STABILITY OF FLOATING BODIES
PROJECT PROPOSAL
PROJECT PLAN
STABILITY
FORMULAE AND
DEFINITIONS
THE LAB SHEET
PROJECT SCHEDULE
MEETING MINUTES
PROJECT SELECTION
BUDGET AND RISK PLAN
MARKET ANALYSIS
FINAL DESIGN
MANUFACTURE
PRODUCT DESIGN SPECIFICATION
REFERENCES

SHIP NOMENCLATURE

The main body of a ship is called the hull, and the deck at the top of the hull is called the main deck. Anything above the main deck is called the superstructure. The bottom line of the hull is called Keel. The distance from the bottom of the hull to the waterline is called the draught and the distance from the waterline to the main deck is called the freeboard. As a ship gets loaded with cargo or passengers and fuel it gets heavier and so must displace more water to increase the buoyancy to equal the new weight, and so the draught increases and the freeboard decreases.
Hull Depth = Draught + Freeboard

THE LAWS OF FLOATATION

Archimeds' Principle

States that when a body is wholly or partially immersed in a liquid, it experiences an upthrust (apparent loss of weight - termed Buoyancy force (Bf)), equal to the mass of liquid displaced.

Law of Flotation

States that every floating body displaces it’s own mass of the liquid in which it floats.

DISPLACEMENT

The displacement of a ship (or any floating object) is defined as the number of tonnes of water it displaces. It is usual to consider a ship displacing salt water of density 1.025 t/m3, however, fresh water values of displacement (1.000 t/m3) are often quoted in a ship’s hydrostatic data.

The volume of displacement is the underwater volume of a ship afloat i.e. the volume below the waterline.

To calculate the displacement (W) of a ship the following needs to be known:
                - The volume of displacement (V)
                - The density of the water in which it floats (r)
Since:  Mass = Volume X Density
the mass, or displacement, of a ship is calculated by:
Displacement = Volume of Displacement X Water Density

STABILITY

The Forces Involved



Consider the weight of the ship to be a single force acting through a single point, its centre of gravity (CG), and the buoyancy of the water to be another single force acting through another single point, the centre of buoyancy (CB). The centre of buoyancy is the point which would have been the centre of gravity of the water which the ship has displaced. For submarines, whether on the surface or submerged, the centre of buoyancy is usually above the centre of gravity, but for most surface ships the centre of gravity is above the centre of buoyancy.The goal is to keep the CG vertically in line with the CB. Unfortunately, the most stable position is always going to be with the CG hanging below the CB like a rock hanging from a string. To keep the ship from turning upside down, the CB now needs to move under the ship before it rotates all the way over. As the ship rotates in the direction of tipping, the hull pushes down into the water on that side while the other side lifts out of the water. This action of adding volume (buoyancy) on the side you are tipping and subtracting volume on the other side will cause the center of buoyancy to move toward the side you are tipping. If the boat is shaped to be stable, the CB will move out to the side faster than the CG.

As a boat tips the buoyancy is moved. In the picture at right, the blue line is the original "even-keel" waterline. As the boat tips to the right the wedge shaped green volume (b) lifts out of the water and the other wedge of purple (c) sinks into the water. The original center of buoyancy (Ba+b) is moved to the point Ba by the subtraction of volume (b) and then moved even more by the addition of volume (c). It is this motion of the buoyancy which creates stability.The change in buoyancy happens due to changes of volume near the waterline. This is why initial stability is dependant on the waterline shape and width and not on the shape below the waterline. Because it is only the water near the waterline that is initially effected by tipping, it is only the shape near the waterline that effects initial stability.

Stability Curves

The stability curve is a graph of the horizontal distance (GZ) between the Center of Buoyancy (CB) and the Center of Gravity (CG). When you are tipping to port, as long as the CB is farther to port than the CG, the graph will stay positive. The horizontal distance (GZ)is proportional to the righting moment, or the amount of force the boat will apply to returning upright.

As long as the righting moment is positive, the boat will have a tendancy to return upright unless some other force is applied. When the graph goes negative, you will need to apply some bracing force to return upright.



Often the "Y" axis is given in the units of "foot pounds" instead of "GZ". GZ in this case is in feet. To get "foot pounds" just multiply by the displacement weight in pounds. Feet times pounds equals "foot pounds". So if the weight of the boat is 40 lbs and the paddler weights 200 lbs, maximum will be 0.047 ft x (40+200)lbs = 11.28 foot pounds.





Reading the Stability Curve

There are several aspects such as: the height at a given heel angle, the slope of the curve at any given angle and area under the curve from zero degrees out to a given angle. The height of the curve tells how much force the boat is creating to return upright. The slope of the curve indicates the resistance to further tipping. The area under the curve corresponds to how much energy is absorbed by the boat when it is tipped.

The stability curve (red) can be broken down into several identifiable points. Obviously, the first is the height of the curve. Given any two boats tipped to the same angle, the one with the higher curve at that angle will apply more force to return upright, so it will feel stiffer or more stable. The next thing to look at is the slope of the curve at 0 degrees. The curve that climbs more steeply will have a greater initial stability and feel stiffer. The peak of the curve is where the stability starts to diminish. Having this point either be higher or at a greater angle of heel will make the boat feel like it has more secondary stability. By looking at the area under the curve until the peak of the curve (the dark blue area) you can get one value for the secondary stabilty. The combined blue areas is an indication of how much tipping energy the boat can absorb before a capsize is inevitable. The point of final stability where the line crosses zero is the angle beyond which capsize is inevitable without bracing.

Constant Waterline Width


Above are 5 different boats with their stability curves. Although the boats have varying widths, the waterline width and shape is the same in all boats. The slope of the curve near zero is nearly identical regardless of the different shapes above and below the waterlines. This is because initial stability is not dependant on the overall shape of the boat, only the waterline width and shape.

Although you would expect a round bottomed (red) boat to be the least stable, in this case it has the highest overall stability because it flares out a lot above the waterline. And even though the "flared" (blue) shape has similar overall width, the volume distribution of the rounded shape gives it more stability. Any shape that widens above the waterline will tend to have more secondary stability.

Constant Overall Width

Using the same basic hull shapes below are the curves when overall widths are the same. Now, the round bottom is much less stable because the waterline width is much less. This demonstrates why knowing the overall width of a ship is not that informative. One will learn more by asking for both the overall width plus the width at the waterline.


As discussed earlier, Initial stability is the resistance of the boat to tip just a little bit. The slope of the line at the beginning of the stability curve indicates this resistance. In fact, the slope of the line at any point along the stability curve indicates how much more force will be required to make the kayak tip just a little bit more. Put another way, the slope shows how much an additional tipping force will effect the boat if it is already tipped. A shallower, flatter slope means that an additional force will have more effect.

Secondary stability is generally related to the maximum height of the stability curve. Obviously, a higher maximum righting moment will be more stable. But the angle at which the curve reaches the maximum is also important because that indicates how far one can heel the boat before you begin losing stability. One way of combining the height and angle of maximum righting moment is to look at the size of the area between the curve and the horizontal zero line. This indicates the work or energy required in tipping the boat to that point. A larger area under the curve indicates that it will take more effort to tip the boat.

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©  Copyright  Binoy Perumpalath,
If you wish to copy, change or alter in anyway please contact Binoy Perumpalath at binoy@binoydesign.com
Last modified on 07 April 2004.