Talk:Skew arch

Different elevations?
I've never heard of an arch bridge that links two different elevations being called a skew arch. A skew arch is formed when the abutments are not perpendicular to the face, giving a plan view that is in the shape of a parallelogram rather than a rectangle. I agree that a masonry skew arch involves some complex stone cutting (George Stephenson's Rainhill bridge being an excellent example) but a skew arch constructed of brick is much simpler, the important factor being that the courses of brick forming the barrel are aligned at an angle from the horizontal that's equivalent to the skew angle itself, causing the barrel to take on a helical shape, rather than the cylindrical shape of a regular arch. The only bricks that need special cutting are the ones whose ends form part of the face of the arch, if stone voussoirs are not used, as in the photograph accompanying the article, which shows five courses making up the barrel. In many cases, however, even these bricks are left uncut giving an irregularity between the different courses forming the arch barrel and the spandrels, as can be seen at the extreme left edge of the photo at http://www.flickr.com/photos/loose_grip_99/1806212402/. 83.104.249.240 (talk) 03:37, 8 May 2009 (UTC)
 * The term "Skew arch" is not uncommon. --Rod Starling (talk) 20:43, 21 May 2009 (UTC)
 * The correct name for an arch linking two different elevations is a rampant arch, an example being an arch carrying a stairway. Rampant arches are occasionally, though incorrectly, referred to as skew arches. As WP is an encyclopædia this article ought to concern itself with oblique or skew arches with a separate article on rampant arches being written, if necessary. MegaPedant (talk) 16:12, 16 August 2009 (UTC)


 * The angle of the brick courses making up the intrados of a skew arch built to the helicoidal pattern isn't actually the same as the skew angle. According to the various Victorian texts the theoretical angle β of the coursing planes of the intrados is related to the skew angle θ by the relationship π tan β = 2 tan θ, though the actual angle β' is always a little smaller than this theoretical value. Either way, the angle of the bricks in a real skew arch is somewhat less than the skew angle. Note that those texts tend to be inconsistent and contradictory in their interpretation of the terms skew angle and angle of obliquity. While ostensibly they refer to the same thing be prepared, when reading those texts, to switch back and forth between the quoted angle and its complement. To avoid this source of confusion I'd like to suggest sticking to the following meaning of skew angle: the angle by which the skew arch differs from a right or regular arch. So a regular arch would have a zero skew angle, while skew angles of 20°, 30° and 40° represent arches that are progressively more and more oblique. MegaPedant (talk) 21:01, 23 August 2009 (UTC)

No longer stub class
I've re-rated the article as Start class. MegaPedant (talk) 09:52, 11 August 2009 (UTC)
 * I think it's worthy of C-class rating. 93.174.217.140 (talk) 16:55, 2 September 2009 (UTC)
 * That's nice and, though it's well on the way, I don't think it's quite there yet. It would be useful if someone else could check through what's currently written and add some well referenced facts. I've got more to add on Fox and the corne de vache and ribbed sections and the Construction section is only just started. There are also a couple of s . I have them somewhere but I've read through so many pages of Victorian texts recently I don't know quite where at the moment! Although many of these Victorian texts have been scanned and therefore preserved for posterity it's frustrating that, while the quality of the text is generally good with some of it even searchable, whoever performed the scanning often didn't see fit to include the plates, making it difficult to follow he author's argument through to completion. MegaPedant (talk) 23:14, 2 September 2009 (UTC)

A. J. Adie
Could this be Alexander James Adie? The initials are correct and the dates are feasible but the article describes him as an optician and maker or medical instruments. Could he possibly have been a railway engineer and builder of bridges too? 170 years on it seems unlikely but you never know; he was a Fellow of the Royal Society of Edinburgh, along with Thomas Telford and James Watt, after all. MegaPedant (talk) 01:56, 10 September 2009 (UTC)


 * Yes it could! I've found a reference: "Adie, Alexander James Born in Edinburgh on 16 December 1808 and died near Linlithgow on 3 April 1879. Educated at Edinburgh High School and Edinburgh University. apprenticed to James Jardine. Resident engineer on the Bolton and Preston Railway under Rastrick where his works included flying arches at Chorley and a skew bridge over the Lancaster Canal. Between 1847 and 1863 he was civil engineer and manager of the Edinburgh & Glasgow Railway" here. The article in turn cites John Marshall's Biographical Dictionary of Railway Engineers. MegaPedant (talk) 05:53, 29 January 2010 (UTC)
 * No, it isn't! The name is the same but the dates of birth and death differ. Damn. MegaPedant (talk) 05:57, 29 January 2010 (UTC)
 * Mystery solved! The optical instrument maker was the father; the railway engineer the son. (ref) MegaPedant (talk) 19:38, 15 February 2010 (UTC)

Logarithmic method - has Rankine made an error?
The article says "However, the courses are not parallel, being thinner towards the acute angle of the abutment and thicker towards the obtuse angle," and this is backed up by the Rankine reference. However, looking at the diagram showing the development, corners O and G, where the courses are thicker are clearly acute angles, while corners Q and S, where the courses are thinner are clearly obtuse angles. Has Rankine made an error? I'll look for an alternative reference. MegaPedant (talk) 21:48, 15 September 2009 (UTC)


 * The diagram on p.154 of Schofield (bottom right) agrees with the one in the article (which was taken from Culley, Treatise on the Theory of Construction of Helicoidal Oblique Arches) and it's looking as though the great W. J. M. Rankine did in fact make an error. Hmmm... How to deal with it? The article needs to be corrected but then the reference will no longer be valid. Can Schofield's diagram be used as a replacement, or is that verging on WP:OR? For the time being I'll leave it alone but insert a hidden note while I mull it over. I'm feeling very lonely. There must be someone else who's obsessed with skew arches out there, surely... MegaPedant (talk) 10:25, 18 September 2009 (UTC)


 * I've been mulling for a long time and I think I have it. I'll write down my thoughts here and update the article later. If you think about the plan view of a skew bridge, it is a parallelogram, with two acute angles, diagonally opposed and two obtuse angles, diagonally opposed. Now think about one of the corners of the bridge where the plan view has an acute angle. An example is the Rainhill Skew Bridge and is shown in the photo on the right. The acute angle between the face and abutment is the one on the left of the photo, while the obtuse angle is on the right, hidden behind the lamp post. Now, look at the quoins on the left side of the arch: the angle between the face of the arch and the intrados of the barrel is obtuse. My conclusion is that Schofield, Culley and common sense are all correct and that Rankine, when he says that in a logarithmic arch the courses are thinner towards the acute angle of the abutment he really means that they are thinner towards the acutely angled quoin, which itself is located next to the obtuse angle of the abutment. Whew! I glad that one's sorted out. Now I've just got to tweak the article. —MegaPedant 00:54, 25 January 2011 (UTC)

Things to research

 * Elliptical and three-centred skew arches
 * Provide a given span with less rise. Useful when vertical clearance is limited: problem is exacerbated by the fact that the span "on the skew" must always be greater than the span "on the square" by the factor sec &theta;.
 * Buck (pp. 42-43) rejects elliptical skew arches as unsafe and too complex.
 * So does Culley (p. 94): "Elliptical oblique arches are not recommended, both on account of their structural weakness and the difficulties involved in their construction."
 * Brunel, however, embraced them, building a number of right and skew elliptical bridges: Maidenhead, Gatehampton (right); Moulsford (skew) Maidenhead (right), Gatehampton (slightly skewed, according to British Listed Buildings), Moulsford (markedly skewed).


 * Skew arches in concrete, steel (or iron) and timber
 * Timber: Bath Viaduct (Brunel, GWR), ref. Fernández.
 * Iron: Attercliffe Road, Sheffield, six cast iron ribs. Partick Bridge, Glasgow, cast iron ribs.


 * The 21st century approach to the problem of crossing an obstacle at an oblique angle
 * Pour concrete abutments, add prefabricated girder or reinforced concrete deck.


 * Try to find an example of the corne de vache method of construction
 * Overbridge near Wells Cowley Bridge Junction (Brunel, GWR)? A377 Cowley Hill.  done


 * Try to find a photo of one of Adie's equilibrated bridges
 * Bridge over Lancashire Leeds & Liverpool Lancaster Canal?
 * Work in progress. See Adie's logarithmic bridge section below. done —MegaPedant 00:22, 25 January 2011 (UTC)

MegaPedant (talk) 10:37, 18 September 2009 (UTC)
 * Research William Froude's contribution to skew bridge design. done

The Buck limit
I had to revert an edit made, I have no doubt, in good faith regarding Southdown Road Skew Bridge in the section on ribbed skew arches. George W. Buck calculated a limit on the angle of obliquity beyond which he claimed a helicoidal skew arch would not be stable. Since he specified this limit in terms of the angle of obliquity (the complement of the skew angle) it actually forms a lower bound to that value. Therefore, given Buck's proposed limit of 25°40′ and, given also the angle at which the Midland Main Line crosses Southdown road (25°), the proposed bridge would have an angle of obliquity of 25°, which falls just outside Buck's limit (by 40′) and would have a skew angle of 65°. It might be more useful to quote the Buck limit in terms of the skew angle, in which case it becomes a maximum, or upper bound, at 90° − 25°40′ = 64°20′. In this case it is more easily seen that the bridge, with it's skew angle of 65° exceeds this limit. I'll have a go at re-wording the article. MegaPedant (talk) 01:19, 14 February 2010 (UTC)

When was Finlay Bridge built?
The date given by McCutcheon is 1797 but I'm beginning to wonder is that's a typo in his book. The Penny Cyclopædia suggests, but doesn't explicity say, that Chapman built the bridge in 1787, which is the date originally specified, though not cited, in the Store Street Aqueduct article. I'm looking for another reference that backs up either one or the other? —MegaPedant 19:28, 23 February 2010 (UTC)


 * Well, Schofield says 1787 so I'm going to change the date back. —MegaPedant 20:18, 23 February 2010 (UTC)

Adie's logarithmic bridge
I've finally located and confirmed that bridge 74A that carries the Bolton to Preston railway line over what is now called the Leeds and Liverpool Canal but what was originally to be the southern end of the Lancaster Canal (hence my confusion over its name, above), near Chorley, is indeed one of Adie's equilibrated arches. I've found three photographs of it on the Internet, the best of which (in terms of revealing the logarithmic courses) is here. There's also a photograph from the other side of the bridge here. Unfortunately, I can't use either in the article as they are not copyright free. I'm going to have to visit Chorley and take a walk along the towpath with my camera when the weather improves. I'll make the journey by train, of course, and pass over the bridge once on the way there and again on the way back. —MegaPedant 00:06, 9 January 2011 (UTC)
 * I asked the author's permission to release one of his photos into the public domain and to my delight he sent me a set of six that he'd taken that very day, with his permission to do whatever I like with them. Cheers, mate! Thank you for your generosity. I've added two to the article - any more would make it unbalanced. Perhaps bridge 74A deserves an article (with a gallery) of its own. —MegaPedant 00:31, 25 January 2011 (UTC)

Assessment comment
Substituted at 06:20, 30 April 2016 (UTC)

Advantages of skew arches?
Does the skew arch have any advantages over a conventional arch, apart from its ability to bridge a road intersecting at a non-right angle? I ask this because I have noticed that, in the original London & Blackwall railway arches (c. 1840) quite a few of the arches are skew, even though there was no need for them to be so. Does this construction give superior strength, for example? And if not, why did they bother? Ttocserp 21:16, 21 December 2016 (UTC)
 * The date of those would be interesting, as would be their construction type and design.
 * The advantage of a skew bridge is for when two skewed paths need to cross - there's no advantage otherwise. A skewed arch then allows the lower path to be crossed with the shortest possible arch. If the arch wasn't skewed but was on the same alignment, then it would have to be longer.
 * The disadvantage of a skewed arch is that it needs to be designed in a more complex way than a straight arch - otherwise the axial end loads turn into transverse side loads and the arch topples. There are two ways to do this: to split the arch into a series of straight arches, each of which is simple, and to slide them relative to each other like a deck of cards - this was mostly done with cast-iron arch frames (see the Rochdale Canal bridge photo). Otherwise the arch needs to be designed by a three dimensional method, such as the helicoidal arch, rather than the simplified two dimensional arch which allows the usual simplification. These model where the loads (both axial and transverse) are going and supports them.
 * Initially, skew arches weren't trusted. In 1830 they were seen as a risky proposition. A few years later though, more of them had been built, the methods for designing them were known and especially the way to communicate this design to the local bricklayers. Stephenson, the chief engineer of the Blackwall, probably never designed one himself, but he had permitted one (Swin Bridge) on the Stockton & Darlington. For a constrained site in London they make sense. Andy Dingley (talk) 21:49, 21 December 2016 (UTC)


 * There is a sequence of 6 consecutive skew arches immediately before the viaduct crosses the Limehouse Cut canal (travellling in an easterly direction). A photograph of one of them is here: .  As you can see this one has nothing to do with spanning a road at a skewed angle -- there never was a road.  And if you get a chance to look at the other 5 on the ground it'll become apparent that they too were not built skewed because of a need to span a skewed road.   So, it seems someone went to the trouble of building skew arches when there was no need to accommodate non-orthogonal roads.  I find it interesting to ask why.  Here are some data.
 * These arches must have been built about 1839, and definitely at some time between 28 July 1836 (Act of Parliament obtained) and 4th July 1840 (ceremonial opening). It is commonly said that Stephenson was the engineer to the L&BRy, and while the mechanical engineer of this railway was indeed Robert Stephenson, I don't believe he was responsible for the civil engineering.   At any rate the brick arches were the work of William Cubitt (no relation): J.E. Connor, Stepney's Own Railway: A History of the London & Blackwall System, 12 (Connor & Butler, 2nd ed, 1987).  Other sources agree.
 * The original viaduct north of Limehouse Basin (including the 6 consecutive skew arches in question) survives to this day, it having been declared a Grade II listed building. . Of course, it now carries the Docklands Light Railway.
 * The viaduct had to meet tight specifications. It had to bridge the Regent's Canal, and then only about 200 yards later the Limehouse Cut, while all the time proceeding "with a gradual rise of 1 in 400".  The viaduct was made from conventional arches of two sizes (87 feet or 30 feet).  Since I can't see that an integral number of arches of predetermined size can be fitted into a predetermined linear distance -- except by amazing coincidence -- I wonder whether the purpose of having this sequence of 6 consecutive skewed arches immediately before launching over the Limehouse Cut was to adjust for the irregularity of the distance.  Presumably 6 skewed arches takes up more longitudinal space than 6 conventional arches, and you can adjust the length by adjusting the skew angle.  I am not an engineer, but wonder whether a second purpose of having skewed arches was to compensate for an irregular distance.  I.e if a regular arch has a linear length L but the distance to be traversed is a non-integral multiple of L, skew some of your arches to make the maths come out right?Ttocserp 15:05, 5 January 2017 (UTC)
 * Is the viaduct curved? Otherwise I can't see why they'd be skewed either.
 * Curved viaducts were a problem. Brunel built the first big one at Goitre Coed in South Wales in 1841. Like the skewed arch, it was hard to build such a viaduct initially because the end loads from each arch weren't balanced by the adjoining arch (as in a conventional viaduct). I wonder if skewing arches might have been an attempt to manage this around a curve? Andy Dingley (talk) 19:58, 5 January 2017 (UTC)
 * It's curved but only very slightly. Not enough to be significant.  This map   gives a qualitative idea.  I estimate the RoC (crudely) as at least 1 mile.  Curving can't be the explanation, because most of the curvature is coped with by arches that are, to all intents and purposes, non-skewed.  Thus all the arches in the above map are non-skewed, apart from the sequence of 6 immediately before the 87 foot arch over the Limehouse Cut, which are dramatically skewed.   To put it another way, there is no difference, or anyway no discernible difference, in the curvature of the "skewed" and "non-skewed" sectors of the viaduct.
 * What's wrong with the 'need to fit an integral number of arches into a predetermined linear distance' hypothesis?Ttocserp 21:47, 5 January 2017 (UTC)