Heeled athwart ship stability study for a typical sharpie derivative hull shape
This simple study was done as a result of questions and discussion posted on the Bolger EGroups Mailing List (http://www.egroups.com/list/bolger/info.html) Check it out!
Also, see the valuable and interesting links relating to sailboat design at the end of this page.
The following study and graphic representations (below) examines what the physical attributes are of a flat-bottomed, plumb sided, form stable hull as the boat is heeled through angles progressing from zero through ninety degrees. The resulting forces are stated in the following terms: Righting Moment is measured in foot pounds, the righting force builds (or decreases) as the righting arm lengthens or shortens due to the relative degree of heel**. Force At The Rail is measured in pounds and indicates the amount of weight (force) required pressing down on the rail to heel the boat to a specific degree. OR, conversely the amount of weight on the windward rail required to return the hull heeled (X) degrees back to a zero degree heeling attitude.
In fact, at a little before 45 degrees heel, the righting arm reverses (which is stated in negative numbers), and it's at about this point that the ballast weight and/or heavy bottom begins to come into play to bring the boat back upright.
**CLICK HERE TO GO TO A BRIEF DISCUSSION OF THE THEORY OF HULL STABILITY
Keep in mind that while internal ballast installed and secured in this type of hull can lower the relative center of gravity and thus increase stability, it is NOT intended to increase the stiffness (sail carrying ability) or resistance to heeling. Any resistance to heeling is achieved by the width of the bottom of the hull (called form stability). Internally placed (and well secured) ballast in a sharpie is to lower the center of gravity and to ensure that the hull is self-righting (rescuing) in the case of knockdown or even a full capsize but does not increase stiffness and resistance to heeling as does ballast when located at the end of a long salient keel (forming a very long lever arm) well below the canoe body. Also keep in mind that a long lever (that is, the ballast located deep below the boat doesn't change the center of gravity, or increase the length of the GZ.
Most form stable hulls have lower raw ballast to displacement ratio's than other types of sailboats. Quite often in sharpie derivative boats the ratio is around 25%, where round bottomed boats run about 35-40% (modern racer/cruiser) and slack bilged boats often go as high as 50% (Herreshoff Nereia)
As you can see, from the following diagrams, the optimum angle of heel for this type hull is 15 degrees or slightly less. I find in actual sailing conditions slightly smaller angles (in the 10-14 degree range) keeps the boat on its feet and works well if not better than larger angles. We're talking of sailing to windward, and of course, the shape, type and aspect of sail plan has to be taken into account. However I believe that this hull form should not be pressed beyond fifteen degrees as a general rule. This means that careful management of sail area relative to wind strength is important--probably more so than other with other hulls. It is equally important that the style of rig be easy and fast to manage especially when it comes to reducing sail area.
Also let me call your attention to the stability curve which accompanies each drawing of each angle of heel. Notice that all the curves maintain pretty much the same appearance as should be the case. This indicates symmetry of displacement as the underwater shape changes throughout the various aspects of heel.
Located below this illustration is a brief discussion of a hull's ability to carry sail, and a summary of, and general comments concerning stability. Finally, at the end of this page is a link to another page which contains a comparison study between this hull unballasted and the same hull with about 2,000 Lbs of ballast.
POWER TO CARRY SAIL
Once you know the stability of a sailing design, you can go on to calculate stiffness’’ or ‘‘tenderness.’’ The added factor here is the heeling leverage of the yacht’s sail plan. There are two commonly--used measures of a sailing design’s power to carry sail - the Dellenbauqh Angle and the Wind Pressure Coefficient. However, describing these methods is beyond the scope of this discussion so I'll not go farther at this time.
SUMMARY - SOME GENERAL COMMENTS CONCERNING STABILITY
From the foregoing, we can gather a few general guidelines. The stability of a boat is determined by the length of her righting arm or GZ. This is in turn governed by
a.) The hull shape, which determines the amount of lateral movement of the center of buoyancy and height of the metacenter, and;
b.) The height of the center of gravity. It is generally known that:
a.) Lowering the CG increases the GZ, which increases stability.
b.) Wide beam and hard (firm) bilges increases the lateral movement of the center of buoyancy and raises the metacenter, thus adding to stability.
c.) An excessive amount of GM can have the detrimental effect of making the vessel's rolling motion excessively quick. This is not a problem in the design of smaller craft but should be given consideration in the design of craft with a LWL of over 30 ft.
d.) The GZ decreases rapidly once the decks are awash, thus a high freeboard is one method of maintaining stability at the large angles of heel.
e.) As "free surface" water creates a movement of weight to the low side, negating the assumption of a fixed center of gravity, it is essential to keep the hull free of such water by careful design of hull openings and windows and the installation of adequate scuppers, freeing ports, and pumps. Tanks should be kept narrow in their athwart ship dimension to minimize the "free surface" effect of their contents rushing to the low side.
f.) As a guide, modern 40-50% ballast ratio sailboats will have their CG's at a height slightly above or below the LWL.
g.) Since powerboats generally are unballasted, their CG's will be considerably above the LWL. Halfway between the LWL and the top of the deck at side amidships is a good first guess.
Design Links:
Sailing Design Ratio Calculator (Carl's Sailing Calculator) *****Excellent!