Talk:Airy points

Airy Points aren't about minimising bending, droop or shortening horizontal direction

The comment that the support at the Airy points limits bending or droop suggests that their function was to limit the deflection of the beam. Airy was concerned with the support of length standards as part of the 1844 revision of length standards in the UK. As such, he derived the condition for supporting a beam at two points in such a way that the ends of the beam remained parallel. It is this condition that gives rise to the location of the Airy points. Peter R Hastings 12:53, 11 February 2016 (UTC)

Airy wasn't addressing deflection of the beam, he looking at upper surface length expansion, and sought to find a solution with equal amounts of concave & convex. In his paper in "Memoirs of the Royal Astronomical Society" vol. 15 (1846) "On the Flexure of a Uniform Bar", his description is "and I undertook to investigate the position of the rollers which, supposing the pressure equal and the intervals equal, would so sustain the bar that its surface should not sensibly be lengthened.

The already referenced "Appendix C: Flexing of length bars" also supports this definition "The chosen solution is to support the bar on two points whose positions are chosen to make the ends of the bar vertical and parallel with each other. These are termed the 'Airy points' of the bar".

A summary of different support types from "Linear Motion Systems. A Modular Approach for Improved Straightness Performance" Nijsse, G.J.P. is: Airy point support: ≈0.2113l; provides parallel end surfaces, used for long end gauges and line scales with the pattern in the top plane Bessel point support: ≈0.2203l; results in minimum shortening in the horizontal direction, used for line scales with the pattern in the neutral plane Minimum bending: ≈0.2232l; overall bending is minimal, equal deflection for middle point and end points

I think "support a length standard in such a way as to minimise bending or droop" (which isn't the intent of Airy points) should change to "support a length standard in such a way that the ends remain parallel (so that the length is well defined)"

Ivan Hamilton (talk) 14:55, 24 June 2016 (UTC)

@Ivan Hamilton: I tried to overhaul the article to describe the points properly. It could still use improvement (other editors solicited!), but I hope it's better. 71.41.210.146 (talk) 12:27, 30 August 2016 (UTC)

Derivation?

Anyone fancy adding a section on the derivation of this spacing value? Also the proof of its insensitivity to precise position. Andy Dingley (talk) 12:42, 2 June 2016 (UTC)

@Matthiaspaul, Andy Dingley, and Just plain Bill: I didn't add the derivation, but have significantly overhauled the article. Found some nice illustrations! Ping to previous editors: what do you think of the article now? I think I've improved it a lot, but the organization and phrasing could still use work. Preferably by another editor; I'm not satisfied with it, but I haven't managed to come up with something I like better.

(I'd also really like a source describing optimal support of line standards, i.e. the more general two-parameter solution for the Bessel points of a length standard of length a inscribed on a bar of overall length a+2e.)

71.41.210.146 (talk) 14:24, 31 August 2016 (UTC)

Location of Bessel points not clear

I've found sources for three different locations for the Bessel points:

Alternative Bessel point locations

Spacing	From end	Sources	Comments
0.5594	0.2203	Mitutoyo Obishi PhD thesis	Most commonly seen, but sources are not very authoritative
0.5506	0.2247	Derivation in German de:Bessel-Punkt	Wish I could understand it. wikipedia.de believe it.
0.630	0.185	A different thesis	Seems obviously wrong; included to show prevalence of misinformation

The fact that en.wikipedia and de.wikipedia contain flatly conflicting information is not a good situation. I'd love to resolve the conflict. 71.41.210.146 (talk) 02:42, 3 December 2016 (UTC)

I think the value 0.22031 is the correct value and wikipedia.de should correct their article. The book Handbuch der physikalischen maasbestimmungen is a German language source they could use. The value appears on page 180. The book Darstellung der untersuchungen und maassregeln is cited as the original source of the value by some articles, but I could not find it in the text. The paper A revised treatment is a more recent paper that shows the derivation of the value. This increases the confidence in accuracy of this value. — Preceding unsigned comment added by E2 e8 (talk • contribs) 00:45, 22 May 2017 (UTC)