initial stability of a ship

Absolutely true, you're absolutely right, jehardiman, I have NEVER talked about fixed axes. It would have been a great blunder. Thank you for your clarification of what, in my opinion, was not necessary to clarify.
By the way, what do you mean : "a vessel moves in 3 space"?. Are there 2 space or 7 space? Sorry for the joke. Thanks.

 

are you kidding me?
do you really think that, i do not know, that a vessel is moving in all 3 dimensions and that the axis around which it revolves changes all the time?

thank you!

edit:
you must have absolutely misread or misunderstood my post...

 

For the benefit of the OP, to completely describe the motion of a hull you have three dimensions of translation, and three axis of rotation (assuming the shape of the hull does not change). so you have six degrees of freedom, and require six differential equations to fully describe the motion. That is why it is called "metacenter", it is the instantaneous axis of rotation at that moment in time.

 

I found the following explanation on Wikipedia. No further comments but, for the benefit of the OP, he will do well to contrast the different opinions before giving some as correct.

 

No, you are confusing the OP. The "metacenter", as found by the method I described in the linked post, determines the point in which the buoyancy appears to rotate, not the ship. The ship rotates about its CG.

And since no one has actually answered the original question...

Vertical of transverse metacenter is the location, on the coordinate system vertical axis (usually referenced to the keel or CG) where the transverse metacenter (I.e. a metacenter claculated using the transverse waterplane inertia) is located, in this case 5.920 m.

Transverse metacentric radius is the distance above the center of buoyancy that the metacenter is located. It is the radius of the arc that the buoyancy appears to move on if the hull was rotated about the waterplane centerline, in this case 5.796 m.

Note that the metacentric height - the metacentric radius = 0.124 m. This implies the the center of buoyancy is 0.124 m above the axis reference.

Longitudinal transverse metacenter and Longitudinal metacentric radius are the same as above except using the longitudinal waterplane inertia. Again note that longitudinal transverse metacenter - longitudinal metacentric radius = 0.123 m which, allowing for rounding, is consistant in the location of the center of buoyancy.

 

Humbly I must say that, in my opinion, that's not right.

 

Why is the point about which a ship rotates relevant to metrics of initial stability? Are you talking about the actual ship rotating, or about how a diagram is drawn?

 

When you calculate the heeling of the boat, or trim, you must do so assuming that the ship rotates around a point. If the choice of this point is incorrect, heel or trim obtained, or the center of buoyancy will not be correct.
Consider a ship heeled 20 degrees. The attached figure shows the differences that occur in the estimated flotation of the vessel according the selected point of rotation.
Although I've simplified a lot and therefore drawings are totally incorrect they serve to give an idea of ​​the errors that can occur if you choose the wrong rotation point.

 

So you are talking about the need to use the heeled waterline which corresponds to the correct displacement when calculating the heeled center of buoyancy, etc.

 

That's correct. That's what I think right.

 

Transverse and longitudinal metacentres do have specific meanings, and appear quite early in formal ship stability studies. I received these over 50 years ago. Go and look at some formal texts if you want more. I haven't looked through Google links. PRINCIPLES OF NAVAL ARCHITECTURE (published SNAME) is just one such source.

Jehardamin (a few posts ago) has a lot of the answer. Anything appearing here is only going to be brief. However, I don't see "metacentric radius" in current practice, and I deal with a lot of stability particulars.

For small angles of heel (say to perhaps 5 degrees), the buoyancy vertical force acts through a point on the vessel transverse section centreline. This point is the transverse metacentre. A parallel situation applies for a vessel at small pitch/trim angles, for longitudinal metacentre.

The position of the metacentre above the centre of buoyancy (m, ft) is determined by dividing the inertia of the waterplane (m^4, ft^4) by the volume of displacement (m^3, ft^3). It is thus a function of the hull shape and its immersion only. It comes out quite readily from computer hull design packages.

For convenience of subsequent calculation, the transverse metacentre is usually defined as height above vessel primary height datum; conventionally the keel point K.

Metacentric stability is quite significant for surface vessels for small angles of heel, and looms large in stability assessment and compliance with standards. It is part of the rationale for a vessel having positive stability even though its centre of gravity is above its centre of buoyancy. It is also a key element in determining the position of a vessel's vertical centre of gravity by the inclining experiment.

A submerged submarine has no waterplane, and thus no metacentric stability. It gains both longitudinal and transverse stability by having its centre of gravity below its centre of buoyancy (in dived condition). Hence the extensive use of ballast keels.

 

This is correct not only for small angles of heel but for any angle of heel. What happens is that for very small angles of heel, say less than 0.5 degrees, the false metacentre (which is what we call metacentre) coincides almost with the actual metacentre.

 

I'd be interested to hear what you fellows think of this 'presentation'

Form Stability vs. Ballast and Stabilizers

 

Brian

This looks a sound presentation, with a lot of factors of significance. One it didn't touch on was what I see as the two main roles of "stability" for powered vessels.

The first, and usually most prominent, is to generate resistance to (and we hope immunity from) capsize, swamping and other such undesirable activities. The commercial vessel stability criteria I use frequently are essentially geared to this.

The second is the enhancement of seakeeping, persons comfort and the like. One important factor in the "presentation" is the avoidance of synchronous rolling. This is very much a matter of relating vessel performance characteristics (roll period is the big one here) to the environments to which the vessel is exposed. Related to this is the damping of roll - bilge keels and the likes. The use of devices such as flume tanks relates to this area.

One of significance here is reduction of roll acceleration; usually as a trade off against roll amplitude. Here the designer is faced with trying to reduce the initial stability (GM, etc) without prejudicing the risk of capsize.

There is rarely scope for adjusting roll inertia to any great extent.

I've left out the major rationale for "stability" for sailing vessels - sail carrying power; conversion of wind forces into propulsive forces.

 

Actually, a submerged submarine does have a metacentric radius, but no positive metacentritic stability. The BM is calculated for the free surface of the tanks (i.e. the free surface correction, it will be negative, a waterplane removal) and is added (subtracted actually) from the BG. (See NSTM Ch 096).

Which is a point to make... I could just just of easily said the tank free surface was a moving weight that raised the KG rather than lowered the KB. Different numbers but the same GZ. TANSL, you seem to miss this..

TANSL, I'm pretty sure that you have missed the difference between initial stability (i.e. why GM has to be positive) and final stability (i.e. where CB and CG are co-linear and the body stable with positive or negative GM). You really needs to work through the moving/suspended weight and free surface problems. You need to understand why a ball bearing on the deck of a barge results in a negative GM of several hundered feet, and the barge will roll until the ball bearing hits the gunwale but doesn't capsize. Or why 3 solid cubes, identical except in density and all buoyant, float at different aspects (face up or corner up).