Airy points Airy points

-


a beam supported @ airy points has parallel ends.



verical , angular deflection of beam supported @ airy points.


supporting uniform beam @ airy points produces 0 angular deflection of ends. airy points symmetrically arranged around centre of length standard , separated distance equal to







1

/



3


=
0.57735...


{\displaystyle 1/{\sqrt {3}}=0.57735...}



of length of rod.


end standards , standards length defined distance between flat ends such long gauge blocks or mètre des archives, must supported @ airy points length well-defined; if ends not parallel, measurement uncertainty increased because length depends on part of end measured. reason, airy points commonly identified inscribed marks or lines. example, 1000 mm length gauge have airy point separation of 577.4 mm. line or pair of lines marked onto gauge 211.3 mm in each end. supporting artifact @ these points ensures calibrated length preserved.


airy s 1845 paper derives equation n equally spaced support points. in case, distance between each support fraction







c
=
1

/




n

2


−
1




{\displaystyle c=1/{\sqrt {n^{2}-1}}}



the length of rod. derives formula rod extends beyond reference marks.








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