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Sailing downwind with a downwind VMG greater than wind speed

This is a respond to PB's arguments above, put here to avoid further confusion and clutter. PB claims that sailing dw with a dw VMG > 1 is impossible (I'm setting wind speed=1). He asserts that if the analysis is done in the rest frame of the water/ice/ground, this is clear. So let's do it in that frame. I'll ignore drag, treat the sail as if it were flat (for ease in describing angles) and assume the boat can only move parallel to its keel.

Consider an iceboat sailing at 45 degrees to directly dw, with a speed of 1.414 (never mind how it got like that, maybe someone towed it to speed and has just released it). At this moment the boat's VMG=1. According to PB the force of the wind should act to slow the boat down, and according to everyone else it should speed it up (assuming the sail is trimmed correctly, of course). So consider a parcel of air moving at wind speed that collides with the sail. Because the boat (and sail) has a vmg=1, this happens only because the sail is also moving perpendicular to the wind - but it does happen. The collision pushes the sail in the direction perpendicular to its plane. Since the plane of the sail is nor parallel to the keel of the boat, this clearly accelerates the boat (again, assuming the sail is oriented correctly).

It's easy to see this if you draw a diagram. Make the wind blow towards 12:00 o'clock or 0 degrees, so it's blowing from 6:00 o'clock. The boat is moving up the page and to the right, at 45 degrees (so towards 1:30) with a speed of 1.414 as above. The sail is (say) at 15 degrees to the boat, so its tack (the corner closest to the mast) is pointing towards 2:00. Collisions with air push the sail and boat perpendicular to the sail, towards 11:00. That has a positive component towards 1:30 that accelerates the boat, and another towards 10:30 that is perpendicular to the keel and does nothing. Therefore, if friction etc. are small enough, the boat will accelerate to a VMG>1 and (with one tack/jibe) can beat a balloon to a point straight dw. Waleswatcher (talk) 11:50, 9 June 2010 (UTC)

It's very refreshing to see what is an obviously honest attempt to address the real issues, and very helpful, as it lets me immediately make some compelling points against a very plainly drawn example. Thank you. (1) "According to PB ...": You nearly have my POV correct but not quite. In the frictionless situation you describe I am NOT claiming that the vessel is slowed down, I am claiming that it is neither slowed down nor speeded up. V=sqrt(2)*(true wind speed) is the limit at 45degs. Obviouly, where there is no friction VMG = (true wind speed) is possible. I am arguing against VMG > (true wind speed). The argument made by others is that VMG > (true wind speed) is possible. It is not. (2) "The sail is at 15 degrees to the boat ...": This is your mistake. At such an angle the sail is luffed - the wind is blowing the wrong way against the sail and is slowing the boat down!Paul Beardsell (talk) 21:57, 9 June 2010 (UTC)

Not true. The air hits the boat from 3:00 in the given situation. Since the tack of the sail points towards 2:00, the air hits the correct sail side which faces 5:00. See computation below.Eyytee (talk) 00:03, 10 June 2010 (UTC)

At angle 45 degrees and speed 1.414 * (true wind speed) the sail must be set directly along the keel line! Draw the diagrams! Such a sail cannot have a boat-forward component of force. The sail along the keel line, at 45degs and V=1.414, has no effect. Setting the sail at 15degs to the keel line is a brake. Thus your argument fails.

To support the above assertion I enter "enemy territory" and calculate apparent wind (s_aw,a_aw) where s_aw is the speed of the apparent wind (i.e. relative to the speed of the boat) and and a_aw is the angle of that apparent wind (i.e. relative to the boat's direction).Paul Beardsell (talk) 21:57, 9 June 2010 (UTC)

Why so complicated? You don't need to rotate the reference frame to align it with the boats axis. Just attach the frame to the boat and keep the orientation (x->east, y->north). Or simply use the vector formula from Apparent_wind : apparent_wind = true_wind - boat_velocity = (0,1) - (1,1) = (-1,0). So the apparent wind comes from east or 3:00, and hits the side of the sail which is facing 5:00.Eyytee (talk) 00:03, 10 June 2010 (UTC)

It is, (as careful application of the Feynman Problem Solving Algorithm does show), ((1-sqrt(2))*(true wind speed),0). [Do you really really really want to see the workings?] The important figure being the 0. The apparent wind in the example given by Waleswatcher is (from the boat's POV = apparent) directly ahead! Any setting of the sail other than amidships acts as a brake. Paul Beardsell (talk) 22:17, 9 June 2010 (UTC)

"The apparent wind in the example given by Waleswatcher is (from the boat's POV = apparent) directly ahead! Any setting of the sail other than amidships acts as a brake." If the first statement were true, the second would be as well. But the first statement is false. The apparent wind velocity is the true wind velocity minus the boat velocity. In my example that's a vector pointing to 9:00 (i.e. the apparent wind is blowing from 3:00 towards 9:00), with magnitude 1. But the boat is pointed at 1:30, so the apparent wind is not directly ahead, it's blowing from 45 degrees to the starboard (right) side of the bow, and so the boat just needs to be close hauled with the clew on the port (left) side. See my comment below for more details and yet another frame.Waleswatcher (talk) 00:33, 10 June 2010 (UTC)

Thanks for the correction on your point of view. But we're still in disagreement, because I claim that the wind will accelerate the boat. I have drawn the diagram and my conclusions are that the boat will accelerate. Are you sure you have the sail oriented along the line between 2:00 and 8:00?

If you're willing to change frames, the simplest one to use is neither the rest frame of the ice nor that of the boat, but rather the rest frame of the wind. In that frame, the ice is moving towards 6 o'clock at speed 1, the boat is aimed at 1:30 but is drifting directly sideways towards 3, and of course the air is at rest. Meanwhile the tack of the sail is pointing at 2:00 (and the clew at 8:00). So forgetting about the hull for a moment, the sail is moving to the right while angled up-right to down-left. Therefore there is a force vector on it up-left, pointing to 11 o'clock to be exact. Projecting that onto the keel, that has a positive component pointing to 1:30 that accelerates the boat. So it's not a brake.

Yes, the rest frame of the true wind makes it even easier than the rest frame of the boat (using apparent wind). Has anyone drawn the diagram in the fixed-true-wind frame yet? Sirclicksalot (talk) 18:05, 17 June 2010 (UTC)

Note that if the sail was set the other way at 15 degrees to the hull, that is with the tack pointing at 1:00, then it _would_ act as a brake. But that's the wrong trim (which is clear if you imagine being on the boat, and think about the apparent wind).Waleswatcher (talk) 00:28, 10 June 2010 (UTC)

I drew a diagram. Please check it. Generacy (talk) 12:18, 10 June 2010 (UTC)

Looks good to me, thanks for drawing it. PB, what do you say? Convinced?Waleswatcher (talk) 13:24, 10 June 2010 (UTC)

Dear Generacy and Waleswatcher: thank you for your valuable contributions. Indeed, the graph that Generacy has drawn is along the lines of what I propose to do, but it might still take me a couple of days. As stated above, it all becomes clear when you draw the force diagrams. And that is not OR, such diagrams are found in many books on sailing.--Gautier lebon (talk) 15:23, 10 June 2010 (UTC)

Typo?

This sentence:

If it can accelerate until it is sailing closer than 45 degrees to the true wind, then its velocity made good downwind will be greater than the velocity of the wind [...]

near the end of the Sailing on a Broad Reach section has a typo: I think it should be

... closer than 45 degrees to the apparent wind ...

Also, it would be more clear if it said

... velocity of the true wind ...

at the end of that phrase.

Sirclicksalot (talk) 01:42, 16 June 2010 (UTC)

You are absolutely correct, thank you for that. I will fix it.--Gautier lebon (talk) 12:03, 17 June 2010 (UTC)

Reference Suggestions

This article appeared in the Catalyst - Journal of the Amateur Yacht Research Society Apr 2009. It contains this Polar diagram from the book The symmetry of sailing by Ross Garrett, Sheridan House Inc., 1996. It also has a section on computing the best VMG, showing that downwind VMGs > true wind are possible.Eyytee (talk) 20:04, 17 June 2010 (UTC)

Problems with the polar diagram: (1) Only a crosswind scale is shown. Often the aspect ratio of diagrams gets mauled by the printer or when otherwise reproduced e.g. on a computer monitor. (2) Even assuming the aspect ratio is 1:1 still it is not all that obvious (without a ruler) that the VMG of the sailboat in the downwind direction exceeds the speed of the wind. Paul Beardsell (talk) 20:40, 17 June 2010 (UTC)

But quote the ref in the article! Paul Beardsell (talk) 20:41, 17 June 2010 (UTC)

The cited article was already cited in the article, it is foonote 41. And the polar chart cited above appears right at the top of the article, so it is already cited. It is true that you need a ruler to actually compute the VMG, but it is obvious at first sight that VMG is greater than wind speed. The argument about scale distortion is a quibble: that sort of distortion is usually less than 5%. Anyway, the diagram in question is merely a publicly available version of a similar diagram published in Bethwaite's book, where the text accompanying the diagram explicitly states that VMG>wind speed. So we have a perfectly reliable source to that effect. And it is already cited and quoted.--Gautier lebon (talk) 07:14, 18 June 2010 (UTC)

It's a quibble but a valid one. And, no, it is not immediately obvious [to me, at least], the perpendicular distance back to the crosswind line is what has to be measured, not the radial distance. Paul Beardsell (talk) 08:32, 18 June 2010 (UTC)

Clarity needed

Restoring the original posting by QuietJohn before it got mangled by postings strewn throughout it by others, making it unreadable. QJ makes important points here which, if addressed, would improve the article. Please leave it intact.

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The critical arbiter of what needs to be said in this article is that it is an encyclopedic entry. Write it as such! Even the discussion page is getting bogged down with proselytizing. It is the purpose of the MAIN ENTRY to report and explain the topic. The lengthy discussion simply indicates that hasn't been accomplished and pollutes the efforts to make a worthy article.

In its current form, it isn't clear whether the article is talking about an interesting theory, or an established fact.

The enthusiasm of the contributors is commendable, but seems to edge over into proselytizing rather than reporting reality. That, perhaps more than anything else raises suspicion, especially when the cited sources I have checked are not quite what they are stated to be.

• If it is a theory without documented confirmation, say so. I'm sure that would be fine as a Wiki entry. What are the predictions? What are the attempts being made to confirm them? And perhaps include several of the 'personal research' results and poorly documented indications that seem to confirm the theory. Bob Dill, author of one particularly "convincing" illustration has an extensive article at ((http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf)) which may have some useful leads. Unfortunately, he quotes no courses relative to wind, doesn't discuss optimum course relative to wind, other than stating "In significant part, their speed is limited by their inability to sail at high speed on a beam reach. This is a function of two things:

• At high apparent wind speeds sails have to be nearly fully sheeted to avoid excessive luffing drag and its attendant negative pitching moment."

Present the theory and exactly what the theory is. Some reasonable looking references seem to be coming along now. If it's an aerodynamic theory, present it as such, talking about forces - such as lift, drag and friction rather than velocities and "thought experiments". Present the mechanics / physics for what it is, rather than helices and billiard balls.

• If it is a fact, present real, verifiable facts based on reliable measures. Citing the BMW Oracle velocities relative to wind and calculating the ratio based on the lower values is fishy to say the least. Another Wiki article notes that the wind gradient meant windspeeds of 15 knots at some height above deck. Such "stretches" add to incredulity rather than credibility. The cited ice (or land) yacht data were vague, reporting only an approximate wind direction and a plotted course, even missing a compass rose.

Suggesting that the phenomenon is so well known that no-one deems it worth writing about is just plain silly.

Yes, I admit I can't check the books - I'm currently sailing in a foreign country - on a high performance, wing masted multihull and don't have library privileges here! The comments still apply to the other citations and the overall article approach. If books explain it, quote the book, redraw diagrams from the books, crediting the original drawings. It shouldn't be this hard!

All I'm asking is that you report reality - honestly and without embellishment. And, of course, I'd like to understand the basis. --QuietJohn (talk) 18:36, 15 June 2010 (UTC)

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Here is the overall response to this posting. Please see below for the point-by-point response.--Gautier lebon (talk) 09:59, 18 June 2010 (UTC)

But that is what we are doing, namely reporting reality honestly and without embellishment. There is no editor who does not believe that downwind VMG greater than windspeed can be achieved. Some people think that the article can be improved, and that is fine. As I proposed elsewhere, please create a new section "Proposed improvement", quote the existing text, and propose an improved text. Then we can all work together to improve the article.--Gautier lebon (talk) 09:59, 18 June 2010 (UTC)

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Here is the mangled version:

The critical arbiter of what needs to be said in this article is that it is an encyclopedic entry. Write it as such! Even the discussion page is getting bogged down with proselytizing. It is the purpose of the MAIN ENTRY to report and explain the topic. The lengthy discussion simply indicates that hasn't been accomplished and pollutes the efforts to make a worthy article.

The discussion page is bogged down by proselytizing from people who refuse to believe an fact known to many, and well documented in the artice: some modern high-performance saiboats, most sandyachts, and all iceyachts, can achived downwind VMG greater than wind speed. The article explains how. But one or two people do not understand the explanation and challenge the citations. The discussion page is about explaining things so that those people can understand. To date, this has been succesful: the skeptics have seen the light, eventually.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

In its current form, it isn't clear whether the article is talking about an interesting theory, or an established fact.

The article makes it perfectly clear that it is presenting established facts, supported by citations.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

The enthusiasm of the contributors is commendable, but seems to edge over into proselytizing rather than reporting reality. That, perhaps more than anything else raises suspicion, especially when the cited sources I have checked are not quite what they are stated to be.

The article reports reality. Please idenity specific discrepancies between the text in the article and the citations. Those should be corrected.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

• If it is a theory without documented confirmation, say so. I'm sure that would be fine as a Wiki entry. What are the predictions? What are the attempts being made to confirm them? And perhaps include several of the 'personal research' results and poorly documented indications that seem to confirm the theory. Bob Dill, author of one particularly "convincing" illustration has an extensive article at ((http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf)) which may have some useful leads. Unfortunately, he quotes no courses relative to wind, doesn't discuss optimum course relative to wind, other than stating "In significant part, their speed is limited by their inability to sail at high speed on a beam reach. This is a function of two things:

• At high apparent wind speeds sails have to be nearly fully sheeted to avoid excessive luffing drag and its attendant negative pitching moment."

Why discuss theories when the purpose of the article is to present (1) established facts and (2) explain why such surprising results can be achieved in reality?--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

Present the theory and exactly what the theory is. Some reasonable looking references seem to be coming along now. If it's an aerodynamic theory, present it as such, talking about forces - such as lift, drag and friction rather than velocities and "thought experiments". Present the mechanics / physics for what it is, rather than helices and billiard balls.

The purpose of the article is not to provide a tutorial on aerodyamics. It is to present what happens in reality and to explain why that happens. The discussion page has turned into a tutorial on the basic physics of sailing because skeptics have claimed that the observerd reality was not possible, for example because of violations of the law of conservation of energy. So naturally the discussion page address that issue.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

• If it is a fact, present real, verifiable facts based on reliable measures. Citing the BMW Oracle velocities relative to wind and calculating the ratio based on the lower values is fishy to say the least. Another Wiki article notes that the wind gradient meant windspeeds of 15 knots at some height above deck.

Acutally that was an incorrect reading of a citation. If you look at the article on wind gradients now, you will see that no such claim is made. What is fishy about noting that a yacht that sails 20 nautical miles downwind in 63 minutes in winds of 7-10 knots quite obviously had a downwind VMG greater than wind speed? Why don't you look at the vidoes of the Cup races? That should convince anybody. I don't know how much more "real" and "verifiable" you can get.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

Such "stretches" add to incredulity rather than credibility. The cited ice (or land) yacht data were vague, reporting only an approximate wind direction and a plotted course, even missing a compass rose.

Suggesting that the phenomenon is so well known that no-one deems it worth writing about is just plain silly.

What do you mean by "no-one"? Book references were given . The phenomenon itself might not be "well known", but it can be explained using well known and widely accepted physics. Scientifically there is nothing new or extraordinary about it, therefore it is "silly" to demand scientific publications about it. Eyytee (talk) 20:12, 15 June 2010 (UTC)

Yes, I admit I can't check the books - I'm currently sailing in a foreign country - on a high performance, wing masted multihull and don't have library privileges here! The comments still apply to the other citations and the overall article approach. If books explain it, quote the book, redraw diagrams from the books, crediting the original drawings. It shouldn't be this hard!

But the article does exactly that: it quotes books, and shows diagrams that are based on what is found in the books!!!--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

All I'm asking is that you report reality - honestly and without embellishment. And, of course, I'd like to understand the basis. --QuietJohn (talk) 18:36, 15 June 2010 (UTC)

But that is exactly what the article does. I'm not sure what you mean by "high performance wing masted multihull". If you mean a boat that, like USA 17, used a rigid wing instead of a sail, then you should be able to reproduce for yourself the kind of performance that is documented in the article. Regarding understanding the basis, the article contains many references that have enabled previous skeptics to understand what is going on. If you could explain more specifically what you do not understand, then perhaps one of the editors could provide an explanation for that.--Gautier lebon (talk) 12:01, 17 June 2010 (UTC)

Apology and thanks

This has taken some time to appear, longer than it should have, but I have genuinely been busy in my "real" life. Firstly, I am sorry I have so arrogantly and dismissively rejected the assertion that sailing downwind VMG better than the wind itself is possible. Secondly, thanks for not being more harsh in your criticism of my arguments re the impossibility thereof, and the tone in which I have sometimes conducted them.

In external correspondence it has been suggested it would be helpful were I to say how and at what point I "saw the light". It was with the vector arithmetic of Eyetee and Waleswatcher early AM UTC 10 June. Nothing speaks louder than the maths. All entreaties to "everyone knows" or the quotes of America's Cup skippers or to the assertions of some sailing author count as for nothing if the maths is not done. Paul Beardsell (talk) 19:43, 17 June 2010 (UTC)

Dear Paul, thank you very much for this. As I stated with regard to previous conversion from disbelief to belief, no apologies are required regarding the initial disbelief. This stuff is counter-intuitive, and it is not easy to explain in writing. I will however accept your apologies regarding the form, because I do think that you should have posted your skepticism to the talk page rather than drastically editing the article. Anyway, I am pleased that we have one more person who now understands the reality.--Gautier lebon (talk) 07:06, 18 June 2010 (UTC)

Your apology would be more convincing if you didn't refer to me as a hoaxter in your next breath (immediately below). Still wrong and still arrogant. Spork33 (talk) 21:38, 17 June 2010 (UTC)

This comment is unclear because it refers to a comment that appears in the section below. That comment is:--Gautier lebon (talk) 07:43, 18 June 2010 (UTC)

However, WP is not a text book, and the article reads like one. It is also not a newspaper yet we are reporting the assertion of the hoaxtersuniversity team as if we were journalists. It's secondary sources we need, as per WP:V.

The "hoaxter" was meant to be ironic and turns around something I said, days ago. I am sure your achievements will speak for themselves. [I look forward to the quality secondary sources which will allow us properly to write about this at WP as per WP:V.] That you may (see, I do it again) have done something seemingly unbelievable and that this provokes disbelief should not surprise you. Imagine you did something and everyone said "so what" or "how obvious". That many find it difficult to believe adds to your achievement. Paul Beardsell (talk) 06:36, 18 June 2010 (UTC)

The DDFTTW section is not based solely on the self-report of the university team. It includes citations to various sources stating that this is possible, to two independent self-reports of actually having constructed a device that did it, to a sailing magazine article on one of those achievements, and to a couple of physics discussion web sites that explain how an initial claim had been thought to be a hoax and then was found to be plausible. So we have, in my opinion, more than adequate reliable secondary sources for this material.--Gautier lebon (talk) 07:40, 18 June 2010 (UTC)

(1) That there are now other citations is the case, now, but once wasn't. However, regarding these citations, still we find recent comments here (not only from me) that some citations do not support assertions in the article. Paul Beardsell (talk) 08:34, 18 June 2010 (UTC)

(2) An important point about "not based solely on the self-report". According to WP:VS the "not based solely" is not the issue. The first hand report should not appear at all! WP is supposed to be based only on WP:VS. We need ideally to quote only from secondary sources. Paul Beardsell (talk) 08:34, 18 June 2010 (UTC)

Neither JB nor I have been too worried about whether our efforts are included in this article as yet. We expect that within the next 2 or 3 weeks we will have a NALSA certified world record doing precisely what we've claimed from the start. I would think there could hardly be a more qualified secondary source. That being said, The evidence for the reality of DDWFTTW is overwhelming. We've built small-scale working models and demonstrated and documented them under carefully controlled conditions, we've built a full-scale manned vehicle and demonstrated it at a NALSA event, we've presented the analysis a dozen different ways, and we've even posted detailed build videos so others could reproduce our results - and many have. But I digress... let's just wait for the NALSA results Spork33 (talk) 08:15, 18 June 2010 (UTC)

Hear, hear! Paul Beardsell (talk) 08:35, 18 June 2010 (UTC)

Outdent. Paul Beardsell says:

According to WP:VS the "not based solely" is not the issue. The first hand report should not appear at all! WP is supposed to be based only on WP:VS.

This is not quite right. There is an exception to the use of secondary sources, see Wikipedia:Verifiability (which is the correct reference) namely the use of self-published sources as sources on themselves. This exception is what allows Wikipedia to include summaries of movies, TV series, etc. Similarly, in the present case, it is OK to use the San Jose University project web site as a source to report on what the San Jose University project says that it is doing. I don't see any justification for waiting for the NALSA results: in my opinion, the section in question is fully compliant with Wikipedia policies.--Gautier lebon (talk) 10:10, 18 June 2010 (UTC)

No, it is not. That you have found an exception doesn't mean your proposed exception is valid. I do not think your reading of the guidelines is sympathetic to the intention thereof. It is always preferable to have reliable secondary sources. I carefully word the following: If GL's reading were correct then the manufacturer of any perpetual motion machine ought to be documented at WP using the "inventor's" own web site as reference. We want WP to be reliable. Therefore we err by excluding true stuff rather than err by including false stuff. Therefore the team's own unverified assertions as to performance, as to achieving what many think (at least at first) to be impossible, must be included in WP only with the utmost circumspection. There is no urgency here. It's a reference book, an encyclopedia. Not the front page of The Times. No hurry, back off, even those who claim to be members of the team here present are content to wait. Paul Beardsell (talk) 10:25, 18 June 2010 (UTC)

Ah yes - but how do you know I'm a member of the team without a second source??? Spork33 (talk) 12:32, 18 June 2010 (UTC)

We don't, but WP:V etc applies to the article, not to its talk page. Paul Beardsell (talk) 14:15, 18 June 2010 (UTC)

Continued criticism of article

Out of politeness I ought to let the dust settle on the above section before continuing but, what the heck: The article is much better than it once was. However, WP is not a text book, and the article reads like one. It is also not a newspaper yet we are reporting the assertions of the hoaxtersuniversity team as if we were journalists. It's secondary sources we need, as per WP:V. It isn't good enough at WP to be merely correct. [Of course, it's better to be correct than wrong, as I quickly admit before too many fingers are pointed.] And there's a touch too much WP:SYN going on also. Paul Beardsell (talk) 19:43, 17 June 2010 (UTC)

The DDFTTW section is not based solely on the self-report of the university team. It includes citations to various sources stating that this is possible, to two independent self-reports of actually having constructed a device that did it, to a sailing magazine article on one of those achievements, and to a couple of physics discussion web sites that explain how an initial claim had been thought to be a hoax and then was found to be plausible. So we have, in my opinion, more than adequate reliable secondary sources for this material.--Gautier lebon (talk) 07:45, 18 June 2010 (UTC)

Just to note one example ... the "Sail Magazine" article in particular is a solid reference and falls well within WP guidelines. The Senior Editor of the magazine did the outside research himself to find out if ddwfttw were theoretically possible and then checked with reliable witnesses who were there to see the Ivanpah runs. He did all this outside of communication with the team (as he should) and team members only found out about it later through other sources. People who say the Blackbird vehicle claims are not independently documented up to WP standards are just wrong. The team were grateful that he did his homework as he should have. ThinAirDesigns (talk) 13:34, 18 June 2010 (UTC)

In particular QuietJohn's questioning above is very much to the point. It is unhelpful to intersperse his careful reasoning with lengthy comments as it makes his arguments difficult to follow, almost unreadable. To paraphrase him as briefly as I can: This is an encyclopedia not Popular Mechanics. Paul Beardsell (talk) 19:52, 17 June 2010 (UTC)

Indeed, I had some trouble understanding whether QuietJohn doubted that downwind VMG > wind speed is possible, or whether he just was saying some combination of (1) the citations are insufficient and (2) there is too much tutorial material in the article. As stated numerous times, I strongly disagree that the citations are insufficient. Regarding the tutorial matieral, my view is that it should be kept to a minimum (in the article, we can have more on the talk page) but some is required, otherwise most people won't understand why VMG greater than wind speed is possible and does not violate the laws of physics.--Gautier lebon (talk) 07:19, 18 June 2010 (UTC)

OK, seeing you agree, I will move your comments interjected into QuietJohn's argument to the end of it. Paul Beardsell (talk) 08:44, 18 June 2010 (UTC)

One example: QuietJohn asserts, as I have, that some of the citations do not support the assertions they seem to. A way forward here is to remove those assertion to the Talk page. I've done that, here, in the past, and it ought to be done again. It's WP policy. Although this time perhaps I'll let someone else do so. Paul Beardsell (talk) 19:58, 17 June 2010 (UTC)

The disputed citations and statements should be left in the article but tagged with in-line templates, and then discussed here. The appropriate tag adding syntax can be found here The tags look like this: {{Citation needed (lead)}}. Here are some examples that might come in handy:1234--Paul (talk) 20:45, 17 June 2010 (UTC)

I fully agree with Paul.H's suggestion from a procedural point of view. From a substantive point of view, I still disagree that there is any text in the article that is not supported by a reliable citation. May I suggest the following? Please open a new section on this talk page, titled "Items to improve", quote the exact text from the article that appears to you not to be supported by a citation. We can then check whether this is the case and either find a supporting citation or remove the text in question.--Gautier lebon (talk) 07:08, 18 June 2010 (UTC)

Another reference suggestion

Marchaj, Czeslaw Anthony, Aero-hydrodynamics of Sailing, Dodd, Mead & Company, New York, 1979. I believe newer revisions are available. Of special interest are Chapter I (High speed sailing, pp. 84-127) and Chapter H (Land and hard-water sailing craft, pp. 128-152) of Part 1. The latter contains speed polars along with the equations for maximum speeds (below). If L/D is 3-4 the maximum Vmg/Vt to leeward is ~ 2.1-2.6.

Max Vmg to windward: (Vmg/Vt)max = 1/2 * (1/sin(ε_A) - 1) at γ = 45 + ε_A/2

Max Vs: (Vs/Vt)max = 1/sin(ε_A) at γ = 90 + ε_A

Max Vmg to leeward: (Vmg/Vt)max = 1/2 * (1/sin(ε_A) + 1) at γ = 135 + ε_A/2

where

ε_A = β = cot^-1(L/D), degrees = angle of course sailed wrt apparent wind

L/D = ratio of lift (L) to drag (D); the equations are worked out for sail drag only but Professor Marchaj makes the point that you can also use overall L/D, where D adds to the sail drag (necessary to get lift) the parasitic drag(hull-air) and friction (hull-water or runner-ice or wheel-ground).

γ = angle of course sailed wrt true upwind, degrees

Alternate formulations using 1/sin(ε_A) = √(1+(L/D)²):

Max Vmg to windward: (Vmg/Vt)max = (√(1+(L/D)²) - 1) / 2

Max Vs: (Vs/Vt)max = √(1+(L/D)²)

Max Vmg to leeward: (Vmg/Vt)max = (√(1+(L/D)²) + 1) / 2

Sirclicksalot talk) 23:17, 17 June 2010 (UTC)

(fixed typo - missing paren in Max Vmg to leeward; converted to greek symbols; added alternative formulations Sirclicksalot (talk) 12:44, 19 June 2010 (UTC))

(Changed lambda to gamma Sirclicksalot (talk) 01:46, 20 June 2010 (UTC))

Very helpful, thank you. I have added this reference.--Gautier lebon (talk) 07:16, 18 June 2010 (UTC)

Conservation of energy

Paul Beardsell asserts (if I understand correctly) that VMG cannot exceed wind speed because to do so would violate the law of conservation of energy. But this is not correct. A balloon that drifts downwind does not use any energy (even though the wind itself does use energy, for example to overcome the friction over the ground). Thus a device can progress dead downwind at the speed of the wind without capturing any energy from the wind.--Gautier lebon (talk) 09:09, 8 June 2010 (UTC)

So what? Paul Beardsell (talk) 09:30, 8 June 2010 (UTC)

So a balloon does not use any energy to drift downwind at the speed of the wind. If a boat can capture some energy from the wind as it moves downwind, then the boat can progress downwind faster than the speed of the wind without violating the law of conservation of energy (since it takes zero energy to drift at the speed of the wind, not counting surface friction). The boat needs the energy to overcome the friction from the surface and, more importantly (especially for an iceboat) the resistance from the induced apparent headwind.--Gautier lebon (talk) 15:42, 10 June 2010 (UTC)

If a device captures some energy from the wind (or has an internal power source), then it can progress downwind faster than the wind. It needs the energy in order to overcome the resistance from the surface (if it is a sailboat or iceboat or sand yacht) and in order to overcome the resistance of the apparent headwind induced by its motion.--Gautier lebon (talk) 09:09, 8 June 2010 (UTC)

This is patently not necessarily true! It assumes the conclusion being "proven". And it's muddled, conflating force with energy. Paul Beardsell (talk) 09:29, 8 June 2010 (UTC)

All right, let's take it step by step. Energy =force x distance. The energy from the wind is required to overcome the resistance encountered by the device when it progresses some distance over some surface. Is that clear? If not, PLEASE go read basic text books which explain this.--Gautier lebon (talk) 09:44, 8 June 2010 (UTC)

Here we have no difference. Paul Beardsell (talk) 10:19, 8 June 2010 (UTC)

That a device can capture energy from the wind while moving dead downwind, and thus achieve dead downwind speed greater than wind speed, can be seen from Talk:Sailing_faster_than_the_wind#Deleted_thought_experiment. Thus, there is no issue related to conservation of energy.--Gautier lebon (talk) 09:09, 8 June 2010 (UTC)

I say the thought experiment is flawed as it takes as a premise that which it purports to prove, again. This is a circular argument. Paul Beardsell (talk) 09:29, 8 June 2010 (UTC)

The tought experiment does not take any premise. It shows how one can build a device that, by storing energy, can achieve average downwind progress faster than the wind.--Gautier lebon (talk) 09:50, 8 June 2010 (UTC)

There were several thought experiments. The one to which I referred were the corkscrewing sailors on the cylinder. Paul Beardsell (talk) 10:19, 8 June 2010 (UTC)

The real question is whether a real boat, such as an iceboat, can capture enough energy from the wind when sailing downwind to overcome the induced apparent headwind and the friction from the surface. That question cannot be answered theoretically, you actually have to build a device and test it. But that is precisely what has been done, for the past 30 years or so, and the original article had ample citations, including from Bentwaithe, who is an authority on the matter.--Gautier lebon (talk) 09:09, 8 June 2010 (UTC)

No it can be answered theoretically because I say it cannot be done, this downwind malarky, theoretically. For something to be done practically when theoretically it can NOT be done falsifies the theory. But the theory on which I am depending is Newtonian mechanics. That's what these downwind chappies say they are falsifying, whether they know it or not. I did start arguing this from a conservation of energy POV but GL said no, consider the force diagrams. Well, the magical force diagrams presented always have a forward force, as if this were a given. And they are mere sketches! I will present proper force diagrams. Paul Beardsell (talk) 09:29, 8 June 2010 (UTC)

So we should take your statement "I say it cannot be done" as sufficiently authoritative to conclude that Benthwaite does not know what he is talking about? You previously argued conservation of energy. You are now invoking Newtonian mechanics. But is is precisely Newtonian mechanics that explains why it is possible to achieve downwind VMG greater than wind speed. Again, the material that you deleted explained that to the satisfaction of many other editors, including several physicists. When looking at this from the Newtonian point of view, please consider that the only forces that count are those induced by the APPARENT wind and by the resistance of the surface.--Gautier lebon (talk) 09:50, 8 June 2010 (UTC)

No! You need take nothing I say on my authority alone. I am NOT trying to put questionable material into WP. You are. I am having a discussion about physical mechanics on a talk page. That's all. You are free to ignore what I say. Paul Beardsell (talk) 10:19, 8 June 2010 (UTC)

Yes, you are trying to put questionable material into WP. You inserted the sentence to the effect that a boat cannot outrun a balloon. You are not merely having a discussion on the talk page, you made major deletions to the article, including deleting all the citations that supported the opposite of your thesis. I am not free to ignore what you say, because you have said that you will continue to delete such material (and citations) from the article.--Gautier lebon (talk) 13:38, 8 June 2010 (UTC)

Further, a cursory examination of the actual performance of USA 17 during the 2010 America's Cup should convince anybody. The yacht covered its downwind leg at VMG of 19 knots, in winds of 5-10 knots. That is, VMG was well over 2 times wind speed. Granted, the wind shifted a bit, but the shifts were not large (less than 20 degrees) and not constant. So there is no way that a balloon would have drifted down to the downwind mark at anywhere near the speed of USA 17. Again, please consider the basic data: downwind VMG of 19 knots in 5-10 knots of wind. What more evidence is required, given that numereous citations (alas, deleted by Paul Beardsell) explain how this is achieved?--Gautier lebon (talk) 09:09, 8 June 2010 (UTC)

This is all unsupported baloney not supported by the citations given. Nowhere is this AC stuff said in terms presented here. It's WP:SYN which is why I removed it from the article. Paul Beardsell (talk) 09:29, 8 June 2010 (UTC)

It was not VMG toward the windward point, it was speed thru the water. All agree, speed thru the water can be faster than the wind. But only at an angle where (speed thru the water)/cos(angle to true wind) < (speed of true wind). And that means the free floating balloon will beat you every time to the directly windward point. Also in a yacht race the DW buoy is not necessarily DW directly as wind changes. The speed to the DW buoy can be greater than true wind speed if the DW buoy is not directly downwind. But a free floating balloon still beats you to the line drawn thru the bouy perpendicular to the wind. Every time. And no sailing book can truthfully say different and no cited reference has so contradicted this truth. Paul Beardsell (talk) 09:36, 8 June 2010 (UTC)

It was not speed through the water, it was speed over the ground. Downwind VMG is the time taken by the boat to cover the distance beween the upwind mark and the downwind mark. The wind changes were not significant enough to affect the calculations. Contrary to what you say, Benthwaite directly contradicts your assertion. Bentwaithe's book (published by a reliable publisher) flats states that downwind VMG can be greater than windspeed, which means that the boat reaches the downwind mark faster than a free floating baloon.--Gautier lebon (talk) 09:42, 8 June 2010 (UTC)

Speed over the ground is NOT REPEAT NOT VMG towards the windward point. Tides aside, speed thru the water and over the ground are the same. Bentwithe does not (from your supplied quotations) say VMG-directly-towards-directly-windward-point exceeds true windspeed. Paul Beardsell (talk) 10:19, 8 June 2010 (UTC)

Actually Bentwaithe does say exactly that: VMG downwind (meaning speed through the water/over the ground in the dead downwind direction) is greater than wind speed. If you had the book, you would see it.--Gautier lebon (talk) 13:36, 8 June 2010 (UTC)

Please feel free to quote him, directly, here. The problem is either you misunderstand or he is wrong, as the Great Bentwaithe has surely not overturned classical mechanics? Paul Beardsell (talk) 15:41, 8 June 2010 (UTC)

I already quoted him adequately in the material that you deleted. Nobody is overturning classical mechanics, the problem is that you are misapplying certain basic physical principles, as many have tried to explain to you, see below.--Gautier lebon (talk) 15:42, 10 June 2010 (UTC)

I only heard of this stuff two days ago, but I already think I have some understanding of how it works. Tell me if the following is right (and if it helps to clear up Paul's misunderstanding). One might think that no vehicle can outrun the wind using wind power alone, on the grounds that the most efficient way to translate wind energy into forward motion is via a flat sail perpendicular to the wind. But this is not true, because when the vehicle is in motion, an angled sail or propeller can slice through the wind more efficiently, effectively absorbing more energy from the wind than the /stationary/ cross-section of the sail or propeller could. By passing through the air at an angle, you are absorbing wind energy at many points in rapid succession, giving you a larger /effective/ cross-sectional area with respect to the wind, without increasing forward friction.

I'm not offering a complete explanation here, just an oversimplified one addressing the question of how you in principle this can absorb more energy than a flat sail could, in a way fully consistent with classical mechanics. Am I at all on track here, and is this at all helpful? ScottForschler (talk) 11:02, 18 June 2010 (UTC)

You are correct, and this is a very good explanation. But we would need a source that says that, in some form or another, before we could add it to the article. Can you find a source that provides that explanation?--Gautier lebon (talk) 08:49, 21 June 2010 (UTC)

Afraid not; I just came up with this on the top of my head trying to think it through on my own. I'd be curious if any technical descriptions of sailing mechanics explain it along similar lines though.ScottForschler (talk) 19:00, 21 June 2010 (UTC)

L/D and VMG to leeward

From the equations above, it turns out that any fixed sail craft with a close-hauled system L/D > 2.83 (√8) can have VMG to leeward faster than true windspeed. Sirclicksalot (talk) 12:54, 19 June 2010 (UTC)

"any boat can make good downwind faster than the real wind"

Even in context the assertion "any boat can make good downwind faster than the real wind" needs to be qualified. Paul Beardsell (talk) 11:03, 18 June 2010 (UTC)

You are correct. I have modified the text to match the citation. Thank you for suggesting this.--Gautier lebon (talk) 08:24, 21 June 2010 (UTC)

Effect of apparent wind

This is not clear, or at least allows for easy misinterpretation:

"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."

1. "As the apparent wind increases" define this term in the previous paragraph.
2. The difference between true wind and apparent wind is due to the velocity of the boat. Yes, the velocity increases because of the acceleration, but it is not the acceleration that causes apparent wind.
3. "further increase in apparent windspeed. Not sure what the significance is here; apparent wind shifting forward always makes less forward force available, not more. What causes the boat to accelerate is that the forward forces generated by the sail are more than the friction and drag forces on the sail and boat. As the boat accelerates and its velocity increases the apparent wind goes forward the ability of the sails to extract momentum (integral of force over time) goes down at the same time the friction and drag forces increase. When the forces are in equilibrium the acceleration stops and the maximum velocity has been reached.

I realize some of this is covered in the next sentence but the separation, and the attention given to apparent windspeed, makes it sound like there is somehow more energy/momentum/force available for acceleration as the apparent windspeed increases. It is in my experience a common misperception, but it is not at all the case and should not be in any way implied. This kind of misunderstanding is what is important to avoid. Even C. A. Marchaj's Sailing Theory and Practice in its original 1964 edition had the slot between foresail and mainsail acting as a converging nozzle providing thrust like a jet, which had a lot of people believing it, but he retracted that in later revisions. Sirclicksalot (talk) 20:14, 18 June 2010 (UTC) (messed up signing this a few times, but it's okay now)

I basically agree with your comments and would welcome a suggestion for how to improve the text. But I disagree with respect to one point. It seems to me that the apparent wind shifting forward does not necessarily make less forward force available. That may or may not be the case, depending on the efficiency of the sails.--Gautier lebon (talk) 08:27, 21 June 2010 (UTC)

Sirclicksalot (talk) 14:03, 23 June 2010 (UTC) I agree that low sail efficiency at extremely large beta (apparent broad reach i.e. near running) may generate less forward force than will be possible as boatspeed increases and the apparent wind goes forward, but that case is not what the article is about; also any boatspeed increase with the apparent wind abaft of abeam causes a drop in apparent windspeed which more than makes up for any increases due to improved beta (see model below). Certainly once the apparent wind approaches abeam and the sail begins acting as a foil the available force must drop with decreasing beta (again see the model below). In any case efficiency has nothing to do with available force anyway. Perhaps the article could say that sail efficiency increases as the apparent wind goes forward from running and broad up to a maximum around the point it comes abeam and drops after that, but to really talk about efficiency it would need to get into L/D plots and define sail efficiency.

A simple model (below) shows that less forward force is indeed available as the apparent wind goes forward i.e. for a constant course relative to a true wind, as the boatspeed increases and the apparent wind angle (beta) gets smaller, the available forward force decreases for the model where the apparent wind is deflected directly astern as well as for the model where the apparent wind is deflected through an angle which is the lesser of a fixed angle or directly astern.

The first image describes the geometry and equations of a simple F = -k delta(Vapparent) model:

The second image is a spreadsheet implementation of the models described above; force is proportional to the quantities labeled "delta Va" in the worksheet. Both Max force (apparent wind deflected directly astern) and Limited force (apparent wind deflected no more than a maximum angle). The plots' ordinates are delta Vapparent which is analogous to available force; the plots' abscissae? are boatspeed which increases with decreasing beta. The plots plainly show that less forward force is available (in this model) as the apparent wind goes forward:

Sirclicksalot (talk) 14:03, 23 June 2010 (UTC)

Thank you for this, but, if I understand correctly, you are assuming that the force is proportional to the magnitude of the apparent wind. But the total force on the sails is proportional to the square of the magnitude of the apparent wind, so the forward force depends on the angle and on the square of the magnitude. That is the relation that I used for the 135-degree table above. But maybe I misundertand your formulas and your table.--Gautier lebon (talk) 11:58, 24 June 2010 (UTC)

Your understanding is close but not quite correct (and my diagram has an error dVapparent/dt should be ΔVapparent). The table has longitudinal delta velocities (not apparent wind). Delta velocities are indeed proportional to the forward force available; the tilde (as in F ~ ΔV) means proportional to. For the steady state or instantaneous case, I am converting

F = d(mV)/dt

into this form:

F = ΔV dm/dt

ΔV is proportional to velocity, and dm/dt is the mass flow rate of air which is constant and is equal the product of density and area and velocity, so the units are correct and the force calculated is proportional to the square of velocity in this approach.

This is equivalent to your table: when using a force formula e.g. lift force

F = C_L S_A q

which is the same as

F = C_L S_A ½ ρ_A V_a²

where

C_L = coefficient of lift

S_A = sail area

q = dynamic pressure due to apparent wind = ½ ρ_A V_a²

ρ_A air density

V_a apparent wind velocity

then the proportionality constant between ΔV and V_a is buried in the coefficient C_L, along with other proportionalities. Sirclicksalot (talk) 15:18, 24 June 2010 (UTC)

Limitations

I note the limit of top speeds flattens out with, and is not proportional to, true windspeed in Figures 3 and 11 of Bob Dill's report (corrected Figure number Sirclicksalot (talk) 12:05, 25 June 2010 (UTC))

 http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf

to the 16th Chesapeake Sailing Yacht Symposium in Annapolis in 2003. What causes this? Is it a real limit? Should it be part of the WP article? Sirclicksalot (talk) 21:00, 18 June 2010 (UTC)

My hunch is that this is due to the fact that the resistance due to the apparent wind (induced by the headwind) increases with the square of velocity. But, unless we have sources explaining that, we should not include it. Separately, thank you for this additional useful citation, which I have added to the article.--Gautier lebon (talk) 08:39, 21 June 2010 (UTC)

I just realized what the limitation is: righting moment. At high wind-relative speeds the apparent wind goes forward so the resultant vector (lift plus drag) is to leeward and nearly perpendicular to the craft. The component force which is perpendicular generates a heeling moment which must be balanced by a righting moment. For any single design of craft and ballast there is a limited righting moment available to balance the heeling moment; that limits the maximum force that can be generated by the sail and therefore the maximum speed of the craft. An increasing wind would eventually tip the craft over if the sail or foil were not eased. This model predicts that the ratio of craft speed to windspeed goes down with increasing wind because easing reduces the L/D; this is borne out in Figures 5 and 12 in Bob Dill's report. Sirclicksalot (talk) 12:05, 25 June 2010 (UTC)

(fixed typo Sirclicksalot (talk) 12:04, 26 June 2010 (UTC))

Mind changer. Light switch

This sentence copied from Criticism Zero, above, was, to me, very important in understanding how sailing downwind with a VMG in the downwind direction greater than the speed of the wind is possible. It allows the apparent wind (a fictitious concept from the POV of a spectator on the shore) to be completely ignored and the fact (i.e. non-fictious concept from the POV of the spectator on the shore) of the boat's progress VMG in the direction of the wind faster than the wind to be understood:

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)

Paul Beardsell (talk) 10:34, 18 June 2010 (UTC)

The apparent wind is not really a 'fictitious concept' from the POV of a spectator on the shore, if you see it as the vectorial difference between air & sail velocities that he observes. Considering it is not different than considering the velocity difference between billiard balls, when analyzing their collision from the table's POV. Yes, I know that it is mathematically identical to a reference frame transformation, but you don't have to interpret it that way, if you want to keep the POV of a spectator on the shore.

Geez, he said "fictitious from the POV of the spectator;" give him a break. I know some have said describing the situation from a different POV has added to the understanding; this is the one that turned him around (and it's mine, all mine, so I get all the strokes, bwahahahaha) Sirclicksalot (talk) 18:06, 18 June 2010 (UTC)

Anyway, if you want an intuitive explanation in the ground frame, I recommend the squeezed wedge analogy.Eyytee (talk) 11:25, 18 June 2010 (UTC)

When discussing the coriolis force we know that it "exists" in certain frames of reference but that in others it is just inertia, Newton 1. But the argument as to whether it is "fictitious" or not continues. The apparent wind, according to the man on the shore, is the true wind. I am not saying that the man on the shore is incapable of understanding the concept of apparent wind but, for him, the wind apparent to the boat is a mental construct, not reality in his frame of reference. That's all I meant by "fictitious". Paul Beardsell (talk) 11:32, 18 June 2010 (UTC)

"The apparent wind, according to the man on the shore, is the true wind." You are hung up on semantics. If the man on the shore is interested in the collision between the sail and the air, then he has to consider the velocity difference between them. But nobody forces him to call this velocity difference by the name "apparent wind".Eyytee (talk) 18:26, 18 June 2010 (UTC)

"for him, the wind apparent to the boat is a mental construct". All vectors are just mental constructs.Eyytee (talk) 18:26, 18 June 2010 (UTC)

PB is not the only one hung up on semantics here: the true wind is a felt reality to the observer on the ground, not just a mental construct, and has a direct analogy to the force on the DDWFTTW craft; and "fictitious" has a connotation given PB's past slights of the boat-at-rest frame in this discussion; and maybe there are still a few raw wounds. But should we get hung up about our favorite stinking reference frame??!! PB: solve the problem in every reference frame; every point of view has potential to increase understanding; it doesn't click for everyone in the fixed observer frame. The rest of you: he's on board, lighten up (don't spoil my - me, mine, all mine, bwahahahaha - victory!). Sirclicksalot (talk) 20:18, 18 June 2010 (UTC)

I think the tutorial, wherever it resides (talk or article), should be done in all three reference frames: supporting medium (ground/water) at rest (wind is true wind); boat at rest (wind is apparent wind); air at rest (wind is ... well, nonexistent). Sirclicksalot (talk) 18:06, 18 June 2010 (UTC)

Oh yeah, for DDWFTTW a fourth frame would be with a blade of the prop at rest (with the cart, wind, and the rest of the world spinning around it, heh;-) (oh right, that's an accelerating frame). Sirclicksalot (talk) 18:06, 18 June 2010 (UTC)

I am becoming more and more convinced that the last of these (recommended by waleswatcher IIRC) is actually going to be the easiest to understand, especially the diagram. Though they are correct and I do understand them and they do demonstrate the principle, I personally (i.e. my opinion) am not satisfied with the existing diagrams in the article, but I have trouble articulating my dissatisfaction (it's something idiotically vague like "it should be more clear and obvious") so until I can offer something better I'll just shut my mouth. Sirclicksalot (talk) 18:06, 18 June 2010 (UTC)

Please don't. Those diagrams remain meaningless to me. Each and every vector and quantity needs to be clearly labelled and defined. I suspect doing so may cause the diagrams to be redrawn. Paul Beardsell (talk) 14:04, 19 June 2010 (UTC)

Mind changer animation

Based on PBs description of which explanation changed his mind I made this animation. It shows how the air can push the boat, even with a DW-VMG > true wind. Is this a good way to explain it? Eyytee (talk) 22:22, 18 June 2010 (UTC)

That is very interesting. Fascinating to watch. But this is where I'm not sure about this frames of reference issue. It is clear that we have a couple of 'cherry-pip squeezing' effects going on at once to achieve something extraordinary. But what is not so clear is, where do those blue wind-balls go next, after the impact with the slab-sail. To my eye, they would bounce off to the right, but as a sailor, I know that the boat is close-hauled and the apparent wind is from bow to stern, so the balls should be deflecting off to the left. (a) Is my eye wrong, or (b) is this an artefact of the unusual (to a sailor) frame of reference, or (c) is this an artefact of using a slab for a sail instead of a thin, curved aerofoil? --Nigelj (talk) 22:53, 18 June 2010 (UTC)

OK having watched it for another few minutes I see it is a combination of (a) and (b): In this frame of reference, the air is indeed deflected down and to the right. To an observer on the boat, this would look like the air travelling down the sail from front to back and being deflected off to starboard as expected when close-hauled. I'm starting to wonder what these diagrams (with deflected air shown) would tell us about 'dirty air' after a boat has passed on any point of sail. Very nice. Thank you. Well done. --Nigelj (talk) 22:58, 18 June 2010 (UTC)

Thanks Nigelj, I was having the same problem. I agree blue dots are

1. deflected upwind (Newton 3 then gives mostly thrust (lift?) and some heeling moment - probably more obvious in boat-at-rest frame i.e. apparent wind), and
2. deflected to the right of the streamline but not as fast as the sail is moving to the right so this is also to the rear of the sail (Newton 3 then gives heeling moment and some drag).

Centerboard or tracking wheels/blades resolves these forces to forward motion against rolling/skating/hull friction, and to heeling moment Everything is there! Sirclicksalot (talk) 02:35, 19 June 2010 (UTC)

Sweet! BRAVO, Eyytee! This shows that the key is the sail being not perpendicular to the wind, which makes the sail's intersection/interaction with a streamline have its VMG to windward wrt the true wind while the craft - to which the sail is attached - is making VMG to leeward wrt the true wind; that is the counter-intuitive part. Man, this explains everything. I get your wedge videos (finally) and they are great, but this presents it better in that it can be grasped quicker, and in the frame where the counter-intuitive part resides (I still agree it's also obvious in the apparent wind frame, but not everyone can go there). I think it's the interaction with the streamline; I'm curious what you think, Eytee. This reference frame appears to be ground/water at rest because centerline of the craft is constant (negligible sideslip if soft water, no sideslip for hard water or land), is that right? Can you make the same vid in the other reference frames (boat at rest at least wrt VMG downwind; and true wind at rest)? I doubt it will show it better but it might. To paraphrase an old quote "sailboats and sails are a watermelon seed between the thumb and forefinger of God." Sirclicksalot (talk) 02:35, 19 June 2010 (UTC)

1. The reaction due to the wind on the sail at any point is (at best) perpendicular to the sailcloth (slightly aft of that due to drag between wind and cloth in reality)
2. That reaction provides a forward-going force component big enough to overcome friction/drag on the hull/wheels/skis, and at the same time when resolved differently, a downwind component big enough to provide the VMG that we are demonstrating here
3. To provide that reaction, the 'wind-balls' have to deflect to the right in this frame of reference (θ_incident = θ_reflected, or slightly worse due to drag between wind and sailcloth), but that's OK as the reaction we get (perpendicular to sail) does all we want of it per 1 and 2
4. To generate lift efficiently when closehauled (i.e. punching into, and partially overtaking the wind in this near-downwind direction), the airflow over the sail must remain laminar, which is why we use cloth aerofoils and not flat sheets of plywood (even though the animation implies this. This slab is OK with wind-balls, but would produce too much turbulence and therefore drag in a real wind vector field). --Nigelj (talk) 10:24, 19 June 2010 (UTC)

It's a bit of a nit to pick, but I am not sure I strictly agree with this last point. The reason we use cloth sails is that they are easy to reef in a storm and to take down at the end of the day and transport; when performance outweighs convenience we use solid wings. Wings are still not sheets of plywood, of course, but even a sheet of plywood, though sub-optimal as a sail, has a lift-drag ratio which is all that is required to move a craft and have a velocity which exceeds the true wind speed if hull drag and friction can otherwise be kept low enough. And maximizing sailing speed by definition requires the lowest achievable angle of attack (a.k.a. β or ε_A), so even those using cloth sails in performance craft (e.g. iceboats) set them as flat as possible as speeds increase, and the thin flat wings used in specialty craft are not any more different from the sheet of plywood than necessary to keep from stalling at the leading edge at a very low angle of attack, which is not a lot. For flat plate aerodynamics see Marchaj, Aero-hydrodynamics of Sailing, 1980, pp 216, 238-241. Btw, some libraries, and probably a lot of college and university libraries, do have at least some edition of one or more of the Marchaj books. E.g. Schenectady, NY, San Jose, CA, San Francisco, CA and Cornell University have them; the Bahamas Library Service, Syracuse, NY and Mountain View, CA does not; Rochester, NY has Sailing Theory and Practice. Sirclicksalot (talk) 14:45, 19 June 2010 (UTC)

Great animation! Possibly the bounce of the blue balls could be shown with the resultant force decomposed into perpendicular vectors, one in the direction of the boat's motion. But even without that change it can still replace (OK, supplement, if you like) most of the diagrams in the article. I would dearly like to know what if any toolset was used to help create the animation. Brilliant! Paul Beardsell (talk) 13:31, 19 June 2010 (UTC)

Thanks. I have added the force vectors in the youtube version of the animation Eyytee (talk) 06:07, 3 July 2010 (UTC)

I held a set square on the stern of the animation's boat and moved it with the stern so as to enable me to see the apparent wind (i.e. from the sailor's POV). Also very instructive. And may (or may not!) be easy enough to generate that view (i.e. boat frame) from the existing animation, Eyytee? That would illustrate the explanations immediately above. Paul Beardsell (talk) 13:52, 19 June 2010 (UTC)

Mind changer animation 2.0

Based on the suggestions I made a new version of the animation (youtube version). It shows all three frames and the trace of an air particle. Obviously the deflection is not realistic as it ignores the interaction of air with air. It is more like a boat in space, mounted on a rail and propelled by balls being shot at the sail. But it is enough to show how downwind VMG > windspeed is possible.Eyytee (talk) 00:25, 23 June 2010 (UTC)

Now I also made a DDWFTTW version of the stream line animation. It shows all three frames and the force vectors (at the end).Eyytee (talk) 14:27, 28 June 2010 (UTC)