Metacentric Height

[Paul Jones]

Hi everyone,

I have a question I am thinking about for an experiment I did involving this topic. The questions I am thinking about are:


Does the position of the metacentre depend on the position of centre of gravity?

If yes, does the metacentric height vary with the angle of heel?

***EDIT Explained experiment a little further below.


Regards,
Paul

[Rick Willoughby]

Hi everyone,

I have a question I am thinking about for an experiment I did involving this topic. The questions I am thinking about are:


Does the position of the metacentre depend on the position of centre of gravity?

If yes, does the metacentric height vary with the angle of heel?


Regards,
John
The answer can be yes and no to the first question. If CofG changes directly vertically it will not alter the metacentric height. If the CofG moves laterally it can alter the metacentric height due to heeling, hopeful it increases to stiffen up. Likewise longitudinal shift in CofG will change trim and this can shift the metacentric height.

Rick W

[Ad Hoc]

"..Does the position of the metacentre depend on the position of centre of gravity?.."

No, it is geometry related, from the buoyancy and the waterline.

"...If yes, does the metacentric height vary with the angle of heel..."

Yes, at small angle of heel, it is small enough to ignore. At large angles of heel the loci of the metacentre can be drawn to produce an "M curve"

[Paul Jones]

To put it into context it was from doing this experiment (image below) where the mass slider was moved from the left to the right (-40, -20, 10, 30, 60) and this was done for three different positions of the vertical sliding mass.

What would the answer be to this question (relating to this experiment)?


http://www.perrytecheducational.com/images/F1_14_rgb.jpg

[Rick Willoughby]

Moving the weight laterally will cause the hull to heel and this changes the transverse metacentric height at the new point of equilibrium.

Rick

[Rick Willoughby]

I should add that the positioning of the weight on the rod will not alter the transverse metacentric height when the slider is centralised but once the hull heels, shifting the weight along the rod at any given lateral position will alter the angle of heel so moving the weight in this case will alter the transverse metacentric height.

Rick W

[hbr]

starting from a hull with an ellips form breadth at deck equal 2*b and the depth of the hull equal to a in vertical position no heeling.
in stead of drawing all the different angles of heel, how can the stability curve be calculated at different angles of heel ?
Do you have a suggestion how to approach this in excel for instance ?

[jehardiman]

To put it into context it was from doing this experiment (image below) where the mass slider was moved from the left to the right (-40, -20, 10, 30, 60) and this was done for three different positions of the vertical sliding mass.

What would the answer be to this question (relating to this experiment)?




Do not confuse the metacenter with the point the vessel rolls around or assume the metacenter controls the amount the vessel rolls.

The location of the metacenter (KM) is only a function of the vessels weight and form. The location of the CG (KG) only effects the GM (i.e. GM = KM-KG) not the metacenter. The GM, not the metacenter, is what effects the moment to heel some small angle (i.e. moment = W*GM*sin theta for small theta) and only if the wall sided assumption is correct. Many hulls never conform to the wall sided assumption, and therefore cannot be analyized by evaluation of GM.

See this discussion on GM...http://www.boatdesign.net/forums/boat-building/calculation-gm-8852.html#post60405 (and please ignore the scarcasm in it).

[Ad Hoc]

Paul

Is that just a suspended weight, which has a slide function to allow it to move from one side to another, or is there some kind of buoyant shape under, which is immersed in water which then has the sliding function? It is not clear what the "box" of tricks is.

Also need to use correct terminology too. If the CoG is off-centre, then it will not cause an angle of heel. It will be 'list'. This should not be confused with the angle of 'loll'.

As I stated above the metacentre is a function of the geometry (which give the location of "B") and the waterplane (which gives the location of the intersection of the perpendicular from the new location of B to its previous location of B) to get M.

It has nothing to do with weight or CoG at all.

[Rick Willoughby]

starting from a hull with an ellips form breadth at deck equal 2*b and the depth of the hull equal to a in vertical position no heeling.
in stead of drawing all the different angles of heel, how can the stability curve be calculated at different angles of heel ?
Do you have a suggestion how to approach this in excel for instance ?

You should start your own thread with this question.

I imagine you are talking about a a hull having a constant elliptical section? Maybe a sketch would help.

In Z-Y plane the equation for an ellipse is:
Y = b * [1 - Z^2/a]^0.5

The waterplane can then be describe simply as a sloping line:
Y = hZ + c

h is the slope of the waterplane relative to the hull. c is determined by integrating the area between the waterplane line and the hull so that the area, At, is constant at any given angle of roll. This can be done numerically in Excel.

Once you have the value for c you can determine the intercepts of the waterplane and the hull. This gives the width of the waterplane. Lets call it Ywp

For a constant section hull the metacentric height can be calculated as:
BMT = {Ywp^3}/12/At

Sounds complex but if you set it up in Excel it is easy to do repeat calculations.

Rick W

[jehardiman]

Now before we go too much further with this, it is important to remember that ultimate stability (i.e resistance to capsize) has nothing at all to do with initial stability (i.e the calculation of GM). For those that are interested, do the calculation of GM for a flat decked barge with a roller skate or marble on deck. You will find that the GM is negative and the barge will loll until the skate/marble hits the bulwark. It is a very enlightening exercise.

[Guillermo]

It has nothing to do with weight or CoG at all.
For a given floatation, of course.


The location of the metacenter (KM) is only a function of the vessels weight and form.

This is more precise, but even for a given displacement the longitudinal and/or lateral position of CoG also influence the transversal KM by modifying floatation, don't you agree?.

Cheers.

[Ad Hoc]

"...for a given displacement the longitudinal and/or lateral position of CoG also influence the transversal KM by modifying floatation, don't you agree?..."

CoG has nothing to do with the location or magnitude of KM.

[jehardiman]

Originally Posted by jehardiman
The location of the metacenter (KM) is only a function of the vessels weight and form.

This is more precise, but even for a given displacement the longitudinal and/or lateral position of CoG also influence the transversal KM by modifying floatation, don't you agree?.

Cheers.

"...for a given displacement the longitudinal and/or lateral position of CoG also influence the transversal KM by modifying floatation, don't you agree?..."

CoG has nothing to do with the location or magnitude of KM.

OK guys, Lets be very clear about the assumptions if we want to get into the more snarky aspects of KM.

The original poster wanted to know if GC effected KM, and the actual answer is No as defined in Axiom 1 below.

Axiom 1) For the static equlibrium condition where a body of arbitrary shape is free floating, the CG and CB are in line, and the location of KM is independent on the CG.

Now, we can contrive relative cases where we compare the KMs of a body of fixed shape and weight under various CG locations relative to some body fixed reference axes. However, each of these cases independently degenerate to Axiom 1 above. (For a really neat trick, try the above of a circular cylinder of various weight floating on it's side...;) )

FWIW, the calculation of KM is only of interest to find GM. And GM is only of interest to determine the initial instant stability, not the dynamic stability or the final stability. Whenever the CG is off centerline of a axisymetric free floating body, the body will "list" until CG and CB are in line. KM only effects the roll rate acceleration to reach this list, not the final static position.

[Ad Hoc]

jehardiman

I'm not sure what you mean by "...get into the more snarky aspects of KM..."

Since you appear to be linking two separate technical issues, viz:
1) What and how to determine KM of "a floating body"
2) Stability and its link with roll period

As you noted in your axiom1), based upon the original Q "..Does the position of the metacentre depend on the position of centre of gravity..", no. Which answers 1).

"... Now, we can contrive relative cases where we compare the KMs of a body of fixed shape.." But the Q doesn't say/ask anything about roll period etc

So just wondering why you then deviated into another topic which just confuses many on here who are not naval architects, by going down the "stability" route?

However, it is still not clear to me, what Paul's 'little box of tricks' is doing, as there is no explanation to whether it is just a hanging weight or a floating body with a pendulum etc.

[Rick Willoughby]

... for a given displacement the longitudinal and/or lateral position of CoG also influence the transversal KM by modifying floatation, don't you agree?.

Cheers.

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

[Ad Hoc]

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!

[Guillermo]

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.

[Ad Hoc]

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.

[Rick Willoughby]

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
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

[jehardiman]

jehardiman

I'm not sure what you mean by "...get into the more snarky aspects of KM..."

Since you appear to be linking two separate technical issues, viz:
1) What and how to determine KM of "a floating body"
2) Stability and its link with roll period

As you noted in your axiom1), based upon the original Q "..Does the position of the metacentre depend on the position of centre of gravity..", no. Which answers 1).

"... Now, we can contrive relative cases where we compare the KMs of a body of fixed shape.." But the Q doesn't say/ask anything about roll period etc

So just wondering why you then deviated into another topic which just confuses many on here who are not naval architects, by going down the "stability" route?

However, it is still not clear to me, what Paul's 'little box of tricks' is doing, as there is no explanation to whether it is just a hanging weight or a floating body with a pendulum etc.

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 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.

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

[Rick Willoughby]

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

[Ad Hoc]

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! :) )

[jehardiman]

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

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.

http://cargolaw.com/images/disaster2001.heavymetal.3.GIF

[Ad Hoc]

J.man

Great picture ;)

[MikeJohns]

Loading is fraught with peril.:)

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

[Guillermo]

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...? ...:confused:

[Rick Willoughby]

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...? ...:confused:

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

[Ad Hoc]

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.

[jehardiman]

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

[MikeJohns]

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.............
Edit: I was wrong, ............. Here is the USCG report.

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

Thanks for the report John.
I'm not sure if this one did go to court for the incorrect weight or if it was another case altogether. There was another case when the transformer was dropped to stop the crane barge capsizing when unloading in Africa, It's in a back issue somewhere in my office and I might be confusing the two.

The submergable heavy lift vessels have had a few spectacular catastrophes too.

Cheers

[Guillermo]

So it seems to have been due to incorrect ballasting and not adequately following of the protocols.
On top of what is said at the report, I'm wondering about the comms between deck and engine room, as it seems they walked from one to the other to open/close valves (1459 hours).
I'm also wandering about what an 'stabilizer pontoon' on the port side was (1422 hours).

Cheers. :confused:

[jehardiman]

I'm also wandering about what an 'stabilizer pontoon' on the port side was (1422 hours).

Cheers. :confused:

A stablizer pontoon is a self-deployed ballast float carried by some heavy lift ships used to move weight/bouyancy outboard and to increase the water-plane area. It seems that in this case it is an active system, not the passive ones I'm familiar with. See the one slide (page 5) in this Jumbo Lift Ship presentation: http://www.hydrographicsociety.nl/documents/hydrographicsociety/downloads/JUMBO%20OffshoreNoordhoek.pdf

I know that some stabilizer "floats" or "tanks" fitted to some vessels are basicaly large free flooding tanks with small openings fitted on the extreme beam. When pressed down by roll, they provide short term bouyancy and when pulled up short term ballast.

[Guillermo]

Thanks jehardiman.
Here the capsizing of another Heavy Lift vessel, the GABRIELLA, in 1986.
http://www.atsb.gov.au/publications/investigation_reports/1986/MAIR/pdf/mair15_001.pdf
It explains the working of the stabilizing pontoons (page 8).

Cheers.

[jehardiman]

Yes, this is a necro thread, but another recent loss due to stability and some of the more tricky things about GM and shifting cargo.

MV Riverdance in England.

http://www.maib.gov.uk/cms_resources.cfm?file=/Riverdance_Report.pdf

[Ad Hoc]

I'll have a good read of that, thanks.
What does 'necro' mean..??

[jehardiman]

What does 'necro' mean..??

From the Greek nekros, a dead body or person, used in Internet forums to describe a thread that posting to had died out. Some forums won't let you revive older threads.

[Ad Hoc]

j.am
I'm aware of the definition, from the Greek origin. Just not the American colloquialism...I'm not american and as such don't fully understand all those colloquial terms that are used and abused in American speech :)

[Guillermo]

I think it is quite useful these forums allowing to "resucitate" necro threads, as this allows to gather information (papers, links, opinions etc) about the thread's matter during time.

Cheers.

[Ad Hoc]

The fact we are posting...just shows, it hasn't died......it is dormant! :)