Metacentric Height

I agree for most cases. If the water plane does not change with roll then the height of the metacentre will not alter. This is true for a cylinder.


In most cases the height of the metacentre alters. If you take the case of a trimaran, for example, where the amas are normally clear of the water and then move the CofG to load one of the amas the metacentre will be much higher.

In the case posed above with the box shaped hull the metacentric height is a function of the induced roll resulting from moving the CofG laterally. Moving the CofG laterally will move the CofB laterally and this alters the second moment of area of the waterplane so the metacentric heigt changes.

Rick W

 

Gessss

Why do people (non-naval architects) consistently miss understand basic terminology and principals.

Metacentric height has nothing to do with CoG. Don't take my word for it....see attached, how one established the location of KM and hence BM.

That's the problem with just pushing buttons on a computer and its program to do all the calculations for you. Doesn't show you how and why, just gives and answer, nowt else!

 

I don't want to be contentious and probably this is rather a bizantine discussion, but I'm with Rick here.
Once again and always talking transverse stability: for a given displacement if moving CoG around alters the shape of the submersed body and the floatation, this alters both KB and BM, thus varying KM. We find this everyday when studying intact transverse stability for the different trims of a vessel.

Cheers.

 

Guillermo

The question is about the metacentre and its relationship with CoG. It says nothing about stability. As i noted previously #15, stability is a different issue. The KM is simply just a function of the floating body and it waterplane.

If you then wish to consider its stability, then of course CoG comes into play; which requires the metacentric height to determine the stability of said floating body. But the original question was trying to link CoG with the metacentre, which one cannot do, since the 2 are unrelated.

 

Guillermo
You are not being contentious. You are spot on. Of course changing trim either for and aft or side to side will usually alter the waterplane. Altering the waterplane alters the metacentric height by definition.

Rick W

 

Paul's little box is a box barge with a vertical rod that can be moved athawartships with a weight that can be moved up and down. The weight is not allowed to pedulate but it allows the CG of the entire body to be moved infinitely about some fixed envelope relative to Cl and BL.

I agree Guillermo, it is a rather esoteric, and probably has more to do with how each of us think about the problem than the actual differences.

However, I think Paul needs to understand that the reason that KM changed was because the underwater shape and waterplane changed, not because the CG changed.

If we have a free floating body of rigid form, fixed weight, and arbitrary shape and we anaylzie it at any arbitrary list referenced to a body coordinate system, there is a unique submerged shape of constant volume and a unique waterplane inertia associated with that volume (there is a single exception to this...lets see if anyone knows what it is). It is the interaction between the unique submerged shape and waterplane inertia that generates a unique metacenter for that list.

I think we can all agree that for a body floating staticly (upright or at any list referenced to a body coordinate system), that the CG and CB are in line and that the metacenter is independent of the vertical location of CG. There are an infinite number of CGs that fall along the CG to BG line, and each is associated with a unique Vertical CG (KG or VCG referenced to the body), Transverse CG (TCG referenced to the body), and GM at that list. But there is only one KM, and that is linked to the list angle, not to the CG.

From my point of view, because there is a infinite number of CG's associated with any unique list angle and therefore unique KM, absolute CG is decoupled from KM.

So in answer to the two questions posed in the original post: No, position of the metacentre does not depend on the position of centre of gravity, but Yes, the metacentric does height vary with the angle of heel

 

John
The notion of list gives the idea that it is something amiss. If you think in terms of trim then the position of CoG can be moved to achieve the preferred mode of operation. A yacht with a canting keel can be trimmed with the mast leaning off vertical in the equilibrium position. Does the yacht have a list or is it trimmed that way.

Likewise I trimmed my yacht bow down in light wind to lift the stern clear of the water. This reduced the wetted surface therby changing the waterplane and BMT. Is this is a list or trim. The boat would certainly be considered as upright in equilibrium but by changing the CofG I changed the BMT.

Rick W

 

Rick

List does not imply there is 'something amiss'. Many designs monohulls especially have slight lists, most not noticable, other than when an inclining expt is performed. But makes no difference to the design nor its ability. Unless of course you are referring to a most noticable list. In which case it would be corrected anyway.

In transverse stability, the change of waterplane, the term 'list' is never used. It is the angle of rotation of the floating body with its associated buoyant wedge of volume that has immersed or emerged, from the previous waterline, see previous post with figures.

In your yacht case, this is trim; longitudinally. Therefore you are now referring to the KML, the longitudinal KM, not the transverse KMT, for "normal" stability reviews. Since the KML is significantly greater than KMT.

jehardiman
(Was one of the 'trick' Qs we had at uni, when doing stbaility! )

 

As Ad Hoc pointed out, your perspective is a little shaded. List, and loll, is something that merchant deal with on a daily basis. They have to load cargo, and make sure that stability is maintained while loading...sometimes that is harder than it looks.

If Paul (the OP) really wants me to go into it, I can go into the more "snarky" aspects of the metacenter and initial stabilty as it concerns final stability. Some thing about it are not obvious and have resulted in some spectacular failures.

 

J.man

Great picture

 

Loading is fraught with peril.

GE has been pursued in court for having the incorrect weight indicated on the transformer.

 

Those images are amazing!
But there's something I do not understand: How is it possible the ship is almost not listing when the transformer is rised from the wagon and then raised over the starboard side of the vessel with the vessel cranes, and then suddenly the vessel capsizes? It should have happened somekind of admonitory listing when taking the load...
If the vessel was using ballasting tanks to counteract the list, as it seems because it capsized port side down, could it have happened the ballast was not quickly enough transferred from the tanks? was it due to an uncontrolled manoeuvre, suddenly shifting the load from starboard to port and there was no time to correct the list with the ballasting water...? ...

 

It looks like a heavy lift vessel so almost certain it is using pumped ballast to maintain trim during the lift. Also it seems the lifting derricks have limited lateral restraint - it would rely on listing to control positioning outboard of the hold. Once they started to slew inboard from such a wide angle a small list away from the dockside would allow the load to swing uncontrolled, through the centreline of the vessel with increasing speed.

Rick W

 

As Mike noted with those pix, the weight stated was incorrect.
Vessel like that shown all have very low GMs. If the mass of the transformer is significantly different from what is expected, when lifting from dock side to vessel it is being raised above the vessels KG, the low GM can become negative very quickly.

 

As I recall, the ship (MV Stellamare) knew the weight, knew it was greater than the combined load of the cranes, but a structural analysis to accept the load was done. The cranes didn't fail. What happened was the ballast was improperly managed (too many slack tanks) and free surface reduction in KM got them, similiar to the MV Cougar Ace and MV Rocknes. Like the marble example, a slack tank can cause an emense reduction in GM.

Edit: I was wrong, the load was within the capacity of the cranes, but they messed up the ballasting, including reduction of KM for fresh water. Here is the USCG report.

http://marinecasualty.com/documents/Stellemare.pdf