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The answer has to do with materials science, aerodynamics, and firefighting. On the materials side of the equation, wetting the sailing canvas commonly used in the "Age of Sail" caused the weave of sailcloth to tighten, resulting in a stiffer and flatter sail. Newton's laws and Bernoulli's principle come to play in terms of physics and aerodynamics.

From a Newtonian point of view, a moving air mass is a force (F=MA) acting upon a sail. By applying force to one side of a sail, a vessel is caused to move in a complimentary direction (with the wind). The flatter a sail is, the more uniformly and efficiently an applied force can act in one direction. The more curved a sail, the more perpendicular force that will be converted into transverse (less-desired) force. In essence, the more the curve, the less the amount of force that will be applied in the desired direction of travel. So, a flatter sail is more efficient...until Mr. Bernoulli steps into the picture.

A sail is also an airfoil in some aspects relative to the wind, so Bernoulli's principle tells us that an airfoil effect also impacts the efficiency of a sail. When a sail is moving through the wind, rather than merely being pushed along, it is in some respect flying through the wind the way an airplane wing flies. If a sail is slightly curved, this airfoil effect can be created, and in some circumstances, the resulting "lift" can have a greater effect on speed of travel than mere force of air mass pushing against a sail.

So, the ideal cloth sail, will be as flat and stiff as possible to maximize Newtonian physics, while still having enough curve to maximize Bernoullian aerodynamics. Although it is believed sailors of the day didn't understand the science behind the value of wetting their sails, they certainly did understand the practical benefits of doing so.

This brings us to the final notion, that of firefighting. As a good many of the ships in that age were subject to attack (war, piracy, etc.), and all were constructed out of flammable materials, fighting fires was a concern. Fires that broke out could threaten masts, rigging, sails, and even the vessels themselves. One of the added benefits of wetting sails was the idea that they were then less prone to damage from fire. It was also common practice to hang buckets of water in the rigging, so that sailors could ladel water out from above to douse flames on sails and rigging lines. In later years, "water engines" were variously used to propel water onto sails and rigging from both below and above.

So, as we can see, wetting sails produces multiple effects that were deemed beneficial. In modern times, we don't face sea battles in sailing ships, and have new materials that allow us to efficiently make stronger sails that can be tightened more to create stiffer/flatter surfaces...but not too flat...

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Q: Why did the USS Constellation wet the sails during a chase?
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