Home Leverage Canoes and Paddles Works Cited About

Buoyancy

[bui-uh n-see]

noun
  1. the power to float or rise in a fluid; relative lightness.1
  2. the power of supporting a body so that it floats; upward pressure exerted by the fluid in which a body is immersed.2
  3. (In science) The upward force that a fluid exerts on an object that is less dense than itself.3

What is a Fluid?

To understand buoyancy one must first have a basic understanding of what a fluid is. A fluid is in its liquid state. Liquids are in the state of matter in between gasses and solids, where the molecules are closely packed, as in a solid, but free to conform to the shape of their container. It is important to note however that a liquid will not always fill its container, creating an obvious surface. If you have seen water come from a tap, you have seen a fluid in action.

What is Buoyancy?

Buoyancy is what allows an object, in our case a canoe, to float in a liquid. But why does a rock sink while a piece of wood floats? Simularly why does an aluminum canoe float when a metal car sinks?

Buoyancy is dependant upon both the density of the object and the density of the water. Mathmatically, in order for an object to float, ρobject ≥ ρliquid where ρ is density, which is equal to the mass (m) divided by the volume (V). Likewise if ρobject is greater than ρfluid the object will sink until the two densities are equal to each other. This is one of the ways some objects, such as submarines, can sink to a certain depth before just hovering there.

Looking back to our example of the canoe, we can now determine why canoes float. As the mass pushes down on the the bottom of the boat water is displaced by the canoe. Once the mass of the water displaced is equal to the mass of the canoe plus the mass of what is inside the canoe the canoe will reach a point of static equalibrium, where it does not sink further nor float higher.

Just for fun, lets determine the depth of water I would need in order to float myself, my partner, my canoe, and my gear in. We will have to make some assumptions, firstly lets assume I have a canoe that is a rectangular prism, 4 meters long, 0.5 meters tall, and 0.5 meters wide. Secondly we will assume that my gear plus the canoe weigh 55 kilograms and my partner and I weight a total of 145 kilograms. The weight of water is 1,000 kilograms per cubic meter.

Mass Volume Density
Water 1,000 kilograms 1 meter3 1 kg/m3
Canoe 200 kilograms 1 meter3 0.2 kg/m3

One fifth of our canoe will be submerged. Since the length of the canoe and the width of the canoe create a constant displacement only the depth the canoe is submerged will change.

(l*w*hwater) = 0.2(l*w*hcanoe)
4.0m*0.5m*hwater = 0.2(4.0m*0.5m*0.5m)
hwater = 0.2(1.0m)/2.0m hwater = 0.1m ≈ 4 inches

These numbers make sense, generally a properly loaded and well guided canoe can make it through 6 inches of water without touching bottom. Our example is not perfect, but it is a reasonable mathmatical model.

Images on this page from R.D. Knight 4