# Vector z-axis definition confusion

Up to DeploymentI am quite confused by the definitions of the xyz coordinate system for Vectors.

(1) The diagram in the Vector manual (attached as a .png file) shows positive Z going INTO the transducer head.

(2) A diagram on the forum (http://www.nortek-es.com/en/knowledge-center/forum/deployment/985047278/854613373/N2008-137-Rev-Vector-Cable-Probe-Orientation.PDF) shows positive Z going OUT of the head.

(3) A posting on the Forum by Atle Lohrmann (http://www.nortekusa.com/en/knowledge-center/forum/velocimeters/675713976?b_start=0) says "the XYZ coordinate systems are not arbitrary but determined by the question "What does the XYZ system have to look like if the compass/tilt sensor transform is to be correct?""

(1) and (2) contradict each other, while (3) implies that the x, y and z directions are changeable, and might be different for the same instrument in different circumstances.

So what I thought was a simple question that ought to have a simple answer may in fact be more complicated than I thought. Still, I will try:

**Does the z-direction on my Vector go INTO the transducer head, or OUT of the transducer head?**

The Vector in question has a head ID of 4906. It does not have a fixed stem--rather the head is on the end of a flexible cable. And by the way, the instrument is currently deployed, so I can't run any bucket tests on it.

I would appreciate an answer soon, preferably before all the US employees take their 4th of July holiday.

**Does the z-direction on my Vector go INTO the transducer head, or OUT of the transducer head?**

When selecting "XYZ" as the coordinate system, the positive Z axis points into the central transducer. The positive X axis is in the direction of the marked receiver arm (or the X-arrow). The Y axis is then defined by the right hand rule. This never changes, but note it is for "XYZ" coordinates only.

When selecting ENU operation, things are slightly more confusing. For ENU coordinates, because of how pitch and roll are defined the Y and Z axes change sign when the orientation is "UP" so the same math can be used in the transforms (this is in one of Atle's comments in the thread you link to).

The drawing you linked above shows how to align a cabled probe with the canister when the compass/tilt sensor is installed *horizontally*. The horizontal part is important there.

The standard Vector (cabled or rigid stem) will have the compass/tile sensor installed for a vertical pressure canister orientation. In this case, with a cabled head, most users will orient the head relative to the canister correctly (i.e. with a cabled head and a vertical case they will match the orientation of the rigid head relative to the canister).

So, for the linked drawing, to ensure the transformations are done correctly, the cabled probe needs to be aligned with the pressure canister in the manner described. If the entire system were rotated 180º around the long axis of the pressure canister, the signs of the Y and Z axes would change and you would find "XYZ when coordinate system is ENU" is the same as "XYZ when coordinate system is XYZ".

Please let me know if that makes sense. I'll be around the rest of today and can respond if needed.

P.J.

and sorry I haven't worked through the full math. I'm trying to finish up revisions on a manuscript and keep getting lost in structure functions.

Thanks for the prompt reply, P.J., and my apologies for the urgent tone--I need to make serious progress on this problem this week, and I had visions of all the US staff taking Thursday and Friday off and not getting back to me until after the long weekend.

I think I understand what is going on now, but I'd like to confirm with you. Please let me know if there is an error in anything I say here: The diagram with the cabled probe is relevant for recording in XYZ mode; it is NOT relevant for our case (we record in beam coordinates and convert to XYZ in Matlab). I take my beam coordinate velocities and perform the coordinate transformation with the transformation matrix T (as extracted from the System data in an "a5 04" data line, with no sign changes to flip the y and z axes):

T = T/4096;

xyz = T*beam

Vx = xyz(:,1);

Vy = xyz(:,2);

Vz = xyz(:,3);

I end up with velocities in the x, y and z directions.

Now here is the important part: the positive direction of Vz calculated this way is ALWAYS *into* the sensor head, regardless of how the sensor head or pressure case is oriented in space. Is this correct?

Hi Kevin,

Yes, a lot of us are taking Friday off. I have no definite plans as of yet though so I may just go and work to take advantage of the air conditioning.

Regarding everything you posted, the only thing I can take issue with is the statement "The diagram with the cabled probe is relevant for recording in XYZ mode." It's actually not relevant for recording in XYZ mode ever. The only time it applies is for recording in ENU to make sure the compass and tilt sensors are interpreted correctly.

Your method is extremely simple. The transformation matrix retrieved either from the Head configuration structure or the *.hdr file after data export converts from BEAM to instrument XYZ. Instrument XYZ is always defined the same when "XYZ" is chosen as the coordinate system; it only changes when ENU is chosen.

So, your method of recording in beam then converting to XYZ using the transformation matrix is correct, and Vz is always into the sensor head in this case.

P.J.

A note for anyway coming across this thread later, the scaling in line 1 of Kevin's code T = T/4096 is needed because the transformation matrix is read from the binary data structure in his case. It is already scaled as reported in the *.hdr file.

Thanks for the very clear answer, PJ.

I'm actually disappointed in a way, however, because I have an AquadoppHR Profiler co-located with the Vector, and tidal analysis of the currents from the two instruments results in dominant current directions that are almost exactly 180 degrees different. A reversal of the Vector z-direction would have fixed the problem, so now I remain puzzled.

The coordinate system I'm using for the AquadoppHR is illustrated in the attached diagram. I took it from documentation for a Nortek current meter (i.e., not an HR Profiler), but I've been assuming the same axes definitions would hold for an AquadoppHR, as the heads look identical to me. Can you tell me if the xyz directions for the AquadoppHR are as illustrated in this diagram? Again, I'm recording in beam coordinates and converting to XYZ with xyz = T*beam.

Hi Kevin,

The diagram you attached matches how the XYZ coordinate system is defined for the Aquadopp head.

Is there a chance the Vector was rotated so Beam 1 points into the flow instead of with the flow. I.e., the HR Profiler is correct, but the Vector X and Y need to be rotated 180º?

Do the compasses agree? This will give you relative alignment between the two systems. If one shows a heading 180º rotated from the other, that would explain the difference in XYZ results.

P.J.

Hi PJ,

The situation is actually quite complicated. We realized at the last moment that we weren't getting reasonable tilt and roll from the Vector. We assumed that we had mounted the pressure case in an incorrect orientation, but we were pressed for time, so we deployed it as-is, thinking we could record in beam and convert to ENU later, using the pitch, roll and heading from two ADCPs mounted on the same frame. This is the whole reason we are needing to write our own custom routines to handle the data from these instruments.

The attached photo shows the Vector and the Aquadopp as they are mounted on the frame. I've been thinking of the end of the frame with the Nortek instruments as the "front" of the frame.

For the Vector, then, positive Z is pointing "aft", with -y pointing to "starboard" and +x pointing up.

For the AquadoppHR, positive x is pointing "forward", with +y pointing to "starboard" and +z pointing down.

So the answer to your question "do the compasses agree?" is a resounding "YES", because we are using the same compass value for both instruments to convert from XYZ to ENU.

Kevin

Hi PJ,

I thought I'd recap our email exchange here so that anyone looking for the same information will be able to see it, too.

You noticed that the beam-to-xyz transformation matrix for our cabled-head Vector had signs like this:

[ + - - ] [ 0 - + ] [ - - - ]

while you would have expected this:

[ + - - ] [ 0 + - ] [ + + + ]

Generally, Vectors have positive Z pointing *into *the transducer head, positive X pointing out along the marked probe, and positive Y determined by the right-hand rule, but you have concluded that our Vector is non-standard, with positive Z pointing *out *of the transducer head, positive X pointing out along the marked probe, and positive Y determined by the right-hand rule. The directions of positive Z and positive Y are thus reversed for non-standard Vectors.

You say that this is expected to be the case for cabled-head Vectors with horizontal tilt sensors, but that the only sure way of determining the correct coordinate definition to use is to look at the signs of the beam-to-xyz transformation matrix to see if it conforms to the "standard" or non-standard patterns shown above.

Thanks for all your helpwith this.

Cheers,

Kevin

A quick clarification: PJ tells me that in an ideal case, the element of a transformation matrix at row 2, column 1, will be zero. In practice it will not be zero, but should still be a very small number, either positive or negative. In the sign patterns above, then, the zero at (2,1) will probably be a '+' or a '-', but apart from that, the pattern should conform to either the "standard" or "non-standard" pattern.

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