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Where is the axis for Crab angle measurement located?

Started by vnangli, Wed, 16 Sep 2020 22:59

vnangli

I got this question during one of my landing practice. The plane track is right on the extended centerline, but with a crab angle due to cross wind.

About what Reference point on the airplane is the crab angle measured? Is it the CG or the ILS Glidescope antennae or the centerpoint between the main body landing gears?
747 is not an airplane, it is a symbol of inspiration....

Hardy Heinlin

#1
The crab angle (i.e. wind correction angle WCA) is the difference between heading and track. On your grey PFD compass disk the pointer at 12 o'clock indicates your heading, and the white line on that grey disk indicates your track. When the WCA is zero, the track line is vertical. For the WCA precision within 0.0000001 degrees it doesn't matter if the angle is measured at the nose or at the tail. The aircraft length is much smaller than the planet's circumference. Heading and track are longitudinal angles referring to True North. To get a longitudinal difference of 1° when the aircraft is, say, at the equator, at HDG 270°, the aircraft would have to be 60 nm long. In polar zones it may be shorter, but then your heading and track will be grid angles, not longitudinal angles. So you will never get any singularity trouble at the pole :-)

What you are asking for is probably an offset value in meters or feet. That's a distance from a point, not an angle between two lines. A crab angle is an angle, not a distance.


Edit: Text simplified.

Jeroen Hoppenbrouwers

Otherwise stated ... unless the air frame flexes left and right, any (crab) angle is the same everywhere on the whole aircraft.


Hoppie

vnangli

Quote from: Hardy Heinlin on Wed, 16 Sep 2020 23:11

What you are asking for is probably an offset value in meters or feet. That's a distance from a point, not an angle between two lines. A crab angle is an angle, not a distance.


Edit: Text simplified.

Let me try it this way.

Lets say we place the Coordinate system of X,Y, Z.
X along the longitudanal axis, Y axis being perpendicular to X axis but along the wings and Z axis perpendicular to both X and Y axis.
Rotation about X axis would be Roll, rotation about Y would be Pitch and rotation about Z would be Yaw.

The way I was understanding the Crab angle is the measure between the Longitudanal axis and the track. Now, the way I was visualizing this coordinate system tracking on the extended centerline during landing. Thats when, I got this question. Where is the Coordinate system (I just explained above) located?
747 is not an airplane, it is a symbol of inspiration....

Hardy Heinlin

Quote from: Jeroen Hoppenbrouwers on Wed, 16 Sep 2020 23:46
Otherwise stated ... unless the air frame flexes left and right, any (crab) angle is the same everywhere on the whole aircraft.


Hoppie

We're opening a cup of worms :-)

If I don't stop editing my comment, it will end up in a book ...

It depends on the heading. Special angles are: 000, 090, 180, 270.

Otherwise, if the aircraft is hundreds of miles long, the crab may be different at the tail and the nose.

If the ship is as long as the distance from India to Canada, and the ship's longitudinal angle is 300° in India (tail), it will be circa 360° in Canada (nose).

Hardy Heinlin

#5
Quote from: vnangli on Wed, 16 Sep 2020 23:53
The way I was understanding the Crab angle is the measure between the Longitudanal axis and the track.

In my comment I was using the word "longitudinal" in the context of navigational angles on a planetary sphere. You are using it in the context of roll, pitch, and yaw axes; the roll axis being the longitudinal axis. That's a different subject.

When referring to True North, the HDG is the angle between the aircraft's "fuselage line" (longitudinal axis, if you will) and the earth's longitude that the fuselage is crossing. Every longitude is a line going from the True South Pole to the True North Pole. The earth's longitude at the present position is your reference for your True North HDG. That's why it's called longitudinal heading. Whether you use the present longitude at the nose or that at the tail won't make a big difference on your instruments.

Likewise, as long as the track is constant, there won't be any notable difference between the longitudinal track of the nose and the longitudinal track of the tail. Both travel into the same direction.

Will

If I'm understanding your question correctly, the answer is the center of gravity (CG).

I think you're asking this: if I stick a pin vertically through the aircraft from the ceiling down through the floor and into the ground, such that the aircraft pivots around this pin to create the crab in a crosswind landing, where in the aircraft is this pin located? It's the CG.

But Hardy and the others are right that the actual angle between the heading and the track will be exactly the same at any point from the nose to the tail. Sticking with the pin analogy, if you pin the aircraft to the ground through the CG and measure a 15-degree crab angle there, then if you go to the nose of the aircraft and measure the difference between the heading and the track, the answer is still 15 degrees. And if you walk back to the tail and measure the angle between the heading and the track again, the answer is still 15 degrees.

But if the wind changes direction, the aircraft will pivot around the pin (i.e., the CG) to get a new heading in order to keep the same track.

(Keep in mind that the center of gravity here is Σ(d*w) for a bazillion combinations of distance times weight, and it's opposed by a similar collection of lift vectors, some positive and some negative. But the whole assembly pivots around that pin, which goes through the CG.)
Will /Chicago /USA

vnangli

Quote from: Will on Thu, 17 Sep 2020 02:19
...if I stick a pin vertically through the aircraft from the ceiling down through the floor and into the ground, such that the aircraft pivots around this pin to create the crab in a crosswind landing, where in the aircraft is this pin located? It's the CG.


This is exactly what I was trying to ask....Thank you for the analogy, @Will..
747 is not an airplane, it is a symbol of inspiration....