3465:. 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."
3559:), 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.
257:"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.
2263:
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.
2980:
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.
112:
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).
1169:
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
38:
2104:
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.
279:
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.
1977:. 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.
1254:. This exception is what allows Knowledge 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 Knowledge policies.--
2068:
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?--
2405:
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.
116:
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: -->
1996:
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.--
1424:
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.
2400:
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.
133:
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 : -->
3621:
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
3581:
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
3023:
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 -
2960:
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
2533:
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
2404:
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
2103:
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
1791:
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
1773:
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
1524:
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
953:
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
910:
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.
792:
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,
670:
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
526:
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.
171:
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
107:
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
3548:
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
3341:
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
2501:
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'
2460:
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
1995:
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
1562:
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
1447:
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.
358:
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,
2262:
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
2045:
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
1957:
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.
1392:
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,
1057:
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,
935:
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
931:
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
699:
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
278:
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
274:
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?
2399:
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
2122:
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
2067:
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
857:
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
755:
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
694:
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
595:
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
583:
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
115:
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
3280:
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
3017:
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
2979:
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
1470:
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
1423:
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
1281:
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
3650:). 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 : -->
2475:
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
829:
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
132:
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
111:
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
3215:
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
2455:
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
1168:
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
1585:
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
875:
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
784:
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 /
760:)) 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:
636:
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
608:
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 /
600:)) 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:
3361:
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
1739:
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
527:
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: -->
3045:
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
626:
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
2465:
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
3549:
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
1358:
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
1640:
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
2266:
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?
2381:"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."
1827:
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
911:
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.--
3222:
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!).
491:
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.
734:
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.
590:
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.
2145:
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.
3346:
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?
3157:." 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".
1035:(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.
2672:ĪV 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.
315:
2502:
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:
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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).
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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
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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
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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.--
3123:. 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".
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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.
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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
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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.--
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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.--
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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
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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.--
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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.--
3046:
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.
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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.--
2018:
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.
135:(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!
576:
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
2236:
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
3063:" 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)
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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. --
1563:
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.--
954:
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.--
3515:, 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
239:. 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.
2172:
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.--
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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
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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
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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.
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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.
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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.
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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:
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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).
3299:
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.
153:
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.
2580:). Delta velocities are indeed proportional to the forward force available; the tilde (as in F ~ ĪV) means proportional to. For the steady state or instantaneous case, I am converting
3394:
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).
1973:
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
550:
It's a quibble but a valid one. And, no, it is not immediately obvious , the perpendicular distance back to the crosswind line is what has to be measured, not the radial distance.
1958:
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.--
3115:
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
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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.
283:
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?
2202:
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?
1540:
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
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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.--
1916:
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.--
1086:(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
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213:: 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.
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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
207:
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-: -->
471:
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 : -->
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Centerboard or tracking wheels/blades resolves these forces to forward motion against rolling/skating/hull friction, and to heeling moment Everything is there!
768:
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?--
2925:
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
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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.--
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efficiently when closehauled (i.e. punching into, and partially overtaking the wind in this near-downwind direction), the airflow over the sail must remain
3504:, 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
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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.
3391:
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
1875:
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
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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
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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.--
972:
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.
671:
a new section "Proposed improvement", quote the existing text, and propose an improved text. Then we can all work together to improve the article.--
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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?
739:
The article reports reality. Please idenity specific discrepancies between the text in the article and the citations. Those should be corrected.--
764:ā¢ At high apparent wind speeds sails have to be nearly fully sheeted to avoid excessive luffing drag and its attendant negative pitching moment."
604:ā¢ At high apparent wind speeds sails have to be nearly fully sheeted to avoid excessive luffing drag and its attendant negative pitching moment."
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Your understanding is close but not quite correct (and my diagram has an error dVapparent/dt should be ĪVapparent). The table has longitudinal
1031:" was meant to be ironic and turns around something I said, days ago. I am sure your achievements will speak for themselves. That you
106:
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 : -->
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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.
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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
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This is patently not necessarily true! It assumes the conclusion being "proven". And it's muddled, conflating force with energy.
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All I'm asking is that you report reality - honestly and without embellishment. And, of course, I'd like to understand the basis. --
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All I'm asking is that you report reality - honestly and without embellishment. And, of course, I'd like to understand the basis. --
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This is all unsupported baloney not supported by the citations given. Nowhere is this AC stuff said in terms presented here. It's
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proposed exception is valid. I do not think your reading of the guidelines is sympathetic to the intention thereof. It is always
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for example because of violations of the law of conservation of energy. So naturally the discussion page address that issue.--
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harsh in your criticism of my arguments re the impossibility thereof, and the tone in which I have sometimes conducted them.
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But the article does exactly that: it quotes books, and shows diagrams that are based on what is found in the books!!!--
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In its current form, it isn't clear whether the article is talking about an interesting theory, or an established fact.
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In its current form, it isn't clear whether the article is talking about an interesting theory, or an established fact.
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There were several thought experiments. The one to which I referred were the corkscrewing sailors on the cylinder.
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I say the thought experiment is flawed as it takes as a premise that which it purports to prove, again. This is a
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America's Cup skippers or to the assertions of some sailing author count as for nothing if the maths is not done.
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make less forward force available. That may or may not be the case, depending on the efficiency of the sails.--
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discussion; and maybe there are still a few raw wounds. But should we get hung up about our favorite stinking
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1684:(fixed typo - missing paren in Max Vmg to leeward; converted to greek symbols; added alternative formulations
3489:(at best) perpendicular to the sailcloth (slightly aft of that due to drag between wind and cloth in reality)
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perpendicular to the wind, which makes the sail's intersection/interaction with a streamline have its VMG to
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This comment is unclear because it refers to a comment that appears in the section below. That comment is:--
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Suggesting that the phenomenon is so well known that no-one deems it worth writing about is just plain silly.
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Suggesting that the phenomenon is so well known that no-one deems it worth writing about is just plain silly.
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The tags look like this: {{Citation needed (lead)}}. Here are some examples that might come in handy:1234--
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wind speed. So we have a perfectly reliable source to that effect. And it is already cited and quoted.--
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OK, seeing you agree, I will move your comments interjected into QuietJohn's argument to the end of it.
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the theory. Bob Dill, author of one particularly "convincing" illustration has an extensive article at ((
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the theory. Bob Dill, author of one particularly "convincing" illustration has an extensive article at ((
3185:"for him, the wind apparent to the boat is a mental construct". All vectors are just mental constructs.
1290:. No hurry, back off, even those who claim to be members of the team here present are content to wait.
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The article makes it perfectly clear that it is presenting established facts, supported by citations.--
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To provide that reaction, the 'wind-balls' have to deflect to the right in this frame of reference (Īø
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From the equations above, it turns out that any fixed sail craft with a close-hauled system L/D : -->
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You are correct. I have modified the text to match the citation. Thank you for suggesting this.--
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the assertion "any boat can make good downwind faster than the real wind" needs to be qualified.
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Here is the overall response to this posting. Please see below for the point-by-point response.--
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1234:" is not the issue. The first hand report should not appear at all! WP is supposed to be based
1130:" is not the issue. The first hand report should not appear at all! WP is supposed to be based
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The first image describes the geometry and equations of a simple F = -k delta(Vapparent) model:
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than the true wind in the southerly direction.Sirclicksalot (talk) 03:19, 15 June 2010 (UTC)
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dearly like to know what if any toolset was used to help create the animation. Brilliant!
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Indeed, I had some trouble understanding whether QuietJohn doubted that downwind VMG : -->
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This is not quite right. There is an exception to the use of secondary sources, see
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diagrams from the books, crediting the original drawings. It shouldn't be this hard!
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diagrams from the books, crediting the original drawings. It shouldn't be this hard!
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To support the above assertion I enter "enemy territory" and calculate apparent wind
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university team as if we were journalists. It's secondary sources we need, as per
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is the speed of the apparent wind (i.e. relative to the speed of the boat) and and
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Anyway, if you want an intuitive explanation in the ground frame, I recommend the
1122:(2) An important point about "not based solely on the self-report". According to
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university team as if we were journalists. It's secondary sources we need, as per
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Ah yes - but how do you know I'm a member of the team without a second source???
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Problems with the polar diagram: (1) Only a crosswind scale is shown. Often the
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This is equivalent to your table: when using a force formula e.g. lift force
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hasn't been accomplished and pollutes the efforts to make a worthy article.
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hasn't been accomplished and pollutes the efforts to make a worthy article.
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Based on PBs description of which explanation changed his mind I made this
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is the angle of that apparent wind (i.e. relative to the boat's direction).
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Looks good to me, thanks for drawing it. PB, what do you say? Convinced?
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here. It's a reference book, an encyclopedia. Not the front page of
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1 and (with one tack/jibe) can beat a balloon to a point straight dw.
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3325:. It shows how the air can push the boat, even with a DW-VMG : -->
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This is not clear, or at least allows for easy misinterpretation:
1635:= Ī² = cot(L/D), degrees = angle of course sailed wrt apparent wind
465:
Catalyst - Journal of the Amateur Yacht Research Society Apr 2009
436:
You are absolutely correct, thank you for that. I will fix it.--
134:(true wind speed). The argument made by others is that VMG : -->
3669:. It shows all three frames and the force vectors (at the end).
1879:. Thus, there is no issue related to conservation of energy.--
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physics for what it is, rather than helices and billiard balls.
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physics for what it is, rather than helices and billiard balls.
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2.83 (ā8) can have VMG to leeward faster than true windspeed.
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of the magnitude. That is the relation that I used for the
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Talk:Sailing_faster_than_the_wind#Deleted_thought_experiment
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Sailing downwind with a downwind VMG greater than wind speed
2538:. But maybe I misundertand your formulas and your table.--
2389:
wind increases" define this term in the previous paragraph.
2335:"any boat can make good downwind faster than the real wind"
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the use of self-published sources as sources on themselves
1138:. We need ideally to quote only from secondary sources.
2941:
http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf
2417:(messed up signing this a few times, but it's okay now)
1717:
Very helpful, thank you. I have added this reference.--
1658:
Max Vmg to windward: (Vmg/Vt)max = (ā(1+(L/D)) - 1) / 2
758:
http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf
598:
http://www.sailingscuttlebutt.com/news/08/tt/bobdill.pdf
3384:, I was having the same problem. I agree blue dots are
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Max Vmg to leeward: (Vmg/Vt)max = (ā(1+(L/D)) + 1) / 2
3622:
would illustrate the explanations immediately above.
3485:
The reaction due to the wind on the sail at any point
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the lowest achievable angle of attack (a.k.a. Ī² or Īµ
1090:
citations do not support assertions in the article.
3459:is the counter-intuitive part. Man, this explains
1646:Ī³ = angle of course sailed wrt true upwind, degrees
399:... closer than 45 degrees to the apparent wind ...
359:
such diagrams are found in many books on sailing.--
2889:then the proportionality constant between ĪV and V
1590:Max Vmg to windward: (Vmg/Vt)max = 1/2 * (1/sin(Īµ
1334:etc applies to the article, not to its talk page.
1615:Max Vmg to leeward: (Vmg/Vt)max = 1/2 * (1/sin(Īµ
2845:q = dynamic pressure due to apparent wind = Ā½ Ļ
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1004:
3600:Thanks. I have added the force vectors in the
209:north). Or simply use the vector formula from
3423:! This shows that the key is the sail being
3326:true wind. Is this a good way to explain it?
2087:which is why I removed it from the article.
8:
3667:DDWFTTW version of the stream line animation
3153:, according to the man on the shore, is the
3119:, according to the man on the shore, is the
395:section has a typo: I think it should be
24:Talk:Sailing faster than the wind/Archive 4
1792:apparent headwind induced by its motion.--
403:Also, it would be more clear if it said
1250:(which is the correct reference) namely
2897:, along with other proportionalities.
2456:apparent wind abaft of abeam causes a
231:It is, (as careful application of the
51:Do not edit the contents of this page.
7:
1650:Alternate formulations using 1/sin(Īµ
1269:No, it is not. That you have found
172:a brake. Thus your argument fails.
3642:Based on the suggestions I made a
508:But quote the ref in the article!
31:
237:((1-sqrt(2))*(true wind speed),0)
233:Feynman Problem Solving Algorithm
3602:youtube version of the animation
2508:
2491:
1663:Max Vs: (Vs/Vt)max = ā(1+(L/D))
36:
1222:Outdent. Paul Beardsell says:
3060:from the POV of the spectator;
2893:is buried in the coefficient C
1354:Continued criticism of article
1:
3444:to which the sail is attached
1603:Max Vs: (Vs/Vt)max = 1/sin(Īµ
18:Talk:High-performance sailing
3644:new version of the animation
3435:wrt the true wind while the
1854:Here we have no difference.
1581:Another reference suggestion
689:Here is the mangled version:
415:at the end of that phrase.
3694:
3638:Mind changer animation 2.0
3057:Geez, he said "fictitious
3013:Mind changer. Light switch
3679:14:27, 28 June 2010 (UTC)
3661:00:25, 23 June 2010 (UTC)
3632:13:52, 19 June 2010 (UTC)
3592:13:31, 19 June 2010 (UTC)
3569:14:45, 19 June 2010 (UTC)
3529:10:24, 19 June 2010 (UTC)
3475:02:35, 19 June 2010 (UTC)
3411:02:35, 19 June 2010 (UTC)
3372:22:58, 18 June 2010 (UTC)
3357:22:53, 18 June 2010 (UTC)
3336:22:22, 18 June 2010 (UTC)
3309:14:04, 19 June 2010 (UTC)
3291:18:06, 18 June 2010 (UTC)
3274:18:06, 18 June 2010 (UTC)
3258:18:06, 18 June 2010 (UTC)
3233:20:18, 18 June 2010 (UTC)
3195:18:26, 18 June 2010 (UTC)
3167:18:26, 18 June 2010 (UTC)
3133:11:32, 18 June 2010 (UTC)
3099:11:25, 18 June 2010 (UTC)
3073:18:06, 18 June 2010 (UTC)
3038:10:34, 18 June 2010 (UTC)
3007:12:04, 26 June 2010 (UTC)
2990:12:05, 25 June 2010 (UTC)
2971:08:39, 21 June 2010 (UTC)
2955:21:00, 18 June 2010 (UTC)
2935:12:05, 25 June 2010 (UTC)
2907:15:18, 24 June 2010 (UTC)
2548:11:58, 24 June 2010 (UTC)
2522:14:03, 23 June 2010 (UTC)
2453:14:03, 23 June 2010 (UTC)
2436:08:27, 21 June 2010 (UTC)
2415:20:14, 18 June 2010 (UTC)
2368:08:24, 21 June 2010 (UTC)
2353:11:03, 18 June 2010 (UTC)
2330:12:54, 19 June 2010 (UTC)
2307:19:00, 21 June 2010 (UTC)
2293:08:49, 21 June 2010 (UTC)
2277:11:02, 18 June 2010 (UTC)
2247:15:42, 10 June 2010 (UTC)
1784:15:42, 10 June 2010 (UTC)
1727:07:16, 18 June 2010 (UTC)
1709:01:46, 20 June 2010 (UTC)
1699:(Changed lambda to gamma
1694:12:44, 19 June 2010 (UTC)
1680:23:17, 17 June 2010 (UTC)
1573:07:08, 18 June 2010 (UTC)
1554:20:45, 17 June 2010 (UTC)
1535:19:58, 17 June 2010 (UTC)
1511:08:44, 18 June 2010 (UTC)
1481:07:19, 18 June 2010 (UTC)
1458:19:52, 17 June 2010 (UTC)
1434:13:34, 18 June 2010 (UTC)
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1381:19:43, 17 June 2010 (UTC)
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1318:12:32, 18 June 2010 (UTC)
1300:10:25, 18 June 2010 (UTC)
1264:10:10, 18 June 2010 (UTC)
1209:08:35, 18 June 2010 (UTC)
1179:08:15, 18 June 2010 (UTC)
1148:08:34, 18 June 2010 (UTC)
1100:08:34, 18 June 2010 (UTC)
1068:07:40, 18 June 2010 (UTC)
1045:06:36, 18 June 2010 (UTC)
1002:07:43, 18 June 2010 (UTC)
982:21:38, 17 June 2010 (UTC)
964:07:06, 18 June 2010 (UTC)
946:19:43, 17 June 2010 (UTC)
921:12:01, 17 June 2010 (UTC)
905:18:36, 15 June 2010 (UTC)
890:12:01, 17 June 2010 (UTC)
868:20:12, 15 June 2010 (UTC)
840:12:01, 17 June 2010 (UTC)
811:If it is a fact, present
803:12:01, 17 June 2010 (UTC)
778:12:01, 17 June 2010 (UTC)
749:12:01, 17 June 2010 (UTC)
729:12:01, 17 June 2010 (UTC)
710:12:01, 17 June 2010 (UTC)
681:09:59, 18 June 2010 (UTC)
665:09:59, 18 June 2010 (UTC)
650:18:36, 15 June 2010 (UTC)
614:If it is a fact, present
560:08:32, 18 June 2010 (UTC)
538:07:14, 18 June 2010 (UTC)
518:20:41, 17 June 2010 (UTC)
502:20:40, 17 June 2010 (UTC)
482:20:04, 17 June 2010 (UTC)
446:12:03, 17 June 2010 (UTC)
427:01:42, 16 June 2010 (UTC)
369:15:23, 10 June 2010 (UTC)
346:13:24, 10 June 2010 (UTC)
328:12:18, 10 June 2010 (UTC)
309:00:28, 10 June 2010 (UTC)
293:18:05, 17 June 2010 (UTC)
267:00:33, 10 June 2010 (UTC)
223:00:03, 10 June 2010 (UTC)
163:00:03, 10 June 2010 (UTC)
3613:06:07, 3 July 2010 (UTC)
2212:15:41, 8 June 2010 (UTC)
2182:13:36, 8 June 2010 (UTC)
2156:10:19, 8 June 2010 (UTC)
2133:09:42, 8 June 2010 (UTC)
2114:09:36, 8 June 2010 (UTC)
2097:09:29, 8 June 2010 (UTC)
2078:09:09, 8 June 2010 (UTC)
2056:13:38, 8 June 2010 (UTC)
2029:10:19, 8 June 2010 (UTC)
2006:09:50, 8 June 2010 (UTC)
1987:09:29, 8 June 2010 (UTC)
1968:09:09, 8 June 2010 (UTC)
1948:10:19, 8 June 2010 (UTC)
1926:09:50, 8 June 2010 (UTC)
1908:09:29, 8 June 2010 (UTC)
1889:09:09, 8 June 2010 (UTC)
1864:10:19, 8 June 2010 (UTC)
1838:09:44, 8 June 2010 (UTC)
1817:09:29, 8 June 2010 (UTC)
1802:09:09, 8 June 2010 (UTC)
1765:09:30, 8 June 2010 (UTC)
1750:09:09, 8 June 2010 (UTC)
393:Sailing on a Broad Reach
249:22:17, 9 June 2010 (UTC)
199:21:57, 9 June 2010 (UTC)
145:21:57, 9 June 2010 (UTC)
127:11:50, 9 June 2010 (UTC)
2374:Effect of apparent wind
1273:exception doesn't mean
1248:Knowledge:Verifiability
472:true wind are possible.
3651:windspeed is possible.
3552:by definition requires
3317:Mind changer animation
3087:squeezed wedge analogy
2866:apparent wind velocity
2536:135-degree table above
2315:L/D and VMG to leeward
1735:Conservation of energy
1244:
1016:
2835:= coefficient of lift
2395:"further increase in
1619:) + 1) at Ī³ = 135 + Īµ
1525:someone else do so.
456:Reference Suggestions
49:of past discussions.
3111:When discussing the
2747:which is the same as
1975:falsifies the theory
1594:) - 1) at Ī³ = 45 + Īµ
407:... velocity of the
391:near the end of the
318:. Please check it.
3453:wrt the true wind;
3447:- is making VMG to
3219:reference frame??!!
2461:nothing to do with
467:. It contains this
3665:Now I also made a
1362:
1034:
1030:
1009:
927:Apology and thanks
2961:to the article.--
1896:circular argument
1360:
1032:
1028:
1007:
99:
98:
61:
60:
55:current talk page
22:(Redirected from
3685:
2571:delta velocities
2512:
2495:
1654:) = ā(1+(L/D)):
1371:going on also.
463:appeared in the
85:
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3648:youtube version
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3419:Sweet! BRAVO,
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1607:) at Ī³ = 90 + Īµ
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622:facts based on
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2299:ScottForschler
2283:explanation?--
2269:ScottForschler
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3008:
3004:
3000:
2999:Sirclicksalot
2991:
2987:
2983:
2982:Sirclicksalot
2978:
2977:
2976:
2975:
2972:
2968:
2964:
2963:Gautier lebon
2959:
2958:
2957:
2956:
2952:
2948:
2947:Sirclicksalot
2942:
2938:
2936:
2932:
2928:
2927:Sirclicksalot
2920:
2908:
2904:
2900:
2899:Sirclicksalot
2888:
2887:
2886:
2885:
2884:
2883:
2882:
2881:
2880:
2879:
2861:
2854:
2844:
2837:
2830:
2829:
2828:
2827:
2826:
2825:
2824:
2823:
2822:
2821:
2820:
2819:
2807:
2806:
2805:
2804:
2803:
2802:
2801:
2800:
2799:
2798:
2769:
2768:
2767:
2766:
2765:
2764:
2763:
2762:
2761:
2760:
2759:
2758:
2746:
2745:
2744:
2743:
2742:
2741:
2740:
2739:
2738:
2737:
2715:
2714:
2713:
2712:
2711:
2710:
2709:
2708:
2707:
2706:
2705:
2704:
2692:
2691:
2690:
2689:
2688:
2687:
2686:
2685:
2684:
2683:
2671:
2670:
2669:
2668:
2667:
2666:
2665:
2664:
2663:
2662:
2648:
2647:
2646:
2645:
2644:
2643:
2642:
2641:
2640:
2639:
2638:
2637:
2625:
2624:
2623:
2622:
2621:
2620:
2619:
2618:
2617:
2616:
2602:
2601:
2600:
2599:
2598:
2597:
2596:
2595:
2594:
2593:
2592:
2591:
2579:
2578:
2577:apparent wind
2573:
2572:
2567:
2566:
2565:
2564:
2563:
2562:
2561:
2560:
2559:
2558:
2549:
2545:
2541:
2540:Gautier lebon
2537:
2532:
2531:
2530:
2529:
2528:
2527:
2526:
2525:
2524:
2523:
2519:
2515:
2514:Sirclicksalot
2511:
2500:
2499:
2498:
2497:
2496:
2494:
2484:
2483:
2482:
2481:
2474:
2473:
2472:
2471:
2464:
2459:
2454:
2450:
2446:
2445:Sirclicksalot
2443:
2442:
2441:
2440:
2437:
2433:
2429:
2428:Gautier lebon
2425:
2420:
2419:
2418:
2416:
2412:
2408:
2407:Sirclicksalot
2398:
2394:
2391:
2388:
2384:
2383:
2382:
2379:
2373:
2369:
2365:
2361:
2360:Gautier lebon
2357:
2356:
2355:
2354:
2350:
2346:
2342:
2334:
2332:
2331:
2327:
2323:
2322:Sirclicksalot
2314:
2308:
2304:
2300:
2296:
2295:
2294:
2290:
2286:
2285:Gautier lebon
2281:
2280:
2279:
2278:
2274:
2270:
2264:
2248:
2244:
2240:
2239:Gautier lebon
2235:
2234:
2233:
2232:
2231:
2230:
2229:
2228:
2227:
2226:
2225:
2224:
2213:
2209:
2205:
2201:
2200:
2199:
2198:
2197:
2196:
2195:
2194:
2193:
2192:
2183:
2179:
2175:
2174:Gautier lebon
2171:
2170:
2169:
2168:
2167:
2166:
2165:
2164:
2157:
2153:
2149:
2144:
2143:
2142:
2141:
2140:
2139:
2134:
2130:
2126:
2125:Gautier lebon
2121:
2120:
2119:
2118:
2115:
2111:
2107:
2102:
2101:
2098:
2094:
2090:
2086:
2082:
2081:
2080:
2079:
2075:
2071:
2070:Gautier lebon
2057:
2053:
2049:
2048:Gautier lebon
2044:
2043:
2042:
2041:
2040:
2039:
2038:
2037:
2030:
2026:
2022:
2017:
2016:
2015:
2014:
2013:
2012:
2007:
2003:
1999:
1998:Gautier lebon
1994:
1993:
1992:
1991:
1988:
1984:
1980:
1976:
1972:
1971:
1970:
1969:
1965:
1961:
1960:Gautier lebon
1949:
1945:
1941:
1937:
1936:
1935:
1934:
1933:
1932:
1927:
1923:
1919:
1918:Gautier lebon
1915:
1914:
1913:
1912:
1909:
1905:
1901:
1897:
1893:
1892:
1891:
1890:
1886:
1882:
1881:Gautier lebon
1878:
1865:
1861:
1857:
1853:
1852:
1851:
1850:
1849:
1848:
1847:
1846:
1839:
1835:
1831:
1830:Gautier lebon
1826:
1825:
1824:
1823:
1822:
1821:
1818:
1814:
1810:
1806:
1805:
1804:
1803:
1799:
1795:
1794:Gautier lebon
1785:
1781:
1777:
1776:Gautier lebon
1772:
1771:
1770:
1769:
1766:
1762:
1758:
1754:
1753:
1752:
1751:
1747:
1743:
1742:Gautier lebon
1734:
1728:
1724:
1720:
1719:Gautier lebon
1716:
1715:
1714:
1713:
1712:
1710:
1706:
1702:
1701:Sirclicksalot
1697:
1695:
1691:
1687:
1686:Sirclicksalot
1682:
1681:
1677:
1674:
1673:Sirclicksalot
1667:
1666:
1662:
1661:
1657:
1656:
1655:
1645:
1644:
1639:
1638:
1630:
1629:
1628:
1614:
1613:
1602:
1601:
1589:
1588:
1587:
1580:
1574:
1570:
1566:
1565:Gautier lebon
1561:
1560:
1559:
1558:
1555:
1551:
1547:
1543:
1539:
1538:
1537:
1536:
1532:
1528:
1512:
1508:
1504:
1500:
1499:
1498:
1497:
1496:
1495:
1494:
1493:
1492:
1491:
1482:
1478:
1474:
1473:Gautier lebon
1468:
1467:
1466:
1465:
1464:
1463:
1462:
1461:
1460:
1459:
1455:
1451:
1435:
1431:
1427:
1422:
1421:
1420:
1419:
1418:
1417:
1416:
1415:
1414:
1413:
1404:
1400:
1396:
1395:Gautier lebon
1391:
1390:
1389:
1388:
1387:
1386:
1385:
1384:
1383:
1382:
1378:
1374:
1370:
1366:
1353:
1345:
1341:
1337:
1333:
1329:
1328:
1327:
1326:
1325:
1324:
1319:
1315:
1311:
1307:
1306:
1305:
1304:
1301:
1297:
1293:
1289:
1285:
1280:
1276:
1272:
1268:
1267:
1266:
1265:
1261:
1257:
1256:Gautier lebon
1253:
1249:
1243:
1241:
1237:
1233:
1229:
1226:According to
1223:
1210:
1206:
1202:
1199:Hear, hear!
1198:
1197:
1196:
1195:
1194:
1193:
1192:
1191:
1190:
1189:
1180:
1176:
1172:
1167:
1166:
1165:
1164:
1163:
1162:
1161:
1160:
1149:
1145:
1141:
1137:
1133:
1129:
1125:
1121:
1120:
1119:
1118:
1117:
1116:
1115:
1114:
1113:
1112:
1101:
1097:
1093:
1089:
1085:
1084:
1083:
1082:
1081:
1080:
1079:
1078:
1077:
1076:
1069:
1065:
1061:
1060:Gautier lebon
1056:
1055:
1054:
1053:
1052:
1051:
1046:
1042:
1038:
1026:
1025:
1024:
1023:
1015:
1013:
1003:
999:
995:
994:Gautier lebon
991:
990:
989:
988:
987:
986:
983:
979:
975:
971:
970:
965:
961:
957:
956:Gautier lebon
952:
951:
950:
949:
948:
947:
943:
939:
933:
926:
922:
918:
914:
913:Gautier lebon
909:
908:
907:
906:
902:
898:
891:
887:
883:
882:Gautier lebon
879:
878:
877:
869:
865:
861:
856:
855:
854:
853:
849:
848:
847:
841:
837:
833:
832:Gautier lebon
828:
827:
822:
818:
814:
810:
809:
804:
800:
796:
795:Gautier lebon
791:
790:
789:
788:
783:
782:
779:
775:
771:
770:Gautier lebon
767:
766:
765:
759:
754:
753:
750:
746:
742:
741:Gautier lebon
738:
737:
736:
730:
726:
722:
721:Gautier lebon
718:
717:
716:
711:
707:
703:
702:Gautier lebon
698:
697:
696:
692:
691:
690:
682:
678:
674:
673:Gautier lebon
669:
668:
667:
666:
662:
658:
657:Gautier lebon
652:
651:
647:
643:
638:
631:
630:
625:
621:
617:
613:
612:
607:
606:
605:
599:
594:
593:
592:
588:
585:
580:
579:
578:
569:
561:
557:
553:
549:
548:
547:
546:
545:
544:
539:
535:
531:
530:Gautier lebon
525:
524:
523:
522:
519:
515:
511:
507:
506:
503:
499:
495:
490:
486:
485:
484:
483:
479:
475:
470:
469:Polar diagram
466:
462:
455:
447:
443:
439:
438:Gautier lebon
435:
434:
433:
432:
431:
430:
429:
428:
424:
420:
419:Sirclicksalot
416:
410:
406:
405:
404:
398:
397:
396:
394:
386:
385:
384:
378:
370:
366:
362:
361:Gautier lebon
357:
356:
355:
354:
353:
352:
347:
343:
339:
335:
334:
333:
332:
329:
325:
321:
317:
313:
312:
311:
310:
306:
302:
294:
290:
286:
285:Sirclicksalot
282:
281:
280:
276:
268:
264:
260:
256:
255:
254:
253:
250:
246:
242:
238:
234:
230:
229:
224:
220:
216:
212:
211:Apparent_wind
208:east, y-: -->
206:
205:
204:
203:
200:
196:
192:
188:
184:
180:
176:
175:
170:
169:
164:
160:
156:
152:
151:
150:
149:
146:
142:
138:
131:
130:
129:
128:
124:
120:
113:
109:
108:to its keel.
101:
95:
92:
90:
87:
84:
80:
78:
75:
73:
70:
68:
65:
64:
56:
52:
48:
47:
42:
35:
34:
25:
19:
3664:
3641:
3551:
3550:
3537:
3517:vector field
3507:To generate
3486:
3461:
3460:
3455:
3454:
3449:
3448:
3443:
3442:
3437:
3436:
3431:
3430:
3425:
3424:
3343:
3320:
3218:
3217:
3154:
3150:
3120:
3116:
3059:
3058:
3028:
3022:
3016:
2997:(fixed typo
2996:
2944:
2924:
2649:F = ĪV dm/dt
2603:F = d(mV)/dt
2576:
2575:
2570:
2569:
2507:
2490:
2462:
2457:
2423:
2403:
2396:
2386:
2380:
2377:
2338:
2318:
2265:
2261:
2066:
1956:
1874:
1790:
1738:
1698:
1683:
1671:
1649:
1626:
1584:
1523:
1446:
1357:
1287:
1283:
1278:
1274:
1270:
1245:
1235:
1231:
1225:
1221:
1131:
1127:
1087:
1005:
934:
930:
894:
874:
844:
820:
816:
812:
763:
733:
714:
693:
688:
687:
686:
654:
639:
635:
623:
619:
615:
603:
589:
586:
582:
575:
574:
573:
489:aspect ratio
461:This article
459:
417:
414:
408:
402:
392:
390:
382:
338:Waleswatcher
301:Waleswatcher
297:
277:
273:
259:Waleswatcher
236:
235:does show),
186:
182:
178:
119:Waleswatcher
114:
110:
105:
82:
50:
44:
2921:Limitations
2859:air density
2842:= sail area
2466:efficiency.
2424:necessarily
179:(s_aw,a_aw)
43:This is an
3462:everything
1755:So what?
1284:no urgency
1279:preferable
858:about it.
817:verifiable
620:verifiable
3502:reflected
3323:animation
3155:true wind
3121:true wind
2463:available
1288:The Times
897:QuietJohn
642:QuietJohn
314:I drew a
94:ArchiveĀ 6
89:ArchiveĀ 5
83:ArchiveĀ 4
77:ArchiveĀ 3
72:ArchiveĀ 2
67:ArchiveĀ 1
3498:incident
3432:windward
3344:apparent
2397:apparent
2387:apparent
2385:"As the
2339:Even in
2237:below.--
1361:hoaxters
1008:hoaxters
821:reliable
624:reliable
411:wind ...
320:Generacy
3513:laminar
3450:leeward
3380:Thanks
2341:context
1828:this.--
1310:Spork33
1171:Spork33
1029:hoaxter
974:Spork33
577:intact.
316:diagram
46:archive
3671:Eyytee
3653:Eyytee
3605:Eyytee
3521:Nigelj
3421:Eyytee
3382:Nigelj
3364:Nigelj
3349:Nigelj
3328:Eyytee
3187:Eyytee
3159:Eyytee
3091:Eyytee
2085:WP:SYN
1627:where
1369:WP:SYN
1232:solely
1128:solely
860:Eyytee
474:Eyytee
299:wind).
215:Eyytee
181:where
155:Eyytee
3519:). --
3438:craft
3149:"The
2808:where
2770:F = C
2716:F = C
2574:(not
1240:WP:VS
1228:WP:VS
1136:WP:VS
1124:WP:VS
1027:The "
824:deck.
379:Typo?
16:<
3675:talk
3657:talk
3628:talk
3609:talk
3588:talk
3565:talk
3525:talk
3509:lift
3493:here
3471:talk
3456:that
3407:talk
3368:talk
3353:talk
3332:talk
3305:talk
3287:talk
3270:talk
3254:talk
3229:talk
3191:talk
3163:talk
3129:talk
3095:talk
3069:talk
3034:talk
3003:talk
2986:talk
2967:talk
2951:talk
2931:talk
2903:talk
2544:talk
2518:talk
2458:drop
2449:talk
2432:talk
2411:talk
2364:talk
2349:talk
2326:talk
2303:talk
2289:talk
2273:talk
2243:talk
2208:talk
2178:talk
2152:talk
2129:talk
2110:talk
2093:talk
2074:talk
2052:talk
2025:talk
2002:talk
1983:talk
1964:talk
1944:talk
1922:talk
1904:talk
1885:talk
1860:talk
1834:talk
1813:talk
1798:talk
1780:talk
1761:talk
1746:talk
1723:talk
1705:talk
1690:talk
1676:talk
1569:talk
1550:talk
1546:Paul
1542:here
1531:talk
1507:talk
1477:talk
1454:talk
1430:talk
1399:talk
1377:talk
1365:WP:V
1340:talk
1332:WP:V
1314:talk
1296:talk
1275:your
1260:talk
1236:only
1205:talk
1175:talk
1144:talk
1132:only
1096:talk
1088:some
1064:talk
1041:talk
1012:WP:V
998:talk
978:talk
960:talk
942:talk
917:talk
901:talk
886:talk
864:talk
836:talk
813:real
799:talk
774:talk
745:talk
725:talk
706:talk
677:talk
661:talk
646:talk
616:real
556:talk
534:talk
514:talk
498:talk
478:talk
442:talk
423:talk
409:true
365:talk
342:talk
324:talk
305:talk
289:talk
263:talk
245:talk
219:talk
195:talk
187:a_aw
183:s_aw
159:talk
141:talk
123:talk
3500:= Īø
3426:not
2778:Ā½ Ļ
1898:.
1238:on
1134:on
1033:may
3677:)
3659:)
3630:)
3611:)
3590:)
3567:)
3527:)
3487:is
3473:)
3441:-
3409:)
3370:)
3355:)
3347:--
3334:)
3307:)
3289:)
3272:)
3256:)
3231:)
3193:)
3165:)
3131:)
3097:)
3071:)
3036:)
3009:)
3005:)
2988:)
2969:)
2953:)
2937:)
2933:)
2905:)
2546:)
2520:)
2451:)
2434:)
2413:)
2366:)
2351:)
2328:)
2305:)
2291:)
2275:)
2245:)
2210:)
2180:)
2154:)
2131:)
2112:)
2095:)
2076:)
2054:)
2027:)
2004:)
1985:)
1966:)
1946:)
1924:)
1906:)
1887:)
1862:)
1836:)
1815:)
1800:)
1782:)
1763:)
1748:)
1725:)
1711:)
1707:)
1696:)
1692:)
1678:)
1623:/2
1598:/2
1571:)
1552:)
1533:)
1509:)
1479:)
1456:)
1432:)
1401:)
1379:)
1342:)
1316:)
1298:)
1271:an
1262:)
1207:)
1177:)
1146:)
1098:)
1066:)
1043:)
1000:)
980:)
962:)
944:)
919:)
903:)
888:)
866:)
838:)
815:,
801:)
776:)
747:)
727:)
708:)
679:)
663:)
648:)
618:,
558:)
536:)
516:)
500:)
480:)
444:)
425:)
367:)
344:)
326:)
307:)
291:)
265:)
247:)
221:)
197:)
161:)
143:)
125:)
3673:(
3655:(
3646:(
3626:(
3607:(
3586:(
3563:(
3557:A
3523:(
3469:(
3405:(
3366:(
3351:(
3330:(
3303:(
3285:(
3268:(
3252:(
3227:(
3189:(
3161:(
3127:(
3093:(
3089:.
3067:(
3032:(
3001:(
2984:(
2965:(
2949:(
2929:(
2901:(
2895:L
2891:a
2864:a
2862:V
2857:A
2855:Ļ
2851:a
2849:V
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