Friday, 8 December 2017

Displacement, Weight, Capacity, and that Sinking Feeling

Recently when asked about one of my canoes and how much it will carry I responded with the numbers I usually give, the boats displacement at various sinkages. I give the displacement at three different depths. For the canoe that I am currently finishing up; if the boat is loaded to sit two inches [5 cm] down in the water it displaces 109 pounds [49 kg.] (for reference approximately, weight of boat plus large pack), at 3” [7.6 cm] it will displace 193 pounds [87 kg] (boat plus 150 lb.[68 kg] paddler), at 4” [10.2 cm] it displaces 284 pounds [129 kg].

None of these numbers tell you what the boat weighs, this boat has not been weighed yet so let’s use a nice round number that is in the right ball park, say 40 pounds [18 kg]. The canoe weighs the same in all three of the instances above, regardless of loading. Displacement varies depending on what you put in the boat, plus the boats weight. Keep this in mind when adding gear to your boat, something that those who fish seem most prone to do, every bit of gear you add subtracts from the live weight (you, passengers or fish it should carry). If a boat weighs 40 lbs.  [18 kg] you weigh, say 150 [68 kg]and you gear for a day trip, including yourself, a paddle, PFD, other safety gear and lunch weigh 7 pounds [3.2 kg], that means that a boat will need to displace 197 pounds [89 kg] to float you and your gear, you can then based on the information above see that this boat is going to float about 3” [7.6 cm] into the water.  

Displacement is simply the weight of the volume of water that the boat must push out of the way to float based on the weights as listed above, fresh water weighs 62.4 pounds per cubic foot, salt water weighs 64, or 1,000 kg/m3 for fresh and for salt water 1,024 kg/m3.  Think of it as the size of the hole you make in the lake or river, in the case of the boat in the example it is a cedar/epoxy lined hole.
To make anything float the object that is to float must displace more than it weighs plus what it is carrying, which is why a flat piece of steel sinks, but if you beat it into a boat like shape it will float. For the example above, the boat, and it does not matter what shape it takes, must displace 3.2 cubic feet (.09m3) of fresh water (3.1 of salt water) to support the load. The shape will not affect the amount of water that must be displaced the shape will affect stability and how the boat moves through the water but not the volume of water displaced.

That brings us to capacity, I use the Transport Canada method as published in TP1332E Construction Standards for Small Vessels as found in section where the very simple method to find a canoes displacement, is the point where the vessel has 178 mm [7 inches] of freeboard, this is referred to as the ‘recommended maximum gross load’. This is measured at the lowest point of the sheerline.

Freeboard is the distance between the water and the top edge of the hull, the sheer being the top edge of the hull. That number for the boat used for illustration purposes in the first paragraph is 172 kg. [379 lbs], it is that simple, but this only applies to canoes, and yes what constitutes a canoe is defined in an earlier section of the publication one that sets the length to beam ration which changes with the canoes length, (4.25 m or less max beam 1/3 of canoe length, 4.25 to 4.9 m - 1/4 of length, over 4.9 m – 1/5 of length) additionally it sets the maximum transom width at 45% of the canoes width. Different boat types naturally have their own standards, and these are further divided based on length and whether they are over or under 6 meters [19.7’].

Another number used is the pounds per inch immersion or PPI, for those using metric terms kg/cm, the number given is based on the boat floating on its designed waterline, this is simply the waterline used in the design drawing. For the boat being used as an example it was 4” [10.2 cm] at which point the boat had a PPI of 96 pounds which is 17 kg/cm, when the boat is floating at this depth it will take 96 pounds to sink it one inch or 17 kg to sink it one centimeter. Those of you who look at the numbers in the first paragraph will notice how this does not match up with the numbers given. The reason for this is that the number changes with the shape of the hull so it will different for nearly all sinkages (unless you have a boat that is box shaped), but it does give a good indication of what happens as you load the boat. For information’s sake this boat would displace 502 kg (1100 lbs.) to the point at which the water reaches the sheer.

The above numbers show you there are some boats that are sold as power canoes that are in fact small power boats from a legislative point of view, and may have had their capacities and horsepower calculated differently. Unlike power boats the horsepower/kilowatt ratings for canoes are selected from a chart based on boat length and not found by calculation. 

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