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 »  Home  »  Sailing  »  Estimating Stability
Estimating Stability
By John Holtrop | Published  01/16/2006 | Sailing | Unrated
Page 5

        With our template in place, we can begin to see what type of boat our designers favor for offshore cruising. Clearly these are not high performance racers. They are large, heavy boats with high static and dynamic stability, which will produce an easy ride with minimal crew fatigue. The calculated template terms are discussed in the following section.

 

DISP / LENGTH RATIO = disp/2240/(.01*lwl)^3

Probably the most used and best understood evaluation factor. Low numbers (resulting from lightweight and long waterlines) are associated with high performance. The general trend for new boats is towards lower ratios that favor higher performance. The trade off is that a light boat will have more violent motion in storms. This requires constant attention to steering and sail trim, resulting in crew fatigue. The ratio decreases with boat length, since heavy boats need less ballast and will be lighter than smaller boats with the same stability. Our template shows acceptable values between 265 and 337.

 

SAIL AREA / DISP RATIO = sail area/(disp/64)^.666

This is basically a ratio of power to weight, calculated using a 100% jib. Most monohull designs range between 16 and 18. Our template numbers are a conservative 15.9 to 16.5. The ratio is independent of boat length

 

HULL SPEED = 1.34*lwl^.5 ,knots

Generally regarded as the highest practical velocity for a displacement boat assuming a reasonable power input (2-3 hp per ton). As a boat's speed increases, the wave it creates becomes longer, creating a trough that moves aft. At hull speed, the trough will be as long as the waterline length, creating a "hole" that the boat just fits. An enormous amount of power (50-100 hp / ton) is required to "climb out" of this hole and transition to higher speeds (planing). The template value is 7.6 knots.

 

VELOCITY RATIO = 1.88*lwl^.5*sail area^.333/disp^.25 / (hull speed)

The numerator of the equation calculates potential maximum speed, using an empirical relationship. Boats with a generous sailplan and light displacement will have a velocity ratio greater than 1. Under powered or extra heavy boats will be less than 1. The template value of 1.07 predicts good performance under sail.

 

BALLAST / DISP RATIO = ball/disp

One indicator of stability, but the center of gravity, center of buoyancy Vs heel angle, and total weight are needed for a complete picture. Values range from a low of .25 to a maximum of .5. The template value of .4 indicates more emphasis on gravity controlled stability rather than form stability.

 

LOA / BEAM RATIO = loa/beam

This ratio measures the fineness of the hull. Fine hulls, having ratios of 3.0 - 4.0 and higher, are long and slender which promotes easy motion, high speed (low drag), and good balance when heeled. Many newer designs favor wider hulls which have larger interior volume, sail flatter, and have high reaching and down wind speed potential. One note of caution when making comparisons, longer boats tend to be finer then short ones. Our template value is 3.4, which is fairly fine. Fine hulls tend to be well balanced and have low inverted stability.

 

CAPSIZE RISK = beam/(disp/(.9*64))^.333

An empirical factor derived by the USYRU after an analysis of the 1979 FASTNET Race. The study was funded by the Society of Navel Architects and Marine Engineers (SNAME). They concluded that boats with values greater than 2 should not compete in ocean races. Values less than 2 are "good". The formula penalizes boats with a large beam for their high inverted stability, and light-weight boats because of their violent response (low roll moment of inertia) to large waves, which are both very important during violent storms. It does not indicate or calculate static stability. Some modern coastal cruisers and many racing designs have problems meeting this criteria. An interesting note, the study concluded that static stability was relatively unimportant in predicting dynamic capsize. Beam and weight were much more important factors. Wide boats give waves a longer lever arm to initiate roll and light weight boats require less energy to roll over; both undesirable attributes in a cruising boat. The template value of 1.7 is very low.

 

COMFORT FACTOR = disp/(.65*(.7*lwl+.3*loa)*beam^1.33)

An empirical term developed by yacht designer Ted Brewer. Large numbers indicate a smoother, more comfortable motion in a sea-way. The equation favors heavy boats with some overhang and a narrow beam. These are all factors that slow down the boat's response in violent waves. This design philosophy is contrary to many modern "racer / cruisers", but it is based on a great deal of real blue water data, not just what looks good in a boat show. A value of 30 - 40 would be an average cruiser. Racing designs can be less than 20, and a full keel, Colin Archer design, could be as high as 60. Our template value of 36 indicates that comfort is a high priority on cruisers.

 

MOMENT OF INERTIA (I) = disp^1.744/35.5

An empirical term developed by SNAME. Large values resist rolling forces. The moment of inertia is very sensitive to the distance items are from the CG. A heavy rig can greatly increase I, with little impact on displacement.

 

ROLL PERIOD (T) = 2*PI*(I/(82.43*lwl*(.82*beam)^3))^.5

The roll period is based on the moment of inertia. The term ".82*beam" has been substituted for the waterline beam due to lack of data. Using ".82" results in a close match for the few boats with measured periods, but more data is needed (If you have measured roll data, email it to me and I’ll include it in my data base). Simply stated, a sailboat’s roll period, in seconds, is inversely proportional to its stability. Unstable boats have long periods, stable boats have short periods. The roll period is very easy to determine, you simply grab a shroud and push / pull until the boat is rocking over a few degrees. Then count the number of full cycles in one minute, and divide into 60. The general rule of thumb is that boats with periods less than 4 seconds are stiff and periods greater than 8 seconds are tender. The template value of 4.05 is near the stiff end of the range, indicating good static stability.

 

STABILITY INDEX = T / (beam*.3048)

This is another empirical term relating period and beam to stability. Values less than 1.0 are considered stiff. Values greater than 1.5 are considered tender. I like this technique because its simple, and includes the hull form, the center of gravity, and the roll moment of inertia, all in one easy to use package. The template boat again leans towards the stiff side, with a value of 1.1.

 


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