Without getting into a lot of detail but, there is a number of mistaken assumptions in your posting. First of all, on most ballasted keel boats, the maximum stability is around 90 degees of heel, at which point there is the maximum spread between the vertical center of gravity and the instantanteous center of bouyancy. Depending on the specifics of the design, the deck hits the water somewhere between 45-55 degrees of heel.
Deepening deadrise lowers the vertical center of buoyancy at low heel angles reducing inititial stability, but within normal, second half of the twentieth century, designs has little impact on stability at high angles of heel. At high angles of heel, the boat pretty much floats on its topsides and so the portion of the hull where the deadrise occurs is located is typically out of the water.
Adding buoayancy in the form of beam increases the amount of force required to get the boat to its limit of positive stability, but it also increases the amount of force required to bring the boat back up again once its passes its its limit of positive stability.
When a boat carries its beam towards its ends there is more buoyancy outboard and so it has more form stability and as a result it takes greater force to right than a boat with a identical beam which occurs only at a single point.
(edit shown in Italics) In hindsight, as I thought about yesterday's post, I thought that this matter of the increase in inverted form stability that results from carrying beam towards the end needs more explanation. If we think about the plan form of a 1960's era boat such as the keel/ centerboarder mentioned earlier in this thread, they carried their beam very far towards their ends compared to more modern IMS/IRC derived designs. If you looked at these boats from above, the 1960's era boats are closer in form to a rectangle and IMS/IRC derived modern boats are more triangular in form. So while the more modern design may have a greater beam, it rarely has as much deck area as the same length 1960's era design.
If you think about calculating form stability, (assuming similar amounts of flare in the topsides which is reasonable since both 1960's era and IMS/IRC derived designs have very little flare) in its simpliest form, the force to over turn is proportionate to the deck area times the lever arm. So for the sake of simplifying our example, we can assume that equal length boats of both eras have similar deck areas (which is not really a fair assumption since modern designs of equal length typically have smaller deck areas) and the modern boat has 20% more beam which is pretty typically the case, and by way of simplifying things the 1960's boat is a rectangle and the modern boat is a triangle. The center of the area of the rectangle form would be at a point that is half its width, while the center of area of the triangle would be at a point one third of its width. In effect, in this simple model, the rectanglar form of the 1960's boat would have 20% more form stability than the triangular form of the modern hull form [1.2= (1 divided by 2)/ (1.2 divided by3)]
Of course this is a bit of an over simplification, since 1960's boats are not literally rectangles and modern boats are not triangles, but what it does show is that modern IMS/IRC derived boats, while somewhat beamier than 1960's era boats do not necessarily have greater inverted form stability,and it fact, they often are carefully modeled to have poor inverted form stability inorder to achieve CE open ocean classifications.
The fascination with current crop of plumb bow, moderate beam, ultra low vertical center of gravity, carefully modelled hull forms is substantially better seakeeping, higher stability forces required to achieve any given heel angle, often higher angles of positive stability, lower resistance through the water permitting smaller sail plans, much more comfortable motions than similar length older style boats and of course greater speed.
Feeling enlightened......Gotta go
Last edited by Jeff_H; 12-09-2007 at 12:57 PM.
Reason: Further explanation