Heeling due to wind

Could anyone here help me calculate this? I'm fresh to this and I don't really understand it yet.
If I got the "idea" right, I'm supposed to calculate the difference in heel angle and then use the wind moment to draw it on the gz curve?

 

Welcome to the forums.

Have you looked up the IMO rules? Straight cookbook from those. Or does your instructor want you to do it from first principles?

 

I've looked at the IMO and there's not information I see regarding using the capsize lever... In the equations I've looked at I'm supposed to have the centroid of the superstructure.. I know these are probably very dumb questions but I'm lost.

 

I'm guessing that the capsize lever is the distance between the centroid of the superstructure and the centroid of the underwater structure.

 

Wouldnt that be really high? It's a passenger ship supposedly.

 

@liyko, I'm afraid you haven't looked hard enough IMO. Open the IMO Stability Code and, in chapter 3.2.2.2, you will find exactly what you are looking for. Of course, without knowing the position of the center of the windage area, you will not be able to do anything.

 

That's probably because the term used in the question, is incorrect and misleading.

When a vessel is stable, the KG (G) is below the metacentric height (M).


Thus when a vessel is heeled, it has a positive righting lever, the GZ.
The GZ being the distance from the horizontal to the heel waterline vertical, shown below.



When the KG (G) is above the location of M, it is a condition of negative stability, also noted above.

It is rare, but some call this condition a capsizing lever (negative stability)
Owing to the fact that the vessel is unstable and thus the vessel shall continue to roll over, unless otherwise prevented from doing so and rest in an equilibrium position - on its side, or inverted.
This is shown here, with its nomenclature:



So, the wording and data in the question is incorrect on many levels.
Having a GZ of 25m is preposterous.

 

Thank you Ad Hoc for that explanation, and thank you all for trying to help me!

What I did so far was use this formula I found in a "ship's stability for mates and masters"


I also found a formula regarding the centroid of the superstructure (most likely not correct) and I got that my PQ is 11.168M, my pressure was 48.58 kgf/m2.
With those put into this equation, my steady wind heeling moment resulted in 1085.08 m/t, this I then divided by my displacement and got a heeling arm of 0.0775m.

I got the same heeling arm if I used this formula from IMO:


So after I got the heeling arm, I drew it on the GZ curve like this and where the wind heeling arm intersected with the curve of static stability, I drew a line down to connect it with degrees and got a result(?) that my ship would lean ~14°.

Am I on the right track or did I do something very wrong?

 

The procedure is correct: obtain the intersection point (the one on the left) of the two curves.
Your ship's initial stability seems a bit low. I don't know what type of hull yours is but perhaps it would be advisable to review the GZ curve, especially at small angles of heel.

 

I think it's not an actual gz curve but more of a mockup.

My instructor wants me to draw and I quote; "the moment of stability of the ship and the moment of the wind must be entered on the diagram
and the moment of the wind, where they collide is an easily determined solution (graphically)"

What does this mean?

 

I think you have correctly done what your instructor asked.
At the point of intersection, the righting arm and the heeling arm are equal, so it is assumed that the wind will not be able to heel the boat any further and, if no other factors intervene, over time equilibrium would be reached at that angle of heel.

 

I've sent him what I've described and the picture aswell, and I got the answer for missing moments. Could it be that he wants me to convert the righting arms in meters to moments and represented on the diagram aswell?

 

It is a somewhat simple question: the heeling moment is equal to the heeling arm multiplied by the ship's displacement.