How do I determine roll given before and after vectors for the orientation of a planes face, belly, and wing?

For example my before (t=0 seconds) vectors are

Face = -0.19i - 0.69j + 0.69k
Belly = -0.92i - 0.12j - 0.37k
Wing = -0.34i + 0.71j + 0.62k

and my after vectors (t=0.03 seconds) are

Face = -0.14i - 0.71j + 0.69k
Belly = -0.93i - 0.15j - 0.34k
Wing = -0.34i + 0.69j + 0.64k

[Jan]

The question is not clear. What does "-0.19i - 0.69j + 0.69k" mean? While 1i and 1j are the imaginary units, what is 0.69k? Please edit the question and add mire details.

[Jim Riggs]

It is common to use i,j, and k as unit (basis) vectors along the x, y, and z axes, respectively.

Still, there is not enough description of the problem. A picture is worth a thousand words. In fact, you might find that when you draw the picture, you will answer your question.

Answer 1

[Matt J]

If you download ABSOR you can use it to figure out the rotation matrix corresponding to the change in the plane's orientation,

Before=[-0.92, - 0.12, - 0.37;
        -.19,-.69,+.69;  
        -0.34, + 0.71, + 0.62].';

Before=Before./sqrt(sum(Before.^2));

After=[-0.14, - 0.71, + 0.69;
       -0.34, + 0.69, + 0.64
       -0.93, - 0.15, - 0.34;].';

After=After./sqrt(sum(After.^2));

reg=absor(Before,After,'doTrans',0);

You can then use the attached utility files to convert to yaw-pitch-roll,

ypr=rot2ypr(reg.R);

roll=ypr(3),

[Jim Riggs]

While the method you suggest may give a good answer, it is still not possible to determine if it is the correct answer without a better specification of the problem.

You need to recognize the built-in assumptions which are implicit in the method. There are six permutations of Euler planar rotations that may be used to produce a rotation matrix (or direction cosine matrix), plus, there are two ways to specify the rotation direction (sign of the rotation angle). This means that any direction cosine matrix represents one of twelve possible combinations of Euler planar rotations.

When I see a set of three parameters with i, j, & k components, I interpret them to be the specification of a vector using i, j, and k basis vectors. Using this interpretation, I do not understand what to do with the three Vectors labeled "Face", "Belly", and "Wing".

On the other hand, if you are interpreting the three sets of three values as a nine-element rotation matrix, there is still insufficient information to develop a solution. There are still twelve different ways to interpret the angles, so more information is needed in order to define the "Roll" angle.

How about it Jeffrey?

[Matt J]

I should add, I suppose, that my conversion routine adheres to definitions of yaw-pitch-roll as described here.

Jeffrey, you should indeed check to see that these conventions agree with yours. I've never heard of the "air norm DIN 9300" standard, but the diagram does match what I always understood to be yaw-pitch-roll axes. One other remark - the vector data you have posted have significant errors (the vectors are significantly non-orthogonal). Maybe that's because you deliberately omitted more than 2 decimal points precision in your post, but just be aware that you will not get very accurate results without additional precision.

[Jeffrey Hanson]

I did truncate the values. I'm also learning by doing, please forgive my ignorance.

To give some context, I've got a Tethered Undersea Kite (it looks like a drone with wings) traveling through the water. It's continually performing a figure 8 along the sphere that is the tether length. At the outer edge of the figure 8 the kite needs to perform a roll such that it's belly is still facing the tether origin. It's important to know how much the kite rolls from point to point because that affects the Lift to Drag Ratio (L/D is a Performance Indicator).

I have the means to determine which way the Face, Belly, and Wing are facing at any given point. So if I could determine Yaw-Pitch-Roll angles from that it would be extremely useful.

[Matt J]

Great, then it seems I answered your question? If so, please Accept-click the answer to certify that it addressed your issue.