Buoyancy and Stability (basic, part 1)

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Why do boats & ships float? Why do they stay right-side up, or why do they capsize? There are some fairly simple laws of physics which govern how vessels behave, and to be good sailors we should understand all this.

Here is a sailboat which has lost both buoyancy and stability. Good thing the sailors are wearing life jackets!

Buoyancy first... why do vessels float (or not)? Anybody who has picked up a container of it knows that water is heavy. If you take a given container, gallon or liter or whatever, and fill with water, of course it becomes much heavier.

To say more precisely, water has a lot of MASS for a given amount (size of container)... or you could say that it has greater DENSITY (link to wikipedia) than many other things we're familiar with... this is the most accurate statement, and it explains things better. After all, our container was full of AIR before we filled it with water, and water has a greater density than air. A bigger bucket full of water would be heavier, but that would not mean that the water in the bgger bucket has a greater density than the water in a smaller bucket.


 

RELATIVE DENSITY- the core of a star is more dense than a brick, which is more dense than water, which is more dense than air, which is more dense than helium...

So far this is common sense. A lot of science -IS- common sense, only put into terms that we can use with math to figure out how much or how little or how fast etc etc. And science has to go beyond what we "know" as common sense from our every day experiences. For example, you might think it's silly to point out that a bucket full of air weighs less than a bucket full of water; our common sense tells us that the density of air is nothing (and that's true, relative to the air all around) but you could not design an airplane using this "common sense."

"Relative Density" is the key to understanding buoyancy. Helium is less dense than air, so a helium balloon is buoyant... in air! If we released a helium balloon on a planet with hydrogen gas as it's atmosphere, that balloon would fall to the ground because helium is more dense than hydrogen!

Is a boat like a balloon? In some ways, yes. It floats in air instead of water... wait a minute, a balloon floats on water too, if it's placed there... unlike a boat, a balloon will rise upward out of sight! Does it go up forever? No, it stops going up once it gets to an altitude where the air density matches that of the material inside the balloon... but doesn't a boat float on top of the water because it is less dense than than the water, but more dense than the air? So a boat rises too, as long as the relative densities of the materials contribute to the force of "buoyancy." Therefor, a balloon is more like a boat than we thought!

BUOYANCY is the force produced by difference in density between an object and the medium surrounding it... an iron weight actually weighs less when immersed in water, although it's MASS remains the same...

In this diagram, we see a 7 pound iron weight lowered into a bucket of water. We've cleverly put a spout into the side of the bucket, and filled it right up to that spout.

As we lower the iron weight into the water, it pushes a volume of water aside. The water level in the bucket starts to rise but instantly runs out the spout. The volume of water pushed aside and out, in other words DISPLACED, is the same as the volume of the iron weight. But because of the difference in density between water & iron, that volume of water weighs only 3 pounds. The force of buoyancy reduces the apparent weight of the iron, but not by enough to make it stay afloat.

In the next diagram, the iron weight is hollowed out. Air is less dense than iron (duh) so now it weighs less, and it floats!

Does it float because there's air inside?

Yes and no... if the weight of the water displaced were less than the weight of the hollowed-out iron,  then it would still sink. But we have not reduced the volume of the iron weight, just it's mass. If we removed 4 1/2 pounds of iron from the middle, then it will now float because the buoyancy can produce enough force to support it against gravity.

Now let's take a big look at buoyancy and how we apply the physics to real vessels. We have a lighthouse, two ships, two submarines, a dirigible, and a brick.

Of course, the lighthouse is on land, so no worries there. We have two warships, one of which is fully loaded with fuel & ammunition, so (as we'd expect) it is lower in the water... it DISPLACES more because of the additional weight. At the advanced level, we will learn how to calculate safe loading & changes in draft & effect on stability.

We also see two submarines. One is very near the surface, maybe the captain is looking thru the periscope. The other is much deeper. Both are held up by the force of buoyancy, carefully balanced against the weight of water in their ballast tanks.

Yes, the US Navy had airships (link)... may have more in the near fuure. What happens to an airship (with regard to bouyancy & altitude) as it burns fuel?

The brick is sinking to the bottom. Because that's what bricks do.





Now for STABILITY... this is the tendency of a vessel to return to upright. There are several ways to measure stability, such as how far over a vessel can heel (lean or tip) before losing stability & capsizing, or the leverage exerted at a certain degree of heel (link to wikipedia).






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You can see why we need to understand buoyancy to understand stability. You can also see that stability must not be taken for granted. Beginner sailors are often nervous when their boat leans over. Their "common sense" is telling them that they are about to have a disaster... but floating vessels follow different rules and given a reasonable level of skill & attention, they're fine. 

However there have certainly been ship capsizes (link to news) and they are always a major disaster!! The fact that Navy ships rarely suffer this problem is a testament to the training & skill of Navy sailors.

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Another of those "common sense into science" pieces... we easily grasp that putting a heavy weight into a boat makes it lower in the water. We can also use common sense to see that if we put the heavy weight low down, the boat will be more stable; if we put the weight up high, the boat will be less
 stable.

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To understand this better, and to get to the point of being able to use a little math to figure out HOW MUCH (remember, it's supposed to be science), we need another physics concept... the 'center of gravity' which is the same thing as the Center Of Mass (link to wikipedia). This is how gravity "knows" if the weight is placed high or low on the vessel. Gravity pulls down on everything, but instead of calculating the force on every single part of the boat and the leverage it produces (possible but tedious) we use a single point at which all the weight of the boat & everything in it, or attached to it,  is focused.


The boat with the weight placed high is less stable, it produces less force to push itself back to level... but how much less? Here once again we see the geometry of the forces of buoyancy & gravity, and the effect of the change in Center Of Gravity by placing the weight up high. The length of the Righting Arm is proportional to the force pushing the vessel back to level.

What would happen if the Righting Arm was the other way around, with gravity pulling down on a point further away from center than buoyancy is pushing upward? Could moving the weight forward or aft on the vessel (instead of up or down) have an effect on it's stability?

Also obvious with common sense- if we move a heavy weight as LOW in the vessel as possible, that will maximize stability. Here is a video of a stability test (link) of a small ocean racing sailboat, the test is an important safety procedure much like our own Capsize Drill!







Review- we've looked at BOUYANCY and the principle of DISPLACEMENT, and the physical properties of DENSITY along with it's corollary Relative Density, the physics term CENTER OF MASS, and now we've begun to put these all together so that we can have a better-than-common-sense understanding of STABILITY. You can see from some of the diagrams that there are more terms we have not yet covered, but we have enough to understand what we need to become good sailors.



Our small boats depend very much on placement of crew & skippers weight. Sometimes in light wind they heel the "wrong" way. Is this harmful?










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Sailing students often hear their instructors tell them it's important to keep the boat from heeling. Once you get used to it, heeling is fun! So why not just let it go?

There will be more lessons on stability later!

(link to GLOSSARY)

... posted by Assistant Coach Douglas King