Why Buoyancy is Imaginary

Roger Long

It is commonly believed that boats, ships, and other floating objects are kept from being pulled under the water by a mysterious force called buoyancy. People read in text books that, whenever water is displaced, the space inside the hole the object makes in the water will develop an upwards force equal to the weight of the water that has been pushed aside. This is an illusion. In nearly four decades of designing boats, researching ship stability and analyzing stability failures, I've had plenty of chance to discuss buoyancy forces with a wide range of people. It is amazing how few ask what causes this upwards force and how many just believe that it is there because a text book said it was.

To understand why buoyancy is an illusion, we first have to think a bit about gravity. We see gravity as the constant pull of objects towards the center of the earth. It takes something to hold an object up against this force. If you don't think so, hold a large pile of books out in front of you at arms length until you finish reading this.

Let's look at a boat floating in still water: If something doesn't hold it up, it will just sink down to the bottom. There is no rigid connection to the earth. Do you see any energy forces here, any hidden engines, hamsters running around in little wheels? No, there is nothing but air, the boat, water, and gravity. We can forget about the air. All it does is exert enough pressure on the surface of the water, through its weight, to raise the boiling point high enough that the water doesn't start drifting away in vapor making the whole discussion pointless.

Here is another situation in which there is just weight and gravity: This is a balance scale with two 10 pound weights on each side. It remains level as long as only gravity is acting on it and the weights on each side are equal. If we now remove one of the weights from the left hand side, that end rises. Most people, if asked what happened, would say that the left hand end went up because gravity pulled the heavier right end down. You wouldn't say that the left end went up because of some mysterious force called "Removancy". However, if you were in a thick fog and all you could see was the left hand end of the scale and were trying to hold it down, you might well think of this 10 pound pressure as a force and even give it a name. This would just be a name for something that gravity is doing. The buoyancy of floating objects is a balance of gravity exactly like the scale except that the mechanisms are harder to understand and the pivot and the other end of the scale are hidden in a fog of complex fluid connections. Gravity, acting on the water, creates pressure. Seawater weights 64 pounds per cubic foot. One foot below the surface, the water pressure is therefore 64 pounds per square foot. Two feet below the surface, it is 128 pounds and so forth, all the way to the bottom, increasing 64 pounds for each 1 foot increase in depth.

Now take a 1 foot square box and put sand in it until is weighs exactly 32 pounds. Put it in the water. It will sink half way. The water pressure half a foot below the surface is 32 pounds, exactly the weight of the box. The pressure on the sides isn't pushing up or down. There is one square foot of bottom with 32 pounds per square foot of water pressure on it so the upwards force created by gravity pulling down on the water and trying to push it into the hole the box makes in the water is exactly equal equal to the weight of the box. This is simply a gravity balance, exactly like the scale, except that the beam and pivot are not needed because the two forces created by gravity are pushing in opposite directions. If you look back at the scale, you will see that all the beam and pivot do is reverse the direction that gravity acts when one end is heavier. The liquid nature of water does the same job.

NOTHING is happening inside the hole that the box makes in the water. The hole simply removes or displaces the weight of water in the same way that fingers took one of the weights off the scale. Gravity then does the same thing it does on the scale, it tries to seek a balance. It takes a thumb on the scale to return the beam to level and hold it there. That thumb is the weight of the floating object.

These principles are the same for all shapes of objects. The math and visualization just get more complicated. They also apply equally to submerged objects. If the top of our cube is 1 foot under water, there will be 64 pounds of downwards force, due to the pressure, on the top. There will be 128 pounds of upwards force, also due to the pressure created by gravity. The difference is 64 pounds, exactly equal to the weight of water displaced. Whether the cube goes up or down depends on how much weight is in it.

Although nothing is happening inside the hole that floating objects make in the water, complex mathematical facts make understanding the shape characteristics of the hole vital to analysis of the buoyancy and stability of floating objects like boats. It turns out that the sum effect of the pressure, in all it's varying amounts and directions, will always be exactly the same as if the space inside the hole were developing a uniform upwards force. It creates an exact mirror gravity image of what you would have if you filled the hole with water, froze it, (pretending for the moment that ice doesn't expand as it freezes), turned it over, and lifted it up in the air. This accident of geometry makes it much easier to pretend that the space in the hole is creating an upwards force than to calculate all the complex pressure effects on the surface. We have adopted this short cut because it gives us exactly the same answers when we set about to predict the behavior of objects in water. Like the person struggling to hold the end of the scale down in the fog, we don't see the rest of the mechanism. We've therefore given this upwards force a name, "buoyancy". Over the years, people have come to think of it as real. Since this illusion doesn't effect the accuracy of the answers they get with their calculations, in a way, it is real. If you want to understand if fully however, you have to recognize that it is just gravity at work, acting on the other end of the scale that you can't see.

Next: Center of Gravity