Stability for Small Boats

As your boat sits at its mooring, two basic forces are at work. Gravity, and buoyancy, which effectively moves your boat upward to the point equal to the weight of the amount of water the boat is pushing out of the way.

The amount of each force exerted is determined by the weight of the boat. A cubic foot of fresh water weighs 62.4 lbs., while a cubic foot of salt water weighs 64 lbs. If you look at a cross-section of your boat's hull, sitting level in the water, you can imagine two theoretical points. The Center of Gravity (CG) will be in the very center of the entire hull space. The other point, the Center of Buoyancy (CB), will be in the center of underwater portion of your boat.

When the CG and the CB are vertically aligned, the boat is level. If your boat is constructed properly, and your gear is stowed correctly, the CG should always stay in the same place. The CB, however, will change position any time the boat begins to list because the amount and shape of the boat under water changes.

The Center of Gravity and the Center of Buoyancy is called the righting arm. The weight of the boat is pushing down at the CG and the weight of the water is pushing up at the CB. This situation creates a rotating force or motion that is called the righting moment.

As long as the force of buoyancy is able to return the boat to an upright position, the situation is called a positive righting moment. If for any reason, the Center of Gravity should shift outside of the Center of Buoyancy, it creates a negative righting moment and the boat is going to capsize.

The ability of any boat to right itself is called stability. It should be evident to anyone that stowing gear and installing equipment on a boat takes thought. Both should be as low in the boat as practical. It's an absolute necessity to make sure that neither can suddenly shift from one side of the boat to the other. Besides careful stowing, another rule to remember is NEVER run parallel to large waves in a boat that is overloaded or too small for the situation. As the waves cause the boat to roll from one side to side, the positions of the GC and the CB are constantly changing. Even a small change during the rolling, such as gear shifting or a passenger moving to the low side, will create a negative righting moment.

VESSEL (STRESS CALCULATION)

A hull is supported in water by the buoyant force of the water that it displaces. The upward buoyant forces acting on the length of the hull equal the downward gravity forces acting throughout the length of the hull. The buoyant and gravity forces are equal and are concentrated at the center of buoyancy and the center of gravity. Individual buoyancy forces are proportional to the cross-sec­tional area of the submerged hull at the point at which they are measured, and the individual gravity forces are measured by the weight of cargo, machinery, equipment, etc., at a point along the hull. When the individual buoyancy and gravity forces are plotted as or­dinates from the same baseline that represents the ship's length, two curves are developed, a buoyancy curve and a weight curve.

The load curve is formed by plotting the differences between weight and buoyancy at individual points along the length of the ship. The load curve crosses the baseline when weight equals buoyancy.
When the load curve is above the baseline, weight is greater than buoyancy, and it is less than buoyancy when the curve is below the line. Since total weight equals total buoyancy, the area of the load curve above the line equals the area below.
When unequal loading is indicated by the load curve, shearing forces and bending moments will be set up in the vessel. The shearing curve is developed by integrating the load curve, a process which calculates the area under the curve. When the shearing curve is integrated the process produces the bending moment curve. Representative curves of shearing force, developed from the above load curve, and bending moment, developed from the shearing force curve.
ABS presents formulae for the calculation of shear stresses caused by loading and wave actions.

Longitudinal strength work sheets are provided to the vessel to help calculations of stress numerals for the various weights added to the light ship displacement. Each added weight (cargo, bunkers, and other variables carried in specified locations), when multiplied by a factor provided a designer, will give a number known as the stress numeral, sometimes a positive number, sometimes a negative one. The algebraic sum of the calculated stress numerals and the stress numerals provided for the light ship equals the net stress numeral. Stress numeral = (actual bending moment/allowable bending moment) x 100.

Since the actual bend­ing moment must be less than the allowable bending moment, the stress numeral must be less than 100. If it is greater than 100 the ship is im­properly loaded and there is a probability that the ship will break due to excessive bending moments.
Maximum bending moments happen in the vicinity of amidships. At this location the shear force is zero, and from this location forward and aft the moment arms of the shear force are maximum.
The computer is now used in figureing this out, it helps in the calculation and is faster.

VESSEL (HOGGING AND SAGGING)

Hogging - is the straining of a ship lightly loaded amidships and more heavi­ly forward and aft, causing the bow and stern to be lower than the middle section.

Sagging - is the straining of a ship heavily loaded amidships and more lightly forward and aft, causing the bow and stern to be higher than the middle section.

Hogging and sagging can be tolerated, but only within limits.
When they exceed acceptable limits, hogging or sagging will cause the hull to crack in the area of greatest stress.
In a improper loading of a vessel, a hogged or sagged condi­tion can be caused by a trochoidal wave action, a action of a wave whose distance between crests is equal to the length of the ship and whose height is 1/20 of its length. When a vessel encounters a wave of that size, it will be hogged when the midsection of the vessel passes over a crest and sagged when the bow and stern sections are supported by crests.
In determining whether a vessel is hogged or sagged it is helpful to clear mental uncertainties if look at draft as a "theoretical" draft and load (midships) draft as an "actual" draft.

VESSEL (STRESS)

A vessel must have strength to with stand the stresses placed on it by large seas, cargo weights, and cargo distribution that is sometimes less than optimum. The first and important requirement in the construction of a vessel is the design. Designs are reviewed by ABS and approved if they measure up to the classification society's standards of safe design. Materials must meet approved specifica­tions, and the construction standards of the building yard must be such that the completed vessel is free of discrepancies that may be do to poor workmanship.

A ship's hull has some longitudinal flexibility built into it; otherwise it would break. But the amount of flexibility is limited by the strength ofthe structure. There must be a compromise between flexibility and strength to produce a ship that is safe under the most adverse conditions that can be expected at sea. Also, loading must be such that the safety of the ship is not compromised.

Consider stresses placed on a vessel the following terms should be known:
Load: the total force in pounds or tons, acting upon a structure.
Stress: the force per unit area, pounds or tons per square inch, acting on a structure. Stress may be compressive (main deck of a sagged ship), tensile (main deck of a hogged ship), or shearing (tendency of one part to slide over another when two forces act in parallel and opposite directions vertically at the boundary between an empty hold and one that is heavily loaded, or horizontally at a butt strap at a point of maximum bend­ing moment)
Strain: a distortion caused by stress.

STABILITY

STABILITY
The static stability of a ship is the measure of her tendency to return to the upright after being inclined by external forces such as wind or waves. A ship's stability is influenced by her underwater form, or shape, and by the amount and position of the weights or loading placed aboard the ship. Determining the dimensions, proportions, and shape of the hull for stability in a properly loaded ship is the business of the ship designer. It is the ship's Master and Chief Mate, who have control over her loading. You must understand the basic principles of stability to avoid loading conditions that will produce too little or too much of it. There are several programs out that help in working with stability, this is just some basic things that are good to know.
WEIGHT AND BUOYANCY - A ship when afloat is acted on by two princi­pal forces, its weight and its buoyancy, that are equal to each other but act in opposite directions. The weight acts downward through a point called the center of gravity. The buoyancy acts upward through the center of buoyancy.

To find the height of the center of gravity of a ship above the keel a very simple principle is used, but it can be complex and time consuming. The weight of each sizeable piece of hull or machinery is multiplied by its distance above the keel. This gives a number of things when added together equal the moment sum. The sum of the weights of all these parts is also made and is the total weight of the ship, This is called ships displacement. Height of the ship's center of gravity above the keel is the moment sum divided by the ship's displacement.

DISPLACEMENT - Should a graving dock be filled with water to the top of the gates and a launch lowered by crane into the water some water will then flow over the top of the gates. If this water is caught in tanks and weighed the weight will be found to be the same as the launch. And the volume is the same as the underwater part of the launch. In other words the vessel removes or displaces a weight of water equal to its own weight. I should mention a displacement ton is 2,240 pounds. The relation of the volume of the underwater part of the vessel to a rectangular block of the same length, beam, and depth is called the fineness coefficient. The displacement of a vessel is then the product of the length, beam, draft, and fineness coefficient all di­vided by thirty-five. In ship stability calculations the center of gravity of the volume of the underwater part of the ship is very important.

The posi­tion of this center of buoyancy fore and aft is called the longitudi­nal center of buoyancy. The position of the center of buoyancy measured in a vertical direction above the keel, or in some cases from the plane of water line is called the vertical center of buoyancy. The same is true of all the usual surface ships.
WORKING BUOYANCY - is the amount of buoyancy available for carrying of cargo, that is the difference in displacement in tons between the ship when light and when loaded down to the Plimsoll mark.

The center of buoyancy curve is a curve showing the height of the vertical center of buoyancy for various drafts of the ship. The freeboard of a ship is the distance from the top of the freeboard deck to the water line. The freeboard deck is the uppermost com­plete deck having permanent means of closing all openings in weather portions of the deck. Freeboard is measured at the center of the ship and if necessary the top of the freeboard deck plank is continued through the water way.

SPECIFIC GRAVITY - is the weight of a given number of cubic inches of a given material divided by the weight of the same number of cubic inches of water. Inertia is the tendency of a body in motion to continue in mo­tion, and if at rest to continue at rest. The moment of inertia of a plane about an axis is the sum of the products of each small part of the surface multiplied by the square of the distance of each part from the axis.
The polar moment of inertia which is used for period of roll is the sum of the weights of all parts of the ship multiplied by the squares of each individual distance from a horizontal line passing fore and aft and through the ship's center of gravity.
The longitudinal metacenter is similar to the transverse meta­center except in a fore-and-aft direction but is not of much im­portance because the period of pitching is so very small compared with the periods of the waves that there is no synchronism set up. The period of seconds of a complete roll of a ship, that is a roll from port to starboard and back to port again
SYNCHRONISM - Is the condition resulting from waves reaching the ship in such succession that each catches the ship at the same period of roll and results in a rapidly increasing amplitude. This can be­come so dangerous that to avoid it the ship's course must be changed.
METACENTRIC CURVES - Are curves showing the heights above the keel of metacenters and centers of buoyancy for varying dis­placements of the ship.
METACENTRIC HEIGHT - Transverse metacentric height is a meas­ure that determines a ship's initial stability. The larger it is in posi­tive value the "stiffer" the ship will be. Should it be too great the ship will be very uncomfortable and if it is too small the ship will be "tender" and her safety may not be what it should be.The distance between the two lines is called righting lever. Which is a kind of force tending to right the ship at any time, is the displacement of the ship multiplied by its righting lever.
WEDGE OF IMMERSION - is the wedge of the ship which will be immersed when the ship is inclined and the wedge of emersion is the corresponding wedge of the ship on the opposite side which will emerge from the water during the operation.
The distance between the center of buoyancy and the transverse metacenter equals the mo­ment of inertia of the water plane about its center line.
TONS PER INCH OF IMMERSION - is given in curves showing the dis­placement change for every inch of increased draft.
Stability studies relate to the tendency of a ship when inclined to resume its upright position. Statical stability is the product of the righting arm multiplied by the displacement.
INITIAL STABILITY - is the stability of a ship at small angles of in­clination as measured by metacentric height and displacement. The curve of stability is a curve giving the righting lever in feet for various large angles of inclination.
RANGE OF STABILITY - is the angle of ship's heel in degrees at which the righting arm disappears and a ship is just as likely to capsize as to right itself. This is only of meaning if all openings by which flooding can take place are closed, and is in general greatest in ships of large freeboard.
DYNAMICAL STABILITY - of a ship is the work done in inclining the ship to any angle and equals the displacement multiplied by the increased vertical separation of the centers of gravity and buoyancy of the ship from upright to an inclined position.
For every ship stability curves are worked out for various drafts and loadings.

The longitudinal metacentric height is computed similarly to the transverse metacentric height except that in computing the moment of inertia of the water plane is taken about an athwartshlp axis passing through or directly above the center of gravity. The longitudinal metacentric height is used in calculating changes of trim. A change of trim is the sum of the change of drafts forward and aft and changes of trim can be caused by a shift of weights on board in a fore-and-aft direction.