What is the precise definition of yaw?

[FizicistsRool]

Precise definition of "yaw"

I'm googled "yaw" for the afternoon and there is a detail that I'm not finding. *One* of my understanding of yaw from my readings is that it is the angle between two /vertical/ planes, one containing the velocity of the moving object and the other containing "longitudinal" axis of the moving object i.e. the front-to-tail axis of the fuselage of an aircraft.

This is my own cobbled together idea of what yaw could *possibly* mean. Nowhere is yaw defined exactly in these terms. Instead, yaw is explained in terms of rotation around the vertical axis, where it sometimes seems that vertical axis refers to the "longitudinal" axis, and somtimes it seems to refer the gravity vector. For now, I assumed the latter.

Even so, there is the question of precisely how to measure the angle between the velocity vector and the direction in which the moving object is facing. The possibilities that come to mind are:

1. Just measure the angle between the two.

2. Both vectors projected onto a completely horizontal plane

3. Both vectors projected onto a plane containing (1) the velocity vector and (2) the intersection of the horizontal plane with the plane that is perpedicular to the velocity vector.

4. Both vectors projected onto a plane containing (1) the "longitudinal" vector and (2) the intersection of the horizontal plane with the plane that is perpedicular to the "longitudinal" vector.

5. Both vectors are projected onto the plane containing (1) the "longitudinal" axis and (2) the wing-tip-to-wing-tip axis.

Thanks for any clarification

 

[SteamKing]

How about this link:

http://www.grc.nasa.gov/WWW/K-12/airplane/yaw.html

It's got pitchers and an illustrative animation.

 

[FizicistsRool]

I did run across that...it doesn't really say, but it looks like the yaw axis is also perpendicular to the longitudinal access of the plane. This would mean it is completely unrelated to the direction of gravity (which contradicts previous material I've read elsewhere). Is that correct?

 

[SteamKing]

For rigid body motion, there are 6 degrees of freedom: 3 in translation and 3 in rotation.

Imagine a body like an airplane. Let's assume that the x-axis runs along the center of the fuselage. The y-axis would run perpendicular to the x-axis from wing tip to wing tip.
The z-axis is perpendicular to the x-y plane.

The 3 translational degrees of freedom are as follows
(direction of motion as indicated):

x: Surge
y: Sway
z: Heave

The rotational degrees of freedom (and the axis about which motion takes place) are:

x: Roll
y: Pitch
z: Yaw

 

[HallsofIvy]

Normally, yes, "yaw" is rotation about a vertical axis. A more general definition is SteamKing's: given an arbitrary set of three mutually perpedicular axes, which we arbitrarily call "x", "y", and "z", think of a ship or airplane aligned along the x-axis with its beam (or wings for an airplane) in the direction of the y-axis. Then "roll" is rotation about the x-axis, "pitch" is rotation about the y-axis, and "yaw" is rotation about the z-axis.

 

[FizicistsRool]

For rigid body motion, there are 6 degrees of freedom: 3 in translation and 3 in rotation.

Imagine a body like an airplane. Let's assume that the x-axis runs along the center of the fuselage. The y-axis would run perpendicular to the x-axis from wing tip to wing tip.
The z-axis is perpendicular to the x-y plane.

The 3 translational degrees of freedom are as follows
(direction of motion as indicated):

x: Surge
y: Sway
z: Heave

The rotational degrees of freedom (and the axis about which motion takes place) are:

x: Roll
y: Pitch
z: Yaw

OK, it sure seems to me like the direction of gravity is completely removed from the definition. For airborne or space things, the z-axis by no means has to be vertical (if the definition of vertical is tethered to the direction of gravity).

 

[FizicistsRool]

Normally, yes, "yaw" is rotation about a vertical axis. A more general definition is SteamKing's: given an arbitrary set of three mutually perpedicular axes, which we arbitrarily call "x", "y", and "z", think of a ship or airplane aligned along the x-axis with its beam (or wings for an airplane) in the direction of the y-axis. Then "roll" is rotation about the x-axis, "pitch" is rotation about the y-axis, and "yaw" is rotation about the z-axis.

I think that the source of my confusion is the word "vertical". Many airborne and space assets can at times be arbitrarily oriented, so vertical by no means has to be defined by the direction of gravity. I take that to be the distinction between the definition above that incorporates the concept of vertical versus the more general definition that only relies on the axes defined by an airplane. Also, for assets without wings (cylindrical shaped), the x-axis falls out of the picture.

 

[viscousflow]

I think that the source of my confusion is the word "vertical". Many airborne and space assets can at times be arbitrarily oriented, so vertical by no means has to be defined by the direction of gravity. I take that to be the distinction between the definition above that incorporates the concept of vertical versus the more general definition that only relies on the axes defined by an airplane. Also, for assets without wings (cylindrical shaped), the x-axis falls out of the picture.

its all arbitrary, however, these things are defined by convention.