Sailing faster than the wind
Encyclopedia
Devices that are powered by sail
s (such as sailboat
s, iceboats and sand yachts
) can sail (that is, advance over the surface) faster than the wind. 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.
The Extreme 40
catamaran can sail at 35 knots (68.6 km/h) in 20–25 knots of wind. The high-performance International C-Class Catamaran
can sail at twice the speed of the wind. Iceboats can typically sail at five times the speed of the wind. By sailing downwind at 135 degrees off the wind, a sand yacht can sail much faster than the wind. The velocity made good
downwind is often over twice as fast compared to the same land yacht sailing directly downwind. 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.
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. 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.
, the wind as seen from the boat will increase and the wind will appear to shift forward. 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.
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). High-performance multihulls can sail at 20 degrees off the apparent wind. 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.
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.
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. It can sail slightly faster, as a multiple of the windspeed, if it sails at a greater angle off the true wind.
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 feet (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. 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.
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.
The table 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.
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.
, 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.
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.
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.
The drawing below shows apparent wind angles and speeds for different boat speeds for a boat sailing downwind at 135 degrees.
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
.
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.
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. 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. Such performance is theoretically possible. An easy-to-grasp animation demonstrating the principle of how it can be possible to go faster than the wind can be found at .
However real boats cannot equal the performances shown in the table, although iceboats can come close to them. Indeed iceboats can make good both upwind and downwind at speeds far greater than the wind. 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. 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 (31.4 km/h), about 1.9 times wind speed. 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.
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 (19.6 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. During the second race, winds were 7 to 8 knots (15.7 km/h). USA reached the windward mark in 59 minutes, so its velocity made good was about 13.2 knots (25.9 km/h), about 1.65 times wind speed. The course was a triangle, so the velocity made good downwind was only 11.5 knots (22.5 km/h), about 1.4 times wind speed. USA averaged 26.8 knots (52.5 km/h), about 3.35 times the wind speed, on the faster first triangular leg.
Other sailboats (such as the 18ft Skiff) can make good downwind at speeds faster than the wind. Indeed, it can be seen from the polar chart for the 18 ft (5.5 m) Skiff that it can make good about 12 knots (23.5 km/h) downwind at a windspeed of 10 knots (19.6 km/h), by jibing back and forth at about 140 degrees off the true wind. The polar chart in Figure PS1 of the cited book High Performance Sailing shows that boats that were sailing in 1996 were able to make good downwind at about 1.5 times the speed of the wind.
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.
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. 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.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 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." Other researchers arrived at similar conclusions.
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. 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. 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. 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. 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. 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. And indeed this was done, as stated above.
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. 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.
. 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."
Sail
A sail is any type of surface intended to move a vessel, vehicle or rotor by being placed in a wind—in essence a propulsion wing. Sails are used in sailing.-History of sails:...
s (such as sailboat
Sailboat
A sailboat or sailing boat is a boat propelled partly or entirely by sails. The term covers a variety of boats, larger than small vessels such as sailboards and smaller than sailing ships, but distinctions in the size are not strictly defined and what constitutes a sailing ship, sailboat, or a...
s, iceboats and sand yachts
Land sailing
Land sailing, also known as sand yachting or land yachting, is the act of moving across land in a wheeled vehicle powered by wind through the use of a sail. The term comes from analogy with sailing. Historically, land sailing was used as a mode of transportation or recreation...
) can sail (that is, advance over the surface) faster than the wind. 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
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...
to the wind and by using the lateral resistance
Lift (force)
A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...
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.
The Extreme 40
Extreme 40
The Extreme 40 is a class of sailing catamaran created by TornadoSport and designed by Yves Loday. 40 feet long and constructed of carbon fibre. They have a top speed of about 40 knots and can sail at about 35 knots in 20-25 knots of wind. The first extreme 40 was launched in 2005. They are...
catamaran can sail at 35 knots (68.6 km/h) in 20–25 knots of wind. The high-performance International C-Class Catamaran
International C-Class Catamaran
The C-Class Catamaran is a high-performance developmental class sailing catamaran. They are very light boats which use rigid wing sails and can sail at twice the speed of the wind...
can sail at twice the speed of the wind. Iceboats can typically sail at five times the speed of the wind. By sailing downwind at 135 degrees off the wind, a sand yacht can sail much faster than the wind. The velocity made good
Velocity made good
Velocity made good, or "vmg," is a term in sailing, and specifically yacht racing, that refers to the component of a sailboat's velocity that is in the direction of the next mark. The concept is useful in sailing, because a sailboat often cannot, or should not, sail directly to a mark to reach the...
downwind is often over twice as fast compared to the same land yacht sailing directly downwind. 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.
In 2009, the world speed sailing record
Speed sailing record
Speed sailing records are sanctioned, since 1972, by the World Sailing Speed Record Council . Records are measured either by average speed over a specified distance or by total distance traveled during a specified time interval...
on water was set by a hydrofoil
Hydrofoil
A hydrofoil is a foil which operates in water. They are similar in appearance and purpose to airfoils.Hydrofoils can be artificial, such as the rudder or keel on a boat, the diving planes on a submarine, a surfboard fin, or occur naturally, as with fish fins, the flippers of aquatic mammals, the...
trimaran
Trimaran
A trimaran is a multihulled boat consisting of a main hull and two smaller outrigger hulls , attached to the main hull with lateral struts...
sailing at 1.71 times the speed of the wind. Also in 2009, the world land speed record for a wind-powered vehicle was set by the sand yacht Greenbird
Greenbird
The Ecotricity Greenbird is a wind-powered vehicle that broke the land speed record for the fastest wind-powered vehicle at the dry Ivanpah Lake on March 26, 2009. It was built by the British engineer Richard Jenkins...
sailing at about three times the speed of the wind.
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 acceleratesAcceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
, the wind as seen from the boat will increase and the wind will appear to shift forward. 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
Aberration of light
The aberration of light is an astronomical phenomenon which produces an apparent motion of celestial objects about their real locations...
.
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.
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
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
of the surface (water or ice), and leeway
Leeway
Leeway is the motion of an object that is floating in the water to leeward due to the component of the wind vector perpendicular to the object’s. The National Search and Rescue Supplement to the International Aeronautical and Maritime Search and Rescue Manual defines leeway as "the movement of a...
(downwind drift). Normal cruising boats yachts can sail at about 45 degrees off the apparent wind
Apparent wind
Apparent wind is the wind experienced by a moving object.-Definition of apparent wind:The Apparent wind is the wind experienced by an observer in motion and is the relative velocity of the wind in relation to the observer....
(50 to 60 degrees off the true wind). High performance racing yachts at about 27 degrees (35 degrees off the true wind). High-performance multihulls can sail at 20 degrees off the apparent wind. 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
Keelboat
Keelboat has two distinct meanings related to two different types of boats: one a riverine cargo-capable working boat, and the other a classification for small- to mid-sized recreational sailing yachts.-Historical keel-boats:...
such as a Soling
Soling
A Soling is a class of open keelboat designed by Jan Linge of Norway in 1965. In 1968, it was chosen from among many other boats to be the men's triple-handed boat for the 1972 Olympics...
can sail at 30 degrees off the apparent wind, an 18ft Skiff
18ft Skiff
The 18ft Skiff is considered the fastest class of sailing skiffs. The class has a long history beginning with races on Sydney Harbour, Australia in 1892. The boat has changed significantly since the early days, bringing in new technology as it became available. Because of the need of strength,...
at 20 degrees, and an iceboat at 7 degrees.
If hull speed
Hull speed
Hull speed, sometimes referred to as displacement speed, is the speed of a boat at which the bow and stern waves interfere constructively, creating relatively large waves, and thus a relatively large value of wave drag...
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
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
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 |
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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. It can sail slightly faster, as a multiple of the windspeed, if it sails at a greater angle off the true wind.
Sailing on a broad reach
As stated in the Introduction of the book High Performance Sailing, 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
Soling
A Soling is a class of open keelboat designed by Jan Linge of Norway in 1965. In 1968, it was chosen from among many other boats to be the men's triple-handed boat for the 1972 Olympics...
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 feet (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. 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.
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
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
to overcome the resistance
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
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.
The table 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 |
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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
Velocity made good
Velocity made good, or "vmg," is a term in sailing, and specifically yacht racing, that refers to the component of a sailboat's velocity that is in the direction of the next mark. The concept is useful in sailing, because a sailboat often cannot, or should not, sail directly to a mark to reach the...
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 windApparent wind
Apparent wind is the wind experienced by a moving object.-Definition of apparent wind:The Apparent wind is the wind experienced by an observer in motion and is the relative velocity of the wind in relation to the observer....
, 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.
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.
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.
The drawing below shows apparent wind angles and speeds for different boat speeds for a boat sailing downwind at 135 degrees.
Speed made good
Most sailingSailing
Sailing is the propulsion of a vehicle and the control of its movement with large foils called sails. By changing the rigging, rudder, and sometimes the keel or centre board, a sailor manages the force of the wind on the sails in order to move the boat relative to its surrounding medium and...
is not done in order to achieve a maximum speed, but in order to go from one point to another. In most sailboat racing
Yacht racing
Yacht racing is the sport of competitive yachting.While sailing groups organize the most active and popular competitive yachting, other boating events are also held world-wide: speed motorboat racing; competitive canoeing, kayaking, and rowing; model yachting; and navigational contests Yacht 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
Tacking (sailing)
Tacking or coming about is a sailing maneuver by which a sailing vessel turns its bow through the wind so that the direction from which the wind blows changes from one side to the other...
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
Velocity made good
Velocity made good, or "vmg," is a term in sailing, and specifically yacht racing, that refers to the component of a sailboat's velocity that is in the direction of the next mark. The concept is useful in sailing, because a sailboat often cannot, or should not, sail directly to a mark to reach the...
.
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
Velocity made good
Velocity made good, or "vmg," is a term in sailing, and specifically yacht racing, that refers to the component of a sailboat's velocity that is in the direction of the next mark. The concept is useful in sailing, because a sailboat often cannot, or should not, sail directly to a mark to reach the...
, 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.
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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
Jibe
A jibe or gybe is a sailing maneuver where a sailing vessel turns its stern through the wind, such that the wind direction changes from one side of the boat to the other...
(also spelled gybing) back and forth. 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. Such performance is theoretically possible. An easy-to-grasp animation demonstrating the principle of how it can be possible to go faster than the wind can be found at .
However real boats cannot equal the performances shown in the table, although iceboats can come close to them. Indeed iceboats can make good both upwind and downwind at speeds far greater than the wind. And so can sand yachts: during the 2009 land speed record, the yacht Greenbird
Greenbird
The Ecotricity Greenbird is a wind-powered vehicle that broke the land speed record for the fastest wind-powered vehicle at the dry Ivanpah Lake on March 26, 2009. It was built by the British engineer Richard Jenkins...
was proceeding at about 3 times the speed of the wind on a course about 120 degrees off the true wind. Thus, its speed made good downwind was about 1.5 times the speed of the wind. During a training run the catamaran Alinghi 5
Alinghi 5
The Alinghi 5 is a LWL, beam sloop-rigged catamaran built by Alinghi for the 33rd America's Cup.It was launched on 8 July 2009 being lifted from the construction shed in Villeneuve, Vaud by a Mil Mi-26 helicopter and carried thereby to Lake Geneva. It was subsequently carried to Genoa, Italy...
, 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 (31.4 km/h), about 1.9 times wind speed. 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.
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 (19.6 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. During the second race, winds were 7 to 8 knots (15.7 km/h). USA reached the windward mark in 59 minutes, so its velocity made good was about 13.2 knots (25.9 km/h), about 1.65 times wind speed. The course was a triangle, so the velocity made good downwind was only 11.5 knots (22.5 km/h), about 1.4 times wind speed. USA averaged 26.8 knots (52.5 km/h), about 3.35 times the wind speed, on the faster first triangular leg.
Other sailboats (such as the 18ft Skiff) can make good downwind at speeds faster than the wind. Indeed, it can be seen from the polar chart for the 18 ft (5.5 m) Skiff that it can make good about 12 knots (23.5 km/h) downwind at a windspeed of 10 knots (19.6 km/h), by jibing back and forth at about 140 degrees off the true wind. The polar chart in Figure PS1 of the cited book High Performance Sailing 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 BlackbirdBlackbird (land yacht)
The Blackbird is a propeller-driven land yacht that was developed specifically to prove that it is possible to sail dead downwind faster than the wind , steady state, powered by the wind only.A good account of the history of the project, with an explanation of how the device works is given in In...
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.
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. 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.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 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." Other researchers arrived at similar conclusions.
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
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
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
Keelboat
Keelboat has two distinct meanings related to two different types of boats: one a riverine cargo-capable working boat, and the other a classification for small- to mid-sized recreational sailing yachts.-Historical keel-boats:...
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. At first, this was considered by some to be a hoax
Hoax
A hoax is a deliberately fabricated falsehood made to masquerade as truth. It is distinguishable from errors in observation or judgment, or rumors, urban legends, pseudosciences or April Fools' Day events that are passed along in good faith by believers or as jokes.-Definition:The British...
, but it was subsequently considered to be a legitimate demonstration of what is theoretically possible. 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
Balloon (aircraft)
A balloon is a type of aircraft that remains aloft due to its buoyancy. A balloon travels by moving with the wind. It is distinct from an airship, which is a buoyant aircraft that can be propelled through the air in a controlled manner....
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. 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. 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. 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. And indeed this was done, as stated above.
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
Perpetual motion
Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not....
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. 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.
Further reading
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 Skiff18ft Skiff
The 18ft Skiff is considered the fastest class of sailing skiffs. The class has a long history beginning with races on Sydney Harbour, Australia in 1892. The boat has changed significantly since the early days, bringing in new technology as it became available. Because of the need of strength,...
. 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."