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Many (including some editors) seem to have a problem understanding how achieving a downwind-VMG greater than true-wind-speed is possible. I propose to include a introductory vector diagram, that shows how the sail can produce a force with a positive forward-component that propels the boat, under this conditions. I cannot upload files yet, so I put the proposed diagram here: [1]. If the diagram needs improvement, I can change it. Eyytee ( talk) 22:13, 7 June 2010 (UTC)
Good start, but the force diagram needs a drag vector, so the true boat velocity can be derived, not just a given...-- Paul ( talk) 00:49, 8 June 2010 (UTC)
At the point where (speed over the ground)/cos(angle to the true wind)=(speed of the true wind) the sail provides no forward force (i.e. in the direction of the keel / wheels / skates). The slightest friction brings the vessel gradually to a halt. But, if all friction is eliminated the downwind point is reached at EXACTLY the same time as the free floating balloon. Paul Beardsell ( talk) 08:33, 8 June 2010 (UTC)
First and foremost, there really don't seem to be any RELIABLE, VERIFIABLE sources. Secondly, what sources there are appear to be reports of original research, none of which has made it through a peer review process since they first appeared in November of 2008.
Wikipedia's recommendations are: Exceptional claims require exceptional sources
Certain red flags should prompt editors to examine the sources for a given claim:
* surprising or apparently important claims not covered by mainstream sources;
* claims that are contradicted by the prevailing view within the relevant community, or that would significantly alter mainstream assumptions, especially in science, medicine, history, politics, and biographies of living persons. This is especially true when proponents say there is a conspiracy to silence them.
Exceptional claims in Wikipedia require high-quality sources.
If such sources are not available, the material should not be included.
The major "sources" in the section are to self-published videos demonstrating original research.
This "issue" has been publicized since at least 2008 with no peer-reviewed publications of such a spectacularly counter-intuitive notion. It is VERY hard to believe that such a scientific breakthrough could remain an orphan with no better explanation than a very dubious "thought experiment".
As indicated in the Wikipedia recommendations for such unauthenticated exceptional claims, this section should not be included.
Possibly a supporting site - but still not up to what I suspect Wikipedia needs - (( http://www.idniyra.org/articles/IceboatSailingPerformance.html)). Polars at (( http://www.west.net/~lpm/hobie/archives/v1-i3/feature3.htm)) show an Aussie 18 almost making downwing VMG of windspeed.
In fact, several sections in the article - The last 2 paragraphs and table in Sailing perpendicular to the wind are erroneous and speculative. Sailing on a broad reach, velocity made good are similarly speculative and unsupported. Aerodynamic drag on the sail is completely ignored. Boat speed is NOT a simple multiple of apparent wind.
I don't currently have library access to the book, "High Performance Sailing". These citations need to be checked and perhaps verified against second sources - even book authors can be wrong!
No problems with sailing faster than the wind - just with a downwind velocity made good greater than windspeed.-- QuietJohn ( talk) 06:17, 14 June 2010 (UTC)
ALmost all of the citations I have checked have been dubious or inaccessible to me. If the NALSA site (which I have looked at and searched for relevant data) has the supporting data, please CITE the web pages that support your claims. I'm quite neutral about the DDWFTTW phenomenon. It doesn't make sense to me, and I haven't found any data to convince me otherwise, so it's either wrong, or the page isn't providing the necessary information. Guide me to the polars- or other corroborating data and I'll be happy to concede. Until then, much of this article isn't appropriate for a Wikipedia entry.-- QuietJohn ( talk) 09:43, 14 June 2010 (UTC)
I know that this section seems hard to believe. Please read the citations and study them carefully before posting comments to the effect that this section is obviously wrong. I too did not believe that this was possible, until I did the research and found the citations given in this section. Others (including a physicist) were also skeptical, but then became convinced, see [7] and [8].-- Gautier lebon ( talk) 08:39, 10 December 2009 (UTC)
I've posted some responses in talk:sailing. Another interesting topic is sailing directly into the wind. I've never seen a turbine / prop craft "work" directly upwind in what I consider to be a controlled test - the so-called proof has been less than convincing. The "spork33" device can be simply adapted to demonstrate that this is possible on land. It's just inefficiency of props and turbines that make it hard to get something to work on water, as there's no fundamental law to say it can't work. In a thought experiment, this can be extended to make something work on water by say dropping and raising large sea anchors, and using energy from the wind through a gearing mechanism to winch the boat forward against the sea anchor, but necessitating the use of a complex device to drop sea anchors "upwind" and raise them with minimal energy loss if sustained progress is to be made. There are other possible variations of the same idea (really not so different from a turbine-prop in principle). Using a sea anchor to hold a boat in position with a turbine harnessing wind energy, storing the energy (ie in a battery) and then using it to propel the craft forward so that progress is made is fine, but this isn't continuous uninterrupted progress, and is somewhat unremarkable. —Preceding unsigned comment added by 202.180.87.174 ( talk) 23:56, 14 December 2009 (UTC)
Indeed the discussion in Talk:Sailing#Downwind_faster_than_the_wind should be read by anybody interested in this topic.-- Gautier lebon ( talk) 12:16, 18 December 2009 (UTC)
I have corrected the introduction and the terminology. Regarding the drawings, the arrows point in the correct directions for the vector algebra to work: just think of the case when the boat is moving directly upwind or directly downwind; I wear thick glasses, so I like the large font, and I presume that others will too, since it does not make the drawings any larger. Regarding performance of normal cruising boats, I just took the figure given in the sailing article; if you don't agree with it, then please update both articles so that they are consistent, and provide a reference. I like the borders on the tables, they are easier to read that way. I don't know what should be cleaned up in "Further Reading", maybe somebody can take care of that. Same regarding general improvement of the language: I've many revisions to the article, incorporating many good suggestions that were made on Talk:Sailing#Downwind_faster_than_the_wind. I don't know what more to do.-- Gautier lebon ( talk) 10:20, 29 January 2010 (UTC)
If you think that anything stated in the article is impossible, please consider that the following two reasons have already been stated, and shown not to apply:-- Gautier lebon ( talk) 11:22, 11 June 2010 (UTC)
1) Velocity made good downwind cannot exceed the speed of the wind because of the laws of conservation of energy
2) Velocity made good downwind cannot exceed the speed of the wind because there is no force on the sails when the boat reaches wind speed.
3) If it were possible to go faster downwind by tacking, then why do people bother with spinnakers?
4) There isn't any easily accessible published data that supports the statements that boats can achieved downwind VMG greater than wind speed.
5) The cited sources are not sufficiently reliable.
A balloon drifts downwind at the speed of the wind. It uses no energy to do that. Similarly, an iceboat can drift dead downwind at very close to the speed of the wind, because the friction of its runners on the ice is negligle.
That is, to proceed downwind at the speed of the wind requires essentially no energy.
If a boat can capture some energy from the wind, then it can use that energy to propell itself downwind faster than the wind. There is no violation of the law of conservation of energy because the energy captured from the wind is used to overcome the resistance of the surface (insignificant in the case of an iceboat) and the resistance of the apparent headwind induced by the boat's progress. As explained in the main article, when a boat sails at an angle to the wind, it can capture energy from the wind, even if its downwind progress is faster than the wind itself. This is because of the apparent wind shift, see below.
Also, it is easy to see that a device can be constructed that can capture the energy from the wind even when moving dead downwind, see below Talk:Sailing faster than the wind#deleted thought experiment.
As explained in the main article, the forward motion of the boat induces a wind that must be added to the true wind in order to find that apparent wind that strikes the sails.
If an iceboat sails dead downwind, then it will soon reach a speed close to the speed of the wind and the apparent wind on the sails will be nearly zero.
But if an iceboat sails downwind at an angle to the wind, there will be an apparent wind shift: the apparent wind will move forward. As explained in the main article, the iceboat will eventually find itself on a broad reach with respect to the apparent wind (apparent wind at 90 degrees to the boat's course). The apparent wind will still generate a forward force component, so the boat will continue to increase in speed and the apparent wind will shift even further forward. As explained in the main article, this can result in velocity made good (progress in the direction of the wind) that is greater than the velocity of the wind.
Note the key point: what drives the boat is the apparent wind, that is what the sails "see" and what the sails react to and what propelles the boat.
Most sailboats cannot accelerate enough when they sail downwind so that the apparent wind shifts to come forward of the beam, and this because the resistance of the water is so large. That is, the resistance from the hull prevents the boat from moving fast enough so that the apparent wind shifts forward of the beam. Therefore, the apparent wind will always be aft of the beam and a spinnaker will increase the speed of the boat. However, downwind progress might still be faster if the boat gybes downwind, even with a spinnaker, and indeed most books on racing tactics say that it will usually be faster to avoid a dead downwind course and to gybe back and forth, even if the sailboat is using a spinnaker.
The article provides citations to various observed data. The most accessible data are those from the first regatta of the 2010 America's Cup. The winning yacht, USA 17, completed the 40 nautical mile course (20 miles dead upwind, 20 miles dead downwind) in 2h32, in 5-10 knots of wind, see for example [9]. If the wind had been 10 knots all the time (which was not the case) and if the downwind VMG had been equal to the wind speed, then USA 17 would have needed 2 hours to complete the downwind leg. That means that it would have completed the 20 mile upwind leg in 32 minutes, that is, at about 40 knots made good, meaning well over 50 knots over the ground. Of course USA 17 did not achieve such speeds upwind: anybody can watch the video and see the displayed upwind speeds, which were just over 20 knots. In fact, it took USA 17 63 minutes to complete the 20 mile downwind leg. Even if winds had been 10 knots (and they were less), the downwing VMG was nearly 2 times wind speed.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
The citations in the article include many web sites, which are easily accessible, and a published book (by Bethwaite) which is still in print and easily available. One of the contributors to this discussion has provided a second book, also still in print and easily available: The Symmetry of Sailing: The Physics of Sailing for Yachtsman, by Ross Garret.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
As explained below, the material in the article is not sufficiently original or suprising to be published in a peer-reviewed scientific journal. So it is not clear what additional citations should be provided.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
As promised, I've developed force diagrams that are meant to make the situation easier to understand. But I'm not convinced that what I have done can be understood easily. At first, I thought of making three diagrams, showing velocities and forces for three situations: (1) standstill (2) apparent wind at 90 degrees (3) apparent wind at 45 degrees. But then I decided to make separate diagrams for the velocities and the forces, with each diagram showing the three situations.-- Gautier lebon ( talk) 12:27, 11 June 2010 (UTC)
I would much appreciate comments on how to make the text below, and the diagrams, easy enough to understand so that they could be incorporated into the main article.-- Gautier lebon ( talk) 12:27, 11 June 2010 (UTC)
Consider an iceboat that is sailing at a course that is 135 degrees off the true wind. At the beginning, the boat is stationary. We will use the value "1" for the speed of the true wind. The apparent wind is equal to the true wind and comes from the same direction as the true wind. The velocity made good (VMG) downwind is zero. This is shown by the value "V0" in the chart below.
The boat will accelerate and will eventually reach a speed equal to to .707 times the speed of the wind. At this point, the apparent wind will come from 90 degrees (broad reach) and the speed of the apparent wind will also be .707. VMG is .5 This is shown by the value "V1" in the chart below.
At this point, the only resistance to forward motion is the friction of the iceboat's runners on the ice. But that is negligible.
So the boat will continue to accelerate and will reach a speed equal to 1.41 times the speed of the wind. At this point, the apparent wind will come from 45 degrees (close hauled) and the speed of the apparent wind will be 1. VMG is 1. This is shown by the value V2 in the chart below.
If the forward component of the force on the sails is sufficient, the boat can continue to accelerate, the apparent wind will shift further forward, and VMG will be greater than 1, that is, greater than the speed of the true wind. That is, the boat will progress downwind faster than the speed of the wind. The text and charts below show the force on the sails and the forward component of that force. It is not possible to determine theoretically whether the forward component at V2 would be sufficient to accelerate the boat further; but measurements of actual iceboat performances show that indeed it is. Iceboats accelerate until they are sailing at about 10 degrees (or less) off the apparent wind, and thus achieve speeds of 5 or more times the speed of the wind. This is the case even if the boat is sailing at 135 degrees off the true wind. So the VMG (progress in the dead downwind direction) is far greater than the speed of the wind.
The chart below shows the apparent wind and the sails on the iceboat when it is at a standstill (V0), on a broad reach (V1) and close hauled (V2). The angle of the sail is half of the angle of the apparent wind, which is the optimal angle in terms of generating a forward driving force. citation needed The force generated by the apparent wind on the sail is proportional to the square of the speed of the apparent wind. citation needed
The chart below shows the forward force resulting from the apparent wind when the iceboat is at a standstill (V0), on a broad reach (V1) and close hauled (V2). The force generated by the wind is perpendicular to the sails. citation needed It can be seen from elementary trigonometry that the forward component of that force is sin(sail angle).
Thus, the forward force when the iceboat is close hauled will be 38% of the total force on the sail. Again, whether or not that is sufficient to accelerate the boat further will depend on the resistance caused by the apparent wind (the headwind induced by the speed of the boat). As stated earlier, in practice it has been found that the force is indeed sufficient to further accelerate the iceboat (and in fact also other high-performance boats, including sailboats, as explained elsewhere in the article).
Here is the table that I've come up with for a course that is 135 degrees off the true wind. Please check the formulas and the calculations.-- Gautier lebon ( talk) 12:41, 15 June 2010 (UTC)
The formulas are:
V: boat speed
Alpha: angle of apparent wind
AW: Apparent wind speed
Boat speed | Alpha | Apparent wind speed | Force of apparent wind | Forward component | Drag component | Ratio drag/forward |
0.10 | 131 | 0.93 | 0.87 | 0.79 | ||
0.30 | 120 | 0.82 | 0.67 | 0.58 | ||
0.50 | 106 | 0.74 | 0.54 | 0.43 | ||
0.71 | 90 | 0.71 | 0.50 | 0.35 | ||
1.00 | 68 | 0.77 | 0.59 | 0.33 | 0.22 | 0.69 |
1.41 | 45 | 1.00 | 1.00 | 0.38 | 0.71 | 1.85 |
2.00 | 29 | 1.47 | 2.17 | 0.54 | 1.91 | 3.54 |
3.00 | 17 | 2.40 | 5.76 | 0.86 | 5.50 | 6.41 |
4.00 | 12 | 3.37 | 11.34 | 1.20 | 11.09 | 9.26 |
5.00 | 9 | 4.35 | 18.93 | 1.54 | 18.68 | 12.10 |
If an iceboat has a sail area of 6 square meters, and if it is sailing at 5 times the speed of the wind, the the foward force will be about 6*1.54 = 9, assuming the lift cofficient is 1. But the lift cofficient is about .66 (according to Bethwaite), so the forward force will be about 6.
The drag component will be about 18. So the speed of 5 times the speed of the wind can be achieved if the frontal surface that creates the drag (the surface of the mast, hull, runners, etc.) is less than 0.33 square meters (18*.33 = 6).
The popular International DN iceboat has a sail area of 6.5 square meters and can achieve 5 times the speed of the wind. This is perfectly consistent with the calculations above, given that the aerodynamically equivalent frontal surface of the iceboat is indeed probably about .33 square meters. citation needed
Why are we settling on English when this can be settled in Math? Both Gautier has posted diagrams above, and I have posted diagrams showing exactly how this works, given drag sufficiently small (doesn't need to be zero). What is appealing about these types of disputes over religious or political, is that they should be able to be resolved very quickly around a chalkboard. I suggest we attempt to do that. Generacy ( talk) 13:31, 14 June 2010 (UTC)
Also, if folk are looking for for more math, here is a link to another extensive treatment by MIT Professor Mark Drela on the topic. His treatment is specifically aimed at a DDWFTTW water craft, but near the end he addresses a ground based wheeled vehicle and makes the following statement "This confirms that the DDWFTTW condition V/W > 1 is achievable with a wheeled vehicle without too much difficulty". http://www.boatdesign.net/forums/attachments/propulsion/28167d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddw2.pdf ThinAirDesigns ( talk) 18:41, 14 June 2010 (UTC)
I have the impression that some people are, at times, confusing some basic concepts. So here is a reminder of what we are talking about.-- Gautier lebon ( talk) 10:43, 15 June 2010 (UTC)
The energy that drives a boat comes from the transfer of kinetic energy from the wind to the boat's sails: the molecules of air strike the sail, a force is induced, and momentum and energy are transferred from the air to the sail.
I don't know whether the following explanation will be helpful, but I'm tossing it in for comment.-- Gautier lebon ( talk) 11:32, 15 June 2010 (UTC)
One can think of the molecules of air as billiard balls, and the sail as a flat panel that is struck by the billiard balls. There is a transfer of kinetic energy and momentum from the balls to the flat panel. If there is no contsraint on the panel, it will wind up moving in the same direction and the same speed as the billiard balls: this is drifting dead downwind at nearly the speed of the wind.
At that point the boat has kinetic energy, but it's velocity does not change.
Now imagine that the flat panel (the sails) and the boat are constrained to travel at an angle (say 135 degrees) to the direction from which the billiard balls are coming. for example because it is mounted on a rail. When the balls hit the panel, there will be a transfer of kinetic energy and momentum, but now the panel does not wind up moving dead downwind, it winds up moving along the rail, that is at an angle with respect to the direction from which the billiard balls are coming.
Consequently, the direction from which the billiard balls are coming changes: they appear to come from further forward as the boat increases in speed. If you adjust the angle of the flat panel, the incoming balls will still create a forward force on the panel (in addition to the sideways force that has to be resisted by the rail on which the panel is mounted). There is still a transfer of energy from the balls to the panel, and the boat may or may not accelerate, depending on the resistance to its motion along the rail.
Now imagine that the billiard balls are relatively spaced out, so that one hits the panel only every second. In between billiard balls, the boat will be slowed down by the resistance of its motion along the rail (assuming that the resistance from the air is negligle, for example because this experiment takes place in a vacuum). If that resistance from its motion along the rail is very small, then the boat will continue to advance along the rail (conservation of momentum and kinetic energy), slowing down only slightly. Then the panel is hit by a new billiard ball: this will result in the transfer of some energy and in an acceleration of the boat.
So the boat will continue to accelerate until the energy lost due to the resistance of its motion along the rail is greater than the energy transferred to it when a billiard ball hits the flat panel.
The boat's ultimate speed depends on the friction from the surface, on how efficiently it captures the energy from the billiard balls, and on how much energy there is in the billiard balls.
Sirclicksalot ( talk) 19:17, 15 June 2010 (UTC)
(updated description of forces' contribution to conservation of momentum Sirclicksalot ( talk) 19:27, 15 June 2010 (UTC))
I have alway preferred this model, it is easier to understand and makes much more sense than the reams of bogus verbiage I have seen over the years invoking Bernoulli and phantom venturis. I used it yesterday to explain all points of sail to a neophyte in about ten minutes. I will try here to extend this description.
As noted above, the billiard billiard ball model is a momentum- and energy-transfer model. That is, generally speaking energy and momentum are transferred between the two media - air and water (or air and land) - and anything those media touch. To be more accurate, it is the differential momentum and differential energy between the air and water that provides the capability to sail. If there is no difference in velocities (vector quantities) between the air and the water, a sailboat cannot move through the water in any direction without an external energy source (paddle, motor, etc.). But if there is no wind over the ground, a sailboat can move on a river with current because of the differential momentum and energy between the still air and the moving water. And now that DDWFTTW has been demonstrated, it is theoretically possible even to sail directly upstream on a calm day.
Ultimately, the existence of differential momentum and energy between the two media are the reason it is possible to move in any direction relative to the true wind, while using that same true wind as the sole motive force.
One thing to note in Gabon's example above is that the flat panel (sail) is perpendicular to the true wind direction. In that case the sail and boat VMGDW (Velocity Made Good DownWind i.e. parallel to the true wind) cannot exceed the true windspeed. Mr. Beardsell's analysis (Physical mechanics, above) is an excellent description of why. The reason I bring this up is to make the point that when momentum transfer occurs, momentum must be conserved, but it is the change in momentum between the wind (billiard ball) before and after it encounters the sail that is transferred to the sail. There is another point to be made here: momentum is a vector so by definition it has a magnitude and a direction; if the direction of the momentum of a billiard ball changes but the magnitude of the momentum does not, that still constitutes a change in momentum transferred from the billiard ball to the sail which changed it. Counter to intuition, the direction and magnitude of the momentum of the incoming medium (true wind, billiard balls, etc) does not matter, only the change in momentum between the incoming and outgoing wind determines the actual momentum transferred. Intuition may say the best performance has to do with making use of the momentum of the wind in the direction it is blowing, but that is not always the case. If the sail can be configured to push (change the momentum of) the wind in a given direction, the sail will experience a force in the opposite direction (Newton's first law plus the concept that a change in momentum per unit time is the same as a force). So, if instead of keeping the sail perpendicular to the true wind it is angled such that the back of the sail is further upwind, it is possible for the boat to be making VMGDW greater than the true windspeed and simultaneously to have the sail's intersection with a true wind streamline moving downwind more slowly than the true wind which means the sails are pushing against i.e. upwind the true wind and receiving a push downwind ([IMG]VMGdwfttw_2.png[/IMG]).
Other important concepts are the conservation of momentum and energy in any inertial reference frame. If a quantity of momentum is extracted (subtracted in a vector sense) from the wind, that same quantity of momentum must be added (again, in a vector sense) to the boat or to the water; note also that a force applied over time is the same as momentum and may be an alternative trade to maintain conservation of momentum. The same goes for energy, which is a scalar (or magnitude only, non-vector) quantity. This is why the boat-fixed reference frame is often the easiest in which to make vector diagrams for analyzing sailing performance: the energy of the apparent wind in the boat-fixed frame does not change because the boat and sail are static and passive and have no external energy sources or sinks with which to give or take energy from the wind or water (ignoring frictional losses for the moment). The advantage that comes from this is simple: the magnitude of the momentum of the wind and the water in this frame do not change. Here is why:
The momentum (M) of a billiard ball (our analog for the wind) is the product of its mass (m) a scalar, and its velocity (V, a vector):
M = m * V
The kinetic energy (KE) of a billiard ball is half the product of its mass and the square of its speed (S = the magnitude of its velocity):
KE = M * S^2 / 2
In a typical apparent wind diagram of a sail, the billiard ball (apparent wind) comes into the sail at some angle of attack off the centerline of the boat and leaves the sail going parallel to the centerline. Because the sail is not moving in this reference frame it can neither give energy to nor receive energy from the billiard ball, so the KE of the ball cannot change (again, ignoring frictional losses for now). Solving for the speeds of the ball coming in and out of its interaction with the sail:
Sin = SQRT(2 * KEin / Min ) Sout = SQRT(2 * KEout / Mout)
Neither the mass of the ball nor its KE change as it goes over the sail (Min=Mout and KEin=KEout) in this reference frame, so the speed of the ball must remain constant (Sin=Sout) in this reference frame. This makes the calculation of the change in momentum of the ball across the sail a simple trigonometric exercise involving the speed of the ball and the angle it is turned by the sail. The change in momentum (a vector) is the same as the force (also a vector) exerted by the ball on the sail.
Sirclicksalot ( talk) 19:17, 15 June 2010 (UTC)
I had started by saying this is WP:OR but no, that's giving me airs and graces. This is plain classical mechanics, unadorned. It's fact, plain and simple. There is no need to put this in the article, this below is the reason other stuff must not go in the article. This is high school physics only. This could easily all be substantiated from WP articles, but there is no need, as it so uncontroversial. If you disagree with it then you are not literate in the most basic physics. Sorry. Leave aside your beliefs that sailing downwind with a VMG towards the directly downwind mark is possible. Leave aside what you've read the skipper of Oracle in the AC as having said. Just stay with the physics. I write this just to try and shake your convictions ever so slightly.
In order for one object to propel another in a given direction (consider two moving balls, or whatever) the first must have a component of it's motion in that direction relative to the motion of the second object. If I am travelling south at 10mph and you collide with me and I end up travelling south at more than 10mph then you must have had a southerly component to your velocity of more than 10mph. Otherwise the collision would have slowed me down in that particular direction. Uncontroversial, and of course we can decompose any particular motion so that it consists of the sum of one NS vector and one WE vector. When considering changes in NS velocity the WE velocity of the colliding objects van be disregarded. That is what vector decomposition lets us do, and it's done all the time in high school and undergraduate physics. It's not controversial and it's not rocket science. (Well, actually it is rocket science, but you get my drift, no pun intended).
So when a particle of the air collides with my yacht and the yacht is accelerated in a particular direction, the particle of the air must have had a velocity component in that direction faster greater in magnitude than the speed velocity component of the yacht in that particular direction.
The question then is, and you should all have seen this coming, if the yacht is going faster than the air in a southerly direction, how can collision with the air accelerate it in a southerly direction? And, sorry to disappoint, that's a rhetorical question, there is no satisfactory answer. Therefore sailing downwind VMG faster than the air is impossible. (I removed Mr. Beardsell's QED here Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)).
You don't need a diagram, do you?
Paul Beardsell ( talk) 14:52, 8 June 2010 (UTC)
Then someone says oh yes you can! And they're the skipper of an America's Cup yacht. Or they have endless qualifications, and they've read every book on yachting, and they've maybe even written one. Or someone has a PhD in Physics and they disagree? Well, then they're wrong, they forget the basics, if they ever knew them. Paul Beardsell ( talk) 14:57, 8 June 2010 (UTC)
The only thing wrong in what was written above here is the claim that there is, and can be, no satisfactory answer to this question: if the yacht is going faster than the air in a southerly direction, how can collision with the air accelerate it in a southerly direction?. It is difficult to explain a satisfactory answer when using a reference frame fixed to the water, but here it is (using the reference frame moving with the boat makes the answer obvious). (removed some snarkiness Sirclicksalot ( talk) 01:24, 16 June 2010 (UTC))
Simply put, the satisfactory answer is that even if the yacht is going faster - in the VMG sense - than the wind in the southerly direction, the portion of the sail, on which the true wind acts and which is not perpendicular to the true wind, can indeed be going more slowly - again in the VMG sense - than the true wind in the southerly direction.
Sirclicksalot (
talk)
03:19, 15 June 2010 (UTC)
The actual steady-state numbers will depend on the actual configuration (sail, hull type - iceboat, land-yacht, etc), but the diagram above clearly demonstrates that there can be a southward force of a southerly true wind on the fixed sail of a craft moving across that wind with a downwind (i.e. southward) VMG greater than the true wind. The angles chosen are not at all optimal but were selected to make understanding the concept as simple as possible. This model has a theoretical limit to the maximum VMG downwind so thermodynamic principles are not violated, which an important criterion in assessing any such model. In the case above the VMG limit is 1/(1-sin(22.5deg) ~ 1.62 * Vt. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
The part of the sail on which the wind acts is indeed, relative to the true wind, moving upwind (again, relative to the true wind - see Note below), and therefore "pushes" northward on the wind, from which Newton's Third Law plainly grants an ongoing thrust southward onto the sail, and, through the rigging, from the sail onto the yacht, more than adequate to counter all frictional forces for iceboats, land yachts, catamarans and other high-performance craft. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC) (Corrected which of Newton's laws was applicable 74.79.24.116 ( talk) 14:55, 17 June 2010 (UTC))
Note: I am not saying the sail is moving upwind relative to the water, only that the part of the sail on which true wind (i.e. a streamline) acts is moving downwind more slowly than the true wind. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
If the sail were perpendicular to the true wind, then Mr. Beardsell's analysis above would of course hold (you can't beat simple physics). However, in the actual case it is obvious that the sail is not perpendicular to the true wind direction, but is instead angled between the boat's velocity vector and the vector perpendicular to the true wind. That angle means that relative to the streamlines of the wind moving south at the true windspeed, the point at which the sail intersects any given streamline is moving more slowly than the true wind directly south along that streamline. You can't beat simple physics, especially when they are done correctly. QED Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
Streamlines are not some sort of hand-waving black magic invention; please stop and attempt to understand them. The vector diagram above is equivalent to moving the sail sideways and slightly down in calm air (less than 22.5 degrees South of West in the diagram, assuming South is down. In that case the angle of the sail is such that the sail would push North on the calm air which means the air would push South on the sail. Anyone who claims to understand the equivalence of different reference frames but thinks this diagram, and the calm-air equivalent description in this paragraph, are not physically realistic needs to show the error(s) in the diagram above and provide a corrected diagram. Continuing with baseless claims that it is not possible with neither correct nor valid supporting arguments may still provide humor for many but is otherwise getting a bit old. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
"So when a particle of the air collides with my yacht and the yacht is accelerated in a particular direction, the particle of the air must have had a velocity component in that direction faster greater in magnitude than the speed velocity component of the yacht in that particular direction."
If the above paragraph was true boats could not tack UP wind, which is an observed fact for centuries.( Eyytee ( talk) 15:52, 8 June 2010 (UTC))
Velocity = speed. Downwind VMG = progress over the water (or ground) towards the downwind mark = cos(ang) time velocity. USA 17 had VMG of 19 knots in 5-10 knots of wind. That is evidence. The models and explanations are found in the material that you deleted, which was all supported by citations, in particular to Bentwaithe's book. Benthwaithe provides polar charts showing VMG greater than wind speed.-- Gautier lebon ( talk) 07:49, 9 June 2010 (UTC)
I have a very simple counter example that disproves PB's statement at the top of this section (in its current form) : Boat is moving perpendicularly to the true wind, and accelerates forward. The magnitude of the velocity component of the air in the direction of the boat's acceleration is zero. The magnitude of the velocity component of the boat in the direction of the boat's acceleration is greater than zero. This is exactly the opposite of PBs claim, that the magnitude of the air's velocity component (in boat's acceleration direction) must be greater than the magnitude of the boat's velocity component (in boat's acceleration direction) Eyytee ( talk) 11:14, 9 June 2010 (UTC)
Paul Beardsell is making a fundamental error in the above analysis. He assumes that the boat interacts only with the air mass. He neglects the interaction with the water. While in reality the resulting acceleration of a boat depends on both forces(keel and sail), and vector diagrams show that the acceleration can be partially opposed to the apparent wind direction( Eyytee ( talk) 15:52, 8 June 2010 (UTC))
Paul Beardsell is correct in saying that the frame does not matter. However, the vector algebra is easier in some frames than in others. The deleted material used the frames that are adopted by all textbooks, precisely because the presentation is simpler. I still cannot understand why Paul refuses to look at Bentwaithe's book, which explains it all.-- Gautier lebon ( talk) 07:59, 9 June 2010 (UTC)
Your criticism here [where? this used to be part of a different thread until moved Nigelj ( talk) 20:04, 8 June 2010 (UTC)] is based on the 'conservation of velocity', which is not a recognised principle. 'Conservation of momentum' is, but as Eyytee says below [well, it's above now, but who cares anymore? Nigelj ( talk) 20:04, 8 June 2010 (UTC)], in order to 'see' momentum being conserved as a sailboat goes by, you would have to 'see' all the disturbances left behind in the air and the water after the sails and the keel have done their thing. Racing sailors are very familiar with 'dirty air' downwind of another boat, but to me that is all too complicated to visualise in such detail. In answer to your rhetorical question, the yacht is going faster than the south-going air, but in a south-westerly direction. By re-using the same magic that allows it to sail upwind, say 30 deg off the wind, it has now overtaken the southerly vector of the wind and is using it's 'upwind' ability to sail 30 deg off an apparent wind that is made up mostly of the wind due to its own movement, plus a small reduction and an angle in that wind due to the angle between its movement and the real wind. Just like in the vector diagrams in the article. One thing that's weird is that, unusually, the wind due to the boat's movement is much larger than the real wind. The real wind mostly serves to add a small angle to the 'movement wind', an angle that this very efficient boat can continue to claw itself along by, close hauled, getting just enough drive to overcome its minimal hull-drag. -- Nigelj ( talk) 18:39, 8 June 2010 (UTC)
OK, I'm outa here. If you are going to start rearranging other people's helpful comments so that they make no sense any more, and flooding the page with your own disordered comments, and getting abusive ("physics-illiterate" indeed!) and SHOUTING, then you can continue to argue without me. After you're done, we'll restore the page to a consensus version, but this is not helpful to improving the article at the moment. -- Nigelj ( talk) 20:04, 8 June 2010 (UTC)
Correct. But what counts is the APPARENT wind, not the true wind. That was explained in the material that you deleted.-- Gautier lebon ( talk) 07:44, 9 June 2010 (UTC)
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Many (including some editors) seem to have a problem understanding how achieving a downwind-VMG greater than true-wind-speed is possible. I propose to include a introductory vector diagram, that shows how the sail can produce a force with a positive forward-component that propels the boat, under this conditions. I cannot upload files yet, so I put the proposed diagram here: [1]. If the diagram needs improvement, I can change it. Eyytee ( talk) 22:13, 7 June 2010 (UTC)
Good start, but the force diagram needs a drag vector, so the true boat velocity can be derived, not just a given...-- Paul ( talk) 00:49, 8 June 2010 (UTC)
At the point where (speed over the ground)/cos(angle to the true wind)=(speed of the true wind) the sail provides no forward force (i.e. in the direction of the keel / wheels / skates). The slightest friction brings the vessel gradually to a halt. But, if all friction is eliminated the downwind point is reached at EXACTLY the same time as the free floating balloon. Paul Beardsell ( talk) 08:33, 8 June 2010 (UTC)
First and foremost, there really don't seem to be any RELIABLE, VERIFIABLE sources. Secondly, what sources there are appear to be reports of original research, none of which has made it through a peer review process since they first appeared in November of 2008.
Wikipedia's recommendations are: Exceptional claims require exceptional sources
Certain red flags should prompt editors to examine the sources for a given claim:
* surprising or apparently important claims not covered by mainstream sources;
* claims that are contradicted by the prevailing view within the relevant community, or that would significantly alter mainstream assumptions, especially in science, medicine, history, politics, and biographies of living persons. This is especially true when proponents say there is a conspiracy to silence them.
Exceptional claims in Wikipedia require high-quality sources.
If such sources are not available, the material should not be included.
The major "sources" in the section are to self-published videos demonstrating original research.
This "issue" has been publicized since at least 2008 with no peer-reviewed publications of such a spectacularly counter-intuitive notion. It is VERY hard to believe that such a scientific breakthrough could remain an orphan with no better explanation than a very dubious "thought experiment".
As indicated in the Wikipedia recommendations for such unauthenticated exceptional claims, this section should not be included.
Possibly a supporting site - but still not up to what I suspect Wikipedia needs - (( http://www.idniyra.org/articles/IceboatSailingPerformance.html)). Polars at (( http://www.west.net/~lpm/hobie/archives/v1-i3/feature3.htm)) show an Aussie 18 almost making downwing VMG of windspeed.
In fact, several sections in the article - The last 2 paragraphs and table in Sailing perpendicular to the wind are erroneous and speculative. Sailing on a broad reach, velocity made good are similarly speculative and unsupported. Aerodynamic drag on the sail is completely ignored. Boat speed is NOT a simple multiple of apparent wind.
I don't currently have library access to the book, "High Performance Sailing". These citations need to be checked and perhaps verified against second sources - even book authors can be wrong!
No problems with sailing faster than the wind - just with a downwind velocity made good greater than windspeed.-- QuietJohn ( talk) 06:17, 14 June 2010 (UTC)
ALmost all of the citations I have checked have been dubious or inaccessible to me. If the NALSA site (which I have looked at and searched for relevant data) has the supporting data, please CITE the web pages that support your claims. I'm quite neutral about the DDWFTTW phenomenon. It doesn't make sense to me, and I haven't found any data to convince me otherwise, so it's either wrong, or the page isn't providing the necessary information. Guide me to the polars- or other corroborating data and I'll be happy to concede. Until then, much of this article isn't appropriate for a Wikipedia entry.-- QuietJohn ( talk) 09:43, 14 June 2010 (UTC)
I know that this section seems hard to believe. Please read the citations and study them carefully before posting comments to the effect that this section is obviously wrong. I too did not believe that this was possible, until I did the research and found the citations given in this section. Others (including a physicist) were also skeptical, but then became convinced, see [7] and [8].-- Gautier lebon ( talk) 08:39, 10 December 2009 (UTC)
I've posted some responses in talk:sailing. Another interesting topic is sailing directly into the wind. I've never seen a turbine / prop craft "work" directly upwind in what I consider to be a controlled test - the so-called proof has been less than convincing. The "spork33" device can be simply adapted to demonstrate that this is possible on land. It's just inefficiency of props and turbines that make it hard to get something to work on water, as there's no fundamental law to say it can't work. In a thought experiment, this can be extended to make something work on water by say dropping and raising large sea anchors, and using energy from the wind through a gearing mechanism to winch the boat forward against the sea anchor, but necessitating the use of a complex device to drop sea anchors "upwind" and raise them with minimal energy loss if sustained progress is to be made. There are other possible variations of the same idea (really not so different from a turbine-prop in principle). Using a sea anchor to hold a boat in position with a turbine harnessing wind energy, storing the energy (ie in a battery) and then using it to propel the craft forward so that progress is made is fine, but this isn't continuous uninterrupted progress, and is somewhat unremarkable. —Preceding unsigned comment added by 202.180.87.174 ( talk) 23:56, 14 December 2009 (UTC)
Indeed the discussion in Talk:Sailing#Downwind_faster_than_the_wind should be read by anybody interested in this topic.-- Gautier lebon ( talk) 12:16, 18 December 2009 (UTC)
I have corrected the introduction and the terminology. Regarding the drawings, the arrows point in the correct directions for the vector algebra to work: just think of the case when the boat is moving directly upwind or directly downwind; I wear thick glasses, so I like the large font, and I presume that others will too, since it does not make the drawings any larger. Regarding performance of normal cruising boats, I just took the figure given in the sailing article; if you don't agree with it, then please update both articles so that they are consistent, and provide a reference. I like the borders on the tables, they are easier to read that way. I don't know what should be cleaned up in "Further Reading", maybe somebody can take care of that. Same regarding general improvement of the language: I've many revisions to the article, incorporating many good suggestions that were made on Talk:Sailing#Downwind_faster_than_the_wind. I don't know what more to do.-- Gautier lebon ( talk) 10:20, 29 January 2010 (UTC)
If you think that anything stated in the article is impossible, please consider that the following two reasons have already been stated, and shown not to apply:-- Gautier lebon ( talk) 11:22, 11 June 2010 (UTC)
1) Velocity made good downwind cannot exceed the speed of the wind because of the laws of conservation of energy
2) Velocity made good downwind cannot exceed the speed of the wind because there is no force on the sails when the boat reaches wind speed.
3) If it were possible to go faster downwind by tacking, then why do people bother with spinnakers?
4) There isn't any easily accessible published data that supports the statements that boats can achieved downwind VMG greater than wind speed.
5) The cited sources are not sufficiently reliable.
A balloon drifts downwind at the speed of the wind. It uses no energy to do that. Similarly, an iceboat can drift dead downwind at very close to the speed of the wind, because the friction of its runners on the ice is negligle.
That is, to proceed downwind at the speed of the wind requires essentially no energy.
If a boat can capture some energy from the wind, then it can use that energy to propell itself downwind faster than the wind. There is no violation of the law of conservation of energy because the energy captured from the wind is used to overcome the resistance of the surface (insignificant in the case of an iceboat) and the resistance of the apparent headwind induced by the boat's progress. As explained in the main article, when a boat sails at an angle to the wind, it can capture energy from the wind, even if its downwind progress is faster than the wind itself. This is because of the apparent wind shift, see below.
Also, it is easy to see that a device can be constructed that can capture the energy from the wind even when moving dead downwind, see below Talk:Sailing faster than the wind#deleted thought experiment.
As explained in the main article, the forward motion of the boat induces a wind that must be added to the true wind in order to find that apparent wind that strikes the sails.
If an iceboat sails dead downwind, then it will soon reach a speed close to the speed of the wind and the apparent wind on the sails will be nearly zero.
But if an iceboat sails downwind at an angle to the wind, there will be an apparent wind shift: the apparent wind will move forward. As explained in the main article, the iceboat will eventually find itself on a broad reach with respect to the apparent wind (apparent wind at 90 degrees to the boat's course). The apparent wind will still generate a forward force component, so the boat will continue to increase in speed and the apparent wind will shift even further forward. As explained in the main article, this can result in velocity made good (progress in the direction of the wind) that is greater than the velocity of the wind.
Note the key point: what drives the boat is the apparent wind, that is what the sails "see" and what the sails react to and what propelles the boat.
Most sailboats cannot accelerate enough when they sail downwind so that the apparent wind shifts to come forward of the beam, and this because the resistance of the water is so large. That is, the resistance from the hull prevents the boat from moving fast enough so that the apparent wind shifts forward of the beam. Therefore, the apparent wind will always be aft of the beam and a spinnaker will increase the speed of the boat. However, downwind progress might still be faster if the boat gybes downwind, even with a spinnaker, and indeed most books on racing tactics say that it will usually be faster to avoid a dead downwind course and to gybe back and forth, even if the sailboat is using a spinnaker.
The article provides citations to various observed data. The most accessible data are those from the first regatta of the 2010 America's Cup. The winning yacht, USA 17, completed the 40 nautical mile course (20 miles dead upwind, 20 miles dead downwind) in 2h32, in 5-10 knots of wind, see for example [9]. If the wind had been 10 knots all the time (which was not the case) and if the downwind VMG had been equal to the wind speed, then USA 17 would have needed 2 hours to complete the downwind leg. That means that it would have completed the 20 mile upwind leg in 32 minutes, that is, at about 40 knots made good, meaning well over 50 knots over the ground. Of course USA 17 did not achieve such speeds upwind: anybody can watch the video and see the displayed upwind speeds, which were just over 20 knots. In fact, it took USA 17 63 minutes to complete the 20 mile downwind leg. Even if winds had been 10 knots (and they were less), the downwing VMG was nearly 2 times wind speed.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
The citations in the article include many web sites, which are easily accessible, and a published book (by Bethwaite) which is still in print and easily available. One of the contributors to this discussion has provided a second book, also still in print and easily available: The Symmetry of Sailing: The Physics of Sailing for Yachtsman, by Ross Garret.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
As explained below, the material in the article is not sufficiently original or suprising to be published in a peer-reviewed scientific journal. So it is not clear what additional citations should be provided.-- Gautier lebon ( talk) 10:16, 15 June 2010 (UTC)
As promised, I've developed force diagrams that are meant to make the situation easier to understand. But I'm not convinced that what I have done can be understood easily. At first, I thought of making three diagrams, showing velocities and forces for three situations: (1) standstill (2) apparent wind at 90 degrees (3) apparent wind at 45 degrees. But then I decided to make separate diagrams for the velocities and the forces, with each diagram showing the three situations.-- Gautier lebon ( talk) 12:27, 11 June 2010 (UTC)
I would much appreciate comments on how to make the text below, and the diagrams, easy enough to understand so that they could be incorporated into the main article.-- Gautier lebon ( talk) 12:27, 11 June 2010 (UTC)
Consider an iceboat that is sailing at a course that is 135 degrees off the true wind. At the beginning, the boat is stationary. We will use the value "1" for the speed of the true wind. The apparent wind is equal to the true wind and comes from the same direction as the true wind. The velocity made good (VMG) downwind is zero. This is shown by the value "V0" in the chart below.
The boat will accelerate and will eventually reach a speed equal to to .707 times the speed of the wind. At this point, the apparent wind will come from 90 degrees (broad reach) and the speed of the apparent wind will also be .707. VMG is .5 This is shown by the value "V1" in the chart below.
At this point, the only resistance to forward motion is the friction of the iceboat's runners on the ice. But that is negligible.
So the boat will continue to accelerate and will reach a speed equal to 1.41 times the speed of the wind. At this point, the apparent wind will come from 45 degrees (close hauled) and the speed of the apparent wind will be 1. VMG is 1. This is shown by the value V2 in the chart below.
If the forward component of the force on the sails is sufficient, the boat can continue to accelerate, the apparent wind will shift further forward, and VMG will be greater than 1, that is, greater than the speed of the true wind. That is, the boat will progress downwind faster than the speed of the wind. The text and charts below show the force on the sails and the forward component of that force. It is not possible to determine theoretically whether the forward component at V2 would be sufficient to accelerate the boat further; but measurements of actual iceboat performances show that indeed it is. Iceboats accelerate until they are sailing at about 10 degrees (or less) off the apparent wind, and thus achieve speeds of 5 or more times the speed of the wind. This is the case even if the boat is sailing at 135 degrees off the true wind. So the VMG (progress in the dead downwind direction) is far greater than the speed of the wind.
The chart below shows the apparent wind and the sails on the iceboat when it is at a standstill (V0), on a broad reach (V1) and close hauled (V2). The angle of the sail is half of the angle of the apparent wind, which is the optimal angle in terms of generating a forward driving force. citation needed The force generated by the apparent wind on the sail is proportional to the square of the speed of the apparent wind. citation needed
The chart below shows the forward force resulting from the apparent wind when the iceboat is at a standstill (V0), on a broad reach (V1) and close hauled (V2). The force generated by the wind is perpendicular to the sails. citation needed It can be seen from elementary trigonometry that the forward component of that force is sin(sail angle).
Thus, the forward force when the iceboat is close hauled will be 38% of the total force on the sail. Again, whether or not that is sufficient to accelerate the boat further will depend on the resistance caused by the apparent wind (the headwind induced by the speed of the boat). As stated earlier, in practice it has been found that the force is indeed sufficient to further accelerate the iceboat (and in fact also other high-performance boats, including sailboats, as explained elsewhere in the article).
Here is the table that I've come up with for a course that is 135 degrees off the true wind. Please check the formulas and the calculations.-- Gautier lebon ( talk) 12:41, 15 June 2010 (UTC)
The formulas are:
V: boat speed
Alpha: angle of apparent wind
AW: Apparent wind speed
Boat speed | Alpha | Apparent wind speed | Force of apparent wind | Forward component | Drag component | Ratio drag/forward |
0.10 | 131 | 0.93 | 0.87 | 0.79 | ||
0.30 | 120 | 0.82 | 0.67 | 0.58 | ||
0.50 | 106 | 0.74 | 0.54 | 0.43 | ||
0.71 | 90 | 0.71 | 0.50 | 0.35 | ||
1.00 | 68 | 0.77 | 0.59 | 0.33 | 0.22 | 0.69 |
1.41 | 45 | 1.00 | 1.00 | 0.38 | 0.71 | 1.85 |
2.00 | 29 | 1.47 | 2.17 | 0.54 | 1.91 | 3.54 |
3.00 | 17 | 2.40 | 5.76 | 0.86 | 5.50 | 6.41 |
4.00 | 12 | 3.37 | 11.34 | 1.20 | 11.09 | 9.26 |
5.00 | 9 | 4.35 | 18.93 | 1.54 | 18.68 | 12.10 |
If an iceboat has a sail area of 6 square meters, and if it is sailing at 5 times the speed of the wind, the the foward force will be about 6*1.54 = 9, assuming the lift cofficient is 1. But the lift cofficient is about .66 (according to Bethwaite), so the forward force will be about 6.
The drag component will be about 18. So the speed of 5 times the speed of the wind can be achieved if the frontal surface that creates the drag (the surface of the mast, hull, runners, etc.) is less than 0.33 square meters (18*.33 = 6).
The popular International DN iceboat has a sail area of 6.5 square meters and can achieve 5 times the speed of the wind. This is perfectly consistent with the calculations above, given that the aerodynamically equivalent frontal surface of the iceboat is indeed probably about .33 square meters. citation needed
Why are we settling on English when this can be settled in Math? Both Gautier has posted diagrams above, and I have posted diagrams showing exactly how this works, given drag sufficiently small (doesn't need to be zero). What is appealing about these types of disputes over religious or political, is that they should be able to be resolved very quickly around a chalkboard. I suggest we attempt to do that. Generacy ( talk) 13:31, 14 June 2010 (UTC)
Also, if folk are looking for for more math, here is a link to another extensive treatment by MIT Professor Mark Drela on the topic. His treatment is specifically aimed at a DDWFTTW water craft, but near the end he addresses a ground based wheeled vehicle and makes the following statement "This confirms that the DDWFTTW condition V/W > 1 is achievable with a wheeled vehicle without too much difficulty". http://www.boatdesign.net/forums/attachments/propulsion/28167d1231128492-ddwfttw-directly-downwind-faster-than-wind-ddw2.pdf ThinAirDesigns ( talk) 18:41, 14 June 2010 (UTC)
I have the impression that some people are, at times, confusing some basic concepts. So here is a reminder of what we are talking about.-- Gautier lebon ( talk) 10:43, 15 June 2010 (UTC)
The energy that drives a boat comes from the transfer of kinetic energy from the wind to the boat's sails: the molecules of air strike the sail, a force is induced, and momentum and energy are transferred from the air to the sail.
I don't know whether the following explanation will be helpful, but I'm tossing it in for comment.-- Gautier lebon ( talk) 11:32, 15 June 2010 (UTC)
One can think of the molecules of air as billiard balls, and the sail as a flat panel that is struck by the billiard balls. There is a transfer of kinetic energy and momentum from the balls to the flat panel. If there is no contsraint on the panel, it will wind up moving in the same direction and the same speed as the billiard balls: this is drifting dead downwind at nearly the speed of the wind.
At that point the boat has kinetic energy, but it's velocity does not change.
Now imagine that the flat panel (the sails) and the boat are constrained to travel at an angle (say 135 degrees) to the direction from which the billiard balls are coming. for example because it is mounted on a rail. When the balls hit the panel, there will be a transfer of kinetic energy and momentum, but now the panel does not wind up moving dead downwind, it winds up moving along the rail, that is at an angle with respect to the direction from which the billiard balls are coming.
Consequently, the direction from which the billiard balls are coming changes: they appear to come from further forward as the boat increases in speed. If you adjust the angle of the flat panel, the incoming balls will still create a forward force on the panel (in addition to the sideways force that has to be resisted by the rail on which the panel is mounted). There is still a transfer of energy from the balls to the panel, and the boat may or may not accelerate, depending on the resistance to its motion along the rail.
Now imagine that the billiard balls are relatively spaced out, so that one hits the panel only every second. In between billiard balls, the boat will be slowed down by the resistance of its motion along the rail (assuming that the resistance from the air is negligle, for example because this experiment takes place in a vacuum). If that resistance from its motion along the rail is very small, then the boat will continue to advance along the rail (conservation of momentum and kinetic energy), slowing down only slightly. Then the panel is hit by a new billiard ball: this will result in the transfer of some energy and in an acceleration of the boat.
So the boat will continue to accelerate until the energy lost due to the resistance of its motion along the rail is greater than the energy transferred to it when a billiard ball hits the flat panel.
The boat's ultimate speed depends on the friction from the surface, on how efficiently it captures the energy from the billiard balls, and on how much energy there is in the billiard balls.
Sirclicksalot ( talk) 19:17, 15 June 2010 (UTC)
(updated description of forces' contribution to conservation of momentum Sirclicksalot ( talk) 19:27, 15 June 2010 (UTC))
I have alway preferred this model, it is easier to understand and makes much more sense than the reams of bogus verbiage I have seen over the years invoking Bernoulli and phantom venturis. I used it yesterday to explain all points of sail to a neophyte in about ten minutes. I will try here to extend this description.
As noted above, the billiard billiard ball model is a momentum- and energy-transfer model. That is, generally speaking energy and momentum are transferred between the two media - air and water (or air and land) - and anything those media touch. To be more accurate, it is the differential momentum and differential energy between the air and water that provides the capability to sail. If there is no difference in velocities (vector quantities) between the air and the water, a sailboat cannot move through the water in any direction without an external energy source (paddle, motor, etc.). But if there is no wind over the ground, a sailboat can move on a river with current because of the differential momentum and energy between the still air and the moving water. And now that DDWFTTW has been demonstrated, it is theoretically possible even to sail directly upstream on a calm day.
Ultimately, the existence of differential momentum and energy between the two media are the reason it is possible to move in any direction relative to the true wind, while using that same true wind as the sole motive force.
One thing to note in Gabon's example above is that the flat panel (sail) is perpendicular to the true wind direction. In that case the sail and boat VMGDW (Velocity Made Good DownWind i.e. parallel to the true wind) cannot exceed the true windspeed. Mr. Beardsell's analysis (Physical mechanics, above) is an excellent description of why. The reason I bring this up is to make the point that when momentum transfer occurs, momentum must be conserved, but it is the change in momentum between the wind (billiard ball) before and after it encounters the sail that is transferred to the sail. There is another point to be made here: momentum is a vector so by definition it has a magnitude and a direction; if the direction of the momentum of a billiard ball changes but the magnitude of the momentum does not, that still constitutes a change in momentum transferred from the billiard ball to the sail which changed it. Counter to intuition, the direction and magnitude of the momentum of the incoming medium (true wind, billiard balls, etc) does not matter, only the change in momentum between the incoming and outgoing wind determines the actual momentum transferred. Intuition may say the best performance has to do with making use of the momentum of the wind in the direction it is blowing, but that is not always the case. If the sail can be configured to push (change the momentum of) the wind in a given direction, the sail will experience a force in the opposite direction (Newton's first law plus the concept that a change in momentum per unit time is the same as a force). So, if instead of keeping the sail perpendicular to the true wind it is angled such that the back of the sail is further upwind, it is possible for the boat to be making VMGDW greater than the true windspeed and simultaneously to have the sail's intersection with a true wind streamline moving downwind more slowly than the true wind which means the sails are pushing against i.e. upwind the true wind and receiving a push downwind ([IMG]VMGdwfttw_2.png[/IMG]).
Other important concepts are the conservation of momentum and energy in any inertial reference frame. If a quantity of momentum is extracted (subtracted in a vector sense) from the wind, that same quantity of momentum must be added (again, in a vector sense) to the boat or to the water; note also that a force applied over time is the same as momentum and may be an alternative trade to maintain conservation of momentum. The same goes for energy, which is a scalar (or magnitude only, non-vector) quantity. This is why the boat-fixed reference frame is often the easiest in which to make vector diagrams for analyzing sailing performance: the energy of the apparent wind in the boat-fixed frame does not change because the boat and sail are static and passive and have no external energy sources or sinks with which to give or take energy from the wind or water (ignoring frictional losses for the moment). The advantage that comes from this is simple: the magnitude of the momentum of the wind and the water in this frame do not change. Here is why:
The momentum (M) of a billiard ball (our analog for the wind) is the product of its mass (m) a scalar, and its velocity (V, a vector):
M = m * V
The kinetic energy (KE) of a billiard ball is half the product of its mass and the square of its speed (S = the magnitude of its velocity):
KE = M * S^2 / 2
In a typical apparent wind diagram of a sail, the billiard ball (apparent wind) comes into the sail at some angle of attack off the centerline of the boat and leaves the sail going parallel to the centerline. Because the sail is not moving in this reference frame it can neither give energy to nor receive energy from the billiard ball, so the KE of the ball cannot change (again, ignoring frictional losses for now). Solving for the speeds of the ball coming in and out of its interaction with the sail:
Sin = SQRT(2 * KEin / Min ) Sout = SQRT(2 * KEout / Mout)
Neither the mass of the ball nor its KE change as it goes over the sail (Min=Mout and KEin=KEout) in this reference frame, so the speed of the ball must remain constant (Sin=Sout) in this reference frame. This makes the calculation of the change in momentum of the ball across the sail a simple trigonometric exercise involving the speed of the ball and the angle it is turned by the sail. The change in momentum (a vector) is the same as the force (also a vector) exerted by the ball on the sail.
Sirclicksalot ( talk) 19:17, 15 June 2010 (UTC)
I had started by saying this is WP:OR but no, that's giving me airs and graces. This is plain classical mechanics, unadorned. It's fact, plain and simple. There is no need to put this in the article, this below is the reason other stuff must not go in the article. This is high school physics only. This could easily all be substantiated from WP articles, but there is no need, as it so uncontroversial. If you disagree with it then you are not literate in the most basic physics. Sorry. Leave aside your beliefs that sailing downwind with a VMG towards the directly downwind mark is possible. Leave aside what you've read the skipper of Oracle in the AC as having said. Just stay with the physics. I write this just to try and shake your convictions ever so slightly.
In order for one object to propel another in a given direction (consider two moving balls, or whatever) the first must have a component of it's motion in that direction relative to the motion of the second object. If I am travelling south at 10mph and you collide with me and I end up travelling south at more than 10mph then you must have had a southerly component to your velocity of more than 10mph. Otherwise the collision would have slowed me down in that particular direction. Uncontroversial, and of course we can decompose any particular motion so that it consists of the sum of one NS vector and one WE vector. When considering changes in NS velocity the WE velocity of the colliding objects van be disregarded. That is what vector decomposition lets us do, and it's done all the time in high school and undergraduate physics. It's not controversial and it's not rocket science. (Well, actually it is rocket science, but you get my drift, no pun intended).
So when a particle of the air collides with my yacht and the yacht is accelerated in a particular direction, the particle of the air must have had a velocity component in that direction faster greater in magnitude than the speed velocity component of the yacht in that particular direction.
The question then is, and you should all have seen this coming, if the yacht is going faster than the air in a southerly direction, how can collision with the air accelerate it in a southerly direction? And, sorry to disappoint, that's a rhetorical question, there is no satisfactory answer. Therefore sailing downwind VMG faster than the air is impossible. (I removed Mr. Beardsell's QED here Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)).
You don't need a diagram, do you?
Paul Beardsell ( talk) 14:52, 8 June 2010 (UTC)
Then someone says oh yes you can! And they're the skipper of an America's Cup yacht. Or they have endless qualifications, and they've read every book on yachting, and they've maybe even written one. Or someone has a PhD in Physics and they disagree? Well, then they're wrong, they forget the basics, if they ever knew them. Paul Beardsell ( talk) 14:57, 8 June 2010 (UTC)
The only thing wrong in what was written above here is the claim that there is, and can be, no satisfactory answer to this question: if the yacht is going faster than the air in a southerly direction, how can collision with the air accelerate it in a southerly direction?. It is difficult to explain a satisfactory answer when using a reference frame fixed to the water, but here it is (using the reference frame moving with the boat makes the answer obvious). (removed some snarkiness Sirclicksalot ( talk) 01:24, 16 June 2010 (UTC))
Simply put, the satisfactory answer is that even if the yacht is going faster - in the VMG sense - than the wind in the southerly direction, the portion of the sail, on which the true wind acts and which is not perpendicular to the true wind, can indeed be going more slowly - again in the VMG sense - than the true wind in the southerly direction.
Sirclicksalot (
talk)
03:19, 15 June 2010 (UTC)
The actual steady-state numbers will depend on the actual configuration (sail, hull type - iceboat, land-yacht, etc), but the diagram above clearly demonstrates that there can be a southward force of a southerly true wind on the fixed sail of a craft moving across that wind with a downwind (i.e. southward) VMG greater than the true wind. The angles chosen are not at all optimal but were selected to make understanding the concept as simple as possible. This model has a theoretical limit to the maximum VMG downwind so thermodynamic principles are not violated, which an important criterion in assessing any such model. In the case above the VMG limit is 1/(1-sin(22.5deg) ~ 1.62 * Vt. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
The part of the sail on which the wind acts is indeed, relative to the true wind, moving upwind (again, relative to the true wind - see Note below), and therefore "pushes" northward on the wind, from which Newton's Third Law plainly grants an ongoing thrust southward onto the sail, and, through the rigging, from the sail onto the yacht, more than adequate to counter all frictional forces for iceboats, land yachts, catamarans and other high-performance craft. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC) (Corrected which of Newton's laws was applicable 74.79.24.116 ( talk) 14:55, 17 June 2010 (UTC))
Note: I am not saying the sail is moving upwind relative to the water, only that the part of the sail on which true wind (i.e. a streamline) acts is moving downwind more slowly than the true wind. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
If the sail were perpendicular to the true wind, then Mr. Beardsell's analysis above would of course hold (you can't beat simple physics). However, in the actual case it is obvious that the sail is not perpendicular to the true wind direction, but is instead angled between the boat's velocity vector and the vector perpendicular to the true wind. That angle means that relative to the streamlines of the wind moving south at the true windspeed, the point at which the sail intersects any given streamline is moving more slowly than the true wind directly south along that streamline. You can't beat simple physics, especially when they are done correctly. QED Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
Streamlines are not some sort of hand-waving black magic invention; please stop and attempt to understand them. The vector diagram above is equivalent to moving the sail sideways and slightly down in calm air (less than 22.5 degrees South of West in the diagram, assuming South is down. In that case the angle of the sail is such that the sail would push North on the calm air which means the air would push South on the sail. Anyone who claims to understand the equivalence of different reference frames but thinks this diagram, and the calm-air equivalent description in this paragraph, are not physically realistic needs to show the error(s) in the diagram above and provide a corrected diagram. Continuing with baseless claims that it is not possible with neither correct nor valid supporting arguments may still provide humor for many but is otherwise getting a bit old. Sirclicksalot ( talk) 03:19, 15 June 2010 (UTC)
"So when a particle of the air collides with my yacht and the yacht is accelerated in a particular direction, the particle of the air must have had a velocity component in that direction faster greater in magnitude than the speed velocity component of the yacht in that particular direction."
If the above paragraph was true boats could not tack UP wind, which is an observed fact for centuries.( Eyytee ( talk) 15:52, 8 June 2010 (UTC))
Velocity = speed. Downwind VMG = progress over the water (or ground) towards the downwind mark = cos(ang) time velocity. USA 17 had VMG of 19 knots in 5-10 knots of wind. That is evidence. The models and explanations are found in the material that you deleted, which was all supported by citations, in particular to Bentwaithe's book. Benthwaithe provides polar charts showing VMG greater than wind speed.-- Gautier lebon ( talk) 07:49, 9 June 2010 (UTC)
I have a very simple counter example that disproves PB's statement at the top of this section (in its current form) : Boat is moving perpendicularly to the true wind, and accelerates forward. The magnitude of the velocity component of the air in the direction of the boat's acceleration is zero. The magnitude of the velocity component of the boat in the direction of the boat's acceleration is greater than zero. This is exactly the opposite of PBs claim, that the magnitude of the air's velocity component (in boat's acceleration direction) must be greater than the magnitude of the boat's velocity component (in boat's acceleration direction) Eyytee ( talk) 11:14, 9 June 2010 (UTC)
Paul Beardsell is making a fundamental error in the above analysis. He assumes that the boat interacts only with the air mass. He neglects the interaction with the water. While in reality the resulting acceleration of a boat depends on both forces(keel and sail), and vector diagrams show that the acceleration can be partially opposed to the apparent wind direction( Eyytee ( talk) 15:52, 8 June 2010 (UTC))
Paul Beardsell is correct in saying that the frame does not matter. However, the vector algebra is easier in some frames than in others. The deleted material used the frames that are adopted by all textbooks, precisely because the presentation is simpler. I still cannot understand why Paul refuses to look at Bentwaithe's book, which explains it all.-- Gautier lebon ( talk) 07:59, 9 June 2010 (UTC)
Your criticism here [where? this used to be part of a different thread until moved Nigelj ( talk) 20:04, 8 June 2010 (UTC)] is based on the 'conservation of velocity', which is not a recognised principle. 'Conservation of momentum' is, but as Eyytee says below [well, it's above now, but who cares anymore? Nigelj ( talk) 20:04, 8 June 2010 (UTC)], in order to 'see' momentum being conserved as a sailboat goes by, you would have to 'see' all the disturbances left behind in the air and the water after the sails and the keel have done their thing. Racing sailors are very familiar with 'dirty air' downwind of another boat, but to me that is all too complicated to visualise in such detail. In answer to your rhetorical question, the yacht is going faster than the south-going air, but in a south-westerly direction. By re-using the same magic that allows it to sail upwind, say 30 deg off the wind, it has now overtaken the southerly vector of the wind and is using it's 'upwind' ability to sail 30 deg off an apparent wind that is made up mostly of the wind due to its own movement, plus a small reduction and an angle in that wind due to the angle between its movement and the real wind. Just like in the vector diagrams in the article. One thing that's weird is that, unusually, the wind due to the boat's movement is much larger than the real wind. The real wind mostly serves to add a small angle to the 'movement wind', an angle that this very efficient boat can continue to claw itself along by, close hauled, getting just enough drive to overcome its minimal hull-drag. -- Nigelj ( talk) 18:39, 8 June 2010 (UTC)
OK, I'm outa here. If you are going to start rearranging other people's helpful comments so that they make no sense any more, and flooding the page with your own disordered comments, and getting abusive ("physics-illiterate" indeed!) and SHOUTING, then you can continue to argue without me. After you're done, we'll restore the page to a consensus version, but this is not helpful to improving the article at the moment. -- Nigelj ( talk) 20:04, 8 June 2010 (UTC)
Correct. But what counts is the APPARENT wind, not the true wind. That was explained in the material that you deleted.-- Gautier lebon ( talk) 07:44, 9 June 2010 (UTC)