Wikipedia:Reference desk/Archives/Science/2024 October 8
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October 8
editWhat percentage of a ship is under water?
editI was wondering how much of a ship is actually under water. Of course we know that weight equals displacement, but what is the relationship between the volumes of the underwater parts to the overall volume of the main hull, and the overall volume of the cubic contents (including superstructure)? For a submerged sub, it's 100% under water - that's easy. But how a about the Japanese battleship Yamato? Or a modern ultra-large crude carrier like the TI-class supertankers? For those we at least get the difference between unloaded and loaded displacement (67,591 tonnes empty - which is still up there with the largest battleships ever built, and 509,484 tonnes fully loaded - which is stupendous). --Stephan Schulz (talk) 11:56, 8 October 2024 (UTC)
- The fraction of volume under water is equal to the density of the ship divided by the density of the water. Problem is, how do you define the volume of the above water parts? Volume of the fully enclosed space, volume of the smallest convex surrounding (sorry, forgot the proper maths term), volume of the bounding box? PiusImpavidus (talk) 16:38, 8 October 2024 (UTC)
- The mathematical term is "convex hull", but for a ship with a tall mast this is not a reasonable approach. A typical ship design has a relatively small number of relatively small openings, such as hatches and ports, that will be closed under severe storm conditions in order to keep the ship from taking water. This creates a closed surface enclosing the ship; it seems reasonable to me to use the enclosed volume for the total volume, also when the hatches and ports are open. This does not work for an open boat, such as a rowboat, but imagine a custom-made cover of fabric for the boat to keep rainwater out and we have again a closed surface that determines a specific volume. --Lambiam 20:38, 8 October 2024 (UTC)
- Indeed. The background (though not quite scientific) is that I'm currently looking for physics gaffes in ancient German pulp SF novels. One of the problems is that the authors don't quite get the square-cube law, and thus their giant spaceships with (so they think) giant masses turn out to have the density of a puff pastry. I would like to get some comparison data for real ships. So for volume think e.g. Space Battleship Yamato. --Stephan Schulz (talk) 21:06, 8 October 2024 (UTC)
- I did calculate an airship. 2500 m high and 1:8:64 aspect ratio. With 10 cm average hull thickness it can lift a whole village into an earthquake area. With 15 cm it doesn't even fly. (There were other assumptions that may modify the numbers slightly) 176.0.162.62 (talk) 21:18, 8 October 2024 (UTC)
- Indeed. The background (though not quite scientific) is that I'm currently looking for physics gaffes in ancient German pulp SF novels. One of the problems is that the authors don't quite get the square-cube law, and thus their giant spaceships with (so they think) giant masses turn out to have the density of a puff pastry. I would like to get some comparison data for real ships. So for volume think e.g. Space Battleship Yamato. --Stephan Schulz (talk) 21:06, 8 October 2024 (UTC)
- The mathematical term is "convex hull", but for a ship with a tall mast this is not a reasonable approach. A typical ship design has a relatively small number of relatively small openings, such as hatches and ports, that will be closed under severe storm conditions in order to keep the ship from taking water. This creates a closed surface enclosing the ship; it seems reasonable to me to use the enclosed volume for the total volume, also when the hatches and ports are open. This does not work for an open boat, such as a rowboat, but imagine a custom-made cover of fabric for the boat to keep rainwater out and we have again a closed surface that determines a specific volume. --Lambiam 20:38, 8 October 2024 (UTC)
- Surely it will depend entirely on the architecture and materials of each individual ship design? I don't see how there could be a simple formula or whatever relating to all ships. For example, the same design could be constructed using any one of many woods of different densities, or of various metals, and the percentage would be different for each variant.
- Consider also vessels using hydrofoils. {The poster formerly known as 87.81.230.195} 94.6.86.81 (talk) 17:15, 8 October 2024 (UTC)
- That's why I listed two concrete examples. --Stephan Schulz (talk) 20:21, 8 October 2024 (UTC)
- Titanic = 100%, submarines = 100%, Enterprise = 0%. --217.149.171.88 (talk) 17:18, 8 October 2024 (UTC)
- If you exclude your parenthetical (including superstructure) there is a term for this ratio which is reserve buoyancy. That is a redirect and probably a more explanatory article would be freeboard. I've looked for a value for Yamato but just WP's Yamato-class battleship#Armor "...designed with a very large amount of reserve buoyancy..." I don't know what would help for the volume of a superstructure but maybe you could put some limit on it by assuming a cuboidal cow (see block coefficient for different types of ships) and noting that metacentric height must be > 0. fiveby(zero) 00:56, 9 October 2024 (UTC)
- Archimedes Principle: buoyant force (upwards) = volume displaced. For a watertight hull with gunwales (outer walls) above the waterline, you draw an imaginary line across the waterline: the volume of non-water-continuous-with-the-sea that's under that line, times weight-density of water (i.e. times density times g), equals the buoyant force. (To set this as an equation, for simple shapes and approximations you can use areas of triangles/prisms, while for more complex shapes you probably want to use integral calculus.)
- With no other forces (such as lift from hydrofoils or flat-bottom planing), the boat's waterline is determined where buoyant force = its total weight -- that is, its total mass times g. (This is mass that you would measure by weighing on drydock, for example -- it's independent of how you would think about floating on water.) If your ship's total mass is unknown, but you generally know about stuff like the enclosed volume and what kind of materials are involved, then you would consider the wall thicknesses, enclosed space, etc.
- Note that the air inside the enclosed space is often ignored in calculations because there is air outside too -- the air outside provides buoyancy as well, but since an enclosed seagoing ship is mostly filled with air, that cancels out. However, for an airship, the buoyancy of air is the critical consideration. SamuelRiv (talk) 19:16, 9 October 2024 (UTC)
- Oil tankers are almost water density compared to modern cruise ships. 100 cubic feet per (long?) ton is an intermediate density once used for measuring ship volumes. The modern volume ton assumes a similar density that increases 0.02 g/cm³ per order of magnitude. Presumably cause square-cube law makes larger ships weaker per ton of structure. The Empire State Building has a mass of 365,000 tons and volume of 37 million cubic feet for a density coincidentally similar to gross ton and gross register ton but the Twin Towers and Sears Tower used a different structural method and have significantly less density. Sagittarian Milky Way (talk) 20:38, 21 October 2024 (UTC)