# Is there a name for change in attitude with respect to time?

I'm in the process of writing a flight-dynamics software program, but I'm not sure what to call the derivatives of the aircraft attitude. If it was in one dimension, they would be the "angular velocity" and "angular acceleration" respectively.

In aviation, is there a special name for these vectors?

• I love a programmer who's serious about naming his symbols. Thank you :) Commented Apr 14, 2016 at 17:04
• @Steve you're welcome. IMHO it's the most important part of the whole business. Commented Apr 14, 2016 at 17:07
• In general 3d physics contexts, "angular velocity" is typically understood to be a 3-vector. I think what you have in mind would better be understood as "magnitude of angular velocity". (In one dimension, I'm not sure how to define rotation ;) but I think I understand what you mean.) Commented Apr 15, 2016 at 5:12
• @Praxeolitic Angular speed? Commented Apr 15, 2016 at 6:53
• @immibis That phrasing would feel unusual to me but the intent would be obvious. I don't know if I'm in the minority there. Commented Apr 15, 2016 at 8:11

The components of attitude vector are called:

• yaw (or heading) is the angle of longitudinal (x) axis in horizontal plane,
• pitch is angle of longitudinal (x) axis from the horizontal and
• roll is angle of lateral (y) axis from the intersection of the yz (orthogonal to longitudinal axis) plane with horizontal.

And their derivatives are usually yaw-rate, pitch-rate and roll-rate. Second derivative names probably vary.

Regarding coordinate system, the first axis, called x, is always longitudinal and positive direction is forward. The second axis, called y, is usually lateral one, but positive direction is right in some systems and left in others. And z completes a right-handed coordinate system (so your vector products work the usual way), so z down if y points right.

Edit: I thought u,v,w is sometimes used as alias for the axis, but actually they are usually rather used for the velocity vector components.

• so extrapolating from this, attitude-rate would be a plausible name for a vector consisting of the changes in yaw, pitch, and roll? Commented Apr 14, 2016 at 11:58
• @NicolasHolthaus, yes, you could call it that. Commented Apr 14, 2016 at 11:59
• I've never heard it called that, but it would make sense. The closest I've seen is "Rate of attitude change" or "Rate of change of attitude" - or specific to each eg "Yaw rate", "Rate of change of pitch", "Roll rate" etc. They tend not to be combined into "attitude rate", but I don't see why they couldn't be - semantically it makes sense. Commented Apr 14, 2016 at 12:48
• "Pitch rate", "roll rate" and "yaw rate" all seem logical for their derivatives. Commented Oct 16, 2019 at 22:16
• @StephenS -- for a different viewpoint see aviation.stackexchange.com/a/98197/34686 Commented Mar 18, 2023 at 16:40

I know this is an old question, but I wanted to throw quaternions (and quaternion rates) and other non-Euler angle attitude (and rate) representations into the mix.

While yaw, pitch, and roll are frequently used for aircraft, quaternions are also used for aircraft and inertial guidance systems. Other attitude representations include principle rotation vectors, direction cosine matrices, classical Rodriguez parameters, and modified Rodriguez parameters. There are also a lot of other Euler angle representations available. All have their pros and cons including existence and type of singularities in the equations.

Hanspeter Schaub (my current graduate advisor) has a coursera course with a lot more information if you're interested.

https://www.coursera.org/lecture/spacecraft-dynamics-kinematics/4-euler-parameter-quaternion-definition-tOeps

I believe you are looking for yaw, pitch and roll:

• Pitching for the nose moving up and down.

• Yawing for the nose moving side to side.

• Rolling for the wings rocking back and forth.

• I'm familiar with the components of attitude, which are pitch, roll, and yaw. What I was looking for was what to call the change in pitch/roll/yaw with respect to time, when all three quantities are grouped into a single vector. Commented Apr 14, 2016 at 12:04

It's important to recognize that

1. while "roll rate" is the rate of rotation about the roll axis which is the rate of change of the bank angle

2. the "pitch rate" is the rate of rotation about the pitch axis which is often not the rate of change of the pitch attitude

and

1. the "yaw rate" is the rate of rotation about the yaw axis which is often not the rate of change of the yaw attitude, i.e. the rate of change of the heading.

If this is unclear, consider what happens if the aircraft rotates about the pitch or yaw axes at bank angles near 90 degrees.

Therefore the terms you are looking for appear to be the "rate of change of the pitch attitude", "rate of change of the heading", and "roll rate", for the rate of change of the pitch, yaw, and roll attitudes respectively.

The "rate of change of the heading" could sometimes be called the "turn rate" as well, but strictly speaking this would usually only be the case if the sideslip angle (and the angle-of-attack) were constant, not changing.2 The "turn rate" is the rate of change of the direction of the horizontal component of the flight path.

Footnotes:

1. Link to an ASE answer using the phrase "yaw angle" to mean heading: What are the exact meanings of roll, pitch and yaw?

2. Or in cases where the sideslip angle and the angle-of-attack are changing in a synchronized way such that the rate of change of heading is (at least momentarily) exactly equal to the rate of change of the horizontal component of the flight path.