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Stability Diagram

In these diagrams, the shape is exaggerated. 

The first 2 diagrams  (A & B) show that the flat bottom canoe is more difficult to tip in calm, flat water.

Diagram C show the idea that the round canoe won't tip as much when riding the side of a large wave

Water in the round bottom canoe will be deeper along the centre line than the flat bottom canoe.

When the canoes with water, tip, the water in the flat bottom canoe will cause a greater shift in the centre of gravity of the water, and the momentum will increase the tendancy to tip