From the 1905 online book,
Problems in Woodworking, is a chapter about canoe paddles. Included is a diagram of a standard beavertail paddle with pear grip showing all the relevant specs for width, length, and thickness. Interesting to note the thinning of the circular shaft (1-1/8th inch) down to 1 inch at the throat of the blade. I generally make the shafts on my paddles 1-1/8th inch thick as well but never really thinned the throat like this plan shows. Logically I wonder if it would weaken the paddle right at this location where the large blade area of this design would presumably concentrate the most force.
Paddle Plans
The most force is not at the throat as you suggest, the most force is always wear the fulcrum resides, the location of the hand on the paddle, in this case. I measured my nephew's new bending branches Loon paddle and it, too, is tapered at the throat. Not sure what benefit this presents. Something else I've noticed in researching paddle design is that several online sources show a paddle that tapers from the center out to the edges of the blade all the way down to the tip, as your picture shows from the old book, but I have never seen a paddle made like this. Again, the BB Loon I just happened to be holding right now is nearly 100% flat across its blade width beginning about 5 inches below the throat. Thanks for the information, BTW, it's been very helpful as I prepare to build my first paddle.
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