1

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?

Azendale
  • 1,313
  • 10
  • 18
  • 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 Oct 11 '23 at 16:34
  • 1
    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? – quiet flyer Oct 11 '23 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 Oct 11 '23 at 18:18
  • Also related --https://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... – quiet flyer Oct 11 '23 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. – Azendale Oct 11 '23 at 19:48
  • @Azendale -- that would be the yaw axis. As per my comment immediately above. From a 90 deg bank with 0 pitch, you could yaw the nose up to a vertical climb if you wanted: 90 degrees pitch. Unless (as your last comment suggests) you are interested in flight attitudes where the instrument capabilities are limited in some way? Not sure what you mean by "edges of the envelope", why should the envelope have any edges at all? Unless you are talking about "gimbal lock", "tumbling", etc? – quiet flyer Oct 11 '23 at 21:16
  • @Azendale The answer provided by me was edited with an additional illustration. An added comment, also provided, may give additional clarity. Think about what you are seeing from within the airplane, and the instrument's measurement frame of reference outside of the airplane. This video by Ryan Anderson may be helpful. link There is another video about the mechanics of the attitude indicator on Ryan Anderson's youtube site. Hopefully this has been helpful... – Thomas Perry Oct 11 '23 at 21:57
  • @quietflyer The edges of the envelope comment was a realization that when I start talking about a 90 degree bank, I might hit a limit on some mechanical device, resulting in tumbling or gimbal lock. But a 90 degree bank is helpful in explaining the question because it makes the axes in reference to the aircraft that used to align to axes in reference to the ground become completely orthogonal -- other than the one we rotate 90 degrees around. – Azendale Oct 11 '23 at 22:40
  • @Azendale -- clearly implicit in the above comments, is the idea that "degrees of rotation about the aircraft's pitch axis" and "degrees of change in the aircraft's pitch "angle" aka pitch "attitude"" are often very different quantities. This ASA question is somewhat relevant: https://aviation.stackexchange.com/q/97987/34686. Note that my own answer (to my own question) turned it into a navigational problem! – quiet flyer Oct 11 '23 at 23:15
  • @Azendale Are we good, here? A link to the attitude instrument simulator at Embry-Riddle University is provided in my comment addressing your additional question (for clarification), below. An interesting question. Thanks for asking! – Thomas Perry Oct 12 '23 at 04:32
  • @ThomasPerry Yes, it has helped. Especially the simulator. I now trust the AI more, knowing what it is saying in a very steep turn. I've done some trig but was having a hard time following what the trig in them was implying -- would you be upset if I accept your answer and then (if I can either find or draw better ones) edited it to try to make it show rather than use trig to explain? I will say I'm also realizing I was having trouble with the definition of "pitch". – Azendale Oct 12 '23 at 14:33
  • @ThomasPerry the last picture of a steep turn helped, though I think I would have understood faster if the triangle was labeled "indicated pitch" and we left out a sub T and added an arc near the bank angle label. – Azendale Oct 12 '23 at 14:37

1 Answers1

1

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 -

enter image description here

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.

enter image description here

enter image description here

...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.

Thomas Perry
  • 1,255
  • 3
  • 9
  • 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? – Azendale Oct 11 '23 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 $\phi$. – Thomas Perry Oct 11 '23 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? – Azendale Oct 11 '23 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. – Thomas Perry Oct 12 '23 at 04:10
  • (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 https://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 -- ) – quiet flyer Oct 12 '23 at 12:15
  • (Observation pertains to TP's comment immed. above and also to understanding the situation of a stunt plane flying in a steady-state constant-altitude non-coordinated knife-edge (90-deg bank) turn with nose held above horizon with top rudder -- ) – quiet flyer Oct 12 '23 at 12:36