 04 '16 at 16:45
  • @mins, yes, the proper name of the "slightly flattened" thing is geoid. Calling it equipotential surface of the "gravitational" field is slightly misleading, because it includes the effect of rotation (I am not sure with the proper terminology in English (I am not native speaker), but believe this is nevertheless the standard term as there don't seem to be specific terms for distinguishing the cases). – Jan Hudec Feb 04 '16 at 16:59
  • @sanchises, the reason to use gyroscope is to separate out the inertial forces from the aircraft's own motion as that is not possible with local measurement either, so the gyroscope provides enough non-locality for that. It still does not separate out the effect of rotation of Earth itself, nor could it, nor does it intend to. – Jan Hudec Feb 04 '16 at 17:01
  • See this for additional details (surely pedantic here, this is just for the sake of curiosity). The slightly flattened thing should be the ellipsoid of reference. The potential is greatly affected by the mountainous masses (or the lack of rocks in abyssal trenches), hence the geoid undulations. – mins Feb 04 '16 at 17:17
  • @JanHudec Ah, like so - I thought you were referring to the instantaneous weight vector which varies with the slightest gust of wind, but if you are referring to the average (non-instantaneous) weight vector, then yes, I fully agree. I'll clean up after me in the comment section :) – Sanchises Feb 04 '16 at 17:30
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An airplane needs to be oriented to a frame of reference which does not change depending on altitude or the elevation of the ground, this is so the pilot will be able to judge the angle of the wing through the air flow. If you used angle between the ground and the horizon then it would be constantly changing depending on your height and the elevation of the ground. If the ground level ahead goes up then the angle between ground and horizon decreases, if the ground level stays the same and you increase altitude the angle increases. If you see the angle diminish you would not know whether it was because of a change in attitude, altitude, or ground elevation.

GdD
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  • So if the Earth were perfectly spherical pitch with respect to the horizon and ground would be the same thing? – Dargscisyhp Feb 04 '16 at 15:40
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    You are misunderstanding what pitch is. Pitch is related to gravity, not the horizon. The horizon is where the ground meets the sky, and changes depending on the elevation of the ground. – GdD Feb 04 '16 at 15:53
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Your question seems to boil down to the following:

Assuming that the earth is a perfect sphere, why does the virtual horizon (i.e., the pitch indicator) point to the horizon? The answer is, it doesn't.

Pitch is determined with gravity, which always 'points' to the center of the earth. The virtual horizon you see on your pitch indicator is always at an angle of 90° (i.e., a straight angle) from that, and only points to the actual horizon in case you were exactly on the ground. This difference is negligible for normal flight (which happens in the very lowest part of the atmosphere). The following is only to demonstrate what is actually happening.

enter image description here

In the above picture, I drew an exaggerated version of what you mean. The red line points to the center of the earth (so, where gravity points), and is the reference of your pitch indicator. The green line is what you will see on your pitch indicator. The blue line is where you actually see the horizon. They don't match up, and that's fine.

A pilot really doesn't care where the horizon is. He cares about maintaining altitude, ascending or descending. Maintaining altitude is done by keeping the airplane level with respect to the center of the Earth, in which case he will make a complete circle around the earth since his velocity vector is always perpendicular to the center of the Earth. Ascending and descending is done by having the pitch above or below this.

From the picture you can see that if the virtual horizon were to point to the actual horizon, you would eventually impact the ground - on a perfectly smooth sphere, it would be a smooth landing too. I guess there's a reason they call it the virtual horizon, eh?

Sanchises
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The "horizon" is a fixed reference that will be the same wherever you are flying. It is fairly straightforward to create an instrument for the cockpit that illustrates pitch and roll with respect to this horizon. It also relates to gravity, since gravity will be pointing straight down with respect to the horizon. Pitching up means you are working against gravity, regardless of what the ground below you is like. Humans have a natural sense of "up" and what is "level", which is based on our perception of gravity.

Showing pitch with respect to the ground would be much more chaotic. You would need some way to know what the ground below the aircraft is doing, at any altitude. The relationship of pitch and power would be even more confusing, as pitch would no longer consistently relate to gravity, and therefore no longer consistently relate to power.

Passengers typically like a smooth and level flight. Airliners flying over mountains would have a wildly changing pitch indication, despite flying "straight and level." If an aircraft wanted to fly level with respect to the ground, it would require steep climbs and descents in these areas. Since air density changes with height above sea level, not the ground, the aircraft's performance would continually change as it stays level with the ground.

If a pilot is concerned about hitting the ground, there are many better ways to avoid that. Traditionally, charts and navigation will allow a pilot to avoid terrain. Technology like radar altimeters have also helped, which shows the pilot how high they are above the ground. Newer systems allow things like synthetic vision if the terrain is not clearly visible.

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fooot
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  • Might be worth pointing out that planes might have a difficult time flying if you kept pitching up and down to stay level with the ground... I think the constant adding and removing of kinetic energy would catch up with you eventually. – Jae Carr Feb 04 '16 at 15:49