A scale model sailing ship ballasted down to the same waterline as the full size ship will need a non scale very deep keel to stop it capsizing. This seems odd. For simplicity assume the full size ship has one mast and one square sail. The hull, beam, mast and yard are all 10m long. (Not a pretty ship!) The sail area is therefore 100 sq m. Then build a half scale model. The hull is now 5 m long but the sail area is only 25 sq m (5m mast x 5m yard). So the model should be more stable than the ship. But the hull, being three dimensional, has gone down not by the square root but by the cube root. So despite the big reduction in sail area the hull has shrunk even more. Hence the need for a deeper keel. Is this right?
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