What can you tell from the numbers?
(I warn all that this is a very long answer to a fairly complicated set of questions)
First of all, I agree with Jack, you need to do a lot more reading. With all due respect comments like the one that you made about seeing "Volvo Ocean racers upsidedown with the crew sitting on the overturned hull waiting for their rescuers" is just plain wrong and suggests very superficial understanding of modern distant racing boats. In the world of offshore monohull distance racing there are two main branches, one that includes boats like the ''Volvo 60''s'' and the other which are based on the ''Open Classes''.
The Volvo based boats tend to be moderately narrow with fine bows and comparatively balanced hulls. They are designed to be good boats on all points of sail and have proven to be quite fast and surprisingly easy to handle. You have never seen a picture of one upside down with the crew waiting to be rescued. That has never happened.
What you may have seen are Open Class boats inverted. Open Class boats go for a very extreme beam and huge sail plans. They are designed to be single handed rather than crewed and they are optimized for reaching and running which is generally what the do most of the way around the world. They tend to be lighter than the Volvo boats, faster on a reach, but the lack the kind of ballast stability that the Volvo boats have. With thier extreme beam the earlier boats were capable of remaining inverted for long periods of time. The newer boats are actually designed to have a self righting ability.
All of that aside, and to try to answer your questions, When you talk about the design of a boat for offshore use there are a lot of desirable features that cumulatively make up a good offshore design. In most cases, moderation is critical as the extremes tend to produce boats that have serious faults.
To talk about the specifics of stability and comfort, both are not just a question of ballast/displacement ratio, or beam to length ratio but a whole range of other factors (such as overall drag, weight and bouyancy distribution) as well.
In a general sense, the core factors that control stability relate to weight distribution and buoyancy distribution, both when the boat is standing essentially upright (Initial stability) and when it is heeled at extreme angles (ultimate stability).
In all cases, a low VCG (vertical center of gravity) is a good thing. There is no such thing as too low a vertical center of gravity for either motion comfort or stability. A low VCG is achieved in a lot of ways such as a high ballast to weight ratio, high density ballast (cast lead) placed low in the water (deep draft and a bulb keel for example), Light weight aloft (light rig, topsides and deck structure, and moderately low freeboard and deck houses), and in a cruising boat storage that occurs low in the boat. So from a VCG standpoint and therefore stability standpoint a high ballast ratio is a good thing.
But ballast ratio alone tells you one small piece of the puzzle. As a boat''s draft becomes shallower, the ballast ratio has to increase to offset the shorter lever arm. As a ballast becomes lower in density (iron, or lead in concrete) it takes up more volume and so ends up being higher in the boat or stretched out longitudinally or both. Modern boats generate enormous stability relative to their ballast to weight ratios, overall drag, and displacement by moving a large percentage of their ballast into a deeply placed bulb at the bottom of their keel.
Then there is the issue of beam. This is a harder topic to explain verbally. Like so many aspects of yacht design, beam is only a one part of the equation that affects motion, and performance. Like weight wide beam is often singled out as having a particularly large affect on sailing performance. While there are broad generalities that can be assumed about the affects of beam on the behavior of a boat, the realities of the affect of beam on any specific design can vary very widely from the assumed generality.
In general, all other things being equal, a boat with a narrow waterline beam will have less initial stability and a motion marked by softer acceleration and de-acceleration. It will be easier to drive through the water meaning that it should have less drag in high winds and low. Narrow boats tend to have an easier time going to windward especially in a chop. Narrow hulls tend to have better directional stability (helping the boat to hold its course better) but all other things being equal having a larger turning circle. They also tend not to develop as much weather helm from heeling because their heeled waterlines are more symmetrical than those of a beamier boat.
Beamier boats tend to have quicker motions, more wetted surface and therefore more drag. They tend to be slowed by wave action. The have more stability when inverted. They have greater initial stability (stability at small angles of heel) but a smaller angle of ultimate stability (the angle at which the stability becomes negative and the boat would rather invert than come up). For normal coastal conditions they require less ballast for a given stability. If coupled with lightweight, they tend to be faster down wind in a moderate to heavy breeze because are more likely to be able to surf or plane. They tend to point upwind better in moderate conditions (a combination of greater stability and more foil length for a given draft). They also tend develop as more weather helm and are more prone to wiping out due to heeling because their heeled waterlines are less symmetrical than those of a narrower boat and wide beam tends to “jack” the rudder and keel out of the water.
Now those were the broad generalities about beam but as I said before boat to boat there are big variations between the normally expected impact of beam and the actual affect of beam. One major reason that there is such a variation is that we tend to talk about the beam of a boat as a single measurement taken at the widest point at the deck. In reality, the actual affects of wide or narrow beam on the performance and comfort of a boat can be altered by a lot of factors. These would include items such as waterline beam, the distribution of beam fore and aft at the waterline and immediately above, the cross-sectional shape of the hull, weight and weight distribution and the amount of free board and height of deck structures.
To really understand the affects of beam you need to understand the affects of form vs. ballast stability. There are three ways that boats develop stability; form (also called stiffness or initial stability), ballast, and dynamic. Of the three, dynamic has the least relevance to displacement boats as they rarely have enough speed to create a useful amount of dynamic stability.
As the name implies, form stability derives from the shape of the hull of the boat. A shallower and wider hull generates more stability than a deeper narrower hull. Visualize a piece of wood lying in the water. On the flat it has a lot of form stability. On edge it has next to none. This is because stability in any floating object comes from the distance between the center of gravity (the balance point for all of the weight in the boat including those things that are part of the boat and those things that can be moved around) and the center of bouyancy (the single point that is the center of all of the volumes under water). In a wider, shallower boat (talking about the part of the boat that is in the water) as the boat heels, the center of bouyancy moves more quickly toward the low side for small increases in heel angle.
Form stability has several problems. First of all at large angles of heel, approaching 90 degrees form stability drops off dramatically. This is the point where it can be needed most. Second form stability tends to give the boat a quicker motion as the boat quickly builds stability and the boat snaps from one hard bilge to another. This is less comfortable for the crew in rough conditions and can be more tiring. Lastly, in the extreme conditions of a blue water passage, a boat that depends on large amounts of form stability also tends to be more stable in an inverted position.
Ballast stability has mostly positives associated with it. All other things being equal, the deeper and heavier the ballast the more stability a boat will have. Ballast that is heavier and deeper also gives the boat a slower, more comfortable motion. Of course like most things in yacht design, there are some tradeoffs in this area as well. If the ballast occurs at the end of a deep keel, the boat cannot get into as shallow water. As you start to shorten the keel length you substantially give up performance for the same stability because you either end up with a low aspect ratio foil or you end up with a big bulb or wings also increasing drag. No mater what the ads say, nothing performs like a deep fin keel in all conditions. They do loose some efficiency in heavy seas but not as much as the long keel proponents like to hypothesize that they loose. Of course deep fins have their own compromises but that is not the point of this discussion.
There was a lot of discussion of the physics of stability. Ignoring dynamic stability for the moment, the stability of a boat simply a product of the weight of the boat times the horizontal distance from the boat’s center of bouyancy and the boat’s center of gravity. To define the terms the center of gravity is the one point (fore and aft, athwartship and vertically) that is the center of all of the weight on the boat. The center of buoyancy is the single point that is the center of all of the weight of the water displaced by the hull.
When the boat is sitting still and not subjected to outside wind or current forces, the center of gravity occurs directly above or below the center of bouyancy. But as the boat heels, the center of buoyancy moves toward lower heeled over side. Discounting for the moment weight being shifted on a boat (such as crew crossing the deck or fluids in a tank seeking the low side of the tank), the center of gravity does not move relative to the hull of the boat as the center of bouyancy does but it does move relative to its previous position. Depending on the shape of the hull and topsides, the hull either “jacks up” or “rolls out” (typically boast with high form stability, and flared topsides) meaning the center of gravity rises, or “sets in” or “rolls down” (typically boast with slab sides, tumblehome and Vee’d or wineglass hull sections) meaning the hull moves lower into the water and the center of gravity lowers at the boat heels.
The center of gravity also rotates about the instantaneous axis of rotation. (I say instantaneous because this axis does not remain fixed but shifts as the boat rolls due to the change in shape of the hull as it heels.) If the center of gravity is above this axis of rotation (Lightly or un-ballasted boats, old IOR boats, and some steel boats and some heavy cruisers with heavy rigs, interiors, topsides and decks and low ballast ratios), it will rotate to leeward to leeward the boat heels reducing the potential righting moment of the boat. On boats with the center of gravity below this axis of rotation (first generation IMS race boats, boats based on IMS type hulls and traditional heavily ballasted deep draft cruisers) the center of gravity shifts away from the center of buoyancy increasing the center of gravity aspect of stability. The reason that a deeper or heavier keel helps stability is that it simply lowers the center of gravity of the boat, which results in a larger separation between the center of buoyancy and the center of gravity for any angle of heel.
Of course moving weight to one windward, moves the center of gravity to windward, and so helps spread the distance between the center of gravity and center of buoyancy, which increases stability. So much so that even on a boat as large as a Volvo 60 (nee Whitbread 60) the crew moves every piece of gear and every crew member (who is not doing a task to leeward) to the windward side of the boat and use hinged stanchions so that the crew can lean out further.
So lets go back and look at the exceptions to the rules above. Normally, beamy boats are assumed to have a quick motion. That is because for a given displacement they are assumed to have a lot more form stability. If you visualize to rectangles of equal area one nearly square and one much wider and shallower obviously the flat rectangle will have more surface area and will rock more quickly from chine to chine. BUT, in the newer wider designs, careful modeling has allowed wider boats with less form stability and more symmetrical heeled waterlines. If you visualize a boat that had a cross-section that looked like a section of a cylinder as it heeled it would not develop as much form stability and so would have a slower motion and the waterline shape would always remain the same shape. Through computer modeling, the portion of the new beamier boats that are in the water act more like the cylinder model and therefore often develop less form stability as they heel than their beam would suggest and therefore have a more comfortable motion. The center of bouyancy still shifts relative to the center of gravity as they heel and with their moderately wider beam relative to the depth of the canoe body (hull in the water without appendages) they are still more effective at increasing the distance between the center of gravity and the center of buoyancy and therefore increasing stability.
Another exception to the generalities about the affects comes from the difference between waterline beam and the beam at the deck, as well as, the distribution of beam fore and aft at the waterline and immediately above the water line. As I said above, we almost always look at beam as the number published in the literature about the boat. That beam has absolutely nothing to do with the behavior of a boat in most conditions because the waterline beam can be substantially different than the beam on deck. Because of that a comparatively beamy boat at the deck level can actually have a narrow waterline and behave like a narrower boat in terms of motion and sailing performance. This is often the case with IOR era boats and Open class boats.
The shape of the topsides affects how quickly a boat becomes beamy as it heels so a narrow beam boat with highly buoyant topsides can behave like a substantially beamier boat as it heels, rolling out quickly developing form stability and a quick snappy motion. Another factor, which is totally ignored, is the distribution of beam along the waterline. If you visualize two boats with the same displacement, waterline length, general cross sectional shape, and waterline beam, but one has a diamond shaped water line plane and the other is a simple rectangle, the boat with the rectangular shape would have more form stability than the boat with the diamond shaped water plane. The rectangle would tend to have a snappier motion as well. Because of that phenomenon a narrow boat that carries its waterline beam to its ends would tend to have more form stability than a beamier boat with more diamond shaped or triangular shaped waterlines. Modern hull forms tend to resemble the diamond model more than the rectangular model and so can have a wider waterline maximum beam than its more traditional models, which tend to push the buoyancy more toward the ends of the boat.
We touched on the affects of the cross-sectional shape of the hull. Basically flat rectangular sections give a lot of initial form stability but with the negative affect of promoting quicker motion. Boats with cylindrical, and deeper Vee’d sections have less form stability and softer accelerations than the flat box model. A beamier boat with cylindrical and deeper Vee’d may actually have a more comfortable motion than a hard chine narrower boat. (That is the principle behind Island Packets and IMS type boats alike)
The weight of a boat comes into play here as well. For a given weight, cross section shape and waterline beam there will be a certain depth of the canoe body. The deeper the canoe body, the lower the form stability. With more weight comes a deeper canoe body and a slower motion for the waterline beam. We also discussed the impact of weight distribution above but in general the lower the vertical center of gravity, the more stability. As a result a light narrow boat can have a lot of stability even if the center of gravity is very low (modern race boats for example) and wide boats can lack stability (some lightly ballasted IOR type boats or shoal draft traditional cruisers for example).
Lastly there is a tendency to think of beamy boats as having great stability in the inverted position. Today manufacturer’s (Hunter and Island Packet for example) are getting around that issue by increasing the height of the boat’s freeboard and deck structures. This increases the angle of the limit of positive stability and makes the boat more unstable in the inverted position by raising the center of gravity higher above the inverted center of buoyancy. Of course high freeboard brings with it a whole range of negatives, such as raising the vertical center of gravity and greater windage, that are outside the scope of this already too long discussion.
There are a few other factors at play here as well. Research suggests that it only takes a breaking wave equal to twice the beam of boat to roll a boat over. In theory this makes a narrow boat more prone to being rolled. In reality there is also the problem that a beamy boat is more likely to dip a piece of its deck into the water and “trip” which somewhat offsets the argument about wave height to beam ratios. A good thing about a very narrow boat is that it less likely to be stable upside down.
These of course are only a piece of the puzzle. Drag comes into play as well. A boat that comparatively has a lot of weight for its sailing length or which has a lot of keel area (long or full length keels) need to carry more sail area. This can become a real problem when slugging it out in heavy conditions. A boat with lower drag can disburse some of the force of the wind by accelerating where as a higher drag boat can only heel. Again at the far extremes of lightweight, a boat will have less inertia and so will be more prone to heave at a higher rate.
In the end the best solution is moderation. Boats like the Saga are too narrow to develop enough initial stability. Boats that are too beamy like Island Packets and the like, also give up a lot for their beam.
I hope this answers your question.
Respectfully
Jeff