# What is the most accurate geometric plane for referencing terrestrial flight attitude?

I have found various definitions for attitude.

1. Merriam Webster: inclination of the three principal axes of an airplane in flight to the relative wind.
2. Wikipedia - Attitude Indicator: the orientation of the aircraft relative to Earth's horizon.
3. In my words, based on my current understanding: the angular orientation of the longitudinal and lateral axes relative to a 2D geometric plane, which is orthogonal to the Earth's average curvature at the point on the surface below the aircraft.

What is the correct reference plane for flight attitude in regards to terrestrial aerodynamic flight?

• Related discussion: Why is pitch measured with respect to the horizon and not the ground? Commented May 10, 2016 at 16:03
• Definition 2 says nothing at all about pointing the aircraft at the horizon. Commented May 10, 2016 at 20:11
• Accurate for what purpose? Definitions 1 and 2 are perfectly accurate if (in case 1) you want to talk about the aircraft's orientation as inclined to the relative wind, or (in case 2) you actually do mean the attitude with respect to the "true horizon line" (somewhat begging the question, but I'll use the language you use). Definitions can't be "blatantly inaccurate". It's possible that they don't reflect actual usage, but that is different than being inaccurate. Also, all of that discussion is irrelevant to your question in the final sentence about what the "correct" reference plane is.
– user13148
Commented May 10, 2016 at 20:42
• For definition 2, the attitude indicator is not referenced to the horizon line, but to the horizontal plane. Increasing altitude doesn't change pitch on a gyroscopic AI. Similarly bank angle is not measured relative to the horizon line sideway, but to the same horizontal plane. The latter is a plane parallel to the surface of the geoid).
– mins
Commented May 10, 2016 at 22:44
• @MortensenAviation, well, that plane is actually parallel to the horizontal (almost, because geoid is not exactly a sphere). But if you are looking at the horizon, you are looking from your position and that plane does not contain your position. Commented May 11, 2016 at 8:53

There are a few definitions because there are a few ways to look at it.

The most general thing to say would be something along the lines of,

An object's angles in pitch, roll and yaw from a set of chosen zero planes

It boils down to what you want to use as your point(s) of reference. Attitude indicators use the horizon and if you really want to talk about it even space ships have gimbals that measure attitude relative to a plane. Your definition assumes only attitudes of aircraft flying over the earth (using the surface as a reference plane) which is valid for most cases but not all.

Furthermore, attitude indicators are referenced to the horizon because it is an easy to find and generally a universal level plane with respect to the Earth's surface. In aircraft flight we care about the Earth's surface because that is where we want to get back to and subsequently not smack into in the process, so its convenient to reference to its plane. Furthermore at high altitudes the horizon is still the horizon; it simply becomes a space/Earth horizon as opposed to a sky/ground horizon.

Here is the view out of the SR-71's cockpit (@73,000ft, this is also the highest-flying non-experimental plane ever made) to illustrate the point.
(source)

To extend the frame of reference explanation, we can look at the Apollo rockets FDAI, which is a nice example of a 3-axis attitude indicator that was referenced to multiple planes instead of a single horizon. In this case the flight attitude was simply the angle from a chosen set of zero planes.

The first one is called "Inertial Stellar". That means that the reference is a 3D system of coordinates which is fix relative to the stars. That does not mean that there's only one system of reference. In fact, there is a system of reference for almost every phase of the mission. Some are reused during the flight and. in order to be accessed multiple times, they are stored in the computer as "REFSMMAT", which stands for REference For Stable Member Matrix.

-- EDIT --

Since the root question has changed somewhat ill add to my answer. Generally speaking airplanes are oriented to the gravitational force below which is taken to be the "vertical". The vertical is often taken to be the tangent of the ground beneath it but since the ground may also not be level this is a generalization. There is a bit of real world discussion involved here since attitude indicators, the point of reference for an aircrafts attitude may not always be perfectly level to the ground. A pilot is mainly concerned with setting his 0 degree point with a pitch that will yield flight that does not increase or decrease in altitude. This is called "straight and level flight". In reality, due to the design of aircrafts this may in fact be a few degrees of pitch away from true 0 on the reference plane. Power settings will also effect this angle.

• Yes, the horizon's definition does not change, but the higher one flies, the smaller the angle between the weight vector and the the longitudinal axis, when pointed at the true horizon, becomes due to Earth's curvature. Commented May 10, 2016 at 16:14
• Should yaw be considered in attitude? Going by a "chosen zero plane" a 180 degree turn would be a change in yaw. IMHO yaw is a separate consideration. It is utilized differently than pitch and roll indications and is referenced to relative wind for the purpose of maintaining coordinated flight or performing slips. I suppose you could reference it to something else, but I can't think of why one would want to. Commented May 10, 2016 at 16:18
• I just added an edit, generally yaw is considered differently but in its purest form attitude has reference to all axis in 3 Space. While aircraft attitude is often only looked at from a pitch/roll perspective, flight attitude may extend to other scenarios.
– Dave
Commented May 10, 2016 at 16:20
• I apologize, I didn't initially write the question to be specific to aerodynamic flight. Space flight is different, and I am not an expert on that, but I would imagine that a yaw reference would be used for 3 dimensional navigation in the way that airplanes use a heading indicator. So yeah, it actually would make sense for it to reflect a 180 degree turn as yaw in that scenario. Commented May 10, 2016 at 16:29
• Yaw would come into play potentially in an INS unit (which many large planes have) as well as in a flight data recorder and the like. But you are correct that commonly airplanes do not display it on a traditional attitude indicator. Modern glass cockpits do integrate a slip/skid display into the attitude section of the screen.
– Dave
Commented May 10, 2016 at 16:57

Attitude is rotation of the body frame of reference (its principal axes, whatever it means) relative to a chosen frame of reference.

For aircraft:

• The body frame of reference is the longitudinal, lateral and vertical axes, where the longitudinal-vertical plane is the plane of symmetry and longitudinal axes is chosen to point generally forward, along cabin floor if there is such a thing.

• The chosen outside frame of reference is the local horizontal, which is plane perpendicular to the local weight¹ vector, and in that plane the main axis is chosen either as projection of either local magnetic inductance vector (magnetic heading) or Earth rotational axis (true heading).

Regarding “true horizon”, in the sense of where the you see the ground/sky boundary, that can't be used for defining attitude at all, because it is not a plane. The line connecting you to the “true horizon” ahead and the line connecting you to the “true horizon” behind is not the same line, so it can't be used as axis.

Instead, horizon is defined in terms of horizontal, the plane orthogonal to the weight vector (and tangent to the Geoid, the ‘idealized’ sea level).

To fly level, your velocity vector must point along the local horizontal. In most aircraft it means your pitch is slightly positive. This is because most aircraft are designed to never need to fly at negative pitch² and as the angle of attack for level flight depends on weight and speed, most of the time your pitch will be slightly positive.

¹ Not “gravity”, because it centrifugal force due to Earth rotation is included. Actually, the instruments measure the value including the centrifugal force due to the movement of the aircraft, which might be slightly different from centrifugal force on stationary object. The immediate measurement also includes the inertial force due to acceleration (the forces can't be distinguished), but this is eliminated by averaging, because the average acceleration (over several minutes) is known to be zero or close enough for practical purposes.

² There are some exceptions that do normally fly slightly nose-down, like B-52, which does it because its unusual gear does not allow it to rotate on take-off, or DHC-6 Twin Otter, which apparently does it to provide better view during slow short take-offs and landings.