Talk:Forces on sails/Archive 1

Lift/Drag ratio and Power
The fisrt section in particular the sentence "Polar curves of lift versus drag initially look like straight lines." is a translation of french wiki effort sur une voile. I have writed this sentence in french wiki. This information come from an article or a book but, i can't remember who it is.

But for me this sentence is wrong, the curve of lift versus Angle of attack are straight lines ; Polar curves of lift versus drag are for me a Parabola.

Also two solutions, the sentence "polar" is thrue, or i have done a mistake when i had read this.

best regards

Erwan1972 (talk) 16:54, 11 July 2011 (UTC)

Confusing
This article is VERY confusing and quite obviously translated from a language other than English or written by a non native speaker. As I can not even figure out the original meaning in many cases, and I do not know the subject well enough, I can not correct anything. — Preceding unsigned comment added by 164.64.39.198 (talk • contribs) 2010-07-07 20:34:34


 * No problem. Initial manual "clean up"  translation is completed.  More  work   needs   doing,  as    I  see   the   original   article   has   since   expanded.  No   doubt   there is room    for    more   expansion   of  the   English   version  independently   as  well. Also the  needs   more   proof  reading,  refinement .   English  references would  be   good.
 * Bcebul (talk) 04:17, 28 March 2011 (UTC)


 * Thanks for all your effort in translating this page from the French, and also to Erwan who I understand is responsible for much of the original French article.


 * There is much useful information here, but it still needs a bit of work to bring it up to wiki standards. One issue is that it immediately "jumps into the deep end" so that the general interest reader may not be able to follow the discussion, or may give up before reading very far.  I'd like to present a simplified introduction aimed at the casual reader, and I will craft something in coming days (or weeks, depending on time).


 * Another issue is that it is quite long. The essence of effective writing is editing out the unnecessary stuff, and I think we need to take a sharp pencil to this article.  Perhaps some subjects can be split out into their own article.  I hope to find some time to address this as well.


 * We also need to look out for unsupported statements, and either find citations, find another way to state it, add citation needed tags, or remove them. Looking forward to working with you on this page. Mr. Swordfish (talk) 19:45, 9 August 2011 (UTC)


 * Today I undid some good faith edits to the introduction. I think it's important for the article to proceed from the simple to the complex and to avoid "throwing the user into the deep end" right in the beginning.  There is plenty of space to elaborate later in the article.


 * In particular, it is possible to resolve the force vector into components of any coordinate system that one might choose. I don't think we need to allude to every possible coordinate system in the introduction.  The usual choice of coordinates is to talk about lift vs drag, so we should present that first.  Other approaches may be appropriate later in the article. Mr. Swordfish (talk) 15:23, 17 October 2011 (UTC)

use of energy in the article and some other issues
There are several places where energy has been used in an article about sail forces. A lot of it is simply wrong. And there is no reason using energy at all, since it's outside of the subject anyway.

For example the part talking about BETZ limit. Kinetic energy as a concept only makes sense in a well defined frame of reference, and that part mixes 2 separate references making it wrong.

In the reference of the boat, the air loses KE, but the sail does not get that energy, instead it goes to mostly turbulence and eventually into heat. The boat is sailing with a constant velocity, hence its KE is a constant. The flow of water does not get any energy either. The flow speed of water at far downstream of the boat is almost the same (just a little less than )far upsteram of the boat, hense the KE of water is the same or more accurately reduced a little and turned into mostly turbulence of water and eventually into heat.

In the reference of the water the BETZ law does not even apply, but is wrong. For a reference of that fact see article on sailing directly downwind faster than true wind in any reliable source with correct physics, including wiki in english. And using apparent wind is not correct in that frame of reference. True wind must be used instead or reference frames are mixed during the analyses, a major mistake in physics.
 * based on formula F = \frac12 \times \rho \times S \times C \times V^2
 * purpose of paragraph is : what i can improved ?
 * \rho
 * C
 * could you correct in article ?
 * i add note Erwan1972 (talk) 14:07, 11 April 2012 (UTC)
 * i add note Erwan1972 (talk) 14:07, 11 April 2012 (UTC)

Some part of the article claim that: \ C \times S represents the percentage of energy recovered over the upper(outer) surface multiplied by the upper(outer) surface area plus the percentage of energy recovered from the lower surface multiplied by the surface area of the lower(inner) surface.

If that claim were correct no wing could have Cl above 2, or else it would recover more than 100% of the energy. Yet in reality max CL of a wing with flaps is well above that even when the reference area of the wing used to calculate CL from lift_force includes the area of the flap. That proves the unsupported and unreferenced claim to be false.
 * flap are not in the case of uniform flow but much more closer of Several sails: multidimensional problem resolution not yet translated.
 * could you correct in article, add a note ?
 * A note was missing ! i have translate from wp:fr sorry !
 * Erwan1972 (talk) 13:59, 11 April 2012 (UTC)

Treatment of aspect ratio is problemeatic. Although Cdi is dependent on AR Di is not. Instead it depends on span(b) (rig height) and apparent windspeed for a given sail force. Ci = {{Cz^2} \over {\pi \times \lambda \times e}} \lambda = {b^2 \over S} Combining those 2 to get rid of lambda gives Cdi/cl = cl*S / (pi * e * b^2 ) The formula linkin lift and cl can be used to get rid of cl*S from the previous result. F_z = \frac12 \times \rho \times S \times C_z \times V^2 or Lift = cl*S * 0.5*rho * v^2, therefore cl*S = Lift / (0.5 * rho * v^2 ) Hence Cdi / Cl = Lift / (0.5 * rho * v^2 * pi * e * b^2 ) But Cdi/Cl = Di / L or Di = L * Cdi/Cl Di = Lift^2 / (0.5 * rho * v^2 * pi * e * b^2 ) And this gives the induced drag (force, not coefficient) regardless of whatever AR is. In sailing lift is limited by max rightning moment quite often, making it practical to use that formula to see induced drag doesn't depend on AR, but Cl instead does since sail area does, if AR is changed while keeping span the same. As a further reference, search for spanloading, a consept used a lot by airplane designers.
 * could you precise this point in article ?
 * i have add this in article Erwan1972 (talk) 08:26, 17 April 2012 (UTC)

As for elliptical lift distribution being an optimum for minimum indiuced drag, it's only true if span is kept the same. If heeling moment is kept the same instead, the optimum lift distribution is linear, not elliptical since it allows using greater span (rig height) for the same heeling moment and same lift force. The result (well known by aerodynamists) can be clearly seen by looking at the planforms of rigid wings on C-class cats, or the wing used on USA17 by BMW_Oracle racing durin AC33.
 * Yes, could you correct in article, add a note ?
 * remark transfered in article Erwan1972 (talk) 14:02, 11 April 2012 (UTC)

Furthermore such basic treatment of optimum distribution of lift are valid in uniform flow, that is without taking into account variation of speed and angle of airflow with altitude, ie twist of apparent wind and more wind higher up. How is total drag of the sail defined anyway, parallel to apparent wind at what height ? It can't be minimized without defining what exactly is to be minimized. If local drag close to mast head are increased by some amount while at the same time local drag close to foot of sail is decreased by the same amount, the net effect is that total sail force points more forward for a given lift. In 2D analyses it means a reduction of drag, while the local drag increased and decreased by the same amount. So minimising sum of local drag at all heights does not lead to minimum of the total drag for the sail as the elliptical as an optimum leading to minimum induceddrag assumes. That should explain why the definition is important and very relevant, yet it's not done !

87.93.222.213 (talk) 18:40, 3 April 2012 (UTC)
 * wiki is free, and you can correct some mistake.
 * In the reference of the boat, the air loses KE, but the sail does not get that energy, instead it goes to mostly turbulence and eventually into heat. The boat is sailing with a constant velocity, hence its KE is a constant. The flow of water does not get any energy either. The flow speed of water at far downstream of the boat is almost the same (just a little less than )far upsteram of the boat, hense the KE of water is the same or more accurately reduced a little and turned into mostly turbulence of water and eventually into heat.
 * with this sentence i can think that to keep the speed of boat i have not need of energy because i have no lost of KE !
 * so a rewriting is difficult, and must be done with a mitigation between : clear and correct.
 * a good think is to add some note for complement explaination.
 * be enjoy for the rewriting
 * best regard Erwan1972 (talk) 15:21, 5 April 2012 (UTC)
 * NB: some mistake could come from french translation that translator have done (me and Bcebul)

Yes, I know that wiki is free, but I beleave articles in it should be written by those using their native languages, which for me isn't english. Knowing sailing physics well just isn't enough in my opinion. On the other hand since most seems to be translations from french, I would hope someone could translate these comments in this page in french to let those french speakers see it who wrote the original article in that language for their comments. I'm hoping they would see the merits and correct their mistakes or point mine if any exist rather than begin pointless deleting & adding wars between interested parties. I can't do that since I don't speak french at all. I see no merit at all in any of the energy related analyses, but I would like to see translated comments from those who wrote it or supports it. Can you check the subject line in french to see if it's the same in french too (about a force instead of physics of sails or something like that) since a lot of this article is about matters having nothing to do with a force on sails. Wouldn't it be beter to change the subjectline rather than deleting most of the article ? — Preceding unsigned comment added by 176.93.12.223 (talk) 18:31, 6 April 2012 (UTC)
 * Yes too.
 * French article is writing at 95% by me. As i'm not god, i have done mistake.
 * It the reason why 5% :)
 * In wp:fr, sailing members have rewrinting some parts 2,3,4 times for have a quite correct texte.
 * When bcebul and me have translate we have see some mistake add some complement.
 * bcebul have mainly improve picture !
 * And in wp:en sailing members have rewrinting some parts too !
 * so each time i see a mistake or improvement i tranfers this to wp:fr or wp:en.
 * as i transfert improvement on wp:fr, as you are more fluent in English, no hesitation, make your correction, improvement, after i do this transfert on wp:fr.
 * best regard
 * cdt
 * Nb: i have add a note for "elliptical shape". But better if you have reference for C-class cats, or USA17 adds this adds this ! — Preceding unsigned comment added by Erwan1972 (talk • contribs) 13:08, 10 April 2012 (UTC)


 * All remarks you have show are now included in article.
 * best regards
 * Erwan1972 (talk) 08:29, 17 April 2012 (UTC)

translation of several sail
Hi,

i want to start translation of several sail (cas de plusieurs voiles), have you some remarks objections ?

best regards

Erwan1972 (talk) 10:25, 2 May 2012 (UTC)

UK or US ?
Hi, i see some revers due to this point. I discover rule of UK vs US thanks to Mr swordfish. I a created this article in a froggy UK English, and after fully correcting in a good English by Bcebul to US form. And i am not offended by this fact. Best regards Erwan1972 (talk) 09:26, 21 September 2012 (UTC)

lede - decompositions of net aerodynamic force
Thanks, Swordfish. Is  the  recent re  edit  ok  re rotational  axes? Bcebul (talk) 21:33, 18 October 2011 (UTC)

oops. Did not   see   your  previous  discussion, Swordfish. Marchaj  talks  about  decomposition of force  re   boat   direction in a  seaway   prior  to   discussion  of    wind   oriented  axes. If  he   thought  it  was that important,  I   think  it  is  appropriate  in the   lede even   before   mentioning   lift and   drag. Thanks  for  pointing  out   confusion  re   torque.Bcebul (talk) 22:33, 18 October 2011 (UTC)

Also, the  plan  is   to  expand   the  Direction  of   force section,  which  precedes  the lift    drag   section,  to  include forces in  the  course axes. So, it is  logical  to  mention  it   first in  the  lead   section.Bcebul (talk) 00:58, 19 October 2011 (UTC)


 * I'm not sure that 'expansion' is what this article needs at the moment. My opinion is that as it is, it's overly long and goes beyond the scope of an encyclopedic article. We should strive to simplify it and make it more accessible to a general audience. Of course, if the expansion clarifies the concepts and makes the article more understandable, I'm all for it. Mr. Swordfish (talk) 15:08, 20 October 2011 (UTC)


 * I concur entirely with  Swordfish. I used to  race 470s and ocean-going  Cutlass class, but  the math in  this article is beyond me and drives me away  from  it. Kudpung กุดผึ้ง (talk) 15:43, 20 October 2011 (UTC)


 * That is the challenge: to make the  article succinct, generally readable and still relevant to sailors on the  water and in  sofas as well as  informative  to  those  like me and I suspect Erwan72  who  crave the physics, math and   engineering. Remember, the first word in the title oozes physics, math  and   engineering. The English article is  not nearly finished. We haven't  even   started on multiple sails. It may take awhile. Books  have  been   written  about  this   subject. I  think the French version re multiple sails is a bit rough and out of  reach of  even  more folks  without tensor calculus. It  doesn't  have  to  be  that  way. Even Fossati, Marchaj and Larsson / Eliasson did not go  that deep in their books.  The  article  is comparatively short (but long  for the  unengaged). More  pictures  and   diagrams   would  be good.  "1000  words"  and all  that to  engage the  multitude.  We could bury some  more of  the  math  in more explanation boxes for the keen.Bcebul (talk) 17:58, 20 October 2011 (UTC)


 * If we're going to make the article succinct and generally readable, we need to get out our sharp editor pencils and start cutting. For now, let's focus on the intro and try to incorporate the ideas of item 7 of WP:NOTTEXTBOOK.


 * It seems to me that the main points to be presented in the intro are:


 * Air flowing past a sail generates forces all along the sail
 * The forces can be combined to make a single net force
 * The net force can be expressed as a sum of lift and drag
 * When the boat is going downwind, the force is almost entirely drag and the wind simply pushes the boat in the direction of the wind
 * When the boat is beating or reaching, air is deflected aft and the boat is propelled forwardvia newtons 3rd law / conservation of momentum
 * (Perhaps a brief discussion on pressure distribution )
 * Sails are used to propel a variety of vessels, not just sailboats


 * I don't think it's important to introduce alternate co-ordinate systems, or make statements about how it's important to understand these things or that engineers need to know it. It's also not important to introduce a lot of specialized terminology.  To that end I propose the following intro:


 * Sails use wind energy to move sailboats, ice boats, sailboards, land sailing vehicles and windmill sails.


 * When air moves past a sail, Aerodynamic forces develop. These forces occur along the entire surface of the sails, but for simplicity they can be summed into one total force vector. In turn this force can be resolved into two components: lift (which is the component perpendicular to the wind direction) and drag (which is the component parallel to the wind direction).


 * When the sailboat is sailing directly downwind (i.e. in the same direction as the wind direction), the force is almost entirely drag force - the wind "pushes" the boat along in the direction of the wind.


 * When the boat is traveling across or into the wind the sails act as  airfoils and propel the boat by redirecting the wind coming in from the side towards the rear.  The wind moves the sail as the sail redirects the air backwards in accordance with the law of conservation of momentum.


 * Perhaps we could also add a brief statement that the forces are not entirely propulsive and contribute to undesirable results such as heeling, leeway, etc. Once we come to some sort of consensus on the intro, we can tackle the rest of the article. Mr. Swordfish (talk) 19:22, 20 October 2011 (UTC)


 * Is it possible to break this up into two seperate articles? One being math intensive for those interested in it, and the other page would be a simplified version for people/sailers to get a better idea without having to be math oriented.Beefcake6412 (talk) 19:13, 20 October 2011 (UTC)


 * (ec)I have not read the article in full, only skimmed through. A couple of opinions still: One, personally I like all that math, it is not usual in WP article but I would not go against it. Two, nevertheless the explanations are very long, veeeery long indeed; hiding under collapsible boxes may sound like a good idea but it is extremely bad, mostly because that's not the usual procedure (and both editors and readers need some consistency). So, if those math explanation stand, they'll better be on a linked article than hidden - Nabla (talk) 19:15, 20 October 2011 (UTC)


 * I think the  lede   should be  kept  very  brief, mentioning  the   gist  of  the  article, forces and  their  importance in  sails,  without   explaining  much if   anything.   Subsequent sections in  the  main  body should  be   organised  from  simple but  accurate introductory  summaries  to more  in depth explanations. Bcebul (talk) 21:56, 20 October 2011 (UTC)


 * hi, this article is a french translation of french wiki (mainly written by me).
 * and on french wiki we have following rule :
 * "Wikipédia est à la fois une encyclopédie généraliste et une encyclopédie spécialisée. Elle est donc composée à la fois d'articles généralistes et d'articles spécialisés."
 * or
 * "Les articles très spécialisés sont ceux qui nécessitent un solide bagage préalable de la part du lecteur pour être compréhensibles. Ils ont a priori leur place sur Wikipédia. Il faut alors tenter d'en présenter une approche vulgarisée dans l'introduction."
 * which can be translate in english by : (Scientific) specialized article are wiki compatible, an Abstract which can be understood by any literate reader of Wikipedia without any knowledge is required.
 * it's the reason why we have complex formula which are translate.
 * best regards Erwan1972 (talk) 20:59, 23 October 2011 (UTC)

In 2011, Mr. Swordfish wrote of the article, "it's overly long and goes beyond the scope of an encyclopedic article.  We should strive to simplify it and make it more accessible to a general audience." From what I see, it has only become longer and less accessible. Take, for example, the last diagram, which sets the context of forces on sails. Something like that should be at the beginning of the article, not at the end. I attempted to include a points of sail diagram that highlighted the modes of forces among luffing, lift and drag, but Bcebul suggested in an edit summary that "point of sail not directly relevant to sail force. incidence angle is. article is primarily about sails not boats." In fact, we're talking about sailing craft (land or sea) and the role that sails have for powering them. So, point of sail is the fundamental starting point, which leads to angle of incidence, mode of force (primarily lift or drag), and further to the details of how to describe lift and drag on sails as they may be configured. Clearly, four years of creating more detail has failed to create the accessibility expected of a Wikipedia article, as explained above by Erwan1972 in 2011. User:HopsonRoad 14:24, 8 March 2015 (UTC)
 * It is a perfectly valid argument that vessel course to wind angle could be a starting point for discussion of force analysis on sails. However, this starting  point is not in any of the standard texts on sail aerodynamics I have read.  Wikipedia strives not to break new ground.  Generally and  roughly, the  approach in  the textbooks is to outline  the relevant basic fluid dynamics physics, then move  to  a discussion of equilibrium of the system based on force component analysis and  steady state dynamics, introduce  mathematical  modelling  and   graphing   tools  especially  the  polar  graph, then  discuss  factors  influencing the relevant force components  such as angle of attack, sail area size and shape, problems related to wind  strength, sea state,  point of   sail,  hull factors, etc.   More sophisticated software  modelling  of  the   whole   system is  left  until  last.  I   believe the  point  of  sail first approach  may  be  more   suited  to a   "how to sail"  instruction article.
 * I see a tendency in some editors of this article to give the drag  and  lift components  unbalanced exclusive attention when rushing to  discuss   sail force and boat  motion.  They  are  very  important  components of total aerodynamic force, but  not  the only  ones.  Arguably, in regards sail and boat efficiency,  the forward drive  vs resistance vs  lateral force  components  are   more   relevant. Similarly an argument  could  be  made  for the  laminar vs detached flow fluid mechanics discussion rather  than  the   components  which are somewhat more  of a   convenience than "real". The  standard  texts also  discuss  this  approach, but  not exclusively.  Also,  the article title  mentions nothing about  boats. Nor  are  sails  exclusive to boats.
 * I am all for accessibility. Remembering that this is  a  subject  more complex  than  many, it is  a  challenge   to  make a  digest  of a  large  and  technical subject without letting  simplification  convey  the   sort  of  conceptual errors I  and  other  editors may  make.   I   believe in  the   discipline of being  able  to   back up (though  not  necessarily cite) any   statement   with  a  reference. Bcebul (talk) 06:27, 9 March 2015 (UTC)
 * Thank you for your perspective, Bcebul. As to the order of events, by the time a student of sail design sees a text on sail aerodynamics, they already have studied the material that I propose for the build-up of this article. No-one has managed to address the issue of accessibility, to date. I propose to do so in the sand box, while preserving your hard work in providing valuable information to the advanced reader. I'm hoping that you will help in this effort, since the article's value-added is mostly your work!


 * Regarding the building blocks of the article, note that the article, Lift (force), has very few equations in it, yet it should be a building block of this article. Perhaps it should be built out to the extent that one sees here, but it is more accessible in introducing the topic. Regarding the scope of the article, note also that the current article uses the words, "boat" and "vessel," whereas you correctly point out that it encompasses ice and land craft, as well. So, I feel that the terms "sailing craft" and "craft" are more general. Cheers, User:HopsonRoad 13:13, 9 March 2015 (UTC)

Expert attention
I think that this article could benefit from expert attention in the area of aerodynamics (though I could not find a suitable wiki-project in that area to use in the template I added). I am a sailor with a science background, and I am sure that this article makes some mistakes when compared to, for example Lift (force). On the other hand, this article often quickly diverts into quite tricky mathematics, some of which I wouldn't know how to check or fix. It is also clear that some parts of this article were written by someone for whom English is not a first language, and, though I'm sure they've done a great job, again I feel that fixing it is beyond me.

Two examples of the kind of things that worry me are, in the section 'Role of wind' there is a lot about air 'particles' bouncing off the sails, which I know is not a good explanation of lift. In the section 'Sailing in stalled flow' the maths seems based on two pressures, but surely there is also a lowering of atmospheric pressure behind a stalled sail, even if we can ignore everything to do with stream lines and turbulence. --Nigelj (talk) 13:01, 12 August 2012 (UTC)


 * I'm in complete agreement with this assessment. It was over a year ago that I suggested that the article needs a thorough going-over with a sharp pencil to remove unsourced material and improve readability.  It's been a year, and I haven't seen much progress.  I do not think the article in it's present form is up to wiki standards and would support moving it off-line to a sandbox until it can be brought up to standard. Mr. Swordfish (talk) 14:07, 20 August 2012 (UTC)


 * I agree too. For a start, the introductory sentence, " Understanding the forces on sails is important for the design and operation of the sails and whatever they are moving, sailboats, ice boats, sailboards, land sailing vehicles or windmill sail rotors" is not only cumbersome, but also fails to comply with Wikipedia practice.  Surely it should begin by saying what "Forces on sails" are, rather than the POV statement "understanding xxx is important...".   Come to that, is "Forces on sails" the best title?  Arrivisto (talk) 22:46, 31 August 2012 (UTC)


 * I have a bigger problem: Looking at the boat speed diagram, there is no way the boat speed should be 14kn when the boat is in irons. In irons, the boat speed is (always) 0 and the apparent wind speed is (always) the actual wind speed (14kn). This isn't abstract theory; this is basic sailing 101. I have no idea what "boat speed" (blue) in chart is supposed to mean, but it does not correspond to reality.  — Preceding unsigned comment added by 66.167.140.240 (talk) 10:46, 19 August 2013 (UTC)


 * I presume you mean this diagram:




 * Agree that it makes little sense. A boat sailing at 0 degrees to the wind (in irons) isn't going anywhere other than backwards. There is so much wrong with this article that I don't know where to even begin trying to fix it.  It's now been another year and the article is still a mess.  Mr. Swordfish (talk) 16:13, 19 August 2013 (UTC)
 * This diagram is too confusing to be useful, let's remove it. a13ean (talk) 17:05, 19 August 2013 (UTC)

Three years later, this article still needs expert attention and better sourcing. Please leave the tags in place until we reach consensus on the talk page to remove them. Mr. Swordfish (talk) 20:34, 6 March 2015 (UTC)
 * Yes. There seems to be a  dearth of willing  "experts". However,  there has been  for  a long  time  an abundance of reference material  for  those   willing  to   digest it and  regurgitate references.  Feel free to edit boldly.  Consensus is  the anchor  of  progress.  In  search of  truth, authority  should always be  tested and treated    with  scepticism.  However, in   Wikipedia  references trump  truth.  I  see  the  article's primary purpose as describing the forces relevant to  sails and sailing. Paramount is summarising  conventional  knowledge about their physical origin,  their  analysis and their relevance to sail and vessel/rotor structure and function.   It is   basically  a  physics/engineering  subject. Care  must   be  taken  not   to express errors  in conventional  terminology and  concepts as  a  result  of reaching   for succinct  readability.  For  this end  see the  many  references. Hopefully the article  will  not  achieve  "reference  clutter" in  the  process.  The article   is  a   bit  thin   on wind   tunnel issues, Navier Stokes equation,  The  Euler   equation,   computational fluid  dynamics, boundary   layer  issues,  aeroelasticity  modelling,  structural  analysis. But   books   have  been  written   on   these  already.  Would  be silly  to   rewrite  here the   many   tomes available  on  the   subject. Some  of  the   sections use   illustrative   examples   to  make  a  point.  The  references   are   littered    with  similar writing devices.  Though   useful,  this   is   not  a  traditional   encyclopedic  writing  structure. I  like   them here. Perhaps   they could  easily   be either referenced   better or  the   points, with  references, made  in  a  more   general  way?

Bcebul (talk) 07:41, 7 March 2015 (UTC)

Too much expert attention?
I jumped in with both feet in an attempt to make this article more accessible by reworking the lede. It suffers, in my opinion, from too much expertise, not too little! It reads more like a text book aimed at those who already understand fluid dynamics, rather than being the slightest bit accessible to non-technical people, who are interested in the topic. That's why I tried to build the lede from the simple to the complex. Clearly, I was too bold in doing so. I've preserved my attempt in my sandbox, if anyone wishes to review what I attempted. In summary, I would request that editors here structure the article from the simple to the technical, so that the average reader can understand at least the basics of what's being presented as suggested in the MOS for methematics. The lede should not be a string of individual sentences; indeed, the whole article is written this way. It should be a series of progressively more complex concepts in paragraph form that reflect the main text. I suggest that someone outline what the article should be in a sandbox and mine the current text, as appropriate, to rebuild it. I use this approach to good effect at Meteor, Meteoroid, Pothole, Cross-country skiing, among others. Sincerely, User:HopsonRoad 22:44, 7 March 2015 (UTC)
 * For a comparison of a text/equation ratio, see Lift (force). Note also that other Wikipedia articles don't have one-sentence paragraphs. I would like to see this article written with better flow. User:HopsonRoad 21:55, 8 March 2015 (UTC)


 * User:HopsonRoad, I don't think we have any serious disagreement here. In the interest of providing some historical context, this article started out as a (poorly) translated copy of an article from the French wikipedia.  Since then, the language has been adapted but many of the citations are to publications written in French and there's a lot of info that is still unsourced.  In short, I know a fair amount about aerodynamics and sailing and can follow citations to see if the cite backs up the assertion in the article, and I have to say that I am not at all confident that much of what appears in the article is correct.


 * Agree that the article contains a level of technical detail beyond what one would expect in an encyclopedia and that it lacks a simple introductory section comprehensible to the general reader.  I would strongly support adapting this article to use the simple-to-complex narrative arc as employed in Lift (force).  So I would encourage you to take a stab at re-writing the article starting with a clean slate.  I've wanted to do something similar but don't really know whrere to start with this article.  Mr. Swordfish (talk) 14:41, 9 March 2015 (UTC)

Introductory illustrations
The following diagrams are examples of what i feel should set the context of this article, two of them are already in the article (middle and end), the third, I proposed:

Something like this should set the stage. The current first image is merely pretty, but doesn't illustrate the topic well, since it represents light airs. A heavy air image with multiple points of sail would be a good second image after the diagram. User:HopsonRoad 14:56, 8 March 2015 (UTC)
 * I propose to build a composite diagram, based on the right-hand image, that incorporates the vectors that sum to apparent wind of the left-hand image and the forces on sails vectors of the middle image. I would make it possible to see in toto and to deconstruct for different parts of the discussion. User:HopsonRoad 15:15, 9 March 2015 (UTC)


 * The standard literature is replete with composite force vector/wind vector/polar graph illustrations. Starting with Eiffel re his polar graph. The Marchaj texts use them. Standard stuff.
 * See this nice article with tidy illustrations:
 * http://www.finot.com/ecrits/Damien%20Lafforgue/article_voiles_english.html
 * Bcebul (talk) 09:29, 10 March 2015 (UTC)


 * Understood, Bcebul. but there's nothing suitable for this article in Wikimedia. Take a look at what I propose in the sandbox, Furthermore, I would like to have uniformity of variables in the illustrations. Right now, they are a hodgepodge. Sincerely, User:HopsonRoad 11:11, 10 March 2015 (UTC)

Re: Forces on Sail  for   three  points of  sail.jpg. It  would   be   good  to   reference  the   size and   direction  of  the  force vectors   based   on calculations   from a   cited   table,  such as  in  Eliasson,  using   the   formula in Relation between aerodynamic force components. Also, it looks a bit  odd  that   the   boat  velocity  vectors all  have   same  value on the  diagram. Bcebul (talk) 00:01, 12 March 2015 (UTC)
 * Referenced speed calculations done   based  on  example   polar  plot from Fossati.Bcebul (talk) 21:41, 12 March 2015 (UTC)
 * http://www.mecaflux.com/en/sailing%20boat%20sail%20simplified%20calculation.htm Here   is  a   web   site   for simple  sail force calculations. Bcebul (talk) 01:55, 12 March 2015 (UTC)

I'll fix the diagram once we have nomenclature and notation decided for the variables in it. Cheers, User:HopsonRoad 00:59, 13 March 2015 (UTC)

Another questionable diagram
Bcebul, I have questions about the above images. I would not say that the sailboats shown in the left-hand image are "running" (propelling the boat primarily with drag forces). I would say that of the left-hand boat in the middle image (first in the article). Instead, the spinnakers shown are primarily generating lift on a broad reach—the angle of attack is in line with the leading edge of the sail, not behind it. Note the significant heeling force.

As to the right-hand image, it's beautiful, but I'm not sure what it's trying to illustrate beyond the fact that man 'o war jellyfish have a "sail," whose function is not illustrated in this image. Sincerely, User:HopsonRoad 14:50, 27 March 2015 (UTC)

Use of the term "turbulent flow"
It seems to me there may be some inconsistencies in the use of the term "turbulent" with respect to the flow around the sail. I am no expert in sailing; I don't even sail. I am interested in the mechanics of it, though, and I have a degree in mechanical engineering with past experience in aerodynamics.

The technical definition of turbulent flow is when the inertial forces of the flow far outweigh the viscous forces, giving a high Renold's number (e.g. ~10^6 and above). Often in this article and others around the internet, it seems that sailors in particular use the term "turbulent flow" to describe what is correctly called "separated flow". Just because the boundary layer separates from the body (hull, sail, wing, baseball, whatever), does not mean there is necessarily turbulent flow. Indeed a turbulent boundary layer is more resistant to separation than a laminar one, a fact that is often used for advantage in reducing drag on wings, cars, and boat hulls, by "tripping" the boundary layer into turbulent flow early, in order to keep the flow attached through greater angles of attack.

So my question is, am I missing something with respect to flow on non-rigid bodies (e.g. sails as opposed to rigid wings)? Stall of a wing occurs when the flow separates, not when the flow goes turbulent. Yet in the sailing world, it seems that people prefer the term "turbulent" flow to describe separated flow. For a fluid dynamics engineer this is a confusing mix of terminology. I kind of wonder/suspect if the fact that the sail is flexible means that the flow must remain laminar to remain attached; in other words does the increased energy in the turbulent boundary layer cause the sail to distort in such a way as to lead to boundary layer separation, when on a rigid wing it would actually improve boundary layer attachment?

Thanks for any explanation / discussion on this. seenhear — Preceding unsigned comment added by Seenhear (talk • contribs) 20:21, 3 April 2015 (UTC)
 * You make a good point, seenhear. See "Flow separation" versus "Turbulence." What you're perhaps hearing from sailors is imprecise conflation of the two concepts. We can clean this up in the article. Cheers, User:HopsonRoad 20:59, 3 April 2015 (UTC)
 * ...Edited to add my username and sig. Seenhear (talk) 18:57, 6 April 2015 (UTC)

Reorganization?
I would like to propose re-organizing this article in a manner that progresses from general to specific, while preserving the hard work that User:Bcebul has done. I would envision first shaping the outline, then bringing content across. I like the feature that occurs in two places where distracting detail remains hidden until the interested reader uncovers it. I recommend using that feature a bit more. Please look at (and edit) the Sandbox and place your comments, below.

I have drafted a lede and an overview for the review and editing of others. User:HopsonRoad 13:33, 16 March 2015 (UTC)

Guidance on making technical articles understandable
Here is some good guidance: Make technical articles understandable. User:HopsonRoad 12:06, 28 March 2015 (UTC)

Let's discuss how to frame this article, in light of the guidance given. My thoughts. Yours? User:HopsonRoad 21:13, 28 March 2015 (UTC)
 * Audience: I suggest that this article should be accessible to anyone, who can master a sailing craft on any point of sail. This would correspond to: "The knowledgeable reader has an education in the topic's field but wants to learn about the topic itself."
 * Technical content: Let's not assume that the reader is familiar with fluid dynamics, but put that level of discussion at the end of introductory material in a given section and towards the end of the article, as a whole. "Increasing the understandability of technical content is intended to be an improvement to the article for the benefit of the less knowledgeable readers, but this should be done without reducing the value to readers with more technical background."
 * Lead section: The lead should reflect the content, logic and flow of the article. "...the lead should provide an understandable overview of the article. While the lead is intended to mention all key aspects of the topic in some way, accessibility can be improved by only summarizing in the lead, and including the technical details in the body of the article."
 * Put the most understandable parts of the article up front: The most understandable parts are points of sail, which generate apparent wind velocities. The second most understandable parts are force components on sails, followed by the reactive forces that make those forces possible.
 * Write one level down: It's reasonable to assume that a sailor has the equivalent of a baccalaureate, so having much of the article understandable by someone graduating from high school would qualify.
 * Add a concrete example: Pictorial illustrations of actual sailing craft, tied to the principles discussed are important here.
 * Explain formulae in English: This is key to understanding, especially if a force or coefficient is proportionate to the square of velocity.
 * Add a picture: We have this covered!
 * Don't oversimplify: No danger here!

Comments on sandbox
Please make your comments, here:
 * Lift and  drag  are   not "modes of   propulsion".  They  are   components  of   total aerodynamic   force.  That is  all. The   forward driving   component "propels"  the  boat. On many angles  of  attack   where   some  attached flow occurs, the lift component   contributes  to  the  forward  component.  However,  even   with   running,   there  is  a   lift   component perpendicular  to  the  apparent   wind  on  sail contributing almost  nothing   to  the   forward   component. On   broad  reaching, drag, parallel to  wind, also  contributes   to  the   forward  component   or  " propulsion".Bcebul (talk) 02:32, 17 March 2015 (UTC)
 * Thank you, Bcebul. I have fixed this in the lede and elsewhere. User:HopsonRoad 11:25, 17 March 2015 (UTC)
 * Take care with the term power. It  has  a  very   specific meaning in  physics. The  article  should stick  with  that narrow context  to avoid confusion.Bcebul (talk) 07:53, 17 March 2015 (UTC)
 * I'm comfortable with its use, here in the lede, [User:Bcebul|Bcebul]]. It bridges between the common understanding of power, appropriate to an encyclopedic introduction and the discussion of force, used in the body. Additionally, there is no broken link in logic, since power is force times distance per unit of time. The force is as discussed in the body; distance and time just fall out with the motion of the vehicle. User:HopsonRoad 11:31, 17 March 2015 (UTC)
 * Discussing the  definition of  sail vs wing is  a  bit beyond  the  scope of this  article. Try sail or  wing for  that. Birds use wings  for   propulsion. Not  relevant here. Bcebul (talk) 08:12, 17 March 2015 (UTC)
 * I've been very explicit to link to Lift (force) and graphically depict the airfoil as an object providing lift, as opposed to a wing, which may constitute many different structures. I differentiated sails from wings in the lede. User:HopsonRoad 11:25, 17 March 2015 (UTC)
 * Whether the turbo fan is moved by natural wind or a jet fueled engine makes no  difference  to the basic fluid  mechanics, or force component descriptions. Not much point  in arguing too much the  differences   here. For brevity,the  article is about  sails only. Things  like   Turbosail can  have  their own  article.Bcebul (talk) 08:12, 17 March 2015 (UTC)
 * I disagree on this point, Bcebul, it's relevant to note that sails are adjusted to a natural force, i.e. the wind, whereas those other airfoils are not. In the body, I have changed the awkward language there. it's appropriate to point to airfoils attached to sailing craft on the fringes of the topic, A turbosail could be mentioned in passing, whereas a kite sail is just out of bounds, in my opinion. A windsurfing sail is an important object lesson because, instead of heeling away from the wind, it is brought windward to provide an upward component of lift that reduces hull drag. User:HopsonRoad 11:25, 17 March 2015 (UTC)
 * Hi there. I was asked to contribute. While I don't have my copy of Marchaj handy, if we're going to rewrite, that should be a primary reference for the maths. From some random website: "Sail Performance, based on C. A. Marchaj's classic Sailing Theory & Practice, has established itself as the standard work on the subject and is now acclaimed as a milestone in sailing literature." I support the idea of "Re-organizing this article in a manner that progresses from general to specific", not only because it makes more sense, but because most people can't read the formulae. However, using this criteria for evaluation the current sandbox is not a significant improvement, and is even perhaps the opposite. I would encourage going so far as to limit any algebra or formulae to a closing section, 'Formulae and calculation' which exclusively approaches the mathematics. All other sections within the article should be general and could have 'see also' links to the latter section. prat (talk) 00:55, 24 March 2015 (UTC)
 * Thank you for your observations, prat. Currently, I don't see the article and the sandbox converging toward "re-organizing this article in a manner that progresses from general to specific" while limiting algebra and formulae to a closing section. Would you consider being bold and doing the necessary work, either in the article or the sandbox to achieve what you suggest? Sincerely, User:HopsonRoad 12:41, 24 March 2015 (UTC)

On further consideration, prat, your standard of no formulae until the end may be too strict. See, for example, Quantum electrodynamics—a WP:Good Article in WikiProject Physics, where the first formula comes about ⅓ of the way into the article and some serious mathematics occurs about half way in. I would be happy, if the non-technical person got the idea by a third of the way in, and the more capable reader could go deeper upon further reading. User:HopsonRoad 21:10, 24 March 2015 (UTC)

Notation
Suggest use  Vsubcript for velocity vectors. S subcript for speed  components of   velocity. e.g. VTW true wind velocity STW true  wind speed Bcebul (talk) 01:38, 11 March 2015 (UTC)
 * Thanks, Bcebul. How do we address the notation in Force components with respect to wind section? Those are scalars, so you're suggesting that the corresponding vector for STW in the textual equations would be VTW in a diagram. Right? I concur with the mathematical rigor, but wonder whether it's more understandable to the lay reader. I'm thinking that, as long as the diagram shows a vector, S can denote its scalar value. User:HopsonRoad 01:58, 11 March 2015 (UTC)


 * The reason for  care  here   is  that vector addition is  not  the  same  as scalar  addition.


 * $$ \mathbf V_{TW} $$ +$$ (- {\mathbf V_{boat}}) $$ $$ \neq V_{TW} + (-V_{boat})$$.


 * I guess it  would   be acceptable to  the  math cognoscenti to  use  the   boldface convention  for   vectors and  plainface for scalars keeping   same  lettering.  The mathematics challenged may miss the   subtlety.  The   vector above script convention is favoured  by  the  Europeans.


 * $$ \vec V_{TW} $$ +$$ (- {\vec V_{boat}}) $$ $$ \neq V_{TW} + (-V_{boat})$$.


 * If we are clear to the  readers in  the  variable  definitions, you are correct I  am wrong. Best  to  stick with the  same lettering.
 * see: Help:Displaying_a_formula
 * https://en.wikipedia.org/wiki/Help:Displaying_a_formula
 * and :
 * https://en.wikibooks.org/wiki/LaTeX/Mathematics
 * Bcebul (talk) 05:04, 11 March 2015 (UTC)

I understand and concur with what you are saying about clarity of notation to distinguish vectors from scalars. My concern was choosing a convention that bridged between textual formulas and diagrams. It's more difficult and graphically fussier to use the vector above convention in a diagram. So, I would favor the boldface convention for ease of rendering and accessibility's sake.
 * OK. Bcebul (talk) 00:01, 12 March 2015 (UTC)

Also, in the table guide to the aerodynamic and hydronamic forces on the boat, the call-outs are bold face as are the explanations, but only some of them are vectors. What's a good way to address this? User:HopsonRoad 16:11, 11 March 2015 (UTC)
 * I  can   fix   that  in  the   diagram. Bcebul (talk) 00:01, 12 March 2015 (UTC)


 * That's great, Bcebul. I recommend that, when you do so, you are satisfied that the notation is what should become standard throughout the article. (See below under Nomenclature.) Also, could you give those illustrations an opaque background, please. User:HopsonRoad 02:21, 12 March 2015 (UTC)

Nomenclature
I'm trying to gather all the different ways of expressing the same variable in the article and present them here, so we can agree on one term. For example, in one place apparent wind velocity is V, in another it's VA, and in another it's VAWe (this latter one is a scalar). Watch this space for items to resolve. User:HopsonRoad 02:11, 12 March 2015 (UTC)
 * Still working  on  that.  But I think some of these are actually different variables. The  last is "apparent effective wind speed" used  for  the force   calculation adjustment for  heeling situations.
 * In the force  equations derived from Bernoulli, V is  the airflow velocity relative to the  sail, i.e. apparent wind. Relativity is often a  trap  for  newcomers.  In  the context  of general aerodynamics, simulations  and   wind  tunnels, true  wind  is  not  even considered, so it is  just V. Only  on  the   water is true wind relevant. Then it needs  to  be   converted to apparent wind  for  any  relevance to sail force.Bcebul (talk) 03:51, 12 March 2015 (UTC)

Hi Bcebul. You might wish to look over the list of variables that I compiled in  a special section in the sandbox. In some cases the notation itself varies, in other cases the nomenclature for the same variable varies. I suggest that you look over variables with conflicts and put your recommendation to the right, e.g. Recommendation: True wind angle: $$ \beta_{TW} $$.

There's more to tackle, but that list addresses the core of the article until the section on Wind and sail interactions.User:HopsonRoad 00:09, 13 March 2015 (UTC)
 * Bcebul, I note that in the section, Relation between aerodynamic force components, the notation for apparent wind changes from α to β and α becomes angle of attack on sail. I don't see a standard for notating those terms, but I feel that they should be uniform within the article. What do you suggest?


 * Also, it's unclear what the diagram, File:boataeropolar.svg, is trying to explain in all its detail. I note only one sail, yet it has a different apparent wind than that of the boat. That would be expected, if there were a jib providing a slot effect, but there's no jib here and it appears to complicate whatever this diagram illustrates. User:HopsonRoad 21:30, 20 March 2015 (UTC)
 * Thanks, HopsonRoad, for pointing that out.  There is  indeed only   one   apparent   wind   velocity.  Fixed.  The  apparent wind  angle is  only  the   same  as   the angle of  incidence of  the  sail if  the  sheeting  angle (or trim angle)  is zero. Still   working  on   consistency of   labels as   time permits. The lift drag curve  for angle of  attack diagram is an  example very    common in   the  Marchaj  and   Fossati texts  to   demonstrate  optimal angles of  incidence.  Another   way   is   to   superimpose boat  lift vs drag    curves  with sail   lift drag curves such as  in   Kimball pg  61 figure 3.15.
 * "...3.4 Why Is Sailing Upwind So Complicated? Is it really necessary to draw so many diagrams and write so many formulas to describe sailing? Sadly, I have been unable to find a shortcut path to the speed diagram. In fact, sailing is really more complicated than all the diagrams and formulas suggest..." Kimball  pg 73
 * Bcebul (talk) 06:17, 23 March 2015 (UTC)

Thanks for getting back, Bcebul. Does this tell the story, correctly to a degree appropriate for an encyclopedia readership? (VA is constant in these examples, which means that either VT or VB varies.)
 * Polar diagrams, showing lift (L), drag (D), total aerodynamic force (FT), forward driving force (FR), and lateral force (FLAT) for different points of sail

These are adapted from Pp. 61-63 Cheers, User:HopsonRoad 14:27, 23 March 2015 (UTC)

Parenthetical referencing
Bcebul. to preserve your references with page numbers I propose to use parenthetical referencing, which will also streamline the reference list. See, for example, how in-line notes link to citations, here. User:HopsonRoad 00:42, 13 March 2015 (UTC)
 * sounds fun Bcebul (talk) 00:52, 13 March 2015 (UTC)

Text ready to bring across?
Bcebul, I'm wondering if you would be amenable to bringing the following two items across from the sandbox: the lede and the Overview? Elsewhere, we appear to have taken divergent paths: in the sandbox I've proceeded from the general picture of sailing craft subject to wind towards the action of airstream on sails. In the, article as it stands, the approach appears to be building out from the specific (airstream on sails) to the general. It would be desirable, if other editors could guide us on which model is preferable. Sincerely, User:HopsonRoad 17:30, 25 March 2015 (UTC)
 * Thanks User:HopsonRoad. Your good work has  been an  inspiration.  I   like  your  diagrams and  have  put  some  more into  the  article. I  have  acted on your  advice  on   restructuring  the  opening. Tightening   the   nomenclature  has   been   useful   for   clarity (still  some  more  to  do).  As  for  the   general   approach, as I   have  already   said,  the   subject  is forces. Though   sail   forces on  a  sailing   craft  are   dependent  on the  craft their  other relevant  forces and their operation, and  the balance of   forces   is  very  important,  the operation  of craft  is  not the prime  subject.   So,  I   have  a  problem    with   your sandbox  lede. It  seems  to  be  the  opening  to  another article and  not directly to  the  point.  I  think  listing  the   nomenclature  in tables the   sand   box   was   useful.  However,  I   think introducing consistent definitions as  needed  in  the main article   is  more   brief  and less  cluttered.  Bcebul (talk) 22:00, 25 March 2015 (UTC)
 * I very much appreciate your thoughtful reply, Bcebul. I understand your desire to keep focus on what happens to the sail. The lede and introduction that I proposed in the sandbox are based on the premise (which is the key point of your fine illustration) that forces on sails are very much dependent on the reactive forces from the sailing craft. I felt that it was important to illustrate the scope of those reactive forces using ice boats in contrast to sailboats, which then leads to the topic of sail configuration to provide the power required by the craft to overcome forward resistance forces. I think that could we could discuss that relationship between applied and reactive forces here to agree on a scope for this article. Then we could work on the lede and introduction. There might also be a companion article on "Forces on sailboat hulls." Cheers, User:HopsonRoad 15:59, 26 March 2015 (UTC)

A quick comment or two: I find the structure of the proposed new article much better than the old one (where, as it seems, editors added chapters in random order, which now makes it difficult to understand the connections between the sections). It is also less technical and easier to understand. Of course, the information in the existing article shouldn't be lost, if possible. Is it intended to merge some sections still? Or transform them into their own articles? --PaterMcFly talk contribs 12:27, 2 August 2015 (UTC)
 * Thank you for your comments, PaterMcFly. I propose that, when the new material is brought across, the entirety of the current version be preserved in the sandbox for future mining. Unfortunately, much of the material presented appears to represent original research, which may be true, but is inadequately referenced. The material that is adequately referenced will be brought across, hopefully with clearer writing than currently exists. Sincerely, User:HopsonRoad 02:31, 3 August 2015 (UTC)
 * Yea, that might be a problem. Most of the diagrams with their explanation can be sourced though. I have a 2012 german book here that reproduces many of the diagrams in this article almost 1:1, giving their original sources. So when the source for some statement is unclear, that might help. --PaterMcFly talk contribs 20:37, 3 August 2015 (UTC)

Per the discussion above and at Peer review/Forces on sails/archive1, I propose to bring across the content at Talk:Forces on sails/sandbox and place the current article content in that sandbox. I feel that the substitute text works better than the current article. A lot of cleanup is still required with the references. Please offer concurrence or not on the move. Absent a consensus against doing so, I would make the move on Friday. Sincerely, User:HopsonRoad 00:49, 5 August 2015 (UTC)
 * I have brought the developmental material across and exchanged it with the pre-existing legacy material. User:HopsonRoad 13:49, 7 August 2015 (UTC)

Planform
The term "planform" is being used in this article to describe the outline shape of a sail. Is this normal usage or has it been mistakenly borrowed from books about aeroplane wings? &mdash; Cheers, Steelpillow (Talk) 12:53, 20 September 2015 (UTC)

Thank you for checking in, Steelpillow. Here is a sampling of citations that use the terminology in reference to sails: Did you have some other term in mind? Sincerely, User:HopsonRoad 19:13, 21 September 2015 (UTC)
 * Minimum Induced Drag of Sail Rigs and Hydrofoils Part 1: Planar Planforms
 * Planform efficiency and effective aspect ratio
 * Planform Sailwing Design using Symmetric Cross Sections
 * The Aero- and Hydromechanics of Keel Yachts by J.W. Slooff p. 301
 * Hi, in aircraft design, use of the term "planform" originated to describe the main wing and perhaps the whole machine, it is not used for vertical surfaces such as the tail fin. When I saw it being used on Wikipedia to describe sails, keels and similar vertical surfaces, I wondered whether this variant usage was standard or whether Wkipedia editors had mistakenly borrowed and misapplied the terminology of specifically aircraft wing aerodynamics. Your example sources show that it is indeed standard and there is no mistake. Thank you for clearing this up for me. &mdash; Cheers, Steelpillow (Talk) 19:24, 21 September 2015 (UTC)

Thanks for your interest and your reply, Steelpillow. The term is applicable to all lifting devices. An aircraft tail fin provides such lift as it contributes to directional stability and even more significantly, when used to offset adverse yaw. The confusing part of the word is "plan...", which implies that we're looking at the outline of a shape in the horizontal plane! Cheers, User:HopsonRoad 00:55, 22 September 2015 (UTC)

Legacy material
The previous version of this article is preserved here for those, who may wish to draw on it for further development. User:HopsonRoad 14:33, 25 September 2015 (UTC)

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