[
Because line standards invariably extend beyond the lines marked on them, the optimal support points depend on both the overall length and the length to be measured. The latter is the quantity to be maximized, requiring a more complex calculation. For example, the 1927–1960 definition of the ]metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
specified that the International Prototype Metre
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and sc ...
bar was to be measured while "supported on two cylinders of at least one centimetre diameter, symmetrically placed in the same horizontal plane at a distance of 571 mm from each other." Those would be the Bessel points of a beam 1020 mm long.
Other support points of interest
Other sets of support points, even closer than the Bessel points, which may be wanted in some applications are:
* The points for minimum sag, 0.5536 times the length. Minimum sag occurs when the centre of the rod sags the same amount as the end points, which is not quite the same thing as minimum ''horizontal'' motion of the ends.
* The node
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two or more curves, lines, ...
s of free vibration, 0.5516 times the length.
* The points for zero central sag (any closer and the beam rises between the support points): 0.5228 times the length.
See also
* History of measurement
The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have ap ...
* History of the metre
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of '' De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and ...
* Neutral plane
In mechanics, the neutral plane or neutral surface is a conceptual plane within a beam or cantilever. When loaded by a bending force, the beam bends so that the inner surface is in compression and the outer surface is in tension. The neutral pl ...
* Test method
A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a test met ...
* Units of measurement
A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
* Weights and measures
A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multip ...
References
*
*
*{{cite thesis , type=Ph.D. thesis , first=Andrew John , last=Lewis , title=Absolute length measurement using multiple-wavelength phase-stepping interferometry , publisher=Department of Physics, Imperial College of Science, Technology and Medicine, University of London , date=2002 , edition=2 , orig-year=1993 , url=http://blog.jartweb.net/?page_id=1410 , accessdate=2015-10-13 , chapter=Appendix C: Flexing of length bars , chapter-url=http://jartweb.net/thesis/AppendixC.pdf
Metrology
Solid mechanics
Statics