# Is the pitch an attitude indicator displays in relation to the ground, or is it in relation to the current aircraft bank?

In the old analog, vacuum powered attitude indicators, does the displayed pitch axis indicate the pitch in relation to the current bank angle, or in relation to the ground (true level)?

To put it another way: if an aircraft was flight in a very steep turn (lets say 70 degrees) would the attitude pitch indication be more affected by rudder inputs or yoke forward/back inputs?

If a stunt plane is flying in knife edge flight with the wings rolled to a bank angle of 90 degrees, does pushing (or releasing) the rudder change the Attitude Indicator pitch indication at all? Or would only pulling or pushing on the yoke change the Attitude Indicators pitch indication?

• Not following the question. Starting with a bank of 70 degrees and a pitch of X... are you asking which of rudder or back pressure would most affect the pitch of the aircraft? Or are you seeking a way in which the instrument indication is affected apart from the attitude of its aircraft?
– Ralph J
Commented Oct 11, 2023 at 16:34
• Prob question could be best answered with a picture of the instrument face in an a/c at 45 or 60 degree bank, with a line drawn showing what two points on the face, the distance between which represents the aircraft's pitch attitude. Do we draw the line straight up and down in the reference frame of the cockpit, or do we draw the line perpendicular to the horizon bar? Commented Oct 11, 2023 at 16:43
• @quietflyer If the former, the value for "pitch" would get larger & larger without bound as the bank angle approaches 90 degrees, and would be undefined at a bank angle of exactly 90 degrees, since the line perpendicular to the floor of the cockpit then doesn't intersect the horizon. Can't see how such a convention could ever possibly be useful; the pitch angle there would change with every roll input.
– Ralph J
Commented Oct 11, 2023 at 18:18
• Also related --aviation.stackexchange.com/a/16538/34686 key sentence -- The rotations are applied in backwards order, first yaw (ψ), then pitch (θ) and finally roll (ϕ). Which implies to me that rolling shouldn't affect the "pitch angle" , but yawing would. So yawing, but not rolling, would affect the displayed pitch attitude-- if the instrument is marked correctly. Not 100% sure about all that but... Commented Oct 11, 2023 at 19:29
• @RalphJ I'm trying to understand what the instrument is telling me at the edges of the envelope of values it can display. I have a pretty good concept of what the control inputs will do to how the plane is flying, and only talk about control inputs as a way to describe how the plane (and thus instrument) is being rotated in space. I could experimentally answer my question w/ a AI out of the plane w/ a vacuum source (spun up while level/still). I would pick it up, rotate it so it showed 90 deg bank with a 0 pitch, and then see which other axis I have to rotate it in to get a pitch indication. Commented Oct 11, 2023 at 19:48

In the old analog, vacuum powered attitude indicators, does the displayed pitch axis indicate the pitch in relation to the current bank angle, or in relation to the ground (true level)?

Yes.

For the illustration given below -

the analogue for the instrument of interest is shown below - Note that pitch is relative to the horizon and measured in the vertical plane aligned with the aircraft center of gravity and tangent to the flight path. Note that $$\alpha_T$$ is greater than the indicated pitch. Follow carefully the elements indicated in these illustrations... "Flight path" is sensed by the pilot along the direction of lift for the path of flight in the banked turn. An actual example in flight for this analogue is shown, below.

...in a steep turn...would the attitude pitch indication be more affected by rudder inputs or yoke forward/back inputs?

Quite clearly, the rudder can change the pitch in a steep bank. The influence of the rudder would be, for instance, to yaw the nose farther above the horizon, or farther below.

If a stunt plane is flying in knife edge flight with the wings rolled to a bank angle of 90 degrees, does pushing (or releasing) the rudder change the Attitude Indicator pitch indication at all?

Yes, if the instrument is working correctly, yawing the aircraft in a 90 deg bank would be indicated by a change in corresponding pitch either above the horizon, or below.

• This answer is in a helpful direction. The drawing of the airplane and a new geometric plane helps. Diagram is a bit busy so I'm having a hard time perceiving it in 3d space. But my core question boils down to, I think, does the distance labeled "arcsin(sin a sub t cos o)" on the instrument face measure a rotation in the geometric plane drawn/shown, or only in the external vertical geometric plane? Commented Oct 11, 2023 at 21:05
• @Azendale an additional illustration was added that may help. All of the elements in the illustrations are shown in the last one, the actual in-flight example. Note that pitch is a seemingly indirect measurement of the instrument which is, however, actually measured directly. I know, this seems complicated... but the instrument solves this presenting the analogue of the measurement as a direct, indicated reading for pitch in actual degrees. Note the alignments... The noted angles are what the instrument is measuring, namely pitch $arcsin(sin\alpha_T cos\phi)$, & angle of bank $\phi$. Commented Oct 11, 2023 at 21:33
• Ok, so, if I understand right: If I go into a 90 degree bank steep turn, no matter how hard I pull the yoke/stick ("up" elevator), I will get no change in pitch. But if I push the rudder to the stop, causing yaw (defined relative to the aircraft) I will cause a change in AI indicated pitch. Correct? Commented Oct 11, 2023 at 22:32
• @Azendale Yes, this is a paradox. $\alpha_T$ is pitch relative to the flight path. In a 90 deg. banked turn, there is no pitch relative to the horizon, only pitch relative to the flight path. Nevertheless, apparently so, in a 90 deg. bank rudder induced yaw bringing the nose above the horizon, or below, would be indicated by corresponding pitch above the horizon, or below. Embry-Riddle University has an excellent pitch-attitude indicator simulation link where you can simulate exactly this situation. Commented Oct 12, 2023 at 4:10
• (It seems these spherical geometry problems may be solved in more than one way-- building the equations upon the assumption of a fully coordinated turn is one valid way but not the only way-- other ways are independent of knowing anything about the flight path or the state of coordination/uncoordination-- came to light here aviation.stackexchange.com/q/97987/34686 -- see esp footnote 3 of my answer-- anyway third diagram is improved now that "pitch" is clearly labelled, thanks -- ) Commented Oct 12, 2023 at 12:15