RE: [PSUBS-MAILIST] Intact Surface Stability

["Alec Smyth" <Asmyth@changepoint.com>]

Cliff,

OK, I just revisited my old books. It was not entirely satisfactory as you will see below.  

Here's the nutshell version:

When you heel a vessel, its weight will always act vertically down through the center of gravity. However the buoyant force acts through the center of buoyancy, which moves to one side, so that the pair of forces creates a righting moment. In your case its a little more complex because you have the battery pods, so there will be a marked increase in righting moment when a pod starts to rise out of the water. 

The first step in the calculation would be to calculate the righting moment for different angles of heel. That is going to be tedious, but at least its simple.  I'm assuming you have no free liquid surfaces in tanks, and no suspended objects. If you do, these have very significant (and detrimental) effects.

Second, chart the righting moments you just calculated as a function of the angle of heel.

Now for the dynamic aspect. If you were to gradually incline your sub, the work done to reach any given angle of heel would be the integral of the righting moment from zero to the final angle. In other words, the area under the curve, from the origin to a vertical line through the corresponding x value. The value of this area is called the "Dynamic Stability" for the angle of heel in question. So,

Third, calculate the dynamic stability for each angle of heel, for example by approximating the area below the curve with trapezoids. Chart a second curve with the dynamic stability values for each angle of heel. 

You would simply enter this curve horizontally with the inclining moment of a dynamic force, to find the approximate angle of maximum heel that would result. Unfortunately, however, at this final and crucial step I had a disappointment. Every example I find in my old books refers to some rather elementary discrete force, such as a gust of wind hitting the sails of a sailboat, the recoil from a battleship firing a broadside, and so on.  In the literature I have on hand I cannot find any correlation between a given wave size or sea state and what dynamic inclining moment might be result from it - I think there might just be too many variables involved as this would depend on the nature of the vessel, the course, etc in addition to the waves themselves.  I do have formulas for the total energy contained in a wave (incredibly high numbers), but that clearly is not the whole story as only some small undefined portion of it would go into trying to heel your sub. 

Probably the best reference I have for this is Fundamentals of Construction and Stability of Naval Ships, by Thomas Gillmer. If you like, I can scan and email you a couple of chapters.

Going back to your original question, I suppose what we need is input from someone who has actually satisfied the certification requirement to see what calculations they presented.

cheers,

Alec

-----Original Message-----
From:	Cliff Redus [mailto:dr_redus@devtex.net]
Sent:	Tue 10/1/2002 4:13 PM
To:	personal_submersibles@psubs.org
Cc:	
Subject:	Re: [PSUBS-MAILIST] Intact Surface Stability

Alec,


> Cliff,
>
> I've got just such texts at home and will see if I can provide you with
something in the evening. The nutshell version is there >are two factors
involved in keeping water out of the hatch; freeboard and roll stability.

Great.  Also can you site the reference text if you find the source you are
looking for.
>
> For a surface vessel, the calculation of roll stability involves something
called the "metacentric height".  When a surface >vessel rolls, it submerges
a greater portion of its hull on the side its rolling to, and this produces
a righting moment. Therefore >surface vessels can have their CB below their
CG yet still be stable. In the case of a submarine, however, we're generally
>speaking of cylindrical hulls. As a cylindrical hull does not vary its
lateral displacement upon rolling, it produces no righting >moment.
Therefore for a cylindrical submarine the calculation will be reduced to a
simple matter of how far below the CB >you can get your CG.

I have a spreadsheet like everyone else that calculates CB and CG.  The CB
calculation also takes into account lost buoyancy associated with a portion
of the sail that is out of the water when surfaced. For my boat I have two
1-atm battery pods located just below the CG.  As such, in a significant
roll on the surface, one of the pods would begin to surface thus producing
a righting moment.

The problem I see with CG-CB and metacentric height approach your talking
about is that it is a static calculation. The table in ABS rules describing
sea state is talking wave height, periods and wind velocity.  This leads me
to think a dynamic stability analysis is called for.
>
> Which brings up something interesting. I know your design has a "flying"
intent, so presumably you are trying to keep CG >and CB very close in the
submerged condition. This means you'd need to do something to improve
surface stability per >ABS. I can't remember where you were putting your
ballast tanks. If they're on the sides, then they'd help.

My goal was to stay just within ABS rules on minimum distance between the CG
and CB in order not to make moment required to roll to high but yet have the
required static stability.

>And are you still thinking of articulating the battery pods to drop the CG?

I am using a +/- 4 inch longitudinal shift of the batteries in the pod to
shift my CG longitudinally.  This give me a +/- 18 deg pitch submerged. I am
not shifting the batteries in heave direction.
>
> I haven't done one of those stability calculations since college, and I
haven't done them at all for Solo since it hasn't a hatch. But I've still
got my books, so more later.

Thanks

Cliff

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