**Preface: **When it comes to discussing stability in yachts and other vessels, nearly impenetrable jargon is often resorted to — terms like “metacentric height”, “GM”, “inclining”, “roll period”. And when the explanation is over, you can see by the glaze in the eyes of the reader or listener that the product of the explanation does not include insight or understanding. Therefore, I propose here to discuss vessel stability in a way that I found effective years ago when I was teaching boatbuilding at Humber College of Applied Arts and Technology in Toronto years ago.

A floating vessel is considered “stable” if its natural tendency is to remain in an upright position, or return to an upright position after being heeled by an external force, whether wind, or sea or something else.

Hydrostatic (buoyant) stability is the result of two interacting forces,* gravity* and *buoyancy*. Gravity pulls a vessel down into the water, while buoyancy works to push it up out of the water.

In a heeled vessel that displays positive stability (the tendency to return to an upright position if left to its own devices), these two forces are located at a distance from one another, and they form a force-couple that works to return the vessel to a position of upright equilibrium.

Gravitational force is related to a vessel’s total mass, which by mathematical averaging, can be considered concentrated at a single point known as the vessel’s center of gravity (CG). This point is located in three-dimensional (Cartesian) space by longitudinal, transverse and vertical coordinates. When considering a hull’s transverse stability, we are concerned primarily with the vertical coordinate of the center of gravity, commonly designated VCG.

Buoyancy is generated by the pressure of the water surrounding the submerged portion of a vessel’s hull. Put crudely, the water displaced by the submerged volume of the hull stubbornly attempts to reoccupy the space from which it has been displaced and, thereby, applies an upward force to the hull. The sum total of this buoyant force can be considered to be concentrated at the geometric center of the vessel’s submerged volume, and is known as the center of buoyancy (CB).

Again, this point is located in three-dimensional space by three coordinates: longitudinal, transverse and vertical. When considering transverse stability, the most important of these is the transverse coordinate, commonly designated as TCB.

It’s important to understand that, barring mishaps like tanks rupturing or major weights tearing loose the vessel heels, its CG remains fixed.

However, while submerged volume remains constant when a vessel is heeled, the three-dimensional *shape* of that submerged volume does not. Instead, as the vessel heels over, the three-dimensional shape of that submerged volume changes, and the three-dimensional coordinates of the geometrical center of submerged volume shift. In particular, in a stabil vessel, the CB moves outward from the vessel’s centerline toward the downward or heeled side.

As a result, a force-couple develops between the downward gravitational force centered at CG, and the upward buoyant force centered at the CB. This force couple works to return the vessel to an upright position of stable equilibrium.

* Figure 1* of the top image illustrates how the CG and CB are aligned, cancelling out one another when a vessel is in upright equilibrium.

*shows how, as the vessel heels, the position of the CG remains fixed but the changing shape of submerged volume results in a shift of the CB outward toward the heeled side. As long as the relative positions of the CG (which does not shift) and the CB (which does shift) remain such that the force couple formed between them works to right a given vessel, that vessel is within her*

**Figure 2**

**range of positive stability.**However, as seen in * Figure 3* of the image above, if external forces continue to heel the vessel further, there comes a point at which …

the relative positions of CG and CB reverse, with the result that the force-couple formed works not to right the vessel, but to capsize her.

The point at which a vessel passes beyond her maximum range of positive stability is usually delineated as a maximum angle of heel, in degrees from upright. Thus, if a vessel reaches her maximum range of positive stability at, say, a 70-degree angle of heel, when she heels past 70 degrees, she will lose any inherent tendency to return to an upright position and, instead, will turn turtle.

Adding ballast low down in a vessel, along her keel, lowers her CG and thereby increases the force of her righting couple, hence her range of positive stability. Which is why so many who seek to evaluate the “offshore or bluewater ability” of a sailing yacht almost lways seek to determine the ratio of ballast that she carries relative to her total weight (or displacement).

However, instead of adding ballast weight to her keel, it would actually be better to take weight out of her mast and rig.

The reason for this is that the VCG of a vessel’s mast and rig is generally located at a distance from her VCG that is *five or more times greater* that the distance between the VCG of her ballast keel and her overall VCG. Which means that for every poiund you might take out of her mast and rig, you would have to add five or more pounds to her ballast keel to get the same effect on stability. Which, BTW, tells you something important about the effectiveness of an epoxy carbon fiber mast in improving a sailing yacht’s stability and performance. But that, my friends is a discussion for another time.

— *Phil Friedman*

Copyright © 2023 by Phil Friedman — All Rights Reserved

## Why Yachts Don't Just Turn Upside Down

Pretty much the first write up of the Titan incident I've seen that is not full of unqualified assumptions and uninformed opinion. Well done on a good article!

Phil, to your point about "fixing" objects to CF structures, I do recall when working with CF masts for some sail vessels having to pay particular attention to how fittings were fastened. Example, we had designed a radar mount for these masts that used compression rings to fix them to the mast, so no holes. Great article, and thanks for bringing science [back] to the table.