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The Mathematics of Sailing

July20

As the previous post indicated, Mathematics is at the heart of every top sport – whether in the data collection and analysis or in the calculation of successful equations to balance performance against each parameter.

In this article from WhyDoMath the goal in yacht design is to find the most efficient shape of the hull its appendages (like the keel), and its sails, etc. so that the boat moves with greatest speed and is more easily maneuverable in the likely range of wind and wave conditions.

Historically these designs were created by master craftsmen but,  from the 1990’s engineers used “simple” models to estimate basic quantities of physical relevance (such as the drag on the hull) prior to construction of the boat.

yacht design

Recent advances allowed mathematicians to work with boat designers and sailors to create more realistic mathematical models for how a sailboat handles in different marine conditions. The solutions to these models are difficult to find, even numerically, for three reasons. First, the equations are not standard and a complete theory that guarantees the existence and uniqueness of the solutions is not yet available.

Second, the equations are so complicated that finding accurate solutions numerically, even on a modern supercomputer, can take a long time.

Third, solutions should simultaneously optimize boat performance in many different conditions.

Mathematicians are essential in this sporting field because they set up the theoretical basis for solving the model equations, develop new numerical algorithms to solve the model equations more quickly (so that the equations modeling a given design could be solved under many different marine conditions), and determined strategies for deciding which of two different designs give generally better results over a variety of weather conditions.

 

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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