```From: gherbert@crl3.crl.com (George Herbert)
Newsgroups: sci.military.naval
Subject: Re: Metacentric Height
Date: 22 Jan 2000 18:52:52 -0800

William D. Allen Sr. <ballensr@home.com> wrote:
>Help...
>My daughter is reading The Perfect Storm by Sebastain Junger. He uses the
>term metacentric height and she wants to know what it is. I don't remember
>the definition.
>Can anyone help with clear terminology?

Certainly.  Quick introduction to ship stability, without the numbers...

There are two ways for something floating to be stable.  One is if
the center of gravity (of all weights in the object) is below the
center of bouyancy (center of the displaced water volume).
In real surface vessels, which extend above the water a lot,
this is not really practical.

The other way is for the hull shape and height of the center of
gravity to be designed in such a way that if it heels a bit to
starboard, that the distance from centerline that the center
of bouyancy moves is greater than the distance from centerline
that the center of gravity moves.  That will produce a force
pushing the ship back towards level, called restoring moment.

For ships with reasonably vertical sides (up to 30 to 40 degrees off
vertical, i.e. nearly every actual ship current and past), within a wide
range of angles of heel, if you tilt the ship then the center of bouyancy
moves to the side an amount depending on the angle, which can be described
as if the center of bouyancy were rotating around an imaginary point
up above the waterline.  This point is called the metacenter.

Metacentric height (GM) is the height from the center of gravity
to the metacenter.  If the metacentric height is positive then
the center of bouyancy does rotate further than the center of
gravity does when the ship heels over, and it's stable and will
return to level (unless pushed over very far or hard).  If the
metacentric height is zero the ship is stable in any orientation
or heel angle, and if it's negative then it's unstable and will
roll until it becomes positive again (or sinks).

Ships with very long metacentric heights are "snappy"; they are very
resistant to rolling over, but are also very uncomfortable to ride in
because they want to snap upright very quickly if they heel over at all.
Ships with very short metacentric heights take a very long time to
roll from side to side, and roll further over given the impact of
a particular wave or wind.  They are more vulnerable to capsizing.

If you take a ship or boat and add more weight up high on the vessel,
then the center of gravity moves up in the vessel's geometry.
As displacement increases due to that added weight the height
of the metacenter over the keel will go up a bit too, but not as fast.
So more weight up high (either added equipment or structure up high,
or water on the deck, or cargo, or whatever else) makes the ship have
less metacentric height, take longer to roll, etc.  Increases its
vulnerability to capsizing.

I hope this explanation makes sense to your daughter, without having
offended Professor Webster too much for not having used the formulas 8-)

-george william herbert
gherbert@crl.com

```

```From: gherbert@crl3.crl.com (George Herbert)
Newsgroups: sci.military.naval
Subject: Re: Metacentric Height-repair, and Query re Submarines
Date: 23 Jan 2000 14:01:06 -0800

B F Lake <bflake@coastnet.com> wrote:
>In previous post I wrote:
>//replace fuel or cargo to maintain sufficient stability as G moves up with
>fuel used and the lesser draft from that reduces the waterplane area and
>moves up B and lowers M which can shrink GM too much.//
>	Of course, B moves down!
>	An example is given in the text of a typical cargo vessel of 10,000tons
>during a voyage, her Cof G might rise as much as 6 " while M might fall by
>2" making a loss of 8" of metacentric height.  If you had 18" to start
>with, this could mean trouble.
>	Also to compare with George's post, where he has G moving with a roll and
>I do not, this is to say wrt the ship while George means wrt to Earth's
>vertical although he said wrt the centreline (think he meant wrt where the
>centreline was when vertical).  G can move with a roll if there is water
>trapped on the deck  or from partially filled tanks (free surface effect)
>or if cargo shifts.

My copy of Principles of Naval Architecture is somewhere in the back
bedroom right now, but as I recall the usual way this all is calculated
is to use a coordinate system based on the ship's keel at maximum depth
and the ships centerline at even keel.

>	BTW , I would still like to know what happens to M in the submerging
>submarine.  [...]

As it immerses, the waterplane area goes to zero and M ceases to have
its surface ship meaning.  Rather, in strict technical terms, the centroid
of the immersed volume becomes fixed once the submarine is immersed so
in technical terms the metacenter merges with the center of bouyancy.
Subs have to have the center of gravity below the center of bouyancy
for this reason.

-george william herbert
gherbert@crl.com
```