Re: [PSUBS-MAILIST] Center of gravity Vs. Center of Bouyancy

["Captain Nemo" <vulcania@interpac.net>]

----- Original Message -----
From: "Captain Nemo" <vulcania@interpac.net>
To: <personal_submersibles@psubs.org>
Sent: Saturday, August 11, 2001 3:33 PM
Subject: Re: [PSUBS-MAILIST] Center of gravity Vs. Center of Bouyancy


> Basically, the idea behind SDM is:  if the design is bottom-heavy,
> top-buoyant, and bilaterally symmetrical enough to assure positive dynamic
> stability about the roll axis, what remains to be determined is the
location
> of the Longitudinal Hydrostatic Center of Gravity (pitch axis) when the
boat
> is submerged in a state of equilibrium, immobile, and at neutral buoyancy.
> Doing this involves: calculating the Longitudinal Center of Weight (LCW) ;
> calculating the  Longitudinal Center of Buoyancy (LCB); and averaging  the
> two variables to find Longitudinal Hydrostatic Center of Gravity (LHCG).


In case I've confused anyone:

A vehicle capable of maneuvering about three axes (airplane, submarine) will
PITCH about the LATERAL AXIS; ROLL about the LONGITUDINAL AXIS, and YAW
about the VERTICAL AXIS.

The variable intersection of the pitch axis forward or aft ALONG
longitudinal axis is the location of the Longitudinal component of the
Hydrostatic Center of Gravity, or LHC/G.

Pitch is bow up / down movement AROUND the  lateral axis, but LHC/G is the
location of that lateral axis ALONG the longitudinal axis, which is a factor
of variable weight / buoyancy forces occurring ALONG (fore / aft) the
longitudinal axis of the vessel.

I could confuse you even more by tossing in weight / buoyancy variables
ALONG the vertical axis which will effect roll AROUND the longitudinal axis;
and even more so by adding in variables ALONG the lateral axis that will
effect roll AROUND the longitudinal axis, but I don't for two reasons:

1. A submarine can be designed to operate more like a dirigible than an
airplane, and maintain positive dynamic stability in an upright attitude.
By exaggerating variables ALONG the vertical axis (designing the boat
sufficiently top buoyant and bottom heavy); and by balancing  variables
ALONG the lateral axis (bilateral symmetry); we can provide the sub with an
automatic self-righting tendency (positive dynamic stability) in roll AROUND
the longitudinal axis.

2. If I didn't do it this way, it wouldn't be "simplified".

Now, Doug (one of our double-dolphin qualified brethren)  pointed out that,
in U.S.NAVY submarine school, notice is made that buoyancy changes occurring
ALONG the vertical axis (up and down) when ballast is varied can effect the
roll of his ship AROUND the longitudinal axis; and wondered if this wasn't a
factor with little subs because we don't use wraparound "saddle" tanks.
Well, my little NAUTILUS uses four saddle tanks; but maintains roll
stability throughout the full range of ballast variations because my boats
VCB and VCW are sufficiently opposed ALONG the vertical axis to nullify
ballast-change-induced adverse rolling tendencies

Don't get me wrong: a change DOES occur in both the big boat and the little
boat; but whether or not that change alters stability depends on the degree
of difference between VCB and VCW.  Apparently, that variable is
comparatively greater in my little sub than it is in Doug's bigger one (mine
is comparatively more top buoyant and bottom heavy than yours is) , so I'm
not as susceptible to the rolling tendencies you describe.

The above is understandable: yours is a sleek and maneuverable craft, rigged
for war and designed for maneuverability and performance; while mine is a
functional version of a fictional design, shaped like a fat shark with a
belly full of tanks and batteries, one big-honkin keel hanging underneath, a
shallow, buoyant compartment topside, and no appreciable sail.   One is for
fighting and one is for fun, as they say.  They are both good at what they
do, but different missions allow for different design considerations.

And of course, there are little subs without saddle tanks; that keep their
ballast tanks high and/or low, so that variations in buoyancy have even less
effect on roll stability.

Ultimately, it all has to do with the balance of buoyancy and weight; and
SDM is a simplified means of dealing with pitch variables, geared to needs
of the average guy trying to design a basic sub in his garage or backyard.

VBR,

Pat