32 people died when the Costa Concordia ran aground in a protected marine park off the coast of Italy. The $US800 million salvage operation to remove the Costa Concordia needs lots of maths.

It is the biggest salvage operation ever undertaken in seafaring history.

THIS IS THE PROBLEM. It is a one off project and the engineers have to hope they get the maths right.

Here’s the plan:

Here are the maths problems:

# Problem 1:

The ship, which is 290 meters (951 feet) long and 36 meters (118 feet) wide, is on its side and full of seawater. It has a displacement of 50,000 metric tons plus the weight of the water inside that, at a guess, could weight 30,000 metric ton. This is a BIG problem. Normal salvage methods cannot be used.To give you an idea of the scale:

50,000 metric ton = 50,000,000 kg

1 London Double Decker Bus = 8,000 kg (Empty) or 12,000 kg full

according to the BBC

The wt of a half-full London = 10,000 kg

## 1 Costa Concordia = 5,000 London Buses

Now add the water.The salvage operation must lift the equivalent, maybe, of 8,000 London Buses.

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# Problem 2:

The ship is resting on a seabed that slopes at an angle of 20^{0}.

Simply winching the ship upright would have it roll down the slope. A horizontal platform must be built that can take the 50,000 metric ton plus load.

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# Problem 3:

The platform has to be built underwater. This will take 111 salvage divers working around the clock to secure the platform and attach cables to the ship.This steel platform weighs three times as much as the Eiffel Tower.

The total weight of the Eiffel Tour = 8,560,000 kg

The weight of the salvage platform = 26,000,000 kg

or 2,600 London Buses.

** ……………………………………………………………….**

Problem 4:

The Costa Concordia must be winched onto the platform slowly. Too quickly it might topple off the platform.

As the 50,000 metric ton ship (plus the weight of trapped seawater) is winched upright the load on the winches decreases (See simplified diag below.) Think of picking up a chair off the floor. As you rotate the chair upwards the load decreases to zero …. when the CENTRE OF GRAVITY lies directly above the PIVOT POINT then gravity works with you and the chair drops with a thud to the floor. Engineers cannot allow 50,000 plus metric ton to drop with a thud. Winches must be carefully controlled. The winching operation took 19 hours.

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# Problem 5:

The Costa Concordia was winched upright on 17 Sept 2013. Floats must now be welded onto the damaged side of the ship. Once the ship is refloated it will be towed away to be broken it up for scrap metal. This will take 2 years.

# UPDATE:

The costa Concordia is floating again. On 27 July 2014 the crippled cruise ship arrived in Genoa, it’s final destination, where it will be broken up for scrap metal. The complex engineering feat to refloat the vessel proved successful.