What Really Sank The Bismarck?

This is not a reopening of the discussion of whether Bismarck was sunk by gunfire from HMS Rodney and HMS King George V, torpedos from HMS Suffolk, scuttling charges set by the Bismarck's crew, or whether seaman 3rd class Fritz von Spigot forgot to jiggle the handle on the forward enlisted men's head & allowed it to run over. No, this is a discussion of what really happens to a ship to make it sink!

Since Big Gun R/C Warship Combat is all about sinking ships, it is appropriate to have some idea of just what happens when a ship sinks.

Most people are able to grasp the concept that, when you let water into the hull of a ship faster than you pump it out, eventually the ship will sink. What they don't necessarily grasp, is exactly why this is. Intuition generally tells people that, by adding the weight of the water entering the hull to the ship, it gets heavier than what the water can support, and it sinks.

Intuition, in this case, is wrong.

First, we need to define what buoyancy is. Fortunately, science has agreed on a definition that we can all agree on and use: Buoyancy is the force experienced by an object when it displaces a fluid. This buoyancy force will be equal to the mass of the displaced fluid (density multiplied by volume) multiplied by the acceleration due to gravity (the scientific way of saying "weight"). If the weight of the object is equal to the weight of the water that is displaced, it will float; if it doesn't, it won't. Fundamentally, what holds a ship up in good or bad weather is its buoyancy. A ship floats because the volume of water that it displaces equals or is greater than its weight. Or, in other words, the "hole" a ship makes in the water occupies a certain volume, and if the ship weighs less than the water it would take to fill the hole, it will float. Similarly, a hot-air balloon floats because it weighs less than the volume of air it takes up. When water seeps or floods into a ship's interior, the vessel is slowly robbed of buoyancy and, eventually, it will be dragged under by its own weight unless the leak can be plugged.

Another term that's worth of definition is Reserve Buoyancy. This is the difference between the amount a vessel would displace if she were watertight and totally submerged, and the amount she actually does displace at her designed draft.

Figure 1 illustrates a simple object (a cube) floating in water, viewed from or sliced through one side:

Figure 1.
Effect Of Buoyancy On A Simple Object.

Let's assume that each square represents 1 cubic inch (1 in3). Remember that we're working in 3 dimensions here, not 2, and this is a cube. That means that, while you can only see 4 of them (shown in gray), there are 4 more "rows" behind what you can see, so there are 16 in3 of the cube below the water line. This is the amount of water that the object (cube or ship) has displaced, or taken the place of: 16 in3. As noted, "cubic inches" is a measure of volume, but displacement is expressed as weight - specifically, the weight of the water that was displaced by the object. We know how much water was displaced: 16 in3. Fresh water has a density of 62.410 lbs/ft3 which can also be expressed as 62.410 lbs/1728 in3 (12 in. in a foot; 123 = 1728) or 62.410 * 16 ounces (oz) = 998.56 oz./1728 in3, or 0.578 oz/in3 - let's just call it 0.6 oz/in3, to keep the numbers simple. So, if 1 in3 of fresh water weighs 0.6 oz, then 16 in3 of fresh water weighs 0.6 * 16 = 9.6 oz. That's the displacement of our cube, 9.6 oz. That's also the weight of the cube, if it's floating (which it is).

Green blocks above the waterline represent reserve buoyancy. The total volume of space occupied by our cube is 64 in3. 0.6 oz * 64 = 38.4 oz, which is the total amount of water that the cube would displace if completely submerged. Since it already displaces 9.6 oz, 38.4 - 9.6 = 28.8 oz, the reserve buoyancy of our cube.

What's important to understand here is that, while each square (cube) is equivalent to every other one in terms of volume, they are not equivalent to one another in terms of weight. Depending on what occupies each cube (square), the weights will be different and the "ship" will float or sink depending on what occupies each space represented.

Let's say this cube represents the hull of a ship, structure only, with no equipment installed. Let's add another 9.6 oz of "equipment", as shown in Figure 2 and represented by purple squares:

Figure 2.
Adding 9.6 oz To The Object.

Note that it doesn't matter where within the object we place the additional 9.6 oz - the total weight (downward force) of the object is now 19.2 oz, which is the amount of water that the cube shell plus its "equipment" displaces. 8 squares are now below the water line. The 9.6 oz of "equipment" will occupy 8 in3, just for the sake of simplicity. There are still 4 "rows" behind the visible one, so there are now 32 in3 below the water line. If water still weighs 0.6 oz/in3, then 0.6 * 32 = 19.2 - the object displaces 19.2 oz. Reserve buoyancy = 38.4 - 19.2 = 19.2 oz, which is now our reserve buoyancy.

Let's suppose we punch a hole in the outer shell of the object and let water into the hull to a 1" depth. This is illustrated in Figure 3.:

Figure 3.
Add 1" Of Water."

Note that the "equipment" displaces water, so only the outer 2 squares "flood". 2 * 4 (the "hidden rows") or 8 in3 of water are now inside the vessel - this water is no longer displaced.. We have not added any weight to the vessel - we have reduced the amount of water that is displaced by 8 in3, or 4.8 oz. Since we had 19.2 oz of reserve buoyancy available prior to admitting the water, the water taken on reduces the reserve buoyancy by 4.8 oz to 14.4 oz.

We should be able to reduce displacement by another 14.4 oz (24 in3) or 1.5" of depth) before sinking, as shown in Figure 4.:

Figure 4.
Another 14.4 oz. - Should Sink, Right??

At this point, all reserve buoyancy is gone, having been replaced by water which is no longer displaced by the hull. The ship still displaces 19.2 oz, and there is still 19.2 oz of buoyancy, so we are still in equilibrium. The next drop of water it takes on should be the one that sinks it!

Figure 5.
On The Bottom - Sunk!

Here we are, on the bottom. That one more drop of water decreased the buoyancy of the vessel beyond what the reserve buoyancy could make up. The inrush of water over the gunwales quickly filled the void space remaining and it plummeted to the bottom. There, with all of the void replaced by water, we have a considerably different picture than at the surface. Notice now that the only thing that displaces any water at all is the 8 in3 of equipment in the bottom. Although the equipment weights 9.6 oz, it displaces only 4.8 oz of water (we're ignoring the displacement of the hull structure for this exercise). So now we have displacement of only 4.8 oz (the weight of the water that is displaced by the now-submerged vessel) while the vessel itself still weights 19.6 oz - just like it always has! If buoyancy is less than weight, it sinks!

Let's look at a modified version of our vessel, with a redistribution of weight:

Figure 6.
Extra Volume Of Equipment, Fitted Up High.
Figure 6 shows a similar cube, but instead of 9.6 oz of equipment in the bottom, occupying 8 in3, there is 4.8 oz the bottom occupying the same volume, plus another 4.8 oz the water line that occupies 16 in3. The weight is the same; the displacement is the same, and it floats on the same waterline. It's still going to take the same reduction in buoyancy (19.2 oz or 32 in3 of water) to sink it. However note that the water level inside is 1/2" higher than in Figure 4, due to the increased internal volume taken up by equipment. When that next drop arrives, putting it "over the edge", there will be less of an inrush of water, because there's less void space to fill - giving the appearance that the ship with more volume of equipment is sinking faster. The truth is that, if both ships are identical in terms of displacement and reserve buoyancy, and the rate at which they fill with water is the same (same-sized holes in the same locations) they will approach the point of sinking at the same rate. Once that point is reached, however, the ship with the greater volume of equipment inside will appear to sink more slowly, due to the greater inrush of water into the ship with more void space. Or, maybe the ship with greater internal void space will take longer to fill that void, delaying the final plunge? You be the judge.

Now, let's get back to the Bismarck.

The Bismarck displaced 50,900t (tonnes; metric tons; 2204.6 lb) when it set sail from Norway. Since it did sail, & not sink, we know that it also weighed 50,900t. It was built mostly of steel plate, with a density of 489.84 lb/ft3.

50,900t * 2204.6 lb / 1t * 1 ft / 489.84 lb = 229,083.25 ft3 of steel.
Sea water has a density of 64.25 lb / 1 ft3:

229,083.25 ft 3 * 64.25 lb/ft3 * 1t / 2204.6 lb = 6676.31t.
6676.31t is the current displacement, in tonnes, of the Bismarck today - that's the amount of water that the steel (all that's left) displaces. There are no more void spaces, only steel (discounting the effects of corrosion). The only part of the ship that displaces any water at all is the solid part. If you could manage to pick up all of the pieces, and reassemble the ship on the ocean floor, it would weigh 50,990t, but it still wouldn't float because it displaces only 6676t.

To be buoyant (i.e., to float) an object must displace more water than it weights. The Bismarck weighs 50,900t, but displaces only 6676t. Therefore, the cause of the Bismarck's sinking is its displacment was reduced to less than its weight.

Return to On The Ways

 NTXBG Home