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Talk:Track transition curve

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1174:. Pasting the images of screenshots into the article gave the article an unprofessional look, stopped the article being editable by anyone except the creator of the screenshots and in the mean-time lowered the previous quality of the article, diluting the content that was already there. Instead of disrupting the quality of the article (in the hope of improving it later), it would instead be better to actively work on a draft version, tweaking experimenting and asking for review ("is it ready yet") on the article Talk: page and then incorporating any comments received. 362: 236: 250: 222: 191: 594:. I consider Rankine and Talbot to be reliable, because they actually give the curves, but the history given in Kellogg is a bit suspect. Crandall seems pretty good from what I've been able to check. I suppose that when my PhD is published, it will be kosher to cite it as well, but for now I've tried my best to stick to verfiable claims and avoid original research. 264: 2484:
Can anybody corroborate the statement that "It is important to note that superelevation is not the same as the roll angle of the rail (also referred to as cant or camber), which is used to describe the "tilting" of the individual rails instead of the banking of the entire track structure as reflected
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If you guys prefer, I will just start a new page calls euler curve or formulation of euler curve but I don't think it is appropriate. Euler curve is concerning about mathematics. Track transition curve is euler curve. I have not seen some mathematics topics call for so many citations when the writing
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Thank you for some further work in adjusting the material slightly, although more work is required, both in the presentation of the text and providing of sources (references). It is likely that Knowledge would benefit most from one or two equations and accompanying prose (normal text) explaining the
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With the advent of computers, it is now so easy to use a computer to compute the coordinates of any points along an Euler spiral. The theoretical background of the spiral has been removed from most engineering text book and are no more taught in most universities. I could not find any references and
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I decide how much time I want to spend in editing the article. Knowledge means voluntarily editing work and gets other users involved. I have done my part which I think my formula are accurate. If somebody dissatisfies with the presentation, let him edit the work. The formula presented in my pdf or
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at they time they were undertaken, but that does not mean that they can't be an improvement in the future! With careful editing, tuning and tweaks, the act of including the mathematic origins of the spiral is a very useful thing to do—it will probably take less than 8 pages of proof to do so! So
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The fonts are whatever the Mediawiki engine choses; it tends to render complicated formulas as PNGs and pass simple equations through as HTML entities. Focusing in on font might be missing the bigger picture; the two previous revisions what were added to the article were a low-resolution JPEG
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Such a problem would not occur if the material was written specifically for Knowledge, using Knowledge syntax and processes from the start. TeX syntax is incorporated within Knowledge as has been the defacto mathematical equation representation (typesetting system) since the 1980s assuring wide
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I highly object to the term "linear spiral". The correct name for the curve is Euler spiral. The much more common name for the curve is "clothoid". Either of these would be fine, but "linear spiral" sounds like making stuff up. Further, Google search reveals that when the term "linear spiral" is
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Ideally we can have a better WYSIWYG editor for formula so that I can cut and paste TeX code from the particular editor to the sandbox. Otherwise the time spent on editing the formula is just too great. When this is multiplied by the number of editors on Knowledge, it is very wasteful of the
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The article would ideally give the history of the use and adaptation of these various spiral forms. Doing so would provide a solid illustration of how technological innovation was both necessitated and encouraged by the Age of Rail - a valuable insight into the social impact of rail.
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There are several different types of mathematical spirals available for use, including the clothoid, the cubic parabola and the lemniscate. Of more common use on railways are the Searles, the Talbot and the AREMA 10-Chord spirals, which are empirical approximations of true spirals.
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I'm guessing that the AREMA reference probably continues on from the quote above to give some further detail about those approximations, their inventors and their history; but it may not. In any case, can anybody provide suitable references to help flesh out this story?
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If you think you can get it up to the level of being fit for inclusion, then I would recommend fixing them to the best of your ability. It is impolite to complain if others attempt to help a requestee with vaguely-specifed complex-formatting but the requestee then
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I owe you guys an apology. Sorry. I assure you not all hard efforts are wasted. I have been keeping to these formula for 10 years and forgotten about the simplification. I just converted some 3 pages of the to 1 page, much of the remaining is still the same.
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entirely. The poor curve has enough names in the literature (I've found Euler spiral, Cornu spiral, clothoid, Railroad Transition Spiral, Holbrook spiral, Glover's spiral, linarc, lince) - it doesn't need more now. I will change it if I hear no objection.
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I am uncomfortable that the first few lines go straight in to "Euler curves". While these are useful to understand the mathematics, the naive reader who has heard of, but does not yet understand the significance of transition curves will be discouraged.
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The primary reason for not integrating the proposed material into the article as-is is that it is highly unsuitable. In PDF/screenshot-form the text is not editable and in copy-and-paste form it is not presentable! Knowledge is something that is both
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by the elevation difference at the "top of rail" ". This seems a bit strange, considering that "superelevation" actually redirects to - where the distinction is drawn between "Track Cant" (= Superelevation) and "Rail Cant" (≠ Superelevation).
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My main concern is with (a). Although the article mostly discusses Euler spirals, it seems to give the impression that's the only curve used, under varying names. However, consider this quotation (from the AREMA reference in the article):
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to ensure the wikifying has been accurate. The PDF is not editable, it is not a wiki, it is not Knowledge; only yourself can make any changes to it. Because it is not in the end Knowledge format, it is still very much at a drafting stage
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I think that the questionable point is in essence saying that cant refers only to canting of the individual rails. If you take that out then I think that the rest is informative. I'll take that phrase out. Maybe that will resolve?
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Agree and I am not departing from improving the last version. In fact I did the incremental changes whereas the pdf file is only provided for reference. I don't know where you got the idea that I wanted you guys to start from scratch
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However, with a clean-up (particular style and formatting), further work, trimming and references I do believe it would contribute to the article. In its present form it remains unsuitable, which reflects why the content has been
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Thirdly, I object to you acting as an administrator when you are not one. I have ever included similar formula text in Knowledge and the formula was later amended by users who prefer TeX. You cannot deprive this right of mine.
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I don't understand why I cannot incorporate the text here and let anybody who does not satisfy with the presentation to get involved with the editing works, instead of letting me to do 100% editing work according to the style?
1997:). We only need to provide the facts, not the working (that is just my hunch, but lets see what a final proposed draft brings). Just the facts are much easier to backup with citations than each step of a complex derivation. 153: 1789:
Come to think about it, you have done a good deal in formating. I did not. What the article lacks is a graphic, i.e. a portion of the Cornu spiral in the first quadrant and begins at the origin. A graph to illustrate:
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where you think it is appropriate. Reference can be added on though I still think that the mathematics is simple! Again, I do not think it is right to deprive other people to have a chance in editing this article.
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Secondly, I have changed the text of the formula so that it is understandable to anybody who has used scientific calculator. What is the point of these formula to a person if he has never used a scientific
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Why Knowledge is not coming up with a 'WYSIWYG' editior for TeX? Shall we ask an opinion from a third person whether the section needs to be removed? E.g. Michael Hardy who is actually an expert in TeX
668:'s comment of 2008 including the term "linarc", the proverbial lightbulb lit up for me. It's a term I'd read many times years ago but could never get a handle on. If these other terms Raph mentioned: 1487:
and my writing are actually cross verifying, though I shall not quote I have used these formula in my computer program that has been cross-checked with other computer program. I am a civil engineer.
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I'm inclined to delete that paragraph - while the distinction is a significant one, it's already explained better elsewhere and seems a bit peripheral to the subject of transition curves. Views?
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The way that the document had been marked for requesting citation was destructive and had been done with a purpose (intending to delete non TeX-formatted writing). This is akin to vandalism.
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Lastly but importantly, if I have to quote published articles only does it mean I cannot devote my knowledge to Knowledge? Then how can Knowledge be called the sum of all human knowledge?--
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Sladen, I did not realize you have done further edition on my user page. But some of your edition is wrong when you use partial differentiation symbol instead of differentiation symbol.
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I agree with you that there is a constant for each integral but the fact that the initial conditions are carefully chosen to be zero and thus the constants of integrals are all zero.--
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all refer to the same thing, please let's have the article document them clearly. With references, of course! ;-) Then other Knowledge readers, too, might be enlightened. Thanks!
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information. I would assume that other contributors such as yourself (vandals excepted) are adding and improving material for the same (or similar) reasons—and therefore should be
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To derive Cornu spiral from the formula 1/R = l^2, all I need is perhaps two pages. However, I have changed the extend section to make it more useful for engineering purpose.--
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Thanks! I've done so, citing as many reliable sources as I can get my hands on. For those who want to read more deeply on the Euler spiral, I've put my draft PhD chapter up at
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and let anybody who does not satisfy with the presentation to get involved with the editing works, instead of letting me to do 100% editing work according to the style? --
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about doing code-drops and having everyone run around patching them up, then starting from scratch at the next code drop; it is about incremental improvement of
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leading from here to the new, main article. It's definitely more of a mathematical subject, with relevance beyond just rail engineering. Good suggestion. --
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Firstly, it is very simple to verify the mathematics. Any body with a good foundation in calculus will be able to verify it. You may check with Raph Levien.
1373:. You, as the original author are in a much better position to fix any inaccuracies since there are no external references (yet) to confirm its accuracy. 758:
equations, backed up by references from elsewhere. The paper itself (if suitably reviewed for accuracy) would perhaps be most suitable for inclusion at
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I expect at the end of the day what is needed is less than a page of equations, each of which is backed up by a reference to a reliable published work (
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for equally choosing to donate their own time and effort. Showing appreciation is a great source of encouragement; even if improved material is not
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spent editing time TeX/Wikifying on the draft earlier, much of which was unnecessary as it has now been deleted from the latest drop of your draft.
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just because it's there in the menu. Once again, if you truly would like help in improving the material in a sandbox or drafting page, then add
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screenshot and some raw text that was not syntactically clear. If you would like to force the inline equations to be always renders you can add
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what and where each issue is and I will further attempt to help you fix them (but again, it would be quicker if you tried yourself). —
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is probably now a good place to start hunting for citations, both within the paper and in-turn in the references that Levien has used.
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Newer so-called tangential switches have curved switch-blades, but there is no room for a transition; at least the jolt is reduced.
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One problem with deriving something from scratch ("original research") is that Knowledge is not about obtaining truth directly, but
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Jai: For the moment, please take this unformatted, overly detailed, unsourced and uncited content elsewhere. Please do not use
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I have done all the new changes to the wiki text, except the formula in literally text format. I am still hopeless with TeX. --
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describes how an article should evolve, rather than obliterating previous changes by large code drops. General guidance is at
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are happy with it, let alone asking others to convert vast swathes to Wiki/TeX and then asking for reviews. In particular
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For the same reason, I also believe a simple illustration on how to adopt the theory (not too in-depth) is also useful. --
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User: namespace, meaning that it will not disrupt the existing article unless there is some material ready for adding. —
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Even if the material were being introduced in the appropriate format it is too specialized for a general encyclopedia:
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Regarding praise; I devote time to Knowledge because I believe it is a useful thing to do, expanding a repository of
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format before they can be included into the final article. The PDF is not editable and the screenshots of the PDF
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I believe this is the right page to discuss the matter and I will stop discussing at your user discussion page. --
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Euler spiral is well known geometry. I cannot find reference to these formula but I think many other people can.
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mathematical spiral forms involved: "the clothoid, the cubic parabola and the lemniscate", along with various
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is a technical designation (Mediawiki capability) and is in no way different to any other established editor (
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when I was doing computer programming. I believe this section is useful as a reference for civil engineers.
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about providing verifiable material that matches the published/reviewed library of human knowledge. (Which
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Yes please Raph, do dive in and fix it! (Especially given you have a handle on the finite differences!). —
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Euler Integrals and Euler's Spiral--Sometimes called Fresnel Integrals and the Clothoide or Cornu's Spiral.
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Are you representing anybody when you are thanking me? Otherwise why do you thank me for my contribution?
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How many of these are mistakes and how many are people not being able to tell the difference between
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Could I politely request that you remove the material from the main article and make any corrections
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I propose to soften the first few lines with a non-tehcnical sentence, if no-one has any objection?
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I have problem in typing formula. If you wish to amend, please help to convert them to wiki text. --
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I am uploaded new pdf file. Reduce to 5 pages with 2 pages of derivation. Please kindly read. --
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I am sorry that I could not provide any reference material as I derived it entirely by myself.--
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Older turnouts had straight switch-blades, so there was always a jolt entering the curved leg.
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or similar, not infinitesimal terms which you described above. I used the wrong description. --
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I am sorry that I could not provide any reference material as I derived it entirely by myself.
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of the syntax, in the hope that others can extrapolate that and apply it to the rest of the
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Long overdue! Just to start you off, I've restored a simpler version, more in keeping with
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this unsuitable content without regard for the improvements to the draft made by others. —
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In which case the material falls into "Original research" and is unsuitable for Knowledge (
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for experimentation/conversion without disrupting the main article until it is ready. —
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itself is self contained. Please refer to people who know the mathematics or calculus.
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American Mathematical Monthly, Volume 25 (1918), pp. 276 - 282. Raymond Clare Archibald
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to make it easier for you to work on wikifying the material prior to inclusion on the
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to your userpage and myself or another editor will be happy to offer assistance. —
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My article is less than perfection. Ya, it need quotes, it can be found, e.g. the
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For those who have helped in editing the page, the mathematics has been moved to
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railways; but even in this limited context, it appears there are at least three
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continuity would mean a sudden change in centripetal acceleration, leading to a
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What about transition curves, or lack thereof, at turnouts, on the curved leg?
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I am giving up in amending the section. You go with it when you are ready. --
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Howto, vague and uncited statements were tagged (as you, yourself requested
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Kah Jai, you are asking others to review substantially changed content in
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ready, the encourage to try harder will hopefully improve it sufficiently.
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What's wrong with overwhelming quantities? I have done it several time.--
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User talk:Sladen#Please do not remove .22Formulation for Euler spiral.22
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attempt at improvement. Thank you for undertaking it. Some of those "
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cover the recommended format and syntax for material on Knowledge.
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Please halt editing for while, I am compiling simplified version. --
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Regarding your third query (only), please be aware that the rôle of
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Formulation of Euler spiral - moved from user Sladen discussion page
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I would encourage any editor to get as many reviews as possible of
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on Knowledge. If you would like to participate, you can visit the
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Please help to convert it to wiki text instead of deleting it.
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I'd like to be clear about: (a) which curves are actually used
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Welcome to Knowledge. I have copied and pasted the content of
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and the designated equation mark-up language. Knowledge is
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article. Once again, many thanks for getting involved. —
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I think that a new page would be preferable, with just a
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This reference is, of course, discussing common use on
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Don't demolish the house while it's still being built.
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However, if you think quote is necessary, You may put
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Hi! I'm a bit late to the party, but ... When I read
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by carrying on and/or fixing any errors introduced. —
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Continuing discussion on formulation of Euler spiral
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we only need to provide the facts, not the working.
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Lastly, it shall be 1192:article and in giving your time to do so. — 940:User talk:Sladen#Formulation of Euler spiral 2016:cover processes for making large changes. 1866:) 02:07, 8 January 2009 (UTC) correction -- 999:I could hardly handle formula in sandbox.-- 216: 2303:lines were tagged, as non-formatted lines 1922:; which will then require wikifying, and 1834: 1814: 1749: 1726: 1681: 1659: 1359:User:Ling Kah Jai/Track transition curve‎ 1023:User:Ling Kah Jai/Track transition curve‎ 975:User:Ling Kah Jai/Track transition curve‎ 966: 728: 528: 483: 477: 437: 431: 407: 401: 396:It seems like a spiral easement requires 1371:it is not yet ready for use on Knowledge 900:User:Ling Kah Jai/Track transition curve 775:User:Ling Kah Jai/Track transition curve 737:User:Ling Kah Jai/Track transition curve 619:The Euler spiral: a mathematical history 592:The Euler spiral: a mathematical history 1686: 1664: 642: 218: 188: 2554:Mid-importance rail transport articles 2189:You are duplicating your additions to 1806:an arbitrary point at coordinate (x,y) 1639:Getting more and more mistakes.Sigh!-- 1021:not editable in a useful manner. The 1942:Ideally you would be willing to work 1172:before it is added in the first place 1064:Why I cannot incorporate the text at 886:The addition of the screenshot was a 7: 942:. Regarding Track transition curve 295:This article is within the scope of 1803:radius of curvature R and Radius Rc 1129:). The threshold for inclusion is 472:Yes, although the right concept is 207:It is of interest to the following 23:for discussing improvements to the 2038:Strongly supporting User:Sladen's 1931:keep it off the article until you 1661: 727:, I have copied the material from 14: 616:Looks like it got published now: 2448:Turnouts aka Switches aka Points 1972:resources put into Knowledge. -- 262: 248: 234: 220: 189: 45:Click here to start a new topic. 2549:C-Class rail transport articles 2197:about sticking to the point. -- 347:This article has been rated as 369:This article lacks sufficient 1: 2532:22:26, 25 December 2017 (UTC) 2518:21:18, 25 December 2017 (UTC) 2500:13:13, 25 December 2017 (UTC) 2138:Motive on adding the section 1698:? Please specifically state 315:WikiProject Trains to do list 42:Put new text under old text. 2559:All WikiProject Trains pages 2335:16:03, 3 February 2009 (UTC) 2316:08:33, 4 February 2009 (UTC) 2292:13:33, 3 February 2009 (UTC) 2276:20:43, 2 February 2009 (UTC) 2258:18:26, 2 February 2009 (UTC) 2235:12:24, 30 January 2009 (UTC) 2207:12:00, 30 January 2009 (UTC) 2184:11:40, 30 January 2009 (UTC) 2159:10:34, 10 January 2009 (UTC) 2078:20:21, 25 January 2009 (UTC) 1982:07:20, 10 January 2009 (UTC) 1561:lots of notes here and there 1013:The equations need to be in 327:Knowledge:WikiProject Trains 2169:== Please stop vandalism == 2140:Formulation of Euler spiral 2128:06:51, 9 January 2009 (UTC) 2104:06:49, 9 January 2009 (UTC) 2056:11:38, 8 January 2009 (UTC) 2044:Knowledge is not a textbook 2034:11:16, 8 January 2009 (UTC) 1912:07:43, 8 January 2009 (UTC) 1898:06:31, 8 January 2009 (UTC) 1884:08:52, 8 January 2009 (UTC) 1777:01:12, 8 January 2009 (UTC) 1712:16:04, 7 January 2009 (UTC) 1669:{\displaystyle \partial \,} 1649:14:49, 7 January 2009 (UTC) 1634:16:04, 7 January 2009 (UTC) 1610:13:17, 7 January 2009 (UTC) 1595:16:04, 7 January 2009 (UTC) 1575:13:15, 7 January 2009 (UTC) 1549:13:07, 7 January 2009 (UTC) 1534:11:44, 7 January 2009 (UTC) 1507:12:20, 7 January 2009 (UTC) 1472:12:34, 7 January 2009 (UTC) 1446:12:39, 7 January 2009 (UTC) 1432:12:26, 7 January 2009 (UTC) 1406:12:20, 7 January 2009 (UTC) 1387:11:59, 7 January 2009 (UTC) 1348:11:35, 7 January 2009 (UTC) 1313:09:42, 7 January 2009 (UTC) 1273:09:57, 7 January 2009 (UTC) 1246:09:28, 7 January 2009 (UTC) 1202:08:41, 7 January 2009 (UTC) 1188:for wanting to improve the 1078:07:20, 7 January 2009 (UTC) 1039:11:47, 6 January 2009 (UTC) 1009:11:42, 6 January 2009 (UTC) 991:11:17, 6 January 2009 (UTC) 960:10:55, 6 January 2009 (UTC) 920:10:35, 7 January 2009 (UTC) 870:06:10, 7 January 2009 (UTC) 843:10:12, 7 January 2009 (UTC) 809:06:01, 7 January 2009 (UTC) 787:05:30, 7 January 2009 (UTC) 749:11:26, 6 January 2009 (UTC) 716:11:12, 6 January 2009 (UTC) 691:Formulation of Euler spiral 632:08:06, 7 January 2009 (UTC) 604:22:22, 30 August 2008 (UTC) 582:22:07, 29 August 2008 (UTC) 567:14:02, 29 August 2008 (UTC) 512:14:02, 29 August 2008 (UTC) 330:Template:WikiProject Trains 50:New to Knowledge? Welcome! 2575: 2443:17:04, 13 April 2013 (UTC) 2390:Choosing an easement curve 1952:already sufficient quality 686:16:27, 13 April 2013 (UTC) 545:{\displaystyle r=c\theta } 353:project's importance scale 2384:21:54, 1 March 2011 (UTC) 2365:21:27, 1 March 2011 (UTC) 1797:the ending circular curve 1691:{\displaystyle \delta \,} 457:. Does that sound right? 368: 346: 243: 215: 80:Be welcoming to newcomers 2475:03:33, 4 July 2015 (UTC) 2423:approximations to them. 1854:length measurement L, Ls 1845:{\displaystyle \theta s} 1760:{\displaystyle d\theta } 2480:Superelevation and Cant 2164:Readdition of unsourced 1822:{\displaystyle \theta } 1420:overwhelming quantities 1190:track transition curve‎ 552:, which is a different 467:13:46, 9 May 2008 (UTC) 333:rail transport articles 2409: 1846: 1823: 1761: 1738: 1692: 1670: 1066:Track transition curve 979:Track transition curve 674: 660:Terminology revisited! 546: 493: 447: 417: 365: 197:This article is rated 75:avoid personal attacks 25:Track transition curve 2404: 2000:The help material at 1847: 1824: 1762: 1739: 1693: 1671: 1521:require citation mark 969:File:Euler Spiral.pdf 820:). Please remove it. 731:File:Euler Spiral.pdf 670: 547: 494: 492:{\displaystyle G^{2}} 448: 446:{\displaystyle C^{1}} 418: 416:{\displaystyle C^{2}} 364: 100:Neutral point of view 1833: 1813: 1748: 1725: 1680: 1658: 1058:I don't understand: 760:wikisource:Main Page 527: 476: 430: 400: 105:No original research 2522:I think that works. 1794:the initial tangent 1937:User:Michael Hardy 1842: 1819: 1757: 1737:{\displaystyle dL} 1734: 1688: 1687: 1666: 1665: 735:into a sandbox at 542: 489: 443: 413: 366: 298:WikiProject Trains 203:content assessment 86:dispute resolution 47: 1920:a non-Wiki format 1422:to an article. — 719: 702:comment added by 389: 388: 385: 384: 381: 380: 293: 292: 183: 182: 66:Assume good faith 43: 2566: 2224: 2218: 2170: 1851: 1849: 1848: 1843: 1828: 1826: 1825: 1820: 1766: 1764: 1763: 1758: 1743: 1741: 1740: 1735: 1697: 1695: 1694: 1689: 1675: 1673: 1672: 1667: 1584: 1495:Fresnel integral 1181:not improvements 973:to a sandbox at 972: 970: 896:did get involved 734: 732: 718: 696: 666:User:Raph Levien 653: 647: 551: 549: 548: 543: 498: 496: 495: 490: 488: 487: 452: 450: 449: 444: 442: 441: 422: 420: 419: 414: 412: 411: 375:inline citations 373:and/or adequate 335: 334: 331: 328: 325: 266: 257: 256: 252: 245: 244: 239: 238: 237: 232: 224: 217: 200: 194: 193: 185: 179: 178: 164: 95:Article policies 16: 2574: 2573: 2569: 2568: 2567: 2565: 2564: 2563: 2539: 2538: 2482: 2450: 2392: 2347: 2222: 2216: 2168: 2166: 2143: 1831: 1830: 1811: 1810: 1787: 1746: 1745: 1723: 1722: 1678: 1677: 1656: 1655: 1582: 1485:Frenes integral 1377:familiarity. — 1333: 1179:The edits were 968: 944:oldid=262282718 934: 730: 697: 693: 662: 657: 656: 648: 644: 525: 524: 520: 479: 474: 473: 459:—Ben FrantzDale 433: 428: 427: 403: 398: 397: 394: 332: 329: 326: 323: 322: 294: 289:March 30, 2011 268: 267: 233: 230: 201:on Knowledge's 198: 121: 116: 115: 114: 91: 61: 12: 11: 5: 2572: 2570: 2562: 2561: 2556: 2551: 2541: 2540: 2537: 2536: 2535: 2534: 2481: 2478: 2449: 2446: 2391: 2388: 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2011: 2007: 2003: 1999: 1996: 1995: 1989: 1988: 1983: 1979: 1975: 1970: 1969: 1968: 1967: 1960: 1959: 1958: 1957: 1953: 1949: 1945: 1941: 1938: 1934: 1930: 1925: 1921: 1917: 1916: 1914: 1913: 1909: 1905: 1900: 1899: 1895: 1891: 1886: 1885: 1881: 1877: 1873: 1869: 1865: 1861: 1853: 1839: 1836: 1816: 1808: 1805: 1802: 1799: 1796: 1793: 1792: 1791: 1784: 1778: 1774: 1770: 1754: 1751: 1731: 1728: 1719: 1718: 1717: 1716: 1713: 1709: 1705: 1701: 1683: 1653: 1652: 1651: 1650: 1646: 1642: 1635: 1631: 1627: 1623: 1619: 1614: 1613: 1612: 1611: 1607: 1603: 1596: 1592: 1588: 1579: 1578: 1577: 1576: 1572: 1568: 1560: 1557: 1556: 1555: 1550: 1546: 1542: 1538: 1537: 1536: 1535: 1531: 1527: 1522: 1514: 1513: 1508: 1504: 1500: 1496: 1492: 1491: 1490: 1489: 1488: 1486: 1473: 1469: 1465: 1461: 1460: 1459: 1458: 1457: 1456: 1455: 1454: 1447: 1443: 1439: 1435: 1433: 1429: 1425: 1421: 1417: 1413: 1409: 1408: 1407: 1403: 1399: 1394: 1393: 1392: 1391: 1388: 1384: 1380: 1375: 1372: 1368: 1364: 1363:demonstration 1360: 1356: 1352: 1351: 1350: 1349: 1345: 1341: 1336: 1330: 1314: 1310: 1306: 1302: 1301: 1300: 1299: 1298: 1297: 1296: 1295: 1294: 1293: 1292: 1291: 1290: 1289: 1274: 1270: 1266: 1262: 1261: 1255: 1254:Administrator 1251: 1250: 1247: 1243: 1239: 1234: 1230: 1227: 1226: 1225: 1224: 1223: 1222: 1221: 1220: 1219: 1218: 1217: 1216: 1215: 1214: 1203: 1199: 1195: 1191: 1187: 1182: 1178: 1173: 1170: 1166: 1162: 1158: 1154: 1149: 1146: 1143: 1142: 1136: 1132: 1131:verifiability 1128: 1124: 1120: 1116: 1113: 1109: 1105: 1101: 1100: 1099: 1098: 1097: 1096: 1095: 1094: 1093: 1092: 1091: 1090: 1079: 1075: 1071: 1067: 1063: 1060: 1059: 1057: 1054: 1053: 1052: 1051: 1050: 1049: 1048: 1047: 1040: 1036: 1032: 1028: 1024: 1020: 1016: 1012: 1011: 1010: 1006: 1002: 998: 997: 996: 995: 992: 988: 984: 980: 976: 971: 964: 963: 962: 961: 957: 953: 946: 945: 941: 936: 935: 931: 921: 917: 913: 909: 906: 904: 901: 897: 893: 889: 885: 884: 883: 882: 881: 880: 879: 878: 871: 867: 863: 858: 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101: 98: 97: 96: 87: 83: 81: 78: 76: 72: 69: 67: 64: 63: 57: 53: 52:Learn to edit 49: 46: 41: 40: 37: 36: 32: 26: 22: 18: 17: 2508: 2507: 2490: 2487: 2483: 2460: 2457: 2454: 2451: 2433: 2429: 2425: 2420: 2416: 2412: 2410: 2405: 2400: 2395: 2393: 2355: 2352: 2348: 2327:Ling Kah Jai 2324:Euler spiral 2300: 2284:Ling Kah Jai 2250:Ling Kah Jai 2212: 2176:Ling Kah Jai 2167: 2151:Ling Kah Jai 2148: 2144: 2139: 2120:Ling Kah Jai 2096:Ling Kah Jai 2039: 2018:WP:IMPERFECT 1991: 1974:Ling Kah Jai 1951: 1947: 1943: 1932: 1928: 1923: 1919: 1904:Ling Kah Jai 1901: 1890:Ling Kah Jai 1887: 1876:Ling Kah Jai 1868:Ling Kah Jai 1860:Ling Kah Jai 1857: 1788: 1785:Continue ... 1769:Ling Kah Jai 1699: 1641:Ling Kah Jai 1638: 1621: 1617: 1602:Ling Kah Jai 1599: 1567:Ling Kah Jai 1564: 1553: 1541:Ling Kah Jai 1526:Ling Kah Jai 1520: 1518: 1499:Ling Kah Jai 1493:Correction: 1482: 1464:Ling Kah Jai 1438:Ling Kah Jai 1419: 1415: 1411: 1398:Ling Kah Jai 1370: 1366: 1362: 1355:on the draft 1354: 1340:Ling Kah Jai 1337: 1334: 1305:Ling Kah Jai 1260:WP:NOBIGDEAL 1257: 1253: 1238:Ling Kah Jai 1185: 1180: 1171: 1168: 1164: 1160: 1156: 1152: 1138: 1134: 1130: 1126: 1122: 1118: 1111: 1107: 1104:well-written 1103: 1070:Ling Kah Jai 1026: 1018: 1001:Ling Kah Jai 952:Ling Kah Jai 949: 938:copied from 937: 895: 891: 862:Ling Kah Jai 814: 801:Ling Kah Jai 763: 723:As noted at 704:Ling Kah Jai 694: 675: 671: 663: 645: 618: 521: 395: 348: 313:. See also: 307:project page 296: 282: 272: 271: 209:WikiProjects 171: 165: 157: 150: 144: 138: 132: 122: 94: 19:This is the 2396:in practice 2357:Afterbrunel 2062:User:Sladen 1992:again, see 1232:calculator? 1165:presentable 1157:presentable 698:—Preceding 596:Raph Levien 559:Raph Levien 518:Terminology 504:Raph Levien 426:. That is, 148:free images 31:not a forum 2543:Categories 2006:WP:FORMULA 1800:the spiral 1620:go in and 1169:verifiable 1019:definitely 500:continuity 424:continuity 392:Continuity 371:references 311:discussion 2524:Zeusfaber 2509:North8000 2492:Zeusfaber 2421:practical 2002:WP:LAYOUT 1994:WP:VERIFY 1186:thank you 1141:WP:VERIFY 1135:not truth 1123:hopefully 770:WP:VERIFY 88:if needed 71:Be polite 21:talk page 2467:Tabletop 2413:American 2195:WP:TOPIC 2060:Thanks, 1933:yourself 1618:does not 1161:editable 1153:editable 712:contribs 700:unsigned 317:and the 56:get help 29:This is 27:article. 2463:turnout 2372:WP:LEDE 2066:the fix 2022:WP:HELP 2010:WP:BOLD 1809:angles 1700:exactly 1418:adding 1108:thanked 888:WP:BOLD 824:removed 351:on the 199:C-class 154:WP refs 142:scholar 2308:Sladen 2227:Sladen 2220:helpme 2213:revert 2064:, for 2026:Sladen 2014:WP:BRD 1962:again. 1929:please 1704:Sladen 1626:Sladen 1587:Sladen 1424:Sladen 1416:before 1379:Sladen 1265:Sladen 1194:Sladen 1031:Sladen 983:Sladen 912:Sladen 892:anyone 835:Sladen 817:WP:NOR 779:Sladen 766:WP:NOT 741:Sladen 624:Sladen 574:Sladen 324:Trains 228:Trains 205:scale. 126:Google 2417:ideal 1954:text. 1263:). — 1127:truth 1112:quite 830:times 827:three 554:beast 169:JSTOR 130:books 84:Seek 2528:talk 2514:talk 2496:talk 2471:talk 2461:See 2439:talk 2435:yoyo 2380:talk 2361:talk 2331:talk 2312:talk 2288:talk 2272:talk 2254:talk 2231:talk 2203:talk 2180:talk 2155:talk 2124:talk 2100:talk 2074:talk 2068:. -- 2052:talk 2030:talk 2012:and 2004:and 1978:talk 1908:talk 1894:talk 1880:talk 1872:talk 1864:talk 1829:and 1773:talk 1708:talk 1676:and 1645:talk 1630:talk 1606:talk 1591:talk 1571:talk 1545:talk 1530:talk 1503:talk 1468:talk 1442:talk 1428:talk 1402:talk 1383:talk 1344:talk 1309:talk 1269:talk 1258:see 1242:talk 1198:talk 1167:and 1155:and 1139:See 1133:and 1074:talk 1035:talk 1027:your 1005:talk 987:talk 956:talk 916:talk 866:talk 839:talk 815:see 805:talk 783:talk 768:and 764:See 762:. 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