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So what determines the height of a mast?
It is unusual to find many cruising boats with a higher ratio than 1.3, however. [links]
Note there are some performance boats designed with masts that are too tall for the craft’s weight, assuming that the weight of the crew will balance out the sail area.
i The ratio sail area to displacement is obtained by dividing the sail area by the boat's displaced volume to the power two-thirds.
i The Displacement Length Ratio (DLR) is a figure that points out the boat's weight compared to its waterline length. The DLR is obtained by dividing the boat's displacement in tons by the cube of one one-hundredth of the waterline length (in feet).
The DLR can be used to compare the relative mass of different sailboats no matter what their length: [links]
Upwind: under 18 the ratio indicates a cruise oriented sailboat with limited performances especially in light wind, while over 25 it indicates a fast sailboat.
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There are a lot of factors that contribute to mast height, not the least of which is boat size. Obviously, boats need a sail plan proportionate to their length, beam, and displacement in order to be efficient. The type of sail plan varies based on what the boat is used for.
A gaff-rigged vessel with a typical mast has a good chance of surviving a snapped stay as the mast can support itself. A Bermuda-rigged vessel, more likely than not, could lose its mast immediately after the standing rigging goes down.
Today's high-tech racing sailboats have many more options to choose from. Composite materials, such as carbon fiber, are increasingly common due to their astounding strength-to-weight ratio. Alloy masts are also fairly common. Steel masts exist, but their use is usually confined to small sailboats and dinghies.
The four-sided sail has a much greater area per foot of height than the triangular sail, so the mast doesn't need to be quite as high. Additionally, shorter masts can be thicker and stay within the same weight limits as a taller mast, so they can be thicker and stronger.