vectors and the continual recalculation of wind angles and the Pythagorean Theory are central geometry concepts used regularly by sail racing tacticians and helmsmen.
1. America’s Cup: The America’s Cup is both the world’s most famous sailboat race series (other than maybe the Olympics) and is also the trophy awarded to the winner of the America’s Cup races. Racing teams from all over the world compete for this trophy. The America’s Cup is the oldest active sailboat race in international sport. The next racing series is already occurring and will culminate in 2013 in San Francisco.
2. Beating: When one sails a boat toward the wind, it is called beating.
3. Close Hauled Tack: When one is beating, and one is sailing as close to the wind without being in irons and not being in the no sail zone, one is sailing on a close hauled tack. In Etchells, generally the close hauled tack is 25 degrees off the wind direction.
4. Etchells: Etchells is a one design boat first created in the 1960s by boat designer, Skip Etchells. An Etchells is a sleek 30 feet six inches long sailboat that has a main sail, a jib, and a spinnaker. It is one of the most well-known competitive one class boats in the world.
5. Head-to-Wind: Head-to-wind is another sailboat racing expressing for being in irons.
6. In Irons: A boat cannot sail directly into the wind or its sails will flap and flog. When sails are flapping and flogging, you are sailing into the wind and your boat cannot move forward. This sailing condition is called “In Irons.”
7. Lay Line: A lay line is the course on which a boat sailing as close to the wind as it can without going into irons and can make the mark without altering course.
8. Mark: A Mark is a buoy, float, or other geographical element (like a lighthouse) that boats sail around in a race.
9. No Sail Zone: When a boat is in irons, a boat is in the “no sail zone.”This means that the boat cannot move forward against the wind.
10. Off the Wind: When a sailor is not sailing on a close hauled tack, his boat is off the wind.
11. Port Tack: If one is beating close to the wind and the wind is coming over the left side of the boat, one is on a port tack. The sails are on the right or starboard side of the boat.
12. One Design: One Design boats are identical boat designs that use the same sails and equipment. One Design sailing emphasizes sailing skills when one races.
13. Rhumb Line: The Rhumb Line is the most direct line to your destination point, which when you are racing is the next mark. Rhumb lines take into account the curvature of the earth.
14. Right of Way: Right of way involves sailboat racing rules that dictate who has the right to sail in front of or near other sailboats. Right of way is very important because sailboats that have achieved right of way can sail in front of other sailboats or gain a tactical racing advantage over other sailing competitors.
15. Starboard Tack: If one is beating close to the wind and the wind is coming over the right side of the boat, one is on a starboard tack. The sails are on the left or port side of the boat.
16. Wind Direction: Wind direction is the direction that the wind is blowing. Because wind directions are continually changing, understanding and computing wind direction is a critical factor in sailboat racing.
A) Completive sailing has become a recognized international sport.
1. First international sailing competition originated in the 1800s with the America’s Cup.
2. One design boats originated in the 20th Century.
3. Use of geometry in sailing can be found in ancient times. More recently, sailing technology has relied on geometry to improve the technology of sailboat racing.
B) Race tactics and strategy have become increasingly important in one design racing.
1. Since “one design” boats are identical, sailing skills become the key factor in winning races.
2. Since “one design” boats technically all go the same speed, traveling less distances and obtaining “right of way” becomes very important.
3. Since sailboats must always sail at an angle to the wind (to avoid being head-to-wind), a sail boat racer can never sail directly to a mark. Therefore, determining the most efficient angles to sail at to sail the least distance to the mark with the most wind becomes critical.
C) A sailor cannot sail directly into the wind, the boat will be “in irons,” and the sails will flap and flog. A sailor needs to avoid this “no sail zone.” A boat can only sail at an angle to the wind. Etchells typically must sail at least 25 degrees “off the wind.”
Sailing toward the wind is called “beating.” If you sail as close to the wind as you can without being in irons, than you are tacking. If the wind is coming over the left side of the boat, it is called a “port tack.” If the wind is coming over the right side of the boat, it is called a “starboard tack.”
A sailor tacks to port and starboard as he beats windward toward a destination, which typically in a race is a mark.
D) There are three interrelated calculations that are made on every tack.
1. You need to look at your compass and identify the compass reading to the mark. This creates your first geometric vector, which is known as the “rhumb line.” Technically, this term relates to ocean sailing and accounts for the curvature of the Earth, but in sailboat racing on Puget Sound or Lake Washington it means a direct compass bearing on the mark. In perfect conditions, the “rhumb line” is the same as the “lay line,” which is the course on which a boat sailing as close to the wind as it can without going into irons and can make the mark without altering course. Unfortunately, the wind rarely cooperates with this geometric convergence, so sailing up wind means you have to tack a lot. To determine the “rhumb line” you can use a variety of different electronic devices including binoculars with magnetic readings, GPS navigational equipment, and different types of compasses including, the electronic compass shown below. Mark Brink and my father, the experts I relied upon, used a Tacktick Micro Compass.
2. After you calculate the “rhumb line” you then calculate the wind direction. You then make your first set of calculations by determining whether you should be on starboard or port tack as you attempt to most quickly and efficiently sail to the mark. Maintaining the most direct course to the mark using a “close-hauled tack” is a critical factor in winning sailboat races.
3. Understanding wind angles and comparing them to the angle to the mark can determine the most effective angle to sail the boat. As the boat sails on a close-hauled tack, Mark Brink and my father took a Tacktick Compass reading for the direction of each close-hauled tack. In Etchells, typically a close-hauled tack can go no closer than 25 degrees to the wind. The calculation is as follows
X= Rhumb Line
Y= Wind Direction
To determine the close-hauled starboard tack:
Starboard Tack: Y-25 degrees
To determine the close-hauled port tack:
Port Tack: Y+25 degrees
4. Since wind direction, current, and the location of other boats continually changes on the course, the efficient and effective use of geometry is critical. Wind changes continually so the calculation of whether one should be on port tack or starboard tack as you try to stay as close toward the rhumb line happens continuously. In the drawing below the oscillation of the wind ten degrees will tell the sailor whether he should be on the port tack or the starboard tack.
Assuming that the wind direction was at 190 degrees (south southwest) then the calculation would be:
Starboard Tack: Y-25 degrees 190 = Y-25: Y= 165
Port Tack: Y+25 degrees 190= Y+25: Y= 215
Assuming that the mark was at 180 degrees (the Rhumb line or X), then the boat sailing against a wind of 190 degrees would want to be on the starboard tack because the calculation on the starboard tack would only be a 15 degree angle off the Rhumb Line whereas the port tack would be an angle of 35 degree angle.
X – 165 = 180-165=15
X-215= 180-215 = -35
With a twenty degree wind shift to port, the wind would be coming from 170 degrees, or south southeast.
The calculation to determine the close-hauled starboard tack would be:
Starboard Tack: 170 = Y-25: Y= 145
The calculation to determine the close-hauled port tack would be:
Port Tack: 170 = Y+25: Y= 195
Assuming that the wind changes 20 degrees to port or to 1780 degrees, then you would make a close-hauled tack to port to 195 degrees because the calculation on the close-hauled tack would only be a 15 degree angle off the Rhumb Line whereas the starboard tack would be an angle of 35 degree angle.
X – 145 = 170-145=35
X – 195= 170-195 = -15
E) Understanding geometry, particularly the Pythagorean Theorem, is essential to winning races. The formula for the Pythagorean Theorem is:
A2 + B2 = C2
This formula is used the most frequently to determine the distance to the mark based on the vectors that and angles that are determined each time that a boat tacks. In short, Puget Sound or Lake Washington races, the distances are short and wind and current are more important in making tactical sailing decisions. However, in long distance races such as the Victoria to Maui race that my father and Mark Brink completed this summer, the use of the Pythagorean Theorem, in conjunction with rhumb lines and weather information, become critically important.