## Assumptions and Physical Constraints for the Titanic Flotsam Raft

This article confines itself to the mathematics of buoyancy: would they sink or float? We will ignore other considerations, such as exposure and hypothermia.

The calculations are in metric:

- Kg = Kilogram = 2.2 pounds = 2.2 lb
- M = metre = 39 inches = 39″ = 3.28 feet = 3.28′
- Kg/M^3 = Kilograms per cubic Metre

Let’s assume calm winds and no waves on the Atlantic, with salt water at a density of 1025 Kg/M^3. Water is more dense when it is colder, reaching maximum density at +4C. Sea water is also denser than pure, due to the dissolved salt. Pure water at about 4 degrees Centigrade has a density of 1.000, and weighs 1,000 Kg/M^3 .

The density of wood used for lumber depends, in part, on the type of tree. Let’s assume they are floating on Canadian spruce, with a density of 450 Kg/M^3.

Pine’s density is somewhat over 500, while oak’s is well over 700; ebony would sink in fresh water, with a density of about 1200 Kg/M^3.

Let’s also assume that the door upon which Rose floats is 78″ x 31″ x 0.5″, or 2M x 0.8M x 0.0127M, based on an actual fragment of a door from the *Titanic* which was one-half of an inch thick.

Since 1″=2.54cm=0.0254M, the door would be 0.127 metres thick.

Let’s also assume that Rose weighed 134 pounds, or 61 Kg, and that Jack weighed 158 pounds or 72 Kg.

## A Realistic 1-Door Raft Sinks Under Kate’s Weight

If the door is 2×0.8×0.0127 metres, its total volume is 0.02032 cubic metres. At a density of 0.45, its weight is 9.1444 Kg. If fully submerged at the surface, it would displace 0.02032 cubic metres of water weighing 0.02032M^3 X 1025Kg = 20.828Kg. The net buoyancy is 20.828 – 9.1444 = 11.6836Kg.

Since Kate weighs 61Kg, she and her makeshift raft would sink until her body displaces about 50Kg of water. While this would spare her some swimming effort, it fails to provide for her safety under the conditions this article requires, and she certainly wouldn’t be floating on top of the water.

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