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Why Don't Cruise Ships Fall Over

I've pondered this often as I stood on deck 15 or 16 and looked down at the sea. Cruise ships are so tall it really doesn't look like they should be able to stay upright. This time, though, I did some research that I want to share (with those who are interested). I have to admit that I had a bit of a boost because my father studied Naval Architecture as a second career. SPOILER ALERT: this will get a little technical and confusing--sorry.

Like anything else that floats upright, ships need to be stable (that is they need to be able to right themselves if the wind or waves push them over a little). Ships manage this by balancing gravity (pulling them down) and buoyancy (pushing them up). To understand this, it's important to understand the ideas of center of gravity and center of buoyancy.

To find the center of gravity of any object you just need to add up the weights and positions of all of its parts. For a ship this includes the hull, superstructure, furniture, engines, and so forth, but not the people. When you add up all the weights, you should get the whole weight of the ship. When you find the center of gravity, the ship will behave as though all the weight was in a ball at that point. This has two important implications. First, if you're near the center of gravity, you should feel less motion than anywhere else on the ship (the ship's moving around the center of gravity). Second, the downward pull of gravity works exactly the same on a hypothetical ball at the center of gravity as it would on the whole ship.

The center of buoyancy is the same idea except that it's the center of the upward push of the water or more accurately of the hole the ship has made in the water. Gravity is trying to sink the ship. Buoyancy is pushing back to keep it afloat. What Archimedes found out a long time ago was that the weight of the ship will be exactly the same as the water the ship displaces (the water that would have been where the hull of the ship is below the waterline). This doesn't seem right intuitively because the ship is made of steel, which is much heavier than the same amount of water. It works because the ship is mostly empty and air is much lighter than water.

The center of buoyancy is always below the waterline. To be stable, the center of gravity must be above the center of buoyancy. Ships can be made stable because the center of gravity doesn't move relative to the ship, but the center of buoyancy does as the ship rolls (moves from side-to-side). The way the center of buoyancy moves depends on the shape of the hull (the center of buoyancy is the center of the volume of the hull below the waterline). For stability, the center of buoyancy needs to move further in the direction of the roll than the center of gravity does.

Hopefully, an example will make this clearer. Suppose the wind is blowing on the left or port side of the ship. The ship will respond by leaning to the right or starboard side. The center of gravity doesn't move with respect to the ship, but the ship is leaning over, so the center of gravity is leaning over to the right too, trying to pull the ship over onto it's side. If the center of buoyancy leans even further to the right, it will push the ship back upright.

Of course, to make all this work the center of gravity can't be too high up in the ship. Cruise ships do this by putting lots of weight down in the bottom decks where passengers never get to go. So, what's down there? Well, engines, fuel, fresh water, sewage, and so forth. My guess is that the center of gravity of most cruise ships is about midships around deck 4 (the heavy stuff is all down on decks 1 and 2). For cruise ships, designers want stability, but not too much of it. If the ship is too stable, it rights itself very quickly resulting in an uncomfortably choppy motion.

There are two types of hull design that have been found to be stable: deep and narrow or shallow and wide. In the old days, cruise ships were deep and narrow. Modern cruise ships are shallow and wide. The older ships were faster, but more likely to yaw (waggle from side-to-side). Combined with pitch (rocking from front-to-back), this gave them a sickening corkscrewing motion in heavy weather. The shallow and wide design also gives cruise ships access to more (shallow water) ports and saves fuel.

It shouldn't be surprising that ships need to be certified (by their port of registry). This involves testing the design of the ship when it's anchored, when it's moving, and in various possible disasters. Typical types of disasters that have to be planned for include ripping a big hole in the bottom of the ship, having fuel or other liqueds sloshing around in the bottom deck, and having all the passengers run to one side of the ship to look at whales.