Buoyancy

Why concrete ships float

A ship made of any material, concrete, steel, wood, or plastic will only stay afloat while the buoyancy, is greater than its weight. The buoyancy or upward force from the sea is equal to the weight of the water displaced. So a 10 ton ship will sink into the water until 10 tons of water has been pushed aside. Add 5 tons of cargo and it will sit deeper in the water with 15 tons of water displaced.

The reason for this can best be explained by looking at a ship in a small harbor with lock gates. As the ship sinks into the water, the water is pushed sideways and this causes the water level in the dock to rise, the upward force on the boat is caused by the weight of the water you have caused to rise trying to get back to a level position. It is the same force in or out of the dock.

Concrete as a solid block sinks as it uses up less space than the same weight of water, when you spread it out on a frame enclosing air, it takes up a greater space than the weight of the equivalent volume of water and floats.

An old wooden ship, encased in Ferrocement, will usually sit higher in the water after, and needs to have extra ballast added to bring it back down to its original level.

The amount of space within the ship above the water line and below the point water could enter is the reserve buoyancy.

Ferrocement ships

Ships made of cement and wire sandwich material have been around for a long time, and some over 150 years old are still in use. They are as strong as steel ships, and as flexible as wooden ships. Far stronger than plastic/fiber craft. Most are built from scratch but some are Ferrocement added around an old ships hull, often after it has had problems that would no longer make it serviceable. As the deck and sometimes sub structures inside are all part of the whole structure they form a very strong box and even when ships have gone to ground on reefs they are often in reasonable condition if not re-floated for some years.

Many are DIY designs and the only real problem they have encountered in the construction is difficulty in controlling the thickness of the coating and therefore the weight. They are usually therefore made, floated and then ballast added to get them into trim.

Ferrocement ships that are damaged can be repaired to the same condition as before.

Floating dry dock

A floating dry dock is a ship, it has chambers or tanks that can be flooded and a small ship sailed on to or into the dry docks hold area. The tanks are then pumped out often by forcing compressed air in, and the dry dock complete with ship rises until the ship is out of the water and can be worked on. Re-floating is the reverse process. The amount of water the dry dock replaces is equal to the weight of dry dock and ship in for repairs.

Why did The Titanic sink

The Titanic was said to be an unsinkable ship, in that it was constructed with a number of dividers across the ship, so in theory a hole would cause only a single compartment to flood. It was designed so a number of compartments could be holed, yet stay afloat. Many people say it sank because too many compartments were holed, however this is not the real reason it sank. The compartments were not complete, but dividers that went only up to a level, and although well above the water level, when the water got into a number of sections, the front went down and water spilled over the dividers flooding compartments that were not holed. When sufficient were flooded the front went down and the back complete with some water came out of the ocean, the weight at this point broke the ship in two.

With some other ships when the holds start to flood you see the tops split open, this is because the deck and top of the hold is not strong enough to hold the pressure.

If you try an experiment with a plastic bottle. Tie a weight to the neck, and without any top on it, throw it into the water. Although water can get in, the weight will keep it upright and as air cannot escape, it will continue to float.

Mathematically

The density of fresh water is 1000kg/cubic m. 1 cubic foot weighs 62.391lbs

Sea water if higher and varies, the North Atlantic being the highest, reaching in places 1040. One cu ft of salt water weighs 64lbs or 1/35 ton.

The displaced weight of water is equivalent to buoyancy.

Put simply, if you have a box measuring 12 foot by 12 foot, 3 foot deep and was to push it into the water fully you would need a weight including the material the box is made of =12x12x3/35 tons = 12.34 tons, which I would suggest is so heavy that you could not balance it on to this small space.

To get displacement of a ship in tons L x B x D x Co / 35, where L is the length at water level, B is the breadth at water level, D is the draught mid ship, all in feet, Co is the bloc coefficient this is percentage of a square that a cross section of the hull takes up /100, average craft about 0.45.

In metric units the formula is tonnes= L x B x D x Co x 1.025, , where the measurements are as above but in metres.

So if we had a small island 500ft x 200ft x 50ft high but 25ft in the water, and a square block shape therefore a Co of 1 we get 500x200x25x1/35=71,428.6 tons. This means that the weight of the construction, wire, cement, dividers, construction of buildings, services, contents, people and other items on the island will need to come to this weight for the island to sit 25ft in the water, lighter and it floats higher, more weight and it sits deeper. The weight would have to be twice the figure we computed before all 50 ft would be in the water and the island would sink. In practice all islands, will probably not have solid hulls, and all will need ballast (weights added, possibly as water in tanks) so that they can be adjusted as development occur.

The shape of the hull effects stability, the above example is for ease of calculations only.

Practical planning would involve deciding on the size and shape of the part of the island in the sea, and then itemizing as accurately as you can the component parts that was to be used to build both the island and its contents. Breaking the whole task down into small parts would make this fairly easy to do. Once this was all added up, you could take this from the calculated displacement, and know how much ballast you would need to add, some of which may be built in solid, and some adjustable. In practice when making Ferrocement ships they are made and floated, prior to ballast being added as the skin thickness makes a lot of difference to the weight, and they can be better balanced and adjusted once afloat.

A floating island

The island being large and hollow, will sit in the water at a level where its weight is equal to the water displaced, construct buildings on it and it will sit deeper in the water.

The exact point the island or ship settles at will be effected by the level of salt in the water, temperature and air pressure. It will ride slightly highest in winter in the North Atlantic and sit lower in the water in fresh water and warmer climates. The differences can be seen on the side of many ships by the marks of the Plimsole line. Clearly fine adjustment using ballast is necessary however the larger the structure the smaller the effect of a then relatively smaller weight.