DYNAMIC STABILITY

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        How stable should an offshore cruising boat be? Does it heel to much? Is it likely to be rolled over in a storm? If it does roll over, will it right itself quickly? Before we can answer these questions and evaluate the suitability of a boat for offshore use, we need to understand that what we normally call "stability" is really composed of two factors, static stability and dynamic stability.

    Static Stability is familiar to most of us because it largely determines the angle of heel (roll) developed by a sailboat under constant wind conditions. Some of the roll can be reduced by changing the center of gravity (hiking out or moving ballast), reducing sail area, or running off slightly (avoid the wind). Under light to moderate conditions, the ideal cruising boat should carry enough sail to perform well and have enough static stability to avoid excessive heel.

    The most important factors that increase static stability are heavy displacement, low center of gravity, and a center of buoyancy that shifts outboard quickly when the boat heels (strongly related to beam). Most cruising monohulls exhibit positive static stability out to heel angles of 130 degrees, with the highest righting moment occurring around 65 degrees. Multihulls peak higher and sooner than monohulls and capsize at lower angles.

    Dynamic Stability controls how much the boat rolls in response to a transient wind gust or violent wave. The ideal cruising boat should resist these dynamic forces long enough for them to pass safely by. Reducing sail area will usually help reduce dynamic roll, and the boat can often be steered around the worst waves, but our ideal cruiser should have enough dynamic stability "built in" to survive an encounter with a strong gust or rogue wave without capsizing. If the worst does happen, and our ideal boat gets rolled 180 degrees, it should right itself quickly.

    Heavy displacement helps dynamic stability, but the center of gravity is not much of a player and a large beam actually makes the response worse (beamy boats catch the wave early and give it more leverage and time to act on the hull). Once inverted, the increased static stability associated with beam becomes a liability since it keeps the boat inverted for a longer period of time. Light and beamy boats often have high Capsize Risk (see definitions). The most important factor in dynamic stability, however, is the boat’s roll moment of inertia. Without getting into much math, the roll moment of inertia is proportional to the square of the transverse distance between the boat and its center of gravity. The squared term makes the calculation very sensitive to how far heavy objects are from the center of gravity.

    For example, a dingy with two people sitting fore and aft on the centerline has a smaller roll moment of inertia than the same dingy with the people sitting side by side. Both boats weight the same, have the same center of gravity, and the same center of buoyancy (same static stability), but moving the people off the centerline greatly increases the roll moment of inertia. Since the roll moment of inertia is proportional to the square of the distance from the center of gravity, deep ballast and long heavy masts have the most impact. A large roll moment of inertia is desirable for a cruising boat because it increases the total time and energy required to capsize the vessel. Boats with large moments of inertia have long roll periods and are highly resistant to rapid changes. Multihulls have a very large roll moment of inertia because the hulls are quite far from the center line.

    Static or Dynamic Stability. Which is best? Can we have both? The trade off between static and dynamic stability forces us into a compromise situation where there is no single correct answer. Heavier boats have more static and dynamic stability, but less performance. Wide beam boats have high static stability, but they also have a higher capsize risk and more inverted stability. Wide beam is generally associated with lighter weight, higher performance boats, which will have a short roll period and low roll moment of inertia. High performance boats also typically have smaller section masts and less rigging. This reduces the weight aloft and increases static stability, but greatly reduces the moment of inertia. A heavy cruising boat with a deep bulb keel, heavy spars, lots of rigging, and a radar mounted above the spreaders will have a large roll moment of inertia, a long roll period, and be very resistant to wind gusts and waves.

    The best we can do is to make our evaluations based on our expected use. A coastal cruiser, for example, may except the dynamic stability penalties associated with wide beam. A blue water cruiser probably won’t. Similarly, carbon fiber spars may increase static stability (good for light air performance) but they will greatly reduce the roll moment of inertia (see example). While static stability will always be a critical sailboat parameter, the dynamic characteristics of a cruising boat should be understood since they can be very important under storm conditions.

 

example

The following boats have similar LOA, Beam, Ballast / Disp ratio, and Draft. The "Racer" design has 50% less displacement, 50% longer righting arm (due to a flatter bottom and lower center of gravity), and a 66% lighter weight rig. Both boats are subjected to a constant 30,000 ft.lb. overturning moment, which is less than their maximum static righting moment. The simulation begins with an under damped condition which allows the overturning force to capsize the boat. The damping is then increased until the boat oscillates rather than capsizes, eventually damping out to a constant heel angle. The first case gives us the time to capsize, the second lets us measure the period of oscillation. Under static conditions, damping is largely determined by the rate that water is swept away by the keel as the boat rolls. The lateral area of the underbody normally controls damping (deep keels and centerboards help), however in a storm the keel may be in breaking water (froth) and the damping forces drop dramatically, allowing the boat to heel more.

                                                RACER CRUISER

Disp., lb                                   16000         24000

Hull, lb                                     9300         13900

Ballast, lb                                 6400          9600

Mast and Rig, lb                          300          500

Roll Period, sec                           4.6            5.7

 

Static Stability

Righting Arm, ft                                2.4             1.6

Max. Righting Moment, ft.lb            38347          38399

Heel at Max. Moment, deg.              62              64.5

 

Dynamic Stability

Moment of Inertia, lb.ft.sec^2         17304          26522

Time to heel 30 degrees, sec              .9             1.1

Time to heel 60 degrees, sec             1.4             1.7

Time to heel 90 degrees,sec              2.0              2.5

Time to Capsize, sec                        2.8              3.6

 

    The first thing we notice is that the light weight racer has a much shorter roll period than the cruiser. Its tempting to claim that this indicates more static stability, however this is not completely accurate. Static stability does reduce the roll period, but so do other factors such as the roll moment of inertia. When we look at the actual values for static stability, both boats are about the same. Even though the racer ends up with a longer righting arm, the cruiser’s heavy displacement compensates for it since static stability is a function of both.

    The big difference is in dynamic stability. The Cruiser has a 53% bigger roll moment of inertia, which greatly slows down its response to the overturning moment, resulting in the increased roll period. At 90 degrees heel, the cruiser lags the racer by 1/2 a second. At the point of capsize, this time difference has increased to .8 seconds. In a sever storm this could be the difference between an unpleasant knockdown and a life threatening capsize.

 

DEFINITIONS

DISP / LENGTH RATIO = disp/2240/(.01*lwl^3) Probably the most used and best understood boat evaluation factor. Low numbers (resulting from light weight and long waterlines ) are associated with high performance and quick response

SAIL AREA / DISP RATIO = sail area/(disp/64)^.666 This is a ratio of power to weight, calculated using a 100% jib. We want a cruiser with enough power to sail well but not so much sail that the crew is fatigued by constant sail changes or worried about having a fragile oversize rig.

BALLAST RATIO = weight of ballast / displacement

CAPSIZE RISK = beam/(disp/.9*64)^.333 A seaworthiness factor derived from the USYRU analysis of the 1979 FASTNET Race, funded by the Society of Navel Architects and Marine Engineers. The formula penalizes wide boats for their high inverted stability and light weight boats because of their violent response to large waves

ROLL PERIOD = Time in seconds to complete one cycle. The roll period can be measured by starting the boat rolling slightly (at the dock) and averaging the time for several cycles.

 

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