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It seems like a spiral easement requires ${\displaystyle C^{2))$ continuity. That is, ${\displaystyle C^{1))$ continuity would mean a sudden change in centripetal acceleration, leading to a jerk. Does that sound right? —Ben FrantzDale (talk) 13:46, 9 May 2008 (UTC)[reply]

Yes, although the right concept is ${\displaystyle G^{2))$ continuity, as only the intrinsic shape of the curve is important, not the parameter.Raph Levien (talk) 14:02, 29 August 2008 (UTC)[reply]

I highly object to the term "linear spiral". The correct name for the curve is Euler spiral^{[t 1]}. 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 used, it most often refers to the linear equation ${\displaystyle r=c\theta }$, which is a different beast 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. Raph Levien (talk) 14:02, 29 August 2008 (UTC)[reply]

Yes please Raph, do dive in and fix it! (Especially given you have a handle on the finite differences!). —Sladen (talk) 22:07, 29 August 2008 (UTC)[reply]

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 The Euler spiral: a mathematical history. 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. Raph Levien (talk) 22:22, 30 August 2008 (UTC)[reply]

Looks like it got published now: The Euler spiral: a mathematical history, congratulations Raph! (When is the full PhD thesis due?... ;-). —Sladen (talk) 08:06, 7 January 2009 (UTC)[reply]

Terminology revisited!

Hi! I'm a bit late to the party, but ... When I read User:Raph Levien'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:

... I've found Euler spiral, Cornu spiral, clothoid, Railroad Transition Spiral, Holbrook spiral, Glover's spiral, linarc, lince ... Raph Levien (talk) 14:02, 29 August 2008 (UTC)

all refer to the same thing, please let's have the article document them clearly. With references, of course! ;-) Then other Wikipedia readers, too, might be enlightened. Thanks! yoyo (talk) 16:27, 13 April 2013 (UTC)[reply]

Please help to convert it to wiki text instead of deleting it. —Preceding unsigned comment added by Ling Kah Jai (talk • contribs) 11:12, 6 January 2009 (UTC)[reply]

As noted at User talk:Sladen#Please do not remove .22Formulation for Euler spiral.22, I have copied the material from File:Euler Spiral.pdf into a sandbox at User:Ling Kah Jai/Track transition curve for experimentation/conversion without disrupting the main article until it is ready. —Sladen (talk) 11:26, 6 January 2009 (UTC)[reply]

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 Wikipedia would benefit most from one or two equations and accompanying prose (normal text) explaining the equations, backed up by references from elsewhere. The paper itself (if suitably reviewed for accuracy) would perhaps be most suitable for inclusion at wikisource:Main Page. (See WP:NOT and WP:VERIFY). It is advantageous if the proposed additions could be improved up to the standard of Wikipedia in a sandbox, in this case User:Ling Kah Jai/Track transition curve. Once again, thank you for getting involved. —Sladen (talk) 05:30, 7 January 2009 (UTC)[reply]

I am sorry that I could not provide any reference material as I derived it entirely by myself.--Ling Kah Jai (talk) 06:01, 7 January 2009 (UTC)[reply]

In which case the material falls into "Original research" and is unsuitable for Wikipedia (see WP:NOR). Please remove it.

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 removed[1] three[2] times[3] with appropriate suggestions for improvement. —Sladen (talk) 10:12, 7 January 2009 (UTC)[reply]

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? --Ling Kah Jai (talk) 06:10, 7 January 2009 (UTC)[reply]

The addition of the screenshot was a WP:BOLD attempt at improvement. Thank you for undertaking it. Some of those "anyone" were not satisfied with the presentation and did get involved. The involvement removed the unfinished content to a drafting area, and provided suggestions on how to improve the presentation of the draft (at User:Ling Kah Jai/Track transition curve) up to the level of Wikipedia. The involvement demonstrated proper formatting by converting sections to TeX[4][5]. Your recent change (revert) appears to have restored[6] this unsuitable content without regard for the improvements to the draft made by others. —Sladen (talk) 10:35, 7 January 2009 (UTC)[reply]

copied from User talk:Sladen#Formulation of Euler spiral. Regarding Track transition curve oldid=262282718

I have problem in typing formula. If you wish to amend, please help to convert them to wiki text. --Ling Kah Jai (talk) 10:55, 6 January 2009 (UTC)[reply]

Welcome to Wikipedia. I have copied and pasted the content of File:Euler Spiral.pdf to a sandbox at User:Ling Kah Jai/Track transition curve‎ to make it easier for you to work on wikifying the material prior to inclusion on the Track transition curve article. Once again, many thanks for getting involved. —Sladen (talk) 11:17, 6 January 2009 (UTC)[reply]

I could hardly handle formula in sandbox.--Ling Kah Jai (talk) 11:42, 6 January 2009 (UTC)[reply]

The equations need to be in TeX format before they can be included into the final article. The PDF is not editable and the screenshots of the PDF definitely not editable in a useful manner. The User:Ling Kah Jai/Track transition curve‎ page is just another wiki page, but is under your User: namespace, meaning that it will not disrupt the existing article unless there is some material ready for adding. —Sladen (talk) 11:47, 6 January 2009 (UTC)[reply]

I am sorry that I could not provide any reference material as I derived it entirely by myself.

I don't understand:

• Are you representing anybody when you are thanking me? Otherwise why do you thank me for my contribution?
• Why I cannot incorporate the text at Track transition curve 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? --Ling Kah Jai (talk) 07:20, 7 January 2009 (UTC)[reply]

1. Regarding praise; I devote time to Wikipedia because I believe it is a useful thing to do, expanding a repository of well-written 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 thanked for equally choosing to donate their own time and effort. Showing appreciation is a great source of encouragement; even if improved material is not quite ready, the encourage to try harder will hopefully improve it sufficiently.
2. One problem with deriving something from scratch ("original research") is that Wikipedia is not about obtaining truth directly, but is about providing verifiable material that matches the published/reviewed library of human knowledge. (Which hopefully is truth). The threshold for inclusion is verifiability and not truth (See WP:VERIFY). As to finding published references, Raph Levien's PhD extract[7] 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.
3. 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! Wikipedia is something that is both editable and presentable. Material can always be improved further, but it does need to be editable, presentable and verifiable before it is added in the first place. 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.

The edits were not improvements 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 once again, I (myself, just me) would like to thank you for wanting to improve the track transition curve‎ article and in giving your time to do so. —Sladen (talk) 08:41, 7 January 2009 (UTC)[reply]

• 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.
• 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 calculator?
• Thirdly, I object to you acting as an administrator when you are not one. I have ever included similar formula text in Wikipedia and the formula was later amended by users who prefer TeX. You cannot deprive this right of mine. --Ling Kah Jai (talk) 09:28, 7 January 2009 (UTC)[reply]

Regarding your third query (only), please be aware that the rôle of Administrator is a technical designation (Mediawiki capability) and is in no way different to any other established editor (see WP:NOBIGDEAL). —Sladen (talk) 09:57, 7 January 2009 (UTC)[reply]

• Lastly but importantly, if I have to quote published articles only does it mean I cannot devote my knowledge to Wikipedia? Then how can Wikipedia be called the sum of all human knowledge?--Ling Kah Jai (talk) 09:42, 7 January 2009 (UTC)[reply]

Continuing discussion on formulation of Euler spiral

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.

I believe this is the right page to discuss the matter and I will stop discussing at your user discussion page. --Ling Kah Jai (talk) 11:35, 7 January 2009 (UTC)[reply]

Could I politely request that you remove the material from the main article and make any corrections on the draft at User:Ling Kah Jai/Track transition curve‎. As noted in the edit summaries, the TeX was done as a demonstration of the syntax, in the hope that others can extrapolate that and apply it to the rest of the draft material. In some places (because of the lack of brackets and unbounded integrals). The fact that it was unclear what the intended formula was, is a clear sign that it is not yet ready for use on Wikipedia. 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.

Such a problem would not occur if the material was written specifically for Wikipedia, using Wikipedia syntax and processes from the start. TeX syntax is incorporated within Wikipedia as has been the defacto mathematical equation representation (typesetting system) since the 1980s assuring wide familiarity. —Sladen (talk) 11:59, 7 January 2009 (UTC)[reply]

Why Wikipedia 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 --Ling Kah Jai (talk) 12:20, 7 January 2009 (UTC)[reply]

I would encourage any editor to get as many reviews as possible of draft material, before adding overwhelming quantities to an article. —Sladen (talk) 12:26, 7 January 2009 (UTC)[reply]

What's wrong with overwhelming quantities? I have done it several time.--Ling Kah Jai (talk) 12:39, 7 January 2009 (UTC)[reply]

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.--Ling Kah Jai (talk) 12:34, 7 January 2009 (UTC)[reply]

My article is less than perfection. Ya, it need quotes, it can be found, e.g. the Frenes integral 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.

Correction: Fresnel integral --Ling Kah Jai (talk) 12:20, 7 January 2009 (UTC)[reply]

Euler spiral is well known geometry. I cannot find reference to these formula but I think many other people can.

However, if you think quote is necessary, You may put require citation mark 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. --Ling Kah Jai (talk) 11:44, 7 January 2009 (UTC)[reply]

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.--Ling Kah Jai (talk) 13:07, 7 January 2009 (UTC)[reply]

I feel that the article has been messed with:

• inconsistent fonts in symbol section and formula
• lots of notes here and there

--Ling Kah Jai (talk) 13:15, 7 January 2009 (UTC)[reply]

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 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 \, at the end (a small TeX space) to force PNG. —Sladen (talk) 16:04, 7 January 2009 (UTC)[reply]

I am giving up in amending the section. You go with it when you are ready. --Ling Kah Jai (talk) 13:17, 7 January 2009 (UTC)[reply]

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 does not go in and finish the job by carrying on and/or fixing any errors introduced. —Sladen (talk) 16:04, 7 January 2009 (UTC)[reply]

Getting more and more mistakes.Sigh!--Ling Kah Jai (talk) 14:49, 7 January 2009 (UTC)[reply]

How many of these are mistakes and how many are people not being able to tell the difference between ${\displaystyle \partial \,}$ and ${\displaystyle \delta \,}$? Please specifically state exactly 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). —Sladen (talk) 16:04, 7 January 2009 (UTC)[reply]

I decide how much time I want to spend in editing the article. Wikipedia 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 jpg files are accurate. Lastly, it shall be ${\displaystyle dL}$ or ${\displaystyle d\theta }$ or similar, not infinitesimal terms which you described above. I used the wrong description. --Ling Kah Jai (talk) 01:12, 8 January 2009 (UTC)[reply]

Continue ...

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:

• the initial tangent
• the ending circular curve
• the spiral
• radius of curvature R and Radius Rc
• an arbitrary point at coordinate (x,y)
• angles ${\displaystyle \theta }$ and ${\displaystyle \theta s}$
• length measurement L, Ls

However, I cannot do graphic on computer. --Ling Kah Jai (talk) 02:07, 8 January 2009 (UTC) correction --Ling Kah Jai (talk) 02:07, 8 January 2009 (UTC) --Second correction --Ling Kah Jai (talk) 08:52, 8 January 2009 (UTC)[reply]

Please halt editing for while, I am compiling simplified version. --Ling Kah Jai (talk) 06:31, 8 January 2009 (UTC)[reply]

I am uploaded new pdf file. Reduce to 5 pages with 2 pages of derivation. Please kindly read. --Ling Kah Jai (talk) 07:43, 8 January 2009 (UTC)[reply]

Kah Jai, you are asking others to review substantially changed content in a non-Wiki format; which will then require wikifying, and checking again to ensure the wikifying has been accurate. The PDF is not editable, it is not a wiki, it is not Wikipedia; only yourself can make any changes to it. Because it is not in the end Wikipedia format, it is still very much at a drafting stage please keep it off the article until you yourself are happy with it, let alone asking others to convert vast swathes to Wiki/TeX and then asking for reviews. In particular User:Michael Hardy 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.

Ideally you would be willing to work in Wiki-syntax and the designated equation mark-up language. Wikipedia is not 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 already sufficient quality text.

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 again.

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 Wikipedia, it is very wasteful of the resources put into Wikipedia. --Ling Kah Jai (talk) 07:20, 10 January 2009 (UTC)[reply]

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 (again, see WP:VERIFY). 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.

The help material at WP:LAYOUT and WP:FORMULA cover the recommended format and syntax for material on Wikipedia. WP:BOLD and WP:BRD cover processes for making large changes. WP:IMPERFECT describes how an article should evolve, rather than obliterating previous changes by large code drops. General guidance is at WP:HELP. —Sladen (talk) 11:16, 8 January 2009 (UTC)[reply]

Strongly supporting User:Sladen's we only need to provide the facts, not the working. Even if the material were being introduced in the appropriate format it is too specialized for a general encyclopedia: Wikipedia is not a textbook.--Old Moonraker (talk) 11:38, 8 January 2009 (UTC)[reply]

Thanks, User:Sladen, for the fix. --Old Moonraker (talk) 20:21, 25 January 2009 (UTC)[reply]

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. --Ling Kah Jai (talk) 06:49, 9 January 2009 (UTC)[reply]

I have done all the new changes to the wiki text, except the formula in literally text format. I am still hopeless with TeX. --Ling Kah Jai (talk) 06:51, 9 January 2009 (UTC)[reply]

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 when I was doing computer programming. I believe this section is useful as a reference for civil engineers.

For the same reason, I also believe a simple illustration on how to adopt the theory (not too in-depth) is also useful. --Ling Kah Jai (talk) 10:34, 10 January 2009 (UTC)[reply]

== Please stop vandalism == Don't demolish the house while it's still being built. --Ling Kah Jai (talk) 11:40, 30 January 2009 (UTC)[reply]

You are duplicating your additions to Euler's spiral, an article concerning mathematics, on this page about railways. Why? Please see WP:TOPIC about sticking to the point. --Old Moonraker (talk) 12:00, 30 January 2009 (UTC)[reply]

Jai: For the moment, please take this unformatted, overly detailed, unsourced and uncited content elsewhere. Please do not use revert 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 ((helpme)) to your userpage and myself or another editor will be happy to offer assistance. —Sladen (talk) 12:24, 30 January 2009 (UTC)[reply]

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 itself is self contained. Please refer to people who know the mathematics or calculus. Ling Kah Jai (talk) 18:26, 2 February 2009 (UTC)[reply]

I think that a new page would be preferable, with just a Template:Main leading from here to the new, main article. It's definitely more of a mathematical subject, with relevance beyond just rail engineering. Good suggestion. --Old Moonraker (talk) 20:43, 2 February 2009 (UTC)[reply]

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. Ling Kah Jai (talk) 13:33, 3 February 2009 (UTC)[reply]

Howto, vague and uncited statements were tagged (as you, yourself requested[8]) without regard the formatting. Twice as many TeX-formatted lines were tagged, as non-formatted lines[9]. I hope you will be able to solve all of these issues regardless of on which article you propose the additions; once again, thank you for getting involved with Wikipedia. —Sladen (talk) 08:33, 4 February 2009 (UTC)[reply]

For those who have helped in editing the page, the mathematics has been moved to Euler spiral Ling Kah Jai (talk) 16:03, 3 February 2009 (UTC)[reply]

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.

I propose to soften the first few lines with a non-tehcnical sentence, if no-one has any objection?

Afterbrunel (talk) 21:27, 1 March 2011 (UTC)[reply]

Long overdue! Just to start you off, I've restored a simpler version, more in keeping with WP:LEDE, from an earlier edit. Perhaps even now too technical and a knowledgeable editor could make it more accessible still. --Old Moonraker (talk) 21:54, 1 March 2011 (UTC)[reply]

I'd like to be clear about: (a) which curves are actually used in practice ... (b) in the various railways administrations; not just North American but also others, e.g. Australian, European, Indian etc. (This would help with NPOV.)

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):

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.

This reference is, of course, discussing common use on American railways; but even in this limited context, it appears there are at least three ideal mathematical spiral forms involved: "the clothoid, the cubic parabola and the lemniscate", along with various practical approximations to them.

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.

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?

yoyo (talk) 17:04, 13 April 2013 (UTC)[reply]

What about transition curves, or lack thereof, at turnouts, on the curved leg?

Older turnouts had straight switch-blades, so there was always a jolt entering the curved leg.

Newer so-called tangential switches have curved switch-blades, but there is no room for a transition; at least the jolt is reduced.

See turnout. Tabletop (talk) 03:33, 4 July 2015 (UTC)[reply]

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 by the elevation difference at the "top of rail" ". This seems a bit strange, considering that "superelevation" actually redirects to [Cant(road/rail] - where the distinction is drawn between "Track Cant" (= Superelevation) and "Rail Cant" (≠ Superelevation).

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?

Zeusfaber (talk) 13:13, 25 December 2017 (UTC)[reply]

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? North8000 (talk) 21:18, 25 December 2017 (UTC)[reply]

I think that works.Zeusfaber (talk) 22:26, 25 December 2017 (UTC)[reply]