Sideways

My first ride out along the Lachine Canal had to be shortened when my ankle started complaining so I stopped by the caboose/cantine where the path crosses the canal at Avenue Dollard.

In any case, it was nice to be near any body of water as I pondered my imminent return to work on my ship after four months of recovery.

A large portion of the work conducted by the Coast Guard is deploying, recovering and maintaining aids to navigation such as buoys. So, it was with a professional and critical eye that I regarded the spar buoy near the bridge. (The buoys in the Lachine Canal are maintained by Parks Canada and not the Coast Guard.)

These buoys are made of plastic with polystyrene inside and some added weight in the bottom to act as ballast. They are designed to float upright with about two thirds of the body of the buoy submerged. However, the trick is to determine how much weight to add to the bottom of the buoy to get it to float right otherwise it will lean over as in the picture above.



Here is where Math class comes in. You need to determine how deep in the water the buoy will float just by its own weight alone and then determine how much more weight it will take to float the buoy to the right depth. In order to do this, you will need the dimensions of the buoy such as this one from Tideland:

From here we go back to Archimedes Principle that states that an object immersed in water will displace a volume of water equal to the object's weight. If the volume of the object compared to its weight is greater than the volume of water of the same weight, then the object will float.

Now, since the body of the buoy is shaped like a cylinder, we can work out the amount of the buoy that will be submerged due to its own weight.

From the information given in the specifications, the weight of the buoy is 39kg.

The formula for the area of a circle is:  Area = Pi x R x R. For the cross section of our buoy this works out to: 3.14 x 18.4 x 18.4, which comes out to 1,063.6 square centimeters. Since, a cubic centimeter of fresh water weighs 1 gram, then submerging the buoy 1 centimeter will displace 1.0636 kg of water.

So, given the weight of the buoy of 39kg, the buoy will be submerged 39/1.0636 or 36.7 centimeters in the water.

However, the length of the body of the buoy is 124 centimeters and we want to submerge the buoy up to 2/3 of its length, which would be 83 centimeters. The difference between 83 and 36.7 is 46.3 centimeters, and since each centimeter further into the water displaces 1.0636 kg of water, the weight needed to add to the bottom of the buoy to float it properly is 46.3 x 1.0636 or 49.2kg.

The reason buoys are designed to float properly only by adding weight to them is because they are anchored to the bottom, usually with chain. If the buoy floated properly by itself then it would sink too low in the water once the chain was attached to it. In addition, buoys can be placed in varying depths of water so that the weight of the submerged chain pulling down on the buoy will vary with the depth of water.

In some cases, where the water is deep enough, the weight of the chain is sufficient to float the buoy properly. However, in shallow water, there is not enough chain weight to submerge the buoy the correct amount so we have to add additional weight, which we call a counterweight.

So, in places like the Lachine Canal, if you see a buoy leaning over sideways it is because it has lost its counterweight or the person who put it out there in the first place didn't do his job properly!