Sailing faster than the wind


Sailing faster than the wind

Devices that are powered by sails (such as sailboats, iceboats and sand yachts) can sail (that is, advance over the surface) faster than the wind.[1] Such devices cannot do this when sailing dead downwind using simple square sails that are set perpendicular to the wind, but they can achieve speeds greater than wind speed by setting sails at an angle to the wind and by using the lateral resistance of the surface on which they sail (for example the water or the ice) to maintain a course at some other angle to the wind.[2][3][4][5][6][7]

The Extreme 40 catamaran can sail at 35 knots (65 km/h) in 20–25 knots of wind.[8] The high-performance International C-Class Catamaran can sail at twice the speed of the wind.[9] Iceboats can typically sail at five times the speed of the wind.[10] By sailing downwind at 135 degrees off the wind, a sand yacht can sail much faster than the wind.[11] The velocity made good downwind is often over twice as fast compared to the same land yacht sailing directly downwind.[11] The catamarans that will be used for the 2013 America's Cup are expected to sail upwind at 1.2 times the speed of the true wind, and downwind at 1.6 times the speed of the true wind.[12][13][14]

In 2009, the world speed sailing record on water was set by a hydrofoil trimaran sailing at 1.71 times the speed of the wind.[15][16] Also in 2009, the world land speed record for a wind-powered vehicle was set by the sand yacht Greenbird sailing at about three times the speed of the wind.[17]

Contents

Sailing perpendicular to the wind

For example, a boat can sail a course that is perpendicular to the true wind (that is, at 90 degrees with respect to the true wind). As it accelerates, the wind as seen from the boat will increase and the wind will appear to shift forward.[18] This is the same effect that causes rain to appear to fall at angle when seen from a moving car, and is equivalent to the astronomical phenomenon of aberration of light.

As the wind increases in speed and shifts forward (because of the acceleration of the boat), the sails have to be trimmed in order to maintain performance. This causes the boat to further accelerate, thus causing a further increase in windspeed and a further forward windshift.

Eventually, the sails cannot be trimmed any further and an equilibrium is reached. Although the boat is sailing perpendicular to the true wind, its sails are set for a close hauled course.[19]

The actual speed of the boat in such a situation depends on the wind speed, how close to the wind it can sail, the strength of the wind, the resistance of the surface (water or ice), and leeway (downwind drift). Normal cruising boats yachts can sail at about 45 degrees off the apparent wind (50 to 60 degrees off the true wind). High performance racing yachts at about 27 degrees (35 degrees off the true wind).[20] High-performance multihulls can sail at 20 degrees off the apparent wind.[21] Iceboats can sail even closer to the apparent wind. According to the data provided on p. 406 of the cited book High Performance Sailing, a fast keelboat such as a Soling can sail at 30 degrees off the apparent wind, an 18ft Skiff at 20 degrees, and an iceboat at 7 degrees.[22]

If hull speed is not a limiting factor, and if the strength of the wind is sufficient to overcome the surface resistance, then the speed of the boat as a multiple of the wind speed will depend only on how close it can sail to the wind. For example, assuming that surface resistance is negligible (as for an iceboat), if a boat sails at 90 degrees to the true wind, but at 45 degrees to the apparent wind, then it must be sailing at the same speed as the true wind. That is, if the wind speed is V, then the boat's speed is also V. Elementary trigonometry and elementary vector operations can be used to show that, if a boat sails at 90 degrees to the true wind, but at alpha degrees to the apparent wind, and the wind speed is V, then the boat's speed must be V×cotan(alpha). The table below shows the values of this function, as a multiple of windspeed.

Alpha Multiple of windspeed
45
1.00
40
1.19
35
1.43
30
1.73
25
2.14
20
2.75
15
3.73
10
5.67

Hull speed is not a limiting factor for an iceboat nor for high-performance multihulls. So a boat capable of sailing at 10 degrees off the apparent wind (which is the case for many iceboats) that sails at 90 degrees to the true wind will be sailing nearly 6 times faster than the wind.[23] It can sail slightly faster, as a multiple of the windspeed, if it sails at a greater angle off the true wind.[24]

Sailing on a broad reach

As stated in the Introduction of the book High Performance Sailing[5], in the section Tacking Downwind, "any boat which runs 'square' must necessarily sail downwind at some speed less than the wind's speed whereas any boat which tacks downwind has no theoretical limit to its speed. Ice yachts, for example, can tack downwind at average speeds many times the wind speed."

The same book states, in section 24.2, "In a True Wind of 15 knots, the Soling crew will sail the close reach and reaching legs in Apparent Winds little stronger than True Wind. ... The 18-foot Skiff crew sails the cross wind legs in much stronger Apparent Winds which approach 30 knots. Even on the broad reaching legs they must still sail in a strong Apparent Wind which blows from ahead, so they still need to use strong-wind 'going-to-windward' handling techniques even though they are sailing downwind." Figure 24.2 of the book provides vector graphics that show how the 18-foot (5.5 m) Skiff can sail downwind faster than the speed of the wind.

From the detailed data provided for the 2009 record set by a sand yacht, it can be seen that the record was achieved when the yacht's course was about 120 degrees off the true wind.[25] That is, the yacht was moving faster than the wind although the true wind was behind it. This is possible because the speed of the yacht results in a large forward wind shift, so that the yacht is close hauled with respect to the apparent wind.[26]

Suppose that a boat is at a standstill, then starts to sail on a course that is 135 degrees off the true wind (the value 135 is chosen for this explanation in order to simplify certain calculations). The boat will accelerate, so the apparent wind will be less than the true wind and will shift forward of the true wind. If the boat can reach a speed equal to the speed of the true wind, then the apparent wind will be perpendicular to the boat's course and its speed will be about 71% of the true windspeed. If that reduced apparent windspeed still generates sufficient force to overcome the resistance of the surface, then the boat will further accelerate.

That is, the situation will be the same as the one explained above, since the boat is now accelerating after having reached a course perpendicular to the apparent wind. In practice, most boats sailing on the water cannot overcome the resistance of the water in order to reach speeds equal to the speed of the wind. However, iceboats can do so, because the resistance of the surface is very small. Thus, an iceboat that starts sailing on a broad reach will continue to accelerate until it is close-hauled with respect to the apparent wind.[27]

The table[28] and diagram below illustrate this situation. The vector labelled "boat speed" represents the relative wind resulting from the boat's progress through the water, that is, the wind that is induced by the boat's motion: its speed is the same as the speed of the boat and its direction is directly opposite to the direction of the boat's motion. Both boat speed and apparent wind speed are shown as a fraction (or multiple) of true wind speed, which is represented by the vertical vector at the left of the diagram.

Boat speed Alpha Apparent wind speed
0.10
131
0.93
0.30
120
0.82
0.50
106
0.74
0.71
90
0.71
1.00
68
0.77
1.41
45
1.00
2.00
29
1.47
3.00
17
2.40
4.00
12
3.37
5.00
9
4.35

This diagram shows the vector diagram for a boat sailing at 135 degrees off the true wind

Note that, if a boat can accelerate until it is sailing at 45 degrees off the apparent wind when sailing 135 degrees off the true wind, then its speed will be 1.41 times the speed of the true wind. Thus its velocity made good downwind will be equal to the velocity of the true wind. If it can accelerate until it is sailing closer than 45 degrees to the apparent wind, then its velocity made good downwind will be greater than the velocity of the true wind: see the more detailed discussion in the section Speed made good below.

Vector diagrams and formulas

As explained in the article on apparent wind, a boat's forward motion creates a corresponding head wind of the same strength in the opposite direction. That head wind must be combined with the true wind to find the apparent wind.[29]

The drawing below shows the vector operations and resulting calculations for sailing upwind. Alpha is the angle of the apparent wind. Beta is the course of the boat with respect to the true wind. The true wind is assumed to be equal to 1 in order to simplify the formulas. Note that the true wind is added using vector addition to the head wind created by the boat's speed.

This diagram shows the vector operations and calculations to find the speed of a boat sailing upwind

The drawing below shows the vector operations and resulting calculations for sailing downwind. Alpha is the angle of the sails to the apparent wind. Beta is the course of the boat with respect to the true wind. The true wind is assumed to be equal to 1 in order to simplify the formulas. Note that the true wind is added to the head wind created by the boat's speed.

This diagram shows the vector operations and calculations to find the speed of a boat sailing downwind

The drawing below shows apparent wind angles and speeds for different boat speeds for a boat sailing downwind at 135 degrees.

This diagram shows boat speed as a multiple of true wind speed for various angles of apparent wind

Speed made good

Most sailing is not done in order to achieve a maximum speed, but in order to go from one point to another. In most sailboat racing the objective is to sail a certain distance directly upwind (to a point called the upwind mark), and then to return downwind, as fast as possible.

Since sailboats cannot sail directly into the wind, they must tack in order to reach the upwind mark (this process is called beating or working to the mark). This lengthens the course, thus the boat takes longer to reach the upwind mark than it would if it could have sailed directly towards it. The component of a sailboat's speed that is in the direction of the next mark is called the velocity made good.[30]

If a boat sails perpendicular to the wind, it will never reach the upwind mark. So, in racing, speed is not everything. What counts is the velocity made good, that is, the progress towards the upwind mark. Again, simple trigonometry can be used to calculate the velocity made good. The tables below show velocity made good, again as a multiple of windspeed, and again assuming negligible surface resistance. The first column indicates the course as an angle off the true wind. Alpha is again the closest angle to the wind at which the boat can sail. The calculation assumes that the boat accelerates until the apparent wind is alpha degrees off the bow.

Upwind made good as multiple of windspeed Downwind made good as multiple of windspeed
Alpha
Alpha
Course 10 15 20 25 30 35 40 45
10
20 0.94 0.32
30 1.71 0.87 0.44 0.18
40 2.21 1.25 0.77 0.47 0.27 0.12
50 2.38 1.42 0.94 0.64 0.44 0.29 0.17 0.08
60 2.21 1.37 0.94 0.68 0.50 0.37 0.27 0.18
70 1.71 1.08 0.77 0.57 0.44 0.34 0.27 0.20
80 0.94 0.61 0.44 0.34 0.27 0.21 0.17 0.14
90 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Course 10 15 20 25 30 35 40 45
100 1.00 0.67 0.50 0.40 0.33 0.27 0.23 0.20
110 1.94 1.32 1.00 0.81 0.67 0.58 0.50 0.44
120 2.71 1.87 1.44 1.18 1.00 0.87 0.77 0.68
130 3.21 2.25 1.77 1.47 1.27 1.12 1.00 0.91
140 3.38 2.42 1.94 1.64 1.44 1.29 1.17 1.08
150 3.21 2.37 1.94 1.68 1.50 1.37 1.27 1.18
160 2.71 2.08 1.77 1.57 1.44 1.34 1.27 1.20
170 1.94 1.61 1.44 1.34 1.27 1.21 1.17 1.14
180 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

It can be seen that a boat that can sail closer than 20 degrees to the apparent wind can make good upwind faster than the real wind.

Many boats can make good downwind faster by not sailing dead downwind, but instead jibing (also spelled gybing) back and forth.[31] If the boat can accelerate until the apparent wind is alpha degrees off the bow, then it can be seen from the table above that it can make good downwind faster than the true wind.[32] Such performance is theoretically possible.[33] An easy-to-grasp animation demonstrating the principle of how it can be possible to go faster than the wind can be found at [34].

However real boats cannot equal the performances shown in the table,[35] although iceboats can come close to them. Indeed iceboats can make good both upwind and downwind at speeds far greater than the wind.[36][37] And so can sand yachts: during the 2009 land speed record, the yacht Greenbird was proceeding at about 3 times the speed of the wind on a course about 120 degrees off the true wind.[17] Thus, its speed made good downwind was about 1.5 times the speed of the wind. During a training run the catamaran Alinghi 5, one of the competitors for the 2010 America's Cup, covered 20 nautical miles (37 km) to windward and back in 2.5 hours in 8-9 knot winds, so its average velocity made good was 16 knots (30 km/h), about 1.9 times wind speed.[38] This is consistent with the yacht being able to sail at about 15 degrees off the apparent wind, see the table above. Indeed, the catamaran sails so fast downwind that the apparent wind it generates is only 5-6 degrees different to that when it is racing upwind; that is, the boat is always sailing upwind with respect to the apparent wind.[39]

During the first race of the 2010 America's Cup, the winning yacht USA sailed 20 nautical miles (37 km) to windward in 1 hour 29 minutes, in winds of 5 to 10 knots (19 km/h). Thus its velocity made good upwind was about 1.8 times windspeed, consistent with being able to sail about 13 degrees off the apparent wind when sailing upwind. It sailed 20 nautical miles (37 km) downwind in 1 hour 3 minutes, so its velocity made good downwind was about 2.5 times windspeed, consistent with being able to sail about 14 degrees off the apparent wind when sailing downwind.[40][41][42][43] During the second race, winds were 7 to 8 knots (15 km/h). USA reached the windward mark in 59 minutes, so its velocity made good was about 13.2 knots (24.4 km/h), about 1.65 times wind speed. The course was a triangle, so the velocity made good downwind was only 11.5 knots (21.3 km/h), about 1.4 times wind speed. USA averaged 26.8 knots (49.6 km/h), about 3.35 times the wind speed, on the faster first triangular leg.[44][45][46]

Other sailboats (such as the 18ft Skiff) can make good downwind at speeds faster than the wind.[47] Indeed, it can be seen from the polar chart[48] for the 18 ft (5.5 m) Skiff that it can make good about 12 knots (22 km/h) downwind at a windspeed of 10 knots (19 km/h), by jibing back and forth at about 140 degrees off the true wind.[47][49][50] The polar chart in Figure PS1 of the cited book High Performance Sailing[5] shows that boats that were sailing in 1996 were able to make good downwind at about 1.5 times the speed of the wind.

Sailing dead downwind faster than the wind

On July 3, 2010, the propeller-powered land yacht Blackbird set the world's first certified record for going directly downwind, faster than the wind, using only power from the wind. The yacht achieved a dead downwind speed of about 2.8 times the speed of the wind.[51][52][53]

The Blackbird was designed and built by Rick Cavallaro and John Borton of Sportvision in association with the San Jose State University aeronautics department. It was driven for the record by Rick Cavallaro.[54] They had set out at the end of 2009 to definitively demonstrate that it was possible to build a vehicle which can go directly downwind, faster than the wind, powered only by the wind, steady state.[55][56][57][58]After proposing this design, and presenting the analysis to demonstrate its viability, the Blackbird team learned that others had previously conceived of and built similar designs - most notably Andrew Bauer of Douglas Aircraft built and demonstrated such a vehicle in 1969 based on an analysis presented in a student's paper from some 20 years earlier. Unfortunately, no compelling evidence exists to prove whether or not the goal was truly achieved in this case. One notable example of a more recent analyses on the topic was presented on an internet forum In 2009 by an MIT professor[59] he concluded that such a device could be built in practice, and that "the DDWFTTW condition V/W > 1 is achievable with a wheeled vehicle without too much difficulty."[60] Other researchers arrived at similar conclusions.[61][62][63]

At first, it would seem impossible to sail dead downwind faster than the wind: a wind-driven machine cannot progress dead downwind faster than the wind using only sails. This is because the apparent wind will be zero if the speed of the boat equals the speed of the wind, so the boat cannot possibly go any faster than that.

However, in theory, it can sail dead downwind faster than the wind using only energy obtained from the wind while moving (that is, it does not need to stock energy while in the port). Some sort of mechanical device can be used to transfer energy from the surface on which the machine is moving in order to increase the speed of the machine. Some might say that this is not sailing properly speaking, because the boat's speed is influenced by devices other than the sails. However, it is 'sailing' in the sense that the boat is propelled only by energy obtained from the wind. Note that a conventional keelboat's performance is also very much improved by a device other than the sail: its keel.

And indeed a cart has been built and demonstrated that uses a propeller linked to its wheels (without batteries or electrical power generators) to sail dead downwind faster than the wind.[55] [64] At first, this was considered by some to be a hoax, but it was subsequently considered to be a legitimate demonstration of what is theoretically possible.[65][66] Indeed, as explained above, sources indicate that high-performance sailboats and iceboats can sail downwind at speeds greater than the wind, in the sense that their velocity made good downwind is faster than the wind (that is, they will arrive at the downwind mark of a course faster than would a balloon released from the upwind mark). Thus no fundamental law of physics is violated by a device that sails dead downwind faster than the wind.

The Blackbird is based on the same principle: it is a cart whose wheels are linked to a propeller.[55][56] On 7 and 8 March 2010, the team reported testing their vehicle on a motor-driven moving belt (treadmill), showing that it would advance against the belt, which means that it can progress dead downwind faster than the wind.[56] On 24 March 2010, the team ran the vehicle on the Ivanpah dry lake bed south of Las Vegas, Nevada, showing that it could accelerate dead downwind from a standstill and reach velocities well in excess of wind speed.[55][67][68][69][70] That is, the vehicle was progressing dead downwind faster than the wind. Officials of the North American Land Sailing Association (NALSA) were in attendance and one NALSA Board of Directors member (Bob Dill) was there for every run and collected his own rough wind and GPS data. This was not a NALSA sanctioned event but was presented as a demonstration to the NALSA Board of Directors that the vehicle was capable of progressing dead downwind faster than the wind. Subsequently, the team worked out the details with NALSA for rules and instrumentation related to an upcoming official NALSA ratified test and record.[55][56] And indeed this was done, as stated above.[51]

It is important to stress that even as the wind-powered cart referred to above is actually going "upwind", it would not move at all if the wind speed relative to the ground is zero. In other words, it requires the wind to be moving in the same direction as it does for it to work. If, for example, an initially moving cart enters a region where the wind speed relative to the ground is zero, it would eventually stop due to energy dissipation (e.g. friction) even as it is heading "upwind" within the region. The wind-powered cart referred to above therefore would not necessarily violate the laws of conservation of energy, nor is it a perpetual motion machine, as it harnesses its energy from the kinetic energy contained in the wind. If enough of the wind energy is harnessed, the machine can (at least in theory) use it to propel itself, even at speeds faster than the wind.[6] The cart is an example of a device that, while respecting the laws of physics, appears at first sight to be in perpetual motion: a so-called apparent perpetual motion machine.

Notes

  1. ^ Jobson, Gary (1990). Championship Tactics: How Anyone Can Sail Faster, Smarter, and Win Races. New York: St. Martin's Press. pp. 323. ISBN 0312042787. "... as the boat speeds up the apparent wind direct goes further and further forward without stalling the sails and the apparent wind speed also increases - so increasing the boat's speed even further. This particular factor is exploited to the full in sand-yachting in which it is common for a sand yacht to exceed the wind speed as measured by a stationary observer." 
  2. ^ A clear explanation, with diagrams, is given at "The physics of sailing". http://www.animations.physics.unsw.edu.au/jw/sailing.html.  and at "Physics for Architects: Can Sailboats Sail Faster than the Wind?". http://physicsforarchitects.com/Sailing_against_the_wind.php. 
  3. ^ An explanation with a video is given at "The Physics of Sailing: Physicists Explain How To Sail Faster than the Wind". http://www.sciencedaily.com/videos/2007/1208-physics_of_sailing.htm. 
  4. ^ A more detailed discussion is given at "The physics of sailing (article published by MIT)". http://web.mit.edu/preis/www/18.384/18.384__Undergraduate_Seminar_in_Physical_Applied_Mathematics/Project_topics_files/Anderson_PhysicsToday_2008.pdf. 
  5. ^ a b c A very comprehensive explanation of all aspects of the topic is found in the book: Bethwaite, Frank (2007). High Performance Sailing. Adlard Coles Nautical. ISBN 9780713667042.  See in particular Chapter 16.
  6. ^ a b See also the explanation at Terence Tao. "Sailing into the wind, or faster than the wind". http://terrytao.wordpress.com/2009/03/23/sailing-into-the-wind-or-faster-than-the-wind/. Retrieved 2010-8-25. 
  7. ^ A simple explanation is given at "Sailblogs: More on sailing faster than the wind". Sailblogs. September 6, 2008. http://www.sailblogs.com/member/speedtech/?xjMsgID=67124. Retrieved 2010-8-25. 
  8. ^ "About eXtreme 40". eXtreme40. http://www.extreme40.org/extreme40.asp?pid=152. Retrieved 2010-8-25. 
  9. ^ "The Winged World of C Cats". Sail Magazine. http://www.sailmagazine.com/cclasscats/. Retrieved 2010-8-25. 
  10. ^ See "How fast do these things really go?" in the "Frequently Asked Questions". Four Lakes Ice Yacht Club. http://iceboat.org/faqiceboat.html. Retrieved 2010-8-25. 
  11. ^ a b Bob Dill (July 13, 2003). "Frequently Asked Questions". North American Land Sailing Association. http://www.nalsa.org/faq.htm#3)%20How%20do%20they%20go%20faster%20than%20the. Retrieved 2010-8-25. 
  12. ^ "AC34 Multihull Class Rule Concept Document". 34th America's Cup. http://www.cupinfo.com/downloads/ac34-class-rule-multihull-concept.pdf. Retrieved 14.09.2010. 
  13. ^ "New high performance yachts for 34th America's Cup". 34th America's Cup. 2 July 2010. http://www.cupinfo.com/downloads/ggyc-press-ac34-rule-writing-070110.pdf. Retrieved 14.09.2010. 
  14. ^ The monohull concept for the 34th America's Cup called for a design that would achieve 1.0 times true wind speed upwind and 1.4 times downwind, see "AC34 Monohull Class Rule Concept Document". 34th America's Cup. http://www.cupinfo.com/downloads/ac34-class-rule-canting-monohull-concept.pdf. Retrieved 14.09.2010. 
  15. ^ The 500-meter record was 51.36 knots, achieved in 30 knots of wind by Hydroptère, a hydrofoil trimaran, see "Hydroptère World Records". World Sailing Speed Record Council. September 23, 2009. http://www.sailspeedrecords.com/index.php?option=com_content&view=article&id=104:wssr-newsletter-no-177-hydroptere-world-records-230909&catid=2:news&Itemid=5. Retrieved 2010-8-25. 
  16. ^ "Official web site of l'Hydroptère". http://www.hydroptere.com/. Retrieved 2010-8-25. 
  17. ^ a b The record was 126 mph (203 km/h) with winds of 30–50 mph (48–80 km/h), see Bob Dill (4/5/2009). "Measurement report for Speed Record Attempt Made by Richard Jenkins in the Yacht Greenbird on March 26, 2008". North American Land Sailing Association. http://www.nalsa.org/MeasuremantReport/MeasuremantReport.html. Retrieved 2010-8-25. 
  18. ^ Forward means making a smaller angle relative to the bow than the angle that the true wind makes relative to the bow. This phenomenon is explained in most sailing manuals, see for example p. 82 of The New Glénans Sailing Manual. David & Charles. 1978. ISBN 0715374702.  Or see p. 32 and p. 122 of The New Complete Sailing Manual. Dorling Kindersley. 2005. ISBN 9781405302555. 
  19. ^ An explanation of how this applies to iceboats can be found at the bottom of the "FAQ published by the Four Lakes Ice Yacht Club". http://iceboat.org/faqiceboat.html. Retrieved 2010-8-25. 
  20. ^ The formula for the apparent wind is (using the symbols shown in the vector diagrams) tan(alpha)=sin(beta)/ (Boat speed+cos(beta)). The figures shown for the angle of the apparent wind assume a boat speed around 0.3 times windspeed, say 6 knots for a keelboat in 18 knot winds. The figures for the angle of the true wind are from the main article on sailing.
  21. ^ "Russell Coutts Talks About BMW Oracle's Giant Multi-hull". cupinfo.com. April 13, 2009. http://www.cupinfo.com/en/bmwo-multihull-san-diego-coutts-002.php. Retrieved 2010-8-25. 
  22. ^ See also p. 204 of the cited book High Performance Sailing
  23. ^ See page 204 of the cited book High Performance Sailing.
  24. ^ The maximum multiple of windspeed is achieved at an angle of 90+alpha off the true wind. For alpha = 45, the maximum multiple of windspeed is 1.41 at an angle of 135 degrees off the true wind.
  25. ^ See the charts at the end of "the official measurement report". http://www.nalsa.org/MeasuremantReport/MeasuremantReport.html. Retrieved 2010-8-25. 
  26. ^ See section 16.13 and in particular Figure 16.10 of the cited book High Performance Sailing, and more generally Chapter 24
  27. ^ See the bottom of the "FAQ published by the Four Lakes Ice Yacht Club". http://iceboat.org/faqiceboat.html. Retrieved 2010-8-25. 
  28. ^ The values in the table are derived from the formulas shown in the section Vector diagrams and formulas
  29. ^ A detailed explanation, with examples, can also be found in Figure 24.2 of the cited book High Performance Sailing
  30. ^ If a boat sails at an angle beta to the true wind, then its velocity made good is cos(beta)*boat_speed.
  31. ^ Zack Leonard (11-06-2003). "Basic Downwind Performance, Part Two". SailNet. http://www.sailnet.com/forums/racing-articles/20717-basic-downwind-performance-part-two.html. Retrieved 2010-8-25. 
  32. ^ It should be noted that, in such a situation, the boat is jibing with respect to the true wind, but it is tacking with respect to the apparent wind, because of the apparent wind shift.
  33. ^ See Marchaj, Czeslaw Anthony (1979). Aero-hydrodynamics of Sailing. Dodd, Mead & Company, New York.  See in particular Chapter I (High speed sailing, pp. 84-127) and Chapter H (Land and hard-water sailing craft, pp. 128-152) of Part 1. The latter contains speed polars along with the equations for maximum speeds and states that it can be expected that the maximum ratio of downwind VMG to true wind would be in the order of 2.1-2.6.
  34. ^ "Animation demonstrating the principle of how it can be possible to go faster than the wind". http://sifter.org/~simon/journal/20101107.h.html. 
  35. ^ On 8 November 2009, the Hydroptère covered one nautical mile at an average speed of just over 50 knots, in 30-35 knots of wind, while sailing at 130 degrees off the true wind, see "Dans le mille". Hydroptère. http://www.hydroptere.com/actu_detail.php?id_actu=58#centre. Retrieved 2010-8-25. . Its velocity made good downwind was therefore about equal to the speed of the true wind.
  36. ^ Bob Dill (November 2004). "Putting Numbers on Iceboat Performance". North American Land Sailing Association. http://www.nalsa.org/Articles/Cetus/Iceboat%20Sailing%20Performance-Cetus.pdf. Retrieved 2010-8-25. 
  37. ^ See in particular pages 3 and 4 of Bob Dill (March 2003). "Sailing Yacht Design for Maximum Speed". Scuttlebutt.com. http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf. Retrieved 2010-06-21. 
  38. ^ "Training in Racing Mode". Consorcio Valencia. February 4, 2010. http://33rd.americascup.com/en/actualite/news/training-in-racing-mode-19-1216. Retrieved 2010-8-25. 
  39. ^ "Friday the Third, PT 1?". Consorcio Valencia. February 11, 2010. http://33rd.americascup.com/en/actualite/news/friday-the-third-pt-1-19-1957. Retrieved 2010-8-25. 
  40. ^ Pierre Nusslé (February 13, 2010). "La démonstration de puissance d’Oracle brise le rêve d’Alinghi". Tribune de Genève. http://www.tdg.ch/actu/sports/demonstration-puissance-oracle-brise-reve-alinghi-2010-02-12. Retrieved 2010-8-25. 
  41. ^ "First blood to USA – News – 33rd America's Cup". Consorsio Valencia. 2007-06-25. http://33rd.americascup.com/en/actualite/news/first-blood-to-usa-19-2362. Retrieved 2010-8-25. 
  42. ^ "BMW ORACLE Racing Wins Race One". BMW ORACLE Racing. 2003-09-30. http://bmworacleracing.com/en/news/articles/00_10_01/0212_3.html?track.refer=/en/news/current/overview.html&track.type=news. Retrieved 2010-8-25. 
  43. ^ "America's Cup, the numbers of a victory". Yacht Online. http://www.yachtonline.it/americas-cup-2010-valencia/americas-cup-the-numbers-of-a-victory. Retrieved 2010-03-09. 
  44. ^ "USA win 33rd America's Cup Match – News – 33rd America's Cup". Consorcio Valencia. http://33rd.americascup.com/en/actualite/news/usa-win-33rd-america-s-cup-match-19-2827. Retrieved 2010-8-25. 
  45. ^ "BMW ORACLE Racing crosses the finish line ahead in Race Two". BMW ORACLE Racing. 2003-09-30. http://bmworacleracing.com/en/news/articles/00_10_01/0214_3.html?track.refer=/en/news/current/overview.html&track.type=news. Retrieved 2010-8-25. 
  46. ^ See minute 30 of podcast interview with USA 17 designer Mike Drummond at "Oracle Racing’s USA 17". Omega Tau. 20 July 2011. http://omegataupodcast.net/2011/07/71-oracle-racings-usa-17/. Retrieved 12 August 2011. ; a clear explanation of how the boat can sail downwind at more than twice the speed of the wind is given at minute 59 of the interview.
  47. ^ a b Yoav Raz (April 2009). "Sailboat speed Vs. wind speed". Amateur Yacht Research Society (Catalyst, Journal of the Amateur Yacht Research Society). http://sites.google.com/site/yoavraz2/sailingboatspeedvs.windspeed. Retrieved 2010-08-25. 
  48. ^ A good discussion of polar charts for sailboats can be found at Stan Honey and Jim Teeters (June 10, 2008). "Get Your Performance on Target". Sailing World. http://www.sailingworld.com/from-the-experts/boat-speed/get-your-performance-on-target-1000061573.html. Retrieved 2010-8-25. 
  49. ^ According to the polar chart in section 24.1 (Figure 24.1) of the cited book High Performance Sailing the 18ft Skiff can make good 13 knots downwind in 10 knots of wind and 20 knots in 15 knots of wind.
  50. ^ Another good explanation of a polar chart, which indicates that a high-performance boat can make good downwind faster than the wind, is found at page 123 of The New Complete Sailing Manual. Dorling Kindersley. 2005. ISBN 9781405302555. 
  51. ^ a b "Direct Downwind Record Attempts". NALSA. August 2, 2010. http://www.nalsa.org/DownWind.html. Retrieved August 6, 2010. 
  52. ^ Livingstone, Kimball (August 1, 2010). "A NALSA Record: DDWFTTW". Blue Planet Times. http://kimballlivingston.com/?p=3922. Retrieved August 6, 2010. 
  53. ^ Livingstone, Kimball (August 2, 2010). "Downwind Noir: The Record". Blue Planet Times. http://kimballlivingston.com/?p=3922. Retrieved August 6, 2010. 
  54. ^ A good account of the history of the project, with an explanation of how the device works (and why it does not violate any laws of physics) is given in Rick Cavallaro (August 27, 2010). "A Long, Strange, Trip Downwind Faster Than the Wind". Wired. http://www.wired.com/autopia/2010/08/ddwfttw/all/1. Retrieved 14.09.2010. 
  55. ^ a b c d e Cort, Adam (April 5, 2010). "Running Faster than the Wind". sailmagazine.com. http://sailmagazine.com/racing/running_faster_than_the_wind/. Retrieved April 6, 2010. 
  56. ^ a b c d "Ride Like the Wind (only faster)". http://www.fasterthanthewind.org/. Retrieved April 6, 2010. 
  57. ^ Boyle, Rebecca (June 2, 2010). "Wind Powered Actually Moves Faster Than Wind Speed, Answering Tricky Physics Question". popsci.com. http://www.popsci.com/cars/article/2010-06/wind-powered-car-looks-odd-answers-tricky-physics-question. Retrieved July 1, 2010. 
  58. ^ Barry, Keith (June 2, 2010). "Wind Powered Car Travels Downwind Faster Than The Wind". wired.com. http://www.wired.com/autopia/2010/06/downwind-faster-than-the-wind/. Retrieved July 1, 2010. 
  59. ^ Drela, Mark. "DDFTTW Power Analysis". http://www.boatdesign.net/forums/attachments/propulsion/28168d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddwe.pdf. Retrieved June 15, 2010. 
  60. ^ Drela, Mark. "Dead-Downwind Faster Than The Wind (DFTTW) Analysis". http://www.boatdesign.net/forums/attachments/propulsion/28167d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddw2.pdf. Retrieved June 15, 2010. 
  61. ^ Gaunaa, Mac; Øye, Stig; Mikkelsen, Robert (2009). "Theory and Design of Flow Driven Vehicles Using Rotors for Energy Conversion". Marseille, France: Proceedings EWEC 2009. http://orbit.dtu.dk/getResource?recordId=241183&objectId=2&versionId=1. , A lecture about upwind-carts & DDWFTTW-carts at the Technical University of Denmark
  62. ^ Bauer, Andrew (1969). "Faster Than The Wind". Marina del Rey, California: First AIAA. Symposium on Sailing. http://projects.m-qp-m.us/donkeypuss/wp-content/uploads/2009/06/Bauer-Faster-Than-The-Wind-The-Ancient-Interface.pdf. , Picture of Bauer with his cart
  63. ^ Such a device was built and tested in 2006, see Goodman, Jack (January 2006). "Down wind faster than the wind". Catalyst (Journal of the Amateur Yacht Research Society). http://www.ayrs.org/DWFTTW_from_Catalyst_N23_Jan_2006.pdf. Retrieved 21-09-2010. 
  64. ^ "March Chu-Carroll is wrong, take two". Word Munger. December 4, 2008. http://wordmunger.com/?p=1002. Retrieved 2010-8-25. 
  65. ^ Mark C. Chu-Carroll (December 3, 2008). "Wind-powered Perpetual Motion". Scienceblogs (Good Math, Bad Math). http://scienceblogs.com/goodmath/2008/12/windpowered_perpetual_motion.php. Retrieved 2010-8-25. 
  66. ^ "Counter-intuitive Science". Learning Computation. December 5, 2008. http://learningcomputation.com/blog/2008/12/counter-intuitive-science.html. Retrieved 2010-8-25. 
  67. ^ Wolff, Eric (June 10, 2010). "Impossible-Seeming Wind Vehicles Might One Day Produce Abundant Energy". Discover Magazine. http://blogs.discovermagazine.com/sciencenotfiction/2010/06/10/impossible-seeming-wind-vehicles-are-quite-real%E2%80%94and-might-one-day-produce-abundant-energy/. Retrieved August 6, 2010. 
  68. ^ Barry, Keith (July 8, 2010). "Team Goes Downwind 2.5 Times Faster Than the Wind". Wired Magazine. http://www.wired.com/autopia/2010/07/downwind-faster-than-the-wind-possible-and-theyll-prove-it. Retrieved August 6, 2010. 
  69. ^ Wojdyla, Ben (July 6, 2010). "Wind-Powered Car Proves Internet Naysayers Wrong". Jalopnik. http://jalopnik.com/5556198/wind+powered-car-proves-internet-naysayers-wrong. Retrieved August 6, 2010. 
  70. ^ Boyle, Rebecca (June 1, 2010). "Wind-Powered Car Actually Moves Faster Than Wind Speed, Answering Tricky Physics Question". Popular Science. http://www.popsci.com/cars/article/2010-06/wind-powered-car-looks-odd-answers-tricky-physics-question. Retrieved August 6, 2010. 

Further reading

  • Bethwaite, Frank (first published in 1993; new edition in 1996, reprinted in 2007). High Performance Sailing. Waterline (1993), Thomas Reed Publications (1996, 1998, and 2001), and Adlard Coles Nautical (2003 and 2007). ISBN 9780713667042. 

This book provides a comprehensive description of technological developments up to 1993 that have permitted the developments of sailboats that can sail faster than the wind. It covers in particular the 18ft Skiff. It also covers in detail boat and sail handling techniques (course to sail, sail trim, handling waves, etc.) required to reach high speeds. Rod Carr, former British Olympic Sailing Team Manager stated: "[This book] represents a breakthrough in the way it related the theoretical aspects of wind, sea state and rig shape to the way a crew would sail and handle a boat during a race."

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