In the third and fourth parts of the Sewol posts I will explore the basic principles of vessel stability. In other words, I will attempt to explain, hopefully without getting too far into the weeds (and they can get pretty deep), 1) why ships float, and 2) why they remain upright −and sometimes don’t. I may lighten the tone a bit. Certainly not out of any disrespect for the victims of this tragedy, but because this part of the series is all about math and physics and I can just imagine your eyes beginning to glaze over already. But this is important to understanding what happened and I’d like you to read it. Please note that the numbers and calculations that are used here are purely for illustration and do not bear any relationship to the Sewol or any other ship.

First let’s look at the question of why ships float?

For this discussion we are going to use the metric system as opposed to our system (whatever it’s called) and fresh water as opposed to sea water because, as you will see, it makes the math a whole lot simpler. We can even avoid fractions. In fact, it’s so simple you can put your calculators away for the time being.

Some basic metrics: One cubic meter of volume displaces one metric ton of fresh water. Simple right? That’s 31.315 cubic feet displaces 2,204 lbs. of fresh water. See why we’re using the metric system?

Let’s assume we are gifted 5,000 metric tons of steel with which to build ourselves a ship. It’s left in our front yard in the shape of a large cube with a volume of 3,000 cubic meters. Delighted with our gift we take it down to the nearby fresh water harbor, walk out to the end of a pier and toss it off to see if it will float.

Nope! Big splash and straight to the bottom. What happened? Well, our cube had 5,000 tons of mass (gravity) pulling it down, and 3,000 tons of displacement, or buoyant force, pushing it up (3,000 cubic meters of volume equals 3,000 metric tons of water, remember? It’s in the paragraph you just read). So we had 2,000 tons more weight or mass (G) pulling our cube down than buoyant force (B) pushing it up and our cube sank.

So we fish the thing out of the drink and haul it back to our front yard, climb inside and hammer it out until our 5,000 ton cube has a volume of 7,000 cubic meters. Back to the pier we go with our cube which is now larger but weighs the same, and we toss it over. Now what happens? Big splash again and −

Congratulations, we’ve made our first ship. It’s not very useful but it floats, and for a ship, that's important. But why does it float? It's still 5,000 tons of steel. Well, the first thing we notice is that although it didn’t sink to the bottom it’s not sitting on top of the water either. It’s partly submerged. How far is it submerged? Well it turns out that it submerged until it displaced exactly its own weight, 5,000 tons (5,000 cubic meters) of water. That’s a rule −a principle of physics.

You remember learning how Newton discovered gravity when he got hit on the head by an apple while sitting under tree, right? Did you believe that? Me neither, but it's a good story? Well anyway, Archimedes discovered something also. A lot of things actually. But one of the things he discovered that is important to our discussion is that he could determine the volume of irregularly shaped objects (including himself) very accurately by getting into his already full bath tub and then measuring the volume of water that his body displaced out of the tub. Mrs. Archimedes may not have been happy with this but Archimedes was absolutely ecstatic. So much so that, as the story goes, he leaped from his tub and ran naked into the streets of Syracuse (Greece − not New York) yelling “eureka!” No doubt he was excited because he saw this as his big chance to have a principle named after himself.

His principle, Archimedes’ Principle, is stated in his treatise

Next time we’ll look at the question of how ships remain upright. Not quite so easy but stick with it.

First let’s look at the question of why ships float?

For this discussion we are going to use the metric system as opposed to our system (whatever it’s called) and fresh water as opposed to sea water because, as you will see, it makes the math a whole lot simpler. We can even avoid fractions. In fact, it’s so simple you can put your calculators away for the time being.

Some basic metrics: One cubic meter of volume displaces one metric ton of fresh water. Simple right? That’s 31.315 cubic feet displaces 2,204 lbs. of fresh water. See why we’re using the metric system?

Let’s assume we are gifted 5,000 metric tons of steel with which to build ourselves a ship. It’s left in our front yard in the shape of a large cube with a volume of 3,000 cubic meters. Delighted with our gift we take it down to the nearby fresh water harbor, walk out to the end of a pier and toss it off to see if it will float.

Nope! Big splash and straight to the bottom. What happened? Well, our cube had 5,000 tons of mass (gravity) pulling it down, and 3,000 tons of displacement, or buoyant force, pushing it up (3,000 cubic meters of volume equals 3,000 metric tons of water, remember? It’s in the paragraph you just read). So we had 2,000 tons more weight or mass (G) pulling our cube down than buoyant force (B) pushing it up and our cube sank.

So we fish the thing out of the drink and haul it back to our front yard, climb inside and hammer it out until our 5,000 ton cube has a volume of 7,000 cubic meters. Back to the pier we go with our cube which is now larger but weighs the same, and we toss it over. Now what happens? Big splash again and −

**it floats!!**Congratulations, we’ve made our first ship. It’s not very useful but it floats, and for a ship, that's important. But why does it float? It's still 5,000 tons of steel. Well, the first thing we notice is that although it didn’t sink to the bottom it’s not sitting on top of the water either. It’s partly submerged. How far is it submerged? Well it turns out that it submerged until it displaced exactly its own weight, 5,000 tons (5,000 cubic meters) of water. That’s a rule −a principle of physics.

You remember learning how Newton discovered gravity when he got hit on the head by an apple while sitting under tree, right? Did you believe that? Me neither, but it's a good story? Well anyway, Archimedes discovered something also. A lot of things actually. But one of the things he discovered that is important to our discussion is that he could determine the volume of irregularly shaped objects (including himself) very accurately by getting into his already full bath tub and then measuring the volume of water that his body displaced out of the tub. Mrs. Archimedes may not have been happy with this but Archimedes was absolutely ecstatic. So much so that, as the story goes, he leaped from his tub and ran naked into the streets of Syracuse (Greece − not New York) yelling “eureka!” No doubt he was excited because he saw this as his big chance to have a principle named after himself.

His principle, Archimedes’ Principle, is stated in his treatise

*On Floating Bodies*that describes buoyant force.**The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.**That’s it, Archimedes’ Principle. And it explains why ships float. It follows from this principle that once our 7,000 cubic meter cube was submerged to the point where it displaced its own weight (5,000 metric tons) of fresh water (5,000 cubic meters) it stopped sinking and floated. Easy, right?Next time we’ll look at the question of how ships remain upright. Not quite so easy but stick with it.