Since the early days of sailing, ships have undergone a continuous improvement in design
so that todayï¿½s modern sailboats, at casual glance, may give the appearance of having the
ability to travel upwind (against the wind). In actuality, a sailboat can not travel
directly into the wind but employs sailing technique known a ï¿½tacking,ï¿½ to zigzag across a
The shape of the sail and the hull of the boat are the major factors that have allowed
sailboats to more closely approach the ability of sailing upwind. In the early years of
sailing ships, the European ships had a square sail design. This design only allowed for
sailing with a favorable wind (ï¿½before the wind, or wind on the quarterï¿½). With trade
expanding into the East, Europeans were exposed to triangular sails in use on small boats
in the orient. It was observed that these triangular sails allowed for navigation using a
half wind (wind at 90 degrees to the boat), which further increased the shipï¿½s maneuvering
ability ï¿½ particularly in port, where ships previously were ï¿½dead in the waterï¿½ without a
favorable wind. European vessels incorporated the triangular sails fore and aft of the
mainsails for the purpose of navigating out to sea to catch the favorable trade winds for
the square sails to utilize.
The use of triangular sails caught on as the sail shape of choice as other benefits to the
design were realized. By using a triangular sail design and centerboard (overdeveloped
keel), it was possible to travel against the wind using a technique known as tacking.
Tacking allows the boat to travel forward with a wind at right angles to the boat. The
boat travels for a time at an angle toward its desired course (to the right for instance),
then the captain swings the boom of the sail and tacts back across the desired course at
an angle to the left in a zig-zag fashion. In this way, tacking allows the boat to use
prevailing wind from many other angles than in earlier sailing methods.
Since the boat is dependent on the wind for propulsion, the strength of the wind and the
area of the sail used to catch the wind obviously play a part ï¿½ but how does a wind at
right angles to the boat allow the boat to move forward?
This is accomplished with a bit of vector mathematics. The wind is the large force vector
in the equation. As the wind pushes at approximate right angles to the boat, the boatï¿½s
large keel (underwater wing shaped centerboard), poses a very large drag force against the
boat being pushed in the direction of the wind. Since the keel is aligned with the length
of the boat, the boat really wants to travel forward, and the resultant thrust vector is
in that direction.
The shape of the sail also provides forward thrust. As the triangular sail inflates with
a wind it creates an airfoil shape. As subsequent wind passes around the sail (airfoil),
negative pressure is induced out front of and on the leeward side of the sail. This in
turn causes surrounding air to rush into the sail and propel the boat further. This
sail/airfoil action is compounded, as the boat travels faster, the wind around the sail
creates more negative pressure, causing the boat to travel faster causing more negative
pressure and so forth.
Stephen Portz, Technology Teacher, Space Coast Middle School, FL
'The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.'